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Back-mixing in liquid-liquid extraction spray columns 1967

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The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of JEFFREY ERNEST HENTON B.Sc, U n i v e r s i t y of Leeds, 1964 MONDAY, OCTOBER 2, 1967, AT 3:30 P.M. IN ROOM 207 CHEMICAL ENGINEERING BUILDING COMMITTEE IN CHARGE Chairman: B. N. Moyls Dr. K.L. Pihder Dr. N. Epstein Dr. J.S.. Forsyth . Dr. E. Peters Dr. R.M.R. Branion Dr. A. M i t c h e l l External Examiner: T. Vermeulen Professor, Department of Chemical Engineering U n i v e r s i t y of C a l i f o r n i a , Berkeley, C a l i f o r n i a , U.S.A. .Research Supervisor: S..D. Cavers BACKMIXING IN LIQUID-LIQUID EXTRACTION SPRAY COLUMNS ABSTRACT Backmixing of the continuous phase was studied i n l i q u i d - l i q u i d spray columns of various geometries, for various flowrates of the two phases, and for various drop size d i s t r i b u t i o n s . The dispersion or eddy d i f f u s i o n model was used to characterize the a x i a l mixing of the continuous phase, from a d i s t r i b u t o r of sodium chloride tracer (soluble i n the continuous phase only)„ The steady state form of the model was u t i l i z e d to c a l c u l a t e a x i a l eddy d i f f u s i v i t i e s from these r e s u l t s . The tracer studies showed that the a x i a l eddy d i f f u s i v i t y i s independent of the continuous phase flowrate and the column height. A x i a l eddy d i f f u s i - 2 2 v i t i e s between 7-ft. /hr. and 31-ft. /hr. were obtained in a 1%-in. I. D. column. Low dispersed phase flow- rates and large drop sizes r e s u l t e d i n high a x i a l eddy d i f f u s i v i t i e s . Increasing the column diameter to 3-in. resulted i n s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s between 6.3 and 17.3 times larger. The hold-up of dispersed phase was measured by means of a piston sampler. The hold-up increases approximately l i n e a r l y with increasing dispersed phase s u p e r f i c i a l v e l o c i t y and tends to be s l i g h t l y higher for increased continuous phase s u p e r f i c i a l v e l o c i t i e s . A smaller drop size r e s u l t e d i n an increased hold-up. Drop siz e d i s t r i b u t i o n s were measured.. They always show two peaks, one at 0.02-in. diameter, and the other at a much larger s i z e , the actual . value of which depends on the nozzle t i p diameter used to disperse the drops. The mixing cell-packed bed analogy was used to predict Peclet numbers i n a spray column. The , agreement between these and measured Peclet numbers i s good for drops of about 0.15-in. equivalent diameter but becomes progressively worse as the drop m s i z e i s reduced. AWARDS 1964-1967 Commonwealth Scholarship 1966-1967 Finning Tractor Graduate Scholarship GRADUATE STUDIES F i e l d of Study: Chemical Engineering Related Studies Mass Transfer S.D. Cavers S t a t i s t i c s D.A. Ratkowsky F l u i d and P a r t i c l e Dynamics R„M„R. Branion Linear Algebra Wm.R. Simons Other Studies Mass and Heat Transfer Analogies N. Epstein Surface E f f e c t s J. Leja Optimization K..L. Pinder Computer Programming K. Teng BACK-MIXING IN LIQUID-LIQUID EXTRACTION SPRAY COLUMNS by JEFFREY ERNEST HENTON B. Sc., U n i v e r s i t y of Leeds, 196V A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1 9 6 7 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives„ I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f C//<£TA7 / £ / 3 ^ £~/^<r / A/£~"<~~ f l / / ^ ^ ~ T h e " U n i v e r s i t y of " B r i t i s h Columbia Vancouver 8S Canada Date 2 (9scs&&u- 176 7 i A B S T R A C T B a c k m i x i n g o f t h e c o n t i n u o u s p h a s e w a s s t u d i e d i n l i q u i d - l i q u i d s p r a y c o l u m n s o f v a r i o u s g e o m e t r i e s , f o r v a r i o u s f l o w r a t e s o f t h e t w o p h a s e s , a n d f o r v a r i o u s d r o p s i z e d i s t r i b u t i o n s . T h e d i s p e r s i o n o r e d d y d i f f u s i o n m o d e l w a s u s e d t o c h a r a c t e r i z e t h e a x i a l m i x i n g o f t h e c o n t i n u o u s p h a s e . A x i a l c o n c e n t r a t i o n p r o f i l e s w e r e m e a s u r e d u p s t r e a m , w i t h r e s p e c t t o t h e c o n t i n u o u s p h a s e , f r o m a d i s t r i b u t o r o f s o d i u m c h l o r i d e t r a c e r ( s o l u b l e i n t h e c o n t i n u o u s p h a s e o n l y ) . T h e s t e a d y s t a t e f o r m o f t h e m o d e l w a s u t i l i z e d t o c a l c u l a t e a x i a l e d d y d i f f u s i v i t i e s f r o m t h e s e r e s u l t s . T h e t r a c e r s t u d i e s s h o w e d t h a t t h e a x i a l e d d y d i f f u s i v i t y i s i n d e p e n d e n t o f t h e c o n t i n u o u s p h a s e f l o w r a t e a n d t h e c o l u m n h e i g h t . A x i a l e d d y d i f f u s i v i t i e s b e t w e e n 7 - f t . / h r . a n d 3 1 - f t . / h r . w e r e o b t a i n e d i n a 1 ^ - i n . 1. D . c o l u m n . L o w d i s p e r s e d p h a s e f l o w r a t e s a n d l a r g e d r o p s i z e s r e s u l t e d i n h i g h a x i a l e d d y d i f f u s i v i t i e s . I n c r e a s i n g t h e c o l u m n d i a m e t e r t o 3-i&» r e s u l t e d i n s u p e r f i c i a l a x i a l e d d y d i f f u s i v i t i e s b e t w e e n 6.3 a n d 17 .3 t i m e s l a r g e r . T h e h o l d - u p o f d i s p e r s e d p h a s e w a s m e a s u r e d b y m e a n s o f a p i s t o n s a m p l e r . T h e h o l d - u p i n c r e a s e s a p p r o x i m a t e l y l i n e a r l y w i t h i n c r e a s i n g d i s p e r s e d p h a s e S u p e r f i c i a l v e l o c i t y a n d t e n d s t o b e s l i g h t l y h i g h e r f o r i n c r e a s e d c o n t i n u o u s p h a s e S u p e r f i c i a l v e l o c i t i e s . A s m a l l e r d r o p s i z e r e s u l t e d i n a n i n c r e a s e d h o l d - u p . i i Drop s i z e d i s t r i b u t i o n s were measured. They always show two.peaks, one a t 0 . 0 2 - i n . diameter, and the other a t a much l a r g e r s i z e , the a c t u a l value of which depends on the nozzle t i p diameter used to d i s p e r s e the drops. • The mixing c e l l - p a c k e d bed analogy was used to p r e d i c t P e c l e t numbers i n a spray column. The agreement between these and measured P e c l e t numbers i s good f o r drops of about 0 . 1 5 - i n . e q u i v a l e n t diameter but becomes p r o g r e s s i v e l y worse as the drop s i z e i s reduced. i i i TABLE OF CONTENTS INTRODUCTION - Previous work ! - Mathematical models j_o, - Object of t h i s work , 27 THEORY - A p p l i c a t i o n of the d i s p e r s i o n model t o runs w i t h no mass t r a n s f e r 30 - A p p l i c a t i o n of the d i s p e r s i o n model t o l i q u i d - l i q u i d e x t r a c t i o n 32 APPARATUS. ... - 36 EXPERIMENTAL PROCEDURE : - Column-operation 60 f Sampling technique s t u d i e s w i t h mass t r a n s f e r . 61 - Search f o r a s u i t a b l e t r a c e r 67 - Sampling technique s t u d i e s w i t h no mass t r a n s f e r . 69 - A x i a l eddy d i f f u s i v i t y and di s p e r s e d phase hold-up.... t 70 - Concentration p r o f i l e s w i t h mass t r a n s f e r 84 RESULTS AND DISCUSSION - R e s u l t s of sampling technique s t u d i e s 86 - D i s c u s s i o n of sampling technique s t u d i e s cjx i v - A x i a l eddy d i f f u s i v i t y , drop s i z e d i s t r i b u t i o n , and di s p e r s e d phase hold-up s t u d i e s i n the l-g--in. I . D. column 10^ - A x i a l eddy d i f f u s i v i t y and drop s i z e d i s t r i b u t i o n s t u d i e s i n the 3-in. I. D. column 1J+3 - V i s u a l observations of the motion of the drops 150 - Concentration p r o f i l e s w i t h mass t r a n s f e r 15X CONCLUSIONS. 