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Fundamentals and technology of wafer drying Laytner, Frank 1989

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Fundamentals and Technology of Wafer Drying by Frank Laytner B.Sc.F., University of Toronto, Toronto, O N , 1978. M.S. , University of California, Berkeley, C A , 1980. A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R OF PHILOSOPHY in T H E F A C U L T Y O F G R A D U A T E STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A August, 1989 © Frank Laytner, 1989 In presenting this thesis in partial fulfillment of the requirements for an advanced de-gree at The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemical Engineering The University of British Columbia 2216 Main Mall Vancouver, BC, Canada V6T 1W5 August, 1989 Abstract The commercial rotary dryers used to dry wood wafers (of approximate dimensions 0.63 mm thick, 50 mm wide and 76+ mm long) for the production of panelboard are modified versions of agricultural dryers and have not been designed for the optimal drying of wood wafers. The lack of available information on wafer drying necessitated that the first goal of this research was the characterization of wafer drying behaviour. After the important parameters of wafer drying were identified, the applicability of fiuidized bed technology to wafer drying was assessed and an industrial size dryer was designed. The proposed fiuidized bed wafer dryer was then compared to a commercial rotary dryer in terms of energy efficiency. Wafer drying behaviour was investigated in two factorial experiments. Three lengths of wafers (25 mm, 44 mm and 63 mm) were individually dried in a 0.15 m draft tube at temperatures of 90°C, 120°C and 150°C. The statistical analysis of the resultant drying rate curves showed that the drying behaviour of aspen wafers was influenced by the effect of wafer length on the external heat and mass transfer rates to the wafer surface, and on the length of internal pathways for bulk flow and diffusion of water. The external drying conditions had a decreasing effect on drying rate until about 10% moisture content at which time drying became limited by internal heat and mass transport. The initial assessment of fiuidized bed technology for wafer drying used a 0.15 m semi-cylindrical column for the determination of wafer drying rate curves and wafer behaviour in a fiuidized bed of inert particulate solids at excess superficial velocities of 0.25 to 1.0 m/s. Wafer drying times in a bed of 0.5 mm sand at 150°C were about 40% of the drying times for wafers dried by forced convection of air at the same temperature and twice the superficial velocity (~ 1 m/s). Wafer movement in the fiuidized bed followed the circulation patterns of the emulsion phase and was thus dependent on the bubbling behaviour of the bed. A minimum excess superficial velocity of 0.25 m/s (depending on distributor design) was required to prevent permanent settling of the wafers to the distributor. Preliminary experimentation on a 2-compartment bed showed that wafers could be circulated through the two compartments in near plug flow. However, the application of this technique to a 4-compartment continuous fiuidized bed wafer dryer was unsuccess-ful because of the separation of sand and wafers caused by slugging beds in two of the compartments. A preliminary design was prepared for an industrial size, 5-compartment fiuidized bed wafer dryer to approximate plug flow of wafers by a series of well-mixed fiuidized beds in series. The design calculations showed that this dryer was more efficient in terms of energy and plant space than a conventional triple pass rotary dryer. u Contents A B S T R A C T i i LIST OF T A B L E S ix LIST OF F I G U R E S xiv A C K N O W L E D G E M E N T S xix I N T R O D U C T I O N 1 1 Fundamentals of Wafer Drying 4 1.1 B a c k g r o u n d R e v i e w o f V e n e e r a n d P a r t i c l e D r y i n g 4 1.1.1 I n t r o d u c t i o n 4 1.1.2 D r y i n g T h e o r y f o r T h i n W o o d S a m p l e s 5 C l a s s i c a l D r y i n g R a t e T h e o r y 5 M o d e l l i n g W o o d D r y i n g 6 1.1.3 E x p e r i m e n t a l D r y i n g R a t e s f o r V e n e e r s a n d P a r t i c l e s 15 E f f e c t o f E x t e r n a l D r y i n g C o n d i t i o n s o n V e n e e r D r y i n g R a t e s . . . 16 E f f e c t s o f M a t e r i a l P r o p e r t i e s o n D r y i n g R a t e s 17 1.1.4 A s p e n W a f e r D r y i n g 24 A n a t o m i c a l C o n s i d e r a t i o n s 24 E x p e r i m e n t a l W a f e r D r y i n g 24 A C o n c e p t u a l M o d e l o f A s p e n W a f e r D r y i n g 28 1.2 M e t h o d s a n d M a t e r i a l s — F u n d a m e n t a l s o f W a f e r D r y i n g 3 0 1.2.1 I n t r o d u c t i o n 3 0 1.2.2 A s p e n W a f e r P r o d u c t i o n 3 0 i i i 1 . 2 . 3 A s p e n W a f e r P r o p e r t i e s 3 1 1 . 2 . 4 D r y i n g A p p a r a t u s f o r S i n g l e W a f e r T e s t s 3 2 1 . 2 . 5 P r o c e d u r e f o r S i n g l e W a f e r D r y i n g E x p e r i m e n t s 4 1 1 . 2 . 6 C a l c u l a t i o n o f D r y i n g T i m e s a n d D r y i n g R a t e s 4 1 1 . 2 . 7 I n i t i a l T e s t s o f t h e D r y i n g A p p a r a t u s 5 0 1.2.8 F a c t o r i a l D r y i n g E x p e r i m e n t s 5 2 1 .3 R e s u l t s a n d D i s c u s s i o n 5 4 1 . 3 . 1 A n a l y s i s o f W a f e r D r y i n g T i m e s 5 4 1 . 3 . 2 A n a l y s i s o f W a f e r D r y i n g R a t e s 5 8 R e s u l t s o f t h e 3 x 3 F a c t o r i a l E x p e r i m e n t 5 8 R e s u l t s o f t h e 1 x 3 F a c t o r i a l E x p e r i m e n t 6 4 E f f e c t o f E x t e r n a l H e a t k. M a s s T r a n s f e r C o n d i t i o n s o n W a f e r D r y i n g 6 4 T h e E f f e c t o f W o o d S t r u c t u r e o n W a f e r D r y i n g R a t e 7 3 A C o n c e p t u a l D r y i n g H i s t o r y f o r W a f e r s 7 5 1 .4 C o n c l u s i o n s 7 8 1 .5 I m p l i c a t i o n s 7 9 2 Assessment of Fluidized Bed Technology for Wafer Drying 80 2 . 1 B a c k g r o u n d R e v i e w 8 0 2 . 1 . 1 F l u i d i z e d B e d D r y i n g 8 0 2 . 1 . 2 F l u i d i z e d B e d D r y i n g o f W o o d W a f e r s 8 1 2 . 1 . 3 W a f e r C i r c u l a t i o n i n a F l u i d i z e d B e d o f I n e r t S o l i d s 8 4 2 . 2 C o n f i g u r a t i o n C o n s i d e r a t i o n s f o r a F l u i d i z e d B e d W a f e r D r y e r 8 6 2 . 3 W a f e r H a n d l i n g i n a F l u i d i z e d B e d o f I n e r t S o l i d s 8 8 2 . 3 . 1 E x p e r i m e n t a l E q u i p m e n t a n d P r o c e d u r e s 8 8 I n t r o d u c t i o n 8 8 T h e F l u i d i z e d B e d C o l u m n 8 8 S e l e c t i o n o f B e d M a t e r i a l s 9 2 W a f e r C i r c u l a t i o n T e s t s 9 5 M e a s u r e m e n t a n d A n a l y s i s o f W a f e r C i r c u l a t i o n 9 8 M o v e m e n t a t t h e D i s t r i b u t o r P l a t e 9 9 iv T w o - C o m p a r t m e n t B e d T e s t s 9 9 W a f e r L o a d i n g C a p a c i t y o f a F i u i d i z e d B e d 1 0 0 2 . 3 . 2 R e s u l t s a n d D i s c u s s i o n 1 0 1 W a f e r H a n d l i n g . . . , 1 0 1 W a f e r C i r c u l a t i o n P a t t e r n s i n a F i u i d i z e d B e d o f S o l i d s 1 0 1 W a f e r C i r c u l a t i o n i n a F i u i d i z e d B e d o f S a n d 1 0 3 S h o r t C i r c u i t i n g o f t h e W a f e r C i r c u l a t i o n P a t t e r n 1 0 9 M i n i m u m E x c e s s S u p e r f i c i a l V e l o c i t y R e q u i r e d f o r W a f e r C i r c u l a t i o n 1 1 0 E f f e c t o f C o m p a r a t i v e D e n s i t i e s o f S o l i d s a n d W a f e r s 1 1 5 C i r c u l a t i o n o f W a f e r s i n a T w o - C o m p a r t m e n t F l u i d i z a t i o n B e d . . . 1 1 6 W a f e r L o a d i n g C a p a c i t y o f a F i u i d i z e d B e d 1 2 0 2 . 4 W a f e r D r y i n g i n a F i u i d i z e d B e d o f I n e r t S o l i d s 1 2 3 2 . 4 . 1 E x p e r i m e n t a l P r o c e d u r e 1 2 3 2 . 4 . 2 W a f e r D r y i n g i n a S m a l l F i u i d i z e d B e d o f S a n d 1 2 6 C o n v e c t i o n v e r s u s F i u i d i z e d B e d D r y i n g o f W a f e r s 1 3 4 2 . 5 S u m m a r y a n d C o n c l u s i o n s • • • 1 4 4 2 . 5 . 1 W a f e r H a n d l i n g i n a F i u i d i z e d B e d o f S o l i d s 1 4 4 W a f e r D r y i n g i n a F i u i d i z e d B e d o f S a n d 1 4 6 3 D e s i g n a n d D e v e l o p m e n t o f a n E x p e r i m e n t a l C o n t i n u o u s D r y e r 1 4 7 3 . 1 I n i t i a l D e s i g n a n d C o n s t r u c t i o n 1 4 8 3 . 1 . 1 D r y i n g C h a m b e r 1 4 8 3 . 1 . 2 W a f e r F e e d a n d R e m o v a l U n i t 1 5 3 3 . 1 . 3 W a f e r F e e d S y s t e m 1 5 4 3 . 1 . 4 W a f e r R e m o v a l S y s t e m 1 5 4 3 . 1 . 5 A i r S u p p l y a n d C o n t r o l 1 5 7 3 . 1 . 6 H e a t S u p p l y a n d C o n t r o l 1 5 7 3 . 2 I n i t i a l O p e r a t i n g C o n d i t i o n s 1 6 2 3 . 3 E v a l u a t i o n o f t h e E x p e r i m e n t a l D r y e r 1 6 4 3 . 3 . 1 S u m m a r y o f T e s t s , O b s e r v a t i o n s a n d M o d i f i c a t i o n s 1 6 4 3 . 3 . 2 W a f e r R e s i d e n c e T i m e T e s t s 1 7 0 v 3.3.3 W a f e r D r y i n g T e s t s 1 7 4 3.4 C o n c l u d i n g R e m a r k s o n t h e E x p e r i m e n t a l C o n t i n u o u s D r y e r 1 8 1 4 Configuration of Industrial Fluidized Bed Wafer Dryer 182 4 . 1 I n t r o d u c t i o n . . 1 8 2 4 . 2 D e t e r m i n a t i o n o f t h e N u m b e r o f C o m p a r t m e n t s i n t h e I n d u s t r i a l D r y e r . . 1 8 5 4.2.1 P r e d i c t i n g W a f e r R e s i d e n c e T i m e s i n M u l t i p l e C o m p a r t m e n t F l u -i d i z e d B e d s 1 8 5 4.2.2 M o i s t u r e C o n t e n t D i s t r i b u t i o n o f W a f e r s D r i e d i n M u l t i p l e C o m p a r t -m e n t F l u i d i z e d B e d s 1 8 7 4.2.3 N u m b e r o f C o m p a r t m e n t s B a s e d o n C o m p a r t m e n t S i z e a n d T o t a l H o l d u p 1 8 8 4.3 C i r c u l a t i o n o f t h e I n e r t P a r t i c l e s T h r o u g h a 5 - C o m p a r t m e n t F l u i d i z e d B e d D r y e r 1 9 2 4 . 4 W a f e r F e e d a n d R e m o v a l S y s t e m s 1 9 6 4 . 5 W a f e r D r y i n g i n a M u l t i - C o m p a r t m e n t F l u i d i z e d B e d D r y e r 1 9 7 4 . 6 W a f e r D r y i n g i n a T r i p l e - P a s s D r u m D r y e r 2 0 3 4 . 7 C o m p a r i s o n o f W a f e r D r y i n g i n a T r i p l e - P a s s D r u m D r y e r a n d a M u l t i -C o m p a r t m e n t F l u i d i z e d B e d D r y e r 2 0 6 4 . 8 C o n c l u s i o n 2 0 8 5 Conclusions 209 N O M E N C L A T U R E 211 R E F E R E N C E S 214 A P P E N D I C E S 223 A Coefficients for Polynomial Equation Used to F i t Drying Curve Data 223 B Statistical Discussion of the Analyses of the Wafer Drying Times and Drying Rates 234 B . l A n a l y s i s o f W a f e r D r y i n g T i m e s 2 3 4 B . 2 A n a l y s e s o f D r y i n g R a t e s f r o m t h e 3x3 F a c t o r i a l E x p e r i m e n t 2 3 8 v i B.3 Analyses of the Drying Rates from the 1 x 3 Factorial Experiments 249 C Predicted Initial Wafer Drying Rate and Dimensionless Numbers Char-acterizing the Drying System Used in the 3 x 3 and 1x3 Factorial Exper-iments 254 C.l Introduction 254 C.2 Mean Absolute Humidity and Partial Pressure Water Vapour in Drying Medium 255 C.3 Development of Radiative Heat Transfer Coefficient Equation 256 C.4 Radiative Shape Factors 259 C.5 Computer Programs to Calculate Predicted Drying Rates and Dimensionless Numbers that Characterize the Drying System Used in the 3 x 3 and 1 x 3 Factorial Experiments 264 D Predicting Wafer Circulation Rates 279 E Drying Curve Equations (Exponential Curve-Fit of Experimental Data) 284 F Predictions of Wafer Drying Times and Rates for Fluidized Bed and Forced A i r Drying for the 0.15 m Half-Column Experiments 285 F.l Prediction of Wafer Drying Times for Fluidized Bed Drying 285 F.2 Prediction of Wafer Drying Rates At or Near Saturation for Fluidized Bed and Forced Air Drying for the 0.15 m Half-Column Experiments 288 F.2.1 Introduction 288 F. 3 Computer Programs to Calculated Predicted Drying Rates and Dimension-less Numbers that Characterize the Drying System Used in the 0.15 m Half-Column 291 G Construction of the Four Compartment Column and Windbox 304 G. l Thermocouples and Pressure Taps 304 G.2 Column Modifications 305 G. 3 Windbox Construction 307 H Fabrication and Calibration of the Wafer Feed and Removal Unit 310 H. l Wafer Feed System 310 vn H.2 Wafer Removal System 314 H. 3 Support and Attachment of the Wafer Feed and Removal Unit 315 I Heater Design and Specifications 316 I. 1 Calculation of Compartmental Heating Requirements 316 1.2 Fabrication of the 9 kW "Porcupine" Element Heaters 322 1.3 Fabrication of the 4.4 kW Booster Heater 325 J Calibration of the Copper Slag Feed Unit 327 K D r y i n g Curve for Wafers Dried in a Fiuidized Bed of Sand at 120° C 329 L Energy Balance for Five Compartment Fiuidized Bed Dryer 330 M Energy Balance for Triple-Pass D r u m Dryer 333 viii List of Tables 1.1 Fractional Distribution of Diffusion Modes for Transverse Moisture Move-ment in Woods of Different Densities (Stamm, 1964) 9 1.2 Experimental Drying Tests (Stanish and Kayihan, 1984) 22 1.3 Velocity Profile Measurements for the Single Wafer Drying Apparatus. . . 38 1.4 Effect of Velocity Profile on Relative Magnitudes of External Heat Transfer Coefficients 40 1.5 Comparison of Graphical and Computer Generated Drying Rates for a Wafer 63 mm Long Dried at 90° C 48 1.6 Summary Statistics for Preliminary Drying Runs 51 1.7 Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2 55 1.8 Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2 56 1.9 Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 X 3 Factorial Experiment 1 , 2 57 1.10 Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2 59 1.11 Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2 60 1.12 Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2 61 1.13 Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 1 x 3 Factorial Experiment 65 1.14 Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 150°C in the 3 x 3 Factorial Experiment. ... 67 1.15 Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 120°C in the 3 x 3 Factorial Experiment. ... 68 i x 1.16 Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 90°C in the 3 x 3 Factorial Experiment 69 1.17 Measured and Predicted Quantities Describing the External Transfer Con-ditions for Wafer Drying in the 1 x 3 Factorial Experiment 70 2.1 Properties of Inert Solids and of the Resultant Fluidized Beds at Minimum Fluidization and Minimum Bubbling 94 2.2 Predicted Fluidized Bed Properties 95 2.3 Distributor Plate Types and Measured Distributor Pressure Drops for the Superficial Velocities Used in the Circulation and Drying Experiments. . . 97 2.4 Times Between Apperances of Wafers at the Fluidized Bed Surface for the Wafer Circulation Studies in a Fluidized Bed of Sand 105 2.5 Predicted Fluidized Bed Properties of Ottawa Sand for the Excess Superfi-cial Velocities Used in the Wafer Circulation and Drying Experiments and a Static Bed Height of 0.150 m 1 112 2.6 Predicted Fluidized Bed Properties of Polypropylene for the Excess Super-ficial Velocities Used in the Wafer Circulation and Drying Experiments and a Static Bed Height of 0.150 m 1 113 2.7 Times Between Appearances of Wafers at the Fluidized Bed Surface in the Two-Compartment Fluidized Bed U — Umf = 0.25 m/s in Compartment 1. 120 2.8 Wafer Loading Capacity for Fluidized Bed of Sand at Excess Velocities of 0.25, 0.50, 0.75 and 1.0 m/s 121 2.9 Experimental Conditions Used to Establish the Wafer Drying Curves for Wafers Dried by Immersion in a Fluidized Bed of Sand and by Forced Con-vention 124 2.10 Predicted1 and Experimental Drying Rates for a Saturated Wafer Dried in a Fluidized Bed of 0.497 mm Sand 133 2.11 Predicted and Experimental Drying Rates for a Saturated Wafer Dried in the Empty 0.15 m Diameter Half-Column 138 2.12 A Comparison of Wafer Drying Times from 125% to 3% Moisture Content for Wafers Dried by Forced Air Convection and by a Fluidized Bed of Sand. 139 3.1 Properties of Sand and Copper Slag Particles and Their Respective Fluidized Bed Characteristics at \Jmf 1 162 3.2 Summary of Tests and Modifications Performed on the Experimental Dryer. 165 x 3.3 Quantities of Wafers and Particles Fed and Removed from the Dryer During the First Wafer Residence Time Test 170 3.4 Quantities of Wafers and Particles Fed and Removed from the Dryer During the Second Wafer Residence Time Test 172 3.5 Results of the Continuous Fiuidized Bed Wafer Drying Test at 60°C. ... 174 4.1 Mean Residence Times Required to Obtain a Mean Wafer Content of 3% in a Series of Fiuidized Beds Operating at 120°C 187 4.2 Moisture Content Distributions,for Wafers Exiting from Multi-Compartment Fiuidized Bed Dryers Operating at 120°C 189 4.3 Determination of the Minimum and Maximum Number of Compartments. 191 4.4 Calculation of the Circulation Rate of Sand Through the 5-Compartment Fiuidized Bed Dryer 193 4.5 Average Wafer Residence Times and Inlet and Outlet Moisture Contents for the Five-Compartment Fiuidized Bed Dryer Operating at 120°C 197 4.6 Energy Balance for a Five Compartment Fiuidized Bed Wafer Dryer 1 , 2. Pro-ducing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Ovendry Basis) 198 4.7 Energy Balance for a Triple-Pass Drum Dryer Producing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Oven Dry Basis) 1 205 4.8 Comparison of Triple-Pass Drum Dryer with the Proposed Five-Compartment Fiuidized Bed Dryer for Drying Wafers at a Rate of 2.53 kg/s (Oven Dry Basis) 206 A.l Polynomial Coefficients for 25 mm Wafers Dried at 90°C 224 A.2 Polynomial Coefficients for 44 mm Wafers Dried at 90°C 225 A.3 Polynomial Coefficients for 63 mm Wafers Dried at 90°C 226 A.4 Polynomial Coefficients for 25 mm Wafers Dried at 120°C 227 A.5 Polynomial Coefficients for 44 mm Wafers Dried at 120°C 228 A.6 Polynomial Coefficients for 63 mm Wafers Dried at 120°C 229 A.7 Polynomial Coefficients for 25 mm Wafers Dried at 150°C 230 A.8 Polynomial Coefficients for 44 mm Wafers Dried at 150°C 231 A.9 Polynomial Coefficients for 63 mm Wafers Dried at 150°C 232 xi A.10 P o l y n o m i a l C o e f f i c i e n t s f o r 25 m m W a f e r s D r i e d a t 150°C, H o r i z o n t a l t o t h e F l o w o f A i r 233 A . 11 P o l y n o m i a l C o e f f i c i e n t s f o r 44 m m W a f e r s D r i e d a t 150°C, H o r i z o n t a l t o t h e F l o w o f A i r 233 A . 12 P o l y n o m i a l C o e f f i c i e n t s f o r 63 m m W a f e r s D r i e d a t 150°C, H o r i z o n t a l t o t h e F l o w o f A i r 233 B . l S u m m a r y o f t h e A n a l y s e s o f V a r i a n c e o f D r y i n g T i m e s f r o m t h e 3x3 F a c -t o r i a l E x p e r i m e n t 235 B.2 S u m m a r y o f t h e A n a l y s e s o f V a r i a n c e o f D r y i n g T i m e s f r o m t h e 3x3 F a c -t o r i a l E x p e r i m e n t U s i n g a L o g a r i t h m i c T r a n s f o r m a t i o n t o E l i m i n a t e M u l t i -p l i c a t i v e E f f e c t B e t w e e n T e m p e r a t u r e a n d L e n g t h 237 B.3 R e s u l t s o f T u k e y ' s T e s t o f A d d i t i v i t y f o r t h e D r y i n g R a t e D a t a f r o m t h e 3x3 F a c t o r i a l E x p e r i m e n t 243 B.4 S u m m a r y o f t h e A n a l y s e s o f V a r i a n c e f o r W a f e r D r y i n g R a t e s a t D i f f e r e n t M o i s t u r e C o n t e n t s f r o m t h e 3x3 F a c t o r i a l E x p e r i m e n t 1 245 B . 5 S u m m a r y o f t h e A n a l y s e s o f V a r i a n c e f o r W a f e r D r y i n g R a t e s a t D i f f e r e n t M o i s t u r e C o n t e n t s f r o m t h e 1x3 F a c t o r i a l E x p e r i m e n t 253 C . l C a l c u l a t i o n o f M e a n A b s o l u t e H u m i d i t y a n d P a r t i a l P r e s s u r e W a t e r V a p o u r i n D r y i n g M e d i u m 255 C.2 I n t e g r a l s o f E q u a t i o n C.5 a n d t h e C a l c u l a t i o n o f Fi-2, i ^ i - i a n d F2-1 f o r t h e D r y i n g S y s t e m i n t h e 3x3 F a c t o r i a l E x p e r i m e n t 262 C.3 I n t e g r a l s o f E q u a t i o n C.5 a n d t h e C a l c u l a t i o n o f Fi~2, F1-1 a n d F2-1 f o r t h e D r y i n g S y s t e m i n t h e 1x3 F a c t o r i a l E x p e r i m e n t 263 C.4 L i s t o f V a r i a b l e s U s e d i n C o m p u t e r P r o g r a m s 264 C.5 C a l c u l a t i o n o f P r e d i c t e d D r y i n g R a t e s f o r V e r t i c a l l y O r i e n t e d W a f e r s (3x3 F a c t o r i a l E x p e r i m e n t ) N o t I n c l u d i n g t h e E f f e c t s o f R a d i a t i o n 267 C.6 C a l c u l a t i o n o f P r e d i c t e d D r y i n g R a t e s f o r V e r t i c a l l y O r i e n t e d W a f e r s (3x3 F a c t o r i a l E x p e r i m e n t ) I n c l u d i n g t h e E f f e c t s o f R a d i a t i o n 271 C.7 C a l c u l a t i o n o f P r e d i c t e d D r y i n g R a t e s f o r H o r i z o n t a l l y O r i e n t e d W a f e r s (1 x 3 F a c t o r i a l E x p e r i m e n t ) N o t I n c l u d i n g t h e E f f e c t s o f R a d i a t i o n 274 C.8 C a l c u l a t i o n o f P r e d i c t e d D r y i n g R a t e s f o r H o r i z o n t a l l y O r i e n t e d W a f e r s (1 x 3 F a c t o r i a l E x p e r i m e n t ) I n c l u d i n g t h e E f f e c t s o f R a d i a t i o n 278 x n D.l Predicted and Observed Velocities of the Emulsion Phase and for a Large Sphere Circulating in a Fiuidized Bed of 0.550 mm Glass Ballotini (U — Umf = 0.228) 280 D.2 Experimental Conditions of Nienow et al. (1978) 281 F.l Comparison of Experimental Wafer Drying Times with Veneer Drying Times Predicted Using Equations Developed by Babailov and Petri (1974). . . . 286 F.2 List of Variables Used in Computer Programs 291 F.3 Calculations of Predicted Saturated Wafer Drying Rates for Wafers Dried in a Fiuidized Bed of 0.497 mm Sand Using the Heat and Mass Transfer Correlations of Cobbinah et al. (1987) 294 F.4 Calculations of Predicted Saturated Wafer Drying Rates for Wafers Dried in a Fiuidized Bed of 0.497 mm Sand Using the Heat and Mass Transfer Correlations of Prins et al. (1985 and 1986) 297 F.5 Calculations of Predicted Saturated Wafer Drying Rates for Wafers Dried in Forced Convection. Heat and Mass Transfer Coefficients are Calculated Using the Nominal Superficial Velocities 300 F.6 Calculations of Predicted Saturated Wafer Drying Rates for Wafers Dried in Forced Convection. Heat and Mass Transfer Coefficients were Calculated Using the Distriutor Plate Orifice Velocities 303 H. l Wafer Feed System Calibration Test Results 311 I. 1 Heat Requirements for Each Compartment of the 4-Compartment Fiuidized Bed Dryer 319 1.2 Porcupine Heating Element Specifications 323 1.3 Silicon Carbide Element Specification 325 L.l Energy Balance for Five Compartment Fiuidized Bed Wafer Dryer" Produc-ing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Oven Dry Basis) 330 M.l Energy Balance for Triple-Pass Drum Dryer Producing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Oven Dry Basis) 333 x n i List of Figures 1.1 Typical rate of drying curve, constant drying conditions (Treybal, 1980) . . 6 1.2 Modes of transverse moisture diffusion through wood 9 1.3 Drying rate curve form established by Comstock (1971) 11 1.4 Relationship between the drying times calculated using the generalized rate equations and the actual drying times for about 100 arbitrarily selected veneer samples (Comstock, 1971) 19 1.5 Particle drying unit (Stanish and Kayihan, 1984) 22 1.6 Minute anatomy of Bigtooth Aspen. (Populus grandidentala). (a) cross-section; (b) tangential (Panshin and DeZeeuw, 1980) 25 1.7 Cross-sectional view of intervessel pitting in northern red oak showing the layers of the cell wall. Electron micrograph by W.A. Cote, Jr. (Siau, 1984a). 26 1.8 Drying comparison for aspen flake at 95°C (Test No. 7) (Stanish and Kayi-han, 1984) 27 1.9 Saturated wafer volume measurement apparatus, (a) prior to measurement; (b) during measurement 33 1.10 Positioning of glass pipe and baffle in convection oven 35 1.11 Attachment of wafer to wire rod suspended from the Mettler Electronic bal-ance. Type K thermocouple positioned 12.7 mm from the water monitored drying temperature 36 1.12 Experimental equipment used for the controlled drying of single wafers in air (showing the circulation of air in the oven) 37 1.13 Comparison of the measured velocity profile for the central section of the drying apparatus and the calculated fully developed laminar velocity profile. 39 1.14 Drying curve of a 63 mm wafer dried at 90°C showing every 10th data point. 43 1.15 Drying rates for the drying curve data of Figure 1.14 determined by the calculation of a series of slopes of the drying curve by linear regression. . . 44 xiv 1 . 1 6 E x p e r i m e n t a l d r y i n g c u r v e d a t a p o i n t s o f F i g u r e 1 . 1 4 a n d t h e f i t t e d p o l y n o -m i a l c u r v e ( e v e r y 2 0 t h p o i n t ) 4 6 1 . 1 7 D r y i n g d a t a o f F i g u r e 1 . 1 4 r e a d y f o r m e a s u r e m e n t b y t h e m a n u a l m e t h o d o f c a l c u l a t i n g d r y i n g r a t e s 4 7 1 . 1 8 C o m p a r i s o n o f g r a p h i c a l ( p o i n t s ) a n d c o m p u t e r ( s o l i d c u r v e ) g e n e r a t e d d r y -i n g r a t e c u r v e s f o r a w a f e r 6 3 m m l o n g d r i e d a t 9 0 ° C 4 9 1 . 1 9 D r y i n g r a t e v e r s u s m o i s t u r e c o n t e n t f o r a l l e x p e r i m e n t a l c o n d i t i o n s i n t h e 3 x 3 f a c t o r i a l e x p e r i m e n t . E a c h c u r v e r e p r e s e n t s a m e a n o f 4 0 w a f e r s . ( W a f e r l e n g t h p a r a l l e l t o a i r flow) 6 2 1 . 2 0 D r y i n g r a t e v e r s u s m o i s t u r e c o n t e n t f o r e a c h w a f e r l e n g t h i n t h e 1 x 3 f a c t o r i a l e x p e r i m e n t 6 6 2 . 1 A p p a r a t u s f o r c i r c u l a t i o n o f f i u i d i z e d s o l i d s ( P r u d e n et ai, 1 9 7 6 ) 8 7 2 . 2 E x p e r i m e n t a l f i u i d i z e d b e d u n i t u s e d i n w a f e r c i r c u l a t i o n a n d d r y i n g t e s t s . 8 9 2 . 3 H a l f - c o l u m n p r e p a r e d f o r t h e w a f e r c i r c u l a t i o n t e s t s 9 0 2 . 4 R e a r v i e w o f h a l f - c o l u m n u s e d f o r w a f e r h a n d l i n g a n d d r y i n g e x p e r i m e n t s . 9 1 2 . 5 H a l f - c o l u m n p r e p a r e d f o r t h e t w o - c o m p a r t m e n t b e d t e s t s ( l e f t - c o m p a r t -m e n t 1; r i g h t - c o m p a r t m e n t 2 ) 9 3 2 . 6 W a f e r c i r c u l a t i o n p a t t e r n s a t U — Umf = 0 . 2 5 m / s f o r ( a ) T y p e 2 a n d ( b ) T y p e 3 d i s t r i b u t o r p l a t e s 1 0 2 2 . 7 N o r m a l i z e d c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s o f t h e t i m e s b e t w e e n a p p e a r -a n c e s o f w a f e r s a t t h e b e d s u r f a c e f o r d i f f e r e n t (U — Umf) 1 0 6 2 . 8 N o r m a l i z e d c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s o f t h e t i m e s b e t w e e n a p p e a r -a n c e s o f w a f e r s a t t h e b e d s u r f a c e f o r t h e t h r e e d i f f e r e n t d i s t r i b u t o r s . . . . 1 0 7 2 . 9 T h e 2 - c o m p a r t m e n t b e d i n o p e r a t i o n a t e x c e s s s u p e r f i c i a l v e l o c i t i e s i n c o m -p a r t m e n t 1 o f ( a ) 0 . 1 m / s , ( b ) 0 . 2 5 m / s a n d ( c ) 0 . 5 m / s 1 1 7 2 . 1 0 N o r m a l i z e d c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n o f t h e t i m e s b e t w e e n a p p e a r -a n c e s o f w a f e r s a t t h e s u r f a c e f o r c o m p a r t m e n t 2 f o r t h e 2 - c o m p a r t m e n t f i u i d i z e d b e d f o r U - Umf = 0 . 2 5 m / s 1 1 9 2 . 1 1 D r y i n g c u r v e f o r w a f e r s d r i e d i n a f i u i d i z e d b e d o f 0 . 4 9 7 m m s a n d a t 9 0 ° C . 1 2 7 2 . 1 2 D r y i n g c u r v e f o r w a f e r s d r i e d i n a f i u i d i z e d b e d o f 0 . 4 9 7 m m s a n d a t 1 2 0 ° C . 1 2 8 2 . 1 3 D r y i n g c u r v e f o r w a f e r s d r i e d i n a f i u i d i z e d b e d o f 0 . 4 9 7 m m s a n d a t 1 5 0 ° C . 1 2 9 2 . 1 4 C o m p a r i s o n o f t h e f i t t e d d r y i n g c u r v e s f o r w a f e r s d r i e d i n a f i u i d i z e d b e d o f 0 . 4 9 7 m m s a n d a t 9 0 ° C , 1 2 0 ° C a n d 1 5 0 ° C 1 3 1 xv 2 . 1 5 C a l c u l a t e d d r y i n g r a t e c u r v e s f o r t h e w a f e r s d r i e d i n f i u i d i z e d b e d o f 0 . 4 9 7 m m s a n d a t 9 0 ° C , 1 2 0 ° C a n d 1 5 0 ° C 1 3 2 2 . 1 6 D r y i n g c u r v e f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t a s u p e r f i c i a l v e l o c i t y o f 0 . 4 9 m / s a n d a t e m p e r a t u r e o f 1 5 0 ° C . 1 3 5 2 . 1 7 D r y i n g c u r v e f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t a s u p e r f i c i a l v e l o c i t y o f 0 . 7 3 m / s a n d a t e m p e r a t u r e o f 1 5 0 ° C . 1 3 6 2 . 1 8 D r y i n g c u r v e f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t a s u p e r f i c i a l v e l o c i t y o f 0 . 9 9 m / s a n d a t e m p e r a t u r e o f 1 5 0 ° C . 1 3 7 2 . 1 9 C o m p a r i s o n o f fitted d r y i n g c u r v e s f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t m e a n v e l o c i t i e s o f 0 . 4 9 , 0 . 7 3 a n d 0 . 9 9 m / s a n d a t e m p e r a t u r e o f 1 5 0 ° C 1 4 0 2 . 2 0 D r y i n g r a t e c u r v e s f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t m e a n v e l o c i t i e s o f 0 . 4 9 , 0 . 7 3 a n d 0 . 9 9 m / s a n d a t e m p e r a t u r e o f l 5 0 ° C 1 4 1 2 . 2 1 C o m p a r i s o n o f t h e c a l c u l a t e d d r y i n g r a t e c u r v e s f o r w a f e r s d r i e d a t 1 5 0 ° C i n f i u i d i z e d b e d o f 0 . 5 m m s a n d b y f o r c e d c o n v e c t i o n a t m e a n v e l o c i t y o f 0 . 9 9 m / s . 1 4 3 3 . 1 E s t i m a t e d t i m e f o r d r y i n g w a f e r s f r o m 9 0 % t o 3 % m o i s t u r e c o n t e n t b a s e d o n t h e e x p e r i m e n t a l d r y i n g c u r v e f o r w a f e r s d r i e d i n a f i u i d i z e d b e d o f 0 . 5 m m s a n d a t 1 5 0 ° C 1 4 9 3 . 2 T h r e e d i m e n s i o n a l r e p r e s e n t a t i o n o f c o n t i n u o u s f i u i d i z e d b e d w a f e r d r y e r . . 1 5 0 3 . 3 S c a l e d d r a w i n g o f a 0 . 4 3 m s i d e o f t h e f l u i d i z a t i o n c o l u m n 1 5 1 3 . 4 S c a l e d d r a w i n g s o f t h e t w o 0 . 2 5 m s i d e s o f t h e fluidization c o l u m n 1 5 2 3 . 5 W a f e r f e e d a n d r e m o v a l u n i t f o r t h e c o n t i n u o u s f i u i d i z e d b e d w a f e r d r y e r . . 1 5 5 3 . 6 ( a ) W a f e r f e e d a n d r e m o v a l u n i t ; ( b ) W a f e r r e m o v a l s c r e e n 1 5 6 3 . 7 S c a l e d d i a g r a m s o f t h e c o m p a r t m e n t 3 9 k W p o r c u p i n e e l e m e n t h e a t e r . . . 1 5 9 3 . 8 S c a l e d d i a g r a m o f 4 . 4 W s i l i c o n c a r b i d e e l e m e n t h e a t e r f o r c o m p a r t m e n t 1. 1 6 0 3 . 9 A r r a n g e m e n t o f " P o r c u p i n e " e l e m e n t 9 k W h e a t e r s a n d b o o s t e r h e a t e r a r o u n d w i n d b o x o f d r y e r 1 6 1 3 . 1 0 C u r v e d b a f f l e i n c o m p a r t m e n t 2 u s e d t o d i r e c t t h e s l u g s o f s a n d i n t o c o m -p a r t m e n t 3 1 7 1 3 . 1 1 T e m p e r a t u r e p r o f i l e s f o r c o m p a r t m e n t 1 f o r d r y i n g a t 6 0 ° C 1 7 5 3 . 1 2 T e m p e r a t u r e p r o f i l e s f o r c o m p a r t m e n t 2 f o r d r y i n g a t 6 0 ° C 1 7 6 xvi 3.13 Temperature profiles for compartment 3 for drying at 60°C 177 3.14 Temperature profiles for compartment 4 for drying at 60°C 178 3.15 Temperature profiles for compartment 1 for drying at 70°C 180 4.1 Residence time distributions or exit age distribution curves for N ideally mixed reactors in series (Levenspiel, 1972) 183 4.2 Mean wafer moisture content based on average residence times for fluidized beds in series 186 4.3 Schematic diagrams of the top and side view of three possible methods for circulating sand in a 5-compartment fluidized bed dryer 195 4.4 Cross-section of a compartment 1 membrane wall 200 4.5 Scaled diagram of a twin triple-pass drum drying system 204 B.l Response curves for the 3x3 analysis of variance of drying times vs. drying temperature from 125% to 3% moisture content 239 B.2 Response curves for the 3x3 analysis of variance of drying times vs. wafer length from 125% to 3% moisture content 240 B.3 Response curves for the 3x3 analysis of variance of drying times vs. wafer length from 125% to 30% moisture content 241 B.4 Response curves for the 3x3 analysis of variance of drying times vs. wafer length from 30% to 3% moisture content 242 B.5 Response curves for the 3x3 analysis of variance of drying rates vs. wafer length at 90% moisture content 246 B.6 Response curves for the 3x3 analysis of variance of drying rates vs. wafer length at 30% moisture content : 247 B.7 Response curves for the 3x3 analysis of variance of drying rates vs. wafer length at 5% moisture content 248 B.8 Response curves for the 3x3 analysis of variance of drying rates vs. drying temperature at 90% moisture content 250 B.9 Response curves for the 3x3 analysis of variance of drying rates vs. drying temperature at 30% moisture content 251 B.10 Response curves for the 3x3 analysis of variance of drying rates vs. drying temperature at 5% moisture content 252 xvii C.l Cross-section of drying apparatus showing the glass pipe and the suspended wafer • • 257 C.2 Schematic diagram of the drying system used to develop the equations for calculating radiative shape factors. Arrows indicate direction of evaluation of the contour integrals 260 G.l Fluidization column in cross-section showing the method of fastening the dividers into position. Scale 2.5mm:lmm 306 G. 2 The 4-compartment windbox 308 H. l Calibration curve for wafer feed system 313 I. 1 Estimated proportion of drying at 150°C in each of the four compartments of the experimental continuous fluidized bed dryer based on residence times of 18 s in compartments 1 and 3 and 3 s in compartments 2 and 4 318 1.2 Configuration of a 3 kW porcupine heater element 324 1.3 End view of 4.4 kW Booster heater showing the packing of each element, the arrangement of elements in the heating chamber, and electrical connections between elements and to the external electrical box 326 J.l Calibration curve for the continuous feed of copper slag particles into com-partment 1 328 xvm Acknowledgements I wish to express my thanks to my research supervisors Drs. Epstein, Grace and Pinder for their continued support of my research and council given me whenever needed. I would also like to acknowledge the interest of MacMillan Bloedel Research in my work, their assistance in providing research materials for my experimentation and their sponsorship of my scholarship applications. Special thanks are due to Hugh Ackroyd, Clive Brereton and David Taylor for their willingness to discuss my research and their advice and encouragement, and to Lisa Brandly for her excellent work on the compilation of this thesis. Lastly, I would like to thank the staff of the Department of Chemical Engineering and the Pulp and Paper Centre for their assistance throughout my Ph.D. studies. xix To Suzanne, and my parents. For your love and encouragement. xx Introduction T h e c o n c e p t o f w a f e r b o a r d a s a p r o d u c t i s t o u s e l o w v a l u e f o r e s t r e s o u r c e s ( s u c h a s t h e a s p e n / p o p l a r f o r e s t s f o u n d a c r o s s n o r t h e r n C a n a d a ) t o p r o d u c e a s t r u c t u r a l p a n e l b o a r d a i m e d a t r e p l a c i n g p l y w o o d a s t h e s h e a t h i n g u s e d i n m o s t r e s i d e n t i a l a n d l i g h t b u i l d i n g c o n s t r u c t i o n . W a f e r s a r e c u t f r o m r o u n d w o o d t o h a v e a t h i c k n e s s o f a p p r o x i m a t e l y 0 . 6 3 m m , a w i d t h o f a b o u t 5 0 m m a n d a l e n g t h o f 7 5 m m o r l o n g e r . T h e f r e s h l y c u t a s p e n w a f e r s h a v e a g r e e n m o i s t u r e c o n t e n t o f 6 0 % t o 1 5 0 % ( d r y b a s i s ) . H o w e v e r , b e f o r e b e i n g c o m b i n e d w i t h p h e n o l - f o r m a l d e h y d e r e s i n a n d p r e s s e d i n t o a b o a r d , t h e y m u s t b e d r i e d t o a p p r o x i m a t e l y 3 % m o i s t u r e c o n t e n t . T h e w a f e r b o a r d m a n u f a c t u r i n g p r o c e s s d e v e l o p e d a s a n e x t e n s i o n o f t h e p a r t i c l e b o a r d m a n u f a c t u r i n g p r o c e s s , t h e f o r m e r u s i n g m a n u f a c t u r e d " e n g i n e e r e d " w a f e r s a s o p p o s e d t o w o o d w a s t e s (e.g. p l a n e r s h a v i n g s , s a w d u s t , a n d h a m m e r - m i l l e d s l a b s a n d e d g i n g s ) . R e s u l t i n g f r o m t h i s d e v e l o p m e n t , t h e o n e t o t h r e e p a s s r o t a r y d r y e r s c u r r e n t l y u s e d t o d r y w a f e r s a r e a d a p t a t i o n s o f p a r t i c l e b o a r d f u r n i s h d r y e r s ( w h i c h i n t u r n w e r e m o d i f i c a t i o n s o f a g r i c u l t u r a l d r y e r s ) . A l t h o u g h a v a r i e t y o f d i f f e r e n t d r y e r s h a v e b e e n r e c e n t l y d e v e l o p e d f o r p a r t i c l e b o a r d f u r n i s h ( f l a s h d r y e r s , a n d j e t d r y e r s ( S t i p e k , 1 9 8 2 ) , s i n g l e p a s s r o t a r y d r y e r w i t h " t w o - s t e p " d r y i n g p r o c e s s a n d a n " i n t e g r a t e d " f l i g h t i n g s y s t e m ( V a l a , 1 9 8 2 ) ) , i m p r o v e m e n t s t o t h e w a f e r d r y i n g p r o c e s s h a v e f o c u s s e d o n r e d u c i n g t h e c o s t o f t h e e n e r g y s u p p l i e d t o t h e d r y e r ( V a j d a , 1 9 8 0 ) . T h e r e a r e n u m e r o u s d i s a d v a n t a g e s t o u s i n g d i r e c t - f i r e d r o t a r y d r y e r s f o r w a f e r d r y i n g . 1 The inlet temperature of the drying medium is limited because the hot gases are mixed directly with the wood wafers. The inlet temperature is thus limited by the combustibility and thermal degradation of the wood (Kossatz, 1982; Vala, 1982). This is a disadvantage in that the higher the inlet temperature, the more efficient the drying process (Kossatz, 1982). The mixing of the hot incoming gases directly with the wafer furnish can also create a considerable fire hazard since the inlet temperatures are well above the temperature required for the spontaneous combustion of dry wood (Kossatz, 1982). Mechanical failure of the dryer, sparks from the burner or furnish with a low initial moisture content may result in fires. Fines in the furnish are actually burnt in the gas stream as drying progresses (Watson, 1984). Chemical deactivation of the wafer surface (with respect to the resin bonding to the wood) (Plagemann et al., 1984; Kossatz, 1982) and blue haze pollution (products of the thermal degradation of the wood) (Kossatz, 1982,; Stipek, 1982) both result from high inlet gas temperatures and overly severe drying conditions. The poor contacting between the drying medium and the wafers both in the direct-fired rotary dryers and, the steam coil heated Pondorf type dryer necessitate long wafer residence times in the dryer and thus, large dryers are required to accommodate mill wafer flow requirements. The large size of the equipment and the plug flow of gas and wafers through the dryer make control of the drying process difficult since the dryer is controlled by the temperature of the exhaust gas. The conveying of the wafers through the passes of a rotary dryer or by the rotating paddles of the Pondorf type dryer results in breakage of the wafers and thus lowers wafer quality. The objective of this research is to develop a wafer dryer that is more efficient than current dryers by adapting fiuidized bed technology to the wafer drying process. It is hy-pothesized that drying wood wafers in a fiuidized bed of inert solids will result in faster drying, higher dried wafer quality and greater dryer efficiency than is possible using con-2 ventional drying techniques. The lack of available information on wafer drying necessitates that the first goal of this research is to characterize wafer drying behaviour. After the im-portant parameters of wafer drying have been identified then the applicability of fiuidized bed technology to wafer drying are assessed. Finally, the results of these two sections are incorporated into the development of a continuous fiuidized bed wafer dryer. 3 Chapter 1 Fundamentals of Wafer Drying 1.1 Background Review of Veneer and Particle Drying 1.1.1 Introduction Previous research efforts on the drying of wood products have focussed primarily on the drying of lumber. Although this is reasonable considering the importance of lumber to the forest products industry and the problems that exist in obtaining adequate control over the lumber drying process, it has tended to cause research into the drying of other wood products to be neglected. Some research has been undertaken on veneer drying in the development of faster, more efficient dryers for the plywood manufacturing process. However, the comparative ease in drying veneer as opposed to lumber coupled with the maturity of plywood as a product (vis-a-vis the increasing scarcity of peeler sized logs and the gradual replacement of plywood by wafer and strand boards), has limited continued research in this area. The drying of wood furnish for use in particleboard and waferboard manufacture has been the subject of little attention. This is probably the result of the relatively recent development of the products. The lack of reported research on wafer drying makes it necessary to predict wafer dry-ing behaviour using the results from drying studies on veneer and particleboard furnish since they are the closest to wafers in form. Unfortunately, there is little agreement in the literature as to the dominant drying mechanisms for either of these two materials. The 4 conflict appears to arise from differences between the various studies both in the selection of the experimental conditions and materials, and in the interpretation of the results. Both the theoretical and experimental results from these studies will be reviewed with the goal of developing a conceptual model of wafer drying. 1.1.2 Drying Theory for Thin Wood Samples Classical Drying Rate Theory In the late 1920's and early 1930's, Sherwood published a series of papers that introduced the concept of rate curve analysis to drying (Comings, 1983). Whereas the drying curve (moisture content vs. time) yielded little information about how the material dried, the drying rate curve (constructed by drawing tangents to the drying curve at various points along its length and plotting the slopes of these tangents against the corresponding moisture contents) showed distinct inflection points which Sherwood attributed to changes in the dominant mechanism of drying. Although different materials resulted in a wide variation of drying rate curve shapes, a standard drying rate curve (Figure 1.1) appears to have been adopted for teaching purposes (Treybal, 1980). This traditional drying rate curve has two distinct zones: a constant rate period and a falling rate period. In the constant rate drying period the external drying conditions (temperature, air velocity, and humidity) control the rate of drying. All energy transferred to the material being dried is used in the evaporation of water. The water at the surface is replenished by the capillary flow of water from the interior of the material being dried (Comings and Sherwood, 1934). The falling rate period is divided into a period of decreased wetted surface area drying, and a period where drying is controlled by the internal diffusion of water. As the material dries out and air replaces the water wicked to the surface, the capillary system in the 5 o o O. o > a> o <u B ll 0 O.t 0.2 0.3 0.4 X- kg moisture/kg dry solid F I G U R E 1.1: Typical rate of drying curve, constant drying conditions (Treybal, 1980) material becomes discontinuous and thus is unable to maintain a completely wetted surface. In this period of decreased wetted surface area drying, the drying rate is still proportional to the external driving force, but the wetted surface area from which evaporation occurs is constantly decreasing. This period is characterized by a linearly decreasing drying rate as shown in Figure 1.1. Once the flow of water to the surface has been completely interrupted by the intrusion of air into the capillary system, a drying front is formed below the surface of the material. As the free water recedes deeper into the material, the drying front progresses toward the core until the material has reached an equilibrium moisture content with the external drying conditions. During this portion of the falling rate period, drying is controlled by the diffusion of water from the wet core of the material to its surface. 6 Model l ing Wood Dry ing The mathematical descriptions of falling rate drying and Sherwood's pioneering studies were based on Fick's Second Law with a liquid water gradient as the driving force (Sher-wood, 1931) " M = D*» (1.1) dt dx 2 where M is the moisture content t is the time D is the molecular diffusion coefficient of water vapour Assuming a uniform initial moisture content distribution in the material, that evapora-tion takes place at the surface and that there is negligible resistance to vapour diffusion at the surface, one may integrate Equation (1.1) to provide a relation between the moisture content of the material and the drying time. For an infinite slab, Sherwood developed the following equation for E, the total free moisture content over the initial moisture content: 7TZ s(-f)2(^) + Ie-9(f)2(^) + ... (1.2) where 9 is the time K is the diffusion constant of water through the solid x is the half thickness of the slab Newman (I931a,1931b) developed equations for the falling rate period similar to those of Sherwood except that the resistance to vapour diffusion at the surface was included in the derivation. The rate of drying at any time would then vary in the same direction as the free water concentration at the surface and thus be consistent with the moisture content gradient driving force (Newman, 1931a,1931b). In a later publication, Sherwood (1936), stressed the limitations of the "diffusion" equations. Drying experiments conducted on 2.5 cm thick slabs of wood showed that a significant portion of the water contained in wood did not evaporate at the surface of the wood but at some point within the slab. It was also noted that the diffusion coefficient was not constant with changing thicknesses of wood. These results led Sherwood to conclude that although the integrated "diffusion" equations fitted the wood drying data well, the agreement was fortuitous and not theoretically sound. Water movement in wood was attributed primarily to capillary flow through the wood's porous structure. It is unclear in this work whether Sherwood was referring to the inapplicability of the "diffusion" equations to the constant rate period, or to the falling rate periods. It is perhaps this confusion that resulted in a critique of the "diffusion" equation by Hougen et al. (1940). Comparing the moisture content profiles generated by the "diffusion" equation with experimental moisture content profiles for several different materials. Hougen et al. concluded that in the drying of hygroscopic solids such as wood, the movement of water by internal diffusion was limited to the last stage of drying where only bound or sorbed water exists in the solid. Stamm (1964) outlined the different pathways that may be taken by bound water diffusing through wood as shown in Table 1.1 and Figure 1.2. A single diffusion coefficient would appear to be inappropriate even in^describing bound water movement through wood. In the written discussion following the article, Hougen voiced concern over the misap-plication of the diffusion equations through the lack of understanding of its limitations. Nevertheless, modelling on wood drying by a simple diffusion equation has proven to be very attractive to many researchers despite the inherent theoretical problems. The use of high gas temperatures and velocities to dry veneer and particleboard furnish has resulted in short or non-existent constant rate drying periods. In many studies, the falling rate curves were assumed to be diffusion controlled and an overall diffusion coefficient for the wood was calculated using Fick's Second Law based on either a water vapour pressure (Wen and Loos, 1969) or a moisture content gradient driving force (Salin, 1984; Malte et ai, 1977; Laity et al, 1974; Atherton and Welty, 1972; Fleischer, 1953; Bethel and Hader, 1952). Fleischer found that although an integrated diffusion equation predicted the 8 TABLE 1.1: Fractional Distribution of Diffusion Modes for Transverse Moisture Movement in Woods of Different Densities (Stamm, 1964). (kg/m3) (1) Cell wall + lumen (2) cell wall only (3) lumen - lumen 200 0.86 0.02 0.12 400 0.69 0.10 0.21 800 0.31 0.47 0.21 FIGURE 1.2: Modes of transverse moisture diffusion through wood. where 1. diffusion in cell wall and in lumens; 2. diffusion in the cell wall only; 3. diffusion from lumen to lumen via the pits 9 d r y i n g t i m e o f 6 . 3 m m v e n e e r s a t 6 5 . 5 ° C , t h e d i f f u s i o n c o e f f i c i e n t K v a r i e d c o n t i n u o u s l y w i t h m o i s t u r e c o n t e n t f o r t h e s a m e v e n e e r s a t h i g h e r t e m p e r a t u r e s , ( 1 2 1 ° C a n d 1 7 7 ° C ) a n d f o r t h i n n e r v e n e e r s ( 3 . 2 m m , 1 . 5 9 m m , a n d 0 . 7 9 m m ) . A n e x p r e s s i o n w a s d e v e l o p e d r e l a t i n g t h e h e a t t r a n s f e r r e d t o t h e v e n e e r , t h e h e a t o f v a p o r i z a t i o n o f w a t e r o c c u r r i n g d u r i n g d r y i n g a n d t h e d r y i n g r a t e c u r v e . T h i s r e l a t i o n s h i p s h o w e d t h a t t h e l i n e a r d e c r e a s e i n d r y i n g r a t e w i t h t i m e r e s u l t e d f r o m t h e h e a t t r a n s f e r r e d t o t h e v e n e e r a n d n o t f r o m d i f f u s i o n . C o m s t o c k ( 1 9 7 1 ) a n d M i l l i g a n a n d D a v i e s ( 1 9 6 3 ) a l s o c o n c l u d e d t h a t t h e h e a t t r a n s f e r r e d t o t h e v e n e e r w a s t h e c o n t r o l l i n g m e c h a n i s m i n v e n e e r d r y i n g . T h e c o r r e l a t i o n s d e v e l o p e d b y C o m s t o c k a r e p a r t i c u l a r l y i n t e r e s t i n g b e c a u s e t h e y p r e d i c t v e n e e r d r y i n g c u r v e s ( r e g a r d l e s s o f i n i t i a l m o i s t u r e c o n t e n t ) b a s e d o n b o t h p r o c e s s v a r i a b l e s ( t e m p e r a t u r e a n d v e l o c i t y ) a n d v e n e e r v a r i a b l e s ( t h i c k n e s s a n d d e n s i t y ) . C o m s t o c k d i v i d e d t h e d r y i n g r a t e c u r v e i n t o t w o s t r a i g h t l i n e f a l l i n g r a t e s a s s h o w n i n F i g u r e 1.3 a n d d e s c r i b e d e a c h s e c t i o n i n t e r m s o f t h e s l o p e ( B ) a n d i n t e r c e p t ( A ) o f t h e i n i t i a l f a l l i n g r a t e p e r i o d a n d t h e b r e a k p o i n t m o i s t u r e c o n t e n t ( C ) w h e r e t h e s e c o n d f a l l i n g r a t e p e r i o d b e g i n s . T h e t w o e q u a t i o n s a r e t h e n i n t e g r a t e d t o g i v e for Mnitial > C, M f i n a l > C ^ . m . 1 , f A + BM{ D r y i n g T i m e = t = - I n ^ T ^ -f o r Mi >C,Mf <C D r y i n g T i m e = t = — I n B A + BMi A + BMf ( 1 . 3 ) A + BM} + A+ BC I n M J J (1.4) f o r Mi <C,Mf <C D r y i n g T i m e = t C A + BC. Mi_ Mf (1.5) T h e c o e f f i c i e n t s A a n d B w e r e t h e n s h o w n e x p e r i m e n t a l l y t o b e l i n e a r l y r e l a t e d t o t e m p e r -a t u r e a n d v e l o c i t y : A = {Aa + AbV)(T- 1 0 0 ) ( 1 . 6 ) 1 0 F I G U R E 1 .3 : D r y i n g r a t e c u r v e f o r m e s t a b l i s h e d b y C o m s t o c k ( 1 9 7 1 ) . B = Ba + BbV ( 1 . 7 ) w h e r e Aa, At r e p r e s e n t t h e i n t e r c e p t a n d s l o p e r e s p e c t i v e l y o f t h e l i n e A / ( T - 1 0 0 ) v s . v e l o c i t y Ba, Bi, r e p r e s e n t t h e i n t e r c e p t a n d s l o p e r e s p e c t i v e l y o f t h e l i n e B v s . v e l o c i t y T i s t h e a i r t e m p e r a t u r e V i s t h e a i r v e l o c i t y A i r v e l o c i t y d i d n o t a f f e c t t h e i n t e r c e p t A b e l o w 1 0 0 ° C . T h e f i n a l s t a g e i n t h e d e v e l o p -m e n t o f t h e g e n e r a l p u r p o s e d r y i n g c u r v e e q u a t i o n s w a s t h e m u l t i p l e c o r r e l a t i o n o f d r y i n g t i m e w i t h t h i c k n e s s a n d d e n s i t y o f t h e v e n e e r s . E q u a t i o n s ( 1 . 6 ) a n d ( 1 . 7 ) w e r e a d j u s t e d f o r t h e e f f e c t s o f t h i c k n e s s a n d d e n s i t y d e t e r m i n e d b y t h i s r e g r e s s i o n t o g i v e t h e f i n a l e q u a t i o n s f o r A a n d B / r \ - 119 / \ -0.87 A=(Aa + AbV) (T - 1 0 0 ) \^—J (^j-J ( 1 . 