16U NOMENCLATURE. , 168 LITERATURE CITED ^ 3 APPENDICES I DISPERSION MODEL THEORY. ^ I I MIXING CELL - PACKED BED ANALOGY and SPRAY COLUMN - PACKED BED ANALOGY ^ 9 I I I ANALYSIS OF PISTON SAMPLE RESULTS TO PRODUCE THE AVERAGE CONTINUOUS PHASE CONCENTRATION, EXCLUDING THE CONTRIBUTION FROM WAKES, IN THE PISTON SAMPLE AT THE TIME OF SAMPLING.. , 197 IV TABULATED RESULTS. 203 V DETAILS OF THE APPARATUS 230 VI DIMENSIONS OF THE GLASS PORTIONS IN THE COLUMN TEST SECTIONS AND MEASUREMENT OF PURGE TIMES 256 V LIST OF TABLES 1. Key to Figure 9 . 38 2. Key to Figure 21 , 3. Sampling Studies with Hook and Bell-Probes and Piston.......... k. Sampling Studies with Hook and Bell-Probes, Hypodermic Needles, and Piston ^2 5. Sampling Technique Studies with No Mass Transfer..... 94 6. Time to Reach Steady State in the l§--in. I. D. Column under Conditions of no Mass Transfer 135 7. • Effect of Tracer Feed 'Rate on Reduced Concentration Profiles and Axial Eddy Diffusivity in the l i - i n . I. D. Column 136 8. Reproducibility of Results, for Axial Eddy Diffusivity in the l | - i n . I, D. Column 137 9. Cross-Sectional Homogeneity in the 1-g-in. I. D. Column 139 10. Effect of Sampling Rate on the Reduced Concentration Profile in the 1^-in. I. D. Column 2.I+0 11. Effect of Order of Sampling on the Measured Concen- tration Profile i n the l-g--in. I. D. Column l i + 2 12. Effect of Column Height on the Measured Concen- tration Profile and Axial Eddy Diffusivity in the 1^-in. I. D. Column... vi 13. Steady State Times for the 3-in. I. D. Column 1̂ 7 Reproducibility of Results for the 3-in. I. D. Column... lk8 15. Cross-Sectional Homogeneity in the 3-in. I. D. Column........... , 1̂ 9 16. Comparison of Axial Eddy Diffusivity by Mass Transfer Studies and Tracer Studies , 156 IV-1. Data Sheet 20k IV-2. Calculation of Quantities used for the Calculation of E. .... 207 IV-3. Typical Computer Results 213 IV-k. Axial Eddy Diffusivity Results for the 1^-in. I. D« Column.............. 21^ IV-5. Superficial Axial Eddy Diffusivity Results for the 3-in. I. D. Column.... .. 219 IV-6. Typical Drop Size Distribution Results 221 IV-7. Drop Size Distributions in the l^--in. I. D. Column.. 222 IV-8. Drop Size Distributions in the 3-in. I. D. Column... 22^ IV-9. Concentration Studies with Mass Transfer in the 1^-in. I. D. Column. 225 IV-10.The Relation Between.E and & 226 IV-ll.Calculated Values of E for Various Values of K^a and J... 227 v i i IV - 1 2 . C a l c u l a t e d Values of E f o r Various Values of m 228 IV - 1 3 . E q u i l i b r i u m Data f o r A c e t i c A c i d D i s t r i b u t e d Between MIBK-Saturated Water and Water-Saturated MIBK a t 70°F.. 229 VI - 1 . Dimensions of the Glass P o r t i o n s i n the Column Test Sections 256 1 v i i i LIST OF FIGURES 1. Schematic Diagram of a Spray Column..... 2 2. Solute Concentration Profile in a Spray Column...... 5 3. Mass Balance Over a Section of a Spray Column 6 h. Continuous Phase Recirculation 7 5. Hook and Bell-Probes 12 6. Concentration Profiles in a Spray Column lh 7. Concentration Profiles in a Spray Column 15 8. Piston Sampler. 17 9. Schematic Flow Diagram for the l§--in. I. D. Column.. 37 10. 1^-in. I. D. Column hi 11. Short 1^-in.I. D. Column , 43 12. Long 1-g-in. I. D, Column.. ,.. 44 13. .1^-in. I. D- Column for Comparing Hook and Bell- Probes and Piston Sampler Results ^ lh. l|:-in. I. D. Column for Comparing Hypodermic Needle, Hook and Bell-Probes; and Piston Sampler Results.... 15. Nozzle Tip Patterns. J. D. = 0.126-in. (l^-in. I. D. Column) hQ 16. Nozzle Tip Patterns. I. D. = 0.103-in. (l-|-in. I. D, Column). 49 ix 17. Nozzle Tip Patterns. I. D. = 0.086-in. ( l ^ - i n . I. D. Column) 50 18. Nozzle Tip Patterns. I. D. = 0.053-in. ( l | - i n . I. D. Column) 19. Photographic Conditions , 53 20. I. D. Column.......... cu 21. Schematic Flow Diagram for the 3-in. I. D. Column 55 22. Nozzle Tip Patterns. I. D. = 0,102-in. (3-in. I. D. Column) 58 23. Optical Distortion Investigation, 1^-in. I. D. Column 75 2k. Optical Distortion Investigation, 3-in. I. D. Column • • •«• 8 l 25. Sampling Technique'Studies with Hook and Bell-Probes and Piston... 90 26. Sampling Technique Studies with Hook and Bell-Probes, Hypodermic Needles and Piston 93 27. Sampling Technique Studies with no Mass Transfer 95 28. Reduced Concentration Profiles..... 108 29. Axial Eddy Diffusivity in the l | - i n . I. D.. Column HO 30. Comparison of Axial Eddy Diffusivity as Determined in this Work with That of Other Workers. 112 30a. Comparison of Dispersion Number i n This Work with That for Packed Beds ; 113 X 31. . Predicted and Calculated Peclet Numbers, d = 0.155-ln H 5 P 3 2 . Predicted and Calculated Peclet Numbers, d = 0 . 1 3 5 - i a 1 1 6 p 3 3 • Predicted and Calculated Peclet Numbers, d p = 0 . 1 2 5 - i n 1 1 7 3 4 . Predicted and Calculated Peclet Numbers, d = 0 . 0 9 5 - i n 1 1 8 P 3 5 - Percentage Error in the Equivalent Diameter due to Optical Distortion in the 1^-in. I. D. Column 1 2 1 3 6 . Drop Size Distribution for Fun 5 0 , Average Nozzle Tip Diameter = Q .103-in.... 1 2 5 3 7 . Photographs at Operating Conditions Corresponding to Runs Indicated. Magnification Factor = 3 • • • • 3-27 3 8 . Drop Size Distribution for Run 1 3 0 , Average Nozzle Tip Diameter = 0 . 1 2 6 - i n 1 2 8 3 9 . Distribution of Totai Percent of Volume of Drops for Run 5 0 , Average Nozzle Tip Diameter = 0 . 1 0 3 - i n . . 1 2 9 kO. Dispersed Phase Hold-up, d = 0 . 1 5 5 - i n 1 3 0 P kl. Dispersed Phase Hold-up, d = 0 . 1 3 5 - i n 1 3 1 P k2. Dispersed Phase Hold-up, d p = 0 . 1 2 5 - i n 1 3 2 U 3 . Dispersed Phase Hold-up, d = 0 . 0 9 5 - i n 1 3 3 kk. Superficial Axial Eddy Diffusivity in the 3-in. I . D. Column lbk 4 5 . Percentage Error in the Equivalent Diameter due to Optical Distortion in the 3-in. I. D. Column 1^6 x i h6. Equilibrium Curve f o r A c e t i c A c i d D i s t r i b u t e d Between MIBK- Saturated Water and Water-Saturated MIBK at 70°F 153 p V7. Minimizing f o r Run J I , 158 1+8. The E f f e c t on E of Varying the Methpd of Flux C a l c u l a t i o n and of Varying K^a f o r Run J I 159 49. The E f f e c t on E of Vari a t i o n s i n m f o r Run J I 160 50. Measured and F i t t e d Concentration P r o f i l e s f o r R u n J l . . , ... 2.61 1-1. Solute Mass Balance i n the Continuous Phase .. igfo. I I I - l . Lower Portion of a Spray Column 201 I I I - 2 . The E f f e c t of Time on a Pis t o n Sample 202 V - l . P i s t o n Sample C o l l e c t i o n Flask f o r Large Hold-ups.... 233 V - 2 . Hypodermic Needle I n s t a l l e d f o r Sampling 234 V - 3 . Sampling Valve f o r Hypodermic Needle 235 V-U. Tracer I n j e c t i o n System... 236 V-5. Tracer D i s t r i b u t o r . . . . 237 V-6. 0.126-in. I.D. Nozzle Tips, Nozzle T i p Support P l a t e , and Nozzle T ip Caps.......... 238 V-7. 0.086-in. I.D. Nozzle Tips, Nozzle T i p Support P l a t e , and Nozzle T i p Plugs 239 V-8. . 0.053-in. I.D. Nozzle Tips, Nozzle T ip Support Plate and Nozzle T i p Plugs...., 2k0 V'9« Perspex Box f o r the 1^-in. I.Dr Column Photographs... 2U1 x i i V-10. L i g h t S h i e l d f o r the l§-in. I . D. Column Photographs. 242 V - l l . Lower end of the 3 - i n . I . D. Column 243 V-12. S p e c i a l Pyrex Reducer f o r the 3-in. I . D. Column 244 V-13. Nozzle S h e l l f o r the 3-in. I . D. Column 24-5 V-l4. Nozzle T i p s , Nozzle T i p Support P l a t e , and Nozzle T i p Plugs f o r the 3-in. I . D. Column 246 V-15- Flow S t r a i g h t e n e r f o r the 3-in. I . D. Column Nozzle.. 2 47 V - l 6 . Nozzle Securing P l a t e and R e t a i n i n g Nut f o r the 3 - i n . I . D. Column , , 2U8 V-17. End P l a t e f o r the Bottom of the 3-in. I . D. Column... 249 V-18. E l g i n Head f o r the 3-in. I . D. Column • 250 V-19. Upper End P l a t e f o r the E l g i n Head of the 3-in. I . D, Column ,. 251 V-20. Lower End P l a t e f o r the E l g i n Head of the 3-in. I . D. Column.. 252 V-21. Lower End P l a t e Packing f o r the E l g i n Head of the 3 - i h . I . D. Column 253 V-22. Perspex Box f o r the 3-in. I . D. Column Photographs... 254 V-23. Flange f o r the Photographic S e c t i o n of the 3-in. I . D. Column. .' 