8 ) 11 / r \ -1.19 / . \ -0.87 * = (zr) (£) <19» where L\ and pi are the thickness and density for which A0, A, B0, and B\ were determined, and L and p are the variables thickness and density. The breakpoint moisture content, C, was found to be independent of thickness or density. Its value for softwoods was approximately 17% moisture content (all moisture contents expressed on an ovendry basis) for veneer thickness of 2.5 mm to 4.8 mm but, for 0.98 mm Yellow Birch it was only 12% moisture content. The reason for this difference was not stated. The exponents of the thickness and density correction factors were also used by Corn-stock to comment on the controlling drying mechanism during veneer drying. If diffusion was the limiting drying mechanism, then the drying times should have been roughly pro-portional to the square of thickness and density. However, the exponents of 1.19 and 0.87 for thickness and density respectively were closer to the first power relationship of external heat transfer to drying time. Comstock further stated that, since the exponent for thick-ness was greater than that of density, perhaps conduction of heat through the dried outer layer of wood to the drying front also had a limiting effect on drying. The use of integrated diffusion equation with averaged diffusion coefficients and cor-relations as developed by Comstock has generally been discontinued in favour of more sophisticated models having a sounder theoretical basis. The new generation of models differ from the earlier works primarily in the realization that the drying of wood involves a series of complex interactions between liquid and vapour pressure driven flow, vapour and bound water diffusion, internal heat conduction, and external heat and mass transfer (Stanish et al., 1986; Dorri et al., 1985; Kayihan and Stanish, 1984; Skaar and Kuroda, 1984; Roques and Cornish, 1980; Spolek and Plumb, 1980; Fortes and Okos, 1978). An-other important development was the use of a chemical potential gradient as the driving force for diffusion of bound water through wood (Stanish, 1986; Siau et ai, 1986; Siau and 12 Z i n , 1 9 8 5 ; S i a u , 1 9 8 3 a , 1 9 8 3 b , 1 9 8 4 b ; K a w a i et ai, 1 9 7 8 ) . S t a n i s h ( 1 9 8 6 ) r e v i e w e d t h e m a t h e m a t i c a l e x p r e s s i o n s f o r b o u n d w a t e r d i f f u s i o n d e v e l -o p e d b y S t a n i s h et al. ( 1 9 8 6 ) , S i a u ( 1 9 8 3 b , 1 9 8 4 b ) , S k a a r a n d S i a u ( 1 9 8 1 ) , a n d K a w a i et al. ( 1 9 7 8 ) a n d c o m p a r e d t h e i r e f f e c t i v e n e s s i n e v a l u a t i n g t h r e e s e p a r a t e s e t s o f d a t a f r o m t h e l i t e r a t u r e . S t a n i s h et al.'s ( 1 9 8 6 ) i n c l u s i o n o f a s e p a r a t e t e r m f o r w a t e r v a p o u r d i f f u s i o n d u r i n g d r y i n g b e l o w t h e fibre s a t u r a t i o n p o i n t a n d t h e i r d e v e l o p m e n t o f a c h e m i c a l p o t e n -t i a l g r a d i e n t t h a t c o u l d b e q u a n t i f i e d u s i n g l o c a l t e m p e r a t u r e s a n d w a t e r v a p o u r p r e s s u r e s r e s u l t e d i n a m o d e l w h i c h f i t t e d t h e d a t a s i g n i f i c a n t l y b e t t e r t h a n d i d t h e o t h e r m o d e l s . F u r t h e r m o r e , t h e v o l u m e a v e r a g i n g t e c h n i q u e e m p l o y e d i n d e v e l o p i n g t h e e x p r e s s i o n s , a n d t h e a s s u m p t i o n o f a l o c a l i z e d t h e r m o d y n a m i c e q u i l i b r i u m b e t w e e n w a t e r v a p o u r a n d b o u n d w a t e r f o r m e d a l o g i c a l a n d w o r k a b l e b a s i s f o r a w o o d d r y i n g m o d e l . T h i s i s a v a s t i m -p r o v e m e n t o v e r t h e d e t a i l e d , a n d o f t e n c o n v o l u t e d t h e o r e t i c a l t h e r m o c h e m i c a l d e s c r i p t i o n s o f b o u n d w a t e r i n w o o d f o u n d i n t h e f o r m u l a t i o n s o f t h e a c t i v a t e d w a t e r m o l e c u l e g r a d i e n t d r i v i n g f o r c e ( S i a u a n d B a b i a k , 1 9 8 3 ; S k a a r a n d S i a u , 1 9 8 1 ) , t h e c h e m i c a l p o t e n t i a l g r a d i -e n t o f b o u n d w a t e r ( S i a u , 1 9 8 3 b ; 1 9 8 4 b ) , a n d t h e s p r e a d i n g p r e s s u r e g r a d i e n t d r i v i n g f o r c e ( N e l s o n , 1 9 8 6 a , 1 9 8 6 b , 1 9 8 6 c ; S k a a r a n d B a b i a k , 1 9 8 2 ) . I n a r e v i e w o f t h e m a t h e m a t i c a l m o d e l l i n g o f w o o d d r y i n g , Z w i c k ( 1 9 8 5 ) f a v o u r e d t h e m o d e l d e v e l o p e d b y S t a n i s h et al. ( 1 9 8 6 ) o v e r i r r e v e r s i b l e t h e r m o d y n a m i c m o d e l s , a n d o v e r o t h e r m e c h a n i s t i c m o d e l s b e c a u s e o f i t s r e l a t i v e s i m p l i c i t y , i t s c o m p l e t e d e s c r i p t i o n o f t h e n u m e r o u s t r a n s p o r t m e c h a n i s m s , a n d i t s p r o v e n p e r f o r m a n c e . I n l i g h t o f t h e a b o v e , S t a n i s h et al.'s m o d e l w i l l b e u s e d t o d e v e l o p a c o n c e p t u a l m o d e l o f w o o d w a f e r d r y i n g . S t a n i s h et al. d e v e l o p e d a s y s t e m o f o n e - d i m e n s i o n a l d i f f e r e n t i a l e q u a t i o n s b a s e d o n m a t e r i a l a n d e n e r g y b a l a n c e s w h i c h i n c o r p o r a t e d e x p r e s s i o n s f o r t h e m a s s a n d h e a t t r a n s p o r t m e c h a n i s m s f o r e a c h o f t h e t h r e e p h a s e s o f w a t e r i n w o o d ( l i q u i d , v a p o u r , a n d b o u n d w a t e r ) . T h e r e s u l t a n t e q u a t i o n s w e r e t h e n c o u p l e d w i t h e x p r e s s i o n s f o r l o c a l p h a s e e q u i l i b r i a t o p r e d i c t t h e d r y i n g p r o c e s s i n l u m b e r . A n a d v a n t a g e o f t h i s m o d e l 13 l i e s i n i t s a b i l i t y t o d e t e r m i n e t h e r e l a t i v e i m p o r t a n c e o f t h e d i f f e r e n t t r a n s p o r t m e c h a n i s m s a t a n y p o i n t d u r i n g d r y i n g . B a s e d o n t h e m o d e l l i n g o f t h e d r y i n g o f 5 0 m m s e c t i o n s o f S o u t h e r n P i n e a n d D o u g l a s -f i r u n d e r v a r i o u s e x t e r n a l d r y i n g c o n d i t i o n s , S t a n i s h et al. d e s c r i b e d t h e d r y i n g p r o c e s s a t a i r t e m p e r a t u r e s o f 7 5 ° C a n d 1 2 5 ° C ( v e l o c i t y = 7 m / s a n d d e w p o i n t = 1 0 ° C ) . A t b o t h t e m p e r a t u r e s t h e e x t e r n a l s u r f a c e o f t h e w o o d d r i e d r a p i d l y w i t h a c o r r e s p o n d i n g i n c r e a s e i n t h e i n t e r n a l w o o d t e m p e r a t u r e . A f t e r t h e r e m o v a l o f t h e s u r f a c e w a t e r , a w e t - l i n e d r y i n g f r o n t d e v e l o p e d w i t h a n o u t e r l a y e r o f w o o d b e l o w t h e f i b r e s a t u r a t i o n p o i n t a n d a n i n s i d e c o r e t h a t s t i l l r e t a i n e d s o m e f r e e w a t e r . S i n c e t h e m o v e m e n t o f w a t e r f r o m t h e w o o d i n t e r i o r t o t h e d r y i n g f r o n t w a s s l o w e r t h a n t h a t f r o m t h e d r y i n g f r o n t t o t h e s u r f a c e o f t h e w o o d , t h e f r o n t p r o g r e s s e d t o w a r d t h e c e n t r e l i n e o f t h e w o o d . T h e i r s i m u l a t i o n o f d r y i n g a t 7 5 ° C , i n d i c a t e d t h a t t h e t e m p e r a t u r e g r a d i e n t a c r o s s t h e e x t e r n a l b o u n d a r y l a y e r w a s m u c h g r e a t e r t h a n t h a t f r o m t h e c e n t r e l i n e t o t h e s u r f a c e o f t h e w o o d . T h i s s h o w e d t h a t a t 7 5 ° C e x t e r n a l h e a t t r a n s f e r w a s a l i m i t i n g m e c h a n i s m . I n t e r n a l m o i s t u r e t r a n s p o r t w a s a l s o d e t e r m i n e d t o b e l i m i t i n g t h e r a t e o f d r y i n g b e c a u s e t h e w a t e r v a p o u r p r e s s u r e g r a d i e n t f r o m t h e d r y i n g f r o n t t o t h e s u r f a c e o f t h e w o o d w a s c o n s i d e r a b l y h i g h e r t h a n o f t h a t a c r o s s t h e e x t e r n a l b o u n d a r y l a y e r . I n d r y i n g a t 1 2 5 ° C , t h e i n t e r n a l t e m p e r a t u r e o f t h e w o o d r o s e t o a p p r o x i m a t e l y 1 0 0 ° C , a n d b o i l i n g o f l i q u i d w a t e r o c c u r r e d i n t h e w o o d p o r e s a t t h e r e c e d i n g d r y i n g f r o n t . T h e g a s p h a s e a t t h e d r y i n g f r o n t w a s s h o w n t o c o n s i s t e n t i r e l y o f w a t e r v a p o u r a t a b o u t 1 a t m o s p h e r e , a n d w a s c o n v e y e d t o t h e s u r f a c e o f t h e w o o d p r i m a r i l y b y b u l k f l o w . A f t e r a l l l i q u i d w a t e r h a d b e e n r e m o v e d f r o m t h e w o o d , t h e t e m p e r a t u r e a t t h e c e n t r e l i n e o f t h e w o o d r o s e a b o v e 1 0 0 ° C . B o u n d w a t e r t h a t e v a p o r a t e d i n t o t h e l u m e n s ( i n t e r n a l c e l l u l a r c a v i t i e s ) o f t h e w o o d w a s a l s o t r a n s p o r t e d p r i m a r i l y b y b u l k f l o w t o t h e s u r f a c e o f t h e w o o d . S i n c e t h e g a s p e r m e a b i l i t y o f t h e w o o d d i d n o t a p p e a r t o h i n d e r b u l k f l o w o f w a t e r v a p o u r , i t w a s c o n c l u d e d t h a t m o i s t u r e t r a n s p o r t m e c h a n i s m s w e r e n o t l i m i t i n g t h e d r y i n g r a t e . 14 A n e x a m i n a t i o n o f t h e c a l c u l a t e d t e m p e r a t u r e g r a d i e n t s s h o w e d t h a t t h e y w e r e i n i t i a l l y t h e s a m e a s i n d r y i n g a t 7 5 ° C a n d t h u s d r y i n g w a s c o n t r o l l e d b y e x t e r n a l h e a t t r a n s f e r . H o w e v e r , a s t h e d r y i n g f r o n t r e c e d e d t h e t e m p e r a t u r e g r a d i e n t f r o m t h e c e n t r e l i n e t o t h e s u r f a c e o f t h e w o o d i n c r e a s e d w h i l e t h a t a c r o s s t h e e x t e r n a l b o u n d a r y l a y e r d e c r e a s e d . T h u s , d u r i n g t h e l a t t e r p o r t i o n o f t h e d r y i n g p r o c e s s t h e i n t e r n a l r a t e o f h e a t c o n d u c t i o n w a s t h e l i m i t i n g m e c h a n i s m . T h i s d e s c r i p t i o n o f d r y i n g a t h i g h t e m p e r a t u r e s m a t c h e d t h e e x p e r i m e n t a l o b s e r v a t i o n s o f H a n n ( 1 9 6 4 ) i n d r y i n g Y e l l o w - p o p l a r l u m b e r , a n d f o r 3 . 2 m m v e n e e r d r y i n g ( C o m s t o c k , 1 9 7 1 ) . I t w a s a l s o s i m i l a r t o t h a t u s e d b y D o r r i et al. ( 1 9 8 5 ) i n d e v e l o p i n g a m o d e l f o r t h e d r y i n g o f " c h u n k y " w o o d p a r t i c l e s . T h e c o u p l e d n a t u r e o f h e a t a n d m a s s t r a n s f e r i n d r y i n g , a s d e t a i l e d b y S t a n i s h et al.'s m o d e l , i s e v i d e n t i n t h a t t h e a m o u n t o f h e a t c o n d u c t e d i n t o t h e w o o d d e t e r m i n e s t h e p r o p o r t i o n o f b o u n d w a t e r t h a t v a p o r i z e s i n t o t h e l u m e n v e r s u s t h a t w h i c h d i f f u s e s t h r o u g h t h e w o o d s u b s t a n c e t o t h e s u r f a c e . A n i n c r e a s e i n t h e r e s i s t a n c e t o i n t e r n a l h e a t t r a n s f e r w o u l d r e s u l t i n a r e d u c t i o n o f t h e e q u i l i b r i u m v a p o u r p r e s s u r e o f b o u n d w a t e r a n d a n i n c r e a s e i n t h e q u a n t i t y o f b o u n d w a t e r t h a t m u s t d i f f u s e t h r o u g h t h e w o o d s u b s t a n c e p a t h w a y . T h u s , i n t e r n a l h e a t - t r a n s f e r - l i m i t e d d r y i n g c a n a l s o b e c o n s i d e r e d t o b e l i m i t e d b y b o u n d w a t e r d i f f u s i o n . 1.1.3 Experimental D r y i n g Rates for Veneers and Particles D r y i n g r a t e s r e p o r t e d i n t h e l i t e r a t u r e m a y b e c l a s s i f i e d a s e i t h e r f o l l o w i n g t h e c l a s s i c a l d r y i n g r a t e c u r v e o r a s h a v i n g a s i n g l e f a l l i n g r a t e r e g i m e . A l t h o u g h d r y i n g r a t e c u r v e a n a l y s e s i s a u s e f u l t e c h n i q u e i n s t u d y i n g t h e d r y i n g b e h a v i o u r o f m a t e r i a l s , i t c a n d i s t o r t t h e e x p e r i m e n t a l r e s u l t s i f i n c o r r e c t l y a p p l i e d . T h e s h a p e o f t h e d r y i n g r a t e c u r v e a n d t h e m a g n i t u d e s o f t h e d r y i n g r a t e s a r e e x t r e m e l y s e n s i t i v e t o t h e s h a p e o f t h e d r y i n g c u r v e . I n m a n y s t u d i e s ( e s p e c i a l l y i n e a r l i e r w o r k s ) n o t e n o u g h d a t a p o i n t s w e r e t a k e n t o a l l o w 15 t h e d r y i n g c u r v e t o b e d r a w n a c c u r a t e l y . D r y i n g r a t e c u r v e s c a l c u l a t e d f r o m d r y i n g c u r v e s h a v i n g s i x d a t a p o i n t s o r f e w e r m a y b e f o u n d i n n u m e r o u s s t u d i e s ( L a i t y et al., 1 9 7 4 ; A t h e r t o n a n d W e l t y , 1 9 7 2 ; L o o s , 1 9 7 1 ; L o o s a n d W e n , 1 9 7 0 ; M i l l i g a n a n d D a v i e s , 1 9 6 3 ) . U n f o r t u n a t e l y , s o m e r e s e a r c h e r s d i d n o t r e p o r t t h e i r d a t a ( S a l i n , 1 9 8 4 ; B a b a i l o v a n d P e t r i , 1 9 7 4 ; C a r r u t h e r s a n d B u r r i d g e , 1 9 6 3 ; B e t h e l a n d H a d e r , 1 9 5 2 ) r e n d e r i n g t h e i r c o n c l u s i o n s o n d r y i n g r a t e s s u s p e c t . I n s o m e i n s t a n c e s i t a p p e a r e d t h a t t h e d r y i n g c u r v e w a s f o r c e d t o a s s u m e a c e r t a i n s h a p e t o f o l l o w t h e c l a s s i c a l d r y i n g r a t e t h e o r y p r e d i c t i o n s . T h i s s e e m e d t o b e e s p e c i a l l y p r e v a l e n t i n t h e o b s e r v a t i o n o f a c o n s t a n t d r y i n g r a t e p e r i o d ( S a l i n , 1 9 8 4 ; M a l t e et ai, 1 9 7 7 ; L a i t y et ai, 1 9 7 4 ) . Effect of External Drying Conditions on Veneer Drying Rates D e s p i t e t h e i n a c c u r a c i e s o f t h e d r y i n g r a t e a n a l y s e s a n d t h e w i d e v a r i e t y o f e x p e r i m e n t a l c o n d i t i o n s a n d v e n e e r t h i c k n e s s e s u s e d i n t h e d i f f e r e n t e x p e r i m e n t s , i t i s p o s s i b l e t o o b s e r v e d e f i n i t e t r e n d s i n d r y i n g r a t e b e h a v i o u r . T h e d e v e l o p m e n t o f v e n e e r d r y e r s h a s s e e n e x p e r i m e n t a t i o n w i t h h i g h e r t e m p e r a t u r e s a n d a i r v e l o c i t i e s w i t h e a c h n e w s t u d y . F o r a v e n e e r t h i c k n e s s o f 2 . 5 m m A t h e r t o n a n d W e l t y ( 1 9 7 2 ) a c h i e v e d c o n s i d e r a b l y r e d u c e d d r y i n g t i m e s a n d s h o r t e r c o n s t a n t r a t e p e r i o d s c o m p a r e d t o t h o s e o b t a i n e d b y B e t h e l a n d H a d e r ( 1 9 5 2 ) b y u s i n g h i g h e r g a s t e m p e r a t u r e s ( 2 0 4 ° - 4 2 7 ° C v s . 1 4 9 ° C ) a n d d i r e c t e d f l o w o f s u p e r h e a t e d s t e a m (3 m / s ) . U s i n g t h e s a m e d r y i n g s y s t e m a s A t h e r t o n a n d W e l t y , L a i t y et al. ( 1 9 7 4 ) s h o w e d t h a t h i g h a i r v e l o c i t i e s ( 1 5 - 4 5 m / s ) f u r t h e r r e d u c e d t h e d r y i n g t i m e a n d t h e p e r i o d o f c o n s t a n t r a t e d r y i n g o f t h e 2 . 5 m m v e n e e r . T h e c o n s t a n t r a t e d r y i n g r e g i m e w a s f o u n d n o t t o o c c u r d u r i n g t h e d r y i n g o f 3 . 2 m m v e n e e r u s i n g h i g h t e m p e r a t u r e s a n d h i g h v e l o c i t y a i r j e t s i m p i n g i n g a t a n a n g l e o f 9 0 ° t o t h e s u r f a c e o f t h e v e n e e r ( C o m s t o c k , 1 9 7 1 ; M i l l i g a n a n d D a v i e s , 1 9 6 3 ) . L o o s ( 1 9 7 1 ) a c h i e v e d a h i g h e r d r y i n g r a t e f o r 2 . 5 m m v e n e e r d r i e d i n a f l u i d i z e d b e d o f s a n d t h a n c o u l d 1 6 be obtained at the same temperature for any other drying system. In this progression of experiments, external heat and mass transfer rates were increased so that they no longer represented the limiting mechanism of drying. The rate of moisture removal from the veneer surface was increased until the internal resistance of the wood to drying became significant. If a constant rate period of drying were to exist, it would be expected that the internal temperature of the veneer would be close to the wet bulb temperature for the drying medium. Laity et al. (1974) claimed that a period of stable internal temperature of about 100°C was evidence of a constant rate period, even though the wet bulb temperature for their experiments was approximately 50°C. Fleischer (1953) observed that once the internal temperature of 3.2 mm veneer reached 100°C the temperature gradient from the centreline to the surface of the veneer disappeared. This was attributed to an equalization of water vapour pressure throughout the cross-section as the water at the drying front began to boil. The description of drying at 125°C given by the modelling results of Stanish et al. (1986) also provides an explanation for the stabilization of the internal temperature at 100°C. It is indicative of boiling of the liquid water in the pores at the receding drying front. The humidity of the drying medium was found to have no significant effect on the drying rate of veneer during drying above 100°C (Fleischer, 1953). The water vapour that evaporated at the drying front or from the cell walls would be transported out the veneer mainly by bulk flow. Water vapour diffusion would no longer be a limiting factor, since at temperatures above 100°C there was no limit to the quantity of water vapour that could exist in air. Thus, above 100°C, the humidity of the drying medium would no longer be a significant variable (Treybal, 1980). 17 Effects of Material Properties on Drying Rates T h e p r o p e r t i e s o f t h e m a t e r i a l b e i n g d r i e d p l a y a n i m p o r t a n t r o l e i n l i m i t i n g d r y i n g r a t e s . T h e r e a r e s e v e r a l s p e c i e s - d e p e n d e n t p r o p e r t i e s w h i c h m a y a f f e c t d r y i n g b e h a v i o u r : d e n s i t y ; i n i t i a l m o i s t u r e c o n t e n t ; g a s a n d l i q u i d p e r m e a b i l i t i e s . A l l o f t h e s e p r o p e r t i e s m a y a l s o v a r y w i t h i n a s p e c i e s d u e t o d i f f e r i n g t r e e g r o w t h c o n d i t i o n s ( s o i l t y p e , c l i m a t e ) , s e a s o n o f y e a r i n w h i c h t h e t r e e w a s h a r v e s t e d , a g e o f t r e e w h e n h a r v e s t e d , a n d , b i o l o g i c a l v a r i a t i o n s f r o m t r e e t o t r e e ( P a n s h i n a n d D e Z e e u w , 1 9 8 0 ) . T h e w o o d ' s f r a c t i o n a l v o i d s p a c e ( p r e d o m i n a n t l y c e l l l u m e n s ) , t h e q u a n t i t y o f b o u n d w a t e r p e r u n i t v o l u m e o f w o o d , t h e i n i t i a l m o i s t u r e c o n t e n t a n d t h e t h e r m a l c o n d u c t i v i t y o f w o o d a r e a l l r e l a t e d t o t h e d e n s i t y o f w o o d . A t t e m p e r a t u r e s b e l o w 1 0 0 ° C , a h i g h d e n s i t y w o o d s h o u l d d r y m o r e s l o w l y t h a n a w o o d h a v i n g a l o w d e n s i t y b e c a u s e o f t h e g r e a t e r q u a n t i t y o f b o u n d w a t e r t h a t m u s t d i f f u s e o u t o f t h e d e n s e w o o d a s o p p o s e d t o t h a t i n t h e l i g h t e r w o o d . A c c o r d i n g t o S t a n i s h et al. ( 1 9 8 6 ) , a t t e m p e r a t u r e s a b o v e 1 0 0 ° C t h e b u l k t r a n s p o r t o f w a t e r v a p o u r e v a p o r a t e d f r o m t h e w o o d s u b s t a n c e t h r o u g h t h e w o o d ' s p o r o u s s t r u c t u r e g r e a t l y r e d u c e s t h e a m o u n t o f b o u n d w a t e r t h a t m u s t d i f f u s e t h r o u g h t h e w o o d . A s d i s c u s s e d i n S e c t i o n 1 . 1 . 3 C o m s t o c k ( 1 9 7 1 ) s h o w e d t h a t e x t e r n a l h e a t t r a n s f e r t o v e n e e r w a s t h e p r e d o m i n a n t d r y i n g m e c h a n i s m . D e n s i t y w a s t h e r e f o r e i m p o r t a n t m a i n l y i n i t s d e t e r m i n a t i o n o f t h e a m o u n t o f w a t e r t o b e e v a p o r a t e d p e r u n i t s u r f a c e o f w o o d . A t l o w m o i s t u r e c o n t e n t s ( e s p e c i a l l y b e l o w t h e fibre s a t u r a t i o n p o i n t ) , d e n s i t y a l s o a f f e c t s i n t e r n a l h e a t t r a n s f e r b e c a u s e t h e m o r e w o o d s u b s t a n c e p e r u n i t v o l u m e (i.e. t h e d e n s e r t h e w o o d ) t h e h i g h e r t h e r a t e o f t h e r m a l c o n d u c t i o n t h r o u g h t h e w o o d . I n d e v e l o p i n g c o r r e l a t i o n s f o r t h e p r e d i c t i o n o f v e n e e r d r y i n g t i m e s , C o m s t o c k ( 1 9 7 1 ) i n c o r p o r a t e d i n i t i a l m o i s t u r e c o n t e n t a n d d e n s i t y o f t h e v e n e e r s i n t o t h e final e q u a t i o n s . F o r v e n e e r h a v i n g t h e s a m e d e n s i t y a n d t h i c k n e s s , s a m p l e s h a v i n g d i f f e r e n t i n i t i a l m o i s t u r e c o n t e n t s t e n d e d t o f o l l o w t h e s a m e d r y i n g r a t e v e r s u s m o i s t u r e c o n t e n t c u r v e . T h e i n i t i a l m o i s t u r e c o n t e n t o f t h e v e n e e r w a s n o t o n l y s p e c i e s - d e p e n d e n t , b u t a l s o m a y b e g r e a t l y 18 1000 5 0 0 tn Q z o o UJ £ 200 2 CD ? 100 >-cc a a U l < 50 O _ l < o 20 20 A LOBLOLLY PINE O DOUGLAS FIR Q YELLOW BIRCH OPEN • HEARTWOOO SHAOED•SAPWOOD _L 50 100 200 5O0 MEASUREO ORYING TIME (SECONOS) 1000 F I G U R E 1 .4 : R e l a t i o n s h i p b e t w e e n t h e d r y i n g t i m e s c a l c u l a t e d u s i n g t h e g e n e r a l i z e d r a t e e q u a t i o n s a n d t h e a c t u a l d r y i n g t i m e s f o r a b o u t 1 0 0 a r b i t r a r i l y s e l e c t e d v e n e e r s a m p l e s ( C o m s t o c k , 1 9 7 1 ) . i n f l u e n c e d b y t h e p e r c e n t a g e o f h e a r t w o o d t o s a p w o o d i n t h e v e n e e r . C o m s t o c k u s e d h i s g e n e r a l i z e d c o r r e l a t i o n s w i t h c o e f f i c i e n t s d e t e r m i n e d f o r D o u g l a s - f i r t o d e t e r m i n e t h e d r y i n g t i m e s o f 0 . 9 8 m m Y e l l o w B i r c h ( h e a r t w o o d a n d s a p w o o d ) , 2 . 5 m m t o 4 . 8 m m D o u g l a s - f i r ( h e a r t w o o d a n d s a p w o o d ) a n d L o b l o l l y P i n e ( s a p w o o d ) . F i g u r e 1.4 i l l u s t r a t e s t h a t t h e e q u a t i o n s d e v e l o p e d f o r D o u g l a s - f i r p r o d u c e d g o o d r e s u l t s w i t h b o t h B i r c h a n d L o b l o l l y P i n e . T h e figure a l s o s h o w s t h a t t h e h e a r t w o o d / s a p w o o d r a t i o a n d s p e c i e s h a d l i t t l e e f f e c t o n d r y i n g r a t e e x c e p t b y t h e i r i n f l u e n c e o n i n i t i a l m o i s t u r e c o n t e n t a n d b y t h e e f f e c t o f s p e c i e s o n d e n s i t y . G a s a n d l i q u i d p e r m e a b i l i t i e s o f w o o d a r e i n f l u e n c e d p r i m a r i l y b y s p e c i e s - d e p e n d e n t p r o p e r t i e s s u c h a s c e l l u l a r s t r u c t u r e , c e l l u l a r o c c l u s i o n s , a n d t h e d e p o s i t i o n o f e x t r a c t i v e s , 19 a n d b y c e l l u l a r o c c l u s i o n s a n d t h e d e p o s i t i o n o f e x t r a c t i v e s c a u s e d b y t h e t r a n s f o r m a t i o n o f s a p w o o d i n t o h e a r t w o o d ( W a r d , 1 9 8 6 ; P e r n g et ai, 1 9 8 5 ; S i a u , 1 9 8 4 ; P e t t y , 1 9 8 1 ; T e s o r o et al., 1 9 7 4 ; K i n n i n m o n t h , 1 9 7 3 ; S t a m m , 1 9 6 3 ) . C o n s i d e r i n g t h e a b o v e d i s c u s s i o n o f C o m s t o c k ' s w o r k , i t f o l l o w s t h a t g a s a n d l i q u i d p e r m e a b i l i t i e s o f w o o d h a v e a l i m i t e d e f f e c t o n t h e d r y i n g r a t e o f v e n e e r s d r i e d u n d e r c o n d i t i o n s o f h i g h e x t e r n a l r a t e s o f h e a t a n d m a s s t r a n s f e r . T h i s o b s e r v a t i o n s u p p o r t s t h e c o n c l u s i o n t h a t i n t e r n a l h e a t t r a n s f e r w a s t h e c o n t r o l l i n g t r a n s p o r t m e c h a n i s m i n t h e h i g h t e m p e r a t u r e d r y i n g o f w o o d ( S t a n i s h et al., 1 9 8 6 ; C o m s t o c k , 1 9 7 1 ; H a n n , 1 9 6 4 ; M i l l i g a n a n d D a v i e s , 1 9 6 3 ) . F u r t h e r m o r e , t h e s t e a m g e n e r a t e d i n t e r n a l l y d u r i n g h i g h t e m p e r a t u r e d r y i n g m a y r e d u c e t h e e n c r u s t a t i o n o f p i t m e m b r a n e s a n d o c c l u s i o n o f v e s s e l s s u g g e s t e d b y r e s e a r c h o n s t e a m p r e t r e a t m e n t t o w o o d d r y i n g ( K i n n i n m o n t h , 1 9 7 3 ; M a c K a y , 1 9 7 1 ) , t h u s i n c r e a s i n g t h e r a t e o f m o i s t u r e t r a n s p o r t i n h e a r t w o o d t o a l e v e l c l o s e t o t h a t i n s a p w o o d . T h e s h a p e o f t h e m a t e r i a l b e i n g d r i e d i s a n o t h e r p r o p e r t y t h a t h a s b e e n s h o w n t o a f f e c t d r y i n g r a t e s . I n t h e e x p e r i m e n t s c o n d u c t e d o n v e n e e r d r y i n g o n l y t h e v e n e e r ' s t h i c k n e s s w a s v a r i e d b e c a u s e a s h e e t o f v e n e e r i s t y p i c a l l y 1 . 2 2 m X 2 . 4 m b u t o n l y 0 . 7 9 m m t o 6 . 3 m m t h i c k . I t w o u l d b e u n r e a s o n a b l e t o e x p e c t t h e h e a t o r m a s s t r a n s p o r t i n t h e t a n g e n t i a l o r l o n g i t u d i n a l p l a n e s o f t h e v e n e e r s h e e t t o s i g n i f i c a n t l y a f f e c t t h e d r y i n g r a t e a s c o m p a r e d t o t h e h e a t a n d m a s s t r a n s p o r t a c r o s s t h e 0 . 7 9 m m t o 6 . 3 m m r a d i a l p l a n e . T o e n s u r e t h a t t h e e x p e r i m e n t s p r o d u c e d r e a l i s t i c r e s u l t s , a l l r e s e a r c h e r s i n t h e s t u d i e s e x a m i n e d f o r t h i s r e v i e w u s e d a m i n i m u m v e n e e r l e n g t h o f 0 . 1 5 m a n d t h e v e n e e r w a s o f t e n e n d - s e a l e d t o p r e v e n t a n y p o s s i b l e e n d e f f e c t s c a u s e d b y t h e l o n g i t u d i n a l s t r u c t u r e o f t h e w o o d . T h e e f f e c t o f t h i c k n e s s o n d r y i n g r a t e w a s e x a m i n e d u n d e r t h r e e w i d e l y d i f f e r i n g d r y i n g c o n d i t i o n s . F l e i s c h e r ( 1 9 5 3 ) d r i e d v e n e e r s r a n g i n g i n t h i c k n e s s f r o m 0 . 7 9 m m t o 6 . 4 m m a t t e m p e r a t u r e s o f 6 5 . 5 ° C t o 1 7 7 ° C a n d , p a r a l l e l - t o - v e n e e r a i r v e l o c i t i e s o f 1 . 0 2 t o 6 . 1 m / s . H i s c a l c u l a t i o n s s h o w e d t h a t d r y i n g w a s p r o p o r t i o n a l t o t h i c k n e s s r a i s e d t o a p o w e r o f 1 . 3 4 . C o m s t o c k ( 1 9 7 1 ) u s e d v e n e e r t h i c k n e s s e s o f 0 . 9 8 m m t o 4 . 8 m m , d r y i n g t e m p e r a t u r e s f r o m 20 1 4 9 ° C t o 2 6 0 ° C , a n d 9 0 ° i m p i n g i n g a i r v e l o c i t i e s o f 1 6 m / s t o 3 9 m / s i n d e t e r m i n i n g t h a t d r y i n g t i m e w a s p r o p o r t i o n a l t o ( t h i c k n e s s ) 1 1 9 . B a b a i l o v a n d P e t r i ( 1 9 7 4 ) d r i e d 0 . 6 5 m m t o 1 . 9 m m t h i c k v e n e e r s i n a f i u i d i z e d b e d o f s l a g p a r t i c l e s a t t e m p e r a t u r e s o f 1 0 5 ° C t o 2 8 0 ° C . T h e y f o u n d t h a t d r y i n g t i m e w a s l i n e a r l y p r o p o r t i o n a l t o t h i c k n e s s . T h e p r o g r e s s i o n o f t h e e x p o n e n t s o f t h i c k n e s s f r o m 1 . 3 4 t o 1 w i t h i n c r e a s i n g r a t e s o f e x t e r n a l h e a t a n d m a s s t r a n s p o r t s u g g e s t s t h a t , l i k e d e n s i t y , t h e e f f e c t o f t h i c k n e s s o n d r y i n g r a t e i s p r e d o m i n a n t l y o n t h e q u a n t i t y o f w a t e r t h a t m u s t b e r e m o v e d p e r u n i t o f s u r f a c e a r e a . T h e d i m e n s i o n o f t h e l o n g i t u d i n a l p l a n e w a s c o n s i d e r e d i n t h e d e v e l o p m e n t o f t h e -o r e t i c a l p a r t i c l e d r y i n g m o d e l s f o r d r y i n g " c h u n k y " w o o d p a r t i c l e s o f s h a p e 3 t o 5 :2 :1 ( l e n g t h : w i d t h : t h i c k n e s s ) h a v i n g a v e r a g e l e n g t h s o f 1 . 7 5 m m t o 3 . 4 m m ( D o r r i et al., 1 9 8 5 ; M a l t e et ai, 1 9 7 6 ) . M a l t e et al. ( 1 9 7 6 ) p r o p o s e d t h a t d r y i n g c o u l d b e d i v i d e d i n t o t h r e e s t a g e s : h e a t t r a n s f e r c o n t r o l l e d u n t i l a c r i t i c a l m o i s t u r e c o n t e n t w a s r e a c h e d ; m o i s t u r e c o n t e n t i n f l u e n c e d b e t w e e n t h e c r i t i c a l m o i s t u r e c o n t e n t a n d a b o u t 2 0 % m o i s t u r e c o n t e n t ; a n d , d i f f u s i o n c o n t r o l l e d b e l o w 2 0 % m o i s t u r e c o n t e n t . B e l o w t h e c r i t i c a l m o i s t u r e c o n t e n t i t w a s h y p o t h e s i z e d t h a t t h e e n d g r a i n a r e a s p r o b a b l y r e m a i n e d w e t t e d b e c a u s e o f t h e u n h i n d e r e d l o n g i t u d i n a l p a t h f o r i n t e r n a l m o i s t u r e flow. H o w e v e r , t h e i r e q u a t i o n s o n l y u t i l i z e d m o i s t u r e t r a n s p o r t a c r o s s t h e t h i c k n e s s ( o r s m a l l e s t d i m e n s i o n ) o f t h e p a r t i c l e s . D o r r i et al. ( 1 9 8 5 ) u s e d t h e d a t a f r o m t h e w o r k o f M a l t e et al. t o c o m p a r e t h e r e s u l t s o f t h r e e d i f f e r e n t n u m e r i c a l m o d e l s f o r d r y i n g . T h e s e m o d e l s w e r e b a s e d o n a p h y s i c a l m o d e l s i m i l a r t o t h a t d e v e l o p e d b y S t a n i s h et al. ( 1 9 8 6 ) . S i n c e c a p i l l a r y a n d p r e s s u r e - d r i v e flow o f l i q u i d w a t e r , a n d , d i f f u s i o n a n d p r e s s u r e - d r i v e n flow o f w a t e r v a p o u r a r e m u c h f a s t e r i n t h e l o n g i t u d i n a l p h a s e t h a n i n e i t h e r o f t h e t r a n s v e r s e p h a s e s , D o r r i et al. u s e d t h e l o n g i t u d i n a l d i m e n s i o n o f t h e p a r t i c l e i n t h e i r o n e - d i m e n s i o n a l m o d e l s . S t a n i s h a n d K a y i h a n ( 1 9 8 4 ) d r i e d a v a r i e t y o f p a r t i c l e s u n d e r w e l l - c o n t r o l l e d d r y i n g c o n d i t i o n s ( T a b l e 1 .2 ) t o e v a l u a t e t h e i r t w o d i m e n s i o n p a r t i c l e d r y i n g m o d e l . F i g u r e 1.5 s h o w s t h e e x p e r i m e n t a l p a r t i c l e d r y i n g u n i t . T h i s a p p a r a t u s a l l o w e d t h e c h a n g i n g w e i g h t 21 T A B L E 1.2: Experimental Drying Tests (Stanish and Kayihan, 1984). Species Size (mm) Initial M C (% dry basis) Air Temperature (°C) Douglas-fir sawdust 5-7 mesh 175 95 Douglas-fir sawdust 0.5-1.0 mesh 180 95 Douglas-fir sawdust 5-7 mesh 224 200 Douglas-fir sawdust 0.5-1.0 mesh 181 200 Douglas-fir sawdust 0.5-1.0 mesh 116 95 Douglas-fir sawdust 5-7 mesh 146 200 Aspen 0.63 x 18.8 x 25.5 134 95 Cahn Balance A Infared Furnace Air r u Particle Weight Gas Temp. a-IR Sensor I Surface Temp. - D Data Acquisition System I F I G U R E 1.5: Particle drying unit (Stanish and Kayihan, 1984). 22 o f t h e p a r t i c l e s a n d t h e i r s u r f a c e t e m p e r a t u r e , a n d t h e t e m p e r a t u r e o f t h e a i r i m m e d i a t e l y u p s t r e a m o f t h e s a m p l e t o b e c o n t i n u o u s l y m o n i t o r e d a n d a u t o m a t i c a l l y r e c o r d e d a t r e g u l a r i n t e r v a l s . I n m o d e l l i n g t h e d r y i n g o f s a w d u s t , t h e d i m e n s i o n s o f t h e l o n g i t u d i n a l p l a n e a n d o f o n e o f t h e t r a n s v e r s e p l a n e s w e r e a s s u m e d t o b e t h e k e y d i m e n s i o n s . H o w e v e r , o n l y t h e t r a n s v e r s e p l a n e s w e r e u s e d i n t h e t w o - d i m e n s i o n a l m o d e l l i n g o f a s p e n w a f e r d r y i n g . T h e c r o s s - s e c t i o n a l s u r f a c e s o f t h e w a f e r w e r e s e a l e d w i t h e p o x y f o r t h e e x p e r i m e n t a l d r y i n g . T h e a s s u m p t i o n t h a t t h e l o n g i t u d i n a l p l a n e d i d n o t s i g n i f i c a n t l y i n f l u e n c e t h e r a t e o f d r y i n g m a y n o t b e v a l i d f o r w a f e r d r y i n g . S i a u ( 1 9 8 4 a ) l i s t e d a p p r o x i m a t e r a t i o s o f l o n g i t u d i n a l v e r s u s t r a n s v e r s e t r a n s p o r t c o e f f i c i e n t s f o r u n s t e a d y - s t a t e flow i n s o f t w o o d s a s : T h e r m a l C o n d u c t i v i t y DhL/^hT = 2 . 5 H y d r o d y n a m i c ( B u l k ) F l o w DPL/DPX = 1 0 , 0 0 0 o r m o r e M o i s t u r e D i f f u s i o n D G L / D G T = 2 - 4 a t MC = 2 5 % 5 0 - 1 0 0 a t MC = 5 % U s i n g t h e m e t h o d o u t l i n e d b y S i a u t o d e t e r m i n e t h e r e l a t i v e s i g n i f i c a n c e o f d i f f u s i o n i n t h e t r a n s v e r s e a n d l o n g i t u d i n a l p l a n e s a t 9 5 ° C , l o n g i t u d i n a l e f f e c t s m a y o n l y b e n e g l e c t e d a b o v e 1 5 % m o i s t u r e c o n t e n t ( a s s u m i n g a l e n g t h - t o - t h i c k n e s s r a t i o o f a b o u t 2 4 f o r a n a s p e n w a f e r ) . I f c a p i l l a r y flow i s c o n s i d e r e d o r i f t h e d r y i n g t e m p e r a t u r e e x c e e d s 1 0 0 ° C ( a n d t h u s b u l k flow o f w a t e r v a p o u r o c c u r s ) , t h e n l o n g i t u d i n a l e f f e c t s s h o u l d n o t b e n e g l e c t e d , r e g a r d l e s s o f m o i s t u r e c o n t e n t o r l e n g t h o f w a f e r . A l t h o u g h S i a u c a l c u l a t e d t h e a b o v e r a t i o s u s i n g a c o n c e p t u a l m o d e l o f flow t h r o u g h a s o f t w o o d , t h e i m p o r t a n c e o f t h e l o n g i t u d i n a l p l a n e i n d r y i n g p a r t i c l e s a n d w a f e r s o f h a r d w o o d s h o u l d b e s i m i l a r t o o r g r e a t e r t h a n t h a t d e m o n s t r a t e d f o r s o f t w o o d s . T h e v e s s e l s i n h a r d w o o d s ( a n d e s p e c i a l l y i n d i f f u s e p o r o u s s p e c i e s ) p r o v i d e a n e x c e l l e n t p a t h w a y f o r t h e b u l k flow o f l i q u i d w a t e r , a n d f o r b u l k flow a n d d i f f u s i o n o f w a t e r v a p o u r . P e t t y ( 1 9 8 1 ) s h o w e d t h a t t h i s v e s s e l p a t h w a y c a n b e c o n t i n u o u s f o r u p t o 1 5 0 m m i n s y c a m o r e w o o d . F u r t h e r m o r e , P r a k ( 1 9 7 0 ) c o n c l u d e d t h a t e v e n t r a n s v e r s e p a t h w a y s t h r o u g h Y e l l o w - p o p l a r w e r e i n e f f e c t l o n g i t u d i n a l p a t h s b e c a u s e o f t h e t r a n s v e r s e c r o s s - o v e r p o i n t s w h i c h h a v e t h e l o w e s t r e s i s t a n c e t o flow. 2 3 1.1.4 Aspen Wafer Drying Anatomical Considerations W a f e r b o a r d i s m o s t c o m m o n l y m a n u f a c t u r e d f r o m P o p u l u s s p e c i e s ( B a l s a m P o p l a r , T r e m -b l i n g A s p e n , a n d B i g t o o t h A s p e n ) w a f e r s . T h e s e w a f e r s a r e c u t s o t h a t t h e l o n g i t u d i n a l p l a n e i s t h e l a r g e s t d i m e n s i o n r a n g i n g f r o m 2 5 m m i n o l d e r p r o c e s s e s t o 1 0 2 m m i n s t a t e -o f - t h e - a r t m a n u f a c t u r i n g p l a n t s . T h e g r a i n o r i e n t a t i o n o f a w a f e r ' s w i d t h a n d t h i c k n e s s m a y b e e i t h e r t a n g e n t i a l o r r a d i a l , o r a c o m b i n a t i o n o f b o t h . T h e w a f e r w i d t h i s t y p i c a l l y | t o | o f i t s l e n g t h , w h i l e t h e w a f e r t h i c k n e s s i s u s u a l l y 0 . 6 3 m m . F i g u r e 1 .6 i s a m a g n i -f i c a t i o n o f t h e m i n u t e a n a t o m y o f B i g t o o t h A s p e n . T h e l a r g e p o r e s o r v e s s e l s , a r e a b o u t 4 0 t o 6 0 m i c r o n s i n d i a m e t e r a n d m a y b e c o n s i d e r e d c o n t i n u o u s i n t h e l o n g i t u d i n a l p l a n e o f w a f e r s . B a s e d o n F i g u r e 1 . 6 ( a ) , t h e c r o s s - s e c t i o n o f a 0 . 6 3 m m x 5 0 m m w a f e r w o u l d c o n t a i n r o u g h l y 3 2 0 0 v e s s e l s w h i c h w o u l d a c c o u n t f o r 2 0 - 3 0 % o f t h e w a f e r ' s v o l u m e . B o t h t h e v e s s e l s a n d t h e f i b r e c e l l s ( t h e s m a l l e r p o r e s w i t h t a p e r e d e n d s ) a r e i n t e r c o n n e c t e d b y s t r u c t u r e s c a l l e d p i t s ( F i g u r e 1 . 7 ) . A m e m b r a n e o f r a n d o m l y o r i e n t e d c e l l u l o s e m i c r o f i b -r i l s a c r o s s t h e p i t s t r u c t u r e s e p a r a t e s a d j o i n i n g c e l l s . S i a u ( 1 9 8 4 b ) h y p o t h e s i z e d t h a t t h e o b s e r v e d flow o f fluids t h r o u g h t h e p i t m e m b r a n e p r o g r e s s e d v i a a t o r t u o u s p a t h t h r o u g h t h e m i c r o f i b r i l s o f t h e p i t m e m b r a n e . P o p u l u s s p e c i e s w o o d m a y v a r y g r e a t l y i n p e r m e a b i l i t y d e p e n d i n g o n t h e p r e s e n c e o f t y l o s e s i n t h e h e a r t w o o d v e s s e l s , t h e e n c r u s t a t i o n o f t h e h e a r t w o o d p i t m e m b r a n e s w i t h e x t r a c t i v e s a n d t h e o c c u r r e n c e o f w e t w o o d ( W a r d , 1 9 8 6 ; P e r n g et ai, 1 9 8 5 ) . P e r n g et al. r e p o r t e d t h e l o n g i t u d i n a l g a s p e r m e a b i l i t y o f a s p e n h e a r t w o o d t o b e a p p r o x i m a t e l y 7 % t h a t o f t h e s a p w o o d , w h i l e W a r d o b t a i n e d v a l u e s o f 0 . 7 t o 1 . 3 % . I n v i e w o f t h e r e l a t i v e r a t e o f l o n g i t u d i n a l t o t r a n s v e r s e t r a n s p o r t c o e f f i c i e n t s , t h e d i f f e r e n c e i n l o n g i t u d i n a l g a s p e r m e a b i l i t y b e t w e e n s a p w o o d a n d h e a r t w o o d i s u n i m p o r t a n t i n w a f e r d r y i n g . 2 4 x— 75 x t—75X (a) (b) F I G U R E 1.6: Minute anatomy of Bigtooth Aspen. (Populus grandidentala). (a) cross-section; (b) tangential (Panshin and DeZeeuw, 1980) 25 F I G U R E 1.7: Cross-sectional view of intervessel pitting in northern red oak showing the layers of the cell wall. Electron micrograph by W.A. Cote, Jr. (Siau, 1984a). 26 Drying Rate (%/min) or Temperature (°C) Moisture Content (% dry basis) F I G U R E 1.8: Drying comparison for aspen flake at 95°C (Test No. 7) (Stanish and Kayi-han, 1984). Experimental Wafer Dry ing The only reported results of wafer drying were in a study by Stanish and Kayihan (1984). Using the drying apparatus shown in Figure 1.5, they dried an aspen wafer at 95°C and at an air velocity of 0.14 m/s (parallel to the longitudinal plane of the 0.63 mm X 18.8 mm X 25.5 mm wafer). The cross-sectional surfaces were sealed with epoxy so that the ex-perimental results could be compared using their two-dimensional model. The drying rate curve and the surface temperature curve for the aspen wafer are given in Figure 1.8. The drying behaviour of the aspen wafer can be described using these two curves. As a result of the mild drying conditions, the wafer dried from 134% moisture content to about 80% moisture content before reaching the maximum drying rate. The drying rate 27 during this period would be controlled by external heat and mass transfer. The period of drying from 80% MC to about 30% MC showed a steady parabolic decrease in drying rate and a slow rise in wafer surface temperature. This would correspond to a period of decreased wetted surface area drying, the first section of the falling rate period described in Section 1.1.3. The final period of drying from 30% to 0% MC was controlled by internal heat transfer and bound water diffusion. Since all liquid water had been removed from the wafer surface, its temperature rose rapidly to the dry bulb temperature. A Conceptual Model of Aspen Wafer Drying The drying of aspen wafers at temperatures below 100°C or under conditions of low heat and mass transfer would be expected to follow a drying rate curve similar to Figure 1.8. However, -it is expected that a constant rate period and a higher maximum drying rate would have occurred had the end grain not been sealed by epoxy. Free water moves by capillary flow primarily to the wafer surfaces where its evaporation rate is limited by the external rates of heat and mass transfer. As the capillary system weakens, the flow of free water to the surface and thus the wetted surface area of the wafer decreases. External heat and mass transfer still limit the drying rate of the wetted sections. However, with the development of a drying front below the unsaturated areas, drying in these regions becomes limited by the diffusion of water vapour from the front to the surface. The resultant drying rate curve would show a smooth transition from the constant rate period to a parabolically decreasing drying rate. Eventually, all free water has been evaporated, and the drying rate is limited by diffusion of bound water through the wood substance to the nearest air/wood substance interface (e.g. lumens or vessels). There are no sharp transitions from one drying period to the next in wafer drying because of the multiple drying zones in a drying wafer at any time after the constant rate period. If the temperature and air velocity are increased so that external heat and mass transfer 28 rates are no longer limiting, the flow of water to the wafer surface is less than the evapora-tion rate and a drying front would be formed. If the wafer temperature stays below 100°C, then the remainder of the drying curve would follow the same trends outlined above, only at a higher overall drying rate. However, if the wafer temperature rises above 100°C the rate of bound water vaporization into the pore structure of the wood is no longer limited by the bound water/water vapour equilibrium relationships. Furthermore, water vapour may now exit the wood by bulk flow as well as by diffusion. Since a much faster pathway for moisture movement exists at wood temperatures above 100°C than below 100°C, the internal rate of heat transfer becomes the limiting drying mechanism. The drying rate curve at high temperatures would reflect this change in mechanisms by being closer to linear than parabolic. 29 1.2 Methods and Materials — Fundamentals of Wafer Dry-ing 1.2.1 Introduction This series of experiments was undertaken to gain basic understanding of wafer drying behaviour to supplement the knowledge obtained from the literature. Drying temperature and wafer length were selected as parameters for this work because of their effects on drying behaviour as inferred by the examination of veneer and particle drying in Section 1.1.3. Drying temperatures straddled the boiling point of water (90°C, 120°C and 150°C), and wafer lengths ranged from 25 mm to 63 mm. The use of aspen wood in this investigation reflects its importance in the waferboard industry. 1.2.2 Aspen Wafer Production Freshly cut, debarked aspen logs bucked into 0.86 m lengths were obtained from MacMillan Bloedel's waferboard plant in Hudson Bay, Saskatchewan. The logs were soaked in water, placed in plastic bags and stored at 2°C until needed. Prior to cutting the wafers or "waferizing", three logs were randomly selected and cut into 0.15 m lengths. After discarding the end pieces, the remaining sections were waferized using a pilot plant scale C A E waferizer at C A E Manufacturing, Vancouver. The waferizer was set to cut wafers having a nominal length and thickness of 89 mm and 0.63 mm respectively. The three large plastic bags of wafers produced were then stored at 2°C. Aspen wafers of three different lengths and of equal widths were required for the drying experiments. Since the wafers varied considerably in size and shape a guillotine cutter was used to produce uniform rectangular wafers 25 mm, 44 mm and 63 mm in length and 32 mm in width. The cut wafers were then weighted down in a large beaker of distilled water and saturated in a vacuum oven by drawing a full vacuum for 30 minutes followed by a gradual reintroduction of air into the oven. Al l wafers remained submerged after removing the 30 weights from the beaker. Wafers were subsequently stored at 2°C for a minimum of 72 hours before use in the drying tests. 1.2.3 A s p e n Wafer Properties The bulk density of the green wafers (prior to saturation) was measured by sprinkling the wafers into a 0.29 m x 0.29 m X 0.20 m preweighed box and then weighing the filled box. This procedure was repeated ten times. The green wafer bulk density was determined as 125 kg/m3 (coefficient of variation (CV) of 0.1051). An average green moisture content of the wafers was also determined by weighing 25 wafers randomly selected from the three bags. Each green wafer was placed in a preweighed glass bottle and weighed to four decimal places. The wafer and bottle were placed in an oven at 105°C for 24 hours, following which they were removed to a desiccator, cooled to room temperature and reweighed. An average moisture content of 87.7% was calculated with a CV. of 0.238. Based on the wide range of green wafer moisture contents (43.6% to 151.3%) it was decided to saturate all wafers prior to drying. The maximum moisture content normally found in freshly cut aspen is 125%. By saturating the green wafers to a moisture content greater than 200%, the drying data recorded during the set-up of the equipment and while bringing the oven up to the drying temperature could be discarded without losing infor-mation about wafer drying below 125% moisture content. This procedure also simplified the analysis of the data since then all wafers had been dried from 125% to 0% moisture content, eliminating initial moisture content as a variable. Comstock (1971) showed that veneers having different initial moisture contents followed the same drying rate curve. It was assumed that this behaviour also applies in aspen wafer drying. Wafer thickness and green volume (for calculating green density) were measured for each wafer used in the drying chamber. Prior to every run the saturated wafer was shaken 31 s e v e r a l t i m e s t o r e m o v e e x c e s s s u r f a c e w a t e r . T h e w a f e r w a s t h e n c l i p p e d o n t o a w i r e r o d b y t h e v e r y t i p o f o n e o f i t s c o r n e r s . T h e r o d a n d w a f e r w e r e l o w e r e d i n t o a t a r e d b e a k e r o f d i s t i l l e d w a t e r , s o t h a t t h e w a f e r w a s e n t i r e l y i m m e r s e d j u s t b e l o w t h e s u r f a c e o f t h e w a t e r . T h e a p p a r a t u s u s e d i s s h o w n i n F i g u r e 1 .9 . S u s p e n d i n g t h e w a f e r i n t h e w a t e r i s e q u i v a l e n t t o a d d i n g a q u a n t i t y o f w a t e r t o t h e b e a k e r h a v i n g t h e s a m e v o l u m e a s t h e w a f e r . S i n c e t h e d e n s i t y o f w a t e r a t r o o m t e m p e r a t u r e i s 1 0 0 0 k g / m 3 , t h e n e w r e a d i n g o n t h e t o p l o a d i n g b a l a n c e c o u l d t h e n b e c o n v e r t e d t o t h e v o l u m e o f t h e g r e e n w a f e r (i.e. 0 . 7 g « 0 . 7 c m 3 ) . T h i s p r o c e d u r e w a s t h e n r e p e a t e d , t h e a v e r a g e o f t h e t w o v a l u e s b e i n g r e c o r d e d a s t h e g r e e n v o l u m e f o r t h a t w a f e r . T h e g r e e n d e n s i t y f o r e a c h w a f e r w a s c a l c u l a t e d u s i n g t h e o v e n d r y m a s s o f t h e w a f e r ( t h e f i n a l r e c o r d e d m a s s f r o m e a c h w a f e r d r y i n g t e s t ) a n d t h e g r e e n v o l u m e . W a f e r t h i c k n e s s w a s m e a s u r e d i m m e d i a t e l y a f t e r t h e r e m o v a l o f t h e w a f e r f r o m t h e d r y i n g c h a m b e r . U s i n g a m i c r o m e t e r a c c u r a t e t o 0 . 0 0 2 5 4 m m , t h r e e m e a s u r e m e n t s w e r e t a k e n a n d a v e r a g e d t o o b t a i n t h e o v e n d r y w a f e r t h i c k n e s s . S i n c e w a f e r s a r e o f t e n s l i g h t l y w e d g e s h a p e d a c r o s s t h e i r w i d t h , t h e t h r e e p o i n t s o f m e a s u r e m e n t f o r m e d a d i a g o n a l a c r o s s t h e w a f e r ( t w o o p p o s i n g c o r n e r s a n d a c e n t r e p o i n t ) . 1.2.4 Drying Apparatus for Single Wafer Tests T h e d r y i n g a p p a r a t u s f o r t h e s i n g l e w a f e r t e s t s w a s a s s e m b l e d s o t h a t i n d i v i d u a l w a f e r s c o u l d b e d r i e d i n a n a i r s t r e a m h a v i n g c o n s t a n t t e m p e r a t u r e , h u m i d i t y , a n d d i r e c t i o n o f f l o w w h i l e c o n t i n u o u s l y m o n i t o r i n g w e i g h t l o s s . A l t h o u g h b u d g e t c o n s t r a i n t s d i d n o t a l l o w t h e c o n s t r u c t i o n o f a s y s t e m a s e l e g a n t o r p r e c i s e a s t h a t o f S t a n i s h a n d K a y i h a n ( 1 9 8 4 ) ( s h o w n i n F i g u r e 1 . 5 ) , t h e i n i t i a l t e s t r u n s s h o w e d t h a t t h e d r y i n g a p p a r a t u s d e v e l o p e d w a s s u f f i c i e n t l y a c c u r a t e a n d p r e c i s e f o r t h e d r y i n g e x p e r i m e n t s . A F i s h e r E c o n o t e m p f o r c e d c o n v e c t i o n o v e n w a s m o d i f i e d t o p r o v i d e a u n i d i r e c t i o n a l f l o w o f a i r p a s t t h e s u s p e n d e d w a f e r . T h e f l o o r o f t h e o v e n w a s c o n s t r u c t e d s o t h a t h e a t e d 3 2 to to (a) (b) F I G U R E 1.9: Saturated wafer volume measurement apparatus, (a) prior to measurement; (b) during measurement. air was blown upward along the four walls while cooled air was drawn into the heated plenum chamber through a set of holes in the centre. To reinforce this circulation pattern, two 0.15 m high by 0.15 m diameter Q V C glass pipe sections were stacked over the centre holes. Since a wafer suspended in this centre section still showed considerable circular motion, a 0.51 m X 0.31 m baffle was placed along one of the oven side walls to eliminate any swirling air flow. Figure 1.10 shows the positioning of the glass pipe and baffle in the convection oven. The wafer to be dried was attached to a 76 mm long, 1.59 mm diameter wire rod by a small alligator clip (Figure 1.11). This assembly was hooked to a 0.31 m wire suspension rod that ran through the exhaust vent at the top of the oven and the table 0.1 m above the oven to the bottom weighing hook of a Mettler electronic balance (accurate to 0.0001 g). The balance was positioned so that the wafer was centred in the glass pipe sections. To counteract the weight of the suspension rod, two aluminum weights were placed on the pan of the balance and the balance tared to zero each time the equipment was started up. A n I B M - A T computer was used to record every 1 mg weight change during drying. A diagrammatic representation of the drying apparatus is shown in Figure 1.12. The temperature of the circulating air was monitored by a Type K thermocouple po-sitioned 12.7 mm from the leading edge of the wafer (Figure 1.11). This temperature was maintained at the desired level ( ± 2 ° C ) by adjusting the thermostatic control of the oven. The velocity profile across the 0.15 m glass pipe was measured using a Kurz series 440 constant temperature thermal anemometer. To obtain this measurement, the two 0.15 m high sections of glass pipe were replaced by a single 0.31 m length of 0.15 m ABS pipe with a 6.3 mm swagelock tube fitting positioned so that the anemometer probe could be inserted at the height corresponding to the leading edge of the suspended wafer. To accommodate the insertion of the probe, the oven door was replaced by a waferboard panel which effectively sealed the oven. The probe thus passed through the waferboard panel and 34 F I G U R E 1 . 1 0 : Positioning of glass pipe and baffle in convection oven. 35 F I G U R E 1.11: Attachment of wafer to wire rod suspended from the Mettler Electronic balance. Type K thermocouple positioned 12.7 mm from the water monitored drying temperature. 36 TO COMPUTER FORCED CONVECTION OVEN 6 LASS PIPE--JJL 4-I 1 ELECTRONIC ' BALANCE WIRE -SUSPENSION ROD -WOOD WAFER F I G U R E 1 . 1 2 : Experimental equipment used for the controlled drying of single wafers air (showing the circulation of air in the oven). 37 T A B L E 1 . 3 : V e l o c i t y P r o f i l e M e a s u r e m e n t s f o r t h e S i n g l e W a f e r D r y i n g A p p a r a t u s . P o s i t i o n o f M e a s u r e m e n t V e l o c i t y A v e r a g e ( f p m ) ( m / s ) C e n t r e o f p i p e 5 5 - 6 5 0 . 3 0 5 4 1 m m f r o m c e n t e r 4 5 - 5 5 0 . 2 5 4 5 3 m m f r o m c e n t r e 4 5 - 5 0 0 . 2 4 3 6 4 m m f r o m c e n t r e 4 0 - 4 5 0 . 2 1 6 7 0 m m f r o m c e n t r e 4 0 - 4 5 0 . 2 1 6 A v e r a g e v e l o c i t y o f a i r s t r e a m • 4 8 . 5 0 . 2 4 7 t h e A B S p i p e v i a t h e s w a g e l o c k f i t t i n g . T h e m e a s u r e m e n t p a t t e r n a c r o s s t h e p i p e d i v i d e d t h e c r o s s - s e c t i o n i n t o e q u a l a r e a a n n u l i f o r a n 8 p o i n t t r a v e r s e . H o w e v e r , t h e l e n g t h o f t h e p r o b e l i m i t e d t h e m e a s u r e m e n t s t o o n l y h a l f t h e c r o s s - s e c t i o n . T a b l e 1 .3 p r e s e n t s t h e r e s u l t s o f t h e v e l o c i t y p r o f i l e m e a s u r e m e n t s . V e l o c i t y fluctuated c o n s i d e r a b l y w i t h i n t h e r a n g e s g i v e n f o r e a c h p o s i t i o n o f m e a s u r e -m e n t . T h e m e a s u r e d v e l o c i t y p r o f i l e w a s p l o t t e d a n d c o m p a r e d w i t h t h e f u l l y d e v e l o p e d l a m i n a r flow p r o f i l e : ( 1 . 1 0 ) w h e r e Vz i s t h e v e l o c i t y i n t h e a x i a l d i r e c t i o n Vmax i s t h e m e a s u r e d m a x i m u m v e l o c i t y ( a t t h e p i p e c e n t r e ) r i s t h e r a d i a l d i s t a n c e f r o m t h e c e n t r e o f t h e p i p e R i s t h e r a d i u s o f t h e p i p e T h e m a x i m u m v e l o c i t y w a s t a k e n a s 0 . 3 0 5 m / s . T h e t w o v e l o c i t y p r o f i l e s a r e p r e s e n t e d i n F i g u r e 1 . 1 3 . T h e flatter m e a s u r e d v e l o c i t y p r o f i l e w a s e x p e c t e d s i n c e t h e s h o r t l e n g t h o f p i p e a h e a d o f t h e p o i n t s o f m e a s u r e m e n t w a s n o t l o n g e n o u g h t o d e v e l o p a f u l l y d e v e l o p e d p a r a b o l i c v e l o c i t y p r o f i l e . F o r Re = 1 3 1 4 w i t h t h e o v e n a t 1 5 0 ° C , i t w a s c a l c u l a t e d t h a t a r u n o f 7 . 0 m o f 0 . 1 5 m p i p e w o u l d b e r e q u i r e d b e f o r e a fully d e v e l o p e d l a m i n a r v e l o c i t y 3 8 0.40 0.35 0.30 CO ^ 0 . 2 5 >-tz O 0.20 _ l Ld > c r 0.15 < 0.10 0.05 -0.00 i—1—r — r i — 1 — i — r • MEASURED VELOCITY PROFILE - - CALCULATED FULLY DEVELOPED LAMINAR VELOCITY PROFILE I • I J i L J L 0 10 20 30 40 50 60 70 80 RADIAL DISTANCE FROM THE CENTRE OF THE PIPE (mm) F I G U R E 1.13: Comparison of the measured velocity profile for the central section of the drying apparatus and the calculated fully developed laminar velocity profile. 39 T A B L E 1.4: Effect of Velocity Profile on Relative Magnitudes of External Heat Transfer Coefficients. Wafer Size (mm) V Distance from Centre (mm) Measured Velocity (m/s) y r0.5 (oc hr) Percent Difference* {%) 25 13 0.29 0.54 3.84 44 22 0.28 0.53 1.92 63 32 0.27 0.52 * based on a wafer size of 63.5 mm profile would be obtained (Bird et ai, 1960). To ensure that the velocity profile did not confound the results of the drying experi-ments by causing a significant gradient in external heat or mass transfer across the wafer dimension perpendicular to the direction of air flow, the relative magnitudes of the ex-ternal heat transfer coefficients for different wafer dimensions were examined. Using the measured velocity profile in Figure 1.13 and the relation, hr<xVr0-5 (1.11) where hr is the average external heat transfer coefficient at a distance V from the centre of the pipe Vr is the average velocity at a distance 'r' from the centre of the pipe the relative differences between external heat transfer coefficients for wafers having dimen-sions of 25 mm, 44 mm and 63 mm perpendicular to the air flow were calculated. Table 1.4 shows that within the range of wafer sizes used, the velocity profile had only a slight effect on the magnitude of the external heat transfer coefficient. 40 1.2.5 Procedure for Single Wafer Dry ing Experiments P r i o r t o a s e r i e s o f d r y i n g r u n s , t h e s a t u r a t e d w a f e r s t o b e u s e d w e r e r e m o v e d f r o m c o l d s t o r a g e a n d w a r m e d t o r o o m t e m p e r a t u r e b y p l a c i n g t h e m i n a b e a k e r o f d i s t i l l e d w a t e r . T h e c o n v e c t i o n o v e n ( w i t h b a f f l e , g l a s s p i p e a n d w i r e s u s p e n s i o n r o d a l r e a d y i n p o s i t i o n ) w a s t u r n e d o n a n d a l l o w e d t o r e a c h t h e d e s i r e d d r y i n g t e m p e r a t u r e . O n c e t h e r e a d o u t o n t h e e l e c t r o n i c b a l a n c e h a d s t a b i l i z e d , t h e b a l a n c e w a s t a r e d t o z e r o . T h e o v e n w a s n e x t o p e n e d a n d t h e w a f e r a t t a c h m e n t r o d w a s h o o k e d o n t o t h e s u s p e n s i o n r o d . T h e o v e n w a s c l o s e d a n d a l l o w e d t o r e a c h t h e d r y i n g t e m p e r a t u r e a g a i n . T h e w e i g h t o f t h e w a f e r a t t a c h m e n t r o d r e a d f r o m t h e b a l a n c e w a s e n t e r e d i n t o t h e c o m p u t e r t o b e s u b t r a c t e d f r o m e v e r y r e c o r d e d w e i g h t d u r i n g t h e d r y i n g r u n . T h e d r y i n g a p p a r a t u s w a s n o w r e a d y t o s t a r t t h e d r y i n g t e s t s . T h e h u m i d i t y o f t h e a m b i e n t a i r w a s m e a s u r e d a t t h e s t a r t o f e a c h s e r i e s o f d r y i n g r u n s u s i n g a s l i n g p s y c h r o m e t e r . B e f o r e e a c h r u n , t h e s a t u r a t e d v o l u m e o f t h e s e l e c t e d w a f e r w a s m e a s u r e d . T h e o v e n w a s t u r n e d t o i t s h i g h e s t t e m p e r a t u r e s e t t i n g a n d t h e w a f e r ( s h a k e n o n c e a g a i n t o r e m o v e e x c e s s s u r f a c e w a t e r ) w a s c l i p p e d o n t o t h e w a f e r a t t a c h m e n t r o d . T h e o v e n d o o r w a s q u i c k l y c l o s e d a n d t h e c o m p u t e r d a t a l o g g i n g s t a r t e d i m m e d i a t e l y . C o n c u r r e n t l y , t h e t i m e f r o m s h u t t i n g t h e o v e n d o o r t o r e a c h i n g t h e d r y i n g t e m p e r a t u r e w a s m e a s u r e d b y s t o p w a t c h . U p o n r e a c h i n g t h e d r y i n g t e m p e r a t u r e , t h e o v e n w a s t u r n e d d o w n t o t h e p r e d e t e r m i n e d s e t t i n g f o r t h a t d r y i n g t e m p e r a t u r e a n d t h e e l a p s e d t i m e r e c o r d e d . D r y i n g c o n t i n u e d u n t i l t h e r e w a s l e s s t h a n a 1 m g w e i g h t c h a n g e i n 5 m i n u t e s . T h e w a f e r w a s t h e n r e m o v e d , m e a s u r e d f o r t h i c k n e s s , a n d n u m b e r e d . 