255 " A x i i i ACKNOWLEDGEMENTS The author would l i k e to express h i s s i n c e r e g r a t i t u d e t o Dr. S. D. Cavers f o r h i s a s s i s t a n c e , encouragement, and h e l p f u l c r i t i c i s m s o f f e r e d throughout the course of t h i s p r o j e c t . Thanks are extended to a l l members o f the f a c u l t y and s t a f f of the Department of Chemical Engineering, The U n i v e r s i t y of B r i t i s h Columbia f o r t h e i r readiness and w i l l i n g n e s s i n d i s c u s s i n g both theoret- i c a l and p r a c t i c a l problems a s s o c i a t e d w i t h the work. P a r t i c u l a r a p p r e c i a t i o n i s o f f e r e d to Dr. K. L. P l n d e r . f o r the loan of a telephoto lens and t o Mr. R. Brandt f o r making most of the machined parts e s s e n t i a l f o r t h i s study.. The author i s indebted to Dr. Duncan of the B r i t i s h Columbia Research C o u n c i l f o r h i s suggesting the use of sodium c h l o r i d e as a t r a c e r and f o r p r o v i d i n g the use of the atomic abs o r p t i o n spectrophoto- meter. F i n a n c i a l support was most g r a t e f u l l y r e c e i v e d i n the form of sch o l a r s h i p s from the Commonwealth Sch o l a r s h i p and F e l l o w s h i p Committee of the E x t e r n a l A i d O f f i c e , Ottawa, and, from the F i n n i n g T r a c t o r Company, Lt d . Funds for' the equipment were provided by the N a t i o n a l Research C o u n c i l . 1 I INTRODUCTION 1. PREVIOUS WORK Liquid.-liquid e x t r a c t i o n i s used widely f o r separating components which are more d i f f i c u l t or expensive to separate by other methods such as d i s t i l l a t i o n , evaporation, or p r e c i p i t a t i o n . E x t r a c t i o n processes u s u a l l y are preferred i f the two components to be separated have s i m i l a r b o i l i n g points, or i f one of the components i s heat' s e n s i t i v e or present i n small amounts. Countercurrent extraction i n v e r t i c a l towers can be c a r r i e d out when the r a f f i n a t e and extract phases d i f f e r appreciably i n density. Although sieve-plate, bubble cap, and packed towers are more commonly found i n i n d u s t r i a l use "...the spray tower i s the more a t t r a c t i v e f o r experimentation because of i t s inherent s i m p l i c i t y , and a l s o because of the greater possible range of flowrates of the two (phases)..." ( l ) Figure 1 shows diagrammatically how each phase i s introduced i n t o and removed from a spray tower. In the system- shown the l e s s dense phase i s dispersed through nozzle t i p s located at the lower end of the column. The dispersed phase drops r i s e through the descending continuous phase and coalesce at the i n t e r f a c e at the upper end of the column. Many workers have studied spray column operation. The knowledge gained i n the main represents an accumulation of small contributions. 2 CONTINOUS PHASE INLET . • • * •••* * • • • • _ • . ••• •• • .«. ••••. •• - • • • * • •••••• . • • . • • • • • : . . . . ;.. . • .DISPERSED PHASE OUTLET INTERFACE CONTINUOUS ^ PHASE OUTLET DISPERSED PHASE NOZZLE TIPS DISPERSED PHASE INLET FIGURE 1. SCHEMATIC DIAGRAM OF A SPRAY COLUMN 3 The designs of the continuous phase i n l e t and d i s p e r s e d phase o u t l e t used I n the present study were f i r s t proposed by Blanding and E l g i n (2) . Optimum nozzle t i p diameters and dispersed phase f l o w r a t e s i n the nozzle t i p s f o r r e p r o d u c i b l e , more or l e s s uniform drop s i z e have been suggested by Johnson and B l i s s (3) and l a t e r by others (U,5 ,6 ,7 ,8) . From about the e a r l y 1930's workers began to perform l a b o r a t o r y s c a l e experiments i n attempts to d i s c o v e r simple laws or t o formulate c o r r e l a t i o n s which a p p l i e d t o spray tower operation (2,3,9,10,11,12,13)• T h e i r r e s u l t s i n d i c a t e t h a t the extent of e x t r a c t i o n i s dependent upon the f l o w r a t e s of the two phases, the d i r e c t i o n of s o l u t e t r a n s f e r (x.e. from d i s p e r s e d phase to continuous phase or v i c e v e r s a ) , which phase'7 i s d i s p e r s e d , drop s i z e , column dimensions, and sometimes upon i n l e t s o l u t e c o n c e n t r a t i o n s . A l l these workers analysed only the column i n l e t and o u t l e t s o l u t e concentrations of each phase. L i c h t and Conway in 1 9 5 0 pointed out that the mass t r a n s f e r process should be considered as t a k i n g place i n three separate stages - i ) drop formation, i i ) drop r i s e , and i i i ) drop coalescence. Geankoplis and Hixson ( l ) , a l s o i n 1950, r e v o l u t i o n i z e d techniques i n spray column experimentation by t a k i n g samples of the continuous phase from w i t h i n an opera t i n g column. This was accomplished by lowering a hook-shaped sampling probe, (as shown i n the sketch below) i n t o the column and then a p p l y i n g a s l i g h t vacuum to the upper end of the probe. Continuous phase/was drawn i n t o the probe without e n t r a i n i n g any d i s p e r s e d phase. y They observed t h a t the b a s i c f l o w p a t t e r n w i t h i n the column d i d not appear to be a f f e c t e d by the probe. I n 1951 Geankoplis, Wells and Hawk (15) extended Geankoplis and Hixson's work, again u s i n g an i n t e r n a l sampling probe, to measure the s o l u t e c o n c e n t r a t i o n p r o f i l e i n the continuous phase. A t y p i c a l experimental s o l u t e c o n c e n t r a t i o n p r o f i l e i n the continuous phase i s shown i n F i g u r e 2. Geankoplis and co-workers n o t i c e d a sharp change, or e n d - e f f e c t , i n s o l u t e c o n c e n t r a t i o n i n the continuous phase a t the i n t e r f a c e . They thought " . . . t h a t the l o c a t i o n of the end e f f e c t a t the continuous phase i n l e t may be caused by the inherent turbulence e f f e c t of coalescence of bubbles a t the i n t e r f a c e . . . " (.15)- They made an allowance f o r t h i s end e f f e c t by c a l c u l a t i n g a f i c t i t i o u s height of column i n which there would c :occur the same amount of mass t r a n s f e r as appeared to occur a t the i n t e r f a c e . To c a l c u l a t e s o l u t e concentrations i n the di s p e r s e d phase a t va r i o u s e l e v a t i o n s i n the column the use of mass balances was attempted. On the b a s i s t h a t the s u p e r f i c i a l f l o w r a t e s of both phases 5 LU I to 2 < O X § a cc tn o z i s o LU h-D _ J O co DISTANCE FROM T H E T O P OF THE C O L U M N INTERFACE N O Z Z L E TIPS FIGURE 2- SOLUTE CONCENTRATION PROFILE IN A SPRAY COLUMN. are not a f f e c t e d by s o l u t e c o n c e n t r a t i o n changes experienced i n the column, a m a t e r i a l balance on s o l u t e around the c o n t r o l zone shown i n Figure 3 r e s u l t e d i n the f o l l o w i n g equation. Thus D + LC°C ~ LC CC + LD CD 0 I 0 \ _L 1 CD = L j <CC - ^ + CD 6 . C O N T R O L Z O N E FIGURE 3 . MASS BALANCE OVER A SECTION OF A SPRAY COLUMN. Although some turbulence was observed i n the continuous phase ( l ) -no allowance f o r i t s e f f e c t was i n c l u d e d i n the mass balance. Geankoplis continued h i s work i n v o l v i n g continuous phase sampling w i t h Kreager (l6) and l a t e r w i t h Vogt (17)> M o r e l l o and Poffenberger (l8) were the f i r s t to suggest p o s i t i v e l y t h a t the continuous phase d i d not move through the column i n e f f e c t i v e plug flow, but t h a t there was r e c i r c u l a t i o n w i t h i n t h a t phase. They s a i d t h a t the r e c i r c u l a t i o n , which was l a t e r t o be c a l l e d backmixing, may be caused by thermal c u r r e n t s , d e n s i t y d i f f e r e n c e s or by the f r i c t i o n of the drops c a r r y i n g some of the continuous phase along w i t h them. 7 They portrayed the idea diagrammatically as shown i n Figure k. CONTINUOUS P H A S E IN D ISPERSED P H A S E IN D ISPERSED P H A S E OUT CONTINUOUS P H A S E O U T FIGURE k. CONTINUOUS PHASE RECIRCULATION. I t can be seen t h a t the simple mass balance given i n Equation 1 based on plug f l o w of both phases i s not v a l i d . • '" Although M o r e l l o and Poffenberger ( l 8 ) gave a p h y s i c a l p i c t u r e of backmixing, Newman (19) pointed out th a t the" end-effect which had been observed by e a r l i e r workers could be explained i n terms o f backmixing of the continuous phase. A l s o he presented the f o l l o w i n g argument t o show th a t the s o l u t e c o n c e n t r a t i o n i n the dispersed phase a t some poi n t i n the column cannot be c a l c u l a t e d by a mass balance over short s e c t i o n s of the column.,. Newman accounted f o r backmixing by c o n s i d e r i n g a f l o w of continuous phase countercurrent t o the main f l o w of continuous phase. This backniixing flow was exactly compensated "by an Increased main flow- of continuous phase. I t was assumed that the r e s u l t i n g main flow of continuous phase was r a d i a l l y homogeneous at a given column elevation. The plug flow model and Newman's backmixing model are shown i n the following sketch. (a) PLUG FLOW MODEL (b) BACKMIXING. MODEL For plug flow of both phases, as shown i n (a) of the above sketch, c^ i s given by Equation 2. i ' c^ = L„ (c - c°) + cj" D _C C C D For /backmixing of the continuous phase, as shown i n (b) above, a solute mass balance over the lower section of column y i e l d s L c i + ( L + L ) c = L c + L c ° + L c D D C B C D D C C B B Thus CD = LC ( cC " C C } + 4 + .LB ( CC " C B ) 4 equation t o o b t a i n c^. For the same reason c a p a c i t y c o e f f i c i e n t s and H.T.U. values f o r short s e c t i o n s of column cannot be d e r i v e d from the knowledge of t e r m i n a l c o n d i t i o n s and the s o l u t e c o n c e n t r a t i o n p r o f i l e i n the continuous phase. Campos (20) c a l c u l a t e d the height of tower i n which there would occur the same amount of mass t r a n s f e r as appeared to have produced the end-effect at the continuous phase i n l e t of the column. He noted a l s o t h a t backmixing of the continuous phase may cause end-effects i n spray towers. The e x i s t e n c e of a backmixing stream i n the form of wakes t r a v e l l i n g w i t h the dispersed phase drops has been demonstrated p h o t o g r a p h i c a l l y (21, 22, 23,-24), and L i and Z i e g l e r (25) say "In general the process of backmixing i n spray towers i s b e l i e v e d to be I n i t i a t e d l a r g e l y i n the wakes of d r o p l e t s " . Letan and Kehat (26, 27) have worked w i t h spray column heat exchangers. They e x p l a i n continuous phase backmixing e f f e c t s by means of a model i n which continuous phase i s supposed to be c a r r i e d along i n the form of wakes, w i t h the d i s p e r s e d phase drops. G i e r and Hougen (28) used hypodermic syringes to draw o f f continuous phase samples and b e l l - s h a p e d probes to c o l l e c t d i s p e r s e d phase samples. 1 0 The accompanying sketch shows an example of each sort of probe used by them- Probes of each sort were d i s t r i b u t e d along the length of the column. It =3S A bel l -probe sample contained both dispersed and continuous phases. The- sample was allowed to reach equilibrium*and then each phase was analysed for solute . A simple mass balance on solute i n the b e l l - probe, sample at the times of c o l l e c t i o n and analys is r e s u l t s i n Equation 5- V c + v " c = V c a + V c a D D C C D D C C Therefore In order to ca lculate c^ from Equation 6 an estimate of c^, at the ' e levat ion of the b e l l - p r o b e , was made from a p lot of the concentration of solute i n the hypodermic syringe samples versus column height. i . e . no change i n concentration of^either-phase with time. 11 G i e r and Hougen c a l c u l a t e d values of H.T.U., based on conc e n t r a t i o n d i f f e r e n c e s i n the disp e r s e d phase, by g r a p h i c a l i n t e g r a t i o n u s i n g the measured co n c e n t r a t i o n p r o f i l e s . T h e i r F i g u r e 17 shows the so l u t e -concentration i n the disp e r s e d phase as determined by means of • Equation 6. f o r one of t h e i r runs i n which s o l u t e was t r a n s f e r r e d from the continuous phase to the disp e r s e d phase. These concentrations are greater than those which could be obtained from c a l c u l a t i o n by means of Equation 2 which i s based on plug"flow of both phases. This r e s u l t i s i n agreement w i t h Newman's suggestions (Equation k). As a r e s u l t the. H.T.U. values c a l c u l a t e d by g r a p h i c a l i n t e g r a t i o n were correspondingly lower than those c a l c u l a t e d from the column t e r m i n a l c o n d i t i o n s assuming plug f l o w of both phases. Patton (29) took samples from an ope r a t i n g spray column u s i n g the hypodermic needle and i n v e r t e d f u n n e l technique of G i e r and Hougen. He found a considerable drop i n the continuous phase s o l u t e c o n c e n t r a t i o n a t the i n t e r f a c e which was not matched by a p r o p o r t i o n a l drop i n the so l u t e c o n c e n t r a t i o n i n the dispersed phase. He concluded t h a t the d i s c o n t i n u i t y i n the so l u t e c o n c e n t r a t i o n p r o f i l e i n the continuous phase a t the i n t e r f a c e was due to b u l k mixing of the continuous phase i n the column. A development• of the sampling technique of Geankoplis and coworkers ( l ) and of G i e r and Hougen (28) was used by Ewanchyna and Cavers (30, 3 l ) - They made use of a hook-shaped probe f o r continuous phase sampling and a be l l - s h a p e d probe f o r dispersed phase sampling. The probes were lowered i n t o the op e r a t i n g column a t the ends of s t a i n l e s s s t e e l tubes as shown i n Figure 5* Samples were drawn i n t o the probes and 12 FIGURE 5« HOOK AND BELL-PROBES and along the sample lih.es toy the use of a water a s p i r a t o r . Acetic a c i d was transferred between an aqueous continuous phase and a methyl i s o b u t y l ketone (MIBK) dispersed phase. The aqueous phase was saturated with MIBK and the MIBK phase saturated with water. The "solute concentration p r o f i l e i n each phase was measured at various combinations of phase flowrates. Plots were made showing the dependenc of capacity c o e f f i c i e n t s on flowrates and also of H.T.U. values on flowrates. The causes of end e f f e c t s i n spray columns were explained c l e a r l y and v e r i f i e d experimentally. The measured concentration p r o f i l e s f o r a t y p i c a l run with solute being t r a n s f e r r e d from the continuous aqueous phase to the- dispersed MIBK phase are shown i n Figure 6. The l i n e s FB and GE are the measured concentration p r o f i l e s f o r the dispersed phase and- the continuous phase r e s p e c t i v e l y . I t was assumed that no backmixing took place i n the dispersed phase. This assumption was based on the v i s u a l observation that the drops appeared to r i s e up the column without c i r c u l a t i n g back on t h e i r paths (28, 30, 3 l ) - I f i"t i s assumed i n ad d i t i o n that no backmixing takes place i n the continuous phase then Equation 2, which i s based on plug flow of both phases, can be used to ca l c u l a t e the l i n e GD. When the drops of dispersed phase a r r i v e at the i n t e r f a c e they do not coalesce immediately but remain as part of a drop layer there. Undoubtedly mass tr a n s f e r takes place i n t o these drops during t h e i r sojourn at the i n t e r f a c e . Ewanchyna and Cavers a t t r i b u t e d the concentration jumps BA ( i n the dispersed phase) and CD to t h i s i n t e r f a c e mass t r a n s f e r . Ik z g i — < a: o z o o UJ h- -I o CO CONTINUOUS P H A S E O U T L E T D ISPERSED PHASE INLET" CONTINUOUS C r5 *PRASE u INLET NOZZLE H E I G H T U P C O L U M N D I S P E R S E D P H A S E O U T L E T INTERFACE FIGURE 6. CONCENTRATION PROFILES IN A SPRAY COLUMN. They a t t r i b u t e d the change DE to a x i a l mixing of the continuous phase. The l i n e GH i s the concentration p r o f i l e which would be expected f o r perfect mixing of that phase under conditions such that the solute concentration i n the aqueous stream leaving the column was that given by point G. I t can be seen that the measured aqueous phase solute concentration p r o f i l e (GE) l i e s between that expected f o r perfect mixing (GH) and that f o r true countercurrent flow (GD). Evidently the continuous phase does undergo some a x i a l mixing. 