1.2.6 Calculat ion of Dry ing Times and Dry ing Rates E a c h d r y i n g r u n p r o d u c e d a d a t a f i l e o f b e t w e e n 3 0 0 a n d 9 0 0 r e c o r d s ( d e p e n d i n g o n d r y i n g t e m p e r a t u r e a n d w a f e r l e n g t h ) . E a c h r e c o r d c o n s i s t e d o f a w a f e r w e i g h t o b t a i n e d f r o m t h e b a l a n c e a n d t h e t i m e o n t h e c o m p u t e r ' s i n t e r n a l c l o c k a t w h i c h t h e w e i g h t w a s r e c o r d e d . 41 T h e d a t a f i l e s f o r a s e t o f r u n s w e r e d o w n l o a d e d t o a m a i n f r a m e c o m p u t e r f o r a n a l y s i s . T h e w a f e r i d e n t i f i c a t i o n n u m b e r , w a f e r t h i c k n e s s , w a f e r l e n g t h , s a t u r a t e d v o l u m e , d r y i n g t e m p e r a t u r e a n d t i m e r e q u i r e d b y t h e o v e n t o r e a c h t h e d r y i n g t e m p e r a t u r e a t t h e s t a r t o f e a c h r u n w e r e a l s o e n t e r e d i n t h e m a i n f r a m e c o m p u t e r a s s e p a r a t e f i l e s f o r e a c h w a f e r . U s i n g t h e t w o c o r r e s p o n d i n g f i l e s f o r a s i n g l e w a f e r , g r e e n d e n s i t y , s a t u r a t e d m o i s t u r e c o n t e n t a n d d r y i n g t i m e s f r o m 1 2 5 % t o 3 % m o i s t u r e c o n t e n t a n d f r o m 3 0 % t o 3 % m o i s t u r e c o n t e n t w e r e c a l c u l a t e d . T h e d r y i n g r a t e s o f t h e w a f e r w e r e a l s o d e t e r m i n e d f o r e v e r y 5 % c h a n g e i n m o i s t u r e c o n t e n t . A l i n e a r r e g r e s s i o n o f t h e d a t a p o i n t s i n c l u d e d i n e a c h i n t e r v a l o f m o i s t u r e c o n t e n t ( u s u a l l y 1 0 t o 2 0 p o i n t s ) g a v e a n e s t i m a t e o f t h e s l o p e o f t h e d r y i n g c u r v e a n d t h u s o f t h e d r y i n g r a t e f o r t h e m i d p o i n t m o i s t u r e c o n t e n t o f t h e i n t e r v a l . T h e r e s u l t i n g d r y i n g r a t e v s . m o i s t u r e c o n t e n t c u r v e s h o w e d d i s t i n c t t r e n d s b u t a l s o e x h i b i t e d a n u n u s u a l l y l a r g e v a r i a t i o n , g i v e n t h e u n i f o r m i t y o f t h e r a w d a t a . F i g u r e 1 . 1 4 i s a t y p i c a l g r a p h o f t h e r a w d a t a , a n d F i g u r e 1 . 1 5 i s t h e c o r r e s p o n d i n g d r y i n g r a t e v s . m o i s t u r e c o n t e n t c u r v e c a l c u l a t e d u s i n g a s e r i e s o f l i n e a r r e g r e s s i o n s . B e f o r e c o m p a r i n g t h e d r y i n g r a t e s b e t w e e n w a f e r s , i t w a s n e c e s s a r y t o e s t a b l i s h w h e t h e r t h e o b s e r v e d v a r i a t i o n s w e r e a r t i f a c t s o f t h e m e t h o d u s e d a n d , i f s o , t o a n a l y z e t h e d a t a u s i n g a n i m p r o v e d t e c h n i q u e . I d e a l l y , t h e w a f e r d r y i n g c u r v e w o u l d b e c h a r a c t e r i z e d b y a n e q u a t i o n w h i c h c o u l d t h e n b e d i f f e r e n t i a t e d t o d e t e r m i n e t h e d r y i n g r a t e c u r v e . T h i s m e t h o d w o u l d h a v e t h e a d d e d b e n e f i t o f r e d u c i n g t h e c u m b e r s o m e d a t a f i l e t o a s i n g l e e q u a t i o n . H o w e v e r , a s d i s c u s s e d i n S e c t i o n 1 . 1 . 3 , t h e e q u a t i o n m u s t f i t t h e d a t a v e r y w e l l o r t h e r e s u l t i n g d r y i n g r a t e c u r v e w o u l d n o t b e a c c u r a t e . A s e t o f n i n e d a t a f i l e s r e p r e s e n t i n g e a c h c o m b i n a t i o n o f w a f e r l e n g t h a n d d r y i n g t e m p e r a t u r e w a s u s e d t o d e t e r m i n e t h e b e s t f i t t i n g f o r m o f e q u a t i o n . A 5 t h o r d e r p o l y n o m i a l o f t h e f o r m y = a + b\x + b^x2 + 6 3 1 3 + 64X 4 + 6 5 1 5 fit a l l n i n e d a t a files t o a n r 2 > 0 . 9 9 9 0 . T h e d r y i n g r a t e c u r v e s c a l c u l a t e d f r o m t h e s e e q u a t i o n s w e r e s m o o t h c u r v e s h a v i n g t h e s a m e b a s i c s h a p e a s t h e d r y i n g r a t e c u r v e s c a l c u l a t e d b y t h e 42 6.0 7.5 9.0 TIME (minutes) 15.0 F I G U R E 1.14: Drying curve of a 63 mm wafer dried at 90°C showing every 10th data point. 43 1.0 (0 » E LU I— < O 0.6 0.4 >-or Q 0.2 i i i ©•••< 0©Oo° ° oo 0.0 • 1 L J i L 0 40 80 120 160 200 240 PERCENT MOISTURE CONTENT F I G U R E 1.15: Drying rates for the drying curve data of Figure 1.14 determined by the calculation of a series of slopes of the drying curve by linear regression. 44 s e r i e s o f l i n e a r r e g r e s s i o n s . F i g u r e 1 . 1 6 p r e s e n t s t h e 5 t h o r d e r p o l y n o m i a l fit o f t h e d a t a i n F i g u r e 1 . 1 4 . T o c h e c k t h e a c c u r a c y o f t h e d r y i n g r a t e s c a l c u l a t e d f r o m t h e 5 t h o r d e r p o l y n o m i a l s , t h e s a m e s e t o f d a t a files w a s a n a l y z e d u s i n g a g r a p h i c a l t e c h n i q u e . T h e d a t a f r o m e a c h f i l e w e r e p l o t t e d a n d e a c h p l o t w a s e n l a r g e d t o fill a 0 . 2 8 m x 0 . 4 3 m s h e e t . A c u r v e t h a t a p p e a r e d t o f i t t h e d a t a b e s t w a s t h e n d r a w n t h r o u g h t h e d a t a p o i n t s . H o r i z o n t a l l i n e s w e r e d r a w n t o i n t e r s e c t t h e c u r v e a t t h e v a l u e s o f m o i s t u r e c o n t e n t w h e r e a d r y i n g r a t e w a s t o b e c a l c u l a t e d . F i n a l l y , a 6 . 2 m m h i g h l y p o l i s h e d r a z o r b l a d e w a s u s e d t o d e t e r m i n e t h e l i n e p e r p e n d i c u l a r t o t h e c u r v e a t e a c h i n t e r s e c t i o n p o i n t . T h e p e r p e n d i c u l a r w a s l o c a t e d b y a l i g n i n g t h e c u r v e o n t h e f a r s i d e o f t h e b l a d e w i t h t h e r e f l e c t i o n o f t h e c u r v e o n t h e n e a r s i d e o f t h e b l a d e s o t h a t t h e c u r v e a p p e a r e d c o n t i n u o u s . F i g u r e 1 . 1 7 s h o w s t h e d a t a f r o m F i g u r e 1 . 1 4 p r e p a r e d f o r m e a s u r e m e n t . D r y i n g r a t e s w e r e c a l c u l a t e d f r o m t h e c o t a n g e n t o f t h e a n g l e f o r m e d b y t h e i n t e r s e c t i o n o f t h e h o r i z o n t a l l i n e s a n d t h e l i n e s d r a w n p e r p e n d i c u l a r t o t h e d r y i n g c u r v e . T a b l e 1 .5 a n d F i g u r e 1 . 1 8 c o m p a r e t h e d r y i n g r a t e s c a l c u l a t e d f r o m t h e d a t a o f F i g -u r e 1 . 1 4 u s i n g t h e m a n u a l a n d t h e p o l y n o m i a l f i t m e t h o d s . T h e p e r c e n t d i f f e r e n c e s b e -t w e e n t h e d r y i n g r a t e s ( b a s e d o n t h e m a n u a l m e t h o d v a l u e s ) r a n g e d i n a b s o l u t e v a l u e f r o m 0 . 2 1 2 % t o 1 2 . 6 1 % a n d a v e r a g e d 3 . 5 0 % . I t c o u l d b e a r g u e d t h a t t h e p o l y n o m i a l fit m e t h o d w a s i n c a p a b l e o f f i t t i n g t h e s t r a i g h t l i n e p o r t i o n o f t h e d r y i n g c u r v e a s s h o w n i n F i g u r e 1 . 1 7 . H o w e v e r , c o n s i d e r i n g t h a t t h e s t r a i g h t l i n e w a s d r a w n t h r o u g h t h e o s c i l l a t i o n s i n t h e d r y i n g c u r v e , t h a t t h e t w o m e t h o d s d i f f e r e d i n t h i s r e g i o n b y o n l y 2 . 2 3 % , a n d m o s t i m p o r t a n t l y t h a t f r e s h l y c u t a s p e n w a f e r s r a r e l y e x c e e d 1 2 0 % m o i s t u r e c o n t e n t , t h e t w o m e t h o d s w e r e d e e m e d t o b e o f e q u a l a c c u r a c y . I n t h e n i n e d a t a s e t s a n a l y z e d b y t h e t w o m e t h o d s n o n e o f t h e d r y i n g c u r v e s h a d a s t r a i g h t l i n e s e c t i o n b e l o w 1 2 0 ° C m o i s t u r e c o n t e n t . B e l o w 1 2 0 % t h e a v e r a g e p e r c e n t d i f f e r -e n c e b e t w e e n t h e t w o m e t h o d s f o r a l l n i n e d a t a s e t s w a s 4 . 1 8 % a n d r a n g e d f r o m 2 . 0 5 % t o 4 5 0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 TIME (mlnufes) F I G U R E 1.16: Experimental drying curve data points of Figure 1.14 and the fitted poly-nomial curve (every 20th point). 46 TIME (minutes) F I G U R E 1.17: Drying data of Figure 1.14 ready for measurement by the manual method of calculating drying rates. 47 T A B L E 1.5: Comparison of Graphical and Computer Generated Drying Rates for a Wafer 63 mm Long Dried at 90°C. Drying Rates Drying Rates M (Graphical) (Computer) % Difference1 (%) (g/m 2- s) (g/m 2- s) 230 0.449 0.463 (3.11) 220 0.449 0.467 (4.00) 210 0.449 0.470 (4.67) 200 0.449 0.470 (4.67) 190 0.449 0.468 (4.22) 180 0.449 0.465 (3.55) 170 0.449 0.461 (2.66) 160 0.449 0.456 (1.549) 150 0.449 0.450 (0.212) 140 0.449 0.443 1.347 130 0.449 0.436 2.91 120 0.432 0.427 1.157 110 0.389 0.419 (7.71) 100 0.398 0.409 (2.76) 90 0.411 0.398 3.16 80 0.375 0.386 (2.93) 70 0.371 0.373 (0.539) 60 0.338 0.357 (5.62) 50 0.329 0.339 (3.04) 40 0.309 0.316 (2.27) 30 0.277 0.285 (2.89) 20 0.235 0.243 (3.40) 10 0.1538 0.1732 (12.61) 5 0.1102 0.1069 2.99 parentheses indicate negative values 48 40 80 120 160 200 240 P E R C E N T MOISTURE CONTENT F I G U R E 1.18: Comparison of graphical (points) and computer (solid curve) generated drying rate curves for a wafer 63 mm long dried at 90°C. 49 6 . 5 4 % . T h e i n c r e a s i n g c u r v a t u r e o f t h e d r y i n g c u r v e w i t h d e c r e a s i n g m o i s t u r e c o n t e n t c o m -b i n e d w i t h t h e i n c r e a s e d s p r e a d b e t w e e n d a t a p o i n t s a n d t h e l o n g e r o s c i l l a t i o n s a s s o c i a t e d w i t h d r y i n g a t h i g h e r t e m p e r a t u r e s a n d s h o r t e r w a f e r l e n g t h s c a u s e d t h e m a n u a l m e t h o d t o b e s u b j e c t i v e . F u r t h e r m o r e , i n a c c u r a c i e s i n t h e d r a w i n g o f t h e l i n e s p e r p e n d i c u l a r t o t h e d r y i n g c u r v e , o r i n t h e m e a s u r e m e n t o f t h e a n g l e f o r m e d b e t w e e n t h e s e l i n e s a n d a h o r i z o n t a l l i n e c o u l d c a u s e a n e r r o r o f | ° a n d t h u s a b o u t a 2 % e r r o r i n t h e c a l c u l a t i o n o f t h e d r y i n g r a t e . B a s e d o n t h e a b o v e d i s c u s s i o n c o m p a r i n g t h e t w o m e t h o d s o f a n a l y s i s , i t w a s d e c i d e d t o f i t a l l d a t a t o a 5 t h o r d e r p o l y n o m i a l u s i n g a U B C S A S s t a t i s t i c a l p a c k a g e " N L I N " f o r n o n - l i n e a r l e a s t s q u a r e s r e g r e s s i o n . 1.2.7 Init ial Tests of the Drying Apparatus A s e t o f p r e l i m i n a r y d r y i n g r u n s w a s p e r f o r m e d t o e s t a b l i s h t h e p r e c i s i o n o f t h e d r y i n g a p p a r a t u s a n d m e t h o d o f m e a s u r e m e n t s , a n d t h e s a m p l e s i z e r e q u i r e d f o r f u t u r e t e s t s . T w e n t y s a t u r a t e d 6 3 m m l o n g w a f e r s w e r e d r i e d i n d i v i d u a l l y a t 9 0 ° C a c c o r d i n g t o t h e p r o c e d u r e d e s c r i b e d i n S e c t i o n 1 . 2 . 5 . T h e w a f e r s w e r e t h e n r e s a t u r a t e d a n d t h e e n t i r e p r o c e s s r e p e a t e d . P a i r e d c o m p a r i s o n t - t e s t s ( S n e d e c o r a n d C o c h r a n , 1 9 7 6 ) w e r e p e r f o r m e d f o r t h e v a l u e s o f i n i t i a l m o i s t u r e c o n t e n t , g r e e n d e n s i t y , o v e n d r y t h i c k n e s s a n d d r y i n g t i m e f r o m 1 2 5 % t o 3 % m o i s t u r e c o n t e n t . T h e r e s u l t s o f t h e s e c o m p a r i s o n s w e r e u s e d a s a n i n d i c a t o r o f t h e p r e c i s i o n o f t h e v o l u m e , t h i c k n e s s a n d w e i g h t m e a s u r e m e n t t e c h n i q u e s a s w e l l a s t h e w a f e r s a t u r a t i o n p r o c e d u r e . T a b l e 1 . 6 p r e s e n t s t h e r e s u l t s o f t h e 4 0 d r y i n g t e s t s . T h e g r e e n d e n s i t i e s o f t h e r e d r i e d w a f e r s w e r e s i g n i f i c a n t l y l a r g e r t h a n t h o s e o b t a i n e d f r o m t h e w a f e r s p r i o r t o t h e f i r s t d r y i n g r u n s . W o o d t h a t h a s b e e n o v e n d r i e d ( t o 0 % m o i s t u r e c o n t e n t ) u n d e r g o e s c h e m i c a l c h a n g e s ( b o n d i n g b e t w e e n h y d r o x y l g r o u p s o f a d j a c e n t c h a i n s o f c e l l u l o s e ) t h a t p r e v e n t s i t f r o m a t -t a i n i n g i t s i n i t i a l g r e e n v o l u m e u p o n r e s a t u r a t i o n ( S t a m m , 1 9 6 8 ) . T h e r e s a t u r a t e d w a f e r s 5 0 T A B L E 1 .6: S u m m a r y S t a t i s t i c s f o r P r e l i m i n a r y D r y i n g R u n s . D r i e d x1 C V . 2 (%) R e d r i e d x 1 C V . 2 (%) t T e s t 3 A v e r a g e P e r c e n t D i f f e r e n c e (%r G r e e n D e n s i t y ( k g / m 3 ) 3 3 9 7 . 8 8 3 5 9 7 . 3 5 1 5 . 6 5 * * * 6 . 0 2 O v e n D r y T h i c k n e s s ( m m ) 0 . 6 3 4 1 8 . 5 0 0 . 6 3 9 1 8 . 6 4 2 . 3 2 * * 0 . 8 8 3 I n i t i a l M o i s t u r e C o n t e n t (%) 2 1 9 8 . 0 6 2 1 8 8 . 8 1 0 . 2 6 9 N S - 4 . 9 1 D r y i n g T i m e F r o m 1 2 5 % t o 3 % M C ( m i n u t e s ) 8 . 1 4 1 8 . 8 3 8 . 2 9 2 1 . 7 1 . 5 5 7 ^ s - 4 . 0 2 m e a n o f 2 0 w a f e r s c o e f f i c i e n t o f v a r i a t i o n = ( S t a n d a r d D e v i a t i o n / m e a n ) x 1 0 0 * * * - s i g n i f i c a n t a t o c = 0 . 0 0 1 ; ** - s i g n i f i c a n t a t o c = 0 . 0 1 ; N ' S ' - n o t s i g n i f i c a n t a t , o c = 0 . 0 5 a b s o l u t e v a l u e s o f t h e p e r c e n t d i f f e r e n c e s b e t w e e n t h e t w o r u n s f o r e a c h w a f e r w e r e u s e d i n t h i s a v e r a g e w o u l d t h u s h a v e s m a l l e r v o l u m e s , a n d t h e r e f o r e h i g h e r g r e e n d e n s i t i e s t h a n t h o s e m e a -s u r e d i n i t i a l l y . S i n c e t h e a v e r a g e p e r c e n t d i f f e r e n c e b e t w e e n t h e t w o s e t s o f r u n s w a s o n l y 6 . 0 % d e s p i t e t h e o b s e r v e d t r e n d , i t w a s f e l t t h a t t h e v o l u m e m e a s u r e m e n t t e c h n i q u e w a s a c c e p t a b l e . T h e r e w a s a l s o a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n t h e o v e n d r y t h i c k n e s s e s b e t w e e n t h e t w o s e t s o f d r y i n g t e s t s . H o w e v e r , s i n c e t h e a v e r a g e p e r c e n t d i f f e r e n c e w a s o n l y 0 . 8 8 % , t h i s d i f f e r e n c e w a s c o n s i d e r e d t o b e u n i m p o r t a n t a n d t h e s t a t i s t i c a l s i g n i f i c a n c e a r e s u l t o f t h e h i g h p r e c i s i o n o f t h e m e a s u r e m e n t s . T h e m e t h o d u s e d f o r s a t u r a t i n g t h e w a f e r s w a s a l s o s h o w n t o r e s u l t i n r e p r o d u c i b l e r e s u l t s s i n c e t h e i n i t i a l m o i s t u r e c o n t e n t s o f t h e t w o s e t s o f r u n s s h o w e d a n a v e r a g e p e r c e n t d i f f e r e n c e o f 4 . 9 a n d w e r e n o t s i g n i f i c a n t l y d i f f e r e n t a t t h e 9 5 % l e v e l o f c o n f i d e n c e . 51 F i n a l l y , t h e r e w e r e n o s i g n i f i c a n t d i f f e r e n c e s i n t h e i n d i v i d u a l p a i r s o f d r y i n g t i m e s f r o m 1 2 5 % t o 3 % m o i s t u r e c o n t e n t , a n d t h e a v e r a g e d r y i n g r a t e c u r v e s f o r t h e t w o s e t s o f t e s t s d i s p l a y e d o n l y m i n u t e d i f f e r e n c e s . T h e s e r e s u l t s p r o v i d e d t h e c o n f i d e n c e i n t h e d r y i n g a n d w e i g h i n g a p p a r a t u s t h a t w a s n e c e s s a r y b e f o r e p r o c e e d i n g w i t h t h e m a i n e x p e r i m e n t s . T h e s t a n d a r d d e v i a t i o n f o r t h e d r y i n g t i m e s f r o m 1 2 5 % t o 3 % m o i s t u r e c o n t e n t w a s c a l c u l a t e d a s 1 . 5 3 m i n u t e s f o r t h e 2 0 w a f e r s t h a t w e r e d r i e d i n i t i a l l y . T h i s v a l u e w a s u s e d t o c a l c u l a t e t h e m i n i m u m n u m b e r o f w a f e r s t o b e d r i e d a t e a c h t r e a t m e n t l e v e l . A s s u m i n g t h a t a 1 0 % c h a n g e i n d r y i n g t i m e ( 0 . 8 1 m i n u t e s ) c o n s t i t u t e d a r e a l d i f f e r e n c e b e t w e e n t r e a t m e n t s , t h e m i n i m u m s a m p l e s i z e w a s d e t e r m i n e d b y a n i t e r a t i v e p r o c e d u r e t o b e 2 8 . H o w e v e r , a s a m p l e s i z e o f 4 0 w a s e v e n t u a l l y s e l e c t e d t o p r o v i d e a m a r g i n o f s a f e t y . T h i s t r a n s l a t e s i n t o t h e a b i l i t y t o d e t e c t a d i f f e r e n c e i n d r y i n g b e t w e e n t w o t r e a t m e n t s o f 4 1 s e c o n d s a t a 9 5 % l e v e l o f p r o b a b i l i t y . 1.2.8 F a c t o r i a l D r y i n g Experiments T w o f a c t o r i a l e x p e r i m e n t s w e r e u n d e r t a k e n t o i n v e s t i g a t e t h e e f f e c t s o f w a f e r l e n g t h a n d d r y i n g t e m p e r a t u r e . T h e first e x p e r i m e n t h a d a 3 x 3 d e s i g n , t h r e e l e n g t h s o f w a f e r s ( 2 5 m m , 4 4 m m a n d 6 3 m m ) a n d t h r e e d r y i n g t e m p e r a t u r e s ( 9 0 ° , 1 2 0 ° , a n d 1 5 0 ° C ) . E a c h t r e a t m e n t c e l l c o n s i s t e d o f 4 0 d r y i n g r u n s ( r e p e t i t i o n s ) . T h e w a f e r s w e r e h u n g i n t h e d r y i n g a p p a r a t u s w i t h t h e w a f e r l e n g t h ( l o n g i t u d i n a l o r i e n t a t i o n ) p a r a l l e l i n g t h e d i r e c t i o n o f a i r f l o w . A n a n a l y s i s o f c o v a r i a n c e w a s p e r f o r m e d o n t h e w a f e r d r y i n g t i m e s f r o m 1 2 5 % t o 3 % m o i s t u r e c o n t e n t , 1 2 5 % t o 3 0 % m o i s t u r e c o n t e n t ( F i b r e S a t u r a t i o n P o i n t ) a n d f r o m 3 0 % t o 3 % m o i s t u r e c o n t e n t ( t y p i c a l m o i s t u r e c o n t e n t o f w a f e r s u s e d i n w a f e r b o a r d p r o d u c t i o n ) . T h e w a f e r d r y i n g r a t e s f o r t h e n i n e t r e a t m e n t s w e r e c o m p a r e d a t 5 % , 1 0 % , 1 5 % , 2 0 % , 3 0 % , 4 0 % , 6 0 % , 9 0 % a n d 1 2 5 % m o i s t u r e c o n t e n t s u s i n g a n a l y s i s o f v a r i a n c e ( a s e p a r a t e a n a l y s i s a t e a c h m o i s t u r e c o n t e n t ) . 5 2 The second factorial experiment was designed to verify that the effect of wafer length on wafer drying was not solely the result of the relationship between wafer length and external heat and mass transfer. To this end, wafers were positioned in the drying apparatus with their lengths perpendicular to the direction of the air flow. Thus, unlike the first factorial experiment the boundary layer adjacent to the wafer surfaces would develop over the same distance (wafer width 32 mm) regardless of wafer length. Since the drying rate curves from the previous experiment showed similar trends with drying temperature at each wafer length, the second set of experiments were conducted for the three wafer lengths at 150°C only. The number of repetitions in each treatment cell was reduced to 20 based on a recalculation of sample size using the sample variance of the 360 wafers from the first experiments. The analysis of the wafer drying rates for the three treatments was the same as for the previous experiment. 53 1.3 R e s u l t s a n d D i s c u s s i o n 1.3.1 Analysis of Wafer D r y i n g Times M e a n w a f e r d r y i n g t i m e s , t h i c k n e s s e s a n d s a t u r a t e d d e n s i t i e s f o r e a c h s e t o f 40 w a f e r s i n t h e 3x3 f a c t o r i a l e x p e r i m e n t a r e p r e s e n t e d i n T a b l e s 1.7, 1.8 a n d 1.9. T h e c o e f f i c i e n t s o f v a r i a t i o n a r e a l s o s h o w n f o r e a c h m e a n a s a n e s t i m a t e o f t h e v a r i a b i l i t y o f t h e d a t a b e t w e e n w a f e r s i n e a c h t r e a t m e n t , a n d f r o m t r e a t m e n t t o t r e a t m e n t . T h e c o e f f i c i e n t s o f t h e p o l y n o m i a l e q u a t i o n s u s e d t o f i t t h e d r y i n g c u r v e d a t a a r e g i v e n i n A p p e n d i x A . T h e t i m e r e q u i r e d t o r e d u c e t h e w a f e r m o i s t u r e c o n t e n t f r o m 125% t o 30% m o i s t u r e c o n t e n t w a s f o u n d t o b e a p p r o x i m a t e l y 60% o f t h e d r y i n g t i m e f r o m 125% t o 3% m o i s t u r e c o n t e n t r e g a r d l e s s o f e x p e r i m e n t a l t r e a t m e n t . T h e c o n s t a n c y o f t h i s r a t i o i m p l i e s t h a t t h e m e c h a n i s m s i n v o l v e d i n d r y i n g w a f e r s d o n o t c h a n g e w i t h d r y i n g m e d i u m t e m p e r a t u r e o r w a f e r l e n g t h . T h e c o e f f i c i e n t s o f v a r i a t i o n o f t h e d r y i n g t i m e s f r o m 30%-3% m o i s t u r e c o n t e n t w e r e c o n s i s t e n t l y l a r g e r t h a n t h o s e f o r 125% t o 30% m o i s t u r e c o n t e n t . W a f e r p r o p e r t i e s , s u c h a s t h i c k n e s s a n d d e n s i t y t h a t h a v e a s i g n i f i c a n t e f f e c t o n d r y i n g b e h a v i o u r ( a s d i s c u s s e d i n S e c t i o n 1.1.3), b u t w e r e n o t a c c o u n t e d f o r i n t h e e x p e r i m e n t a l d e s i g n c o u l d b e e x e r t i n g a g r e a t e r i n f l u e n c e o n w a f e r d r y i n g a t l o w e r m o i s t u r e c o n t e n t s t h a n a t h i g h e r m o i s t u r e c o n t e n t s . T h e e f f e c t o f t h i c k n e s s a n d d e n s i t y o n t h e d r y i n g m e c h a n i s m s a s s o c i a t e d w i t h l o w m o i s t u r e c o n t e n t s ( t r a n s v e r s e m o i s t u r e d i f f u s i o n a n d t h e r m a l c o n d u c t i v i t y ) i s g r e a t e r t h a n o n t h e t r a n s p o r t p h e n o m e n a a t h i g h e r m o i s t u r e c o n t e n t s ( v a p o u r a n d l i q u i d b u l k flow, e x t e r n a l m a s s a n d h e a t t r a n s f e r ) a n d t h u s r e s u l t s i n a h i g h e r v a r i a b i l i t y i n d r y i n g t i m e s b e t w e e n w a f e r s i n a n y t r e a t m e n t . A p p e n d i x B p r e s e n t s a d e t a i l e d d i s c u s s i o n o f t h e s t a t i s t i c a l a n a l y s e s o f t h e d r y i n g t i m e s a n d d r y i n g r a t e s o f t h e 3x3 a n d 1x3 f a c t o r i a l e x p e r i m e n t s . T h e e f f e c t s o f d r y i n g t e m p e r a t u r e a n d w a f e r l e n g t h o n d r y i n g t i m e s i n t h e 3x3 f a c t o r i a l e x p e r i m e n t w e r e s t r o n g l y s i g n i f i c a n t . H o w e v e r , t h e s t a t i s t i c a l a n a l y s i s s h o w e d t h a t t h e e f f e c t s o f d r y i n g t e m p e r a t u r e 54 TABLE 1.7: Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions 150°C 25 mm Cell 7 150°C 44 mm Cell 8 150°C 63 mm Cell 9 Drying Time 125-3% (min) 3.35 (0.1012) 3.54 (0.1611) 3.85 (0.1114) Drying Time 125-30% (min) 2.11 (0.0925) 2.22 (0.1184) 2.46 (0.1098) Drying Time 30-3% (min) 1.243 (0.1223) 1.316 (0.278) 1.394 (0.1176) Thickness3 (mm) 0.652 (0.0843) 0.634 (0.0678) 0.636 (0.0881) Green Density 4 (kg/m3) 365 (0.0709) 342 (0.0749) 359 (0.1987) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (= standard deviation/mean) Mean thickness and coefficient of variation for all 360 wafers is: 0.639 mm (0.0841) Mean density and coefficient of variation for all 360 wafers is: 354 kg/m3 (0.0831) 55 TABLE 1.8: Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions 120°C 120°C 120°C 25 mm 44 mm 63 mm Cell 4 Cell 5 Cell 6 Drying Time 4.40 4.88 5.53 125-3% (0.1314) (0.1114) (0.1113) (min) Drying Time 2.75 3.07 3.47 125-30% (0.1158) (0.0973) (0.1077) (min) Drying Time 1.660 1.811 2.06 30-3% (0.1663) (0.1391) (0.1211) (min) Thickness3 0.634 0.650 0.637 (mm) (0.0915) (0.0585) (0.0612) Green 359 339 352 Density 4 (0.0636) (0.0801) (0.0652) (kg/m3) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (= standard deviation/mean) Mean thickness and coefficient of variation for all 360 wafers is: 0.639 mm (0.0841) Mean density and coefficient of variation for all 360 wafers is: 354 kg/m3 (0.0831) 56 TABLE 1.9: Mean Drying Times, Thickness and Saturated Density for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions 90° C 25 mm Cell 1 90°C 44 mm Cell 2 90°C 63 mm Cell3 Drying Time 125-3% (min) 6.79 (0.1230) 7.22 (0.1154) 8.26 (0.1508) Drying Time 125-30% (min) 4.14 (0.1020) 4.43 (0.0963) 5.07 (0.1467) Drying Time 30-3% (min) 2.655 (0.1612) 2.79 (0.1520) 3.19 (0.1626) Thickness3 (mm) 0.640 (0.0813) 0.647 (0.0665) 0.626 (0.1342) Green Density 4 (kg/m3) 373 (0.0718) 347 (0.0712) 353 (0.0827) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (= standard deviation/mean) Mean thickness and coefficient of variation for all 360 wafers is: 0.639 mm (0.0841) Mean density and coefficient of variation for all 360 wafers is: 354 kg/m3 (0.0831) 57 and wafer length were multiplicative. Thus, they were not independent effects but combined synergistically to affect drying time. An increase in drying temperature from 90°C to 120°C produced a much greater re-duction in drying time than an increase from 120°C to 150°C. This trend was observed for drying times for all three ranges of moisture content 125% to 3%, 125% to 30%, and 30% to 3%. The cause of this trend could not be interpreted from the drying time data. Each drying time represents the sum of the effects of all the different mechanisms that occur during wafer drying. Thus, it is not known whether the observed trends of drying times with temperature result from the dependence of water moisture diffusivity, partial pressure or vapour pressure on temperature, or if the increase in radiant heat transfer with temperature is a contributing factor. A multiplicative effect between drying temperature and wafer length has also been identified but cannot be explained using the results of these analyses. Furthermore, the variability in drying times between wafers as a result of differing wafer properties was great enough to blur the highly significant effect of wafer length on drying time as evidenced by the comparison of cell means presented in Appendix B, Table B.2. All of the above arguments indicate that the analysis of drying times is not sufficient to interpret adequately the effects of drying temperature and wafer length on the drying behaviour of wafers, and that an explicit examination of the wafer drying rates is warranted. 1.3.2 A n a l y s i s of Wafer D r y i n g Rates Results of the 3 x 3 Factorial Experiment The drying rate data obtained from the 3 x 3 factorial experiment are summarized in Tables 1.10, 1.11 and 1.12 and presented graphically in Figure 1.19. Several similarities between the drying rate curves may be seen in Figure 1.19. None of the experimental conditions produced a constant rate drying period in the range of moisture contents studied. 58 T A B L E 1.10: Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions Moisture 25 mm 44 mm 63 mm Content 150°C 150°C 150°C (%) Cell 7 Cell 8 Cell 9 125 1.167 1.002 0.913 (0.0509) (0.0432) (0.0362) 120 1.151 0.991 0.903 (0.0522) (0.0439) (0.0363) 110 1.117 0.966 0.882 (0.0555) (0.0449) (0.0364) 100 1.080 0.938 0.860 (0.0593) (0.0457) (0.0366) 90 1.041 0.909 0.837 (0.0634) (0.0473) (0.0378) 80 0.999 0.878 0.811 (0.0676) (0.0500) (0.0400) 70 0.954 0.842 0.781 (0.0714) (0.0537) (0.0428) 60 0.905 0.803 0.747 (0.0745) (0.0583) (0.0456) 50 0.850 0.758 0.707 (0.0768) (0.0635) (0.0479) 40 0.786 0.703 0.656 (0.0785) (0.0693) (0.0496) 30 0.708 0.635 0.591 (0.0807) (0.0765) (0.0516) 20 0.602 0.541 0.502 (0.0853) (0.0868) (0.0556) 15 0.530 0.477 0.442 (0.0903) (0.0946) (0.0587) 10 0.433 0.391 0.363 (0.1022) (0.1084) (0.0631) 5 0.271 0.253 0.241 (0.2177) (0.1853) (0.1006) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (standard deviation/mean) 59 T A B L E 1.11: Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions Moisture 25 mm 44 mm 63 mm Content 120°C 120°C 120°C (%) Cell 4 Cell 5 Cell 6 125 0.861 0.744 0.661 (0.0512) (0.0367) (0.0416) 120 0.850 0.735 0.654 (0.0529) (0.0377) (0.0425) 110 0.825 0.716 0.640 (0.0563) (0.0393) (0.0442) 100 0.798 0.695 0.624 (0.0601) (0.0411) (0.0461) 90 0.770 0.672 0.607 (0.0642) (0.0431) (0.0479) 80 0.739 0.649 0.587 (0.0687) (0.0457) (0.0497) 70 0.706 0.623 0.564 (0.0732) (0.0490) (0.0514) 60 0.669 0.595 0.538 (0.0778) (0.0530) (0.0532) 50 0.628 0.562 0.507 (0.0826) (0.0580) (0.0551) 40 0.580 0.523 0.469 (0.880) (0.0644) (0.0574) 30 0.522 0.473 0.420 (0.0949) (0.0722) (0.0605) 20 0.443 0.404 0.354 (0.1045) (0.0816) (0.0650) 15 0.390 0.356 0.310 (0.1107) (0.0867) (0.0685) 10 0.318 0.290 0.252 (0.1193) (0.0926) (0.0743) 5 0.202 0.1796 0.1617 (0.1764) (0.1396) (0.1064) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (standard deviation/mean) 60 T A B L E 1.12: Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 3 x 3 Factorial Experiment 1 , 2. Experimental Conditions Moisture 25 mm 44 mm 63 mm Content 120°C 120°C 120°C (%) Cell 1 Cell 2 Cell 3 125 0.586 0.5020 0.448 (0.0279) (0.0338) (0.0418) 120 0.579 0.497 0.444 (0.0288) (0.0348) (0.0423) 110 0.564 0.484 0.434 (0.0310) (0.0366) (0.0433) 100 0.546 0.471 0.423 (0.0336) (0.0386) (0.0443) 90 0.527 0.457 0.411 (0.0368) (0.0407) (0.0456) 80 0.506 0.441 0.397 (0.0405) (0.0429) (0.0471) 70 0.483 0.422 0.382 (0.0448) (0.0455) (0.0491) 60 0.457 0.402 0.364 (0.0496) (0.0485) (0.0516) 50 0.427 0.378 0.342 (0.0549) (0.0524) (0.0549) 40 0.393 0.349 0.316 (0.0611) (0.0574) (0.0591) 30 0.351 0.313 0.283 (0.0690) (0.0644) (0.0648) 20 0.295 0.264 0.237 (0.0797) (0.0753) (0.0730) 15 0.258 0.231 0.206 (0.0873) (0.0845) (0.0791) 10 0.209 0.1863 0.165 (0.1004) (0.1037) (0.0897) 5 0.1305 0.1137 0.096 (0.1767) (0.2171) (0.1483) All means are calculated from 40 values. Values in parentheses are the coefficients of variation (standard deviation/mean) 61 20 40 60 80 100 120 MOISTURE CONTENT (<$ F I G U R E 1.19: Drying rate versus moisture content for all experimental conditions in the 3x3 factorial experiment. Each curve represents a mean of 40 wafers. (Wafer length parallel to air flow). 62 Only the slowest drying wafers (90°C, 63 mm long) approached a constant rate drying period, and then only at moisture contents in excess of 120% (as shown in Figure 1.18). All the drying rate curves had the same parabolic decrease in drying rate with moisture content. Increases in wafer length corresponded with non-linear decreases in drying rate. This trend can be observed for all three drying temperatures. Increases in drying temperature also resulted in non-linear changes in drying rate. Examining the coefficients of variation for the mean drying rates presented in Table 1.10, 1.11 and 1.12, the variation between the data in each cell is seen to be significantly less than for the drying time data (Table 1.7, 1.8 and 1.9). Only at the 5% moisture content level does the within-cell variability become large. As in the drying time results, the coefficients of variation were fairly constant at each moisture content. This indicates that a logarithmic transformation of the data was re-quired prior to the analyses of variance as discussed in Appendix B. The ANOVA showed highly significant temperature effects and somewhat lesser but still strongly significant length effects for the entire range of moisture contents. No drying temperature x wafer length interactions were present. Thus, a multiplicative effect between drying temperature and wafer length existed from 125% to approximately 10-20% moisture content. At 5% moisture content, there was no multiplicative effect, nor was there a significant interaction. Drying temperature and wafer length exerted completely independent effects on drying rate. 6 3 Results of the 1 x 3 Factorial Experiment Table 1.13 summarizes the results of the 1x3 factorial experiment and Figure 1.20 presents the same data in graphical form. The drying rate curves from this experiment had the same parabolic shape as those for wafers dried at 150°C in the 3 x 3 factorial experiment. However, a major difference between the two sets of curves may be seen. The three curves effectively become one at about 20% moisture content whereas in the 3 x 3 factorial exper-iment the three drying rate curves at 150°C remain separate along their entire length. The second difference is that an increase in wafer length resulted in a linear decrease in drying rate as opposed to the non-linear decrease in drying rate observed in the 3 x 3 factorial experiment (Figure 1.19). The effect of wafer length on drying rate determined by the analyses of variance does not extend below 40% moisture content. It is possible that with an increase in sample size the length effect would be shown to be significant to a moisture content below 40% as observed in Figure 1.20. Effect of External Heat and Mass Transfer Conditions on Wafer Drying The effect of wafer length on drying rate differed in the two factorial experiments. In the 3 x 3 factorial experiment the length effect was significant at all moisture contents, while in the 1 x 3 factorial it was only significant to approximately 40% moisture content. Tables 1.14, 1.15, 1.16 and 1.17 list the external transfer coefficients calculated for the different experimental conditions. The correlations used to obtain these coefficients (Treybal, 1980), Nu a v = 0.664Re°-5Pr .0.33 (1.12) and Sh a v = 0.664Re°-5Sc' ,0.33 (1.13) 64 T A B L E 1.13: Mean Drying Rates at Different Moisture Contents for Wafers Dried in the 1 x 3 Factorial Experiment. Moisture Content (%) Experimental Conditions 150°C 25 mm 150°C 44 mm 150° 63 mm 125 1.064 0.995 0.944 (0.0417) (0.0302) (0.0589) 120 1.048 0.982 0.928 (0.0458) (0.0277) (0.0514) 110 1.016 0.955 0.897 (0.0529) (0.0278) (0.0455) 100 0.981 0.927 0.868 (0.0587) (0.0315) (0.0468) 90 0.944 0.894 0.839 (0.0633) (0.0365) (0.0496) 80 0.903 0.859 0.810 (0.0669) (0.0423) (0.0531) 70 0.858 0.821 0.778 (0.0699) (0.0487) (0.0577) 60 0.809 0.777 0.742 (0.0727) (0.0549) (0.0631) 50 0.753 0.727 0.699 (0.0755) (0.0604) (0.0678) 40 0.689 0.669 0.647 (0.0789) (0.0648) (0.0708) 30 0.611 0.597 0.581 (0.0837) (0.0682) 0.0721) 20 0.511 0.503 0.492 (0.0914) (0.0720) (0.0745) 15 0.445 0.441 0.433 (0.0970) (0.0760) (0.0794) 10 0.359 0.362 0.357 (0.1029) (0.0862) (0.0954) 5 0.225 0.243 0.245 (0.1284) (0.1518) (0.1910) All means are calculated from 20 values Values in parentheses are the coefficients of variation (standard deviation/mean) 65 O.o ' ' 1 ' 1 ' * ' 1 ' * ' * ' * 0 20 40 60 80 100 120 140 PERCENT MOISTURE CONTENT F I G U R E 1.20: Drying rate versus moisture content for each wafer length in the 1x3 factorial experiment. Each curve represents a mean of 20 wafers. Drying temperature 150°C, wafer length perpendicular to air flow. 66 T A B L E 1.14: Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 150°C in the 3 x 3 Factorial Experiment. Wafer length (m) 0.025 0.044 0.063 Wet Bulb Temperature1 (°C) 42.5 42.5 42.5 Predicted Initial 2 Wafer Surface 50.5 52.5 54.0 Temperature1 (°C) Convective Heat Transfer Coefficient 13.18 9.96 8.33 (W/m2-K) Initial 2 Radiant Heat Transfer 9.85 10.05 10.16 Coefficient1 (W/m2-K) Mass Transfer Coefficient1 12.69 9.52 7.92 (g/m2-s) Predicted Initial 2 Drying Rate 1.001 0.854 0.778 (g/m2-s) Experimental Initial 2 1.148 1.019 0.981 Drying Rate 3 , 4 (0.0998) (0.1285) (0.0975) (g/m2- 8) For method of calculation see Appendix C After the drying oven reached the dry bulb temperature Experimental drying rates averaged for 40 wafers in each treatment cell Values in parentheses are the coefficients of variation for each mean drying rate (standard error/mean) 67 T A B L E 1.15: Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 120°C in the 3 x 3 Factorial Experiment. Wafer length (m) 0.025 0.044 0.063 Wet Bulb Temperature1 (°C) 38.3 38.3 38.3 Predicted Initial 2 Wafer Surface 44.6 46.3 47.5 Temperature1 (°C) Convective Heat Transfer Coefficient 13.21 9.98 8.35 (W/m2-K) Initial 2 Radiant Heat Transfer 8.26 8.44 8.53 Coefficient1 (W/m2-K) Mass Transfer Coefficient1 12.98 9.77 8.14 (g/m2-s) Predicted Initial 2 Drying Rate 0.703 0.591 0.533 (g/m2-s) Experimental Initial 2 0.868 0.745 0.726 Drying Rate3'4 (0.0907) (0.0709) (0.0701) (g/m2- s) For method of calculation see Appendix C After the drying oven reached the dry bulb temperature Experimental drying rates averaged for 40 wafers in each treatment cell Values in parentheses are the coefficients of variation for each mean drying rate (standard error/mean) 68 TABLE 1.16: Measured and Predicated Quantities Describing the External Transfer Con-ditions for Wafer Drying at 90°C in the 3 x 3 Factorial Experiment. Wafer length (m) 0.025 0.044 0.063 Wet Bulb Temperature1 (°C) 33.4 33.4 33.4 Predicted Initial 2 Wafer Surface 37.9 39.2 40.1 Temperature1 (°C)  Convective Heat Transfer Coefficient 13.23 10.00 8.57 (W/m2-K)  Initial 2 Radiant Heat Transfer 6.72 6.89 6.96 Coefficient1 (W/m2-K)  Mass Transfer Coefficient1 13.08 9.86 8.23 (g/m2-s)  Predicted Initial 2 Drying Rate 0.448 0.371 0.330 (g/m2-s)  Experimental Initial 2 0.592 0.518 0.483 Drying Rate 3 , 4 (0.0780) (0.0833) (0.1343) (g/m2- s) For method of calculation see Appendix C After the drying oven reached the dry bulb temperature Experimental drying rates averaged for 40 wafers in each treatment cell Values in parentheses are the coefficients of variation for each mean drying rate (standard error/mean) 69 TABLE 1.17: Measured and Predicted Quantities Describing the External Transfer Con-ditions for Wafer Drying in the 1 x 3 Factorial Experiment. Wafer Length (m) 0.025 0.044 0.063 Dry Bulb Temperature (°C) 150 150 150 Wet Bulb Temperature (°C) 42.5 42.5 42.5 Predicted Initial 2 Wafer Surface Temperature1 (°C) 51.2 51.3 51.4 Convective Heat Transfer Coefficient1 (W/m2-K) 11.79 11.79 11.79 Initial 2 Radiative Heat Transfer Coefficient1 (W/m2- K) 9.87 10.03 10.10 Mass Transfer Coefficient1 (g/m2- s) 11.31 11.31 11.31 Predicted Initial 2 Drying Rate 1 (g/m2- s) 0.935 0.941 0.944 Experimental Initial 2 Drying Rate3-4 (g/m2- s) 1.175 (0.0273) 1.097 (0.0752) 1.069 (0.0570) For method of calculation see Appendix C After the drying oven reached the dry bulb temperature Experimental drying rates average for 20 wafers in each treatment cell Values in parentheses are the coefficient for each mean drying rate (standard error/mean) 70 w h e r e P r > 0.6 R e L < 8 x 105 a r e f o r a n i s o t h e r m a l s e m i - i n f i n i t e flat p l a t e s u b m e r g e d i n a fluid h a v i n g a u n i f o r m v e l o c i t y p r o f i l e w i t h a d e v e l o p i n g t h e r m a l a n d m o m e n t u m b o u n d a r y l a y e r s t a r t i n g a t t h e l e a d i n g e d g e o f t h e p l a t e . T h e s e c o r r e l a t i o n s w e r e c o n s i d e r e d t o b e a p p l i c a b l e t o t h e e x p e r i m e n t a l d r y i n g s y s t e m b e c a u s e o f t h e r e l a t i v e l y flat v e l o c i t y p r o f i l e o f t h e a i r s t r e a m ( F i g u r e 1.13) a p p r o a c h i n g t h e l e a d i n g e d g e o f t h e s u s p e n d e d w a f e r , t h e n e g l i g i b l e w a f e r t h i c k n e s s a n d t h e a s s u m p t i o n t h a t t h e w a f e r t e m p e r a t u r e w a s c o n s t a n t a t t h e w e t b u l b t e m p e r a t u r e w h i l e d r y i n g a t o r n e a r s a t u r a t e d c o n d i t i o n s . T h e e x t e r n a l t r a n s f e r c o e f f i c i e n t s a n d o t h e r v a l u e s t h a t c h a r a c t e r i z e t h e d r y i n g s y s t e m f o r t h e d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s a r e p r e s e n t e d i n A p p e n d i x C . I n t h e 3x3 f a c t o r i a l e x p e r i m e n t s , t h e e x t e r n a l h e a t a n d m a s s t r a n s f e r c o e f f i c i e n t s c h a n g e d w i t h w a f e r l e n g t h s i n c e w a f e r l e n g t h w a s p a r a l l e l t o d i r e c t i o n o f a i r flow. H o w e v e r , i n t h e 1x3 f a c t o r i a l t h e e x t e r n a l h e a t a n d m a s s t r a n s f e r c o e f f i c i e n t s r e m a i n e d c o n s t a n t w i t h w a f e r l e n g t h b e c a u s e w a f e r l e n g t h w a s p e r p e n d i c u l a r t o t h e d i r e c t i o n o f a i r flow, a n d t h e u n c h a n g i n g w a f e r w i d t h p a r a l l e l t o t h e a i r flow. T h u s , t h e e f f e c t o f w a f e r l e n g t h i n t h e 1x3 f a c t o r i a l c o u l d n o t h a v e r e s u l t e d f r o m t h e e x t e r n a l t r a n s f e r c o n d i t i o n s b u t m u s t i n s t e a d r e s u l t f r o m s o m e i n t e r n a l d r y i n g m e c h a n i s m s . T h e l e n g t h e f f e c t o f t h e 3x3 f a c t o r i a l a l s o h a d a n i n t e r n a l l e n g t h c o m p o n e n t , b u t s i n c e t h e l e n g t h e f f e c t w a s s i g n i f i c a n t a t a l l m o i s t u r e c o n t e n t s , a s e c o n d t y p e o f l e n g t h e f f e c t m u s t e x i s t r e s u l t i n g f r o m c h a n g e s i n e x t e r n a l t r a n s f e r c o e f f i c i e n t s w i t h c h a n g e s i n w a f e r l e n g t h . F u r t h e r m o r e , t h e n o n - l i n e a r d e c r e a s e s i n d r y i n g r a t e w i t h i n c r e a s e s i n w a f e r l e n g t h o b s e r v e d i n F i g u r e 1.19 r e s u l t f r o m t h e n o n - l i n e a r d e c r e a s e s i n e x t e r n a l t r a n s f e r c o e f f i c i e n t s w i t h t h e i n c r e a s e s i n w a f e r l e n g t h . T h e s t a t i s t i c a l a n a l y s e s p e r f o r m e d o n t h e 3x3 f a c t o r i a l d a t a s h o w e d t h a t a m u l t i p l i c a -t i v e e f f e c t b e t w e e n d r y i n g t e m p e r a t u r e a n d w a f e r l e n g t h e x i s t e d u n t i l a b o u t 10% m o i s t u r e 7 1 content. This multiplicative effect shows the significance of external heat and mass transfer on the wafer drying rate. For example, the rate of external heat transfer to the wafer may be expressed as the product of the external heat transfer coefficient (oc length - 0 5) and the temperature difference between the drying medium and the wafer surface. The decreasing significance of the multiplicative effect with decreasing moisture content results from the reduction in the driving forces of external heat and mass transfer as the wafer surface dries out and heats up. The non-linear increases in drying rate with increases in drying temperature that could not be resolved by the analyses of drying times may now be interpreted. Since external heat and mass transfer to the wafer exert a significant effect on drying rate, it can be assumed that radiative heat transfer to the wafer, and not the dependence of diffusivity, partial pressure or vapour pressure on temperature, is the dominant cause of the non-linearity of drying rates with temperature. In the drying chamber, the glass pipe that surrounded the wafer radiated heat to the wafer. The radiative heat transfer coefficients for the different temperatures and wafer lengths have been calculated and are presented in Tables 1.14, 1.15 and 1.16. Assuming that the wafer surface was wet and at the temperature calculated (Tables 1.14, 1.15, 1.16), the amount of heat absorbed by the wafer would increase non-linearly with temperature. This effect, however, would greatly decrease as the wafer dried, not only because the wafer absorbtivity decreased with the decreasing surface moisture content (Kollman and Cote, 1969), but because the wafer surface temperature increased, thus decreasing both the radiant heat transfer coefficient and the temperature difference between the glass pipe and the wafer surface. Since the radiative heat transfer coefficients presented in Tables 1.14, 1.15 and 1.16 were calculated for a continuously wetted wafer surface, they represent the maximum coefficients possible. The wafer surface at 125% moisture content may still have a considerable number of wet patches and be at a relatively low temperature, as the results 72 of Stanish and Kayihan (1984) indicate (Figure 1.8), and thus would be affected by radiant heat transfer. It is not known at what moisture content radiative heat transfer ceases to affect the wafer drying rate. Tables 1.14, 1.15, 1.16 and 1.17 present predicted and experimental initial drying rates for the wafer just after the drying oven reached its set-point temperature. For the predic-tions of wafer drying rates the wafer surface was assumed to be continually wetted. Since the experimental wafer moisture content at this point in the drying period was at or near complete saturation (greater than 200%), this was considered to be a good assumption. Considering the coarse measurement of air velocity in the drying tube and assumptions inherent in the use of the boundary layer theory correlations for a submerged flat plate, the agreement between the experimental and predicted drying rates is quite good. Without taking into account the radiative heat transfer, the predicted drying rates do not follow the same trends with changing experimental conditions nor are the values close to the experimental drying rates. The Effect of Wood Structure on Wafer Dry i n g Rate The previous section identified an effect of wafer length on drying rate that resulted from an internal drying mechanism acting in the longitudinal orientation. This effect was large at high moisture contents and gradually tapered off until it completely disappeared at about 30-40% moisture content. At high moisture contents it is expected that capillary flow of water occurs in the large vessels of aspen. However, at 125% moisture content, the vast majority of the vessels would be empty, assuming that they would lose water faster than other wood elements. A rough approximation of the volume of the vessels in aspen is 30% of the total wood volume. This value was obtained by superimposing an enlargement of a micrograph of the aspen cross-section (Figure 1.6(a)) on a fine grid to determine the surface area of the wood 73 o c c u p i e d b y v e s s e l s . S i n c e v e s s e l s a r e a p p r o x i m a t e l y c y l i n d r i c a l t h e v o l u m e o c c u p i e d b y t h e v e s s e l s c o u l d t h e n b e e s t i m a t e d . T h e m a x i m u m m o i s t u r e c o n t e n t t h a t c o u l d b e o b t a i n e d i f a l l t h e v o i d s i n t h e w o o d s t r u c t u r e a r e f i l l e d a n d t h e w o o d s u b s t a n c e ( c e l l w a l l s ) h a v e a d s o r b e d t h e m a x i m u m p o s s i b l e a m o u n t o f w a t e r i s g i v e n ( B e a l l , 1 9 7 7 ) b y : 00\ — - 0 . 6 5 3 ( 1 . 1 4 ) '« / w h e r e m m a x i s t h e f r a c t i o n a l m a x i m u m m o i s t u r e c o n t e n t a n d ps i s t h e s a t u r a t e d d e n s i t y ( k g d r y w o o d / m 3 w a f e r ) . U s i n g t h e s a t u r a t e d d e n s i t y o f t h e a s p e n w a f e r s f r o m t h e 3 x 3 f a c t o r i a l e x p e r i m e n t (p, = 3 5 4 k g / m 3 ) , a m a x i m u m m o i s t u r e c o n t e n t o f 2 1 7 % w a s o b t a i n e d . A c u b i c m e t r e o f a s p e n a t 2 1 7 % m o i s t u r e c o n t e n t w o u l d c o n t a i n 7 6 8 k g o f w a t e r . A s s u m i n g a w a t e r d e n s i t y o f 1 0 0 0 k g / m 3 a n d a v e s s e l v o l u m e o f 3 0 % o f t h e w o o d , t h e w a t e r c o n t a i n e d i n t h e v e s s e l s o f t h e c u b i c m e t r e o f w o o d i s 3 0 0 k g . I f t h e v e s s e l s h a d l o s t a l l t h e i r w a t e r , t h e n t h e m o i s t u r e c o n t e n t o f t h e a s p e n b l o c k w o u l d b e a p p r o x i m a t e l y 1 3 2 % . I n a f r e s h l y c u t a s p e n w a f e r , s o m e v e s s e l s w i l l c o n t a i n w a t e r e v e n t h o u g h t h e m o i s t u r e c o n t e n t i s b e l o w 1 3 2 % . T h e m a j o r i t y o f t h e v e s s e l s w i l l , h o w e v e r , b e e m p t y a n d t h u s c a p i l l a r y flow t h r o u g h t h e v e s s e l s i s n o t p r o b a b l e . C a p i l l a r y flow c o u l d o c c u r b e t w e e n t h e l o n g i t u d i n a l p a r e n c h y m a a n d f i b r e c e l l s a d j o i n i n g t h e v e s s e l s , a l t h o u g h t h e flow o f w a t e r w o u l d b e g r e a t l y r e s t r i c t e d b y t h e i m p e r m e a b l e n a t u r e o f t h e p i t m e m b r a n e s t h a t e x i s t b e t w e e n t h e c e l l s ( S i a u , 1 9 8 4 a ) . F l o w w o u l d b e p r i m a r i l y i n a t r a n s v e r s e d i r e c t i o n t o t h e n e a r e s t v e s s e l w h e r e t h e w a t e r w o u l d b e e v a p o r a t e d a n d p r o c e e d b y d i f f u s i o n a n d / o r b u l k flow o u t o f t h e w a f e r . T h i s e x p l a n a t i o n i s c o n s i s t e n t w i t h t h e d i s a p p e a r a n c e o f t h e i n t e r n a l e f f e c t o f w a f e r l e n g t h a t 3 0 - 4 0 % m o i s t u r e c o n t e n t , s i n c e a t t h e s e m o i s t u r e l e v e l s t h e r e i s l i t t l e f r e e w a t e r l e f t i n t h e w o o d a n d t h e c a p i l l a r y s y s t e m b e c o m e s d i s c o n t i n u o u s . I t i s p o s s i b l e t h a t s o m e c a p i l l a r y flow i n t h e l o n g i t u d i n a l d i r e c t i o n m i g h t a l s o o c c u r i n t h e l o n g i t u d i n a l p a r e n c h y m a a n d f i b r e c e l l s . H o w e v e r , c o n s i d e r i n g t h e s m a l l e v a p o r a t i v e s u r f a c e a t t h e e n d s o f t h e w a f e r a n d t h e r e s t r i c t e d n a t u r e o f c a p i l l a r y flow, t h i s c o m p o n e n t 74 of the internal length effect on drying rate can be neglected. It is not known whether the water vapour moves through the vessel by diffusion, by bulk flow or by both mechanisms. Regardless of which transport mechanism is responsible, it is expected that an increase in the length of the pathway would cause a decrease in the drying rate. This relationship was observed in the results of the 1 x 3 factorial presented in Figure 1.20. The lack of a multiplicative effect between drying temperature and wafer length at 5% moisture content seems logical since at low moisture contents external heat and mass transfer are not expected to limit wafer drying. The presence of a significant length effect independent of drying temperature at 5% moisture content is a function of the relative rates of bound water diffusion through the longitudinal and transverse pathways in wood. As discussed in Section 1.1.4, Siau (1984a) listed the approximate ratio of longitudinal to transverse bound water diffusivities at 5% moisture content as 50-100. This ratio is high enough that given the wafer geometry, wafer length should have a significant influence. A Conceptual Dry ing History for Wafers Based on the results of both the drying time and drying rate analyses it is now possible to trace the drying history of a wafer. Starting from the completely saturated state, water is first evaporated from the cell lumens and vessels open to the wafer surface. As drying progresses, water is wicked from the surrounding vessels to replenish the surface water. However, the tortuosity of the capillary system causes the air/water interface to recede into the pores at the surface. This results in a gradual reduction in drying rate, and the absence of a constant rate period. After most of the vessels have lost their free water, the air/water menisci retreat to the minute pores in the pit membranes. Water is then wicked through the longitudinal fibre and parenchyma cell capillary system to the vessels, where it is evaporated and diffuses out of the wafer. 7 5 S i m u l t a n e o u s l y , t h e w a f e r s u r f a c e b e g i n s t o d r y a n d t h e r a d i a t i v e a n d c o n v e c t i v e h e a t t r a n s f e r t o t h e w a f e r b e g i n s t o d e c r e a s e . W i t h t h e w e a k e n i n g a n d e v e n t u a l c o l l a p s e o f t h e c a p i l l a r y s y s t e m a t a p p r o x i m a t e l y 3 0 % t o 4 0 % m o i s t u r e c o n t e n t , w a t e r d i f f u s e s t h r o u g h t h e c e l l w a l l s a n d t h r o u g h t h e l u m e n s a n d v e s s e l s ( a s b o u n d w a t e r a n d w a t e r v a p o u r , r e -s p e c t i v e l y ) t o t h e s u r f a c e o f t h e w a f e r . W h i l e t h e c e l l w a l l s s u r r o u n d i n g t h e v e s s e l s a r e f u l l y s a t u r a t e d w i t h b o u n d w a t e r , w a t e r t h a t e v a p o r a t e d i n t o t h e v e s s e l d i f f u s e s d o w n i t s l e n g t h . H o w e v e r , a f t e r t h e e v a p o r a t i o n o f m o s t o f t h e f r e e w a t e r , a t e m p e r a t u r e a n d m o i s -t u r e c o n t e n t g r a d i e n t d e v e l o p s a c r o s s t h e w a f e r t h i c k n e s s a n d l e n g t h . A s t h e w a f e r d r i e s f r o m a p p r o x i m a t e l y 2 5 % t o 5 % m o i s t u r e c o n t e n t , t h e r e l a t i v e i m p o r t a n c e o f l o n g i t u d i n a l t o t r a n s v e r s e d i f f u s i o n i n c r e a s e s b y a f a c t o r o f a b o u t 2 5 ( S i a u , 1 9 8 4 a ) . B o u n d w a t e r / w a t e r v a p o u r d i f f u s i o n d u r i n g d r y i n g a r e i n i t i a l l y p r e d o m i n a n t l y a c r o s s t h e w a f e r t h i c k n e s s . H o w -e v e r , a s t h e w a f e r d r i e s t o l o w m o i s t u r e c o n t e n t s , b o u n d w a t e r / w a t e r v a p o u r d i f f u s i o n a l o n g t h e l e n g t h o f t h e w a f e r b e c o m e s s i g n i f i c a n t . A s d i s c u s s e d e a r l i e r , t h e e x t e r n a l h e a t a n d m a s s t r a n s f e r s t i l l c o n t r i b u t e t o t h e d r y i n g p r o c e s s a t 1 0 % m o i s t u r e c o n t e n t (i.e. d r y i n g i s n o t c o n t r o l l e d s o l e l y b y d i f f u s i o n ) . F o r t h i s s i t u a t i o n t o a r i s e , t h e w a f e r s u r f a c e m u s t b e n e a r l y d r y a n d a l m o s t a t t h e d r y i n g t e m p e r a t u r e s o t h a t t h e r a t e s o f e x t e r n a l t r a n s f e r a r e l o w e n o u g h t o h a v e a n e f f e c t o n d r y i n g b e h a v i o u r . C o n s i d e r i n g t h e g e o m e t r y o f a w a f e r , i t i s q u i t e p o s s i b l e t o e n v i s a g e a s h a l l o w t e m p e r a t u r e p r o f i l e a c r o s s t h e w a f e r t h i c k n e s s a n d l e n g t h b e c a u s e o f t h e r e l a t i v e l y l a r g e w a f e r s u r f a c e f o r e x t e r n a l h e a t t r a n s f e r a s c o m p a r e d t o t h e p a t h w a y f o r t h e r m a l c o n d u c t i v i t y a c r o s s h a l f t h e t h i c k n e s s o f a w a f e r . A s t e e p g r a d i e n t i n m o i s t u r e c o n t e n t a l s o p r o b a b l y e x i s t s b e c a u s e o f t h e s l o w r a t e o f b o u n d w a t e r / w a t e r v a p o u r d i f f u s i o n f r o m t h e c e n t r e o f t h e w a f e r t o t h e s u r f a c e . T h e c o m b i n e d e f f e c t o f t h e s e t w o g r a d i e n t s e n s u r e s t h a t t h e r a t e o f b o u n d w a t e r / w a t e r v a p o u r d i f f u s i o n t o t h e s u r f a c e i s h i g h e n o u g h t o a l l o w t h e e x t e r n a l t r a n s f e r c o n d i t i o n s t o s t i l l a f f e c t d r y i n g . A s t h e i n t e r i o r o f t h e w a f e r d r i e s a n d h e a t s u p , t h e d i f f u s i o n o f b o u n d w a t e r a n d w a t e r v a p o u r d e c r e a s e s t o a l e v e l w h e r e i n t e r n a l 7 6 diffusion becomes the limiting drying mechanism. Drying is then controlled by the rate of bound water/water vapour diffusion until the wafer is bone dry. The above description of wafer drying is consistent with all the results observed for the wafers dried in this work. It should be noted that in reality there is probably a significant overlap between the dominance of the various drying mechanisms. While one section of the wafer may still contain free water undergoing capillary flow, another section may be controlled by the rate of external mass and heat transfer as moisture diffuses to the wafer surface. It is this gradual transition from one dominant mechanism to another that engenders the parabolic shape of the drying rate curves. 77 1.4 Conclusions T h e l e n g t h o f a w a f e r h a s b e e n s h o w n t o a f f e c t i t s d r y i n g b e h a v i o u r t h r o u g h o u t t h e d r y i n g p e r i o d . I n t h e e a r l y s t a g e s o f d r y i n g , t h e e x t e r n a l h e a t a n d m a s s t r a n s f e r r a t e s a r e d o m i -n a n t d r y i n g m e c h a n i s m s , b o t h o f w h i c h h a v e a n i n v e r s e p r o p o r t i o n a l i t y t o t h e s q u a r e r o o t o f w a f e r l e n g t h . A f t e r t h e f r e e w a t e r i n t h e v e s s e l s h a s b e e n e v a p o r a t e d , f r e e w a t e r t h a t h a s b e e n w i c k e d b y c a p i l l a r y flow t o t h e v e s s e l f r o m t h e s u r r o u n d i n g c e l l l u m e n s e v a p o r a t e s a n d d i f f u s e s a l o n g t h e l e n g t h o f t h e v e s s e l t o t h e e n d s o f t h e w a f e r . T h i s s e c o n d l e n g t h e f f e c t d i s a p p e a r s a t a p p r o x i m a t e l y 30-40% m o i s t u r e c o n t e n t . H o w e v e r , t h e e x t e r n a l h e a t a n d m a s s t r a n s f e r r a t e s c o n t i n u e t o a f f e c t d r y i n g r a t e ( a l b e i t a t a d e c r e a s i n g l e v e l w i t h d e c r e a s i n g m o i s t u r e c o n t e n t ) u n t i l a b o u t 10% m o i s t u r e c o n t e n t . A s m o i s t u r e c o n t e n t d e -c r e a s e s f r o m a p p r o x i m a t e l y 25% t o 5% t h e l o n g i t u d i n a l c o m p o n e n t o f b o u n d w a t e r / w a t e r v a p o u r d i f f u s i o n t h r o u g h t h e w a f e r i n c r e a s e s u n t i l i t r e p r e s e n t s a s i g n i f i c a n t p o r t i o n o f t h e m a s s t r a n s f e r o c c u r r i n g a t l o w m o i s t u r e c o n t e n t s . A s e x p e c t e d , i n c r e a s e s i n d r y i n g t e m p e r a t u r e p r o d u c e d i n c r e a s e s i n d r y i n g r a t e t h r o u g h i n c r e a s e d r a t e s o f i n t e r n a l a n d e x t e r n a l h e a t a n d m a s s t r a n s f e r . H o w e v e r , t h e o b s e r v e d n o n -l i n e a r i n c r e a s e s i n d r y i n g r a t e w i t h i n c r e a s e s i n d r y i n g t e m p e r a t u r e p r o b a b l y r e s u l t e d f r o m t h e c o n t r i b u t i o n o f r a d i a t i v e h e a t t r a n s f e r . T h e c h a n g e s i n d r y i n g t e m p e r a t u r e f r o m 90°C t o 150°C d i d n o t a f f e c t t h e d r y i n g m e c h a n i s m s i n v o l v e d i n w a f e r d r y i n g e v e n t h o u g h t h i s t e m p e r a t u r e r a n g e s p a n n e d t h e b o i l i n g p o i n t o f w a t e r . T h e c o n s t a n t r a t e p e r i o d o f d r y i n g w a s n o t o b s e r v e d a t a n y o f t h e e x p e r i m e n t a l c o n d i -t i o n s . A l t h o u g h e x t e r n a l h e a t a n d m a s s t r a n s f e r w e r e s h o w n t o b e l i m i t i n g m e c h a n i s m s a t h i g h m o i s t u r e c o n t e n t s , t h e g r a d u a l r e t r e a t o f t h e a i r / w a t e r i n t e r f a c e i n t o t h e p o r e s n e a r t h e w o o d s u r f a c e p r e v e n t e d a t r u e c o n s t a n t r a t e p e r i o d . D r y i n g r a t e v e r s u s m o i s t u r e c o n -t e n t c u r v e s s h o w e d n o s h a r p i n f l e c t i o n s a n d w e r e p a r a b o l i c i n s h a p e . T h i s w a s i n d i c a t i v e o f t h e g r a d u a l s w i t c h o v e r f r o m o n e d r y i n g m e c h a n i s m t o t h e n e x t , a n d t h e o v e r l a p p i n g o f 78 drying mechanisms because of the uneven drying behaviour of wood. 1.5 Implications That external heat and mass transfer play an important role throughout the drying of wafers indicates that drying can be improved by a more efficient method of contacting the wafer with the drying medium than is currently available in industrial wafer dryers. The application of fluidized bed technology to wafer drying thus promises to be highly beneficial. The current trend in the waferboard industry is to increase the length of wafer used in production and thus increase the flexural strength of waferboard (or preferably to produce less dense waferboard having the same strength properties, thus lowering production costs). The increased length of the wafers affects the performance of the dryers in that their capacity will decrease non-linearly with increasing wafer length (reflecting the dependence of drying rate on wafer length). 79 Chapter 2 Assessment of Fluidized Bed Technology for Wafer Drying 2.1 Background Review 2.1.1 F l u i d i z e d B ed D r y i n g The widespread application of fluidized bed technology to drying has focussed primarily on the drying of particulates or materials that may be easily fluidized or spouted (e.g. sand, granulated fertilizers, chemical crystals, wheat) (Vanecek et al., 1970; Reay and Baker, 1985). In a fluidized bed dryer, the solids to be dried (usually less than 1.5mm in diameter) form a column of material or bed in the main compartment. The drying gas enters the bottom of the compartment through a perforated plate (or distributor) and flows through the solids being dried. The velocity of this gas must be high enough so that the drag force of the gas on the individual particles overcomes the weight of the particles and yet not so high as to pneumatically convey them out of the dryer. The particles are suspended and agitated by the gas stream. The fluidized bed of solids most often resembles a boiling liquid, and has many similar hydrodynamic characteristics. It is the high velocity of the gas relative to the solids, the agitation of and the interaction between the solids, and the mixing effects of the bubbles as they pass through the bed of solids that create the excellent drying conditions in a fluidized bed. The high external heat and mass transfer in a fluidized bed results in faster drying than can be obtained by other methods. For temperature-sensitive 80 materials, the high degree of mixing allows the use of a high inlet gas temperature. Hot incoming gas equilibrates to the much lower bed temperature about 30 to 40 mm above the distributor plate. Since the gas and solids are in thermal equilibrium throughout most of the bed, the drying process can be controlled by monitoring the exhaust gas temperature and adjusting the inlet gas temperature to account for changes in the evaporative load. The shorter residence time of the gas in fiuidized beds compared to rotary dryers thus allows the drying process to be more responsive to changes in the initial moisture content of the feed. Reay and Baker (1986) classified fiuidized bed dryers as either having well mixed par-ticles or approximately plug flow of particles. Near perfect mixing in a fiuidized bed dryer results in a high thermal efficiency since high inlet temperatures and deep beds may be used. However, it also results in non-uniform drying of the particles (i.e. a wide range of end product moisture contents) because of the unequal residence times of the particles in the bed. A plug flow type fiuidized bed dryer allows all the particles to achieve more or less uniform treatment. These dryers are characterized by a length-to-width ratio of about 10 to 40 and relatively shallow beds. Solids enter one end, move horizontally and leave from the other. Since horizontal mixing is much slower than vertical, this configura-tion limits the amount of particle mixing along the length of the dryer so that near plug flow of particles through the dryer is achieved. The shallow bed depth results in a lower thermal efficiency than in the well mixed fiuidized bed dryer. However, a lower average particle moisture content and a narrower range of end product moisture contents are thus obtainable. 2.1.2 F iu idized Bed D r y i n g of Wood Wafers In Chapter 1 of this thesis, it was determined that external heat and mass transfer between the drying medium and the wafer surface greatly influenced the drying behaviour of wafers 8 1 throughout most of the drying period. The high rates of external heat and mass transfer obtainable in a fluidized bed dryer should therefore result in a much higher wafer drying rate than is possible with gas convection alone. Wood has been dried using fluidized bed technology either by immersion into a bed of inert solids fluidized by hot gas or by fluidization of the wood particles themselves. Milota (1984) fluidized a variety of wood particles, from sawdust to flakes, in developing a well mixed fluidized bed dryer for particleboard furnish. The wood flakes were found to fluidize poorly (if at all) and thus could not be dried adequately as a fluidized bed. Since the wafers to be dried in this research are much larger than those used by Milota, it would appear that they must be dried by immersion. This type of fluidized bed drying differs from that discussed earlier in that the fluidized bed provides only an external medium for drying. Although the drying of wafers in a fluidized bed of inert solids has not been investi-gated previously, a number of researchers have explored the drying of veneers by immersion (Babailov and Petri, 1974; Loos, 1971; Loos and Wen, 1970; Wen and Loos, 1969; Car-ruthers and Burridge, 1964). The only study which progressed beyond the preliminary stage was that by Babailov and Petri (1974) who investigated the effects of bed tempera-ture, inert particle diameter, superficial velocity, and initial bed height on the drying time of thin birch veneers. As particle diameter increased, the drying time of the veneer was found to increase. Optimum superficial velocities, each at a given particle size, increased with inert particle diameter and occurred at XJ/\Jmf — 2.0 to 2.2. The optimal inert particle used by Babailov and Petri (1974) appears to be a Geldart Group B powder (Grace, 1982). The dominant mechanism of heat transfer to an immersed surface or object should then be via the particle convective heat transfer component (Chen and Pei, 1985; Botterill et al., 1984; Saxena and Gabor, 1981; Richardson and Shakiri, 1979; Baskakov et ai, 1973). Richardson and Shakiri (1979) and Baskakov et al. (1973) showed that maximum bed to surface heat transfer rates decrease rapidly with increasing 82 particle diameter. Bed to surface heat transfer models based on penetration theory predict that as the fiuidized particle diameter increases, the renewal rate of particle packets at the submerged surface decreases. This results in a lowered overall rate of heat transfer to the surface, as verified experimentally by Gloski et al. (1984). The observed optimal superficial velocity of approximately 2.0-2.2 U m / (U — U m / = 0.223-0.268 m/s for 0.515 mm particles) used for drying veneer corresponds well with the optimal velocities found for the maximum heat transfer rate to immersed surfaces (Baskakov et al., 1973; Chen and Pei, 1985; Richardson and Shakiri, 1979). The frequency of bubble particle packet interchanges increased up to 2-3 Umj, at which point a maximum heat transfer rate was obtained (Baskakov et al., 1973). Beyond this superficial velocity the exchange frequency was virtually independent of the fluidizing velocity (Baskakov et al., 1973), and the heat transfer rate decreased as the surface was increasingly contacted by bubbles (Richardson and Shakiri, 1979). External mass transfer is not the limiting mechanism in the drying of thin veneers by immersion in a fiuidized bed. External mass transfer is dependent on the interstitial gas velocity (Coelho and Carvalho, 1988; Cobinnah et ai, 1987; Cibrowski and Kopec, 1985; Prins et al., 1985); hence if it had been limiting, the drying rate of the veneer would have been observed to increase with increasing inert particle diameter rather than decrease. The drying of wafers immersed in a fiuidized bed of inert solids will differ from the drying of veneer in that the wafers would be free to circulate rather than being fixed in one position. Cobinnah et al. (1987) concluded that the heat and mass transfer characteristics for a freely circulating object were similar to those for fixed objects. It was observed that below a critical superficial velocity, the free object remained packed in an incipient bubbling bed and that the heat and mass transfer coefficients rose with increasing velocity. Above a critical superficial velocity, the objects circulated through the bubbling bed and had nearly constant heat and mass transfer coefficients. Since the object was continuously in contact 83 with the emulsion phase, the heat transfer coefficient did not reach a maximum value and then decrease with increasing bubble frequency as for fixed probes. Although Prins et al. (1986) demonstrated that the heat transfer to a fixed sphere was slightly greater than to a freely circulating sphere, Rios and Gilbert (1983) showed a strongly opposite effect. Only when the size of the sphere increased to where its mobility in the emulsion phase was restricted did the two values approach each other. Assuming that wafers could be made to circulate freely in a fluidized bed of inert solids, then the optimal fluidization parameters determined for veneer drying may be roughly the optimal conditions for wafer drying. 2.1.3 Wafer C i r c u l a t i o n i n a Fluidized B e d of Inert Solids The circulation of a large body in a fluidized bed depends on the density difference between the body and the emulsion phase, the shape and size of the object, excess superficial velocity, and bubble frequency and diameter. Although different researchers have classified the circulation of a large body in a bed of solids according to different mechanisms and criteria (Rios et al., 1986; Masson et al., 1983; Nienow and Cheesman, 1980; Nguyen and Grace, 1978; Nienow et al., 1978; Pruden et al., 1976), a unified description of the large body's movements can be compiled. Objects that are less dense than the emulsion phase may follow the solids flow following their submersion by jetsam accumulating on their upper surfaces. After the accumulated solids are dislodged by passing bubbles, the object is transported back to the surface by the roof of a rising bubble or bubbles. If the object density roughly equals the emulsion phase density, then it follows much the same path as the solids, moving downward between bubbles and being transported upward in bubble wakes or due to drift. Berruti et al. (1988) observed that 0.71 mm wood tracer particles remained well mixed in a bed of 0.4 mm sand particles at velocities as low as 1.3 Umf (0.286 m/s). The gross circulation patterns of sand in the bed ("gulf-streaming") contributed significantly to the 8 4 circulation of the wood tracers. Free floating wafers in a fiuidized bed are likely to sink quickly from accumulated jetsam (Nienow and Cheesman, 1980), and would be easily cap-tured by passing bubbles because of their flat shape. However, below a certain superficial velocity, irretrievable sinking of large plate-like objects may occur due to insufficient mixing to disturb the accumulated jetsam from the upper wafer surface, and from the decrease in bubble size (and thus in lifting power) with increasing proximity to the distributor (Nienow and Cheesman, 1980; Nienow et al., 1978). Carter et al. (1987) demonstrated that accumu-lated jetsam on the distributor changed the localized pressure drop across the distributor plate causing a spouting action above the jetsam. This phenomenon would preclude the lifting by bubbles of objects settled on the distributor. Rios et al. (1986) and Berruti et al. (1988) emphasized that gross circulation of solids in the bed is a determining factor in large body circulation. Rios et al. (1986) proposed that above the minimum slugging velocity (Um3), the solids circulation in a deep bed becomes dominant over large object density in determining whether the large body will circulate or segregate. The large body's downward velocity in the bed would be nearly equal to that of the emulsion phase. Its upward velocity would be much slower than the bubble rise velocity because of the numerous times it would be caught and released by passing bubbles on its way back to the surface. 85 2.2 Configuration Considerations for a Fluidized Bed Wafer Dryer To achieve maximum thermal efficiency, the dryer should have a deep well-mixed fluidized bed of inert particles. The wafers used in waferboards, however, must be dried to a low moisture content and have a narrow distribution of final moisture contents. This requires plug flow of wafers through the dryer. In a plug flow type dryer, the residence time of the wafers would be governed by the wafer feed rate. The wafer circulation in the bed would be limited by the shallow bed depth and thus wafer mixing along the length of the dryer would be minimized. The wafers should be prevented from forming a layer on the surface of the bed since this would hinder the mixing of the solids, as for a layer of floating packings (Hirama et al., 1981). Formation of a surface layer would thus reduce the rate of heat transfer to the wafers and might also result in uneven drying across the wafer layer. Since this type of dryer has a shallow bed, it is possible that the wafers would remain predominantly at the surface of the bed or on the distributor because of the absence of a strong circulation pattern of solids. If the low thermal efficiency of a plug flow type dryer is also considered, then this design is not attractive. An alternative design to the plug flow type dryer would be to use induced circulation of solids to convey the wafers through the dryer. Pruden et al. (1976) used a baffle to divide a fluidized bed column into two chambers, and an auxiliary air supply allowed the rates of solids circulation to be varied (Figure 1.1). Depending on the different superficial velocities in the two chambers, the circulation time of briquette-sized cylinders could be controlled. Compared to the plug flow type dryer, the deeper bed with this design would make this dryer more efficient, smaller in size, and allow greater control over wafer residence time. 86 9.72" ID FIGURE 2.1: Apparatus for circulation of fluidized solids (Pruden et al., 1976). 87 2.3 Wafer Handling in a Fiuidized Bed of Inert Solids 2.3.1 Experimental Equipment and Procedures Introduction The scope of the experimental assessment of fiuidized bed technology for wafer drying was to observe the circulation patterns of wood wafers in a fiuidized bed and to verify the expected drying behaviour of the wafers. The resulting information (both quantitative and qualitative) was then used in the design of the continuous fiuidized bed dryer presented in Chapter 3 of this thesis. Since the final configuration of the continuous fiuidized bed dryer was not yet known, a wide range of experimental conditions were chosen to bracket the expected operating conditions for the continuous dryer. The Fiuidized Bed Column The 0.15 m diameter half-column (cross-sectional area of 0.0101 m2) used in this part of the work is shown in Figure 1.2. Originally designed as a spouted bed column (Wu, 1985), it was converted to a fiuidized bed column by adding a distributor plate above the conical entrance section. The entire front face of the half-column (0.63 m and 0.10 m heights for column and conical windbox respectively) was a single pane of 6.3 mm thick tempered glass. Gortex gasket (6.3 mm wide and 3.2 mm thick) was used to seal the glass against the stainless steel half-column, the distributor and the windbox as shown in Figure 1.3. The flow patterns of the bed and wafers could thus be observed for the full bed height as well as from the bottom through a transparent distributor plate. Figure 1.4 shows the location of 6.3 mm holes in the column that could be used either for pressure taps or for 6.3 mm type K thermocouple probes. Since the assessment of wafer circulation in a two-compartment bed was also planned, two sets of holes were drilled at each height so that the individual compartment bed properties could be measured and 88 u FIGURE 2.2: Experimental fiuidized bed unit used in wafer circulation and drying tests. A - flow control for primary air; B - conical windbox; C - distributor plate; D - wafer re-trieval screen; E - 0.15 m stainless steel half-column with plate glass front; F - flow control for auxiliary air for use in two compartment bed tests. 89 F I G U R E 2.3: Half-column prepared for the wafer circulation tests. 90 ZD _ l o o 0 Ul m o Ul N g 3 X o CD O z i © ® © © ® © © © LEGEND OF © HOLES FOR ATTACHMENT DIVIDER 6.3mmHOLES FOR PRESSURE OR TEMPERATURE MEASUREMENT INLET FOR AUXILI ARY AIR SCALE i-50r -SIDEARM F I G U R E 2.4: Rear view of half-column used for wafer handling and drying experiments. 91 the probes not interfere with the divider. The 0.20 m high divider was held by three bolts through the back of the column. Gortex gasket was used to seal the divider against the glass. In place, the divider separated the bed into two equal compartments leaving a 51 mm gap between its lower edge and the distributor plate. Figure 1.5 shows the fiuidized bed column set-up for the two compartment bed tests. Auxiliary air required for the two compartment bed tests was introduced into the column 25 mm above the lower edge of the divider as shown in Figure 1.4. The bed could be emptied via a 381 mm diameter sidearm and ball valve located 50 mm above the distributor plate. Primary and auxiliary air were supplied by the building compressed air supply at 0.207 MPa. Their flows were measured by rotameters and regulated by globe valves as shown in Figure 1.2. The primary air could be heated by three 1.5 kW Watlow pipe heaters in series, each controlled by a Barber Coleman controller. The set points of these controllers were determined by the desired inlet gas temperature measured in the conical windbox. Bed and inlet gas temperatures were monitored by an L.E.D. display and a rotary selector switch. Pressures were measured using a manometer filled with blue indicating oil having a density 1.75 times that of water. The wafer retrieval screen, shown in Figure 1.2, was used only in the drying tests as it would have interfered with the wafer movement at the distributor plate during the circulation studies. The screen consisted of a semi-circle of fine wire mesh having an opening size of 12.7 mm. The mesh was cut and bent so that it occupied the entire cross-section of the bed (leaving a minimum clearance for ease of insertion and removal) and had a 12.7 mm lip around its circumference. The mesh was attached to stiff 3.2 mm diameter wire rods at each of its apices. These rods were then braced into position and joined together above the column to form a handle for removal of the screen. The design of the distributor plate is discussed in Section 1.3.1. 92 F I G U R E 2.5: Half-column prepared for the two-compartment bed tests (left - compart-ment 1; right - compartment 2). 93 TABLE 2.1: Properties of Inert Solids and of the Resultant Fluidized Beds at Minimum Fluidization and Minimum Bubbling. Ottawa Sand Polypropylene dp (mm) 0.497 0.549 PP (kg/m3) 2660 1011 Pbulk (kg/m3) 1549 638 Umf (m/s) 0.235 0.137 0.437 0.405 HS (m) 0.150 0.400 HMF (m) 0.157 0.424 &PBEDMF (Pa) 1457 2220 Umb (m/s) 0.244 0.137 Selection of Bed Materials Babailov and Petri (1974) showed that veneer drying times decreased with decreasing inert solids diameter. However, Burridge and Carruthers (1964) found that fine particles (smaller than 0.3 mm) adhered to the veneer during drying and increased the total drying time. The presence of inert solids on the dried wafers is extremely undesirable as this would greatly affect the machining properties of the final board product. An average particle diameter of approximately 0.5 mm was selected based on the above considerations. Two particle types, Ottawa sand and polypropylene, were chosen for the wafer handling studies. Table 1.1 presents the key physical and fluidization properties for these solids. Minimum fluidization was determined graphically as the intersection between the lines of constant pressure drop after fluidization of the bed occurred and rising bed pressure drop prior to fluidization. All tests were performed using an even pitch distributor plate having orifice diameters of 3 mm and an open area of 2.9%. Predicted fluidized bed properties presented in Table 1.2 are in reasonable agreement with the measured values obtained. 94 TABLE 2.2: Predicted Fiuidized Bed Properties. Ottawa Sand Polyethylene Reference1 (Grace, 1982) Ar 10510 5380 (8.1.3) Re m/ 6.99 3.77 (8.1.1) Umf (m/s) 0.223 0.109 (8.1.2) &PBEDmJ (Pa) 2300 2500 (8.1.8) Umb (m/s) 0.223 0.109 Ums (m/s) 0.387 0.239 Baeyens and Geldart (1974) numbers in parentheses refer to equation number in reference cited Although only the sand could be used for the subsequent drying tests, the wafer cir-culation experiments were also performed using the polypropylene particles since their density was considerably less than that of sand. It was reasoned that the reduction in the difference in densities between the emulsion phase and the wafers might improve wafer circulation. However, it should be noted that the cost and availability of a temperature-resistant material having an apparent density equivalent to polypropylene would likely make it impractical on an industrial scale. Wafer Circulation Tests The circulation of dry 25 mm X 32 mm x 0.63 mm wood wafers was studied in fiuidized beds of both sand and polypropylene at four excess velocities, U — Umf = 0.25, 0.50, 0.75 and 1.00 m/s. The wafer size was selected for these experiments because the larger wafers used in Chapter 1 (44 mm X 32 mm, and 63 mm X 32 mm) would have been unlikely to circulate freely in a 0.152 m diameter half-column. A wafer size smaller than 25 mm X 32 mm was deemed undesirable since it might not demonstrate the irretrievable sinking 95 behaviour observed for large plate-like objects (Nienow and Cheesman, 1980) and would not be comparable to the drying results for the smallest wafers in Chapter 1. Wet wafers were not used in the circulation studies because the solids stuck to the wet wafer surface. The static bed height was 0.15 m for all tests, resulting in an inventory of approximately 2.5 kg sand or 1 kg polypropylene charged to the column. In the highest excess velocity condition, a 1.0 m plexiglas extension was added to the column to provide an adequate transport disengagement height for the solids. In preliminary experimentation, it was observed that wafers in a fluidized bed of solids sank irretrievably at relatively low superficial velocities with an even pitch distributor plate, as also observed by Nienow and Cheesman (1980). However, in a spout-fluidized bed wafers were kept in circulation at lower superficial velocities than in a fluidized bed; both the spouting and fluidizing action appeared to be necessary to maintain the wafer circulation. It was also observed that the gross circulation pattern of the solids determined to a large extent the circulation of the wafers. Three types of distributor plates were thus designed to create different patterns of solids circulation in the fluidized bed (Ho et al., 1984; Feng et al., 1985). Table 1.3 describes the three distributor plates and their pressure drop measured at the different excess velocity conditions employed in the circulation experiments. The type 1 distributor was designed as a standard even pitch distribution plate. Types 2 and 3 were designed to stimulate bubble flow in the centre of the column and around its perimeter respectively. The type 2 distributor plate was adopted as a means of simulating the spout-fluid action that appeared promising in the preliminary wafer circulation experimentation. The open area of the three plates was kept nearly constant so that the orifice velocity would not be an additional variable. The differences in the measured pressure drops across the three types of plates at any excess velocity may have resulted from the location of the pressure tap with respect to the localized open area of the different distributor plates (Ho et ai, 1984). 96 TABLE 2.3: Distributor Plate Types and Measured Distributor Pressure Drops for the Superficial Velocities Used in the Circulation and Drying Experiments. Distributor Type 3 1 2 3 No. of orifices 43 42 41 Orifice diameter (mm) 3 3 3 Pitch even - 19mm (circular) (circular) centre1 - 13mm centre1 - 19mm perimeter1 - 19mm perimeter1 - 13mm Open area 2.88% 2.82% 2.75% centre - 61.9% centre - 24.4% Pressure Drop 2 for Velocities Used in Sand Experiments (Pa) Umf = 0.235 m/s 87.2 108.9 131 U - Umf = 0.25 m/s 392 392 414 U - Umf = 0.50 1003 1068 1177 U - Umf = 0.75 2267 2376 2654 U - Umf = 1.00 4773 5057 5710 Pressure Drop 2 for Velocities Used in Polypropylene Experiments (Pa) Umf = 0.137 m/s 21.8 43.6 109.0 U - Umf = 0.25 m/s 261 261 305 U - Umf = 0.50 741 785 828 U - Umf = 0.75 1700 1744 2027 U - Umf = 1.00 3531 3749 4250 ratio of areas for distributor plate zones having different pitches. Centre to perimeter = 1:2 for a static bed height of 0,15 m 97 Three sets of distributor plates of each design were manufactured. Two sets of plates having different orifice sizes of 3 mm and 7 mm were fabricated from 1.6 mm stainless steel. The distributor as installed in the fiuidized bed column consisted of an upper plate having the 3 mm orifices, a lower plate having the 7 mm orifices and a fine stainless steel mesh sandwiched between them to prevent the solids from falling into the windbox. The third set of distributor plates was made from 3.2 mm transparent polycarbonate and had 3 mm orifices. These plates were used to observe wafer movement at the bottom of the bed and at the distributor plate. Measurement and Analyses of Wafer Circulation At the start of each run, the primary air was adjusted to achieve the appropriate superficial velocity. A Sony Betamax video camera and recorder system focussed on the fiuidized bed was then turned on. Four brightly coloured wafers (yellow, pink, blue and striped) were dropped into the fiuidized bed while a stopwatch within the field of view was started. Each run was recorded for 5 minutes or until no wafers reappeared at the surface. At the end of each run the video camera was stopped, the stopwatch reset, and the wafers removed from the bed. The entire procedure was then repeated at the same velocity. Unusual circulation patterns or observations that might not be visible to the video camera were also noted. Since the brightly coloured wafers could only be observed as they appeared at the upper surface of the bubbling bed, the time between appearances of each coloured wafer at the bed surface was adopted as a quantitative measure of wafer circulation. The video tapes were analyzed at slow speed and the times of the first 100 wafer appearances at the bed surface were recorded from the stopwatch hanging beside the fiuidized bed column. The times between appearances were calculated for each coloured wafer and from these, the median time between appearances, and the times corresponding to the 75th and 90th percentiles were determined (Snedecor and Cochran, 1967). A normalized cumulative 98 frequency distribution curve (based on the F(t) residence time distribution curves described in Danckwerts (1953)) for the times between appearances was also constructed for each condition. Wafer Movement at the Distributor Plate From the wafer circulation tests it was found that at an excess velocity of 0.25 m/s, the wafers either circulated or disappeared into the bed depending on the design of the dis-tributor plate. To examine the movement and/or settling behaviour of the wafers in the fluidized bed, a series of runs was performed at U — Umf = 0.25 m/s using the plexiglas plates. Since the inclusion of the fine mesh in the distributor would block the view through the distributor, the solids were kept out of the windbox by starting up the flow of primary air into the empty column and then pouring in a premeasured quantity of inert solids. The video camera could not be positioned to record the bottom of the fluidized bed, so all observations on the coloured wafers' movements at the distributor were qualitative. At the end of each run the bed Was emptied through the sidearm before turning off the fluidizing air. Two-Compartment Bed Tests In these tests the fluidized bed column was converted into a two-compartment bed as shown in Figure 1.5. As in the experimental work of Pruden et al. (1976), the flow of auxiliary air into the compartment on the right (compartment 2) was calculated as a fraction of the volumetric flow of air through the distributor, i.e. of primary air. The auxiliary air entering compartment 2 causes bed density differences between the two compartments, resulting in a flow of sand from the denser bed in compartment 1 to the less dense bed in compartment 2 via the 51 mm gap below the divider. The increased bed height in compartment 2 causes the sand to flow over the divider and back into compartment 1. 99 Since the operating conditions required to circulate the sand and wafers were not known, the primary and auxiliary air flow rates needed to initiate the circulation of sand were experimentally determined first and then adjusted until a continuous circulation of wafers was obtained. Both the type 1 and type 2 distributor plates were used in these tests, the even pitch distributor because of its known bubbling characteristics and the type 2 distributor because of its ability to maintain wafer circulation at low excess superficial velocities. Since the wafers would ultimately be dried in sand, all tests were performed in a fiuidized bed of sand. Wafer Loading Capacity of a Fiuidized Bed The design of a continuous fiuidized bed dryer would require an estimate of the quantity of wafers that can be handled without disrupting the wafer circulation pattern or causing defluidization. Since the geometries of the 0.15 m half-column and the continuous fiuidized bed dryer would be different, this experiment would provide only a rough estimate of the wafer handling capacity of the continuous dryer. Using the distributor plate capable of operating at the lowest excess air velocity (type 2) and a static bed height of 0.150 m, the initial experimental conditions were U — Umf — 0.25 m/s with 10 wafers circulating in a fiuidized bed of sand. The wafer circulation was then observed at the other three superficial velocities before adding another 10 wafers. The addition of wafers was continued until the wafer circulation pattern was completely disrupted at each excess superficial velocity. Qualitative observations of the circulation pattern of wafers were recorded after each addition of ten wafers and after each change in superficial velocity. 100 2.3.2 Results and Discussion Wafer Handling The analysis of the video-taped wafer circulation experiments proved to be tedious and difficult. The brightly coloured wafers were often partly obscured by the solids when they reached the surface of the bed. The times between appearances of the wafers at the bed surface were also quite short, with the median time for wafers circulating in sand approximately 3.5 s. This required viewing for analysis to be done at a slow scanning speed, which caused a loss of resolution. The wafer-circulation-in-sand experiments were completely analyzed. However, the circulation studies performed in a fluidized bed of polypropylene particles could only be examined qualitatively. In the latter case, the wafers circulated faster and were more obscured at the bed surface, making quantitative analysis impossible. No circulation tests were performed for the polypropylene solids at U — Umf = 1.0 m/s because of the high elutriation rate of the particles. Wafer Circulation Patterns in a Fluidized Bed of Solids The wafer circulation patterns in a fluidized bed were influenced primarily by the design of the distributor plate. The excess superficial velocity also affected circulation. For U — Umf < 0.25 m/s the wafers sank irretrievably to the distributor plate. As the excess superficial velocity increased, a distinct wafer circulation pattern would emerge, depending on the distributor plate used. The wafer circulation patterns were best observed using the clear polycarbonate distributor plates and U — Umf ~ 0.25 m/s. The strongest wafer circulation pattern occurred with the Type 2 (pseudo-spout/fluid) distributor plate (Figure 1.6). The wafers appeared to swoop down to the distributor plate around the low open area perimeter and then slide horizontally along the plate to the high open area centre. Once at the centre of the plate, the wafers were entrained by bubbles. 101 (a) JA TT (b) t t t t t t t t t F I G U R E 2.6: Wafer circulation patterns at U - Umf = 0.25 m/s for (a) Type 2 and (b) Type 3 distributor plates. 102 Occasionally a wafer would descend on end towards the centre of the plate. Upon reaching the plate the wafer would tilt slightly and be entrained by bubbles. Figure 1.6(b) depicts the circulation pattern of wafers caused by the Type 3 (high open area near outer perimeter) distributor plate. The wafers could be seen penetrating the bed in the central region and then swooping toward the high open area perimeter where they were entrained by bubbles. The Type 1 or even pitch distributor plate produced the weakest circulation pattern. The wafers descended to the distributor plate in a random fashion, slightly favouring the flat front of the plate to the curved perimeter. The wafers sometimes migrated horizontally to the curved perimeter of the plate before they were entrained. The time-mean circulation pattern thus somewhat resembled that shown in Figure 1.6(b). In all cases, the wafers were observed to follow the gross circulation pattern of the emulsion phase. Ho et al. (1984) and Feng et al. (1985) observed that bubble movement (and thus solids movement) in the bed could be manipulated by changing distributor design. Feng et al. concluded that a distributor plate having regions of different orifice sizes caused horizontal solid circulation because of the non-uniform gas flow through the plate. Bemrose et al. (1985) demonstrated that large jetsam particles migrated to the area of the distributor plate having the highest rate of bubble flow and thus the greatest wake transport of solids. The circulation patterns of the wafers followed this behaviour for distributor Types 2 and 3. At an excess superficial velocity just high enough to keep the wafers in circulation, the wafers descended on edge to the distributor plate in the region of lowest bubbling activity and open area of the plate. The weak wafer circulation pattern observed for the even pitch distributor plate was probably due to the preferential coalescence of bubbles near the walls of the column. This resulted in a wafer circulation pattern roughly similar to that observed for the distributor having high open area around its perimeter (Type 3). 103 Wafer Circulation in a Fiuidized Bed of Sand The results of the detailed analysis of the videotapes of the wafer circulation in the fiu-idized bed of sand are presented in Table 1.4 and in Figures 1.7 and 1.8. Table 1.4 shows that for each distributor plate type, the median time between appearances of the wafer at the surface of the bed does not change with increasing excess superficial velocity, except for U — Umf = 1.0 m/s. In the latter, the median times are less than those for lower excess superficial velocities because the wafers did not remain on the distributor plate for as long before being lifted off and carried away by a bubble. As U — Umf was increased above 0.25 m/s, bubbles in the upper region of the bed probably coalesced to form slugs. Axial mixing in slugging beds is less than that in bubbling beds (Thiel and Potter, 1978) and thus it follows that the quantity of solids transported in slug wakes is less than that in bubble wakes at the same U — Umf. This changeover from bubbling to slugging could account for the unchanging wafer appearance times with increasing excess superifical veloc-ity (Table 2.4). This can be seen by comparing the 75th and 90th percentiles of the times between appearances of the wafer at the bed surface for U — Umf — 0.25, 0.50 and 0.75 m/s with those for U — Umj = 1.0 m/s. It should be noted that even for U — Umf — 1-0 m/s, wafers would occasionally remain on the distributor plate for at least 20 seconds regardless of plate type, as shown in Figure 1.7. It would appear that until the excess superficial velocity was high enough to create voids large enough to easily entrain wafers lying on the distributor plate, distributor types 2 and 3 cycled the wafers in approximately the same time. Figures 1.7(a) and (b) show that the distribution of times between appearances of the wafer at the bed surface for plate types 2 and 3 is similar for the short time intervals. However, the frequency of long time intervals is much greater for the Type 3 plate than for the Type 2 plate. The coalescence of bubbles over the central section of distributor type 2 made it more efficient at keeping the wafers in constant circulation than the type 3 plate. The high open area around the 104 TABLE 2.4: Times Between Apperances of Wafers at the Fluidized Bed Surface for the Wafer Circulation Studies in a Fluidized Bed of Sand. U Umf = 0.25 m/s Median (s) 95% Confidence Interval (s) 1 75th Percentile2 (s) 90th Percentile2 (s) U - Umf = 0.50 m/s Median (s) 95% Confidence Interval (s) 1 75th Percentile2 (s) 90th Percentile2 (s) U - Umf = Q.75 m/s Median (s) 95% Confidence Interval (s) 1 75th Percentile2 (s) 90th Percentile2 (s) U-Umf = 1.0 m/s Median (s) 95% Confidence Interval (s) 1 75th Percentile2 (s) 90th Percentile2 (s) Distributor Plate Type Run 1 Run 2 unable to sustain wafer circulation 3 (3,4) 6 12 3 (2,4) 5 8 2 (2,3) 5 8 3 (2,3) 5 10 3 (2,4) 5 9 3 (2,4) 5 8 Run 1 Run 2 5 (4,6) 8 14 5 (4,6) 9 12 4 (3,5) 8 16 3 (2,3) 6 9 4 (3,5) 6 9 4 (4,6) 7 12 5 (4,6) 8 14 3 (3,4) 6 9 Run 1 Run 2 unable to sustain wafer circulation 5 (5J) 11 26 5 (4,7) 9 18 4 (3,5) 10 14 6 (4,9) 13 28 4 4 (4,6) (3,5) 8 13 7 12 The 95% confidence interval for the median corresponded to the 40th and 60th observations in the 100 observations per run 75th and 90th percentiles are the times below which 75% and 90% (respectively) of the times between appearances fall. 105 0.80 0.60 0.40 0.20 0.0 0 5 10 15 20 25 30 TIME (s) (a) TIME (s) TIME (s) (b) (c) F I G U R E 2.7: Normalized cumulative frequency distributions of the times between appear-ances of wafers at the bed surface for different (U — Umf). (a) U - Umf = 0.50 m/s, (b) U - Umf = 0.75 m/s, and (c) U - Umf = 1.00 m/s. F(t) represents the fraction of total appearances with an appearance interval less than time t. 106 1.00 1 1 1 1 l - ,_ ' . - ._J__.J-- - 1 j,. 0.80 0.60 0.40 0.20 0.0 <7 / / !" Hi U-Umf o.so <«/• o:75 >Vi 1.00 ">/' 10 15 20 TIME (s) 25 30 (a) 1.00 0.80 0.60 0.40 0.20 0.0 r—1 1 1 1 1 1 __•<••• 1 " • ' 1 1 1 1 s —• ^~ • • : d 1 i'J « - « m f 0.25 "V« • 1 1 0.50 "V" 0.7S m/. .' / / 1.00 m/» ¥ V X \ X \ X I . I . I , 10 15 20 TIME (s) 25 30 1.00 0.80 0.60 0.40 0.20 0.0 "1 1 '-h 'If t, i x-!;; 0.50 m/« 0.75 "V« 1.00 -V" 10 15 20 TIME (s) 25 30 ( b ) (c) F I G U R E 2.8: Normalized cumulative frequency distributions of the times between appear-ances of wafers at the bed surface for the three different distributors. (a) type 1 - even pitch ; (b) type 2 - high open area centre; (c) type 3 - high open area perimeter. F(t) represents the fraction of total appearances with an appearance interval less than time t. 107 perimeter of the type 3 plate did not engender as strong a bubble flow pattern as the type 2 plate and thus the wafers remained on its surface longer than on the type 2 plate. The even pitch distributor plate had the shortest median time between appearances of the wafer at the bed surface and the narrowest distribution of times of the three plates at any excess superficial velocity (Figures 1.7(a), (b) and (c)). It is possible that the wafers descending on edge to the distributor plate were entrained by bubbles before they would flatten out horizontally next to the plate. The differences in the distributions of appearance times with different gas distributors appear to result primarily from differences in the lengths of time that wafers remain on the distributor plate before being entrained in the emulsion phase flow due to voids. This effect can be observed in Figure 2.7(c) for wafer circulation at (U — Umf = 1.0 m/s). Examination of the lower end of the normalized cumulative frequency distributions for the type 2 distributor plate in Figure 1.8(b) shows that the curve for U — Umf = 0.25 m/s has a narrower distribution of wafer appearance times around the median then for U — Umf = 0.5 or 0.75 m/s. The increase in superficial velocity caused a shift of the distributions for U — Umf = 0.5 and 0.75 m/s toward a shorter time interval than for U — Umf = 0.25 m/s, but apparently at the expense of the smooth circulation of the emulsion phase and the wafers. This is confirmed by an increased number of wafers sitting on the distributor plate before being entrained by bubbles, as indicated by the upper portions of the distribution curves for U — Umf — 0.5 and 0.75 m/s. As the smooth circulation breaks down with increasing (U — Umf), the distribution of times between appearances of the wafer at the bed surface around the median becomes wider, as shown by the decreasing slopes of the curves at the median. At an excess superficial velocity of 1.0 m/s, the wafers spend less time on the distributor plate (or even settling onto the distributor plate), and this led to the steep slope of the corresponding distribution curve in Figure 1.8(b). 108 The distribution curves for the even pitch distributor shown in Figure 1.8(a) reflect the decreasing frequency of wafers spending long periods of time on the distributor plate with increasing excess superficial velocity. The transition between smooth circulation and "stop and start" circulation for plate types 2 and 3 as shown in Figures 1.8(b) and (c) does not occur for the even pitch plate because of its already weak circulation pattern at U - Umf = 0.25 m/s. Predictions of wafer circulation in fiuidized beds using existing correlations for both large body and emulsion phase movement in fiuidized beds are presented in Appendix D. None of the models were successful in predicting wafer movement. Short Circuiting of the Wafer Circulation Pattern The type of inert solids used did not radically change the wafer circulation patterns dis-cussed in the previous section. However, some short circuiting was observed in the fiuidized polypropylene solids, whereby the wafers would penetrate a short distance into the bed and be caught by a rising bubble and returned immediately to the surface. The amount of short circuiting depended both on distributor plate type and excess superficial velocity. At U — Umf = 0.75 m/s no short circuiting was apparent. The type 2 distributor plate produced some short circuiting at U — Umf = 0.50 m/s. At U — Umf — 0.25 m/s short circuiting occurred for all plate types, especially for the type 2 plate and least for the type 3 plate. That one distributor design produced more short circuiting than another can be related to the different circulation patterns of the wafers. For the type 2 distributor, the centre of the bed bubbled vigorously, leaving only a small area around the perimeter for the wafers to descend to the plate. The large bubbles formed by coalescence in the upper part of the bed would often entrain wafers descending in the upper section of the bed. The type 3 distributor plate displayed the exact opposite pattern. The vigorous bubble flow occurred 109 primarily around the perimeter of the bed leaving a large central section of the bed for the wafers to descend to the plate unimpeded by the large bubbles at the walls of the column. The type 1 or even pitch distributor plate produced more short circuiting than the type 3 plate because of its weaker wafer circulation pattern. The area for wafer descent into the bed was not as well defined as for the type 3 plate, with the result that wafers descending too close to the perimeter of the bed were entrained by bubbles, before they could penetrate far into the bed. No short circuiting occurred for U — Umf > 0.75 m/s because the bubbling was too vigorous to produce a specific wafer circulation pattern. Instead, the wafers descended into the bed by falling through and around voids until reaching the relatively uniformly bubbling fluidization region near the distributor plate where they were entrained back to the surface. Short circuiting of the wafers occurred in the polypropylene bed, but not in the bed of sand, primarily because the difference in densities between the wafers and the emulsion phase was less for the polypropylene than for the sand. The wafers could move more freely in the polypropylene emulsion phase than in sand. In sand, the wafer was trapped in the descending emulsion phase and thus followed its circulation pattern through the bed. M i n i m u m Excess Superficial Velocity Required for Wafer Circulation The bubbling behaviour of the polypropylene solids appeared to be more violent than that of the sand at the same excess superficial velocity. Wafer circulation was maintained at U — Umf = 0.25 m/s for all distributor plate types for the polypropylene solids, while only a type 2 distributor plate could keep all the wafers circulating in a fiuidized bed of sand at this excess superficial velocity. Wafer circulation was tested at U — Umf = 0.1 m/s in the polypropylene solids. Although continuous wafer circulation was not attained with any of the three distributors, the interrupted circulation patterns observed were similar to those 110 observed in sand at U — Umf = 0.25 m/s. Baeyens and Geldart (1986) developed rough correlations according to which bubble size and the total fraction of solids (based on bubble volume) entrained by a bubble seemed to be greater in a bed of polypropylene than in sand. The ability of the polypropylene solids to maintain wafer circulation at a lower excess superficial velocity than sand thus results from the combined effects of particle density and bubbling behaviour. The larger bubbles formed in the bed of polypropylene solids are capable of entraining more solids in their wake and drift than is possible by the bubbles formed in sand. Furthermore, the fraction of solids that can be transported by a bubble in the bed of polypropylene particles is greater than that entrained by an equal sized bubble in a bed of sand because of the lower density of the polypropylene particles. The entrainment of the wafer in either the wake or drift of a bubble appears to be the dominant mechanism in lifting the wafer off the distributor plate. It has been postulated that a swarm of tiny bubbles is responsible for lifting a settled object off the distributor plate (Masson et al., 1983). The initial bubble diameter however is a function of the distributor plate design and the excess superficial velocity and is not expected to change with particle properties (Clift and Grace, 1985). Therefore, the initial bubble diameter cannot account for the observed differences in wafer circulation at low excess superficial velocities. Another possible mechanism for lifting the wafer off the distributor plate is the lifting force of the gas jet issuing from the distributor orifices. Since the mean orifice velocity was lower for the polypropylene particles than for the sand (Tables 1.5 and 1.6) this mechanism can also be discounted. It was originally thought that the wafers, upon reaching the distributor plate, caused localized defluidization, which in turn prevented the wafer from being lifted off the distribu-tor plate. However, at excess superficial velocities too low for maintaining wafer circulation, it was observed that the wafers would still move horizontally on the distributor plate to 111 TABLE 2.5: Predicted Fiuidized Bed Properties of Ottawa Sand for the Excess Superficial Velocities Used in the Wafer Circulation and Drying Experiments and a Static Bed Height of 0.150 m Ottawa Sand (dp U -= 0.497 mm) Reference (Equation No. 0.25 0.50 0.75 1.0 in Reference) Superficial Velocity (m/s) 0.485 0.735 0.985 1.235 Bed Height (m) 0.1867 0.202 0.213 0.222 Grace (1982) (8.1.47) Volume Fraction of Bed Occupied by Bubbles 0.159 0.223 0.264 0.293 Grace (1982) Fractional Bed Expansion 0.1891 0.287 0.359 0.414 Clift and Grace (1985) (3.63) Mean Gas Velocity Through a Distributor Orifice (m/s) 15.31 . 