15 • Ewanchyna and Cavers (30, 31) found t h a t the r e s u l t s of runs w i t h s o l u t e t r a n s f e r r e d from the dispersed phase to the continuous phase supported.the above ideas. With s o l u t e t r a n s f e r r e d to the -continuous phase drops coalesce immediately on reaching the i n t e r f a c e (31, 32, 33, 3^)- As a r e s u l t there was n e g l i g i b l e mass t r a n s f e r a t the i n t e r f a c e and hence no jump i n the dispersed phase con c e n t r a t i o n p r o f i l e there. The r e s u l t s of a t y p i c a l run are shown i n Figure 7- FIGURE 7. CONCENTRATION PROFILES IN A SPRAY COLUMN. 16 The whole of the s o l u t e c o n c e n t r a t i o n change (DE) i n the continuous phase a t the i n t e r f a c e was a t t r i b u t e d t o backmixing of the continuous phase i n the column. Choudhury (35) continued Ewanchyna's work. To a l l o w f o r backmixing of the continuous phase i n the d e r i v a t i o n of an expression f o r (H.T.U.) Qverau_ values, based on a l o g a r i t h m i c mean disp e r s e d phase c o n c e n t r a t i o n d r i v i n g f o r c e , he introduced a c o r r e c t i o n f a c t o r , F , as P r a t t (36) had done f o r packed towers. The question was r a i s e d as t o whether the s o l u t e c o n c e n t r a t i o n i n the continuous phase e n t e r i n g the b e l l - p r o b e w i t h the drops was the same as t h a t e n t e r i n g the hook-probe. I t was thought t h a t the b e l l - p r o b e might sample p r e f e r e n t i a l l y continuous phase which was i n the immediate v i c i n i t y o f the drops. J f t h i s continuous phase were not of the same s o l u t e c o n c e n t r a t i o n as t h a t i n the main b u l k of the continuous phase the use i n Equation 6 of c^ from a hook-probe sample i n order t o c a l c u l a t e c^ i n a b e l l - p r o b e sample would be i n v a l i d . I n order t o t e s t the hook and b e l l sampling technique Hawrelak (37) designed and constructed a p i s t o n sampler. A sketch of t h i s device i s shown i n Figure 8. By moving the p i s t o n from one side of the p i s t o n b l o c k t o the other i t was p o s s i b l e to remove a b u l k sample of both phases from the column and a l l o w the column t o continue o p e r a t i n g . With t h i s device Hawrelak (37), and l a t e r Bergeron (38); 17 BELL- PROBE-* COLJM N— PISTON BLOCK PISTON "ESS A , -HOOK-PROBE FIGURE 8. PISTON'SAMPLER. compared solute concentrations i n the dispersed phase calculated using the h e l l and . hook-probes with those calculated from r e s u l t s using the piston sampler and the hook-probe. I t was necessary to assume that the hook-probe sample was representative of the continuous phase i n the column at the sampling height. However, no d e f i n i t e conclusions were drawn, mainly because the column was run under such conditions that the two phases were near equilibrium at the sampling elevation. Rocchini (39, ̂ 0) studied drop shape and measured drop siz e d i s t r i b u t i o n s i n a spray column by examining close-up photographs taken of an operating column. 18 Dispersed phase hold-ups i n spray towers have been c a l c u l a t e d l a r g e l y from Equation 7 (3)- h = 100 u However, Weaver, Lapidus and E l g i n (hi) determined hold-ups by I s o l a t i n g a s e c t i o n of column between two q u i c k - a c t i n g b a l l valves arid measuring the volume of each phase c o l l e c t e d . Hawrelak (37) and Bergeron (38) measured dispersed phase hold-ups, without d i s - r u p t i n g the column op e r a t i o n , w i t h t h e - a i d of a. p i s t o n sampler described e a r l i e r . I t has been found (3, 3 0 , ' 35 > 42) th a t the dispersed phase hold-up increases .only s l i g h t l y w i t h i n c r e a s i n g continuous phase f l o w r a t e and i s n e a r l y l i n e a r l y dependent on the dispersed phase f l o w r a t e . Hayworth and Treybal (h) and Johnson and B l i s s (3) have observed t h a t the len g t h of a j e t of dispersed phase l e a v i n g a nozzle t i p i n c r e a s e s t o a maximum and then decreases as the f l o w r a t e of dispersed phase i n c r e a s e s . They n o t i c e d t h a t the s i z e of the drops formed at the ends of the j e t s of dispersed phase a l s o increases t o a maximum w i t h i n c r e a s i n g d i s p e r s e d phase f l o w r a t e . However, the dispersed phase f l o w r a t e a t which the maximum drop s i z e occurs i s lower than t h a t a t which the maximum j e t l e n g t h occurs. The c l a i m was made th a t u n i f o r m l y s i z e d drops are produced a t disp e r s e d phase f l o w r a t e s lower than those which give the maximum drop s i z e . The formation of many small drops along w i t h l a r g e r drops has been 19 observed under some operating conditions, (h, k'S)'. Weaver, Lapidus, and E l g i n (hi) found no noticeable change i n drop si z e d i s t r i b u t i o n along the length of a spray column. Garwinand Smith (U3) report that the dispersed phase drop si z e i s independent of the continuous phase flowrate. 2..... MATHEMATICAL • MODELS In order to describe f u l l y a turbulent f i e l d i t i s necessary to know the v e l o c i t y vector at a l l points.and at a l l times. However, such knowledge i s unavailable. Therefore, a measurement of some e f f e c t of the turbulence u s u a l l y i s made i n order to characterize the extent Of the turbulence. Even when the flow patterns i n the turbulent f i e l d are of a complicated, nature a simple mathematical model often adequately describes the mixing taking place. In the past the design of flow reactors has been based l a r g e l y upon two i d e a l i z e d models: plug flow, and completely mixed flow. Plug flow assumes a f l a t v e l o c i t y p r o f i l e , whereas completely mixed flow assumes that the f l u i d i n the vessel i s p e r f e c t l y mixed. The three most popular models which l i e between the two extreme cases are the dispersion, mixing c e l l , and random walk models. For the case of f l u i d flow through a long column or bed the mathematical implications of a l l three models are e s s e n t i a l l y the same (hk, 45 , 46). However, there are'fundamental differences between the premises upon which the models are based. B r i e f o utlines of these models are presented below together with summaries.of some of the more important researches 2.0 which have u t i l i z e d them, f o r interpreting' experimental data. A x i a l mixing of only one phase i s considered i n each case. DISPERSION MODEL I t i s assumed that a x i a l mixing due to turbulence follows a law s i m i l a r to Fick's Law f o r molecular d i f f u s i o n . On t h i s basis a mass balance on solute i n the continuous phase over an incremental section of column y i e l d s Equation 8 f o r the case of no mass t r a n s f e r to or from the continuous phase. (Also see Appendix 1.) Ee i c c - L c 0 c c = e^c c z^ oz 2>t 8 I t i s assumed that r a d i a l homogeneity p r e v a i l s . Wilson (47) solved an equation s i m i l a r to Equation 8 f o r molecular d i f f u s i o n of heat from a point source i n t o a flowing f l u i d . Wilson's s o l u t i o n has been used together with experimental data (4'8, 49, 50) to ca l c u l a t e eddy d i f f u s i v i t i e s i n open ducts on the assumption of Isotropic homogeneous turbulence. Bernard and Wilhelm (51) used a s i m i l a r method to determine eddy d i f f u s i v i t i e s i n packed columns. In 1949 G i l l i l a n d and Mason (52) applied the model to the steady state, operation of an..,alr-fluidized bed.' At steady state c^ i s independent of t and Equation 8 can be integrated (Appendix l) to give Ee dCp = L^Cp - • J dz 9 21 where the constant of i n t e g r a t i o n , J , i s the net f l u x of s o l u t e down the column. I f the t e s t s e c t i o n i s , from the viewpoint of the continuous phase, upstream from the feed p o i n t of t r a c e r , then J = 0 and Equation 9 y i e l d s Equation 10 on i n t e g r a t i o n . _ L̂ f. " Ee . 