24.5 36.8 53.4 Grace (1982) (8.1.58) Initial Bubble Diameter (m) 0.00684 0.00903 0.01062 0.01191 Clift and Grace (1985) Darton et al. (1977) (Table 3.5) Average Bubble Diameter (m) (H/2) 0.0520 0.0724 0.0865 0.0973 Choi et al. (1988) (12) Maximum Stable Bubble Diameter (m) 14.75 14.75 14.75 14.75 Grace (1982) (8.1.36) Average Bubble Rise Velocity (m/s) (H/2) 0.757 1.099 1.405 1.694 Clift and Grace (1985) (3.11 and 3.51) Minimum Slugging Velocity (m/s) 2 0.387 0.387 0.387 0.387 Clift and Grace (1985) (3.70) Deviations from two phase theory were accounted for using a ratio of volumetric flowrate of bubbles to excess gas flow rate of 0.5 (Choi et al., 1988) The hydraulic bed diameter of 0.1023 m (Grace, 1982) (8.1.77) was used as the representative bed diameter 112 TABLE 2.6: Predicted Fluidized Bed Properties of Polypropylene for the Excess Superficial Velocities Used in the Wafer Circulation and Drying Experiments and a Static Bed Height of 0.150 m 1. Polypropylene (dp = 0.549 u-umf mm) Reference (Equation No. 0.10 0.25 0.50 0.75 in Reference) Superficial Velocity (m/s) 0.237 0.387 0.637 0.887 Bed Height (m) 0.1749 0.1891 0.205 0.216 Grace (1982) (8.1.47) Volume Fraction of Bed Occupied by Bubbles 0.0910 0.1590 0.224 0.264 Grace (1982) Fractional Bed Expansion 0.1001 0.1891 0.289 0.359 Clift and Grace (1985) (3.63) Mean Gas Velocity Through a Distributor Orifice (m/s) 7.22 - 12.49 21.0 31.9 Grace (1982) (8.1.58) Initial Bubble Diameter (m) 0.00474 0.00684 0.00903 0.01062 Clift and Grace (1985) Darton et al. (1977) (Table 3.5) Average Bubble Diameter (m) (H/2) 0.0316 0.0515 0.0723 0.0866 Choi et al. (1988) (12) Maximum Stable Bubble Diameter (m) 5.69 5.69 5.69 5.69 Grace (1982) (8.1.43) Average Bubble Rise Velocity (m/s) (H/2) 0.496 0.755 1.098 1.405 Clift and Grace (1985) (3.11 and 3.51) Minimum Slugging Velocity (m/s) 2 0.288 0.288 0.288 0.288 Clift and Grace (1985) (3.70) Deviations from two phase theory were accounted for using a ratio of volumetric fiowrate of bubbles to excess gas flow rate of 0.5 (Choi et ai, 1988) The hydraulic bed diameter of 0.1023 m (Grace, 1982) (8.1.77) was used as the representative bed diameter 113 areas of low bed pressure drop and then "shuffle" randomly in that area. This type of movement was also noted for large jetsam particles by Bemrose et al. (1984). There did not appear to be any defluidized solids associated with the settled wafers because they were constantly moving. Carter et al. (1987) observed that an accumulation of large jetsam particles in a bed of small particles gave rise to spouting action from the top of the jetsam pile. They attributed this phenomenon to the preferential flow of gas through the regions of the distributor covered by the jetsam particles. The piles of jetsam could only be dispersed by the entrainment of the particles from the surface of the pile after fluidization of the surrounding flotsam became sufficiently vigorous, and not by the action of the gas passing through the distributor. Carter et al. (1987) and Bemrose et al. (1984) also observed that the increased gas flow caused by the accumulation of jetsam in one region of the distributor plate drew more jetsam into the area, exacerbating the situation. The settled wafers in this work were observed to behave similarly to the accumulation of large jetsam particles. Not only did the settled wafers promote localized bubbling as they moved about the distributor plate, they also appeared to draw in wafers that had just descended to the distributor plate. Wafers could thus be retained by the distributor plate regardless of superficial velocity. Only nearby entrainment of emulsion phase by a bubble was able to lift settled wafers off the distributor plate. At high excess superficial velocities large bubbles entrained a sufficient quantity of the emulsion phase to pull wafers off the distributor plate. However, at low U — Umf the smaller bubbles were unable to lift the wafer off the plate. Chiba and Nienow (1984) developed a correlation to calculate the maximum diameter of a particle which can be lifted by a bubble wake based on the volume occupied by the 114 bubble wakes and the initial bubble diameter. Using their correlations 6(i7 - Umf)Abed 2 S DB,o = (2.1) DB,o (2.2) where dj = maximum diameter of jetsam particle lifted in bubble wake (m) fw = wake volume/wake and bubble volume DB,O = initial bubble diameter (m) Abed = cross-sectional area of the bed (m) n<i = number of orifices in distributor The maximum diameter of jetsam particle that could be lifted in a bubble wake was calculated to be 10.5 mm (fw = 1/3) at U — Umf — 0.25 m/s. This value is fairly close to the volume equivalent sphere wafer diameter of 9.9 mm. Since the correlation is based on the movement of a volume and not a mass of solids, the close agreement between the predicted object diameters and the volume equivalent sphere for a wafer may indicate that it is the volume of the object and not its density which is the major constraint to entrainment by a bubble wake. It is probable that the flat wafer shape also has some effect on its entrainment because it allows the wafer to lie flush against the distributor plate. Any upward pull on the prone wafer thus has to overcome additional initial drag before wafers orient themselves to more streamlined positions. Effect of Comparative Densities of Solids and Wafers As already noted, the wafers circulating in fluidized beds of sand followed the movements of the emulsion phase more closely than in beds of polypropylene particles. Furthermore, the eruptions of bubbles at the surface of the bed of sand lifted the wafers higher into the freeboard than the eruptions of bubbles in the polypropylene bed. These would appear to be the principal effects of the density differences between the solids and the wafers. 115 The other significant differences observed in the wafer circulation studies resulted from the different bubbling bed behaviour arising from the solids properties alone. Nienow and Cheesman (1980) showed that for U - Umf > 0.2 m/s, large fiat flotsam and jetsam displayed good mixing in a bed of 215 um sand. Rios et al. (1986) also showed that the density of the large spheres circulating in a bed of glass beads had little effect on sphere movement. Under vigorous fluidizing conditions it appears that the buoyancy of the wafer in the fiuidized bed is not an important factor in determining overall wafer circulation patterns. Circulation of Wafers in a Two-Compartment Fiuidized Bed The two-compartment bed (see Section 1.3.1 and Figures 2.4 and 2.5 for details) successfully circulated wafers between the two compartments having different excess superficial veloci-ties albeit for a very limited range of operating conditions. For the even pitch distributor plate, the sand was made to circulate around the compartment divider at U — Umf = 0.1 m/s in compartment 1 and U — Umf = 0.403 m/s (which includes an auxiliary flow that is 25% of the total primary air flow rate) in compartment 2. Although the circulation of sand was the smoothest observed in all subsequent tests with this distributor (as shown in Fig-ures 1.9(a), (b) and (c)), the wafers sank irretrievably to the distributor plate. As in the earlier wafer circulation tests, the even pitch distributor could not keep the wafers in cir-culation at U — Umf — 0.25 m/s (Figure 1.9(b)). An excess superficial velocity of 0.5 m/s caused slugging to occur in both compartments as shown in Figure 1.9(c). The erratic bed behaviour prevented a definite circulation pattern from being established. Both sand and wafers were tossed from compartment to compartment with the bursting of each slug at the bed surface. The movement of sand under the divider into compartment 2 was coun-teracted by the entrainment of sand by large bubbles or slugs rising in compartment 1, thus creating an uneven flow pattern. The influence of the bed in one compartment on the 1 1 6 (a) (b) (c) F I G U R E 2.9: The 2-compartment bed in operation at excess superficial velocities in com-partment 1 of (a) 0.1 m/s, (b) 0.25 m/s and (c) 0.5 m/s. The auxiliary air flow in compartment 2 was 25% that of the primary air flow. contents of the other compartment considerably limited the operation of this apparatus. This effect should be eliminated in a multicompartment (3 or more) system since adjacent beds would not be connected at both top and bottom. Good circulation of both sand and wafers was obtained using the type 2 distributor plate and an excess superficial velocity of 0.25 m/s. Four auxiliary air flow rates, 20%, 25%, 30% and 35% of the primary air, corresponding to excess superficial velocities in compartment 2 of 0.679, 0.727, 0.776 and 0.824 m/s, were tested. A minimum auxiliary air flow rate of about 20% of the primary air was needed to establish a definite sand circulation pattern at U — Umf = 0.25 m/s. Auxiliary air flow rates of 30% and 35% of the primary air flow rate created too much turbulence in compartment 2 (and thus in compartment 1) to produce an even circulation pattern. At U — Umf = 0.5 m/s, the circulation pattern broke down, as for the even pitch distributor tests at the same excess superficial velocity. The results of the wafer circulation tests for the two successful runs of the two-compartment bed are presented in Table 1.7 and in Figure 1.10. The two compartment circulation doubled the time between appearances of the wafers at the bed surface compared with the corresponding single compartment tests (Table 1.4). There does, however, appear to be a problem with lifting the wafers off the distributor plate as evidenced by the levelling off of the distributions presented in Figure 1.10 at F(t) « 0.85 to 0.90. Figure 1.10 also indicates that moderate changes of the excess superficial velocity in compartment 2 does not appreciably affect the circulation pattern of wafers. Although few experimental results were obtained for the two compartment bed, mul-tiple compartments appear to provide one method for increasing the residence times of wafers circulating in a fiuidized bed while approaching plug flow conditions. The single inlet for auxiliary air greatly hindered the development of even bubble flow in compart-ment 2. Separate windboxes for each compartment should stabilize the bubble pattern in compartment 2 and reduce the duration of wafers remaining on the distribution plate. 118 TIME (s) F I G U R E 2.10: Normalized cumulative frequency distribution of the times between appear-ances of wafers at the surface for compartment 2 for the 2-compartment fluidized bed for U - Umf = 0.25 m/s. F(t) represents the fraction of total appearances which have an appearance interval less than time t. 119 TABLE 2.7: Times Between Appearances of Wafers at the Fluidized Bed Surface in the Two-Compartment Fluidized Bed U - Umf = 0.25 m/s in Compartment 1. (u-umf) in Compartment 2 (m/s) 0.679 0.727 Median (s) 10 11 95% Confidence Interval (s) (9,13) (8,13) 75th Percentile (s) 15 19 90th Percentile (s) 47 57 Wafers that settle to the plate in compartment 1 migrate to compartment 2, as discussed previously and can then be entrained by the large bubbles which result from the increased excess superficial velocity. This effect did not occur in the present experimental setup because of the uneven bubble pattern caused by introducing the auxiliary air as a single jet 76 mm above the distributor plate. Despite the even pitch distribution plate, a stagnant zone of sand was created at the base of compartment 2 as demonstrated in Figures 1.9(a), (b) and (c). Other improvements to the apparatus would include a baffle above compartment 2 to direct the sand and wafers back into compartment 1 and an adjustable divider to allow the height of the opening (and thus the circulation rate of sand) to be adjusted (Kuramoto et at., 1986). Wafer Loading Capacity of a Fluidized Bed The capacity of a fluidized bed of sand to maintain good wafer circulation under conditions of high wafer loading appears to be quite limited, except at high excess superficial velocities. Table 1.8 summarizes the results of this set of experiments. At a low percentage of the total bed volume, the wafers began to interfere with the established circulation pattern. 120 TABLE 2.8: Wafer Loading Capacity for Fluidized Bed of Sand at Excess Velocities of 0.25, 0.50, 0.75 and 1.0 m/s. Number of Wafers U - Umf (m/s) Description of Changes in Bed Behaviour with Increasing Wafer Loading 0.25 0.50 0.75 1.0 Maximum for good wafer circulation 20 (0.566)2 60 (1.620) 80 (2.10) 4001 (9.56) Circulation pattern of wafers begins to break down. Downward wafer movement interferes with upward wafer movement. Wafers are getting stuck in clumps on distributor plate. Uneven bubbling and occasional channelling or slugging 60 (1.679) 80 (2.15) 120 (3.12) A layer or cap of wafers forms on the bed surface (consisting of ~ | to | of the wafers in the bed). The formation of the cap gives rise to slugging which breaks up cap to resume wafer circulation. Wafers sit longer on the distributor plate and are very slowly entrained by bubbles. 140 (3.83) 160 (4.21) 240 (6.05) Breakdown of circulation pattern-sand occasionally moves through the wafers until a slug breaks up the large wafer cap. 160 (4.36) 200 (5.20) 280 (6.99) Above approximately 240 wafers, it was not possible to defluidize the bed and then regain wafer circulation upon turning the supply air back on. Instead the sand fluidized between the immobile wafers. Numbers in parentheses are the percentage of total bed volume occupied by the wafers. Bed volumes for U - Umf = 0.25,0.50,0.75 and 1.0 m/s are 1.80 x 10~3, 1.87 X 10~3, 1.91 x 10~3 and 1.94 x 10~3 m 3 respectively. 121 The addition of more wafers eventually led to the formation of a cap of wafers on top of the bed which would inhibit bubble flow until a large bubble or slug would disperse the cap and allow circulation to resume. Clumps of wafers that settled onto the distributor plate caused temporary stagnant regions, often leading to the formation of a cap of wafers on the bed surface. The total breakdown of the wafer circulation in the bed was characterized by sand occasionally moving up through the wafers until a slug would disperse the large cap of wafers at the bed surface. It appears that the flotsam particles interfere with the bubbling behaviour of the jetsam by causing uneven bubble flow and emulsion phase movement. For future work, it is recommended that the quantity of wafers in the fiuidized bed of sand be restricted to approximately 2% of the bed volume. 1 2 2 2.4 Wafer Drying in a Fiuidized Bed of Inert Solids 2.4.1 Experimental Procedure Unlike the single wafer drying experiments described in Chapter 1, it was not possible to continuously monitor the weight loss of the wafer while it dried in the fiuidized bed. Although the most accurate method of establishing the wafer drying curves would have been to dry from saturation the same set of wafers for increasing periods of time, the procedure of resaturating the wafers after each drying test was considered to be too lengthy. An alternative method tested consisted of using the same wafer for the entire drying period. The wafer was removed from the fiuidized bed at specific times during the drying period, weighed and replaced in the bed to continue drying for a further interval. A major drawback to this method (besides being restricted to drying one wafer at a time) was that 30 s were required to remove each wafer from the bed, weigh it and replace it in the bed. These lengthy interruptions in the drying process negate the accuracy achieved by using the same wafer for all measurements. It was eventually decided to use a separate set of saturated wafers for each drying test. Preweighed wafers would be dried for a desired length of time, removed from the bed and weighed. A new set of preweighed saturated wafers would then be dried for a longer period of time than the previous set, removed from the bed and weighed. Removing the wafers from the bed using the wafer retrieval screen described in Section 1.3.1 and placing them into a weighing bottle required 6 s. The amount of water lost through drying in this time interval was established to be less than 2|% of the water lost for the drying time interval at the lowest drying temperature. This maximum error decreased with each increase in wafer drying time i.e. with the amount of water evaporated during each test. The experimental conditions for all the drying tests are listed in Table 1.9. A series of initial tests were performed to permit the total drying time at each fiuidized bed temper-123 TABLE 2.9: Experimental Conditions Used to Establish the Wafer Drying Curves for Wafers Dried by Immersion in a Fiuidized Bed of Sand and by Forced Convention. Temperature (°C) Superficial Velocity (m/s) Incremental Drying Times Used to Establish Wafer Drying Curves w Fiuidized Bed Drying 2 90 0.485 0.735 0.985 0, 30, 60, 90, 120, 150 0, 30, 60, 90, 120, 150 0, 30, 60, 90, 120, 150 120 0.485 0.735 0.985 0, 30, 45, 60, 75, 80, 90, 100 0, 30, 45, 60, 75, 90 0, 30, 45, 60, 75, 90 150 0.485 . 0.735 0.985 0, 10, 15, 25, 35, 45, 55, 60 0, 15, 25, 35, 45, 55, 60 0, 15, 25, 35, 45, 55, 60 Forced Convection Drying 3 150 0.485 0.735 0.985 0, 60, 120, 180, 210, 240 0, 60, 120, 150, 165, 180 0, 60, 90, 105, 120, 135, 150 A separate set of 5 wafers was used for each drying time. All sets of wafers were weighed prior to drying (time=0). Fiuidized bed drying in the 0.15 m half-column with a static bed height = 0.150 m. Forced air drying in an empty 0.15 m half-column. 124 ature to be estimated. The incremental drying times were then chosen based on the total drying times. The fluidized bed temperatures were selected to correspond to the drying temperatures in Chapter 1. The superficial velocities matched those used in the wafer circulation study except that the highest excess velocity in that study, U — Umf = 1.0 m/s, could not be achieved since the transport disengagement height of the sand particles ex-tended beyond the top of the stainless steel column. All drying tests were conducted with the type 2 (pseudo-spout/fluid) distributor plate since it was the only plate capable of circulating wafers at U — Umf = 0.25 m/s. Each set of wafers dried consisted of five wafers. Since the drying curves were to be constructed using the average moisture content for each set of wafers, fewer wafers per set would make each average less representative of the true wafer drying behaviour. A further restriction on the number of wafers per set was the method of controlling the drying temperature. Since it was desired to simulate continuous drying conditions and since only the inlet temperature of the drying gas could be controlled, the number of wafers dried at any time had to be kept to a minimum to avoid a significant drop in bed temperature upon inserting the wafers into the bed. A series of forced convection drying tests (Table 1.9) was also performed at 150°C for comparison with the fluidized bed drying results. In these experiments the wafers were placed in a 76 mm high covered basket made from 3.2 mm stainless steel wire mesh and placed inside the empty column next to the distributor plate. Drying tests for both fluidized bed and forced convection drying in the half-column followed the same procedure. The drying apparatus was equilibrated at the test conditions. The set of preweighed saturated wafers was dropped into the column as the stopwatch was started. After the desired time interval had elapsed, the wafers were removed from the apparatus using either the wafer retrieval screen or by pulling out the covered basket. The five wafers were quickly placed in a preweighed bottle, which was then sealed and weighed. 125 This routine was repeated for each incremental drying time. All sets of wafers were then ovendried and weighed so that the average moisture content attained after each incremental drying time could be calculated. The drying experiments were replicated for each set of experimental conditions. The analysis of the drying curves produced from these experiments was less rigorous than that for the single wafer tests in Chapter 1 because of the limited number and precision of the data points. The need to remove the initial wafer weight discrepancies between sets of wafers by expressing the changes in weight during drying on a fractional moisture content basis also reduced the accuracy. Since both the experimental and analytical methods used for establishing the drying curves were not of high precision, it was decided that the least biased method of determining the drying rate curves for these data would be to perform a least-squares curve-fit on the data. The resultant drying rate curves calculated from the derivatives of the drying curve equations would have the correct magnitude but possibly not the appropriate shape of curve (since this depends heavily on the type of equation used to fit the drying curve). 2.4.2 Wafer Drying in a Small Fiuidized Bed of Sand The data obtained in the semi-cylindrical column used to determine wafer drying curves at each drying temperature (90°C, 120°C and 150°C) are plotted in Figures 1.11, 1.12 and 1.13 respectively. It is seen that the excess superficial velocity does not appear to affect the drying behaviour of the wafers. Although these results could indicate that drying was controlled by internal mechanisms, it is also possible that the external transfer coefficients were constant over the range of superficial velocities studied. Previous research on heat and mass transfer to an immersed sphere moving freely in a fiuidized bed of solids (Cobbinah et al., 1987; Coelho and Guedes de Carvalho, 1988; Prins et al, 1985 and 1987; Rios and Gibert, 1984) has shown that for U — Umf > 0.2 m/s heat and mass transfer coefficients 126 TIME (s) F I G U R E 2.11: Drying curve for wafers dried in a fluidized bed of 0.497 mm sand at 90°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. 0 20 40 60 80 100 120 TIME (s) F I G U R E 2.12: Drying curve for wafers dried in a fluidized bed of 0.497 mm sand at 120°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. 0 10 20 30 40 50 60 70 TIME (s) F I G U R E 2.13: Drying curve for wafers dried in a fluidized bed of 0.497 mm sand at 150°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. are constant. Babailov and Petri (1974) showed that the external heat transfer rate to thin veneers dried in fiuidized bed of slag particles had a dominant effect on drying rate. It is postulated that wafer drying in a fiuidized bed of sand exhibits a similar dependence on external heat transfer. Figures 1.11 to 1.13 also show the drying curves obtained by least square fitting of the data at each drying temperature to a function of the form, m = a + be~ct. The equations fitted to the data are presented in Appendix E. The r 2 for all three curves was greater than 0.997. However, the 95% confidence limits shown for each curve provide a more accurate measure of the goodness of fit. Figure 1.14 presents data and drying curves for each drying temperature. Figure 1.15 shows drying rate curves calculated from the drying curves in Figure 1.14. Although the linear drying rate curves result from using an exponential curvefit for the drying curves, it can be assumed that the drying rate curves should be nearly linear to at least 30-40% moisture content. The linearity of the drying rate curves and uniform increase in drying rate with drying temperature suggest that the rate of external heat transfer to the wafer limited drying, as in the decreased wetted surface area drying described by Treybal (1980). Appendix F compares the experimental drying times and rates with published correla-tions. Table 1.10 presents the transfer coefficients calculated by the correlations of Prins et al. (1986) and Cobbinah et al. (1987) and compares the predicted initial drying rates with the wafer drying rates at or near saturation (200% moisture content). The correlations of Prins et al. (1985,1986) combine to predict drying rates that are quite close to the ex-perimentally measured values. The drying rates predicted by the correlations of Cobbinah et al. (1987) are approximately | of the experimental results. The unusually low values for the fiuidized bed heat transfer coefficients cause the under-predictions. Unfortunately, none of the experimental drying results used to determine their heat transfer coefficients are presented in their paper, and thus no explanation for the low values can be given. 130 2 4 0 1 — i — r — i — i — i — i — i — r 40 80 120 160 TIME (s) F I G U R E 2.14: Comparison of the fitted drying curves for wafers dried in a fiuidized bed of 0.497 mm sand at 90°C, 120°C and 150°C. 131 F I G U R E 2.15: Calculated drying rate curves for the wafers dried in fluidized bed of 0.497 mm sand at 90°C, 120°C and 150°C. 132 TABLE 2.10: Predicted1 and Experimental Drying Rates for a Saturated Wafer Dried in a Fluidized Bed of 0.497 mm Sand. Drying Temperatures (°C) 90 120 150 Prins et al. Cobbinah et al. Prins et al. Cobbinah et al. Prins et al. Cobbinah et al. Archimedes Number 6823 6823 5629 5629 4725 4725 Reynolds Number (At Umf) 9.43 9.43 8.25 8.25 7.29 7.29 Total Heat Transfer Coefficient (W/m2 C ) 1 277.0 65.0 290.0 68.0 303.0 71.1 Mass Transfer Coefficient (kg/m 2-AH) 1 0.0341 0.0507 0.0319 0.0507 0.0292 0.0507 Predicted Surface Temperature CC) 1 57.0 35.9 66.8 41.9 74.4 46.8 Predicted Initial Drying Rate (kg/m^s) 1 4.01 1.51 6.85 2.29 10.27 3.17 Wafer Drying Rate at 200% Moisture Content (g/m2,s) 3.91 6.40 9.10 Predicted values were based on a sphere having an equivalent surface area of a single wafer. The characteristic length used in all equations was thus a sphere diameter of 23.2 mm 133 Prins et al. (1986) performed a large number of experiments (in excess of 1000) to develop their correlations. Their experimental values agreed well with previously published values for heat transfer to immersed objects (both fixed and freely moving). The success of their correlations in predicting the saturated wafer drying rate confirms the earlier discussion on the independence of heat transfer from excess superficial velocity. Forced Convection versus Fiuidized Bed Drying of Wafers The drying data and calculated drying curves for the forced convection drying of wafers in the empty 0.15 m half-column are presented in Figures 1.16, 1.17 and 1.18 and in Appendix E. It is interesting to note that even though r 2 > 0.996 for each of the fitted exponential curves, the 95% confidence limits are much wider than those obtained for the fiuidized bed drying curves. This results from the smaller number of observations used for fitting the forced-convection curves and from the greater variability in the data than in the fiuidized bed wafer drying tests. The wafers were observed to move rapidly about the 75 mm high wire enclosure throughout the empty column drying. It was originally intended to compare the results of these tests with the fiuidized bed tests at the same drying temperature and superficial velocities. However, it was felt that the superficial or mean velocities did not characterize the velocities of the gas medium experienced by the wafers in the empty column. Since the basket was positioned on top of the distributor plate, the orifice velocities would influence the velocity of air contacting the wafers more than the superficial velocity. The actual velocity of the air contacting the wafer would be between the superficial velocities of 0.49, 0.73 and 0.99 m/s and the corresponding orifice velocities of 15.3, 25 and 37 m/s. Appendix F presents the prediction of the saturated wafer drying rate for both sets of velocities. The correlations of Molstad et al. (1938) for heat and mass transfer for an air stream perpendicular to a free water surface were used in these calculations. These correlations are often used in calculating 134 240 200 A \ z LJ \ \ NT ; \ \ \ \ \ o 160 o ~\ \ v * \ N • \ \ o x Ld Cd \ \ v IST 120 o \ Y \ \ ENT 80 \ \ a \ l_d 40 \ Q_ — \ \ \ \ \ \ \ 8 \ \ 60 120 180 240 TIME (s) 300 F I G U R E 2.16: Drying curve for wafers dried by forced convection in the empty 0.15 m half-column at a superficial velocity of 0.49 m/s and a temperature of 150°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. 240 TIME (s) F I G U R E 2.17: Drying curve for wafers dried by forced convection in the empty 0.15 m half-column at a superficial velocity of 0.73 m/s and a temperature of 150°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. 0 30 60 90 120 150 180 TIME (s) F I G U R E 2.18: Drying curve for wafers dried by forced convection in the empty 0.15 m half-column at a superficial velocity of 0.99 m/s and a temperature of 150°C. Each point represents an average of 5 wafers. Dashed lines represent the 95% confidence limits of the fitted exponential curve. TABLE 2.11: Predicted and Experimental Drying Rates for a Saturated Wafer Dried in the Empty 0.15 m Diameter Half-Column. Predicted Predicted Experimental Wafer Mean Drying Rate Orifice Drying Rate Drying Rate at 200% Velocity Based on Mean Velocity Based on Orifice Moisture Content Velocities Velocities (m/s) (g/m2- s) (m/s) (g/m2- s) (g/m2- s) 0.485 1.19 15.3 3.26 2.51 0.735 1.33 24.5 3.81 2.77 0.985 1.44 36.8 4.36 3.33 the volumetric heat transfer coefficient in rotary dryers. However, it should be noted that they were developed for air velocities of approximately 1-5 m/s. Their use to predict the saturated wafer drying rate is thus questionable and results only from the lack of more suitable correlations. Although radiative heat transfer is included in the calculations, the shape factors used were developed for the single saturated wafer drying rate predictions presented in Appendix A. Table 1.11 compares the results of the predictions using the different velocities to esti-mate heat and mass transfer coefficients. The use of orifice velocities in the predictions pro-duced results closer to the experimental values than did the mean velocities. Figures 1.19 and 1.20 compare the drying curves and drying rate curves respectively, for wafers dried at 150°C for the three mean velocities. These curves only provide a rough approximation of the drying behaviour of wafers at high velocities and at 150°C. Table 1.12 compares the drying times of wafers from 125% to 3% moisture content for all the half-column drying ex-periments. At 150°C, the fiuidized bed of sand dries the wafers more than twice as quickly as forced convection at a mean velocity of 0.99 m/s. Drying times in the fiuidized beds 138 TABLE 2.12: A Comparison of Wafer Drying Times from 125% to 3% Moisture Content for Wafers Dried by Forced Air Convection and by a Fluidized Bed of Sand. Drying Time From 125% to 3% Moisture Content (s) Fluidized Bed at Superficial Velocities of 0.485, 0.735 and 0.985 m/s Bed Temperature (°C) 90 147 120 81.4 150 51.5 Forced Convection at 150°C Mean Velocity (m/s) 0.485 185 0.735 141 0.985 109 139 0 60 120 180 240 300 TIME (s) F I G U R E 2.19: Comparison of fitted drying curves for wafers dried by forced convection in the empty 0.15 m half-column at mean velocities of 0.49, 0.73 and 0.99 m/s and a temperature of 150°C. 140 F I G U R E 2 . 2 0 : D r y i n g r a t e c u r v e s f o r w a f e r s d r i e d b y f o r c e d c o n v e c t i o n i n t h e e m p t y 0 . 1 5 m h a l f - c o l u m n a t m e a n v e l o c i t i e s o f 0 . 4 9 , 0 . 7 3 a n d 0 . 9 9 m / s a n d a t e m p e r a t u r e o f 150°C. 141 operating at 90°C are approximately equivalent to those in the empty column at 150°C at a mean velocity of 0.73 m/s. The differences in drying behaviour between the fluidized bed and forced convection air drying are well illustrated in Figure 1.21. The initial wafer drying rate is approximately three times higher in the fluidized bed, corresponding to the threefold difference in the total heat transfer coefficient between the two methods of drying, namely 95.9 and 303 W/m2oC for forced convection and fluidized bed drying, respectively (Appendix F). 142 CO « « « E 12.0 10.0 O) L d I— < o ct: 8.0 6.0 4.0 2.0 -0.0 FLUIDIZED BEO AT 150 C FORCED CONVECTION AT 150 C & 0.985m/« 40 80 120 160 200 PERCENT MOISTURE CONTENT F I G U R E 2.21: Comparison of the calculated drying rate curves for wafers dried at 150°C in fluidized bed of 0.5 mm sand by forced convection at mean velocity of 0.99 m/s. 143 2.5 Summary and Conclusions 2.5.1 Wafer Handling in a Fiuidized Bed of Solids The circulation of wafers in a fiuidized bed of particulate solids was found to depend on the bubbling behaviour of the bed. The ability of a bubble to lift wafers off the grid depended on the volume of solids that could be entrained in its wake and drift and not on the relative densities of the wafers and the emulsion phase. The density difference between the wafers and the emulsion phase did not greatly affect wafer circulation. The light polypropylene particles did not restrict the radial movement of the wafers in the downward moving emulsion phase as much as the sand did and thus the wafers were occasionally entrained by passing bubbles in the bed of polypropylene particles. This short-circuiting of the wafer circulation pattern disappeared with increasing excess superficial velocity. Short-circuiting was linked both to the density difference between the wafers and the solids and to the bubble flow pattern. No wafer short-circuiting was observed in the fiuidized bed of sand. The effect of distributor design on circulation of the emulsion phase was strongest at an excess superficial velocity of 0.25 m/s for a fiuidized bed of sand. A distributor plate with regions of differing free open area resulted in a solids flow along the distributor from the low to the high open area region. Movement of solids across the dual open area distributor plate led to alignment of the wafers flush against the plate as they migrated over the plate. Once flush with the distributor, their flat shape hindered their entrainment by bubbles. Wafers on the distributor plate acted like large jetsam particles (Carter et ai, 1987), creating localized bubbling which in turn attracted and demobilized more wafers. Only a distributor plate with a high centre open area could keep the wafers in continuous circulation at U — Umf = 0.25 m/s. Coalescence of bubbles in the centre of the bed resulted in pronounced solids movement by wake and drift transport, exerting a sufficient updraught 144 to lift the wafers off the distributor plate. Increasing the excess superficial velocity above 0.25 m/s caused the solids circulation pattern to be less uniform, as the solids movement was increasingly interrupted by rising bubbles. The disjointed flow of the emulsion phase caused the wafer circulation throughout the bed to become more erratic and the wafers to become temporarily trapped on the distributor plate more frequently than at U — Umf = 0.25 m/s. However, at U — Umf > 0.25 m/s, the bubble flow in the bed of sand was high enough (regardless of distributor design) to prevent permanent settling of the wafers on the grid. The even pitch distributor design was superior to the dual open area distributor designs in maintaining uniform wafer circulation because it did not have a strong solids circulation pattern. This was a disadvantage at U — Umj = 0.25 m/s because the bubbles were not large enough to lift settled wafers off the distributor plate. However, at U — Umf > 0.25 m/s, the relatively even bubble flow prevented the flow of solids across the distributor so that wafers were entrained by bubbles before they settled onto the distributor. Increases in the excess superficial velocity from 0.50 m/s to 1.00 m/s did not result in an increase in wafer circulation rate. Slugging may have developed in the upper half of the bed which in turn limited the upward transport of solids and thus the wafers. Although the wafer circulation rates agreed with published experimental values for large body motion in fluidized beds of solids, wafer circulation rates could not be predicted accurately using correlations from the literature. Preliminary experimentation has shown that a two-compartment column is a viable method of controlling the wafer residence time in a fluidized bed. Unfortunately the prim-itive nature of the equipment did not allow an in-depth study of the effect of auxiliary air flow rate on the wafer circulation rate through the two compartments. The maximum volume of wafers that can be accommodated by a fluidized bed without 145 grossly affecting the quality of fluidization has been determined to be approximately 2% of the total bed volume. At higher loadings the wafers cause discontinuities in the emulsion phase which result in uneven bubbling behaviour. Further increases in loading (above 4% of the total bed volume) lead to the formation of a cap of wafers on top of the bed and eventual breakdown of the emulsion phase circulation. Wafer Drying in a Fiuidized Bed of Sand Wafer drying in a fiuidized bed of sand was shown to be independent of excess superficial velocity. It was postulated that this effect resulted not from internal mechanisms con-trolling drying but from the external transfer coefficients being constant over the range of U — Umf studied. This was evidenced by the linearity of the drying rate curves and the uniform increase in drying rates with drying temperature. The wafer drying rates at or near saturation were accurately predicted using the heat and mass transfer correlations developed by Prins et al. (1985,1986). Wafer drying times in a fiuidized bed of sand were approximately 40% of drying times for wafers dried by forced convection of air at the same temperature and a superficial velocity of 0.99 m/s. The threefold increase in the drying rate of wafers at or near saturation dried in the fiuidized bed of sand at 150°C compared with wafers dried by forced convection at a superficial velocity of 0.99 m/s at the same temperature was attributed to the difference in external heat transfer coefficients. Predictions of the saturated wafer drying rate for each method of drying showed that the heat transfer coefficient of the fiuidized bed was approximately three times that for forced convection of air. 146 Chapter 3 Design and Development of an Experimental Continuous Dryer The goal of this segment of the research was to incorporate the knowledge developed in Chapter 2 of wafer drying and handling in fiuidized beds into the construction of an experimental continuous fiuidized bed wafer dryer. This dryer was designed not only to demonstrate the feasibility of fiuidized bed wafer drying but also to investigate the dryer configuration. The scope of this work was limited in that the scale of the dryer was of necessity small compared to the envisaged industrial process. Much smaller wafers than for the manufacture of waferboard (20 mm vs. 75 mm+) were used and thus scale-up to an industrial sized dryer might require additional exploratory work on full-sized equipment. The configuration of an industrial fiuidized wafer dryer and the anticipated scale-up problems are discussed in Chapter 4. 147 3.1 Initial Design and Construction The experimental dryer was designed to operate at a maximum fluidized bed temperature of 150°C. The experimental drying curve for wafers dried in a fluidized bed operating at 150°C (Section 2.4.2) the total drying time from 90% (the approximate average moisture content for wafers used) to 3% moisture content was approximately 42 s (see Figure 3.1). To obtain this residence time in the dryer, a multiple compartment drying chamber was conceived based on the two compartment bed circulation work in Section 2.3.2. In Section 2.3.2 wafers circulated a total distance of 0.51 m (down compartment 1 and up compartment 2) in a median time of 10 s. A wafer residence time of 42 s therefore requires a path length of approximately 2.1 m, assuming the same circulation rate as in the small two-compartment bed. The design of the experimental dryer involved modification of an existing rectangular stainless steel fluidization column (0.25 X 0.43 x 3.0 m high) used previously by George (1980) to have four compartments of equal cross-sectional area. Figure 3.2 depicts the four compartment drying chamber and the caption describes the flow of sand and wafers through it. The overflow of sand from compartment 2 into compartment 3 and from 4 into 1, coupled with the denser fluidized beds in compartments 1 and 3 than in 2 and 4 (resulting from lower superficial velocities), ensures that the pressure heads in compartments 1 and 3 are always greater than in compartments 2 and 4. This causes the sand to circulate. 3.1.1 D r y i n g Chamber The existing fluidization column was selected for modification because of its relatively large cross-sectional area (0.11 m2) and its stainless steel (Type 316L) construction. Figures 3.3 and 3.4 present scaled drawings of the column after addition of 6.3 mm holes and cou-plings required for the instrumentation of each compartment and holes needed to fix the internal dividers into position. Figure 3.3 shows the positions available for pressure taps 148 I • I ' I ' I ' I ' I 1 I 0 10 20 30 40 50 60 70 TIME (s) F I G U R E 3.1: Estimated time for drying wafers from 90% to 3% moisture content based on the experimental drying curve for wafers dried in a fluidized bed of 0.5 mm sand at 150°C. C O M P A R T M E N T 3 COMPARTMENT 2 F I G U R E 3.2: Three dimensional representation of continuous fiuidized bed wafer dryer. Green wafers are fed into compartment 1 and then follow the flow of sand through the col-umn: under the compartment divider into compartment 2; over the divider into compart-ment 3; under the divider into compartment 4; and, over the divider back into compartment 1 where the dried wafers are removed and the sand repeats the cycle. 150 i 2 3 * 3 2 o o o o 1 © 2 3 3 2 o o 1 © o A 2 3 ° 3 2 4 2 3 3 2 O O J o o 4 2 3 ° 3 2 4 2 3 3 2 O O J O o 2 3 ° 3 2 F I G U R E 3.3: Scaled drawing of a 0.43 m side of the fluidization column. This drawing shows the positions of the removable sideplates (l); pressure taps (2); ther-mocouples (3); holes for fixing the internal dividers into position (4); and the device for emptying the column (A). Opposite side is identical. 151 B B O 0.1m B B F I G U R E 3.4: Scaled drawings of the two 0.25 m sides of the fluidization column. This drawings shows the positions of the tempered glass windows (B); the port for emptying the column (A); and the holes for fixing the internal dividers into place. 152 and thermocouples, the first pair of taps in each compartment being 38 mm above the distribution plate, the next pair 102 mm and the remaining 9 pairs at intervals of 190 mm to a maximum height of 1.81 m above the distributor. All thermocouples were 6.3 mm, ungrounded Type K thermocouples. The temperatures in each compartment were sampled and recorded every 12 s by an AT&T X T compatible computer equipped with a Dash-8 A/D board. To minimize the number of modifications as well as to preserve the integrity of the column, the wafer feed and removal unit was designed to fit into the positions occupied by the removable plates on a 0.43 m side of the column. This allowed the bed height to be changed from 0.65 m to 1.41 m, providing ample bed height in each compartment to satisfy the 2.1 m long pathway through the dryer. The distributor from the existing column consisted of two 316L stainless steel plates with a 400 mesh stainless steel screen sandwiched between them. Each plate had 288 holes drilled on an even 25 mm pitch. The upper 13 mm thick plate had 3.4 mm holes providing a total open area of 2.4%, while the lower 7.5 mm thick plate had 6.8 mm holes for an open area of 9.6%. The wafer circulation experiments using different types of distributor plates (Chapter 2) showed that an even pitch distributor was best for keeping the wafers in circulation. Since the existing distributor plate had an even pitch it was used with only minor modifications. A detailed discussion of the construction of the four compartment column and windbox can be found in Appendix G. 3.1.2 Wafer Feed and Removal Unit Both the wafer feed and removal unit had to fit into the 0.18 m x 0.3 m opening in compartment 1 (originally covered by the lowest sideplate on the column). The resulting novel design incorporated a metering bin for the wet wafers and a vibrating screen inside 153 compartment 1 to separate sand from the wafers. Figure 3.5 is a scaled drawing of the wafer feed and removal unit. Photographs of the entire unit and the wafer removal screen appear in Figure 3.6(a) and (b) respectively. 3.1.3 Wafer Feed System Since the wet wafers did not flow, the feed system was patterned after a MacMillan Bloedel picker-roll type former used in the production of the waferboard mat prior to pressing. Referring to Figure 3.5, wet wafers were fed into rotary valve (A) and accumulated in the green wafer storage bin (C). The wet wafers moved along the apron belt (B) toward the fiuidized bed. A series of rotating rakes (D) reduced the pile of wafers to a height of 25 mm as the apron belt proceeded toward compartment 1. The thin mat of wet wafers passed underneath the wafer removal system and fell off the apron belt into compartment 1 just below the vibrating screen (N). 3.1.4 Wafer Removal System The sand and dried wafers overflowed from compartment 4 into compartment 1 and were directed by a baffle (M) away from the column walls onto a vibrating stainless steel screen (N) with 3 mm openings. The 0.21 m X 0.18 m screen sloped downward at a 15° angle removed the wafers from compartment 1 into the upper section of the wafer feed and removal unit. Upon reaching the end of the vibrating screen, the wafers fell onto a vibrating mesh (3 mm openings) chute (at a 15° slope) (O) that transferred the wafers to the side of the unit and into the output rotary valve (P). The sand removed from the wafers on the vibrating screen was returned to compartment 1 via a baffle (Q) below the screen. The sand removed from the wafers on the vibrating chute fell onto the green wafer mat and was returned to compartment 1 with the freshly fed wafers. 154 TOP VIEW SIDE VIEW F I G U R E 3.5: Wafer feed and removal unit for the continuous fluidized bed wafer dryer. A - rotary valve to wafer storage bin; B - apron belt conveyor; C - green wafer storage bin; D - wafer rake back; E , G , I, K - compartments 1 to 4 respectively; F ,H,J ,L - compartment dividers; M - baffle to direct sand and wafers; N - vibrating screen; O - vibrating chute; P - wafer output rotary valve; Q - slide for sand passing through N; 1 - wafer pile moves towards fluidized bed on the apron belt and is formed into a thin mat of wafers by the rake back; 2 - wafers fall off apron belt into compartment 1; 3 - dried wafers and sand from compartment 4 overflow into compartment 1; 4 - dried wafers move along vibrating screen to chute 'O'; 5 - sand passes through vibrating screen, hits Q, and then mixes again with the incoming green wafers. 155 FIGURE 3.6: The wafer feed and removal unit (a), the wafer removal screen (b). 156 Full details of the fabrication and calibration of the wafer feed and removal unit are presented in Appendix H. 3.1.5 Air Supply and Control Since the four compartments of the dryer were operated at different superficial velocities, the air supply to each compartment had to be independently controlled. Air was supplied by the building compressor at 0.45 MPa capable of producing a flow rate of 0.095 m3/s at standard conditions. A regulator reduced the air pressure to 0.136 MPa before the air flowed into a manifold which split it into four equal streams which were fed to 38 mm copper piping. A 6.3 mm fitting was installed in the piping between the regulator and the manifold to provide air pressure feedback for a Mercoid low air pressure safety switch. Each stream of air passed through an orifice meter with corner taps and standard square edged orifice plates having an orifice diameter of 24.8 mm (Crane, 1987). Since the orifice meters were located 0.8 m downstream from the manifold, straightening vanes were placed in the pipes 0.74 m upstream from the meters. The pressure drop across each meter was measured using a 1.0 m long manometer filled with coloured water. The air flows were controlled by 38 mm globe valves located 0.18 m downstream from the orifice meters (Boucher and Alves, 1984). 3.1.6 Heat Supply and Control The heat requirements for each compartment differed according to the superficial veloc-ity and evaporative load in the compartment. Appendix I presents the calculation of the estimated heating requirements for each compartment. Total heat requirements were calculated to be 13.1 kW, 3.9 kW, 6.3 kW and 4.2 kW for compartments 1 through 4 respectively. The corresponding windbox temperatures at maximum load were determined to be 767°C, 162°C, 376°C and 174°C. Since the calculated energy requirements are at best rough estimates, all heaters were 157 oversized. Each compartment had a heater comprised of 3 - 3 kW Kanthal "porcupine" electrical elements arranged as shown in Figure 3.7. The heating requirements for com-partment 1 exceeded the capacity of the 9 kW heaters as well as the maximum operating temperature of the "porcupine" heating elements (about 600°C). A booster heater (Fig-ure 3.8) consisting of 2 sets of 5 silicon carbide elements connected in series was designed to provide an additional 4.4 kW and was capable of operating at temperatures greater than 600°C. Figure 3.9 shows the arrangement of the heaters around the windbox of the dryer. Design details of both types of heaters may be found in Appendix I. Each of the three "porcupine" elements in the 9 kW heater was controlled individually and thus could be turned on or off as needed. In the heaters for compartments 2, 3 and 4, two of the elements were controlled by on-off switches, while the third element was controlled by an Omega CN310 on/off controller. For compartment 1, all three porcupine elements were operated by on/off switches and the two sets of silicon carbide elements in the booster heater were linked to controllers. Feedback for each controller was from a thermocouple located 0.28 m above the distributor in each compartment. In the case of a drop in air pressure to below 0.122 MPa (3 psig) as detected by an in-line Mercoid low pressure safety switch the power to all heaters and to the motors on the feed and removal unit would be shut off. 158 SIDE VIEW F I G U R E 3.7: Scaled diagrams of the compartment 3 9 kW porcupine element heater. 159 TOP VIEW FIGURE 3.8: Scaled diagram of 4.4 W silicon carbide element heater for compartment 1. 160 '(b) F I G U R E 3.9: Arrangement of "Porcupine" element 9 kW heaters and booster heater around windbox of dryer. (a) foreground - compartment 2 - heater, background — compartment 1 - heaters; (b) left bottom - compartment 4 heater, left top - compartment 3 heater. 161 T A B L E 3.1: Properties of Sand and Copper Slag Particles and Their Respective Fluidized Bed Characteristics at U m / 1 . Sand Copper Slag dp (mm) 0.397 0.593 pp (kg/m 3) 2649 3014 Pbuik (kg/m 3) 1510 1531 H 3 (m) 0.48 0.47 U m / (m/s) 0.167 0.338 0.48 0.56 1 at a system pressure of 0.118 MPa and a temperature of 20° C 3.2 Initial Operating Conditions The drying chamber was charged with 80 kg of Ottawa sand to a static bed height in each compartment of 0.48 m. Table 3.1 lists the properties of the sand and copper slag particles (used in the later portion of the experimentation) and their respective fluidized bed characteristics at Umf. Copper slag was used after an insufficient quantity of Ottawa sand remained to charge the column. The excess superficial velocity of 0.4 m/s used in compartments 1 and 3 was selected on the basis of the findings reported in Chapter 2 where for an even pitch distributor, it was shown that at U — Umj••= 0.25 m/s, wafers occasionally remained at the distributor, while at U — Umt = 0.5 m/s, all wafers were kept in circulation. Since the efficiency of the drying process depends in part on the quantity of air that must be heated, a (U — Umj) between the two values was chosen for compartments 1 and 3. The expanded bed height in compartment 1 was predicted to be 0.63 m and thus was lower than the inlet for the wafer feed and removal unit. The excess superficial velocity for compartments 2 and 4 was set at 0.7 m/s to achieve the desired circulation of sand between compartments. 162 Since the minimum superficial velocity for slugging behaviour in the bed was calculated to be 0.27 m/s and the aspect ratio of each compartment was at least 5:1 (height to diameter), all four beds were operating in the slugging regime. 163 3.3 Evaluation of the Experimental Dryer 3.3.1 Summary of Tests, Observations and Modifications The experimental dryer underwent many tests and modifications before its eventual aban-donment. Unlike the experiments in the half-column with a glass front, results from the experimental dryer could only be determined by measurement of the operating conditions, and limited visual observations through the glass ports on either side of the column and after dismantling the equipment. For this reason, the conclusions based on this experimen-tation are somewhat subjective. Table 3.2 summarizes the work performed on the dryer in chronological order. The limited data obtained from the experimentation are discussed in the sections following this summary. It was observed during each of these runs that wafers tended to accumulate in com-partments 1 and 3. The slugging behaviour of the fiuidized beds resulting from the high, small cross-section compartments appeared to impede the flow of wafers through the dryer and cause an accumulation of wafers on the surface of the bed. A similar stratification was observed in a slugging bed of coal and sand (Zhao, 1986). It is possible that the slugs of air rising to the surface of the bed prevented the majority of the wafers from penetrating the lower sections of compartments 1 and 3. Wafers then accumulated in compartments 1 and 3 until the quantity of wafers in the beds caused defluidization as discussed in the section on the wafer handling capacity of the 0.15 m half-column (Section 2.3.2). This seems a more plausible explanation for the plugging of compartment 1 than the postulate that the settling of wafers on the distributor as a result of insufficient superficial velocity. As shown in the 0.15 m half-column work with the distributors having non-uniform distributions of open area, single wafers settled on the zone of low bubbling activity and eventually migrated to the zone of high bubbling activity. Thus, single wafers descending 164 TABLE 3.2: Summary of Tests and Modifications Performed on the Experimental Dryer. Test Conditions Observations Modifications <k Recommendations 1. Cold Bed Startup • circulation of sand • divider between {U — Umf) for comp. between compart- compartment 4 and 1 1 to 4 (m/s): ments not obtained shortened from 1.22 m 0.4, 0.7, 0.4, 0.7 to 1.07 m; divider between compartment 2 and 3 shortened from 1.22 m to 0.91 m • curved baffles (Figure 3.10) installed above comp-artments 2 and 4 to direct circulation • excessive commun- • height of gaps ication between between compartments connected 1 and 2, and 3 and 4 compartments reduced from 0.152 m to 0.076 m 2. Dryer Startup a) (U — Umf) for comp. • the few wafers • increase superficial 1 to 4 (m/s): removed from the velocity to comp. 1; 0.4, 0.7, 0.4, 0.77 dryer were overdried; reduce wafer feed drying temp: 150°C 0.91 kg/min sand rate wafer feed rate: 7.1 g/s removed with the wafers • accumulation of wafers in comp. 1 • comp. 1 started to smoke • feed and removal • air purges added unit filled with underneath the sand knife edge of the conveyer 165 Table 3.2: (continued). Test Conditions Observations Modifications & Recommendations 2. Dryer Startup (continued) b) (U - Umf) for comp. • feed system jammed • replaced teflon 1 to 4 (m/s): • conveyer housing knife edge with 0.5, 0.7, 0.4, 0.7 filled with sand 0.127 mm steel shim drying temp: 150°C stock wafer feed rate: 4.5 g/s • front end of conveyor housing closed in • baffle added above • removal screen to direct sand away from the opening of the feed and removal unit • use plexiglas side-plates to visually determine maximum allowable (U — Umf) for compartment 1 • apron belt degraded • reversed belt by heat • use lower temperature for next drying test 3. Cold Bed Tests a) (U - Umf) for comp. • comp. 1 plugged • increase (U — Umf) to 1 to 4 (m/s): with sand compartment 1 0.47, 0.7, 0.4, 0.77 • decrease wafer feed wafer feed rate: 4.5 g/s rate • knife edge damaged • knife edge thickness increased to 0.254 mm 166 Table 3.2: (continued). Test Conditions Observations Modifications &c Recommendations 4. Wafer Residence Time Tests a) (U — Umf) for comp. • wafers fed and 1 to 4 (m/s): removed 0.38, 0.57, 0.4, 0.59 continuously wafer feed rate: 4.5 g/s over 3-5 min. copper slag feed tests rate: 15 g/s b) conditions same • comp. 1 plugged • replaced knife as (a) except after 13 min. edge copper slag feed continuous • dropped windbox rate: 9 g/s operation and removed • pressure drop screen between across distributor distributor in comp. 1 plates 5 times greater than in comp. 3 5. Drying Tests a) (U — Umf) for comp. • dryer operated • prepare dryer 1 to 4 (m/s): continuously for extended 0.38, 0.57, 0.40, 0.59 for 23 min. run drying temp: 60°C • wafers removed wafer feed rate: 5.3 g/s at about 9% green wafer moisture moisture content: 70% content and copper slag feed were free of rate: 9 g/s copper slag 167 Table 3.2: (continued). Test Conditions Observations Modifications & Recommendations 5. Drying Tests (continued) b) same conditions • comp. 1 plugged • replaced knife as (a) except after 2 min. edge with 0.254 mm green wafer moisture • wafer removal bronze shim stock content: 85% system broke • fixed drive system • attempt 1 more run c) (U — Umf) for comp. • comp. 1 plugged • abandon 1 to 4 (m/s): after 10 min. experimental 0.38, 0.57, 0.40, 0.59 dryer drying temp: 70°C wafer feed rate: 1.3 g/s green wafer moisture content: 90% copper slag feed rate: 9 g/s 168 to the distributor in compartment 1, migrated to compartment 2. The high excess superfi-cial velocity and thus large bubble size in compartment 2 were more than sufficient to lift the wafers off the distributor. 