10 G i l l i l a n d and Mason (52, 53) i n j e c t e d a t r a c e r gas a t a constant r a t e i n t o the bed and measured t r a c e r concentrations at various p o i n t s i n the bed below the l e v e l of t r a c e r i n j e c t i o n . From the slope of a p l o t of I n (c^) versus z they were able t o c a l c u l a t e the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , (eE). The above method f o r e s t i m a t i n g a x i a l eddy d i f f u s i v i t i e s cannot be u t i l i z e d f o r the cases of s i n g l e phase or co-current flows because the process of a x i a l mixing would not, i n t h i s case, c a r r y the t r a c e r upstream i n the continuous phase w i t h respect t o the t r a c e r i n j e c t i o n p o i n t . The model has been a p p l i e d subsequently to the study of pulsed s i e v e - p l a t e e x t r a c t i o n columns (5^, 55), gas-sparged t u b u l a r v e s s e l s (56), r o t a t i n g - d i s k contactors (57, 58); a n d commercial f l u i d i z e d bed c a t a l y s t regenerators (59)* Continuous phase a x i a l eddy d i f f u s i v i t i e s have been determined mostly by c o n s i d e r i n g the e f f e c t downstream, w i t h respect t o the continuous phase, of an unsteady s t a t e i n j e c t i o n of t r a c e r . Equation 8 has been solved f o r i n j e c t i o n of t r a c e r according t o a D i r a c In ( c c ) 22 D e l t a Function or s i n g l e p u l s e , a step f u n c t i o n , and a s i n u s o i d a l f u n c t i o n . These three d i f f e r e n t methods of t r a c e r i n j e c t i o n are discussed b r i e f l y below. D i r a c D e l t a Function With no a x i a l mixing a transverse-homogeneous s i n g l e pulse of t r a c e r i n j e c t e d i n t o a moving stream would appear downstream as a s i n g l e pulse a t a l l times. With some a x i a l mixing, spreading w i t h respect t o di s t a n c e w i t h i n the column of the t r a c e r pulse r e s u l t s . Panckwerts (60) and L e v e n s p i e l and Smith (6l) showed how t o i n t e r p r e t the p l o t of t r a c e r c o n c e n t r a t i o n versus time f o r some po i n t downstream from the place of t r a c e r i n j e c t i o n . Such a p l o t i s c a l l e d a C-curve (60) and the second moment or variance of t h i s curve i s r e l a t e d t o the a x i a l eddy d i f f u s i v i t y . A x i a l eddy d i f f u s - i v i t i e s have been determined by the D i r a c D e l t a F u n c t i o n method f o r packed columns (62, 63, 64), pulsed s i e v e - p l a t e columns (54, 55/ 100), c o i l e d tube r e a c t o r s (66), and l i q u i d - f l u i d i z e d beds (67). Van der Laan (68) showed how t o determine the a x i a l eddy d i f f u s i v i t y from the vari a n c e of a C-curve f o r a f i n i t e l e n g t h of v e s s e l by us i n g the appr o p r i a t e boundary c o n d i t i o n s (60, 69)- A r i s (70) 1 pointed out t h a t i t i s Impossible t o i n j e c t a p e r f e c t pulse of t r a c e r i n t o a column. A l s o he showed, however, t h a t i t i s not necessary f o r the t r a c e r i n j e c t i o n to be i n the form of a p e r f e c t pulse i f one takes the d i f f e r e n c e of the second moments of the C-curves measured a t two d i f f e r e n t p o i n t s i n the column, A r i s ' theory was l a t e r c o r r e c t e d by B i s c h o f f (7 l ) who, together w i t h L e v e n s p i e l (72, 73), presented the theory i n d e t a i l . A x i a l eddy d i f f u s i v i t i e s i n l i q u i d - l i q u i d spray columns a t f l o o d i n g c o n d i t i o n s (74), i n packed beds (75), and i n o r i f i c e p l a t e g a s - l i q u i d r e a c t o r s (76) have been determined by t a k i n g the d i f f e r e n c e of the variances of C-curves. Step F u n c t i o n A step f u n c t i o n of t r a c e r can be introduced i n t o a column by suddenly stopping or s t a r t i n g the f l o w of t r a c e r . A p l o t of down- stream t r a c e r c o n c e n t r a t i o n versus time i s c a l l e d an F-curve (60) or breakthrough curve.. The gradient of the F-curve a t a p a r t i c u l a r value on the time a x i s i s r e l a t e d t o the a x i a l eddy d i f f u s i v i t y . G i l l i l a n d and Mason (53) examined an F-curve f o r a f l u i d i z e d bed i n 1952, but a t t h a t time a t h e o r e t i c a l a n a l y s i s of such a curve had not been developed. In 1953 Danckwerts (60) showed how t o c a l c u l a t e the a x i a l eddy d i f f u s i v i t y from an experimental F-curve. A x i a l eddy d i f f u s i v i t i e s have been determined from breakthrough curves f o r packed beds (46, 60, 77, 78, 79, 80, 8 l , 82), spray columns (42 ) , and r o t a t i n g d i s k contactors (83). Brutvan (84) determined a x i a l eddy d i f f u s i v i t i e s from breakthrough curves i n a spray column where the "dispersed phase was s o l i d spheres. A s t a t i s t i c a l a n a l y s i s of experimental breakthrough curves has been discussed by Klinkenberg (85). l e v e n s p i e l and B i s c h o f f (73) i n d i c a t e d how t o e l i m i n a t e the e f f e c t on the F-curve of the p a r t i c u l a r method of t r a c e r i n j e c t i o n used. The procedure i n v o l v e d t a k i n g measurements at two e l e v a t i o n s i n a column. M i l l e r and 2k King (86) examined the slopes of F-curves measured a t two a x i a l d i s t a n c e s i n a packed bed to c a l c u l a t e a x i a l eddy d i f f u s i v i t i e s . I t should be noted t h a t the F-curve i s the time i n t e g r a l of the C-curve (79)- This f a c t has been demonstrated e x p e r i m e n t a l l y (87). S i n u s o i d a l Function Under the i n f l u e n c e of a x i a l mixing i n a column a s i n u s o i d a l f u n c t i o n of t r a c e r c o n c e n t r a t i o n s u f f e r s both a t t e n u a t i o n and phase l a g . L e v e n s p i e l and B i s c h o f f (73) d e r i v e d equations r e l a t i n g the P e c l e t number t o the a t t e n u a t i o n and phase l a g of a s i n u s o i d a l input of t r a c e r . The s i n u s o i d a l input or frequency response method has been used t o determine P e c l e t numbers f o r gas f l o w and l i q u i d f l o w through random and ordered packed beds (63, 88, 89, 90, 91* 92, 93, 9k, 104). Ebach and White (63) showed how t o evaluate r e s u l t s f o r p e r i o d i c t r a c e r i n p u t f u n c t i o n s which are not s i n u s o i d a l . In l i q u i d - l i q u i d e x t r a c t i o n columns two phase countercurrent f l o w w i t h mass t r a n s f e r i s encountered. The performance of such columns has been p r e d i c t e d on the b a s i s of Equation 8 modified t o i n c l u d e a mass t r a n s f e r term (95> 96, 91, 98) as shown below I - l T h e o r e t i c a l c o n c e n t r a t i o n p r o f i l e s i n e x t r a c t i o n columns have been c a l c u l a t e d f o r various o p e r a t i n g c o n d i t i o n s (99, 100, 101, 102, 103). 