169 F I G U R E 3.10: Curved baffle in compartment 2 used to direct the slugs of sand into compartment 3. 170 T A B L E 3.3: Quantities of Wafers and Particles Fed and Removed from the Dryer During the First Wafer Residence Time Test. Time Wafers Wafers Particles Particles No. of Orange Interval In Out In 1 Out Wafers Removed (min) (kg) (kg) (kg) (kg) 5 1.35 0.36 N.A. 4.73 8 5 1.35 0.36 N.A. 2.09 27 5 1.35 0.45 N.A. 2.73 29 Totals 15 4.05 1.17 — 9.55 61 1 back pressure from compartment 1 occasionally interrupted the flow of particles through the rotary valve and thus an accurate mea-sure of the sand fed was not obtained. 3.3.2 Wafer Residence Time Tests A set of 100 orange coloured wafers were placed at the front of the apron belt so that they were fed in first. The dryer was operated for 5 minutes, then the beds were slumped while the wafers that had exited from the dryer were collected, weighed and the coloured wafers were counted. The sand particles lost from compartment 1 were weighed. The beds were then renuidized. This procedure was repeated three times until it was felt that the dryer could perform continuously. Table 3.3 presents the quantities of wafers and particles fed and removed from the dryer during this test. The first wafer exited from the dryer after 170 s. The wafer accumulation in the bed amounted to 2.9 kg after 15 minutes. This accumulation was observed to be in compartments 1 and 3. The wafer residence time test using the orange wafers was stopped after 15 minutes so that a continuous test of the dryer could be performed. Table 3.3 shows the numbers of orange wafers removed during each time interval. A rough estimate of the median residence time based on the results was determined to be 15 minutes. 1 7 1 TABLE 3.4: Quantities of Wafers and Particles Fed and Removed from the Dryer During the Second Wafer Residence Time Test. Total Total No. of Blue Time Wafers In Wafers Out Wafers Removed (min) (kg) (kg) 1.75 0.47 1 4.0 1.08 — 9 5.0 1.35 0.5 12 8.0 2.16 — 36 10.0 2.70 1.07 23 12.0 3.24 — 20 Totals 12.0 3.24 1.57 1011 1 Since only 100 blue wafers were fed into the dryer, the total number of blue wafers removed includes a few broken wafers. A second cold bed test was run at the same experimental conditions as the first test except that the feed rate of particles to compartment 1 was reduced to 9 g/s (based on the efflux of particles during the last two time intervals of the previous test). Table 3.4 lists the results of this cold bed test. Compartment 1 plugged after approximately 13 minutes of continuous operation. How-ever, the majority of the blue wafers used for the residence time test had been removed after 12 minutes of operation. The median wafer residence time for this test was about 8 minutes and the average wafer residence time was 7.3 minutes. Referring back to Section 2.3.2, it was observed that at U — Umf — 0.5 m/s, wafer loadings greater that about 2% of the total bed volume interfered with the fluidized bed hydrodynamics which caused a layer or cap of wafers to form on the surface of the bed and wafers to clump together and sink to the distributor. It appears that a similar situation 172 occurred in compartments 1 and 3 of the experimental dryer. Although the rate of wafer removal from the dryer increased with the accumulation of wafers in compartments 1 and 3, the accumulation of wafers in compartment 1 eventually caused defluidization. The total quantity of wafers accumulated in the dryer at the end of the second test was approximately 5.3 kg. If the ovendry density for the aspen wafer is assumed to be 390 kg/m3 and bed heights in compartments 1 and 3 are 0.65 m, the wafer loading in compartments 1 and 3 was 27% (volume of wafers/total bed volume) at the time of defluidization in compartment 1. 173 TABLE 3.5: Results of the Continuous Fiuidized Bed Wafer Drying Test at 60°C. Time (min) Total Wafers Fed (O.D. Basis) (kg) Total Wafers Removed (kg) Moisture Content of Dried Wafers (%) Removal Rate (O.D. Basis) (g/s) 5 1.65 0.86 15.9 2.5 8 2.64 1.72 10.1 4.3 11 3.63 2.31 9.1 3.0 14 4.62 2.90 9.0 3.0 23 4.62 1 3.58 7.6 1.2 The wafer feed system ran out of wafers shortly after 14 minutes. 3.3.3 Wafer D r y i n g Tests The dryer was brought up to temperature for run 5(a) (Table 3.2) and allowed to equilibrate for 30 minutes. The wafer and copper slag feeds were started as soon as the circulation of solids was established. The dryer operated very smoothly for the duration of this short test. It was shut down after 23 minutes of operation so that preparations could be made for an extended run. The results of the drying run are presented in Table 3.5. The wafers were dried to approximately 9% moisture content and were free of copper slag particles. Since the re-moval rate of wafers from the dryer was always less than the feed rate, wafers were still accumulating in the dryer but at a much slower rate than in previous tests. The wafers could not be fed fast enough to the feed unit so that after 14 minutes of operation the feed unit had emptied. No wafers were fed while the remaining wafers were removed from the dryer. Figures 3.11 to 3.14 display the bed temperature profiles for compartments 1 to 4 respectively. It should be noted that temperatures recorded by the datalogging system and 174 0 10 20 30 40 50 60 TIME (MINUTES) F I G U R E 3.11: Temperature profiles for compartment 1 for drying at 60°C. A - Establishment of the baseline temperature using the 4.4 kW heater. B - Feed of wafers started. C - Porcupine heating element turned on to counteract drop in bed temperature. D - Second porcupine element turned on. The rise in temperature 50 mm above the dis-tributor may have resulted from a temporary blockage of the compartment. E - Wafer feed system running out of wafers and thus the feed rate of wafers was less than the 5.5 g/s of the previous 14 minutes. Bed temperature rising as the drying load decreased. F - Wafer feed stopped and all heaters shut off. G - End of run. 175 160 -140 Ld 120 cr ID I— < td 100 Q_ Ld Ld 80 CE 60 < Q_ o O 40 20 HEIGHT ABOVE DISTRIBUTOR WINDBOX 50 mm 300mm 680 mm TIME (MINUTES) F I G U R E 3.12: Temperature profiles for compartment 2 for drying at 60°C. A - Establishment of the baseline temperature using a single porcupine element. B - Feed of wafers started. C - Second porcupine element turned on. D - Second porcupine element turned off. E - Wafer feed system running out of wafers. Bed temperature rising as the drying load decreased. F - Wafer feed stopped and heater turned off. G - End of run. 176 i — i — i — i — 1 — i — 1 — r TIME (MINUTES) F I G U R E 3.13: Temperature profiles for compartment 3 for drying at 60°C. A - Establishment of the baseline temperature using a single porcupine element. B - Wafer feed started. C - Second porcupine heating element turned on to counteract the drop in bed temperature. D - Wafer feed system running out of wafers. Bed temperature rising as the drying load decreased. E - Wafer feed stopped and heaters shut off. F - End of run. 177 F I G U R E 3.14: Temperature profiles for compartment 4 for drying at 60°C. A - Establishment of the baseline temperature using a single porcupine heater. B - Wafer feed started. C - Second porcupine element turned on. D - Second porcupine element turned off. The sharp rise in bed temperature may be linked with the partial blockage of column 1 at the same time. E - Wafer feed system running out of wafers. Bed temperature rising as the drying load increased. F - Wafer feed stopped and heater turned off. G - End of run. 178 plotted in these figures were lower than the true values by about 4°C (based on calibration tests at 20°C and 60°C). The data logged values were not adjusted prior to plotting because of the dynamic nature of the system. A description of the temperature profiles in each compartment chronicling the progress of the run accompanies each figure. As can be seen in these figures, the lower temperatures at 680 mm above the distributor during the establishment of the baseline (A) indicated that these thermocouples were located above the bed. However, after circulation of the copper slag started, this temperature difference disappeared. Figure 3.11 shows a sudden increase in the bed temperature 50 mm above the distributor at the 37 minute mark. This sudden increase probably resulted from a temporary blockage of compartment 1 near the distributor. The other three compartments all show signs of the disturbance by an increase in bed temperature. The dramatic increase in bed temperature in compartment 4 can not be explained. For run 5(c) (Table 3.2), the dryer temperature was set at 70°C to produce wafers dried to a moisture content below 9%. The wafer feed rate was set at 1.3 g/s to ensure that the feed rate was not responsible for the defluidization of compartment 1. Compartment 1 plugged after about 10 minutes of operation as can be seen in Figure 3.15. The temperature of the bed at 50 mm above the distributor started to rise above 70°C, 6| minutes into the run and reached a maximum 3| minutes later when compartment 1 defluidized. It appears that the wafers accumulated at or near the distributor prior to the blockage of the compartment. This mechanism was confirmed by observations made while dismantling the dryer. This test concluded the work on the experimental dryer. 179 0 5 10 15 20 25 30 35 40 TIME (MINUTES) F I G U R E 3.15: Temperature profiles for compartment 1 for drying at 70°C. A - Establishment of the baseline temperature using the 4.4 kW heater. B - Feed of wafers started and 2 porcupine elements switched on. C - Compartment started to plug with wafers. D - Compartment defluidized by the plug of wafers. All heaters shut off. E - End of run. 180 3.4 Concluding Remarks on the Experimental Continuous Dryer The experimental continuous dryer runs demonstrated the applicability of a multiple com-partment fiuidized bed and the use of a continuous wafer feed and removal system for wafer drying. The limited amount of data and observations from its operation at 60°C showed that the wafers dried as they progressed through the four compartments before being removed from the dryer by the vibrating removal screen. The collected wafers were dried to about 9% moisture content and were free of copper slag particles after screening. The poor performance of the experimental dryer was a direct result of the drying chamber configuration. The large height/diameter ratio of the compartments and their limited cross-sectional area caused the beds to operate in the slugging regime. The rising slugs of air in compartments 1 and 3 interrupted the downward movement of the wafers with the emulsion phase. The majority of wafers thus remained in the upper portion of the bed, accumulating first at the surface of the bed and then throughout the bed. The high concentration of wafers in the bed fostered clumping of the wafers which then sank to the distributor. Since the bed hydrodynamics were already disturbed by the high concentration of wafers, the clumps of wafers could not be lifted off the distributor plate and defluidization of the bed therefore resulted. Wafers accumulated on the distributor until they blocked the gap between compartments 1 and 2 and interrupted the circulation of the emulsion phase from compartment to compartment. The wafer feed and removal unit could also be vastly improved by the use of a more robust feed system such as a screw conveyer (using the former feed system as a metering bin upstream of the conveyor). The wafer removal system could be improved by increasing the area of the vibrating screen outside of the drying chamber with all solids passing through the screen being continuously returned to compartment 1. 181 Chapter 4 Configuration of Industrial Fluidized Bed Wafer Dryer 4.1 Introduction The difficulties encountered in attempting to obtain wafer circulation in the experimental fluidized bed dryer were caused by slugging in compartments 1 and 3 and by the low compartment cross-sectional diameter to wafer length ratio (~ 7). A rule of thumb used in fluidized bed design to maintain bridge-free motion of particles through gaps is that the bed to mean particle diameter ratio should be at least 20 and larger for wide particle size distributions or angular particles (Grace, 1982). Since waferboard is currently being manufactured using 0.1 m long by 0.04 m wide wafers or strands, a minimum bed diameter of about 2.0 m and a minimum bed depth of 2.0 m are probably needed to obtain a smooth flow of the wafers. Slugging behaviour in a bed having a diameter of 2.0 m can be avoided by restricting bed height to less than 4.0 m (2 X bed diameter). In a compartment of this aspect ratio, the inert particles and wafers will have near perfect mixing and not the near plug flow distribution obtained with the experimental dryer. The uniform residence times required for a narrow moisture content distribution of the dried wafers can be achieved by linking several compartments in series. As the number of perfectly mixed compartments increases, the exit age residence time distribution (E) becomes narrower and approaches a normal distribution (Figure 4.1), eventually approaching plug flow. 182 F I G U R E 4.1: Residence time distributions or exit age distribution curves for N ideally mixed reactors in series (Levenspiel, 1972). 183 The most important parameter in the design of an industrial fiuidized bed wafer dryer is the optimal number of dryer compartments. Since a specific solids circulation pattern (to approximate plug flow) is no longer required, the transfer of sand and wafers from compartment to compartment can be accomplished in a number of ways (as discussed in Section 4.3) and thus becomes a secondary consideration. 184 4.2 Determination of the Number of Compartments in the Industrial Dryer 4.2.1 Predicting Wafer Residence Times in Mult iple Compartment F lu -idized Beds To predict wafer residence times in a series of nearly perfectly mixed fluidized beds, it is assumed that the wafers are uniformly distributed throughout the bed. Since wafers were observed to circulate throughout a bubbling fluidized bed of sand (Section 2.3.2), this is considered to be a reasonable assumption. The residence time distribution of the wafers will thus be the same as for the sand particles and can be predicted using the exit age distribution function for N equal volume perfectly mixed reactors in series (Levenspiel, Combining the exit age distribution with the wafer drying curve as shown in Keey (1972), the mean moisture content of the dried wafers can be determined by presents calculated mean wafer moisture contents based on the mean residence times for fluidized beds in series for wafers dried from 100% to 3% moisture content in a fluidized bed of sand at 120°C. The average residence times required to produce a mean wafer moisture content of 3% as determined from Figure 4.2 appear in Table 4.1. The narrowing of the exit age distribution with increasing number of compartments reduces the average residence time required to meet the target product moisture content. However, the increased benefit of adding each extra compartment decreases as N increases. 1972) (4.1) (4.2) The wafer drying curve used in this equation is presented in Appendix J. Figure 4.2 185 0.50 I — i — n — 1 i ° ' ° 0 0 " " " 2 0 40 60 80 100 120 140 160 AVERAGE RESIDENCE TIME (s) F I G U R E 4.2: Mean wafer moisture content based on average residence times for fiuidized beds in series. Based on Equation 4.2 for wafers dried in a fiuidized bed of sand at 120°C. 186 TABLE 4.1: Mean Residence Times Required to Obtain a Mean Wafer Content of 3% in a Series of Fiuidized Beds Operating at 120°C. Number of Mean Residence Time Standard Deviation* Compartments w w 3 157 90 0.71 4 118 59 0.71 " 5 107 48 0.70 6 100 41 0.70 7 96 36 0.69 8 93 33 0.69 9 90 30 0.69 10 88 28 0.69 Standard deviation calculated by: Mean residence time 2/ # of compartments (Levenspiel, 1972). The integration of the E-curve over the range of ±1 standard deviation from the mean residence time (Table 4.1) shows the gradual approach of the curves to a normal distribution where the area under the curve for ±l«r is 0.68. 4.2.2 Moisture Content Distribution of Wafers Dried in Multiple Com-partment Fiuidized Beds The moisture content distribution of the dried wafers directly affects the manufacturing of waferboard and the efficiency of the drying process. A narrow distribution of dried wafer moisture contents about a mean of 3% is required for the use of certain resin systems e.g. phenol formaldehyde (Watson, 1985). Wet wafers in the core of a mat of wafers will cause steam to be generated during pressing which can rupture the board upon releasing the press. On the other hand, the efficiency of the drying operation decreases with the quantity of wafers that are overdried especially considering the large amount of energy required to overcome the heat of sorption at moisture contents below 3% (approaching 187 0% moisture content, the heat of sorption is 902 kJ/kg water evaporated (Stanish et ai, 1986)). The distribution of dried wafer moisture contents thus provides a criterion for assessing the number of compartments to be used in the industrial fluidized bed dryer. Table 4.2 presents wafer moisture content distributions for increasing numbers of fluidized compart-ments. The times used to evaluate / E^dt were calculated for each moisture content using the wafer drying curve presented in Appendix K. The percentage of wet wafers exiting from the multiple compartment dryers does not differ greatly as the number of compartments is increased. However, the percentage of wafers overdried is greatly reduced by increasing the number of compartments in series. The reduction in the percentage of overdried wafers decreases with each added compartment until 6 compartments in series where the reductions become constant. This reflects the approach of the residence time distributions to a normal distribution. In practice the residence time distribution of wafers in each compartment will differ from that of perfect mixing because the wafers will take a finite length of time to pass from the inlet to the outlet of each compartment. The quantity of freshly fed wafers that are immediately discharged from a perfectly mixed compartment thus represents the worst-case scenario. The actual residence time distribution of wafers in each compartment can only be determined by experimentation. 4.2.3 Number of Compartments Based on Compartment Size and Total H o l d u p The previous sections have shown that although the advantages of increasing the number of compartments in series decrease with each additional compartment, the best dryer per-formance will still be obtained using the maximum number of compartments. The number of compartments is, however, limited by the holdup of sand and wafers in the dryer and 188 T A B L E 4.2: Moisture Content Distributions for Wafers Exiting from Multi-Compartment Fiuidized Bed Dryers Operating at 120°C. Percentage of Wafers in Exit Stream No. of Comp. 100-701 70-502 Moisture Content (%) 50-303 30-154 15-55 5-1 6 < l 7 3 0.145 0.64 2.1 4.3 7.4 7.1 78.3 4 0.067 0.53 2.4 6.1 11.5 11.1 68.3 5 0.023 0.31 2.0 6.3 13.4 13.3 64.7 6 0.0078 0.179 1.64 6.4 15.1 15.5 61.2 7 0.0026 0.099 1.28 6.1 16.3 17.2 59.0 8 0.00086 0.055 1.00 5.9 17.3 18.9 56.8 9 0.00031 0.032 0.81 5.8 18.7 20.6 54.1 10 0.000109 0.0185 0.64 5.5 19.7 22.2 51.9 calculated by evaluating / E^dt between 0 and 11.35 s calculated by evaluating / E^dt between 11.35 s and 20.9 s calculated by evaluating / E^dt between 20.9 s and 34.1 s calculated by evaluating / E^dt between 34.1 s and 49.7 s calculated by evaluating / E^dt between 49.7 s and 68.6 s calculated by evaluating / E^dt between 68.6 s and 83.7 s calculated by evaluating / E^dt between 83.7 s and oo 189 the size of each compartment. The holdup in the dryer is determined by the residence time of particles in the dryer and the feed rate of particles into the dryer. Since the wafers are assumed to be uniformly distributed in each compartment, the wafer feed rate into the dryer and the volumetric percentage of wafers in the bed (or wafer concentration) will determine the feed rate or circulation rate of sand needed to maintain the same wafer concentration. Table 4.3 presents the calculated total bed volume for each multiple compartment dryer and the minimum and maximum number of compartments required to contain the total bed volume for a wafer concentration of 2% of the total bed volume. The wafer feed rate of 2.53 kg/s ovendry basis is the same as that used in the triple pass drum dryer selected for comparison with multi-compartment fluidized bed dryers in Section 4.7. For a wafer concentration of 2% of the total bed volume, the dryer could only contain 3 to 4 compartments. However, since there are still large benefits in wafer moisture content uniformity to be obtained by adding compartments for so few compartments in series, a 5-compartment dryer will be considered. Although the bed height in the dryer will only be 1.73 m, this was felt not to be a problem at a wafer concentration of 2% of the total bed volume. Since a wafer concentration of 2% of the total bed volume was recommended based on the work on the 0.15 m semi-cylindrical column in Section 2.3.2, it is possible that a higher concentration could be handled in a vessel of much higher diameter-to-wafer-length ratio. However, for a 4% concentration of wafers, only a 3 compartment dryer could be used because of the small total bed volume. 190 TABLE 4.3: Determination of the Minimum and Maximum Number of Compartments. Based on Minimum and Maximum Compartment Bed Volumes and the Total Bed Volume in the Dryer for a Wafer Feed Rate of 2.53 kg/s (oven dry basis) and a Wafer Holdup in the Dryer of 2% by Volume. Mean Total Volume Total Bed Number of Compartments Number of Residence of Wafer Holdup Volume Based on Total Bed Volume Compartments Time in Dryer 1 in Dryer 2 Minimum 3 Maximum 4 (») (m3) (m3) 3 157 1.02 51.0 4 6 4 118 0.77 38.3 3 4 5 107 0.69 34.5 3 4 6 100 0.65 32.5 2 4 7 96 0.62 31.0 2 3 8 93 0.60 30.0 2 3 9 90 0.58 29.0 2 3 10 88 0.57 28.5 2 3 A wafer feed rate of 2.53 kg/s (feed rate for a triple pass drum dryer (Wat-son, 1985)) corresponds to a volumetric feed rate of 6.49 X 10~3 m3/s (based on an oven dry density of 390 kg/m3). The total volume of wafer holdup was calculated by multiplying the volumetric feed rate by the average wafer residence time. The total bed volume in the dryer was calculated by dividing the total vol-ume of wafers in the dryer by 0.02, since wafers are assumed to occupy 2% of the bed by volume. The minimum number of compartments needed to accommodate the total bed volume is based on a compartment cross-sectional area of 4.00 m 2 and a bed height of 4.0 m. The maximum number of compartments that could be used to accommo-date the total bed volume is based on a compartment cross-sectional area of 4.0 m 2 and a bed height of 2.0 m. 191 4.3 Circulation of the Inert Particles Through a 5-Compartment Fiuidized Bed Dryer Table 4.4 presents the calculation of the circulation rate of 0.5 mm sand in a 5-compartment fiuidized bed dryer operating with 2% wafers by volume at a superficial velocity of 0.73 m/s. The low concentration of wafers in the bed requires a circulation rate of 372 kg/s of sand. The experimental fiuidized bed dryer described in Section 3 used static head pressure differences between adjacent beds to circulate sand through the gap between adjacent compartments. The static head pressure of the downfiowing bed was maintained at a greater level than that in the adjacent upflowing bed by the continuous addition of slugs of sand from the upflowing bed of the adjacent pair of compartments. Although this method of solids circulation has been investigated by numerous researchers (e.g. Kuramoto et ai, 1986; La Nauze, 1976; Pruden et ai, 1974), each study involved a specific set of experimental conditions that limits the applicability of their results to different systems. The highest solids circulation rate was obtained by La Nauze (1976) using a 0.2 m draft tube in a 0.3 m diameter bed. The 0.168 mm sand travelled down the incipiently fiuidized annulus and up the slugging bed of the draft tube. A maximum gap height between the annulus and the draft tube of 0.28 m produced a solids flow rate in the annulus of 400 kg/s-m 2 at U - Umj = 0.37 m/s in the draft tube. If this flux could be maintained in the 5-compartment dryer, a circulation rate of 372 kg/s would require a gap having a cross-sectional area of 0.93 m 2 . Figure 4.3(a) presents a schematic drawing of this type of circulation through the 5-compartment dryer. This method, however, may not be able to circulate this quantity of sand if the downcomer is operating in the bubbling fluidization regime instead of undergoing incipient fluidization. The addition of a small diameter chamber to each compartment for the upflow of sand also negates the advantage of making the compartment diameter 20 times the wafer length. 192 TABLE 4.4: Calculation of the Circulation Rate of Sand Through the 5-Compartment Fiuidized Bed Dryer Total Bed Volume1 Total Wafer Volume in Bed 1 Volume of Fiuidized Bed of Sand Total Bed Cross-sectional Area 2 Expanded Bed Height Bed Height at U m / 3 Static Volume of Sand 4 34.5 0.7 33.8 20.0 1.73 1.34 15.1 Total Holdup of Sand 5 (kg) (kg/s) 39800 372 Circulation or Feed Rate of Sand Based on a particle residence time of 107 s and a wafer concentration of 2% of the total bed volume. Compartment diameter was 2.0 m. The bed height at Umf was determined using a bed expansion E of 0.287 cal-culated at a superficial velocity of 0.73 m/s for 0.5 mm sand (Section 2.32). The static volume of sand was calculated assuming emf = 0.437 as deter-mined in Section 2.3.1 for 0.5 mm sand. Hmf = H/{l + E). 5 Density of 0.5 mm sand is assumed to be 2630 kg/m3. 193 Sand may also be transferred between compartments using gravity as the driving force. The sand could flow through an orifice between compartments or over a weir as indicated in Figure 4.3(b) and (c) respectively. Trees (1962) investigated the flow of iron ore (density = 3640 kg/m3) through pipes connecting two fluidized beds separated by a vertical distance of 0.63 m. For a 0.20 m diameter pipe, a flow rate of 544 kg/s-m2 was achieved. Based on this system, the first compartment of the 5-compartment dryer would thus have to be approximately 3 m above the collection hopper for the sand and the orifice between compartments would have an approximate diameter of 1 m2. The sand flowing into the collection hopper from compartment 5 would then have to be returned to compartment 1 by a bucket elevator, continuous flow conveyor or pneumatic conveyor. The flow of sand over a weir between compartments is essentially the same as sand flowing through an orifice. However, the layer of sand over the weir must be deep enough that the wafers in the sand are not impeded by the weir. Since both the slug flow transport and weir circulation systems would impede the flow of wafers with the sand, it is recom-mended that the circulation system using orifices between compartments be used for the 5-compartment dryer because of its simplicity and proven ability to handle such systems. Full size cold bed testing would, however, still be required to ensure that the wafers mix uniformly in the bed, and are transported with the sand. 194 TOP VIEW SIDE VIEW DRY WAFERS I i WET t WAFERS 1 HOPPEF 2 (a) IT* o Q DRY HOPPER 5 4 WAFERS I | itl— WET, I WAFERS 1 2 I 3 (b) WAFERS Cc) o a ° 1 a o * 2 ° 3 F I G U R E 4.3: Schematic diagrams of the top and side view of three possible methods for circulating sand in a 5-compartment fiuidized bed dryer. (a) slug flow transport; (b) flow through orifices; (c) flow over weirs. 195 4.4 Wafer Feed and Removal Systems The feed and removal of wafers from the 5-compartment fluidized bed dryer pose no fore-seeable problems that could not be handled by equipment manufacturers. The systems used for transporting and feeding the wafers already exist in waferboard mills and could be used with only minor modifications. In such systems metering of the green wafer flow is done at the exit of the green storage bin and the wafers are transported by screw or belt conveyor to the drying system. The green wafers can then be fed through a rotary valve (or airlock) onto the bed surface of compartment 1. The dried wafers can be removed from the flow of sand exiting from compartment 5 by a screening system similar to that used for the experimental dryer. Full scale tests should be performed to determine the surface area of the screen and optimal mesh size required to handle the flow of sand and wafers. Further tests will be required to determine the maximum quantity of sand that may be included with the wafers without aifecting waferboard processing or final product quality. The screened wafers exit the dryer through a rotary valve and are conveyed to a dry wafer storage bin. It is current practice in the waferboard industry to screen the wafers after they leave the dry storage bin. It may be advantageous to incorporate screening of the dry wafers as part of the dryer wafer removal system. 196 TABLE 4.5: Average Wafer Residence Times and Iniet and Outlet Moisture Contents for the Five-Compartment Fluidized Bed Dryer Operating at 120°C. Compartment 1 2 3 4 5 Average Residence Time (s) 21.4 21.4 21.4 21.4 21.4 Inlet Moisture Content (%) 100 58.4 32.0 16.5 7.7 Outlet Moisture Content (%) 58.4 32.0 16.5 7.7 3.0 4.5 Wafer Drying in a Multi-Compartment Fluidized Bed The multi-compartment fluidized bed dryer design used in this evaluation consists of five equal-sized square compartments, each having a cross-sectional area of 4.0 m 2. The cir-culation of sand and wafers will be accomplished by orifices between compartments (Fig-ure 4.3(b)). To calculate the energy requirements for each compartment, it was first necessary to determine the mean moisture content of the wafers entering and leaving each compart-ment. Equation (4.2) was used to determine the mean exit wafer moisture content based on a mean compartment residence time of 21.4 s (total mean residence time for the 5-compartments/number of compartments). The form of the exit age distribution function was also modified to reflect the addition of each compartment, The calculated moisture contents presented in Table 4.5 were then used to calculate the energy requirements presented in Table 4.6. Although the drying medium of an industrial drying system would most likely be the products of combustion, air was used as the drying medium for the energy requirement calculations of the 5-compartment fluidized bed dryer Dryer (4.3) 197 TABLE 4.6: Energy Balance for a Five Compartment Fluidized Bed Wafer Dryer 1 , 2. Pro-ducing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Ovendry Basis). Compartment 1 2 3 4 5 Superficial Velocity (m/s) 0.75 0.75 0.75 0.75 0.75 Air Mass Flow Rate (kg/s) 3.14 3.14 3.14 3.14 3.14 Initial Wafer Moisture Content (%) 100 58.4 32.0 16.5 7.7 Final Wafer Moisture Content (%) 58.4 32.0 16.5 7.7 3.0 Free Water Evaporated (kg/s) 1.05 0.67 0.051 0 0 Bound Water Evaporated (kg/s) 0 0 0.34 0.22 0.119 Energy Requirements Incoming Air (kW) 320 320 320 320 320 Wood Substance (kW) 275 0 0 0 69 Water in Wafers (kW) 846 0 0 0 6.3 Free Water Evaporation (kW) 2373 1506 114 0 0 Bound Water Evaporation (kW) 0 0 839 622 356 Water Vapour (kW) 41 26 15 8.7 4.6 Transmission Heat Losses (kW) o:5 0.5 0.5 0.5 0.5 Total Energy Requirement (kW) 3856 1853 1289 951 756 Estimated Inlet Air Temperature (°C) 1040 531 375 281 227 Dryer assumed to operate at a bed temperature of 120°C and the bed ma-terial to be 0.5 mm diameter Ottawa sand. See Appendix L for the calculation of the listed quantities. 198 a n d t h e r o t a r y d r y e r . S i n c e b o t h c o m b u s t i o n g a s e s a n d a i r a r e p r e d o m i n a n t l y N2 ( ~ 8 0 % ) , i t w a s f e l t t h a t t h i s s i m p l i f i c a t i o n w o u l d h a v e l i t t l e e f f e c t o n t h e e n e r g y r e q u i r e m e n t c a l c u -l a t i o n s u s e d i n t h e c o m p a r i s o n o f t h e t w o d r y i n g s y s t e m s . T h e e n e r g y r e q u i r e m e n t s o f t h e f i r s t c o m p a r t m e n t a r e h i g h b e c a u s e o f t h e l a r g e r q u a n t i t y o f w a t e r e v a p o r a t e d f r o m t h e w o o d ( 4 8 % o f t h e t o t a l w a t e r e v a p o r a t e d i n t h e d r y e r ) a n d t h e h e a t i n g o f t h e w e t w a f e r s t o t h e w e t b u l b t e m p e r a t u r e o f 1 0 0 ° C . S i n c e t h e e s t i m a t e d t e m p e r a t u r e o f t h e a i r e n t e r i n g t h e first c o m p a r t m e n t ( 1 0 4 0 ° C ) i s w e l l a b o v e t h e s p o n t a n e o u s c o m b u s t i o n t e m p e r a t u r e o f d r y w o o d ( 3 3 0 ° C ) ( B e a l l , 1 9 7 2 ) , t h e w a f e r s m u s t b e p r e v e n t e d f r o m s e t t l i n g o n t o t h e d i s t r i b u t o r . B a s e d o n t h e r e s u l t s o f t h e r e s e a r c h o n t h e 0 . 1 5 m s e m i - c y l i n d r i c a l c o l u m n i n S e c t i o n 2 , a s u p e r f i c i a l v e l o c i t y o f 0 . 7 5 m / s f o r a 0 . 5 m m s a n d (U — Umf « 0 . 5 m / s ) w i l l k e e p t h e w a f e r i n c o n t i n u o u s c i r c u l a t i o n . T h e c i r c u l a t i o n o f 2 5 m m l o n g w a f e r s i n a s p o u t / f l u i d b e d w a s o b s e r v e d p r i o r t o d e -s i g n i n g t h e d i s t r i b u t o r p l a t e s u s e d f o r t h e 0 . 1 5 m s e m i - c y l i n d r i c a l c o l u m n d e s c r i b e d i n S e c t i o n 2 . A l t h o u g h t h e s p o u t / f l u i d b e d p r o v i d e d e x c e l l e n t c i r c u l a t i o n o f t h e w a f e r s , i t w a s n o t c o n s i d e r e d a p p r o p r i a t e f o r t h e s a n d a n d w a f e r c i r c u l a t i o n p a t t e r n r e q u i r e d t o a p -p r o x i m a t e p l u g flow i n a m u l t i p l e c o m p a r t m e n t d r y e r . S i n c e t h e c i r c u l a t i o n o f t h e w a f e r s i n t h e d r y e r i s n o l o n g e r d e p e n d e n t o n t h e i r d e s c e n t t o t h e b o t t o m o f o n e c o m p a r t m e n t b e f o r e e n t e r i n g t h e n e x t c o m p a r t m e n t ( a s i n t h e e x p e r i m e n t a l d r y e r ) , a s p o u t / f l u i d b e d c a n n o w b e r e c o n s i d e r e d . T h e s p o u t / f l u i d d e s i g n c o u l d b e i n v e s t i g a t e d s i m u l t a n e o u s l y w i t h t h e f u l l s c a l e t e s t s o f t h e s a n d c i r c u l a t i o n s y s t e m . T h e p r o b l e m o f w a f e r c o m b u s t i o n m u s t a l s o b e c o n s i d e r e d b e c a u s e o f t h e v a r y i n g w a f e r r e s i d e n c e t i m e s i n e a c h c o m p a r t m e n t . I f e a c h c o m p a r t m e n t a p p r o a c h e s p e r f e c t m i x i n g , t h e r e w i l l b e a f e w w a f e r s t h a t r e m a i n i n e a c h c o m p a r t m e n t f o r a r e l a t i v e l y l o n g t i m e (e.g. a f e w d a y s ) . O n c e d r i e d , t h e s e w a f e r s w i l l b u r n i f t h e y p a s s w i t h i n 4 - 5 c m o f t h e d i s t r i b u t o r , e s p e c i a l l y i n c o m p a r t m e n t 1. H o w e v e r , t h e e x p o s u r e o f a d r i e d w a f e r t o t h e 199 F L U I D I Z E D B E D *- 50 mm-* 25mm r\ r\ C O M P A R T M E N T W A L L FIGURE 4.4: Cross-section of a compartment 1 membrane wall. This configuration increases wall surface area by 29% which for a bed height of 1.73 m creates a total surface area for heat transfer of 17.8 m 2. high inlet air temperature is expected to be brief since it would be quickly entrained in a bubble wake, and transported back into the cooler section of the bed. In the event that a wafer did combust, the low concentration of wafers in the bed of sand, and the high water vapour content of the gas in the bed (0.33 kg water vapour/kg dry air) would inhibit a dryer fire. The use of steam as the drying medium could also resolve the problems with high temperatures because of its greater heat carrying capacity than combustion gases and its lack of combustible gases. It would still be beneficial, however, to reduce the inlet air temperature for compartment 1 to save on the high costs of materials needed to withstand 1000°C temperatures as well as to minimize degradation of the wafers. There are a number of options that can be used to lower the inlet air temperature. The energy requirement for air entering each compartment can be reduced by about 667 kW using the compartment walls as heat transfer surfaces. Figure 4.4 shows a possible config-uration of a membrane wall that will increase the surface area available for heat transfer to the bed by about 29%. If a bed-to-wall heat transfer coefficient of 0.250 kW/m 2 oC is 200 assumed (as determined by Zabrodsky et al., (1978) for 0.515 mm particles at a superficial velocity of 0.75 m/s), then a membrane wall surface area of 17.8 m 2 and a wall temperature of 270°C will lower the required inlet air temperature of compartment 1 to about 900°C. The membrane walls could be heated by either superheated steam, heated oil or electricity (heating elements) depending on the cost and availability of each at the mill. In the event that accidental defluidization of the bed occurs, the temperature of the wall could damage wafers trapped next to it. Beall (1972) showed that a 1 cm 3 cube of ovendry maple exposed to an increase in temperature from 100°C to 277°C over a period of 60 minutes only caused about a 5% mass loss. In light of this slow degradation at the proposed wall temperature and the low concentration of wafers in the bed, accidental thermal degradation of the wafers or fire in the dryer are considered not to be problems. The economics of heating the incoming air versus adding heat through the compartment walls will determine if the other four compartments can benefit from wall-to-bed heat transfer. Another way of reducing the air inlet temperature of compartment 1 would be to increase the superficial velocity and thus lower the quantity of heat that must be carried by each kilogram of air. If the superficial velocity is increased from 0.75 m/s to 0.95 m/s, the compartment 1 inlet air temperature will drop to 879°C (although the energy requirement for compartment 1 would increase to 3941 kW). The change in superficial velocity is not expected to affect the residence time distribution of the wafers in compartment 1. However, this should be verified by experimentation. If the bed hydrodynamics were unfavourably changed by the increase in excess superficial velocity, then using larger particles could be considered (although this would decrease the drying rate of the wafers and thus possibly change the dryer configuration). The inlet air temperature of compartment 1 could be decreased from 1040°C to ap-proximately 733°C by using the compartment walls for heat transfer and increasing the 201 s u p e r f i c i a l v e l o c i t y t o 0 . 9 5 m / s . I f a n e v e n g r e a t e r r e d u c t i o n i n t e m p e r a t u r e i s s t i l l r e q u i r e d t h e n a l t e r n a t i v e s s u c h a s a p l u g f l o w t y p e f i u i d i z e d b e d p r e d r y e r m a y h a v e t o b e c o n s i d e r e d t o r e d u c e t h e d r y i n g l o a d i n c o m p a r t m e n t 1. T h i s w o u l d , h o w e v e r , g r e a t l y i n c r e a s e t h e c o m p l e x i t y a n d e x p e n s e o f t h e d r y i n g s y s t e m a n d s h o u l d b e a v o i d e d i f p o s s i b l e . 202 4.6 Wafer Drying in a Triple-Pass Drum Dryer Wafers are currently dried in large drum dryers such as the triple-pass drum dryer system shown in Figure 4.5 (Watson, 1985). Wafers are fed in through a rotary valve (A) and are mixed with hot combustion gases entering at 510°C. The wafers are blown and tumbled through the three passes (B) and exit into the dropout box (C). The dried wafers exit the dropout box through a rotary valve. The 48°C waste gas passes through a cyclone, and is then pulled through internal draft fans and exhausted up the stack. The energy requirements for one of these drum dryers were calculated for the same feed rate of wafers as used in the previous calculation for the multi-compartment fluidized bed dryer and are presented in Table 4.7. The closeness of the predicted and actual energy requirements and inlet gas temperatures suggest that the assumptions made in calculating the energy requirements are valid. 203 FIGURE 4.5: Scaled diagram of a twin triple-pass drum drying system. This dryer was used by MacMillan Bloedel, Thunder Bay Division to dry 75 mm wafers. (A) rotary valve; (B) 3.7 m diameter x 16.8 m long triple-pass drying chamber; (C) drop-out box; (D) cyclones; (E) internal draft fans; (F) exhaust stack. 204 TABLE 4.7: Energy Balance for a Triple-Pass Drum Dryer Producing Wafers Dried to 3% Moisture Content at a Rate of 2.53 kg/s (Oven Dry Basis)1. Volumetric Air Flow Rate (m3/s) 25.5 Air Mass Flow Rate (kg/s) 21.4 Initial Wafer Moisture Content (%) 100 Final Wafer Moisture Content (%) 3.0 Free Water Evaporated (kg/s) 1.77 Bound Water Evaporated (kg/s) 0.68 Inlet Air and Wafer Temperature (°C) 20 Exhaust Air Temperature (°C) 148 Energy Requirements Incoming Air (kW) 2789 Wood Substance (kW) 440 Water in Wafers (kW) 761 Free Water Evaporation (kW) 3994 Bound Water Evaporation (kW) 1818 Water Vapour (kW) 230 Transmission Heat Losses (kW) 501 Leakage Air (kW) 960 Total Energy Requirement (kW) 11 493 Actual Dryer Energy Input (kW) 11 000 Estimated Inlet Air Temperature (°C) 510 Actual Dryer Inlet Temperature (°C) 510 See Appendix M for the calculation of the listed quantities. 205 TABLE 4.8: Comparison of Triple-Pass Drum Dryer with the Proposed Five-Compartment Fiuidized Bed Dryer for Drying Wafers at a Rate of 2.53 kg/s (Oven Dry Basis). Five-Compartment Drum Dryer Fiuidized Bed Dryer Dryer Size (m) Diameter 3.7 Width 4.6 Length 16.8 Length 6.7 Height 4 Air Mass Flow Rate (kg/s) 21.4 16.5 1 Inlet Gas Temperature (°C) 510 429 2 Outlet Gas Temperature (°C) 148 120 Water Evaporation Rate (kg/s) 2.45 2.45 Total Energy Required (kJ/s) 11 493 8790 Specific Energy Use (kJ/kg water evaporated) 4691 3588 Air mass flow rate of 5-compartment dryer calculated using U — Umj = 0.95 m/s for compartment 1 and 0.75 m/s for the remaining compartments. Mean of inlet temperatures for the 5 compartments. Compartment 1 inlet temperature was reduced from 1040°C to 733°C by increasing (U — Umf) to 0.95 m/s and using the compartment walls as heat transfer surfaces. 4.7 Comparison of Wafer Drying in a Triple-Pass Drum Dryer and a Multi-Compartment Fiuidized Bed Dryer Table 4.8 compares the two drying systems based on the previous calculations in Sec-tions 4.5 and 4.6 with the exception that the 5-compartment bed calculations include an increased superficial velocity to compartment 1. The multi-compartment fiuidized bed dryer requires only about 75% of the energy required by the triple-pass drum dryer to dry the same quantity of wafers. The bulk of the savings in energy results from the reduced air mass flow rate (77% of the triple pass dryer) and lower exhaust gas temperature (120°C vs. 148°C). 206 In each compartment of the fluidized bed dryer, changes in the inlet feed moisture content may be quickly detected by changes in the bed temperature. The inlet gas temper-ature can then be adjusted to maintain the desired bed temperature according to drying load. In a triple-pass drum dryer, the response time to changing inlet feed moisture content is slow in comparison to that in fluidized beds and may be monitored only at the exit of the dryer approximately 50 m downstream from the inlet. It is the superior control of the drying process in the 5-compartment fluidized bed dryer over that in the triple-pass dryer that permits the use of higher inlet gas temperatures and the exhaust of lower temperature waste gas. The fabrication and installation of the multi-compartment fluidized bed is expected to be as expensive as the triple pass drum dryer (~ $1,500,000 Canadian) even though it is considerably smaller in size and requires a lower flow rate of air. The extra costs incurred in its construction will be primarily for the manufacture of the distributors, the instrumentation and controls for each compartment, and the supply of air at approximately 0.14 MPa. A full economic analysis of these two alternatives is beyond the scope of this thesis. 207 4.8 Conclusion Calculations on the operation of a multi-compartment fluidized bed dryer to handle 0.1 m long wafers were based on the beds in each compartment being closer to ideally mixed than to the desired plug flow of the experimental dryer. However, by combining five fluidized beds in series, a narrow wafer residence time distribution could be obtained. The resultant configuration for an industrial sized dryer was shown by calculation to consume 25% less energy than a conventional triple pass drum dryer in drying the same feed rate of wafers from 100% to 3% moisture content. Full scale cold bed tests are recommended to determine the optimal method of circu-lating the sand and wafers between compartments and to test the ability of a spout/fluid bed to prevent wafers from settling onto air distributors. 208 Chapter 5 Conclusions The drying behaviour of aspen wafers in air was found to be significantly influenced by the effect of wafer length on the external heat and mass transfer rates to the wafer surface, and on the length of the internal pathways for bulk flow of water liquid and vapour, and bound water/water vapour diffusion. The external drying conditions had a decreasing effect on wafer drying rate down to about 10% moisture content, at which point drying became limited by internal heat and mass transport in the wafer. These results imply that the rotary dryers used in the waferboard industry will have a reduction in drying capacity with each increase in wafer length used in board manufacture. Furthermore, the wafer drying process could benefit from a more efficient method of contacting the wafer with the drying medium than is currently available in the rotary dryers. Wafers dried much faster in a fiuidized bed than in forced convection of air because of the high rate of heat and mass transfer in fiuidized beds. The resultant drying times in fiuidized beds were about 40% of the drying times for wafers dried by forced convection of air at the same temperature and twice the superficial velocity. However, the need to control the movement of the wafers in a fiuidized bed of particulate solids limited the range of fluidizing conditions which could be used and complicated the application of fiuidized bed technology to wafer drying. Wafer movement in the fiuidized bed followed the circulation patterns of the emulsion 209 phase and was thus dependent on the bubbling behaviour of the bed. Wafers settled to the distributor unless a passing bubble caused it to be carried upward in its wake or drift. The ability of a bubble to lift wafers off the grid appeared to depend on the volume of solids that could be entrained in its wake and drift and not on the relative densities of the wafers and the emulsion phase. A minimum excess superficial velocity of 0.25 m/s (depending on distributor design) was required to prevent permanent settling of the wafers to the distributor. Although preliminary experimentation on a 2-compartment bed showed that wafers could be circulated through the two compartments in near plug flow, the application of this technique to a 4-compartment continuous fluidized bed dryer was not successful. The operation of the continuous experimental dryer was limited by low compartment cross-sectional diameter to wafer length ratio and slugging in downflowing beds. The combination of these two problems caused an accumulation of wafers in the downflowing beds and their eventual defluidization. The surfaces of the dried wafers exiting from the experimental dryer (prior to defluidization) were free of sand. To avoid the problems encountered with the experimental continuous dryer, the pro-posed configuration for an industrial size fluidized bed wafer dryer used a bed diameter of 2 m and a bed height less than 4 m to handle 0.1 m long wafers. Since the particle mixing in a bed of this size would approach perfect mixing rather than plug flow, the proposed fluidized bed dryer was designed to approach plug flow by the linking of several fluidized beds in series. A 5-compartment fluidized bed dryer of this design was shown by calcula-tion to be more efficient than the conventional triple pass drum dryers in terms of energy consumption and the need for plant space. Full size cold bed tests, and an economic comparison of the multi-compartment fluidized bed and rotary dryers will be necessary to determine whether further development work should be done on this drying process. 210 Nomenclature Symbol Definition Units a, b radius and length of glass pipe respectively m A y-intercept of drying rate curve of the initial falling rate period %/s A a intercept of the line A/(T — 100) vs velocity %/s C Ab slope of the line A/(T — 100) vs velocity %/m s Abed cross-sectional area of bed m 2 Ai effect of treatment A -AB{j interaction between effects A and B to produce a third effect -Ar Archimedes number -A x surface area of glass pipe m 2 A 2 surface area of wafer m 2 B slope of drying rate curve of the initial falling rate period 1/s Ba intercept of the line B vs velocity 1/s Bb slope of the line B vs velocity 1/m Bj effect of treatment B -c,d width and length of wafer respectively m C breakpoint moisture content % heat capacity kJ/kg C *i maximum diameter of jetsam particle lifted in bubble wake m dL large body diameter m dp Sauter mean particle diameter mm D molecular diffusion coefficient of water vapour m2/s DB,o initial bubble diameter m e fitting constant, 1.98 X 107 • T - 2 6 3 + 7.78 -E total free moisture content over the initial moisture content true error, variation in the data not attributable to the treatments -E(t) exit age residence time distribution -Ei -E2 e2/l - e2 -f fitting constant, 11.9 x 107 • T - 3' 2 9 + 1.41 -wake volume/wake and bubble volume -F(t) fraction of total appearances with an appearance interval less than time t Fu, Fu, F13 radiation shape factors (1-glass pipe, 2-wafer) -K average external heat transfer coefficient at a distance r from the centre of the pipe W/m2 C H fiuidized bed height m 211 Symbol Definition Units AHb Hmf Ha AHV i 3 (io)m/ k k ki k2 K L Li m M n N Nuav A JP BED m f ?0,1,?0,2 Ql.Q2 r R Re ReL Rtrnf s S hav t t U kg/m2 m2/s m m % differential heat of sorption kJ/kg fluidized bed height at minimum fluidization m static bed height m heat of vaporization J/kg treatment group for effect A -treatment group for effect B -mass transfer factor at minimum fluidization -number of samples per treatment group -average of ki and &2 — maximum convective mass transfer coefficient based on humidity difference fitting constant, 8.75 x 10~4 • pL + 2.98 fitting constant, 4.17 x 10~5 • dL + 1.46 diffusion coefficient of water through solid thickness thickness for which Aa, At, Ba and Bt were determined fractional moisture content fractional maximum moisture content moisture content number of orifices in distributor number of reactors in series average Nusselt number maximum Nusselt number fluidized bed pressure drop at minimum fluidization rate of radiative heat transfer being absorbed by glass pipe and wafer respectively rate of radiative heat transfer being emitted by glass pipe and wafer respectively total radiative heat transfer from glass pipe and wafer respectively radial distance from the centre of the pipe correlation coefficient radius of the pipe Reynolds number -length Reynolds number -Reynolds number at minimum fluidization -veneer thickness mm average Sherwood number -time s mean residence time for reactors in series s mean residence time in each reactor s AH Pa W/m2 W/m2 W m m 212 Symbol Definition Units T air temperature C Ti, T2 surface temperature of glass pipe and wafer respectively K U superficial velocity m/s Um\) minimum bubbling velocity m/s Umf superficial velocity at minimum fluidization m/s Ums minimum slugging velocity m/s ^U-OBJECT upward velocity of a large object in a fiuidized bed of solids m/s V air stream velocity m/s VD downward emulsion phase velocity m/s Vmax measured maximum velocity (at the pipe centre) m/s Vr average velocity at a distance r from the centre of the pipe m/s Vz velocity in the axial direction m/s x half-thickness of the slab m Y ratio of actual bubble flow rate to value predicted by 2-phase theory -Yijk dependent variable -PD volume fraction of solids (based on bubble volume) carried by a bubble due to drift -f3w volume fraction of solids (based on bubble volume) carried by a bubble within its wake -eg volume fraction of bed consisting of bubbles -emf voidage at minimum fluidization ei emissivity of glass -£2 emissivity of wood -9 time s u true mean of dependent variable -p density of wood kg/m3 Pbulk bulk density of particles kg/m3 PL large body density kg/m3 pp particle density kg/m3 ps saturated wood density kg/m3 pi density of wood for which Aa, Ab, Ba and Bb were determined kg/m3 a Stefan-Bolzmann constant W/m2 • K r veneer drying time s 213 References Atherton, G.A. and J.R. Welty, Drying Rates of Douglas-fir Veneer in Superheated Steam at Temperatures to 800°F. Wood Sci. 4(4):209- 218 (1972). Babailov, V . E . and V.N. Petri, Drying Peeled Veneer in a Pseudo-Fluidized Layer of Inert Fine-Granular Material. Lesnoi Zhurnal, 17(l):85-88 (1974). Baeyens, J. and D. Geldart, Solids Mixing. Chapter 5, in Gas Fluidization Technology, ed. D. Geldart, John Wiley and Sons Ltd., Toronto, 97-102 (1986). Baeyens, J. and D. Geldart, "Particle Mixing in a Gas Fluidized Bed", in La Fluidi-sation et ses Applications. Cepadues Editions, Toulouse, France, 182-195 (1973). Baskakov, A.P., B.V. Berg, O.K. V i t t , N.F. Filippovsky, V.A. Kirakosyan, J.M. Goldobin and V.K. Maskaev, Heat Transfer to Objects Immersed in Flu-idized Beds. Powder Tech., 8:273-282 (1973). Beall, F.C, Introduction to Thermal Analysis In the Combustion of Wood. Wood Science, 5(2):102-108 (1972). Beall, F.C, Personal Communication. University of Toronto, Faculty of Forestry, 1977. Bemrose, CR., J.S. M. Botterill, J. Bridgwater and A . W . Nienow, Large Par-ticle Motion on the Distributor of a Fluidized Bed of Sand, in Fluidization V, eds. K. Ostergaard and A. Sorenson, Engineering Foundation, New York, 201-208 (1986). Berruti, F., A.G. Liden and D.S. Scott, Measuring and Modelling Residence Time Distribution of Low Density Solids in a Fluidized Bed Reactor of Sand Particles. Chem. Eng. Sci., 43(4):739-748 (1988). Bethel, J.S. and R.J. Hader, Hardwood Veneer Drying. Forest Prod. J., 5(12):205-215 (1952). Bilbao, R., J. Lezaun and J.C. Abanades, Fluidization Velocities of Sand/Straw Binary Mixtures. Powder Technology, 52:1-6 (1987). Bilbao, R., J. Lezaun, M. Menendez and J.C. Abanades, Model of Mixing-Segregation for Straw/Sand Mixtures in Fluidized Beds. Powder Technology, 56:149-155 (1988). Bird, R.B., W.E. Stewart and E.N. Lightfoot, Transport Phenomena, John Wiley and Sons, Toronto, 1960. Botterill, J.S.M., Y. Teoman and K. R. Yuregir, Factors Affecting Heat Transfer Between Gas-Fluidized Beds and Immersed Surfaces. Powder Tech., 39:177-189 (1984). Botterill, J.S.M., Y. Teoman and K.R. Yuregir, The Effect of Temperature on Fluidized Bed Behaviour. Chem. Eng. Commun., 15:227-238 (1982). 