25 T h e o r e t i c a l c o n c e n t r a t i o n p r o f i l e s . h a v e been compared w i t h e x p e r i - mental p r o f i l e s f o r various l i q u i d - l i q u i d e x t r a c t i o n d e v i c e s . Agreement was good f o r pulsed columns (58, 102) and moderately- good f o r some c o n d i t i o n s of spray column operation (103) and f o r gas absorption-tower operations (105). G o t t s c h l i c h (106) a p p l i e d Equation 8 t o a packed column. In doing so he modified the equation t o take i n t o account stagnant l a y e r s of f l u i d around the packing elements. He re p o r t s t h a t the m o d i f i c a t i o n improves the agreement of experimental r e s u l t s and the t h e o r e t i c a l model. Van Deemter, Zuiderweg, and Klinkenberg (107) used the d i s p e r s i o n model t o c o r r e c t f o r n o n - i d e a l i t y i n chrom- atography due .to a x i a l d i s p e r s i o n . MIXING CELL MODEL Kramers and Alberda (90) drew an analogy between s i n g l e phase f l o w i n a packed bed and a s e r i e s of p e r f e c t mixing v e s s e l s . They assumed a long bed %nd r e s t r i c t e d the magnitude of the p a r t i c l e P e c l e t number. On these bases they showed t h a t the d i s p e r s i o n model and mixing c e l l model y i e l d the same frequency response diagram f o r a s i n u s o i d a l l y v a r y i n g t r a c e r i n p u t . Other workers (kk, 6h, 92, 108, 109) have f o l l o w e d Kramers and Alberda's approach f o r s i n g l e phase f l o w . I t has been shown th a t f o r the analogy t o be v a l i d the P e c l e t number', Pe', must be given by Equation 11, Pe'1- = 2 J 11 where )v i s the r a t i o of the len g t h of a mixing c e l l , cL, to the c h a r a c t e r i s t i c packing dimension, d (See Appendix I I . ) In a P packed bed the a x i a l d i s t a n c e between l a y e r s of packing i s taken t o be equal t o the height of a mixing c e l l . A r i s and Amundson (108) and Jacques and Vermeulen (46) used the Poisson p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n t o describe the residence time d i s t r i b u t i o n of a t r a c e r molecule on the b a s i s of the mixing c e l l model. E p s t e i n ( HO) has developed charts f o r a c o r r e c t i o n f a c t o r which modifies l o g mean d r i v i n g f o r c e s f o r s i n g l e phase f l o w i n packed beds. The model i s based on the analogy between a f i x e d bed of p a r t i c l e s and a s e r i e s of p e r f e c t mixers. T h e o r e t i c a l arguments have been presented r e l a t i n g the d i s p e r s i o n model t o a s e r i e s of p e r f e c t mixing c e l l s w i t h backflow between mixers (45, 100, 111, 112, 113). L i and Z i e g l e r (25) r e c e n t l y have pu b l i s h e d a review of the experimental and theo r - e t i c a l work done on the a p p l i c a t i o n of the d i s p e r s i o n and the mixing c e l l models t o spray and packed towers. RANDOM WALK MODEL The theory f o r the random walk model i s based on E i n s t e i n ' s s t a t i s t i c a l treatment (115). Small packets of f l u i d are assumed to move i n an i n t e r m i t t e n t f a s h i o n , the motion b e i n g over a d i s t a n c e , and l a s t i n g f o r a le n g t h of time, both of which are taken t o be p u r e l y random q u a n t i t i e s . Jacques and Vermeulen (46) show t h a t the random walk model, the mixing c e l l model, and the d i s p e r s i o n model r e s u l t i n the same mathematical equation f o r residence time d i s t r i b u t i o n s . A x i a l eddy d i f f u s i v i t i e s f o r packed beds have been determined u s i n g the random walk model and inp u t of t r a c e r according t o a step f u n c t i o n (46, 116, 117). OBJECT OF THIS RESEARCH In I963 Gerster (127) summarized the work which had been done on the e f f e c t of a x i a l mixing upon the performance of e x t r a c t i o n columns. He suggested t h a t much f u r t h e r work i n the f i e l d of a x i a l eddy d i f f u s i o n was needed. Previous work t o determine a x i a l eddy d i f f u s i v i t i e s i n spray columns has been c a r r i e d out by Hazlebeck and Geankoplis (42) and by Brutvan (84). The former i n v e s t i g a t i o n i n v o l v e d the use of water as the aqueous phase and MIBK as the d i s p e r s e d phase i n a l - ^ - i n . I.D. column. Only one set of nozzle t i p s , which produced drops of about 0.135-in. diameter, was used throughout the work. The step f u n c t i o n i n p u t a p p l i c a t i o n of the d i s p e r s i o n model was used as de s c r i b e d e a r l i e r * "The a x i a l <eddy d i f f u s i v i t y was'found 2 2 t o i ncrease l i n e a r l y between 12-ft./hr. and 22«ft./hr- f o r continuous phase s u p e r f i c i a l v e l o c i t i e s between l O - f t . / h r . f t . 3 2 and 45-ft'./hr. f t . r e s p e c t i v e l y . For a given continuous phase s u p e r f i c i a l v e l o c i t y the a x i a l eddy d i f f u s i v i t y was constant f o r dispensed phase s u p e r f i c i a l v e l o c i t i e s between 1 8 . 4-ft./hr. f t and 5 0-ft./hr. f t . Brutvan performed experiments In 1-in., l§--in. and 2-in. I.D. columns w i t h water as the continuous phase and gla s s beads, of diameters 3, 4, 5, and 6-mm. r e s p e c t i v e l y , as the d i s p e r s e d phase. He, a l s o , used the step f u n c t i o n input a p p l i c a t i o n of the d i s p e r s i o n model. Various d i s p e r s e d phase o p o p s u p e r f i c i a l v e l o c i t i e s between l O - f t ' / h r . f t . and 1 0 0-ftr/hr. f t . and continuous phase s u p e r f i c i a l v e l o c i t i e s between l 4 o - f t . / h r . f t o . g and 780-ft./hr. f t . were s t u d i e d . He found t h a t the a x i a l eddy d i f f u s i v i t y i n c reased w i t h i n c r e a s i n g column diameter, i n c r e a s i n g d i s p e r s e d phase f l o w r a t e , decreasing continuous phase f l o w r a t e and decreasing d i s p e r s e d phase p a r t i c l e s i z e . Both the i n v e s t i - gations of Hazlebeck and Geankoplis and of Brutvan d i d not take i n t o account the problems a s s o c i a t e d w i t h the production of a p e r f e c t step f u n c t i o n as mentioned e a r l i e r . No work has been reported where a x i a l eddy d i f f u s i v i t i e s i n spray columns were determined by means of the steady s t a t e a p p l i c a t i o n of the d i s p e r s i o n model. A c c o r d i n g l y , the obje c t of the present work was t o measure a x i a l eddy d i f f u s i v i t i e s i n an o p e r a t i n g l i q u i d - l i q u i d spray column. The steady s t a t e form of the d i s p e r s i o n model was used i n these i n v e s t i g a t i o n s . Since l i t t l e was known of the e f f e c t of v a r i o u s o p e r a t i n g parameters on eddy d i f f u s i v i t y i t was decided t h a t the e f f e c t s of f l o w r a t e s of the two phases, column l e n g t h , and column diameter on the a x i a l eddy d i f f u s i v i t y should he i n v e s t i g a t e d , A minor o b j e c t i v e i n the form of a p r e l i m i n a r y study was t o f i n d s u i t a b l e methods: f o r sampling the continuous and d i s p e r s e d phases of an o p e r a t i n g spray column. 30 THEORY APPLICATION OF THE DISPERSION MODEL TO. RUNS WITH NO MASS TRANSFER In the present work the d i s p e r s i o n model de s c r i b e d i n the I n t r o d u c t i o n was used. The general assumptions upon which t h i s model i s based are l i s t e d below. 1. Backmixing of the continuous phase can.be represented by F i c k ' s Second Law of D i f f u s i o n w i t h a constant a x i a l eddy d i f f u s i v i t y throughout the column. 2. The molecular d i f f u s i v i t y of any s o l u t e considered i s n e g l i g i b l e compared t o the a x i a l eddy d i f f u s i v i t y . 3- R a d i a l homogeneity p r e v a i l s ' a t constant a x i a l p o s i t i o n . 4 . The v e l o c i t y p r o f i l e i n the continuous phase i s f l a t . 5« Volumetric f l o w r a t e s are constant throughout the column. 