214 Boucher, D.F. and G.E. Alves, "Fluid and Particle Mechanics", in Perry's Chemical Engineers' Handbook, 6th Edition, ed. D.W. Green, McGraw-Hill Book Co., toronto, 5-12 to 5-17 (1984). Carruthers, J.F.S. and M.S. Burridge, The Drying of Veneers in a Fluid Bed. Forest Prod. J., 14(6):251-253 (1964). Carter, B., M. Ghadiri, R. Clift and A.W. Jury, The Behaviour of Large Jetsam Particles in Fluidized Beds. Powder Technology, 52:263-266(1987). Cech, M.Y. and F. Pfaff, "Kiln Operator's Manual for Eastern Canada", FORINTEK Canada Corp., Special Publication SP504ER (1980). Chapman, A.J., Heat Transfer 3rd Edition. MacMillan Publishing Co., N.Y., (1974). Chen, P. and D.C.T. Pei, A Model of Heat Transfer Between Fluidized Beds and Immersed Surfaces. Int. J. Heat and Mass Transfer, 28(3):675-682 (1985). Chiba, T. and A.W. Nienow, "Defluidization of Large Particles Due to Segregation", in Fluidization, eds. D. Kunii and R. Toei, Engineering Foundation, New York, 195-202 (1983). Choi, J.H., J.E. Son and S.D. Kim, Bubble Size and Frequency in Gas Fluidized Beds. Journal of Chemical Engineering of Japan, 21(2):171-178 (1988). Chong, Y.-O., D.J. Nicklin and P.J. Tait, Solids Exchange Between Adjacent Fluid Beds Without Gas Mixing. Powder Technology, 47:151-156 (1986). Ciborowski, J. and J. Kopec, The Mechanism of Mass Transfer from an Immersed Surface to a High Mass Capacity Fluidized Bed. Chem. Eng. J., 31:63-73 (1985). Clift, R. and J.R. Grace, Continuous Bubbling and Slugging. Chapter 3 in Fluidiza-tion, 2nd edition, ed. J.F. Davidson, R. Clift and D. Harrison. Academic Press, (1985). Cobbinah, S.C. Laguerie and H. Gibert, Simultaneous Heat and Mass Transfer Between a Fluidized Bed of Fine Particles and Immersed Coarse Porous Particles. Int. J. Heat and Mass Transfer, 30(2):395-100 (1987). Coelho, M.A.N, and J.R.F. Guedes De Carvalho, Transverse Dispersion in Granu-lar Beds, Part II - Mass Transfer From Large Spheres Immersed in Fixed or Fluidised Beds of Small Inert Particles. Chem. Eng. Res. Des., 66:178-189 (1988). Comings, E.W., Contributions of T. K. Sherwood and Associates to the Field of Drying, Part 1. Drying Technology, l(2):249-273 (1983-1984). Comings, E.W. and T.K. Sherwood, The Drying of Solids. VII, Moisture Movement by Capillarity in Drying Granular Materials. Industrial and Engineering Chemistry, 26(10):1096-1098 (1934). Comstock, G.L., The Kinetics of Veneer Jet Drying. Forest Prod. J., 21(9):104-111 (1971). 215 Cook, E.M. and H.D. DuMont, New Ideas to Improve Dryer Performance. Chemical Engineering, 95(7):70-78 (1988). Crane Canada Inc., Flow of Fluids Through Valves, Fittings and Pipes. Technical Paper No. 410-C, 23rd Edition, Crane Canada Inc., Valve and Industrial Division, Montreal, (1987). Danckwerts, P.V., Continuous Flow Systems - Distribution of Residence Times. Chem. Eng. Sci., 2(l):l-3 (1953). Dorri, B., A.F. Emery and P.C. Malte, Drying Rate of Wood Particles with Longi-tudinal Mass Transfer. Trans. A.S.M.E. J. Heat Transfer, 107(2):12-18 (1985). Feng, D., H. Chen and W.B. Whiting, The Effects of Distributor Design on Fluidized-Bed Hydrodynamic Behavior. Chem. Eng. Commun., 36:317-332 (1985). Fleischer, H.O., Drying Rates of Thin Sections of Wood at High Temperatures. Yale Univ. School of Forest Bull. No. 59. (1953). Fortes, M. and M.R. Okos, A Non-Equilibrium Thermodynamics Approach to Trans-port Phenomena in Capillary Porous Media. Proc. 1st Int. Symp. on Drying, McGill Univ., Montreal, ed. A.S. Mujumdar, 100-108 (1978). George, S.E., Heat Transfer to Tubes in the Freeboard Region of a Fiuidized Bed. Ph.D. dissertation, McGill University, Montreal, 1980. Gloski, D., L. Glicksman and N. Decker, Thermal Resistance at a Surface in Contact with Fiuidized Bed Particles. Int. J. Heat Mass Transfer, 27(4):599-610 (1983). Grace, J.R., Fluidized-Bed Hydrodynamics. Chapter 8.1 in Handbook of Multiphase Systems, ed. G. Hetsroni. Hemisphere, Washington, (1982). Grieg, M., Personal Communication. Senior Analyst, Computing Department, Univer-sity of British Columbia, 1988. Hann, R.W., Drying Yellow-Poplar at Temperatures above 100°C. Forest Prod. J., 14(5):215-221 (1964). Himmelblau, D.M., Basic Principles and Calculations in Chemical Engineering. 3rd Edition, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1974. Hirama, T., T. Adachi and H. Yamaguchi, Lateral Thermal Diffusivity in a Fiu-idized Bed with Floating Packings. Heat Trans. Jap. Res., 8:49-52 (1981). Ho, T.-C, T.K. Chen and J.R. Hopper, Pressure Drop Across the Distributor in Fiuidized Beds with Regular and Irregular Distributor Design, in Fluidization and Fluid Particle Systems: Recent Advances, ed. G.E. Klin-Zing, A.I.Ch.E. Symposium Series, 241(80) :34-40 (1984). Holman, J.P., Heat Transfer. 5th Edition, McGraw-Hill Book Co., Toronto, 1981. Hougen, O.A., H.J. McCauley and W.R. Marshall Jr., Limitations of Diffusion Equations in Drying. Trans. A.I.Ch.E., 36:183-209 (1940). 216 Kawai, S., K. Nakato and T. Sadoh, Moisture Movement in Wood Below the Fiber Saturation Point. Mokuzai Gakkaishi, 24(5):273-280 (1978). Keey, R.B., Drying Principles and Practice. Permagon Press, Toronto, ON (1972). Kininmonth, J.A., Permeability and Fine Structure of Certain Hardwoods and Effects on Drying, III. Problems in Drying of Heartwood. Holzforschung, 27:26-31 (1973). Kollman, F.FJP. and W.A. C6te\ Jr., Principles of Wood Science and Technology, I., Solid Wood. Springer-verlag, New York, NY (1968). Kossatz, G., Physical, Chemical and Thermal Occurrences During the Drying of Wood Particles. Proceedings of the Jubilee Symposia, University of Stellenbosch, Faculty of Forestry, Mededeling Communication, 98(II):748-764 (1982). Kuramoto, M., D. K u n i i and T. Furusawa, Flow of Dense Fluidized Particles Through an Opening in a Circulation System. Powder Technology, 47:141-149 (1986). Laity, W.W., G.H. Atherton and J.R. Welty, Comparisons of Air and Steam as Veneer Drying Media. Forest Prod. J., 24(6):21-29 (1974). L a Nauze, R.D., A Circulating Fluidized Bed. Powder Technology, 15:117-127 (1976). L a Nauze, R.D. and K. Jung, Mass Transfer Relationships in Fluidized-Bed Combus-tors. Chem. Eng. Commun., 43:275-286 (1986). Levenspiel, O., Chemical Reaction Engineering. John Wiley and Sons, Inc., Toronto, 1972. Loos, W.E., Fluidized Bed Drying of Southern Pine Veneer. Forest Prod. J., 21(12):44-49 (1971). Loos, W.E. and C.Y. Wen, Fluidized Bed Drying of Yellow-Poplar Veneer. Forest Prod. J., 20(6):56-58 (1970). Lyman, L.C., Effect of Air Flow on Heat Transfer and Water Evaporation in Jet-Drying Systems. Forest Prod. J., 15(10):453-459 (1965). MacKay, J.F.G., Influence of Steaming on Water Vapor Diffusion in Hardwoods. Wood Science, 3(3):156-160 (1971). Malte, P.C, R.W. Cox, R.J. Robertus, G.R. Messinger and M.D. Strickler, Wood Particle Drying rates. Proc. W.S.U. Particleboard Symp. #11, ed. T. Maloney, 231-257 (1977). Masson, H.A., G.M. Rios, K. Dang Tran and K . C Bourtembourg, Shape and Density Effects on the Behaviour of a Large Isolated Body Moving in a Gas Solid Fluid Bed, in Fluidization, eds. D. Kunii and R. Toei. Engng. Foundation, New York, 185-193 (1983). Milligan, F.H. and R.D. Davies, High Speed Drying of Western Softwoods for Exterior Plywood. Forest Prod. J., 13(l):23-29 (1963). 217 Milota, M., Engineering Study on the Drying of Wood Particles in a Fiuidized Bed. Ph.D. thesis. Oregon State University, Eugene, OR, (1984). Molstad, M.C., P. Farevaag and J.A. Farrell, Rate of Evaporation from a Free Water Surface by a Perpendicular Air Stream. Industrial and Engineering Chemistry, 30(10):1131-1137 (1938). Nelson Jr., R.M., Diffusion of Bound Water in Wood, Part 1: The Driving Force. Wood Sci. Technol., 20:125-135 (1986a). Nelson Jr., R.M., Diffusion of Bound Water in Wood, Part 2: A Model for Isothermal Diffusion. Wood Sci. Technol., 20:235-251 (1986b). Nelson Jr., R.M., Diffusion of Bound Water in Wood, Part 3: A Model for Nonisother-mal Diffusion. Wood Sci. Technol., 20:309-328 (1986c). Newman, A.B., The Drying of Porous Solids: Diffusion and Surface Emission Equations. Trans. A.I.Ch.E., 27:203-220 (1931a). Newman, A.B., The Drying of Porous Solids: Diffusion Calculations. Trans. A.I.Ch.E., 27:310-333 (1931b). Nienow, A.W. and D.J. Cheesman, The Effect of Shape on the Mixing and Segre-gation of Large Particles in a Gas-Fluidized Bed of Small Ones, in Fluidization, ed. J.R. Grace and J.M. Matsen. Plenum Press, New York, 373-380 (1980). Nienow, A.W., P.N. Rowe and T. Chiba, Mixing and Segregation of a Small Propor-tion of Large Particles in Gas Fiuidized Beds of Considerably Smaller Ones. A.I.Ch.E. Symp. 74(176):45-53 (1978). Nguyen, T.H. and J.R. Grace, Forces on Objects Immersed in Fiuidized Beds. Powder Tech., 19:255-264 (1978). Panshin, A.J. and C. de Zeeuw, Textbook of Wood Technology. Volume I, 3rd edition. McGraw-Hill Book Co., Toronto, ON, (1970). Perng, W.R., K.I. Brebner and M.H. Schneider, Aspen Wood Anatomy and Fluid Transport. Wood and Fiber Sci., 17(2):281-289 (1985). Petty, J.A., Fluid Flow Through the Vessels and Intervascular Pits of Sycamore Wood. Holzforschung, 35:213-216 (1981). Plagemann, W.L., E.W. Price and W.E. Johns, The Response of Hardwood Flakes and Flakeboard to High Temperature Drying. J. Adhesion, 16:311- 338 (1984). Prak, A.L., Unsteady-State Gas Permeability of Wood. Wood Science and Technology, 4:50-69 (1970). Prins, W., W. Draijer and W.P.M. van Swaaij, Heat Transfer to Immersed Spheres Fixed or Freely Moving in a Gas-Fluidized Bed, in Heat and Mass Transfer in Fixed and Fiuidized Beds, eds. W.P.M. van Swaaij and N.H. Afgan, Hemisphere Pub. Co., New York, 317-331 (1986). 218 Prins, W., T.P. Casteleijn, W. Draijer and W.P.M. Van Swaaij, Mass Transfer from a Freely Moving Sphere to the Dense Phase of a Gas Fluidized Bed of Inert Particles. Chem. Eng. Sci., 40(3):481-497 (1985). Pruden, B.B., D. Crosbie and B.J.P. Whalley, Circulation of Large Bodies in an Aggregatively Fluidized Bed, in Fluidization Technology, Volume 2, ed. D.L. Keairns. Hemisphere Pub. Co., Washington, 65-86 (1976). Raymus, G.J., Conveying of Bulk Solids, in Perry's Chemical Engineers' Handbook, 6th Edition, ed. D.W. Green, McGraw-Hill Book Co., Toronto, 7-1 to 7-20 (1984). Reay, D. and C.G.J. Baker, Drying. Chapter 16 in Fluidization, 2nd edition, ed. J.F. Davidson, R. Clift and D. Harrison. Academic Press, 529-562 (1985). Richardson, J.F. and K.J. Shakiri, Heat Transfer Between a Gas-Solid Fluidized Bed and a Small Immersed Surface. Chem. Eng. Sci., 34:1019- 1029 (1979). Rios, G.M. and H. Gibert, Heat Transfer Between Gas Fluidized Bed and Big Bodies: Analysis and Explanation of Big Body Mobility Effects, in Fluidization, eds. D. Kunii and R. Toei. Engineering Foundation, New York, 363-370 (1983). Rios, G.M., K. Dang Tran and H. Masson, Free Object Motion in a Gas Fluidized Bed. Chem. Eng. Commun., 47:247-272 (1986). Robinson, J.W., A New Drying Model for Wood Veneer. Presented at North American Wood Drying Symposium, Mississippi State, MS, (1984). Roques, M.A. and A.R.H. Cornish, Phenomenological Coefficients For Heat and Mass Transfer Equations in Wet Porous Media, in Drying '80, Volume 2, Proc. 2nd Int. Symp., ed. A.S. Mujumdar. Montreal, 36-42 (1980). Rosen, H.N., Psychrometric Relationships and Equilibrium Moisture Content of Wood at Temperatures Above 212°F. Wood and Fiber, 12(3):153-171 (1980). Salin, J.-G., Optimization of Veneer Drying. Paperi ja Puu - Papper och Tra, 5:367-369, 373 (1984). Saxena, S.C. and J.D. Gabor, Mechanisms of Heat Transfer Between a Surface and a Gas-Fluidized Bed for Combustor Application. Prog. Energy Combust. Sci., 7:73-102 (1981). Sherwood, T.K., Application of Theoretical Diffusion Equations to the Drying of Solids. Trans. A.I.Ch.E., 27:190-202 (1931). Sherwood, T.K., The Air Drying of Solids. Trans. A.I.Ch.E., 32:150-168 (1936). Siau, J.F., Nonisothermal Moisture Diffusion Experiments Analyzed by Four Alternative Equations. Wood Sci. Technol., 19:151-157 (1985). Siau, J.F., Flow in Wood. Syracuse University Press, Syracuse, New York, (1984a). Siau, J.F., Letter to the Editor. Wood and Fiber Science, 16(4):628-629 (1984b). 219 Siau, J.F., A Proposed Theory for Nonisothermal Unsteady-State Transport of Moisture in Wood. Wood Sci. Technol., 17:75-77 (1983a). Siau, J.F., Chemical Potential as a Driving Force for Nonisothermal Moisture Movement in Wood. Wood Sci., Yechnol., 17:101-105 (1983b). Siau, J.F., Nonisothermal Moisture Movement in Wood. Wood Science, 13(l):ll-13 (1980). Siau, J.F. and M. Babiak, Experiments on Nonisothermal Moisture Movement in Wood. Wood Fiber, 15(l):40-46 (1983). Siau, J.F., F. Bao, and S. Avramidis, Experiments in Nonisothermal Diffusion of Moisture in Wood. Wood and Fiber Science, 18(l):84-89 (1986). Siegel, R. and J.R. Howell, Thermal Radiation Heat Transfer. 2nd Edition, Hemi-sphere Pub. Co., New York (1981). Skaar, C. and M. Babiak, A Model for Bound-Water Transport in Wood. Wood Sci. Technol., 16:123-138 (1982). Skaar, C. and N. Kuroda, Application of Irreversible Thermodynamics to Moisture Transport Phenomena in Wood. Presented at North American Wood Drying Sym-posium, Mississippi State, MS, (1984). Skaar, C. and J.F. Siau, Thermal Diffusion of Bound Water in Wood. Wood Sci. Technol., 15:105-112 (1981). Snedecor, G.W. and W.G. Cochran, Statistical Methods. 6th Edition, Iowa State University Press, Ames, Iowa, 1967. Sparrow, E.M. and R.D. Cess, Radiation Heat Transfer. 2nd Edition, Wadsworth Pub. Co., Inc., Belmont, CA (1970). Spolek, G.A. and O.A. Plumb, A Numerical Model of Heat and Mass Transport in Wood during Drying, in Drying '80, Volume 2, Proc. 2nd Int. Symp., ed. A.S. Mujumdar. Montreal, 84-92 (1980). Spolek, G.A. and O.A. Plumb, Capillary Pressure in Softwoods. Wood Sci. Technol., 15:189-199 (1981). Stamm, A.J., Wood and Cellulose Science. Ronald Press Co., New York, 1964. Stanish, M.A., The Roles of Bound Water Chemical Potential and Gas Phase Diffusion in Moisture Transport Through Wood. Wood Sci. Technol., 19:53-70 (1986). Stanish, M.A. and F. Kayihan, Moisture Transport in Wood Particles During Dry-ing, in The Impact of Energy and Environmental Concerns on Chemical Engineer-ing in the Forest Products Industry, ed. H.N. Rosen, A.I.Ch.E. Symposium Series, 239(80):9-20 (1984). Stanish, M.A., G.S. Schajer and F. Kayihan, A Mathematical Model of Drying for Hygroscopic Porous Media. A.I.Ch.E. Journal, 32(8):1301-1311 (1986). 220 Stipek, J.W., The Present and Future Technology in Wood Particle Drying, in Proc. 16th Int. Particleboard Symp., ed. T.M. Maloney. Washington State University, Pullman, 161-183 (1982). Tesoro, F.O., E.T. Choong and O.K. Kimbler, Relative Permeability and the Gross Pore Structure of Wood. Wood and Fiber, 6(3):226-236 (1974). Thiel, W.J. and O.E. Potter, The Mixing of Solids in Slugging Gas Fiuidized Beds. A.I.Ch.E. Journal, 24(4):561-569 (1978). Trees, J., A Practical Investigation of the Flow of Particulate Solids Through Sloping Pipes. Trans. Inst. Chem. Engineers, 40:287-296 (1962). Treybal, R.E., Mass-Transfer Operations. 3rd Edition, McGraw-Hill Book Co., Toronto, 1980. Vajda, P., The Historical Development of Waferboard Plant Equipment. Canadian Waferboard Symposium Proceedings, FORINTEK Canada Corp. Special Publica-tion, SP 505E, 147-161 (1980). Vala, T., Improved Wood Drying for Board - Processing Industries. Canadian Wafer-board Symposium Proceedings, FORINTEK Canada Corp. Special Publication, SP 508E, 227-233 (1982). Vanecek, V., M. Markvart and R. Drbohlav, Fiuidized Bed Drying. Leonard Hill, Lond (1966). Vanecek, V., M. Markvart, R. Drbohlav and R.L. Hummel, Experimental Ev-idence on Operation of Continuous Fluidized-Bed Driers. Chem. Eng. Prog. Symp. Series, 105(66):243-252 (1970). Ward, J.C, The Effect of Wetwood on Lumber Drying Times and Rates: An Ex-ploratory Evaluation with Longitudinal Gas Permeability. Wood and Fiber Science, 18(2):288-307 (1986). Watson, K., Personal communication. MacMillan Bloedel Ltd., Parallam Division (for-merly: Head of Quality Control, MacMillan Bloedel Ltd., Thunder Bay Division) (1985). Wen, C.Y. and W.E. Loos, Rate of Veneer Drying in a Fiuidized Bed. Wood Sci., 2(2):87-90 (1969). Wu, S.W.M., Hydrodynamics of Gas Spouting at High Temperature. M.A.Sc. dissera-tion, University of British Columbia, (1986). Zabrodsky, S.S., Y.G. Epanov and D.M. Galershtein, On the Dependence of Fiuidized Bed-Wall Heat Transfer Coefficients on the Thermal Conductivity and Volumetric Heat Capacity of the Particles, in Fluidization, Proceedings of the Second Engineering Foundation Conference, eds. J.F. Davidson and D.L. Keairns, Cambridge University Press, 362-375 (1978). 221 Zhao, J.-S., Coal Combustion in Spouted and Spout/Fluid Beds. M.A.Sc. dissertation, University of British Columbia, 1986. Zwick, R.L. , An Overview of Mathematical Models for Moisture Migration in Wood, prepared for: Canadian Forest Service on Contract No: 02-40-12-427, FORINTEK Canada Corp, Vancouver, 1985. 222 Appendix A Coefficients for Polynomial Equation Used to Fit Drying Curve Data The weight vs. time data obtained for drying of individual wafers was fitted using a poly-nomial of the form: y = A 0 + A i • X + A2 • X2 + A3 • X3 + A 4 • X4 + A5 • Xs (A.l) The resultant curves had an excellent fit as shown in Figure 1.16 and discussed in Section 1.2.6. 223 T A B L E A . l : Polynomial Coefficients for 25 mm Wafers Dried at 90°C. Wafer // A o A l A 2 A 3 A A A 5 1 1 . 1421 - 0 . 9 6 8 8 E - -01 0 . 1 1 0 0 E - - 0 2 0 . 7 4 8 3 E - - 0 5 0 . 1 6 7 5 E - - 0 4 - 0 . 5 7 0 2 E - - 0 6 2 1 . 0 2 5 7 - 0 . 9 7 3 3 E - -01 0 . 1 4 2 4 E - - 0 2 - 0 . 1 7 9 6 E - - 0 3 0 . 281 1E-- 0 4 0 . 2 0 3 0 E - - 0 6 3 1 . 15 11 - 0 . 9 1 9 5 E - -01 • 0 . 4 2 4 7 E - - 0 2 0 . 1 1 4 3 E -- 0 2 - 0 . 8 3 0 4 E - - 0 4 0 . 2 8 1 4 E - - 0 5 4 1 . 0 7 7 9 - 1 . 0 1 6 7 E - -01 0 . 4 0 2 7 E - - 0 2 - 0 . 2 7 8 8 E - - 0 3 0 . 2 3 9 8 E - - 0 4 - 0 . 3 9 2 0 E - - 0 6 5 1 . 1 2 4 8 - 0 . 9 7 5 3 E - -01 - 0 . 1 5 3 6 E - - 0 4 0 . 2 1 5 0 E -- 0 3 - 0 . 1 1 3 3 E -- 0 4 0 . 1 1 6 7 E - - 0 5 6 1 . 1 3 9 0 - O . 9 8 9 8 E - -01 0 . 1 8 8 9 E - - 0 2 - 0 . 6 5 0 1 E - - 0 4 0 . 9 5 7 4 E - - 0 5 0 . 1 3 4 3 E - - 0 6 7 1 . 1 163 - 0 . 9 5 9 8 E - -01 -o. 5 3 5 7 E - - 0 4 0 . 1 3 6 5 E - - 0 3 0 . 3 4 8 8 E - - 0 5 0 . 2 8 3 3 E - 0 6 8 0 . 8 4 9 0 - 0 . 8 4 7 1 E -01 - 0 . 3 9 9 8 E ' - 0 2 0 . 1 4 8 1 E - - 0 2 - 0 . 1 7 3 1 E - - 0 3 0 . 1 0 0 8 E - 0 4 9 1 . 0 9 5 5 - 0 . 9 7 1 0 E ' -01 0 . 6 0 9 6 E - - 0 3 0 . 3 2 7 6 E - - 0 3 - 0 . 2 8 9 3 E - - 0 4 0 . 1 4 8 6 E - - 0 5 10 1 , , 0 8 6 8 - 0 . 9 4 5 0 E -01 - 0 . 6 5 12E - 0 3 0 . 3 8 1 9 E - - 0 3 - 0 . 1 4 7 6 E - - 0 4 0 . 6 9 2 5 E - - 0 6 1 1 1 , . 1 0 4 8 - 0 . 9 3 5 5 E -01 0 . 6 3 0 9 E - 0 3 0 . 3 4 8 3 E - - 0 3 - 0 . 2 6 4 3 E - - 0 4 0 . 1 1 7 3 E ' - 0 5 12 1 . , 1 3 2 5 - 0 . 9 3 6 7 E -01 - 0 . 1 3 7 6 E - 0 2 0 . 5 0 0 3 E - - 0 3 - 0 . 3 0 4 9 E ' - 0 4 0 . 121 1E - 0 5 13 1 . . 0 7 7 9 - 0 . 9 9 5 3 E -01 0 . 1 182E - 0 2 0 . 2 6 3 5 E - - 0 3 - 0 . 1 8 2 7 E - - 0 4 0 . 8 6 0 0 E - 0 6 14 1 . , 1 6 14 - 0 . 9 2 7 5 E -01 -o. 3 4 4 7 E - 0 2 0 . 9 1 4 6 E - 0 3 - 0 . 6 6 4 1E-- 0 4 0 . 2 3 3 8 E - 0 5 15 1 . 1 7 8 5 - 1 . 0 4 8 8 E -01 0 . 3 8 1 6 E - 0 2 - 0 . 5 8 3 1 E - 0 3 0 . 6 4 4 4 E ' - 0 4 - 0 . 1 7 4 6 E - 0 5 16 1 . 1 2 8 6 - 0 . 9 9 4 6 E -01 0 . 6 6 8 6 E - 0 3 0 . 3 9 9 2 E - 0 3 - 0 . 4 7 2 4 E - - 0 4 0 . 2 6 5 9 E - 0 5 17 1 . 0 1 6 0 - 0 . 9 2 7 3 E - 0 1 -o. 31 16E - 0 2 0 . 1061 E - 0 2 - 0 . 9 6 1 5 E - 0 4 0 . 4 4 7 8 E - 0 5 18 0 . 9 9 8 4 - 0 . 9 6 6 8 E - 0 1 0 . 1 1 9 8 E - 0 2 0 . 1 4 7 6 E - 0 3 - 0 . 17 1 1 E - 0 4 0 . 2 101E - 0 5 19 1 . 0 1 9 8 - 0 . 9 6 0 7 E - 0 1 - 0 . 6 6 4 2 E - 0 3 0 . 5 5 9 7 E - 0 3 - 0 . 5 8 2 7 E - 0 4 0 . 3 5 0 4 E - 0 5 2 0 1 . 0 5 9 3 - 0 , 9 6 2 8 E - 0 1 - 0 . 7 5 4 6 E - 0 3 0 . 6 8 0 7 E - 0 3 - 0 . 6 9 7 2 E - 0 4 0 3 3 3 2 E - 0 5 2 1 1 . 1 6 7 6 - 0 , 7 0 6 1E - 0 1 - 0 . 5 8 0 7 E - 0 2 0 . 1 0 7 9 E - 0 2 - 0 . 8 1 18E - 0 4 0 . 2 7 5 4 E - 0 5 22 1 . 1 8 3 5 - 0 , , 7 6 9 0 E - 0 1 - 0 . 8 0 4 8 E - 0 2 0 . 1 7 9 7 E - 0 2 - 0 . 1 4 8 7 E - 0 3 0 . 4 8 9 5 E - 0 5 23 1 . 2 2 6 1 - 0 , , 7 9 1 1E - 0 1 - 0 , 6 132E - 0 2 0 . 1 165E - 0 2 - 0 . 7 3 0 9 E - 0 4 0 . 2 0 1 9 E - 0 5 24 1 . 0 8 6 5 - 0 . 9 5 3 6 E -01 - 0 , , 107 1E - 0 3 0 , , 2 9 0 9 E - 0 3 - 0 . 2 2 7 2 E - 0 4 0 . 1625E - 0 5 25 1 . 179 1 - 0 . 7 9 5 3 E - 0 1 -o, . 7 4 4 3 E - 0 2 0 . . 1 6 5 3 E - 0 2 - 0 , 1 3 7 5 E - 0 3 0 . , 4 8 0 5 E - 0 5 2G 0 . 9 9 5 0 - 0 . 9 6 6 6 E - 0 1 0 , , 1 5 2 6 E - 0 2 - 0 , , 3 4 2 1 E - 0 4 0 , , 8 0 9 7 E - 0 5 0 , , 7 0 5 4 E - 0 6 27 1 . 2 0 0 3 - 0 . 8 5 3 3 E - 0 1 - 0 . 5 3 4 6 E - 0 2 0 , . 1 157E - 0 2 - 0 . , 9 0 1 6 E - 0 4 0 , , 3 2 2 7 E - 0 5 28 1 . 2 165 - 0 . 8 4 6 9 E - 0 1 - 0 . 6 3 6 3 E - 0 2 0 . 1 3 6 1 E - 0 2 - 0 , 1 0 9 4 E - 0 3 0 , 3 8 3 2 E - 0 5 29 1 . 1924 - 0 . 8 6 9 3 E - 0 1 - 0 . 5 0 4 0 E - 0 2 0 . 1 184E - 0 2 ? 0 . 9 7 8 7 E - 0 4 0 , 3 6 6 0 E - 0 5 3 0 1 . 1 2 0 9 -o . 7 5 9 7 E - 0 1 - 0 . 1 0 1 5 E - 0 1 0 . 2 2 8 3 E - 0 2 - 0 . 2 0 2 5 E - 0 3 0 . 7 2 9 8 E - 0 5 3 1 1 . 17 50 -o . 0 1 7 11I - 0 1 - 0 . 6 4 I 0 E - 0 2 0 . H O S E - 0 2 - 0 . 1 I77E - 0 3 0 . 4 3 7 7 E - 0 5 32 1 . 2 0 9 7 -o . 8 4 9 4 E - 0 1 - 0 . 6 0 8 4 E - 0 2 0 . 1 5 3 6 E - 0 2 - 0 . 1 2 5 4 E - 0 3 0 . 4 1 4 1E - 0 5 33 1 . 2 4 3 2 - 0 . S 4 7 6 E - 0 1 - 0 . 4 9 6 2 E - 0 2 0 . 1 162E - 0 2 - 0 . 8 3 4 4 E - 0 4 0 . 2 4 0 8 E - 0 5 34 0 . 8 9 7 1 -o . 9 3 4 2 E - 0 1 0 . 1 6 0 5 E - 0 2 - 0 . 3 7 0 4 E - 0 4 0 . 2 2 7 1 E - 0 4 0 . 1 2 4 6 E - 0 7 3 5 1 . 1 8 2 8 -o . 7 6 4 5 E - 0 1 - 0 . 9 3 4 1 E - 0 2 0 . 2 0 1 1 E - 0 2 -o . 1 6 9 1 E - 0 3 0 . 5 8 5 1 E - 0 5 36 1 . 1222 - 0 . 8 1 8 8 E - 0 1 - 0 . 8 7 2 6 E - 0 2 0 . 2 1 9 2 E - 0 2 - 0 . 2 1 0 3 E - 0 3 0 . 8 0 7 5 E - 0 5 37 1 . 3 2 6 2 - 0 . 8 6 1 9 E - 0 1 - 0 . 4 2 9 4 E - 0 2 0 . 9 7 8 5 E - 0 3 - 0 . 7 3 4 3 E - 0 4 0 . 2 3 1 0 E - 0 5 38 1 . 2 1 4 0 - 0 . 8 3 4 8 E - 0 1 - 0 . 5 7 0 5 E - 0 2 0 . 1 3 2 6 E - 0 2 - 0 . 1 0 8 1 E - 0 3 0 . 3 7 7 0 E - 0 5 3 9 1 . 1402 - 0 . 8 8 1 8 E - 0 1 - 0 . 2 5 3 2 E - 0 2 0 . 3 2 9 4 E - 0 3 0 . 4 6 6 4 E - 0 5 - 0 . 3 3 3 6 E - 0 6 4 0 1 . 1 7 0 4 - 0 . 7 7 7 4 E - 0 1 - 0 . 8 4 6 7 E - 0 2 0 . 1 9 0 3 E - 0 2 -o . 1 7 3 7 E - 0 3 0 . 6 6 0 9 E - 0 5 T A B L E A.2: Polynomial Coefficients for 44 mm Wafers Dried at 90°C. Wafer A l A 2 A 3 \ A 5 1 0. 6703 -0 . 6530E-•01 0. 3027E--03 0. 7308E-•04 0. 1958E--05 0. 5890E--06 2 0. 6404 -0 . 67 15E--01 0. 2067E--03 0. 3504E--03 -0 . 3546E-•04 0. 2022E--05 3 0. 6573 -0 . 6370E--01 0. 1391E--03 0. 1741E- 03 -0 . 2 177E-•05 0. 4277E--06 4 0. 6502 -0 . 6501E--01 -0 . 7 177E-03 0. 3309E--03 -0 . 2272E--04 0. 1582E--05 5 0. 65 15 -0 . 6156E--01 -0 . 17 15E-02 0. 5651E--03 -0 . 4532E--04 0. 2 183E--05 6 0. 7 104 -0 . 6838E--01 0. 1 197E-02 0. 135 IE-•03 -0 . 1 159E-04 0. 6380E--06 7 0. 68 16 -o. 6 134E--01 -0 . 2408E--02 0. 8342E--03 -0 . 8359E--04 0. 3838E--05 8 0. 71 10 - 0 . 6634E--01 0. 9226E--03 -0 . 1405E--03 0. 3417E--04 -0 . 1170E--05 9 0. 7482 -0 . 6476E--01 -0 . 1 156E' -02 0. 5079E--03 -0 . 4530E--04 0. 21 10E-05 10 0. 7 143 -0 . 64 10E -01 -0 . 7673E--03 0. 3 163E--03 -0 . 2761E--04 0. 1658E--05 1 1 0. 6907 -0 . 6622E -01 0. 2502E -03 0. 7041E--04 0. 1223E--04 -0 . 3360E -06 12 0. 6486 -0 . 6203E -01 -0 . 1778E -02 0. 7528E--03 -0 . 7384E--04 0. 3515E--05 13 0. 7161 -0 . 5938E -01 -0 . 1805E -02 0. 5027E--03 -0 . 2353E--04 0. 4299E -06 14 0. 6449 -0 . 5787E -01 -0 . 1524E -02 0. 5648E -03 -0. 4801E--04 0. 2141E--05 15 0. 6998 -0 . 6132E -01 -0 . 4 153E -03 0. 3746E--03 -0 . 3425E--04 0. 1593E -05 16 0. 648 1 -0 . 6027E -01 0. 1894E -03 -0 . 4025E--04 0. 2547E--04 -0 . 8 186E -06 17 0 . 7 138 -0 , 6445E -01 0. 8669E -03 0. 1749E -03 -0 . 9996E -05 0. 3257E -06 18 0. . 6469 -0 , .5979E -01 -0 . 1668E -02 0. 3822E -03 -0 . 1578E -04 0. 7789E -06 19 0. .6933 -0 , 6212E -01 -0 . 7839E -03 0. 4145E -03 -0 . 3584E -04 0. 1701E -05 20 0, , 6572 -0 . . 5998E -01 -0 . 2055E -02 0. 61 13E -03 -0 . . 5645E -04 0. 2877E -05 2 1 0. .7325 -0 . 5518E -01 -0 . 4229E -02 0. .1004E -02 -0 . 7532E -04 0. 2387E -05 22 0 .6966 -o. 5972E -01 -0 . 1369E -02 0. 5415E -03 -0. 3580E -04 0. 1003E -05 23 0 . 5862 -0 . 6265E -01 -0 . . 3723E -03 0 .4686E -03 -0 .4442E -04 0. . 2582E -05 24 0 .6913 -o .5929E -01 -o, ,3149E -02 0, . 1029E -02 -o. .9255E -04 0. , 3480E -05 25 0 .6713 -0 .4759E -01 -0. 9447E -02 0 . 2448E -02 -0, . 24 14E -03 0, 9299E -05 26 0 .6349 -0 .4945E -01 -0. ,7048E -02 0 .1828E -02 -0 . 1756E -03 0, 6957E -05 27 0 .5849 -0 .51216 -01 -0, .7577E -02 0 .2375E -02 -0 .2547E -03 0. , 1070E -04 28 0 . 6680 -0 .4978E -01 -0. ,8045E -02 0 .2142E -02 -0 .2152E -03 0 .8576E -05 29 0 .6635 -0 .5286E -01 -0 .5156E -02 0 .1246E -02 -0 .1 1 12E -03 0 . 4455E -05 30 0 . 8046 -0 .5549E -01 -0 . 3668E -02 0 .8220E -03 -0 .61 1 1E -04 0 . 1963E -05 31 0 .6694 -0 .5883E -01 -0 . 1829E -02 0 .3644E -03 -0 .3668E -05 -0 . 2641E -06 32 0 .6264 -0 .5054E -01 -0 .7320E -02 0 .2013E -02 -0 . 1997E -03 0 .8066E -05 33 0 . 73 18 -0 .5577E -01 -0 .4064E -02 0 .9810E -03 -0 .8251E -04 0 .3012E -05 34 0 .5964 -0 .5738E -01 -0 . 2592E -02 0 .9151E -03 -0 .7458E -04 0 .2638E -05 35 0 . 735 1 -0 . 5410E -01 -0 . 4389E -02 0 . 1081E -02 -0 .9423E -04 0 .3450E -05 36 0 . 6966 -0 .5575E -01 -0 .3401E -02 0 .9055E -03 -0 .7027E -04 0 .2393E -05 37 0 . 5474 -0 .5077E -01 -0 .7027E -02 0 .2196E -02 -0 .2336E -03 0 .1020E -04 38 0 . 5475 -0 .5492E -0.1 -0 .5752E -02 0 .2009E -02 -0 .2303E -03 0 . 1097E -04 39 0 .6738 -0 .5485E -01 -0 .5650E -02 0 .1684E -02 -0 . 167 1E -03 0 . 6609E -05 40 0 . 6834 -0 .5824E -01 -0 .2475E -02 0 .6670E -03 -0 .5023E -04 0 .1953E -05 T A B L E A.3: Polynomial Coefficients for 63 mm Wafers Dried at 90°C. Wafer // A„ A, A„ A, A , 0 1 2 3 4 5 1 1 , . 6750 - 1 . 0723E- -01 - 0 . 6614E- •03 0 . 2756E-•03 - 0 . 1487E-•04 0 . 5830E-•06 2 1 . 6953 - 1 . 1262E--01 - 0 . 1221E--02 0 . 2755E-•03 - 0 . 1408E-•04 0 . 7264E-•06 3 1 . 7 159 - 1 . 1428E--01 - 0 . 2226E- -02 0 . 6981E-•03 - 0 . 4682E-•04 0 . 1505E--05 4 1 . 6740 - 1 . 2075E--01 - 0 . 8364E- -03 0 . 489 1E--03 - 0 . 3861E-•04 0 . 1556E-•05 5 1 . 5008 - 1 . 1345E--01 - 0 . 1984E--02 0 . 7497E--03 - 0 . 6985E--04 0 . 3069E--05 6 1 . 563 1 - 1 . 1503E--01 - 0 . 2869E--02 0 . 8637E--03 - 0 . 7417E--04 0 . 3007E--05 7 1 . 8499 - 1 . 1959E--01 0 . 2194E--03 0 . 1915E--03 - 0 . 1233E--04 0 . 6942E--06 8 0 .8522 - 1 . 1 175E--01 - 0 . 2933E--02 0 . 1736E--02 - 0 . 1761E-•03 0 . 1068E--04 9 1 . 8 0 2 0 - 1 . 1835E--01 - 0 . 6975E- -03 0 . 3640E--03 - 0 . 2357E--04 0 . 9145E--06 10 1 . 7205 - 1 . 2001E--01 - 0 . 4561E--03 0 . 3612E--03 - 0 . 2657E--04 0 . 1218E--05 1 1 1 . 507 1 - 1 . 1482E--01 0 . ,154 1E--02 0 . 1317E--03 - 0 . 1080E--04 0 . 6951E--06 12 1 . 2850 - 1 . 1626E--01 0 . 1419E--02 0 . 1007E--03 - 0 . 5294E--05 0 . 1272E--05 1 3 1 . 6248 - 1 . 1763E -01 - 0 . 2856E--02 0 . 7986E--03 - 0 . 5377E--04 o. 1826E--05 14 1 . 6249 - 1 . 2 137E -01 - 0 . 2866E--03 0 . 4042E -03 - 0 . 36 16E--04 0 . 1783E--05 1 5 1 .4233 - 1 . 2248E -01 0 . 24 17E -02 0 . 308 1E -04 - 0 . 13 17E -04 o. 1G7 IE--05 16 1 . 6444 - 1 . 2921E -01 0 . 2290E' -02 - 0 . 2328E' -03 0 . 2619E--04 -o. 2259E--06 17 1 . 5896 - 1 .2322E -01 - 0 . 1343E -03 0 . 4294E -03 - 0 . 4071E--04 0 . 2061E--05 18 0 . 7235 - 1 .2377E -01 0 . 3977E -02 -o. 9434E -03 0 . 3994E--03 - 0 . 2697E--04 19 1 . 5482 - 1 .1756E -01 - 0 . 4136E -02 0 . 1293E -02 - 0 . 1238E--03 0 . 5333E--05 20 1 .6429 - 1 .1938E -01 - 0 . 2062E -02 0 . 7802E -03 - 0 . 7073E--04 0 . 3 164E--05 2 1 1 . 4975 - 1 .0850E -01 0. 1917E -02 - 0 . 5106E -04 0. 6455E -05 0 . 1 102E' -06 22 1 . 5477 - 1 .2348E -01 0. , 323 1E -02 - 0 . 2287E -03 0. 2493E -04 - 0 . 3798E -06 23 1 . 6075 - 1 .1889E -01 0. ,9804E -03 0, . 1681E -03 - 0 . .1301E -04 0. . 8495E -06 24 1 . 5458 - 1 .2473E -01 0, ,1477E -02 0. 1372E -03 - 0 . .1649E -04 0. . 1499E -05 25 1 . 5696 - 1 .2361E -01 0, ,5110E -03 0. , 4203E -03 - 0 . , 44 1 1E -04 0. . 2230E -05 26 1 . 6734 - 1 .2170E -01 0. .1069E -02 0, . 1903E -03 - 0 . , 1 134E -04 0, 5931E -06 27 1 . 5553 - 1 . 2397E -01 0 .5230E -03 0 . 2838E - 0 3 - 0 .1408E -04 0 . 8697E -06 28 1 . 5573 - 1 .2647E -01 0 .3517E -03 0 . 3193E -03 -0 .2928E -04 0 .1799E -05 29 1 . 4985 - 1 .2818E -01 0 .1202E -02 0 . 2477E -03 -0 .2563E -04 0 .2186E - 0 5 30 1 . 4849 - 1 .2304E -01 0 .1645E -02 6 .3982E -04 0 .2019E -05 0 .6919E -06 31 1 .5780 - 1 . 2779E -01 0 .2597E -02 -6 .9532E -04 0 .2048E -04 - 0 . 5356E -06 32 1 . 5043 - 1 . 24 1 1E -01 0 .2882E -03 0 .2028E -03 -0 .8296E -05 0 .1012E -05 33 1 . 6448 - 1 . 1837E -01 - 0 .3230E -02 0 . 86.69E -03 -0 .6999E -04 0 .2747E -05 34 1 . 5900 - 1 .2556E -01 0 .2553E -02 -0 . 5614E -04 0 .1055E -05 o .7464E -06 35 1 . 5072 - 1 .1970E -01 0 .1090E -02 0 . 1872E -03 -0 .1253E -04 0 .1025E -05 36 1 . 444 1 - 1 .2744E -01 0 .1593E -02 0 .9696E -04 -0 .9008E -05 0 . 16 14E -05 37 1 . 485 1 - 1 .2578E -01 0 .2017E -02 - 0 .1842E -03 0 .2499E -04 - 0 .3052E -07 38 1 . 5 182 - 1 .2580E -01 0 .2423E -02 - 0 . 1744E -03 0 .2635E -04 - 0 .3157E -06 39 1 .5917 - 1 .2579E -01 0 .1153E -02 0 .3885E -04 0 .3990E -06 0 .5606E -06 40 1 .5755 - 1 . 1939E -01 - 0 .6477E -04 0 .2886E -03 - 0 .1405E -04 0 .8302E -06 T A B L E A.4: Polynomial Coefficients for 25 mm Wafers Dried at 120' W a f e r # A o A l A2 1 0. 5726 -0 . 9889E--01 0. 1480E--02 2 0. 6393 -0 . 9840E--01 0. 5057E--02 3 0. 6317 -o. 9686E -01 0. 2809E--02 4 0. 7015 - 1 . 0339E--01 0. 4033E--02 5 0. 6679 -0 . 9824E -01 0. 2638E--02 6 0. 6356 - 1 . 0406E -01 0. 9685E--02 7 0. 5369 -0 . 9707E -01 -0 . 3090E -02 8 0. 6898 - 1 . 0140E -01 0. 3533E -02 9 0. 66 19 - 1 . 0046E -01 0. 4024E -02 10 0. 6586 - 1 . 0331E -01 0. 4 1 14E -02 1 1 0. 67 18 - 1 . 0456E -01 0. 39 19E -02 12 0 . 492 1 -0 . 97 14E -01 0. 2275E -02 13 0. 6953 - 1 . 0284E -01 0. 3264E -02 14 0. 6403 -0 . 9534E -01 -0 . 4 18 1 E -03 15 0. 7010 -0 . 9977E -01 0. 7920E -03 16 0. 7246 -0. 9864E -01 0. 1467E -02 17 0. 64 10 -0 . 9430E -01 0. 1619E -02 18 0 . 6035 -0 . 9760E -01 0. 296 1E -02 19 0. 634 1 -0 . 99 15E -01 0. 19 18E -02 20 0. 67 13 -0 , . 9903E -01 0. 1627E -02 2 1 0 . 6016 -0 . 8305E -01 0. 224 1E -02 22 0 . .7017 -0 .6918E -01 -0 . 1742E -01 23 0. . 5873 -0 .6741E -01 -0 . 2507E -01 24 0. . 64 10 -0 .6207E -01 -0 . 2716E -01 25 0 . 6052 -0 .9735E -01 0. 5125E -02 26 0 , 7788 -o .7275E -01 -o, . 1809E -01 27 0 . 5247 -0 .6081E -01 -0, . 3569E -01 28 0 . 6553 -0 . 6348E -01 -o , 256 IE -01 29 0 . 659 1 -0 . 767 1E -01 -0. . 1459E -01 30 0 . 6655 -0 .8012E -01 -0 . 9855E -02 31 0 .6754 -o .734 1E -01 -o. . 1523E -01 32 0 . 6626 -0 .6652E -01 -o . 1946E -01 33 0 . 5908 -0 .6785E -01 -0 .2493E -01 34 0 . 6985 -0 .6909E -01 -o .2257E -01 35 0 . 6297 -0 .6776E -01 -0 . 2558E -01 36 0 . 7273 -0 .7276E -01 -0 . 1675E -01 37 0 . 67 13 -0 .8875E -01 -0 .4179E -02 38 0 . 6990 -0 .6613E -01 -0 . 2386E -01 39 0 . 7037 -0 . 8358E -01 -0 .8878E -02 40 0 . 5787 -0 .7014E -01 -0 .2399E -01 A 3 A5 0. 1727E--02 -0 . 4 161E-03 0. 4 124E-04 0. 4450E--03 -0 . 1077E--03 0. 7 300E--05 0. 2840E--04 0. 3380E--04 0. 1491E--05 -0 . 27 17E--03 0. 5 1 15E--04 0. 1016E--05 -0 . 5175E--03 0. 152 IE--03 -0 . 5544E--05 -0 . 1 121E-02 0. 9893E--04 -0 . 1530E' -05 0. 3495E--02 -0 . 6447E--03 0. 5767E -04 0. 2031E--03 -0 . 5939E -04 0. 8435E -05 -0 . 7182E -04 -0 . 6090E -05 0. 6287E--05 -0 . 8095E' -04 0. 2556E -04 0. 2679E -05 -0 . 1014E--02 0. 2369E -03 -0 . 9753E -05 0. 3636E -04 0. 9969E -04 0. 1005E -04 -0 . 4 123E -03 0. 865 1E -04 0. 1829E -06 0. 1 105E -02 -0 . 1384E -03 0. 1 131E -04 0. 2709E -03 0. 2801E -04 0. 29 19E -06 0. 8 144E -03 -0 . 1 188E -03 0. 7991E -05 0. 3269E -03 -0 . 8368E -05 0. 2570E -05 0. 2872E -03 -0 . 38 18E -04 0. 6565E -05 0. 2791E -03 0. 2070E -05 0. 3947E -05 0. 9552E -04 0. 1 197E -03 -0 . 9209E -05 -0 . 2755E -03 0. 1424E -03 -0 . 97 15E -05 0. 5807E -02 -0. 7300E -03 0. 37 10E -04 0. 1 1 19E -01 -0. . 191 1E -02 0. 1262E -03 0. ,1025E -01 -0 . . 1585E -02 0. 9659E -04 0. 9109E -04 -0. , 3428E -04 0. 5637E -05 0, .6085E -02 -o. ,8085E -03 0, 4246E -04 0. . 1731E -01 -0 . 3361E -02 0. .2509E -03 0. .9892E -02 -0 .1520E -02 0 .9024E -04 0. .6240E -02 -o .9207E -03 0 .5265E -04 0 .4190E -02 -0 .5338E -03 0 .2651E -04 0 .5612E -02 -0 .7139E -03 0 .3481E -04 0 .7157E -02 -0 .9555E -03 0 .4862E -04 0 .1041E -01 -0 . 1764E -02 0 .1208E -03 0 .8093E -02 -0 .1156E -02 0 .6501E -04 0 .1037E -01 -0 .1644E -02 0 .1027E -03 0 .5509E -02 -0 .6652E -03 0 . 3217E -04 0 .2532E -02 -0 .3452E -03 0 .2010E -04 0 .8332E -02 -0 . 1 167E -02 0 .6464E -04 0 .3310E -02 -0 .3685E -03 0 .17 1 1E -04 0 .1037E -01 -0 . 1699E -02 0 .1092E -03 T A B L E A.5: Polynomial Coefficients for 44 mm Wafers Dried at 120°C. Wafer 00 A o A l A 2 A 3 \ A 5 1 1 .1045 - 1 . 4000E -01 0. 2659E--02 0. 2873E -03 0. 4073E--04 -0 . 2413E• -05 2 1 .0577 - 1 . 4480E -01 0. 93 13E--02 -0 . 1063E--02 0. 1 133E--03 -0 . 1705E -Ob 3 1 .0987 - 1 . 44 12E -01 -0 . 2 142E-02 0. 2360E--02 -0 . 3735E--03 0. 2689E -04 4 0 . 967 1 - 1 . 4327E -01 0. 4454E• -03 0. 2423E -02 -0 . 4495E -03 0. 3939E -04 5 1 .0806 - 1 . 3905E -01 -0 . 2186E -02 0. 1759E -02 -o. 2674E--03 0. 2237E -04 6 1 .O707 - 1 . 4623E -01 0. 4795E -02 -0 . 3347E -03 0. 7876E -04 -0 . 7460E -06 7 1 . 1069 - 1 . .4590E -01 0. 5021E--02 0. 6505E -03 -0 . 1203E--03 0. 8106E -05 8 1 . 1387 - 1 . .4670E -01 0. 4623E -04 0. 1910E -02 -0 . 31 17E -03 0. 2138E -04 9 1 .0863 - 1 , , 4475E -01 -0 . 159 1 E -02 0. 2153E -02 -o. 3242E' -03 0. 2282E -04 10 1 . 1 125 - 1 , . 4358E -01 -0 . 2149E -02 0. 2202E -02 -0 . 3355E -03 0. 2321E -04 1 1 1 . 1073 - 1 , . 4236E -01 -0 . 3961E -03 0. 1355E -02 -0 . 1632E -03 0. 1258E -04 1 2 1 .0170 - 1 , .4004E -01 0. 9523E -02 -0 . 1303E -02 0. 1736E -03 -0 . 5350E -05 13 1 .0195 - 1 .4225E -01 0. 5263E -02 0 . 1767E -03 -0 . 947 1E -05 0. 3377E -05 1 4 1 .0236 - 1 .4050E -01 -0 . 1886E -02 0. 2064E -02 -0 . 2966E -03 0. 2446E -04 15 1 .0598 - 1 . 4653E -01 0. 2205E -02 0. 1466E -02 -0 . 2701E -03 0. 2 1 10E -04 16 1 . 1446 - 1 .3935E -01 -0 . 3525E -02 0. 2351E -02 -0 . 2981E -03 0. 1751 E -04 17 1 .0628 - 1 .4207E -01 0. 3572E -02 0. 5219E -04 0. 2644E -04 0. 4335E -05 18 1 .067 1 - 1 .5082E -01 0. 7842E -02 -0 . 3684E -03 0. 12 13E -04 0. 4092E -05 19 1 .0678 - 1 . 4295E -01 -o. 1 163E -02 0. 2267E -02 -0 . 3614E -03 0. 2427E -04 20 1 .0448 - 1 .4355E -01 0. 1977E -02 0. 6319E -03 -0 . 8558E -04 0. 1 154E -04 2 1 1 . 2738 - 1 . 1273E -01 -0 . 2294E -01 0. 7085E -02 -0 . 8361E -03 0. 3914E -04 22 1 . 1086 - 1 .4914E -01 0. 4609E -02 0. 2289E -03 -o. 4345E -04 0. 6709E -05 23 1 . 2 138 - 1 .0521E -01 -0. 2445E -01 0. 7 134E -02 -0 . 8596E -03 0. 4247E -04 24 1 .0873 - 1 .4637E -01 0. 4048E -02 0. 4427E -03 -0 . 8153E -04 0, 8610E -05 25 1 . 2784 - 1 .0854E -01 -0 . 2466E -01 0. 7695E -02 -0 . 9509E -03 0, 4639E -04 26 1 .1512 - 1 .0773E -01 -o .2702E -01 0. .9053E -02 -0. . 1223E -02 0 .6554E -04 27 1 . 204 3 -0 .9399E -01 -0 .335 1E -01 0. .9978E -02 -0. . 1259E -02 0 .6337E -04 28 1 . 204 2 - 1 .0237E -01 -0 .2982E -01 0. .9484E -02 -0, ,1230E -02 0 .6318E -04 29 1 . 1 185 - 1 .0169E -01 -0 .3233E -01 0 . 1 143E -01 -0, , 16 14E -02 0 .8875E -04 30 1 .0431 - 1 .2005E -01 -0 .2048E -01 0 . 8838E -02 -0. ,1358E -02 0 .8210E -04 31 1 . 1973 - 1 .2300E -01 -0 .1693E -01 0 .6404E -02 -0. 8524E -03 0 .4431E -04 32 1 . 1551 - 1 .1770E -01 -0 .1838E -01 0 .6649E -02 -0 . 8048E -03 0 . 3831E -04 33 1 . 1763 - 1 .0419E -01 -o .3208E -01 0 .1050E -01 -0 . 1383E -02 0 .7155E -04 34 1 . 24 14 - 1 .1419E -01 -0 .231 1E -01 0 .7725E -02 -0 .9793E -03 0 .4815E -04 35 1 .0629 - 1 .1077E -01 -0 .2497E -01 0 .8156E -02 -0 .1120E -02 0 .6623E -04 36 1 . 2598 - 1 .1267E -01 -0 .2350E -01 0 .6976E -02 -0 .8600E -03 0 .4387E -04 37 1 . 24 15 - 1 .1248E -01 -0 .2200E -01 0 .7002E -02 -0 .8698E -03 0 . 4396E -04 38 1 .0481 - 1 .0882E -01 -o .2871E -01 0 . 1 129E -01 -0 . 1684E -02 0 .9789E -04 39 1 . 1 158 - 1 .0284E -01 -0 .2953E -01 0 .9602E -02 -0 .1326E -02 0 . 7329E -04 40 1 . 1 130 - 1 .0071E -01 -0 . 2861E -01 0 .9793E -02 -o .1312E -02 0 .6838E -04 T A B L E A.6: Polynomial Coefficients for 63 mm Wafers Dried at 120°C. Wafer // • Ao A l A2 A3 A5 1 1 . .7249 - 1 . 7 1 1 1 E • -01 - o . 1771E--02 Oi, 1579E--02 -0 . 1810E--03 0. 9220E--05 2 1 , 7403 - 1 . 7363E--01 0. 3066E--02 0. 5367E--03 -0 . 8584E--04 0. 5699E--05 3 1 , , 6296 - 1 . 7597E--01 -0 . 1410E--02 0. 1242E--02 -0 . 1284E--03 0. 9050E--05 4 1 , . 5780 - 1 . 7984E--01 0. 2740E--02 0. 3071E--03 -0 . 3616E--04 0. 5823E -05 5 1 . ,44 19 - 1 . 7466E--01 -0 . 1129E--02 0. 1470E--02 -0 . 2099E--03 0. 1938E--04 6 1 ,5184 - 1 . 8089E--01 0. 2233E--03 0. 1308E--02 -0 . 2063E--03 0. 1741E--04 7 1 , 4030 - 1 . 8384E--01 0. 6375E--02 -0 . 4138E--03 0. 5919E--04 0. 5520E--05 8 1 .5083 -1 .8674E--01 0. 4604E--02 0. 2520E--03 - 0 . 1228E--04 0. 5813E--05 9 1 .5027 - 1 .8042E -01 0. 3936E -02 0. 4817E' -03 -0 . 7410E--04 0. 7525E--05 10 1 .3760 -1 .7676E' -01 0. 1860E -02 0. 5123E--03 -0 . 2767E -05 0. 5340E--05 1 1 1 . 5293 - 1 .8617E -01 0. 3982E -02 0. 8958E--04 -0 . 9350E -05 0. 691 1E -05 12 1 .4031 - 1 .8812E -01 0. 7345E -02 -0 . 1022E -02 0. 1657E -03 -0 . 7019E -06 13 1 . 4768 - 1 . 7726E -01 0. 5307E -02 -0 . 3018E -03 0. 7747E -04 -0 . 1309E -05 14 1 . 3082 - 1 .8773E -01 o . 6209E -02 -0 . 5361E -03 0. 7887E -04 0. 6859E -05 15 1 . 5332 - 1 . 7574E -01 0. 7004 E -02 -0 . S060E -03 0. 145 1 E -03 -0 . 4949E -05 16 1 . 5295 - 1 .8988E -01 0. 8073E -02 -0 . 3209E -03 0. 2216E -04 0. 2799E -05 17 1 .6728 - 1 .9259E -01 0. 3467E -02 0. 1005E -02 -0 . 1720E -03 0. 1226E--04 18 1 . 5051 - 1 .8976E -01 0. 4452E -02 0. 5668E -03 -0 . 1647E -03 0. 1895E -04 19 1 .6488 - 1 .9047E -01 0. 9224E -02 - o . 8510E -03 0. 9046E -04 -0 . 1382E -05 20 1 . 3896 - 1 .8819E -01 0. 4510E -02 -0 . 4387E -03 0. 1282E -03 0. 3962E -06 2 1 1 . 4792 - 1 . 5942E -01 -0 . 9906E -03 0. 1225E -02 -0 . 1296E -03 0. 8521E -05 22 1 . 4345 - 1 .7592E -01 0. 6839E -02 -0, 1714E -02 0, , 2584E -03 -0 . 6166E -05 23 1 . 4 156 - 1 .8602E -01 0, 5862E -02 -0, , 1219E -02 0, .2287E -03 -0. . 447 1E -05 24 1 .4425 - 1 .8505E -01 0, 8376E -02 -0, , 1543E -02 0, .2682E -03 -0 . 9538E -05 25 1 . 4767 - 1 . 8485E -01 0, , 7252E -02 -0, , 3552E -03 0. .4723E -04 0. . 2 165E -05 26 1 . 5009 - 1 . 7909E -01 0, .8572E -02 -0. , 8799E -03 0 .8924E -04 0 .4072E -06 27 1 . 3723 - 1 .8059E -01 0, .1520E -02 0 , 107 1E -02 -0 .1125E -03 0 . 1 188E -04 28 1 .4931 - 1 .9105E -01 0 .9213E -02 -0 .8502E -03 0 .1272E -03 -0 .3713E -05 29 1 . 4026 - 1 . 8664E -01 0 . 1254E -01 -0 .1857E -02 0 . 2274E -03 -0 .6975E -05 30 1 . 4-170 - 1 .805 1E -01 0 .8608E -02 -0 .1214E -02 0 .1745E -03 -0 .1242E -05 3 1 1 . 6527 - 1 .7724E -01 0 .1540E -02 0 .7091E -03 -0 .7241E -04 0 .6164E -05 32 1 . 4682 - 1 .8330E -01 0 .4863E -02 -0 .1017E -03 0 .7809E -04 -0 .1548E -05 33 1 . 55 1 1 - 1 . 8524E -01 0 .9283E -02 -0 . 1248E -02 0 . 1787E -03 -0 .5587E -05 34 1 . 5639 - 1 .6713E -01 -0 .8470E -02 0 .34 12E -02 -0 .4296E -03 0 .2599E -04 35 1 . 3695 - 1 .8616E -01 0 .1059E -01 -0 .1749E -02 0 .3139E -03 -0 .1174E -04 36 1 . 5742 - 1 .8394E -01 0 . 4992E -02 -0 .1629E -03 -0 .2245E -05 0 .6346E -05 37 1 . 3749 - 1 .8521E -01 0 .6469E -02 -0 .1049E -02 0 .2517E -03 -0 . 7792E -05 38 1 . 4930 - 1 .7158E -01 -0 .8204E -02 0 .3235E -02 -0 .3739E -03 0 . 2231E -04 39 1 . 3545 -1 .9861E -01 0 .1339E -01 -0 .4571E -02 0 .8584E -03 -0 . 4267E -04 40 1 . 4926 - 1 .8490E -01 0 .5593E -02 -0 .1010E -03 0 .5463E -04 0 .4457E -06 T A B L E A.7: Polynomial Coefficients for 25 mm Wafers Dried at 150°C. Wafer A, K A-, A, A c 0 1 2 3 4 5 1 0. 6500 - 1 . 2939E--01 -0 . 1616E--02 0. 1823E--02 -0 . 3130E--04 0. 6379E--05 2 O. 5564 - 1 . 2309E--01 -0 . 448 1 E--02 0. 1077E--01 -0 . 3229E--02 0. 3593E--03 3 0. 6253 - 1 . 3247E--01 0. 1 1 19E--01 -0 . 1825E--02 0. 3918E--03 -0 . 1333E--04 4 0. 5957 - 1 . 2328E--01 0. 1454E--01 -0. 2062E--02 0. 2833E--03 -0 . 1456E--05 5 0. 5081 - 1 . 2473E--01 -0 . 41 12E-02 0. 9784E--02 -0 . 3060E--02 0. 3972E' -03 6 0. 6147 - 1 . 2919E--01 0. 4666E -02 0. 1631E--02 -0 . 3777E--03 0. 5013E--04 7 0. 5920 - 1 . 2590E -01 0. 6504E -02 -0 . 7975E -03 0. 4895E -03 -0 . 3751E -04 8 0. 5746 - 1 . 2925E' -01 0. 4021E -02 0. 2646E' -02 -0 . 7036E--03 0. 1017E--03 9 0. 5877 -1 . 3393E -01 0. 8705E -02 -0 . 1209E -02 0. 3762E -03 0. 4513E -05 10 0. 6560 - 1 . 3427E -01 0. 8868E -02 -0 . 1336E -02 0. 3406E--03 -0 . 1284E -05 1 1 0. 6270 - 1 . 3759E -01 0. 1457E -01 -0 . 3384E -02 0. 8792E--03 -0 . 6445E -04 12 0. 5920 - 1 . 3072E -01 -0 . 2393E -03 0. 4452E -02 -0 . 8990E -03 0. 9559E -04 13 0. 6401 - 1 . 3430E -01 0. 6866E -02 -0 . 9166E -03 0. 5967E -03 -0 . 4797E -04 14 0. 5446 - 1 . 2441E -01 -0 . 7019E -02 0. 1003E -01 -0 . 3060E -02 0. 3968E -03 15 0. 6944 - 1 . 3620E -01 0. 1 150E -02 0. 7968E -03 0. 6525E -04 0. 9603E -05 16 0. 5659 - 1 . 2792E -01 0. 5890E -02 0. 8394E -03 0. 3499E -05 0. 1053E -04 17 0. 5445 - 1 . 2481E -01 -0 . 3722E -02 0. 8068E -02 -0 . 2334E -02 0. 3067E -03 18 0. 5223 - 1 . 2617E -01 -0 . 2844E -02 0. 7930E -02 -0 . 2182E -02 0. 2809E -03 19 0. 5752 - 1 . 3150E -01 0. 1 1 17E -01 -0. 1865E -02 0. 5670E -03 0. 5588E -05 20 0, , 5703 - 1 . .2535E -01 0. 9391E -02 -0. 2186E -03 -0. 3469E -04 0. 2476E -04 21 0, ,5991 - 1 . ,0505E -01 -0 . 1027E -01 0. 7169E -02 -0. 1308E -02 0. , 1019E -03 22 0 .7033 -0. 9585E -01 -0 . 2388E -01 0. , 1 158E -01 -0. . 1946E -02 0. , 1250E -03 23 0 .6753 - 1 . 0844E -01 -0 . 2004 E -01 0. , 9800E -02 -0. . 1691E -02 0, . 127 1 E -03 24 0 .6363 - 1 , . 1296E -01 -0. 1574E -01 0. 8888E -02 -0. .1552E -02 0, .1207E -03 25 0 . 7640 - 1 .0678E -01 -0. 2174E -01 0. . 1025E -01 -0. .1760E -02 0 .1231E -03 26 0 . 6674 -0 .9339E -01 -0. 3864E -01 0 .1984E -01 -0 ,3969E -02 0 . 3 1 12E -03 27 0 .6728 - 1 .2176E -01 -0. 6367E -02 0 .6514E -02 -0 .1335E -02 0 .1089E -03 28 0 . 6693 - 1 .1546E -01 -o, ,1218E -01 0 .7854E -02 -0 .1399E -02 0 .104GE -03 29 0 . 699 1 -0 .8043E -01 -0, ,4647E -01 0 .2186E -01 -0 .3977E -02 0 .2740E -03 30 0 .6844 -0 .9571E -01 -0 .3492E -01 0 . 1687E -01 -0 . 3217E -02 0 . 2492E -03 31 0 .6385 -1 .1840E -01 -0 .6883E -02 0 .4978E -02 -o .8639E -03 0 .7513E -04 32 0 .7212 -1 .1901E -01 -0 .1096E -01 0 .7097E -02 -0 .1195E -02 0 . 7845E -04 33 0 . 6537 -1 .1573E -01 -0 .1560E -01 0 .9424E -02 -0 .1795E -02 0 . 1476E -03 34 0 . 7209 -0 .9222E -01 -0 .3013E -01 0 .1299E -01 -0 .22 19E -02 0 . 1545E -03 35 0 . 6030 - 1 .0240E -01 -0 .2743E -0 1 0 . 1437E -01 -0 .270GE -02 0 .2000E -03 36 0 . 7 554 -o .7521E -01 -0 .5526E -OI 0 .2353E -0 1 -0 .4 204E -02 0 .2937E -03 37 0 . 6470 -0 .6160E -01 -0 .6612E -01 0 .2964E -01 -0 . 5462E -02 0 .3894E -03 38 0 .6551 -0 .7266E -01 -0 . 4737E -01 0 .2173E -01 -0 .3945E -02 0 .2782E -03 39 0 .6214 -1 .0339E -01 -0 . 192 1 E -01 0 .1052E -01 -0 . 1887E -02 0 . 1396E -03 40 0 . 6536 -0 .9121E -01 -0 . 3016E -01 0 .1593E -01 -0 .3027E -02 0 .2174E -03 T A B L E A.8: Polynomial Coefficients for 44 mm Wafers Dried at 150°C. Wafer // A, K A„ A, 0 1 2 3 A 5 1 0. 9553 - 1 . 7948E--01 -0. 2759E--02 0. 7123E-•02 -0. 1685E-•02 0. 1743E--03 2 0. 8684 - 1 . 84 17E--01 -0 . 5798E--02 0. 1304E-•01 -0 . 3416E-•02 0. 3501E--03 3 0. 8 105 - 1 . 8907E--01 0. 6925E--02 0. 2741E--02 -0 . 1093E--02 O. 2418E-•03 4 1 . 1115 - 1 . 6616E--01 -0 . 1040E--01 0. 6596E-•02 -0 . 1064E-•02 0. 7205E--04 5 1 . 0020 - 1 . 8786E--01 0. 6622E--02 0. 2207E--02 -0. 4491E--03 0. 4940E--04 6 1 . 1769 - 1 . 8978E--01 0. 2907E--03 0. 2686E-02 -0. 4257E--03 0. 4059E--04 7 1 . 0420 - 1 . 9623E--01 0. 9480E--02 -0 . 1001E--02 0. 4246E--03 -0 . 2271E--04 8 0. . 9788 - 1 . 5948E--01 -0 . 2109E--01 0. 1483E--01 -0 . 3023E--02 0. 2383E--03 9 0, . 9698 - 1 . 9501E--01 0. 2182E--02 0. 47 12E--02 -0. 1320E--02 0. 1658E--03 10 0, , 8783 - 1 . 9364E--01 0. 16 17E--01 -0 . 3951E--02 0. 9823E--03 -0 . 3895E--04 1 1 0. , 8986 - 1 . . 8563E--01 1 0 . 4173E--02 0. 7633E--02 -0. 21 13E-02 0. 2912E' -03 12 0 . 9273 - 1 . 8820E -01 0. 1284E--01 -0 . 1758E' -02 0. 2953E--03 0. 1955E' -04 13 0 .9121 - 1 8801E -01 0. 7281E--02 0. 8522E' -03 -0 . 9224E--04 0. 4474E--04 14 0 .9226 - 1 . 8534E -01 -0. 2546E--02 0. 6391E--02 -0. 1420E--02 0. 1542E -03 15 o . 8825 - 1 . 8629E -01 -0. 2829E -02 0. 1038E -01 -0. 3282E -02 0. 4268E -03 16 0 . 9487 - 1 . 9379E -01 0. 2862E--02 0. 314eE -02 -0 . 8879E -03 0. 1388E -03 17 0 .9213 - 1 .8980E -01 0. 8790E -02 0. 159 1 E -02 -0 . 5832E -03 0. 9899E -04 18 0 . 8663 -2 .0983E -01 0. 54 19E--01 - o . 3083E -01 0. 8570E -02 -0. 7745E -03 19 1 .054 1 -2 .1130E -01 0. 3616E -01 - o . 1 128E -01 0. 2049E -02 -0. 121 1E -03 20 1 .0391 - 1 .9833E -01 0. 1 130E -01 - o . 4 186E -02 0. 1354E -02 -0. 1029E -03 2 1 1 . 1231 - 1 .6702E -01 -0. 1023E -01 0. 7472E -02 -0. 1286E -02 0. 8898E -04 22 1 .0381 - 1 .9558E -01 0. 1417E -01 - o . 5927E -02 0. ,1335E -02 -0. 6717E -04 23 1 .0214 - 1 .4476E -01 -0. 4894E -01 0. 2582E -01 -0, ,5456E -02 0, ,4563E -03 24 1 . 1 139 -1 .2944E -01 -0, ,6759E -01 0. . 2965E -01 -0, .5447E -02 0. . 3973E -03 25 1 . 2 149 - 1 .6445E -01 -0 ,3080E -01 0, , 1435E -01 -0 .2550E -02 0 . 1886E -03 26 1 .0893 - 1 .6663E -01 -0, ,3598E -01 0. . 2019E -01 -0 .4107E -02 0 .3396E -03 27 1 . 1824 - 1 .5008E -01 -0 .4495E -01 0. . 1953E -01 -0 .3317E -02 0 .2265E -03 28 0 . 8864 -2 .0788E -01 0. .4958E -01 -0, 2282E -01 0 5393E -02 -0 .4131E -03 29 1 .2114 - 1 .7569E -01 -0 . 2003E -01 0 .1096E -01 -0 . 1943E -02 0 .1399E -03 30 1 . 1836 - 1 .5472E -01 -0 . 3957E -01 0 .1620E -01 -0 .2772E -02 0 .2031E -03 31 1 . 2657 - 1 . 3842E -01 -0 .4088E -01 0 .1367E -01 -0 .1879E -02 0 .1149E -03 32 1 .2081 - 1 .6180E -01 -0 .3576E -01 0 .1519E -01 -0 .2645E -02 0 .1965E -03 33 0 . 7937 - 1 . 1568E -01 -0 .8677E -01 0 .4742E -01 -0 .1075E -01 0 . 9954E -03 34 1 .18 15 - 1 .8338E -01 -0 . 1238E -01 0 .8218E -02 -0 .1509E -02 0 .1152E -03 35 1 .2015 - 1 .4108E -01 -0 . 49 14E -01 0 .2113E -01 -0 .3594E -02 0 .2394E -03 36 1 .0834 - 1 .8288E -01 -0 .8384E -02 0 .8095E -02 -0 .1524E -02 0 .1135E -03 37 1 . 1360 - 1 .8594E -01 -0 .7618E -02 0 .5684E -02 -0 .1085E -02 0 .1026E -03 38 1 .1319 - 1 .7775E -01 -0 .1577E -01 0 .8866E -02 -0 . 1464E -02 0 .1094E -03 39 1 . 1742 - 1 .8019E -01 -0 .1755E -01 0 .1201E -01 -0 .2163E -02 0 .1499E -03 40 1 . 1622 - 1 .7867E -01 -0 .2066E -01 0 . 1256E -01 -0 .2220E -02 0 .1550E -03 T A B L E A.9: Polynomial Coefficients for 63 mm Wafers Dried at 1 5 0 ° C . Wafer / / . A 1 A„ A, A, A 0 1 2 3 4 5 1 1 . 4079 -2 . 3633E--01 0. 2532E--02 0. 1271E--02 -0 . 1415E--03 0. 3882E--04 2 1 . 4262 -2 . 3843E--01 0. 1047E--01 0. 2185E--03 -0 . 1573E--04 0. 1970E--04 3 1 .4610 -2 . 4650E--01 0. 6426E--02 0. 7847E--03 -0 . 2189E--03 0. 5583E--04 4 1 . 23 12 -2 . 3765E--01 0. 4964E--02 0. 4083E--02 -0 . 1 161E--02 0. 1480E--03 5 1 . 3528 -2 . 4525E--01 0. 2159E--01 -0 . 6856E--02 0. 1406E--02 -0 . 6675E--04 6 1 .0143 -2 . 2470E--01 -0 . 2539E--01 0. 3065E--01 -0 . 9145E--02 0. 1026E--02 7 1 .5682 -2 . 4277E--01 0. 1603E--01 -0 . 5545E-02 0. 1165E--02 -0 . 5878E--04 8 1 . 3357 -2 . 5494E--01 0. 2042E--01 -0 . 4796E--02 0. 101 1E--02 -0 . 3421E--04 9 1 .4612 -2 . 3229E--01 0. 1229E--01 -0 . 4682E-03 -0 . 7098E--04 0. 2810E--04 10 1 .3213 -2 . 5854E--01 > 0. 2135E--01 -0 . 4842E--02 0. 8981E--03 -0 . 1003E -04 1 1 1 . 4033 -2 . 5190E--01 0. 9334E -02 -0 . 7643E' -04 -0 . 1 145E--03 0. 6353E -04 12 1 . 4595 -2 . 5162E -01 -0. 1302E -01 0. 1539E -01 -0 . 3902E -02 0. 3669E -03 13 1 . 5888 -2 . 47 10E -01 0. 1 15 1E -01 -0. 9801E -03 0. 1816E -03 0. 1 135E -04 14 1 .4128 -2 . 57 10E -01 0. 1364E -01 -0 . 2338E -02 0. 4332E -03 0. 9998E -05 15 1 . 3063 -2 . 5350E -01 0. 7295E -02 0. 8623E -03 -0 . 1845E -04 0. 3885E -04 16 1 . 1648 -2 . 5033E -01 0. 1998E -02 0. 7623E -02 -0 . 2541E -02 0. 3942E -03 17 1 .4634 -2 . 56G1E -01 0. 9869E -02 -0 . 2622E -03 -0 . 1249E -03 0. 5895E -04 18 1 . 2626 -2 . 5057E -01 0. 4771E -02 0. 3923E -02 -0 . 1 108E -02 0. 1739E -03 19 1 . 4755 -2 . 4332E -01 0. 1720E -01 -0 . 1402E -02 0. 2090E -03 0. 504 1E -07 20 1 . 4795 -2 . .5087E -01 0. 9452E -02 0. 1365E -02 -0 . 4408E -03 0. 7266E -04 2 1 1 .1321 -2 , ,1825E -01 0. 7479E -02 0. 2469E -02 -0 . 5184E -03 0. 8396E -04 22 1 . 4586 -2 . 5721E -01 0. 194 1 E -01 -0. 6027E -02 0. 1407E -02 -0. 7808E -04 23 1 . 3 100 -2 , .5324E -01 0. , 1454E -01 -0. 1445E -02 0. 4341E -03 0. 5294E -05 24 1 .2586 -2. .3747E -01 0. ,1294E -01 -0. .1094E -02 0. 4733E -03 -0. , 1 185E -04 25 1 .4871 -2 .4963E -01 0, .8065E -02 0. .3667E -02 -0 . , 1076E -02 0. , 1 172E -03 26 1 .3234 -2 .3145E -01 -0, .1203E -01 0, ,1324E -01 -0. 2990E -02 0. , 2765E -03 27 1 . 4045 -2 .6236E -01 0 .1704E -01 -0, . 4929E -02 0. . 1 1 3 1 E -02 -0 . 4495E -04 28 1 . 3536 -2 .7183E -01 0 .5769E -01 -0. .2450E -01 0. . 5111E -02 -0 .3366E -03 29 1 . 3022 -2 .5887E -01 0 . 24 1 1E -01 -0 .6099E -02 0 . 1313E -02 -0 .6335E -04 30 1 . 3847 -2 .5461E -01 0 .1969E -01 -0 . 4448E -02 0 .1046E -02 -0 •4375E -04 31 1 . 4829 -2 .4780E -01 0 .1032E -01 -0 . 1921E -02 0 .5235E -03 -0 .1275E -04 32 1 . 36 14 -2 .5613E -01 0 .1438E -01 -0 . 1901E -02 0 .3059E -03 0 .2392E -04 33 1 . 3829 -2 .4757E -01 0 .1383E -01 -0 .3491E -02 0 .9942E -03 -0 .4855E -04 34 1 . 3795 -2 . 1 1 14E -01 -0 .1589E -01 0 . 104 1E -01 - 0 .1890E -02 0 . 1565E -03 35 1 . 2679 -2 .5004E -01 0 .208 1E -01 -0 . 4844E -02 0 .1242E -02 -o .6128E -04 36 1 .08 16 -2 .4732E -01 0 .1986E -01 -0 . 3929E -02 0 .1277E -02 -0 . 2058E -04 37 1 . 2255 -2 .7038E -01 0 .6275E -01 -0 . 2916E -01 0 .6947E -02 -0 . 5406E -03 38 1 .4016 -2 .3445E -01 -o .1510E -01 0 . 1544E -01 - 0 .3525E -02 0 .3055E -03 39 1 .0990 -2 .4615E -01 0 . 4542E -01 -0 .2862E -01 0 .9104E -02 -0 .8787E -03 40 1 . 2909 -2 .3495E -01 0 . 1675E -01 - 0 .3028E -02 0 .7642E -03 -0 . 3995E -04 T A B L E A. 10: Polynomial Coefficients for 25 mm Wafers Dried at 150°C, Horizontal to the Flow of Air Wafer // A o A l A3 A5 1 0 .5921 -1 .2113E -01 0 .4572E -02 -0 .7726E -03 0 .6019E -03 -0 .5589E -04 2 0 .4911 -1 .1905E -01 0 .3203E -02 0 .1962E -02 -0. .2749E -03 0 .6806E -04 3 0 .4483 -1 .1377E -01 0 .4718E -02 0 .2113E -02 -0. .3412E -03 0 .9767E -04 4 0 .6083 -1 .1855E -01 0 .8726E -02 -0 .3441E -03 0 .7985E -04 -0 .134 IE -05 5 0 .5535 • 1 .1860E -01 0 .4426E •02 0 .2100E -02 -0. .6031E -03 0 .7806E -04 6 0 . 5579 - 1 .1802E -01 0 .9140E •02 -0 .1048E •02 0. 3835E -03 •0 .3099E •04 7 0 .5213 -1 .1221E -01 0 .8015E •02 0 . 1639E -02 -0 . 697 7E •03 0 .9310E •04 8 0. . 5594 -1 .1756E -01 0 .7231E •02 o; 7803E -03 -0 . 229SE -03 0 .3010E -04 9 0. .5144 -1 .1488E -01 0, .1053E' •01 -0. .8875E -03 0. 2197E •03 -0 .8740E -05 10 0. .5351 -1 .19Z1E -01 0. .1093E-•01 -0, .7423E •03 0. 2864E •04 0 .2157E -04 11 0. .5903 - 1 .2132E -01 0. .8645E-•02 •0, .1330E -02 0. 2510E •03 0. 7170E -05 12 0. ,5380 -1 , .159 IE -01 0. .1129E-•01 -0 . 2276E -02 0. 7380E •03 -0 . 6563E -04 13 0. 5141 - 1, .1951E •01 0. 8910E-•02 -0 . 9809E •03 0. 6417E. •03 -0 . 7314E •04 14 0. 5092 -1 . .1548E •01 0. 1146E- 01 -0 . 9218E' •03 0. 2499E-•04 0. 3480E •04 IS 0. 5490 -1 . .1495E •01 0. 8987E- 02 - 0 . 7368E-•03 0. 7722E-•04 0. 2513E -04 16 0 . 5313 - 1. 0974E-•01 0. 7340E- 02 0. 1079E-•02 - 0 . 4366E- 03 0. 5680E--04 17 0 . 6016 - 1 . .1813E' •01 0. 8629E- 02 0. 1961E- 03 - 0 . 1437E- 03 0. 2130E-•04 18 0. 5484 - 1 . 1793E-•01 0. 5867E- 02 0. 4393E- 03 0. 6881E- 04 0. 2172E-•05 19 0 . 4932 - 1 . 1129E-•01 - 0 . 6847E- 02 0. 1246E- 01 - 0 . 3624E- 02 0. 4008E-•03 20 0 . 5101 - 1 . 1321E-•01 0. 1202E- 03 0. 6299E- 02 - 0 . 1594E- 02 0. 1515E-•03 T A B L E A . l l : Polynomial Coefficients for 44 mm Wafers Dried at 150°C, Horizontal to the Flow of Air Wafer . . . // A0 *1 A2 A3 A4 A5 1 1 .0089 -1 .B903E--01 0. .5399E •02 0. 2746E-•02 -0 .4835E •03 0. .4589E--04 2 0 .9843 -1 .9521E-•01 0. .8787E •02 0. 6683E •03 0. .6055E •04 0. ,1017E •06 3 1 . 1235 -1 .9632E-•01 0. .7051E-•02 0. . 1894E •02 -0. .4515E •03 0. 4881E-•04 4 0 .9343 -1 .8947E-•01 0. .1047E-•01 -0 . . 1380E' •02 0. .5109E •03 -0 . . 1026E-•04 5 0. .9319 -1 •9265E-•01 0. .1252E •01 -0 . 2275E' •02 0 .8219E •03 -0 . 4835E-•04 6 0. .8887 -1 .9875E' •01 0, 2052E •01 -0 . 6975E-•02 0 .2222E' •02 -0 . , 1842E' •03 7 0. .9818 -1 . .9108E-•01 0. 8B83E •02 0. 6013E' •03 0. .1276E-•03 -0 . . 1230E--04 8 1. • C330 -1 . .7803E-•01 0. 5675E-•04 0. 3509E-•02 -0 . .6593E-•03 0. 6753E-•04 9 0. .9541 -1 . .9816E-•01 0. ,1295E-•01 0. 9435E-•03 -0 . .3106E-•03 0. 4207E' •04 10 0. .9350 -1 , .9009E-•01 0. 1450E-•01 -0 . 6640E-•03 -0 . .8166E •04 0. 4368E-•04 11 0. .8478 - 1. .9275E-•01 0. .1553E-•01 - 0 . 3964E-•02 0. .1365E-•02 -0 . 7488E-•04 12 1. .0273 - 1, .9425E-•01 0. 5988E-•02 0. 3501E-•02 -0 . .7804E-•03 0. 7597E-•04 13 1, .0128 -2 .1775E-•01 0. 5278E-•01 -0 . 2491E-•01 0. .5895E-•02 -0 . 4583E-•03 14 0. .8930 - 1 . •5310E-•01 -0 . 2147E-•01 0. 1677E-•01 -0 . 3767E-•02 0. 3471E-•03 15 0. 9942 -1 . •5687E-•01 -0 . 1813E-•01 0. 1124E-•01 -0 . 2017E-•02 0. 1513E-•03 16 1. .0659 -2 . .0327E-•01 0. 1728E-•01 - 0 . 2235E-•02 0. 3275E-•03 - 0 . 4407E-•05 17 0. .9230 - 1 . .6597E-•01 0. 1060E-•01 0. 2201E-•02 -0 . .7984E- 03 0. 1157E-•03 18 0. .9951 -1 , .8651E-•01 0. 5915E-•02 0. 6217E-•03 0. .3635E-•03 -0 . 4224E' •04 19 1. .0296 -1 . .9399E-•01 0. 1118E-•01 0. 1377E-•03 -0 . . 1193E-•04 0. .1329E' •04 20 0. .9323 - 1 . .8463E-•01 0. 7325E-•02 0. 4117E-•02 -0 . 1152E-•02 0. 1213E-•03 T A B L E A.12: Polynomial Coefficients for 63 mm Wafers Dried at 150°C, Horizontal to the Flow of Air Wafer A , A if 0 1 2 i 1 .2615 -2 .3189E -01 0 . 1714E -01 2 1 .2289 -2 .5067E -01 0 .1217E -01 3 1 .4 308 -2 .6852E -01 0 .1452E -01 i 1 .3623 -2 .4962E -01 0 .1695E -01 5 1 .3215 -2 .6391E -01 0. .1846E -01 6 1 .3729 -2 .5217E -01 0 4128E -02 7 1 .2241 •2. .4502E -01 0. . 1706E -01 8 1 . 4773 -2. .5863E -01 0 .1466E -01 9 1 . 2746 -2 .7094E -01 0. 1330E -01 10 1 . 2729 -2 .6283E -01 0. . 1292E -01 1 1 1 . 4270 -2 . 7 111E -01 0. 8717E -02 12 1 . 3050 -2 8564E -01 0. 6408E -01 13 0 . 74 14 -2. 9352E -01 1. 8406E -01 1 4 1 . 2845 -2 .4681E -01 0. 5431E -02 15 1 . 2689 -2. .7672E -01 0. 3683E -01 16 1 . 4556 -2 6458E •01 0. 1691E -01 17 1 .4835 •2. .7726E -01 0. 4643E -01 18 1 .4120 -2 . 6873E -01 0. 1963E -01 19 1 .4025 -2 . 5598E -01 0. 7875E -02 20 1 .4157 -2 . 6327E -01 0. 2382E -01 A 3 \ A 5 -0 .4725E -02 0 . 1425E •02 -0. .1002E -03 0 .1380E -02 0 .8809E •04 0. .5769E -05 0 .9120E -03 -0 .4900E •03 0. .8034E -04 -0 .1420E -03 -0 .2517E •03 0. .5393E -04 -0 .5153E -03 -0 .2044E •03 0. . 7050E -04 0 .4648E -02 -0 . .7726E •03 0. .631 IE -04 -0. .3209E -03 -0. .7880E •04 0. .4408E -04 0. .9068E -03 -0. .4397E •03 0. 6258E -04 -0 .4235E -03 0 .6776E •03 -0. 5005E -04 -0 .2553E -02 0. .1404E •02 -0. 1192E -03 0. .3236E -02 -0 .7441E •03 0. 8633E -04 -0. .3036E -01 0. .7252E •02 -0 . 5665E -03 -1 . 8973E -01 0. 8948E •01 -0 . 14 15E -01 0 4763E -02 -0 . . 1285E •02 0. 1876E -03 -0. .4582E -02 -0 . .4420E' •03 0. 1709E -03 0, .1723E -02 -0 . 7957E' •03 0. 9045E -04 -0. . 1669E -01 0. 3342E' •02 -0 . 2150E -03 -0 . 2135E -02 0. 1308E' •03 0. 4438E -04 0. 1989E -02 -0 . 1712E-•03 0. 2772E -04 -0 . 1006E -02 -0 . 2507E' •03 0. 5223E -04 233 Appendix B Statistical Discussion of the Analyses of the Wafer Drying Times and Drying Rates B. l Analysis of Wafer Drying Times Wafer drying times were initially subjected to analyses of covariance. Saturated density and wafer thickness were chosen as covariates since variation in either of these two wafer properties affects wafer drying time. A n analysis of covariance is based on the assumption that the slopes of the regression curves of the covariates versus drying time are equal from cell to cell (Grieg, 1988). A statistical comparison of these regression slopes for the 3x3 factorial analysis of drying times showed that this assumption was violated for both covariates and that there was a large interaction between density and thickness as they affect the fluctuations of drying times with drying temperature and wafer length. The differences in thickness and density between wafers in each cell were probably too small to adequately quantify an effect on drying time. The major advantage in using an analysis of covariance was to reduce the variability in wafer drying times by accounting for the effects of thickness and density. However, since the mean drying times, adjusted for thickness and density, could not be used with confidence and since, in designing the 3x3 factorial experiment, the sample size of 40 wafers for each cell was determined on the basis of the variability of wafer drying times including the effects of all wafer properties, it was decided that an analysis of variance was sufficient. 234 T A B L E B.l: Summary of the Analyses of Variance of Drying Times from the 3x3 Factorial Experiment. Moisture Content Range for Each Drying Time ANOVA Temperature Effect Length Effect Temperature X Length Interaction Significantly Different Cell Means 1 (by cell number) 125%-3% ++++2 ++++ +++ (7,8), (8,9), (4,5), (897)3 (65.3) (5.27) (6), (1,2), (3) 125%-30% ++++ ++++ +++ (7,8), (8,9), (4), (5), (1013) (87.4) (5.93) (6), (1), (2), (3) 30%-3% ++++ ++++ ++ (7,8,9), (4,5), (6) (669.1) (36.5) (3.94) (1,2), (3) Based On Tukey's Test of Significance for differences between means at a probability level of 0.95 ++++ significant at a probability of 0.9999 +++ significant at a probability of 0.9990 ++ significant at a probability of 0.990 Values in parentheses are the F-values Table B.l lists the results of the ANOVA for the drying times from 125%-3%, 125%-30% and 30%-3% moisture contents. Both drying temperature and wafer length had strong effects on the drying times for all three ranges of moisture content. Drying temperature, however, was the dominant of the two effects. The significant interaction between the temperature and length effects could be dismissed as an artifact of the large main (temper-ature and length) effects. However, the interaction could also result from lack of normality in the data or a poor fit of the data with the analysis of variance model (non-additivity) (Snedecor and Cochran, 1967). The analysis of variance model has the following form: Yijk = u + A + Bj + ABij + E(ij)k (B.l) 235 where: J k t AB{j E(H)k Ai Bi dependent variable true mean of dependent variable effect of treatment A (deviations added to the true mean caused by treatment t) effect of treatment B (deviations added to the true mean caused by treatment j) interaction between effects A and B to produce a third effect true error, variation in the data not attributable to the treatments treatment group for effect A treatment group for effect B number of samples per treatment group A significant interaction means that the effects of the various treatments have combined to produce a third effect on the dependent variable that is different from the treatments from which it arose or, in other words, that the effects are not additive. If this interaction cannot be explained, then the significance of the main effects must be seriously questioned. In the results from the 3 x 3 factorial experiment, the coefficients of variation for the drying times did not vary greatly from cell to cell (the standard deviations varied directly with the means). This indicates that the significant interaction may result from non-normality or non-additivity, and that a logarithmic transformation would improve the analyses (Snedecor and Cochran, 1967). Tukey's test of additivity was therefore performed for each of the three sets of drying time data to determine if a transformation of the data was required. These tests showed that the data were significantly non-additive at a probability level of 95% and that a logarithmic transformation of the data would be suitable. This result indicates that the effects of drying temperature and wafer length are multiplicative instead of additive. They are not independent effects but combine synergistically to affect drying time. The results of a second set of analyses of variance performed on the transformed data are presented in Table B.2. The effects of temperature and length are still strongly significant, but the interaction has become insignificant. The improvement in the drying time analyses 236 TABLE B.2: Summary of the Analyses of Variance of Drying Times from the 3 x 3 Fac-torial Experiment Using a Logarithmic Transformation to Eliminate Multiplicative Effect Between Temperature and Length. Moisture Content Range for Each Drying Time ANOVA Temperature Effect Length Effect Temperature X Length Interaction Significantly Different Cell Means1 (by cell number) 125%-3% ++++2 ++++ N.S. (7,8), (9), (4), (5), (983)3 (66.0) (1.487) (6), (1,2), (3) 125%-30% ++++ ++++ N.S. (7,8), (9), (4), (5), (1077) (85.4) (1.464) (6), (1,2), (3) 30%-3% ++++ ++++ N.S. (7,8), (8,9), (4,5), (788) (40.1) (1.384) (6), (1,2), (3) Based On Tukey's Test of Significance for differences between means at a probability level of 0.95 significant at a probability of 0.9999 significant at a probability of 0.9990 significant at a probability of 0.990 not significant Values in parentheses are the F-values is also noticeable in the comparisons of cell means. The confidence limits for each mean drying time were reduced in the ANOVA using the log transformation of drying time, and thus there was less overlapping between cells than for the initial ANOVA (Table B.2 versus Table B.l, significantly different cell means). Since the cause of the interaction found in the first ANOVA has been identified, and since the effects of drying temperature and wafer length did not differ greatly between the two ANOVAs, it is now possible to examine the response curves of drying time versus treatment levels based on the initial analysis of variance. Response curves are based on the cell means (mean drying times for each set of conditions) and the mean square error (a ++++ +++ ++ N.S. 237 measure of the variation in the data not attributable to the treatments) from the analysis of variance. The method of calculation generates a linear term and a quadratic term for each curve and then tests the significance of the term against the mean square error. Figure B.l presents the response curves of drying time from 125% to 3% moisture content versus drying temperature for the three different wafer lengths. The curves exhibit the same general trend of drying time with drying temperatures for the three different wafer lengths. The differences in the slopes and shapes of the curves may be attributed to the multiplicative effect of drying temperature and wafer length on drying time as well as to the variability in the data. The quadratic form of the response curves is another indication that the effects of drying temperature and wafer length are not additive. Figure B.2 presents the response curves of drying time from 125% to 3% moisture content versus wafer length at the three levels of drying temperature. Once again the curves exhibit similar trends. However, the effect of drying temperature on drying time is more obvious than in Figure B.l. An increase in drying temperature from 90°C to 120°C produced a much greater reduction in drying time than an increase from 120°C to 150°C. This trend can also be observed in Figures B.3 and B.4, the response curves for drying time versus wafer length from 125% to 30%, and from 30% to 3%, respectively. The cause of this trend cannot be interpreted from the drying time data. B.2 Analyses of Drying Rates from the 3 x 3 Factorial Ex-periment The initial analyses of variance of drying rates at the fifteen selected moisture con-tents showed strongly significant temperature and length effects as well as a significant temperature x length interaction. Following the same procedure as in the analyses of drying times, Tukey's test of additivity was performed on the drying rate data at each of the moisture contents. The results of these tests are presented in Table B.3. These 238 2.00 -1.00 -80 90 100 110 120 130 140 150 DRYING TEMPERATURE (C) F I G U R E B.l: Response curves for the 3 x 3 analysis of variance of drying times vs. drying temperature from 125% to 3% moisture content. Each point represents the mean drying time of 40 wafers. Curves are statistically significant at a 95% level of probability. 239 2.00 -1.00 -20 26 32 38 4 4 50 56 62 W A F E R L E N G T H ( m m ) F I G U R E B.2: Response curves for the 3 x 3 analysis of variance of drying times vs. wafer length from 125% to 3% moisture content. Each point represents the mean drying time of 40 wafers. Curves are statistically significant at a 95% level of probability. 240 9.00 8.00 7.00 <D -t— C 6.00 O >-Q 5.00 4.00 3.00 2.00 1.00 0.0 e 90 c A 120 C • 150 C 20 26 32 38 44 50 56 W A F E R L E N G T H ( m m ) 62 F I G U R E B.3: Response curves for the 3 x 3 analysis of variance of drying times vs. wafer length from 125% to 30% moisture content. Each point represents the mean drying time of 40 wafers. Curves are statistically significant at a 95% level of probability. 241 w <D c 9.00 8.00 7.00 6.00 5.00 UJ o z >-Q 4.00 3.00 2.00 1.00 0,0 e 90 c A 120 C o 150 C 1 J i L 20 26 32 38 44 50 56 WAFER LENGTH (mm) 62 F I G U R E B.4: Response curves for the 3 x 3 analysis of variance of drying times vs. wafer length from 30% to 3% moisture content. Each point represents the mean drying time of 40 wafers. Curves are statistically significant at a 95% level of probability. 242 TABLE B.3: Results of Tukey's Test of Additivity for the Drying Rate Data from the 3 x 3 Factorial Experiment Moisture Content Significance of Transformation (%) on Data Analyses 125 ++1 (122.9)2 120 ++ (130.3) 110 ++ (246) 100 ++ (217) 90 ++ (162.9) 80 ++ (111.7) 70 ++ (95.3) 60 ++ (54.1) 50 ++ (36.5) 40 + (20.7) 30 + (16.72) 20 + (10.88) 15 N.S. (8.89) 10 N.S. (6.57) 5 N.S. (0.583) ++ significant at a probability of 0.99 (Fo.oi,d/=i,3 = 34.12) + significant at a probability of 0.95 (Fo.o5,d/=i,3 = 10.13) N s - not significant values in parentheses are the F-values 243 tests showed that a transformation only has a significant effect on the data from 125% to 20% moisture contents. However, the analyses of variance performed on the data showed a marked improvement in the analyses for all moisture contents except at 5% moisture content. This is not surprising considering the sudden decrease in F-value from 10% to 5% moisture content in Table B.3. Table B.4 is a summary of the analyses of variance performed on the drying rate data. The drying rate data at all moisture contents except 5% were subjected to a logarithmic transformation prior to each analysis of variance. The decrease in the variability of the drying rate data over the drying time data is evident in the comparison of cell means in Table B.4. All cell means are significantly different except at the 5% moisture content level where there is a uniform overlapping of cell means for the three wafer lengths at each temperature. This distinction between cell means is much greater than that in Table B.2 for drying time means. Plotting the response curves from the analyses of variances at the various moisture contents showed that the multiplicative effect was not very strong. Figures B.5, B.6 and B.7 are the response curves of drying rate versus wafer length for the three drying temperatures at 90%, 30% and 5% moisture contents respectively. In Figure B.7, the slight deviations of the response curves at the three drying temperatures from being straight and parallel is an indication of the size of the multiplicative effect (in addition to any natural variations in the data). The large differences in the response curves for the drying time analyses (Figures B.l, B.2, B.3 and B.4) result because drying times are a measure of the cumulative effects over the entire drying period, whereas the drying rate data represent single points in the drying of the wafer. At 30% moisture content, the response curves of Figure B.6 show similar trends to those at 90%, except that they are straighter and closer to parallel. The multiplicative effect thus decreases with decreasing moisture content. Finally at 5% moisture content, the response curves are parallel and straight, so that the effects of drying 244 TABLE B.4: Summary of the Analyses of Variance for Wafer Drying Rates at Different Moisture Contents from the 3 x 3 Factorial Experiment1. Moisture Content Temperature Length Temperature Significantly Different Range for Each Drying Effect Effect X Length Cell Means 4 Time ANOVA Interaction (by cell number) 125 ++++2 ++++ N.S. (3), (2), (1), (6), (5) (8468)3 (1173) (1.405) (4), (9), (8), (7) 120 ++++ ++++ N.S. (3), (2), (1), (6), (5) (8071) (1102) (1.281) (4), (9), (8), (7) 110 ++++ ++++ N.S. (3), (2), (1), (6), (5) (7344) (962) (1.170) (4), (9), (8), (7) 100 ++++ ++++ N.S. (3), (2), (1), (6), (5) (6656) (824) (1.179) (4), (9), (8), (7) 90 ++++ ++++ N.S. (3), (2), (1), (6) (5) (5979) (691) (1.238) (4), (9), (8), (7) 80 ++++ ++++ N.S. (3), (2), (1), (6), (5) (5328) (571) (1.303) (4), (9), (8), (7) 70 ++++ ++++ N.S. (3), (2), (1), (6), (5) (4732) (469) (1.345) (4), (9), (8), (7) 60 ++++ ++++ N.S. (3), (2), (1), (6), (5) (4210) (387) (1.367) (4), (9), (8), (7) 50 ++++ ' ++++ N.S. (3), (2), (1), (6), (5) (3751) (323) (1.383) (4), (9), (8), (7) 40 ++++ ++++ N.S. (3), (2), (1), (6), (5) (3325) (272) (1.413) (4), (9), (8), (7) 30 ++++ ++++ N.S. (3), (2), (1), (6), (5) (2880) (229) (1.470) (4), (9), (8), (7) 20 ++++ ++++ N.S. (3), (2), (1), (6), (5) (2377) (189.5) (1.541) (4), (9), (8), (7) 15 ++++ ++++ N.S. (3),(2),(1),(6),(5) (2085) (167.5) (1.591) (4), (9), (8), (7) 10 ++++ ++++ N.S. (3), (2), (1), (6), (5) (1700) (135.9) (1.776) (4), (9), (8), (7) 5 ++++ ++++ N.S. (3,2), (2,1), (6,5) (552) (33.7) (0.248) (5,4), (9,8), (8,7) A logarithmic transformation was used on the drying rate data for all moisture contents except at 5% moisture content prior to performing the analysis of variance. — significant at a probability of 0.9999 N m S ' - not significant Values in parentheses are the F-values. Based on Tukey's test of significance for difference between means at a probability level of 0.95. F I G U R E B.5: R e s p o n s e c u r v e s f o r t h e 3x3 a n a l y s i s o f v a r i a n c e o f d r y i n g r a t e s v s . w a f e r l e n g t h a t 90% m o i s t u r e c o n t e n t . E a c h p o i n t r e p r e s e n t s t h e m e a n d r y i n g r a t e o f 40 w a f e r s . C u r v e s a r e s t a t i s t i c a l l y s i g n i f i c a n t a t a 95% l e v e l o f p r o b a b i l i t y . 246 FIGURE B.6: Response curves for the 3 x 3 analysis of variance of drying rates vs. wafer length at 30% moisture content. Each point represents the mean drying rate of 40 wafers. Curves are statistically significant at a 95% level of probability. 247 1.00 v> Fo.80 * CD Ld I— < 0.40 >-Q 0.20 0.60 O 90 C A 120 C • 150 C -B --A— - A -O 0.0 2 0 26 32 38 44 50 WAFER LENGTH (mm) 56 62 FIGURE B.7: Response curves for the 3 x 3 analysis of variance of drying rates vs. wafer length at 5% moisture content. Each point represents the mean drying rate of 40 wafers. Curves are statistically significant at a 95% level of probability. 248 temperature and wafer length are independent of each other. The non-linear effect of wafer length observed in Figure B.l and discussed in Sec-tion 1.32 is noticeable in the response curves at 90% moisture content but not at 5% moisture content. Similarly, an examination of the response curves of drying rates versus drying temperature for the three wafer lengths at 90%, 30% and 5% moisture contents respectively (Figures B.8, B.9 and B.10) shows the same decrease in the non-linear effect of drying temperature with decreasing moisture content. At 5% moisture content the in-cremental changes in drying temperature and length in linearly incremental changes in drying rate. B.3 Analyses of the Drying Rates from the 1 x 3 Factorial Experiments The analyses of variance of the drying rates at the selected moisture contents are presented in Table B.5. Although the effect of wafer length on drying rate as determined by the analyses of variance ends at 40% moisture content, it is possible that with an increase in sample size the length effect would be shown to be significant to a moisture content below 40% as observed in Figure 1.20 in Section 1.32. 249 © 25.4mm WAFER LENGTH A 44.4mm WAFER LENGTH a 63.5mm WAFER LENGTH 0.0 80 90 100 110 120 130 140 150 DRYING TEMPERATURE (C) FIGURE B.8: Response curves for the 3 x 3 analysis of variance of drying rates vs. drying temperature at 90% moisture content. Each point represents the mean drying rate of 40 wafers. Curves are statistically significant at a 95% level of probability. 250 F I G U R E B . 9 : R e s p o n s e c u r v e s f o r t h e 3 x 3 a n a l y s i s o f v a r i a n c e o f d r y i n g r a t e s v s . d r y i n g t e m p e r a t u r e a t 3 0 % m o i s t u r e c o n t e n t . E a c h p o i n t r e p r e s e n t s t h e m e a n d r y i n g r a t e o f 4 0 w a f e r s . C u r v e s a r e s t a t i s t i c a l l y s i g n i f i c a n t a t a 9 5 % l e v e l o f p r o b a b i l i t y . 2 5 1 1.00 v> Fo.80 * \ D) Ld I— < Cd o 0.60 0.40 O 25.4mm WAFER LENGTH A 44.4mm WAFER LENGTH • 63.5mm WAFER LENGTH >-Cd Q 0.20 0.0 1 ' 1 1 1 1 1 1 1 i I ' • ' 80 90 100 110 120 130 140 150 DRYING TEMPERATURE (C) F I G U R E B.10: Response curves for the 3x3 analysis of variance of drying rates vs. drying temperature at 5% moisture content. Each point represents the mean drying rate of 40 wafers. Curves are statistically significant at a 95% level of probability. 252 T A B L E B.5: Summary of the Analyses of Variance for Wafer Drying Rates at Different Moisture Contents from the 1 x 3 Factorial Experiment. Significantly Different Moisture Content Length Effect Drying Rates (%) (by Cell Number) 1 125 ++++2 (36.2)3 (3), (2), (1) 120 ++++ (41.3) (3),(2),(1) 110 ++++ (40.6) (3), (2), (1) 100 ++++ (33.4) (3), (2), (1) 90 ++++ (25.9) (3), (2), (I) 80 ++++ (19.15) (3), (2), (1) 70 ++++ (13.47) (3), (2), (1) 60 +++ (9.08) (3,2), (2,1) 50 ++ (5.95) (3,2), (2,1) 40 + (3.80) (3,2), (2,1) 30 N.S. (2.31) (3,2,1) 20 N.S. (1.117) (3,2,1) 15 N.S. (0.541) (3,2,1) 10 N.S. (0.1156) (3,2,1) 5 N.S. (1.599) (3,2,1) Based On Tukey's Test of Significance for differences between means at a probability level of 0.95 significant at a probability of 0.9999 significant at a probability of 0.9990 significant at a probability of 0.990 significant at a probability of 0.950 not significant Values in parentheses are the F-values 2 ++++ +++ ++ + N.S. 253 Appendix C Predicted Initial Wafer Drying Rate and Dimensionless Numbers Characterizing the Drying System Used in the 3 x 3 and 1 x 3 Factorial Experiments C.l Introduction This appendix is composed of five sections. Table C . l shows the calculation of mean abso-lute humidity and partial pressure of water vapour in the drying medium from experimental measurements taken prior to each set of drying runs. These values are used in the calcula-tion of the predicted drying rates (Section C.5). Section C.3 presents the development of an equation for the radiative heat transfer coefficient, and Section C.4 calculates the radiative shape factors required by this equation for the various system geometries found in the 3x3 and 1 x 3 factorial experiments. The equation for the radiative heat transfer coefficient is used in the calculations of predicted initial wafer surface temperatures and drying rates. Section C.5 contains the four computer programs used to calculate the predicted values and the calculated values themselves. 254 C.2 Mean Absolute Humidity and Partial Pressure Water Vapour in Drying Medium T A B L E C . l : Calculation of Mean Absolute Humidity and Partial Pressure Water Vapour in Drying Medium. Saturated Partial 4 Dry Bulb 1 Wet Bulb 1 Relative2 Vapour8 Pressure Absolute5 Temp. Temp. Humidity Pressure of Water Humidity at D.B.T. (°F) (°F) (%) (psi) (psi) (kg H 2 0 / k g Air) 75 64 54.0 0.430 0.232 0.00998 72 60 49.2 0.388 0.1910 0.00819 71 60 51.6 0.375 0.1937 0.00831 74 60 43.2 0.415 0.1794 0.00769 72 63 60.2 0.388 0.234 0.01005 76 64 51.6 0.444 0.229 0.00985 76 64 51.6 0.444 0.229 0.00985 72 62 56.2 0.388 0.218 0.00937 68 55 40.8 0.339 0.1382 0.00590 66 56 52.6 0.316 0.1663 0.00742 75 67 66.0 0.430 0.284 0.01224 74 ' 64 57.4 0.415 0.238 0.01026 74 64 57.4 0.415 0.238 0.01026 69 63 71.6 0.351 0.251 0.01082 73 65 65.2 0.402 0.262 0.01129 69 63 71.6 0.351 0.251 0.01082 72 65 68.8 0.388 0.267 0.01151 Mean Absolute Humidity = 0.00962 kg H 2 0 / k g air Mean Partial Pressure = 0.2238 psi (1543 N/m 2 ) Coefficient of Variation = 17.4% Measured by sling psychrometer prior to each set of drying runs 2 From tabulated values presented in Table 3, Cech and Pfaff (1980) 3 From Steam Tables, Himmelblau (1974) 4 Partial pressure = p e T C e n t r e ' a t i v e h^ity^xsaturated vapour pressure ( H i m m e l b l a U ] 1 9 7 4 ) 5 Absolute Humidity = 0.622 X (partial pressure/(total pressure - partial pressure)) (Treybal, 1980) 2 5 5 C.3 Development of Radiative Heat Transfer Coefficient Equation Following the method of Siegel and Howard (1981), the following four equations may be obtained from Figure C.l. = A L (TT^) ^ ~ 9 0 , L ) Qi = Ai(tjo.i - 1^1 • ?o,i - Fn • qo,2) Q2 = A 2 (jz-^j - 10,2) Q2 = A2(go,2 - F21 • <Zo,i) Rearranging the above equations in the form: Qi + Q2 + <7o,i + <7o,2 = constant, one obtains the four equations for simultaneous solution presented below. Let E\ = ei/1 — c\, Ei - e 2 / l - €2, 1 0 A1E1 0 AxExoT$ (1) 1 0 Ai(Fn - 1) A i ^ i 2 0 (2) 0 1 0 A2E2 A2E2oT4 (3) 0 1 A2F2i -A2 0 (4) 0 A1El - A^Fn - 1) -AiF12 AxExoTf (1)"(2) 1 0 A2E2 A2E2oT4 (3) 1 A2F21 -A2 0 (4) -A2F2i A2E2 + A2 A2E2oTl (3)"(4) AxEi - A^Fn - 1) -AXF12 A\E\oTl (1H2) 256 A i = surface area of glass pipe (6" diameter, 12" high) = 0.1459 m 2 Ai — surface area of 25 mm long wafer = 1.685 X 1 0 - 3 m 2 = surface area of 44 mm long wafer = 2.92 X 1 0 - 3 m 2 = surface area of 63 mm long wafer = 4.15 x 1 0 - 3 m 2 9t,i, <7i,2 = r a * e of radiative heat transfer being absorbed by glass pipe and wafer respectively 9o,i, 1o,i = rate °f radiative heat transfer being emitted by glass pipe and wafer respectively Qi.) Qi — total radiative heat transfer from glass pipe and wafer respectively T i , T2 = surface temperature of glass pipe and wafer respectively FIGURE C . l : Cross-section of drying apparatus showing the glass pipe and the suspended wafer. 257 Dividing (3)-(4) by A2 and (l)-(2) by Ai -F2i (E2 + l) E2aT4 (5) [Ey-Fn + l) -F12 ExoT4 (6) Multiplying (5) by (E\ - Fu + 1) and (6) by -F2i and subtracting we obtain (Ei + l^Ei-Fu + 1)-F21Fl2 E2oT4(Ex - Fn + 1) + F2lExaT4 (7) Therefore, = {{Ezo-TtJE! - Fu + 1)) + F21El0-T4)  9 0 2 (((£„ + 1 ) ( ^ - Fu + 1)) - F21F12) and, Q2 = A2E2{aT4 - q02) The radiative heat transfer coefficient (hr) may then be calculated by: h = Q i h r A2{TX-T2) 2'58 C.4 Radiative Shape Factors Following the method of Sparrow and Cess (1970), the radiative shape factor between two objects may be described by F1-2 — _ * / / (ln r dx\dx2 + ln r dy\dy2 + ln r dz\dz2) (C-l) 27rAi JCL JC2 where r is the distance between points on the contours of the two objects given by: r = ((*i - x2)2 + (yi - y 2 ) 2 + (zi - Z2?)* (C2) For surface A 2 of the wafer in Figure C.2, y 2 = 0 and dv = 0. Therefore Equation C.l becomes: 1 '1-2 = 2^r £ £ (ln [(ix ~ 1 2 ) 2 + y 2 + ( Z i " z ^ 2 1 5 d a : i d : E 2 + ln [(xi - x 2 ) 2 + y\ + (*i - Z 2 ) 2 ] 2 dzidz2^ (C.3) From Figure C.2, the surface area of the glass pipe pertinent to this solution, A\, equals (n • a • b), where a is the radius of the pipe and 6 is the length. The wafer has a width c and length in the flow direction d. Wafer thickness is considered to be negligible. Evaluating the contour-integral around the wafer in the direction indicated and substi-tuting any constant values of x, y and z, one obtains: Fi- , 2^ . 2 . I b + d - zi b-d x 2 — zi 1 2 dx2 > dxi 2n2ab Jci I Jz2=-% + £ In J(x 2 - xi)2 + + ( dx2 dz-y dz2 > dz\ (C.4) 259 FIGURE C.2: Schematic diagram of the drying system used to develop the equations for calculating radiative shape factors. Arrows indicate direction of evaluation of the contour integrals. 260 After evaluating the contour-integral for the glass pipe, Equation C.4 becomes: ( „ - S l ) » + (a* - *») + f * ± ^ - o'* 2n2abFi-2 = T [' _ In Jxi = -a J i 2 = - 2 £ + r p In Jxi=a Jxi — -£ + f P In ( ( s j - ^ - K a 2 - * ? ) + ( + r f* m 2 6 - d dx2dx\ o)2 dx2dx\ dx2dx\ + f In + r >» (- + a) 2 + 0+(z 2 - Z l ) 2 {- + af +Q+(z2- Zl)2 (— + a) 2 + 0 + ( * 2 - z 1 ) 2 ( _ £ _ a ) 2 + 0 + ( 2 2 _ 2 l ) 2 dz 2dzi dz2dz\ i 2 dz2dz\ 2 ci22 dzi (C.5) The eight double integrals in Equation C.5 were evaluated separately using a standard integration routine UBC DDBLGS Double Gaussian integration. The results of the inte-grations and the final calculations of the various shape factors required are presented in Tables C.2 and C.3 for the wafers in the 3 x 3 and 1 x 3 factorial experiments respectively. 261 TABLE C.2: Integrals of Equation C.5 and the Calculation of F1-2, ^ i _ i and F2-1 for the Drying System in the 3x3 Factorial Experiment. Wafer Length 25 mm 44 mm 63 mm Ill 14.7711 15.1205 15.4573 ! h -13.7728 -13.3724 -12.9574 7/3 -13.7728 -13.3724 -12.9574 r r J J4 14.7711 15.1205 15.4573 Sh 18.8264 32.9829 47.1993 He -16.0599 -28.1459 -40.3014 ISr -16.0599 -28.1459 -40.3014 I k 18.8264 32.9829 47.1993 Zfh- 8 7.5296 13.1703 18.7956 Fl-2 0.01059 0.01853 0.02645 ( E / / - r2?r2a6) F1-1 0.9894 0.9815 0.9735 (1 - F L -2) F2-1 0.9170 0.9259 0.9299 -2) 262 T A B L E C.3: Integrals of Equation C.5 and the Calculation of F1-2, and F2-1 f° r the Drying System in the 1 x 3 Factorial Experiment. Wafer Length 25 mm 44 mm 63 mm Ul 11.9088 20.8555 29.8268 Ul -10.9096 -19.1118 -27.3464 JJs -10.9096 -19.1118 -27.3464 11.9088 20.8555 29.8268 I h 23.2171 24.1720 25.0856 Ue -20.4521 -19.3282 -18.1573 Ui -20.4521 -19.3282 -18.1573 Us 23.2171 24.1720 25.0856 7.5285 13.1750 18.8174 F12 0.01059 0.01854 0.02648 (HU^ab) Fu 0.9894 0.9815 0.9735 (1 - F12) F21 0.9170 0.9264 0.9309 ( t * 263 .5 Computer Programs to Calculate Predicted Drying Rates and Dimensionless Numbers that Characterize the Drying System Used in the 3x3 and 1x3 Factorial Experiments T A B L E C.4: L i s t o f V a r i a b l e s U s e d i n C o m p u t e r P r o g r a m s List of Variables A R E A - surface area of wafer (m2) AS, AS1 - latent heat of vaporization (J/kg) CP - specific heat of air (J/kg) DAB - diffusion coefficient of water in air (m2/s) D E N O M - intermediate variable in the mass transfer coefficient calculation DRWB - initial wet bulb drying rate (g/m2s) E l , E2 - intermediate calculations for radiative heat transfer coefficient using the emissivities of glass and wood respectively F l l , F12, F21 - radiation shape factors (1 - glass pipe, 2 - wafer) HC - convective heat transfer coefficients (W/m 2 K) H C K Y , H C K Y l - psychrometric ratio (J/kg) HR - radiative heat transfer coefficient (W/m 2 K) K Y , K Y I - mass transfer coefficient (kg/m2s) L E - wafer length (m) LHS - left hand side, of iterative equation MFCB11 - mole fraction concentration at wafer surface MFCB21 - mole fraction concentration of air of drying medium M F C B M l - log mean mole fraction concentration of air MIU - viscosity of air (kg/ms) NU - Nusselt number P i , P2, P3 - intermediate variables for radiative heat transfer coefficient calculation PA - partial pressure of water in drying medium (N/m 2) PR - Prandtl number PSI - partial pressure of water at surface temperature (psi) PT - total pressure (N/m 2) RE - Reynolds number RHO - density of air (kg/m3) RHS - right hand side of iterative equation SC - Schmidt number SH - Sherwood number S T l , STPSl - intermediate surface temperature (K) and (F) respectively T l , T2 - intermediate variables for radiative heat transfer coefficient calculation T G - temperature of drying medium (K) T K - thermal conductivity of air (W/m K) TWB - wafer surface/wet bulb temperature (C) YSl - saturated absolute humidity (kg HjO/kg Air) 264 1 c 2 C Calculat ions of predicted drying rates for v e r t i c a l l y oriented wafers 3 C (3 X 3 f a c t o r i a l experiment) not including the radiant heat transfer 4 C from the glass pipe to the wafer in the ca lculat ions of wet bulb 5 C temperatures. 6 C 7 REAL RE(9),PR(9),SC(9),SH(9),NU(9),HC(9),KY(9),TWB(9),HCKY(9) 8 REAL LHS,MFCB11,MFCB21,MFCBM1,KY1,HCKY1,0RWB(9).A(9,4,5),X(4) 9 REAL AREA(9),F12(9),F11(9), F21(9) 10 REAL RH0(9),MIU(9),CP(9),TK(9),LE(9).DAB(9).TG(9),AS(9),HR(9) 11 C 12 C Data input for the nine sets of condi t ions. Propert ies of a i r 13 C obtained from Holman (1981), except air-water d i f f u s i v i t i e s which 14 C were calculated using the WiIke-Lee modif icat ion of Hirschfe lder-15 C Bird-Spotz method (Treyba1.1980). 16 C 17 OATA RHO/0.968, .968, .968, .899. .899, .899. .837. .837, .837/ 18 DATA MIU/2.13E-05.2.13E-05.2.13E-05,2.26E-05.2.26E-05.2.26E-05.2.3 19 •8E-05,2.38E-05,2.38E-05/ 20 DATA CP/1010.,1010.,1010.,1013.,1013.,1013.,1017..1017.,1017./ 21 DATA TK/.031,.031,.031,.0331,.0331,.0331,.0352,.0352,.0352/ 22 DATA LE/.0254,.04445,.0635,.0254,.04445..0635,.0254,.04445..0635/ 23 DATA TG/363. .363. .363. .393. ,393. .393. ,423. .423. ,423. / 24 DATA DAB/3.34E-05.3.34E-05.3.34E-05.3.93E-05.3.93E-05.3.93E-05.4.4 25 *9E-05.4.49E-05.4.49E-05/ 26 DATA AREA/1.685E-03,2.92E-03.4.15E-03,1.685E-03.2.92E-03.4.15E-03, 27 *1.685E-03.2.92E-03,4.15E-03/ 36 PT=1.0133E05 37 PA=1543. 38 C 39 C Calculat ion of Dimensionless Numbers that character ize the drying 40 C system. Nusselt and Sherwood Numbers corre la t ion for a submerged 41 C f l a t plate obtained from B i r d , Stewart and Lightfoot (1960). 42 C 43 DO 40 1=1.9 44 SC(I)=MIU(I)/(RH0(I)'DAB(I)) 45 PR(I)=(CP(I)-MIU(I))/TK(I) 46 RE(I)=(RH0(I)•0.294'LE(I))/MIU(I) 47 NU( I )=0.664 * (RE( I) * *0.500) * (PR(I )"0.33) 48 SH(I)=0.664*(RE(I)* *0.500)•(SC(I)* *0.33) 49 HC(I)=NU(I)*TK(I)/LE(I) 50 C - 51 C I terat ive solut ion of surface temperatures and drying rates . 52 C 53 ST1=293.0 54 DO 20 J=1,4000 55 STPS1=((ST1-273.)'9./5.)+32. 56 C 57 C Corre lat ion of vapour pressure with temperature (Rosen, 1980) used 58 C to determine the water vapour pressure at the saturated wafer 59 C surface and thus the saturated absolute humidity at the wafer 60 C surface (Treybal.1980) 61 C 62 PS1 = (1.236E07*EXP(- 9160./(STPS1+4 59.6)))*6894.7 63 MFCB11=(PT-PS1)/PT 64 MFCB21=(PT-PA)/PT 65 DEN0M=MFCB21/MFCB11 66 MFCBMl=(MFCB21-MFCB11)/ALOG(DENOM) 265 67 Y S 1 = ( 0 . 6 2 2 * P S 1 ) / ( P T - P S 1 ) 68 C 69 C C o r r e l a t i o n o f l a t e n t h e a t o f v a p o r i z a t i o n w i t h t e m p e r a t u r e 70 C ( S t a n i s h a n d K a y i h a n , 1 9 8 4 ) . 71 C 72 A S 1 = 2 . 7 0 E 0 6 - ( 1 6 0 . * S T 1 ) - ( 3 . 4 3 * ( S T 1 * " 2 . 0 ) ) 73 C 74 C C a l c u l a t i o n o f m a s s t r a n s f e r c o e f f i c i e n t a n d p s y c h r o t n e t r i c r a t i o 75 C ( T r e y b a l , 1 9 8 0 ) 76 C 77 K Y 1 = 2 8 . 9 7 * M F C B M 1 * S H ( I ) * P T * D A B ( I ) / ( 8 3 1 4 * T G ( I ) * L E ( I ) ) 78 HCKY1=I H C ( I ) / K Y 1 91 C 92 C I t e r a t i v e e q u a t i o n s f o r d e t e r m i n i n g t h e w a f e r s u r f a c e t e m p e r a t u r e 93 C ( T r e y b a l , 1 9 8 0 ) . 94 C 95 L H S = T G ( I ) - S T 1 96 R H S = ( A S 1 * ( Y S 1 - 0 . 0 0 9 6 2 ) ) / H C K Y 1 97 I F ( A B S ( ( L H S - R H S ) / L H S ) . L E . 0 . 0 0 1 ) GO TO 30 98 S T 1 = S T 1 + 0 . 0 1 99 2 0 C O N T I N U E 100 C 101 C T r a n s f e r r a l o f d e s i r e d v a l u e s f r o m t e m p o r a r y v a r i a b l e s t o a r r a y s 102 C d i m e n s i o n e d t o t h e n u m b e r o f c e l l s . 103 C 104 30 T W B ( I ) = S T 1 - 2 7 3 . 105 K Y ( I ) = K Y 1 106 H C K Y ( I ) = H C K Y 1 107 A S ( I ) = A S 1 108 C 109 c C a l c u l a t i o n o f t h e p r e d i c t e d i n i t i a l w a f e r d r y i n g r a t e . 110 c 111 D R W B ( I ) = ( ( H C ( I ) « ( T G ( I ) - S T 1 ) ) / A S ( I ) ) * 1 0 0 0 . 112 4 0 C O N T I N U E 113 c 114 c P r i n t i n g o f k e y v a r i a b l e s d e s c r i b i n g w a f e r d r y i n g f o r e a c h o f 115 c t h e c e l l s . 116 c 117 W R I T E ( 6 , 1 0 0 0 ) ( T G ( J ) . J = 1 . 9 ) 116 W R I T E ( 6 . 1 0 0 0 ) ( L E ( J ) . J = 1 . 9 ) 119 W R I T E ( 6 , 1 0 0 0 ) ( R H 0 ( J ) , J = 1 . 9 ) 120 W R I T E ( 6 . 1 0 0 0 ) (M ILK J ) , J = 1 , 9 ) 121 W R I T E ( 6 , 1000 ) ( C P U ) . J=1 ,9 ) 122 W R I T E ( 6 . 1 0 0 0 ) ( T K ( J ) . J = 1 , 9 ) 123 W R I T E ( 6 . 1000 ) ( D A B U ) . J=1 . 9 ) 124 W R I T E ( 6 , 1000 ) ( R E ( J ) , J = 1 , 9 ) 125 W R I T E ( 6 , 1000 ) ( S C U ) , J=1 . 9 ) 126 W R I T E ( 6 . 1 0 0 0 ) ( P R ( J ) . J = 1 . 9 ) 127 W R I T E ( 6 . 1000 ) ( N U U ) , J = 1 . 9 ) 128 W R I T E ( 6 , 1000 ) ( S H U ) , J = 1 , 9 ) 129 W R I T E ( 6 . 1000 ) ( H C ( J ) . J = 1 . 9 ) 131 W R I T E ( 6 . 1 0 0 0 ) ( K Y ( J ) . J = 1 . 9 ) 132 W R I T E ( 6 , 1000 ) ( H C K Y ( J ) . J = 1 , 9 ) 133 W R I T E ( 6 . 1000 ) ( A S U ) , J=1 .9 ) 134 W R I T E ( 6 , 1000 ) ( T W B U ) . J=1 . 9 ) 135 W R I T E ( 6 . 1000) ( O R W B ( J ) . J = 1 , 9 ) 136 1000 F O R M A T ( 9 G 1 2 . 5 , / ) 137 S T O P 138 END 266 TABLE C.5: Calculation of Predicted Drying Rates for Vertically Oriented Wafers ( 3 x 3 Factorial Experiment) Not Including the Effects of Radiation Cell Number 1 2 3 4 5 6 7 8 9 TG (°K) 363.00 363.00 363.00 393.00 393.00 393.00 423.00 423.00 423.00 LE (m) 0.25400E- 01 0.44450E-•01 0.63500E- 01 0.25400E- •01 0.44450E- •01 0.63500E- 01 0.25400E- 01 0.44450E- 01 0.6350CE- 01 RHO (kg/m ) 0.96800 0.96800 0.96800 0.89900 0.89900 0.89900 0.83700 0.83700 0.83700 MIU (kg-m/s) 0.21300E- 04 0.21300E- •04 0.21300E-•04 0.22600E- •04 0.22800E' •04 0.22800E-•04 0.23800E- 04 0.23800E-•04 0.23800E- 04 CP (J/kg) 1010.0 1010.0 1010.0 1013.0 1013.0 1013.0 1017.0 1017.0 1017.0 TK (W/m K) 0.31000E' •01 0.31000E' •01 0.31000E' •01 0.33100E •01 0.33100E' •01 0.331O0E' •01 0.35200E-•01 0.35200E' •01 0.35200E-•01 DAB (m2/s) 0.33400E' •04 0.33400E •04 O.33400E-•04 0.39300E •04 0.39300E •04 0.39300E •04 0.44900E- •04 0.44900E •04 0.44900E- •04 RE 339.37 593.90 848.43 297.05 519.84 742.63 262.62 459.59 656.55 SC 0.65881 0.65881 0.66881 0.63967 0.63967 0.63967 0.63329 0.63329 0.63329 PR 0.69397 0.69397 0.69397 0.69166 0.69166 0.69166 0.68763 0.68763 0.68763 NU 10.843 14.344 17.144 10.133 13.405 16.022 9.5095 12.580 15.036 SH 10.659 14.100 16.853 9.8753 13.064 15.614 9.2547 12.243 14.633 HC (W/m2 K) 13.234 10.004 8.3696 13.205 . 9.9821 8.3516 13.179 9.9621 8.3349 KY (k , . / , , , 2 R ) n . i n I 7 i c •0 I o. nosor.r •02 O.03319E •02 0.13157E •01 0.99459E •02 0.83213E •02 0.12974E •01 0.98075E •02 0.BS055E •0? 1ICKY (J/kj> !<) 100/1 . 0 1004,5 1004.0 1003.6 1003.6 1003.6 1015.0 l O I I i . n 1015. n AS (J/kg) 0 . 23289E»0? 0.232B9E •07 0 . 2 3 2 8 9 E » 0 7 0.23177E • 07 0.231?7E*07 0.23177E*07 0.23080E^07 0.23080E • 07 0. 230B0E •07 TWB (°C) 33.418 33.418 33.4 18 38.340 38.340 38.340 42.539 42.539 42.539 DRWB (g/m"" s ) 0.32151 0.24304 0.20334 0.46526 0.35170 0.29425 0.61360 0.46383 0.38e07 1 c 2 C Calculat ions of predicted drying rates for ve r t i ca l l y oriented wafers 3 C (3 X 3 f a c t o r i a l experiment) with the radiant heat transfer from the 4 C glass pipe to the wafer included in the calculat ions of wet bulb 5 C temperatures. 6 C 7 REAL RE(9).PR(9),SC(9).SH(9).NU(9).HC(9).KY(9).TWB(9),HCKY(9) 8 REAL LHS,MFCB11.MFCB21,MFCBM1,KY1,HCKY1,DRWB(9),A(9.4.5).X(4) 9 REAL AREA(9).F12(9) ,F11(9),F21(9) 10 REAL RH0(9),MIU(9) .CP(9).TK(9).LEO).DAB(9).TG(9),AS(9),HR(9) 11 C 12 C Data input for the nine sets of condi t ions. Properties of a i r 13 C obtained from Holman- (1981). except air-water d i f f u s i v i t i e s which 14 C were ca lcula ted using the Wilke-Lee modification of Hirschfe lder-15 C Bird-Spotz method (Treyba1.1980). 16 C 17 DATA RH0/0.968. .968, .968..899..899,.899,.837,.837..837/ 18 DATA MIU/2.13E-05.2. 13E-05.2.13E-05,2.26E-05.2.26E-05,2.26E-05.2.3 19 *8E-05.2.38E-05,2.38E-05/ 20 DATA CP/1010. , 1010. , 1010.,1013.,1013..1013.,1017..1017.,1017./ 21 DATA TK/ .031 , .031 , .031,.0331,.0331,.0331,.0352..0352,.0352/ 22 DATA LE/.0254,.04445,.0635..0254..04445,.0635,.0254,.04445,.0635/ 23 DATA TG/363.,363. ,363. ,393. ,393. ,393. ,423. .423. ,423. / 24 DATA DAB/3.34E-05,3.34E-05.3.34E-05.3.93E-05.3.93E-05.3.93E-05,4.4 25 *9E-05.4.49E-05.4.49E-05/ 26 DATA AREA/1.685E-03. 2.92E-03.4.15E-03,1.685E-03,2.92E-03,4.15E-03, 27 •1.685E-03.2.92E-03.4.15E-03/ 28 C 29 C Shape factors for rad ia t ive heat transfer ca lculat ions (see 30 C Appendix I-A). 31 C 32 DATA F12/.01059, .01853, .02645..01059..01853..02645..01059, .01853,. 33 '02645/ 34 DATA F1 1/.9894. .9815. .9735,.9894,.9815,.9735,.9894..9815,.9735/ 35 DATA F21/.9170. .9259i .9299..9170..9259..9299,.9170,.9259..9299/ 36 PT=1.0133E05 37 PA=1543. 38 C 39 C Calculat ion of Dimensionless Numbers that characterize the drying 40 C system. Nusselt and Sherwood Numbers corre lat ion for a submerged 41 C f l a t plate obtained from Bi rd , Stewart and Lightfoot (1960). 42 C 43 DO 40 1 = 1 ,9 44 SC(I)=MIU(I)/-(RH0(I)*DAB(I)) 45 PR(I)=(CP(I)*MIU(I))/TK(I) 46 RE(I)=(RHO(I)*0.294*LE(I))/MIU(I) 47 NU(I)=O.664*(RE(I)**0.50O) ,(PR(I)**0.33) 48 SH(I )=0.664 , (RE(I ) , *0.500)*(SC(I)"0.33) 49 HC(I)=NU(I)'TK(I)/LE(I) 50 C 51 C I terat ive s o l u t i o n of surface temperatures and drying rates. 52 C 53 ST1=293.0 54 DO 20 J=1 ,4000 55 STPS1=((ST1-273.)*9./5.)+32. 56 C 57 C Corre lat ion of vapour pressure with temperature (Rosen, 1980) used 58 C to determine the water vapour pressure at the saturated wafer 268 59 C surface and thus the saturated absolute humidity at the wafer 60 C surface (Treyba 1,1980) 61 C 62 PS1 = ( 1.236E07*EXP(-9160./<STPS1 + 459.6)))*6894.7 63 MFCB11=(PT-PS1)/PT 64 MFCB21=(PT-PA)/PT 65 DEN0M=MFCB21/MFCB11 66 MFCBM1=(MFCB21-MFCB11)/ALOG(OENOM) 67 YS1=(0.622*PS1)/(PT-PS1) 68 C 69 C Corre lat ion of latent heat of vaporizat ion with temperature 70 C (Stanish and Kayihan,1984). 71 C 72 AS1=2.70E06-( 160.*ST1)- (3 .43' (ST1"2.0) ) , 73 C 74 C Calculat ion of mass transfer coe f f i c ien t and psychrometric ra t io 75 C (Treybal.1980) 76 C 77 KY1=28.97*MFCBMTSH(I)*PT*DAB(I)/(8314*TG(I)*LE(I)) 78 HCKY1=HC(I)/KY1 79 C 80 C Calculat ion of rad ia t ive heat transfer coe f f i c ien t (see Appendix 81 C I-A). 82 C 83 E1=0.93/(1.-0.93) 84 E2=0.93/(1.-0.93) 85 T1=5.729E-08*(TG(I)**4) 86 T2=5.729E-08*(ST1**4) 87 P1=E2*T2*(E1 + 1.-F11(I))+F21(I)*E1 * T1 88 P2=P1/((E1+1.-F1KI))*(E2+1)-(F12(I)*F21(I))) 89 P3=-AREA(I)*E2*(T2-P2) 90 HR(I)=P3/(AREAfI)*(TG(I)-ST 1)) 91 C 92 C I terat ive equations for determining the wafer surface temperature 93 C (Treybal,1980). 94 C 95 LHS=(TG(I)-ST1) + (HR(I)MTG(I)-ST1) )/HC!I) 96 RHS=(AS1*(YS1-0.00962))/HCKY1 97 IF (ABS((LHS-RHS)/LHS).LE.0.001) GO TO 30 98 ST1=ST1+0.01 99 20 CONTINUE 100 C 101 C Transferral of desired values from temporary variables to arrays 102 C dimensioned to the number of c e l l s . 103 C 104 30 TWB(I)=ST1-273. 105 KY(I)=KY1 106 HCKY(I)=HCKY1 107 AS(I)=AS1 108 C 109 C Calculat ion of the predicted i n i t i a l wafer drying rate. 110 C 111 0RWB(I)=(((HC(I)+HR(I)) ,(TG(I)-ST1))/AS(I))*1000. 112 40 CONTINUE 113 C 114 C Pr int ing of key var iables descr ib ing wafer drying for each of 115 C the c e l l s . 116 C 269 117 WRITE (6 1000) ( T G ( J ) . J = 1 .9) 118 WRITE (6 1000) (LE(J).J=1.9) 1 19 WRITE (6 1000) (RHO(J),J=1 .9) 120 WRITE (6 1000) (MIU(J),J=1.9) 121 WRITE (6 1000) (CPU) . J=1.9) 122 WRITE (6 1000) (TKU) . J=1 .9) 123 WRITE (6 1000) (DAB(J).J=1 ,9) 124 WRITE (6 1000) (REU) ,J=1,9) 125 WRITE (6 1000) (SCU) , J=1 ,9) 126 WRITE (6 1000) (PRU) . J=1.9> 127 WRITE (6 1000) (NUU) . J=1.9) 128 WRITE (6 1000) (SHU) . J=1.9) 129 WRITE (6 1000) (HCU) . J=1 .9) 130 WRITE (6 1000) (HRU) ,J=1,9) 131 WRITE (6 1000) (KY(J),J=1, 9) 132 WRITE (6 1000) (HCKY(J),J=1,9) 133 WRITE (6 1000) (ASU) . J=1 .9) 134 WRITE (6 1000) (TWBU) . J=1 .9) 135 WRITE (6 1000) (DRW8(J),J=1,9) 136 1000 FORMAT (9G12.5./) 137 STOP 138 END 270 TABLE C.6: Calculation of Predicted Drying Rates for Vertically Oriented Wafers ( 3 x 3 Factorial Experiment) Including the Effects of Radiation C e l l Number 1 2 3 4 5 6 7 8 9 TG (°K) 3 6 3 . 0 0 3 6 3 . 0 0 3 6 3 . 0 0 3 9 3 . 0 0 3 9 3 . 0 0 3 9 3 . 0 0 4 2 3 . 0 0 4 2 3 . 0 0 4 2 3 . 0 0 LE (m) 0 . 2 5 4 0 0 E - • 0 1 0 . 4 4 4 5 0 E - • 0 1 0 . 6 3 5 0 0 E - 0 1 0 . 2 5 4 0 0 E - 0 1 0 . 4 4 4 5 0 E - 0 1 0 . 8 3 5 0 0 E - 0 1 0 . 2 5 4 0 0 E - 0 1 0 . 4 4 4 6 0 E - • 0 1 0 . 6 3 5 0 0 E ' • 0 1 RHO (kg/m3) 0 . 9 6 8 0 0 0 . 9 6 8 0 0 0 . 9 6 8 0 0 0 . 8 9 9 0 0 0 . 8 9 9 0 0 0 . 8 9 9 0 0 0 . 8 3 7 0 0 0 . 8 3 7 0 0 0 . 8 3 7 0 0 MIU (kg m/s) 0 . 2 1 3 0 0 E - • 0 4 0 . 2 1 3 0 0 E - • 0 4 0 . 2 1 3 0 0 E - • 0 4 0 . 2 2 6 0 0 E - • 0 4 0 . 2 2 6 0 0 E - • 0 4 0 . 2 2 6 0 0 E - 0 4 0 . 2 3 8 0 0 E - 0 4 0 . 2 3 8 0 0 E - • 0 4 0 . 2 3 8 0 0 E - • 0 4 CP (J/kg) 1 0 1 0 . 0 1 0 1 0 . 0 1 0 1 0 . 0 1 0 1 3 . 0 1 0 1 3 . 0 1 0 1 3 . 0 1 0 1 7 . 0 1 0 1 7 . 0 1 0 1 7 . 0 TK (W/m K) 0 . 3 1 0 0 0 E • 0 1 0 . 3 1 0 0 0 E • 0 1 0 . 3 1 0 0 0 E • 0 1 0 . 3 3 1 0 0 E - • 0 1 0 . 3 3 1 0 O E - • 0 1 0 . 3 3 1 0 0 E - • 0 1 O . 3 5 2 0 O E - • 0 1 0 . 3 5 2 0 0 E • 0 1 0 . 3 5 2 0 0 E • 0 1 DAB (m 2/s) 0 . 3 3 4 0 0 E • 0 4 0 . 3 3 4 0 0 E • 0 4 0 . 3 3 4 0 0 E < • 0 4 0 . 3 9 3 0 0 E ' • 0 4 0 . 3 9 3 0 0 E - • 0 4 0 . 3 9 3 0 0 E - • 0 4 O . 4 4 9 0 O E - • 0 4 0 . 4 4 9 0 0 E - • 0 4 0 . 4 4 9 0 0 E • 0 4 RE 3 3 9 . 3 7 5 9 3 . 9 0 8 4 8 . 4 3 2 9 7 . 0 5 5 1 9 . 8 4 7 4 2 . 6 3 2 6 2 . 6 2 4 5 9 . 5 9 656.55 SC 0 . 6 5 8 8 1 0 . 6 5 8 8 1 0 . 6 5 8 8 1 0 . 6 3 9 6 7 0 . 6 3 9 5 7 0 . 6 3 9 6 7 0 . 6 3 3 2 9 0 . 6 3 3 2 9 0 . 6 3 3 2 9 PR 0 . 6 9 3 9 7 0 . 6 9 3 9 7 0 . 6 9 3 9 7 0 . 6 9 1 6 6 0 . 6 9 1 6 6 0 . 6 9 1 6 6 0 . 6 8 7 6 3 0 . 5 8 7 S 3 0 . 6 8 7 6 3 NU 1 0 . 8 4 3 1 4 . 3 4 4 1 7 . 1 4 4 1 0 . 1 3 3 1 3 . 4 0 5 1 6 . 0 2 2 9 . 5 0 9 5 1 2 . 5 8 0 1 5 . 0 3 6 SH 1 0 . 6 5 9 1 4 . 1 0 0 1 6 . 8 5 3 9 . 8 7 5 3 1 3 . 0 6 4 1 5 . 6 1 4 9 . 2 5 4 7 1 2 . 2 4 3 14.633 HC (W/m2 "K) 1 3 . 2 3 4 1 0 . 0 0 4 8 . 3 6 9 6 1 3 . 2 0 5 9 . 9 8 2 1 8 . 3 5 1 6 1 3 . 1 7 9 9 . 9 6 2 1 8 . 3 3 4 9 HR (W/m2 K) 6.7 2 2 3 6 . 8 8 7 3 6 .964 1 8 . 2 6 0 5 0 . 4 4 0 8 8 . 5 3 0 7 9 . 6 4 7 9 1 0 . 0 5 2 10.158 KY (kg/m2 s) 0 . 1 3 0 7 7 E • 0 1 0 . 9 8 6 0 8 E • 0 2 0 . 8 2 3 4 7 E - 0 2 0 . 1 2 9 7 8 E • 0 1 0 . 9 7 6 6 0 E • 0 2 0 . 8 1 4 2 2 E • 0 2 0 . 1 2 6 8 7 E •01 0 . 9 5 2 0 1 E • 0 2 0.79193E •02 HCKY (J/kg K) 1 0 1 2 . 0 1 0 1 4 . 5 1 0 1 6 . 4 1 0 1 7 . 5 1 0 2 2 . 1 1 0 2 5 . 7 1 0 3 8 . 7 1 0 4 6 . 4 1052 .5 AS (J/kg) 0 . 2 3 1 8 7 E + 0 7 0 . 2 3 1 5 7 E • 0 7 0 . 2 3 1 3 6 E + 0 7 0 . 2 3 0 3 2 E + 0 7 0 . 2 2 9 9 2 E + 0 7 0 . 2 2 9 6 3 E + 0 7 0 . 2 2 8 9 3 E + 0 7 0 . 2 2 8 4 4 E * 0 7 0 . 2 2 8 0 8 E * 0 7 TWB (°C) 3 7 . 9 1 0 3 9 . 1 9 9 4 0 . 1 3 7 4 4 . 5 9 0 46.289 4 7 . 5 2 0 5 0 . 4 8 8 5 2 . 5 5 9 54.013 DRWB (g/m s) 0 . 4 4 8 3 1 0 . 3 7 0 5 4 0 . 3 3 0 4 8 0 . 7 0 2 8 1 0 . 5 9 0 6 2 0 . 5 3 2 8 7 1 . 0 0 0 9 0 . 8 5 3 7 3 0.7 7 8 0 4 1 c 2 C C a l c u l a t i o n s o f p r e d i c t e d d r y i n g r a t e s f o r h o r i z o n t a l l y o r i e n t e d wafers 3 C (1 X 3 f a c t o r i a l experiment) not i n c l u d i n g the r a d i a n t heat t r a n s f e r 4 C from the g l a s s p i p e to the wafer i n the c a l c u l a t i o n s of wet b u l b 5 C temperatures. 6 C 7 REAL RE(3).PR(3).SC(3).SH(3).NU(3).HC(3),KY(3).TWB(3).HCKY(3) 8 REAL LHS,MFCB11,MFCB21,MFCBM1,KY1.HCKY1.0RWB(3).A(3,4.5).X(4) 9 REAL AREA(3),F12(3),F11(3),F21(3) 10 REAL RH0(3).MIU(3),CP(3),TK(3),LE(3),DAB(3).TG(3),AS(3),HR(3) 11 C 12 C Data input f o r the n i n e s e t s o f c o n d i t i o n s . P r o p e r t i e s o f a i r 13 C o b t a i n e d from Holman (1981), except a i r - w a t e r d i f f u s i v i t i e s which 14 C were c a l c u l a t e d u s i n g the Wilke-Lee m o d i f i c a t i o n of H i r s c h f e l d e r -15 C B i r d - S p o t z method ( T r e y b a l , 1 9 8 0 ) . 16 C 17 DATA RHO/.837,.837..837/ 18 DATA MIU/2.38E-05.2.38E-05.2.38E-05/ 19 DATA CP/1017..1017.,1017./ 20 DATA TK/.0352..0352..0352/ 21 0ATA LE/.0254,.04445..0635/ 22 DATA TG/423..423..423./ 23 DATA 0AB/4.49E-05.4.49E-05.4.49E-05/ 24 DATA AREA/1.685E-03.2.92E-03.4.15E-03/ 32 PT=1.0133E05 33 PA=1543. . 34 C 35 C C a l c u l a t i o n o f D i m e n s i o n l e s s Numbers t h a t c h a r a c t e r i z e the d r y i n g 36 C system. N u s s e l t and Sherwood Numbers c o r r e l a t i o n f o r a submerged 37 C f l a t p l a t e o b t a i n e d from B i r d , Stewart and L i g h t f o o t (1960). 38 C 39 DO 40 1=1.3 40 SC(I)=MIU(I)/(RH0(I)*DAB(D) 41 P R { I ) = ( C P ( I ) * M I U ( I ) ) / T K ( I ) 42 RE( I ) = (RH0( I ) *0. 294*0.03175)/MIL)(I) 43 NU(I)=0.664'(RE(I)**0.500)*(PR(I)**0.33) 44 SH(I)=0.664*(RE(I)••0.500)'(SC(I) " 0 . 3 3 ) 45 HC(I)=NU(I)*TK(I)/0.03175 46 C 47 C I t e r a t i v e s o l u t i o n o f s u r f a c e temperatures and d r y i n g r a t e s . 48 c 49 ST1=293.0 50 00 20 J=1.4000 51 STPS1=((ST1-273.)*9./5.)+32. 52 C 53 C C o r r e l a t i o n o f vapour p r e s s u r e w i t h temperature (Rosen, 1980) used 54 C to determine the water vapour p r e s s u r e at the s a t u r a t e d wafer 55 C s u r f a c e and thus the s a t u r a t e d a b s o l u t e h u m i d i t y at the wafer 56 C s u r f a c e (Treybal,1980) 57 C 58 PS1 = ( 1.236E07*EXP(- 9160./(STPS1 + 459.6)))*6894.7 59 MFCB11=(PT-PS1)/PT 60 MFCB21=(PT-PA)/PT 61 DEN0M=MFCB21/MFCB11 62 MFCBM1=(MFCB21-MFCB11)/ALOG(DENOM) 63 YS1=(0.622*PS1)/(PT-PS1) 64 C 65 C C o r r e l a t i o n o f l a t e n t heat of v a p o r i z a t i o n w i t h temperature 272 66 C ( S t a n i s h and K a y i h a n , 1 9 8 4 ) . 67 C 68 AS1=2. 7 0 E 0 6 - ( 1 6 0 . * S T 1 ) - ( 3 . 4 3 * ( S T 1 * * 2 . 0 ) ) 69 C 70 C C a l c u l a t i o n o f mass t r a n s f e r c o e f f i c i e n t and p s y c h r o m e t n c r a t i o 71 C ( T r e y b a l , 1 9 8 0 ) 72 C 73 KY1=28 . 97 *MFCBM1*SH( I ) *PT*DAB( I ) / ( 8314*TG( I ) *0 .03175 ) 74 HCKY1= HC( I ) /KY1 87 C 88 C I t e r a t i v e e q u a t i o n s f o r d e t e r m i n i n g the wafer s u r f a c e temperature 89 C ( T r e y b a l . 1980 ) . 90 C 91 LHS=TG(I ) -ST1 92 RHS=(AS1 ' (YS1-0 .00962) ) /HCKY1 93 IF ( A B S ( ( L H S - R H S ) / L H S ) . L E . 0 . 0 0 1 ) GO TO 30 94 ST1=ST1+0.01 95 20 CONTINUE 96 C 97 C T r a n s f e r r a l o f d e s i r e d v a l u e s from temporary v a r i a b l e s to a r r a y s 98 C d imens ioned to the number o f c e l l s . 99 C 100 30 TWB(I)=ST1-273. 101 KY(I)=KY1 102 HCKY(I)=HCKY1 103 AS(I)=AS1 104 C 105 C C a l c u l a t i o n o f the p r e d i c t e d i n i t i a l wafer d r y i n g r a t e . 106 c 107 D R W B ( I ) = ( ( H C ( I ) ' ( T G ( I ) - S T 1 ) ) / A S ( I ) ) * 1 0 0 0 . 108 40 CONTINUE 109 c 110 c P r i n t i n g o f key v a r i a b l e s d e s c r i b i n g wafer d r y i n g f o r each o f 111 c the c e l l s . 112 c 113 WRITE (6 . 1000) ( T G ( J ) . J = 1 , 3 ) 114 WRITE (6 .1000) ( L E U ) ,J=1 .3) 115 WRITE (6 .1000) (RH0(J) .J=1 .3) 116 WRITE (6 .1000) (M IU(J ) .J=1 .3 ) 117 WRITE (6 .1000) ( C P ( J ) , J = 1 . 3 ) 118 WRITE (6 .1000) ( T K ( J ) . J = 1 . 3 ) 119 WRITE (6 .1000) ( D A B ( J ) , J = 1 , 3 ) 120 WRITE (6 .1000) ( R E ( J ) . J = 1 , 3 ) 121 WRITE (6 .1000) (SC(J ) ,J=1 ,3) 122 WRITE (6 ,1000) (PR (J) .J=1.3) 123 WRITE (6 ,1000) (NU(J ) . J=1 .3 ) 124 WRITE (6 .1000) ( S H ( J ) . J = 1 . 3 ) 125 WRITE (6 ,1000) ( H C ( J ) , J = 1 , 3 ) 127 WRITE (6 .1000) ( K Y ( J ) . J = 1 . 3 ) 128 WRITE (6 .1000) (HCKY(J) . J=1 .3) 129 WRITE (6 ,1000) ( A S ( J ) . J = 1 . 3 ) 130 WRITE (6 , 1000) <TWB(J),J=1.3> 131 WRITE (6 ,1000) (DRWB(J) ,J=1.3) 132 1000 FORMAT ( 3 G 1 2 . 5 , / ) 133 STOP 134 END 273 T A B L E C.7: Calculation of Predicted Drying Rates for Horizontally Oriented Wafers (1 Factorial Experiment) Not Including the Effects of Radiation C e l l Number 1 2 3 TG (°K) 423.00 423.00 423.00 LE (m) 0.25400E -01 0.44450E -01 0.63500E -01 RHO (kg/m3) 0.83700 0.83700 0.83700 MIU (kg m/s) 0.23800E -04 0.23800E -04 0.23800E -04 CP (J/kg) 1017.0 1017.0 1017.0 TK (W/m K) 0.35200E -01 0. 35200E -01 0.35200E -01 DAB (m 2/s) 0.44900E' -04 0.44900E--04 0.44900E--04 RE 328.28 328.28 328.28 SC 0.63329 0.63329 0.63329 PR 0.68763 0.68763 0.68763 NU 10.632 10.632 10.632 SH 10.347 10.347 10.347 HC (W/m2 K) 11.787 11.787 11.787 KY (kg/m 2 s) 0.11604E- 01 0.11604E- 01 0.11604E- 01 HCKY (J/kg K) 1015.8 1015.8 1015.8 AS (J/kg) 0.23O8OE+O7 0.23O8OE+O7 0.23O80E+O7 TWB (°C) 42.539 42.539 42.539 DRWB (g/m2 s) 0.54882 0.54882 0.54882 274 1 c 2 C Calculat ions of predicted drying rates for hor izonta l ly oriented wafers 3 C (1 X 3 fac to r ia l experiment) with the radiant heat transfer from the 4 C glass pipe to the wafer included in the ca lcu la t ions of wet bulb 5 C temperatures. 6 C 7 REAL RE(3),PR(3),SC(3).SH(3),NU(3),HC(3),KY(3),TWB(3).HCKY(3) 8 REAL LHS.MFCB11.MFCB21,MFCBM1.KY1.HCKY1.DRWB(3).A(3.4.5).X(4) 9 REAL AREA(3) ,F12(3) .F1K3) .F2H3) 10 REAL RH0(3).MIU(3).CP(3).TK(3).LE(3),0AB(3).TG(3),AS(3).HR(3) 11 C 12 C Data input for the nine sets of condi t ions . Properties of a i r 13 C obtained from Holman (1981), except air-water d i f f u s i v i t i e s which 14 C were calculated using the Wilke-Lee modif icat ion of Hirschfe lder-15 C Bird-Spotz method (Treybal,1980). 16 C 17 DATA RHO/.837..837,.837/ 18 DATA MIU/2.38E-05,2.38E-05,2.38E-O5/ 19 DATA CP/1017.,1017..1017./ 20 DATA TK/.0352..0352..0352/ 21 DATA LE/.0254,.04445,.0635/ 22 DATA TG/423. ,423. ,423. / 23 DATA DAB/4.49E-05,4.49E-05,4.49E-05/ 24 DATA AREA/1.685E-03,2.92E-03,4.15E-03/ 24.2 C 24.4 C Shape factors for rad ia t ive heat transfer ca lcu la t ions (see 24.6 C Appendix I-A). 24.8 C 25 DATA F12/.01059,.01854,.02648/ 26 DATA F11/.9894..9815,.9735/ 27 DATA F21/.9170,.9264,.9309/ 36 PT=1.0133E05 37 PA=1543. 38 C 39 C Calculat ion of Dimensionless Numbers that character ize the drying 40 C system. Nusselt and Sherwood Numbers cor re la t ion for a submerged 41 C f l a t plate obtained from B i r d , Stewart and Lightfoot (1960). 42 C 4 3 DO 40 1=1.3 44 SC(I)=MIU(I)/(RHO(I)'DAB(D) 45 PR(I)=(CP(I)*MIU(I))/TK(I) 46 RE(I)=(RHO(I)'0.294*0.03175)/MIU(I) 47 NU(I)=0.664'(RE(I )"0.500) ' (PR(I )"0.33) 48 SH(I )=0.664*(RE(I )"0.500) ' (SC(I )"0.33) 49 HC(I)=NU(I)*TK(I)/0.03175 50 C 51 C I terat ive so lu t ion of surface temperatures and drying rates. 52 C 53 ST1=293.0 54 DO 20 J=1.4000 55 STPS1 = ( (ST1-273.)*9. /5 . ) + 32. 56 C 57 C Correlat ion of vapour pressure with temperature (Rosen,1980) used 58 C to determine the water vapour pressure at the saturated wafer 59 C surface and thus the saturated absolute humidity at the wafer 60 C surface (Treyba1.1980) 61 C 62 PS1 = ( 1.236E07 ' E X P ( - 9160./(STPS1+4 59.6))) '6894 . 7 275 63 MFCB11=(PT-PS1)/PT 64 MFCB21=(PT-PA)/PT 65 DEN0M=MFC821/MFCB11 66 MFCBM1=(MFCB21-MFCB11)/ALOG(DENOM) 67 YS1=(0.622*PS1)/(PT-PS1) 68 C 69 C Correlat ion of latent heat of vaporizat ion with temperature 70 C (Stanish and Kayihan,1984). 71 C 72 AS1=2.70E06-(160.*ST1)-(3.43*(ST1**2.0)) 73 C 74 C Calculat ion of mass transfer coe f f i c ien t and psychrometric ra t io 75 C (Treybal.1980) 76 C 77 KY1=28.97*MFCBM1'SH(I)*PT*DAB(I)/(8314'TG(I)"0.03175) 78 HCKY1=HC(I)/KY1 79 C 80 C Calculat ion of rad ia t i ve heat transfer coef f ic ient (see Appendix 81 C I-A). 82 C 83 E1=0.93/(1.-0.93) 84 £ 2 = 0 . 9 3 / ( 1 . - 0 . 9 3 ) 85 T1=5.729E-08'(TG(I)'*4) 86 T2=5.729E-08*(ST1"4) 87 P1=E2*T2*(E1 + 1.-F11 (I))+F21(I)*E1*T1 88 P2=P1/((E1 + 1.-F11(1))*(E2+1)-(F 12(1)*F21(1))) 89 P3=-AREA(I)*E2*(T2-P2) 90 HR(I)=P3/(AREA(I)MTG(I)-ST1) ) 91 C 92 C I terat ive equations for determining the wafer surface temperature 93 C (Treybal,1980) . 94 C 95 LHS=(TG(I)-ST1)+(HR(I)*(TG(I)-ST1))/HC(I) 96 RHS=(AS1*(YS1-0.00962))/HCKY1 97 IF (ABS((LHS-RHS)/LHS).LE.0.001) GO TO 30 98 ST1=ST1+0.01 99 20 CONTINUE 100 C 101 C Transferral of desired values from temporary variables to arrays 102 C dimensioned to the number of c e l l s . 103 C 104 30 TWB(I)=ST1-273. 105 KY(I)=KY1 106 HCKY(I)=HCKY1 107 AS(I)=AS1 108 C 109 C Calculat ion of the predicted i n i t i a l wafer drying rate . 1 10 C 111 DRWB(I) = (((HC(I)+HR(I))'(TG(I)- ST 1))/AS(I))* 1000. 112 40 CONTINUE 113 C 114 C Pr int ing of key var iables describing wafer drying for each o f 115 C the eel Is. 116 C 117 WRITE (6.1000) (TG(J).J=1.3) 118 WRITE (6,1000) (LE(J),J=1,3) 119 WRITE (6,1000) (RHO(J),J=1,3) 120 WRITE (6.1000) (MIU(J).J=1.3) 276 121 WRITE 122 WRITE 123 WRITE 124 WRITE 125 WRITE 126 WRITE 127 WRITE 128 WRITE 129 WRITE 130 WRITE 131 WRITE 132 WRITE 133 WRITE 134 WRITE 135 WRITE 136 1000 FORMA" 137 STOP 138 END (6.1000) ( C P ( J ) . J = 1 . 3 ) (6 .1000) ( T K ( J ) , J = 1 . 3 ) (6 ,1000) ( D A B ( J ) , J = 1 , 3 ) (6 ,1000) (RE(J ) .J=1 ,3 ) (6 ,1000) ( S C ( J ) , J = 1 , 3 ) (6 ,1000) ( P R ( J ) . J = 1 , 3 ) (6 ,1000) ( N U ( J ) , J = 1 , 3 ) (6 ,1000) ( S H ( J ) . J = 1 , 3 ) (6 ,1000) ( H C ( J ) , J = 1 , 3 ) (6 ,1000) ( H R ( J ) . J = 1 , 3 ) (6 ,1000) ( K Y ( J ) . J = 1 , 3 ) (6 ,1000) ( H C K Y ( J ) . J = 1 , 3 ) (6 ,1000) ( A S ( J ) , J = 1 , 3 ) (6 .1000) (TWB(J) ,J=1 .3 ) (6 ,1000) (DRWB(J) ,J=1,3) ( 3 G 1 2 . 5 , / ) 277 T A B L E C.8: Calculation of Predicted Drying Rates for Horizontally Oriented Wafers (1x3 Factorial Experiment) Including the Effects of Radiation TG (°K) LE (m) RHO (kg/m3) MIU (kg m/s) CP (J/kg) TK (W/m K) DAB (m 2/s) RE SC PR NU SH HC (W/m2 K) HR (W/m2 K) KY (kg/m 2 s) HCKY (J/kg 'K) AS (J/kg) TWB (°C) DRWB (g/m2 s) 1 423.00 0.25400E-01 0.83700 0.23800E-04 1017.0 0.35200E-01 0.44900E-04 328.28 0.63329 0:68763 10.632 10.347 11.787 9.8676 0.11319E-01 1041.4 0.22675E+07 51.230 0.93499 e l l Number 2 423.00 0.44450E-01 0.83700 0.23800E-04 1017.0 0.35200E-01 0.44900E-04 328.28 0.63329 0.68763 10.632 10.347 11.787 10.027 0. 11314E-01 1041.8 O.22873E+07 51 .338 0.94096 3 423.00 0.63500E-01 0.83700 0.23800E-04 1017.0 0.35200E-01 0.44900E-04 328.28 0.63329 0.68763 10.632 10.347 11 .787 10.100 0.11312E-01 1042.0 0.22872E+07 51.387 0.94370 278 Appendix D Predicting Wafer Circulation Rates Rios et al. ( 1 9 8 6 ) observed that at U — Umf = 0 . 2 2 8 m/s the density and diameter of a sphere circulating in a fluidized bed of 5 5 0 fim glass beads did not affect its upwards and downwards velocities (sphere properties and velocities are presented in Table D.l). Furthermore, the downward sphere velocity had the same magnitude as the measured downward emulsion velocity, and the upward sphere velocity was only slightly higher than the measured upward emulsion velocity. From the experimental values for sphere velocity (presented in Table D.l) and an average bed height of 0 . 1 8 m (from the wafer circulation in sand experiments), the time required for a sphere to circulate down to the distributor plate and back to the bed surface was calculated to be 2 . 4 s. Since this value agreed reasonably well with the times between appearances of the wafer at the bed surface presented in Table 2 . 4 , it was decided to use the data of Rios et al. ( 1 9 8 6 ) to evaluate the model of Nienow et al. ( 1 9 7 8 ) for large object movement in a fluidized bed of particulate solids. The model consisted of the following equations: E / U - O B J E C T = 0 . 0 3 1 6 • k(U - Umf) 0.5 (D.l) where t7u_0BJECT is the upward velocity of a large object in a fluidized bed of solids (m/s) k is the average of two constants used in the curve-fit, ki and k2 h = - 8 . 7 5 x 1 0 ~ 4 • pL + 2 . 9 8 (D.2) 2 7 9 T A B L E D . l : Predicted and Observed Velocities of the Emulsion Phase and for a Large Sphere Circulating in a Fluidized Bed of 0.550 mm Glass Ballotini