6. A t e s t s e c t i o n of column i s considered i n which no hydrodynamic property i s a f f e c t e d by the column t e r m i n a l c o n d i t i o n s . 7. There i s no backmixing of the disp e r s e d phase. Determination of A x i a l Eddy D i f f u s i v i t i e s In a d d i t i o n t o the above assumptions the f o l l o w i n g assumptions were made f o r determining a x i a l eddy d i f f u s i v i t i e s . 1. The a x i a l eddy d i f f u s i v i t y i n the continuous phase i s not 31 a f f e c t e d by the chemical nature of the s o l u t e . 2. The s o l u t e d i s s o l v e s only i n the continuous phase, The theory i s developed f o r a t e s t s e c t i o n of column which l i e s , from the viewpoint of the continuous phase, upstream from the p o i n t of i n j e c t i o n of t r a c e r . The downstream fl o w of t r a c e r due t o b u l k f l o w of the continuous phase i s equated t o the backflow of t r a c e r by a x i a l eddy d i f f u s i o n t o give L c c c = Ee d c c c T z - 12 E - i s the a x i a l eddy d i f f u s i v i t y and (Ee) i s the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y . Obviously Equation 12 r e s u l t s from Equation 8 a t steady s t a t e . As mentioned e a r l i e r , a l s o , the s o l u t i o n of Equation 12 i s L z Ee = In (c ) CO 13 where c i s the value of c at z = 0. I t can be seen from CO C Equation 13 t h a t a p l o t of In c versus z has a slope of L C 0 Ee" i f the model holds good. D e r i v a t i o n s of Equations 12 and 13 are given i n Appendix I . P r e d i c t i o n of P e c l e t Number by the M i x i n g C e l l Analogy As mentioned i n the I n t r o d u c t i o n the analogy between s i n g l e 32 phase flow through a packed bed and through a series of perfect mixers r e s u l t s i n the following l i m i t a t i o n on the p a r t i c l e Peclet Number, Pe'. (See Appendix II.) Pe'- = 2 J where > = ^ d P where d̂ _ i s the distance between layers of packing pieces. I t i s suggested that the above analogy can be extended to spray column operation by allowing the co-ordinate axes of reference to move at the same v e l o c i t y as the r i s i n g dispersed phase drops. As shown i n Appendix I I ; on t h i s basis a spray column tends, mathematically speaking, towards a packed bed. I f the drops are assumed to be arranged i n some, simple l a t t i c e structure, ~\ can be expressed purely i n terms of h . Therefore the predicted drop Peclet number i s a simple function of h only. Equations f o r p r e d i c t i n g the drop Peclet number, Pe, from the hold-up, h, have been derived i n Appendix I I f o r s i x d i f f e r e n t l a t t i c e arrangements of drops. APPLICATION OF THE DISPERSION MODEL TO LIQUID-LIQUID EXTRACTION On the b a s i s of the dispersion model the reduced concentration of solute i n the continuous phase of a l i q u i d - l i q u i d e x t r a c t i o n column i s given by Equation l h . 33 where C c = Aexp j ^ Z ) + Bexp (^Z) - Q 14 \ = c<- M2+ p , 2oc= L QH + I^aH , Ee L D P = ( LD - 15 16 2 mL-pEe Q = Jm . , CO D C y 17 18 19 and A.and B are constants of i n t e g r a t i o n . Equations ik t o 19 i n c l u s i v e correspond t o Equations 1-13; 1-14, 1-15; 1-10, 1-11, and I - l 6 i n Appendix I . I f the s o l u t e c o n c e n t r a t i o n p r o f i l e s are a v a i l a b l e f o r both phases of a l i q u i d - l i q u i d e x t r a c t i o n spray column the ca p a c i t y c o e f f i c i e n t , (Kj-,a), can be c a l c u l a t e d by means of Equation 20. V = h f D C D * H / ( c c " CD) 20 34 The i n t e g r a l i n Equation 20 i s evaluated g r a p h i c a l l y over the le n g t h of t e s t s e c t i o n , H. The volu m e t r i c f r a c t i o n of continuous phase, e, i n the column can be measured by means of a p i s t o n sampler (37)- For steady-state operation the net f l u x , J , of s o l u t e down the column must be the same at any e l e v a t i o n i n the column. J can be c a l c u l a t e d from a knowledge of the s u p e r f i c i a l ^ v e l o c i t i e s of, both phases and s o l u t e concentrations i n the streams e n t e r i n g and l e a v i n g the column by means of Equation 21. J * \ [ ( L c c J - L ^ ) + (L cc° - L D c J ) ] ^ Boundary c o n d i t i o n s f o r Equation Ik have been suggested by Danckwerts (60). These could be used t o c a l c u l a t e the values of A and B i n t h a t equation. Then, i f an estimate of the a x i a l eddy d i f f u s i v i t y , E, were a v a i l a b l e , the con c e n t r a t i o n p r o f i l e of s o l u t e i n the continuous phase could.be p r e d i c t e d by means of Equation l 4 . However, the boundary c o n d i t i o n s r e l y on the-assumption t h a t the d i s p e r s i o n model i s a p p l i c a b l e a t the ends o f the spray column. Some doubt e x i s t s as to whether t h i s assumption i s v a l i d because the hydrodynamic f l o w patterns are much d i f f e r e n t i n the E l g i n head a t the upper end of the column, and i n the c o n i c a l s e c t i o n a t the lower end of the column, than i n the column proper. Another method f o r c a l c u l a t i n g values of A and B c o n s i s t s of f i t t i n g Equation lk t o a measured s o l u t e c o n c e n t r a t i o n p r o f i l e i n the continuous phase. In c a r r y i n g out t h i s curve f i t t i n g , an estimate of the a x i a l eddy d i f f u s i v i t y , E, i s obtained. Since Equations 35 15 to 1 9 i n c l u s i v e i n v o l v e E, values of E can be chosen by t r i a l and e r r o r t o produce the best f i t of Equation 14 t o the measured concentration p r o f i l e . One method of f i t t i n g Equation 1 4 t o an experimental p r o f i l e i s toy means of the l e a s t squares technique. Estimates of the values of A and B are obtained by minim i z i n g the sum of the squares of the d i f f e r e n c e s between measured concentrations and those given by Equation 14. That'is, the value of given by Equation 22, must be a minimum. ^ = 5[°C "  AQM\Z) - Bexp(> 2Z) + Q ] 2 22 I f Equation 22 i s d i f f e r e n t i a t e d p a r t i a l l y w i t h respect t o A and t h i s ' r e s u l t equated t o zero, and then again w i t h respect t o B, and that- r e s u l t equated t o zero, two simultaneous equations i n A and B, Equations 23 and 2 4 , r e s u l t . . A ^ e x p C ^ Z ) ) 2 + B ^ e x p ^ Z ^ x p O g Z ) ) ^ ( ( ^ e x p C X ^ ) ) + Q ^ e x p O ^ Z ) 23 A ^ ( e x p ( > 1 Z ) e x p ( ^ 2 Z ) ) + B ^ ( e x p ( > 2 Z ) ) 2 ^ ( C ^ e x p O ^ Z ) ) + Q ^ e x p ^ Z ) 24 Equations 23 and 2 4 can toe solved f o r A and B. This process can toe repeated f o r various assumed values of the a x i a l eddy d i f f u s i v i t y , 2 E. The value of E which r e s u l t s i n the lowest value of A . i s one estimate of the tru e value of E. 36 i APPARATUS The o r i g i n a l apparatus was designed and b u i l t by Le Page ( l l 8 ) . However, i t has been modif i e d by others (37, 38, 39) and by the author. A schematic f l o w diagram of one arrangement of the apparatus used i n the present work i s shown i n "Figure 9« This arrangement was used f o r t r a c e r s t u d i e s w i t h no interphase mass t r a n s f e r i n a l-§--in. I.D. column. A key t o Figure 9 i s presented i n Table 1. A l l c o n t r o l valves were s t a i n l e s s s t e e l needle valves w i t h T e f l o n packing. The c e n t r i f u g a l pump, P su p p l i e s the constant head tank, E, w i t h d e - i o n i s e d water from the storage tank,. A. Water flows from the constant head tank, E, through the c o n t r o l v a l v e , J , and rotameter, G, t o the E l g i n head, M, of the column. Water flows, down, as the continuous phase, through the column proper, R, l e a v i n g . a t the lower end of the column and passing through the i n t e r f a c e c o n t r o l v a l v e , X, and rotameter, Y, t o the r e c e i v i n g tank, B. MIBK i s s u p p l i e d t o the constant head tank, F, by the c e n t r i f u g a l pump, P from the supply tank, D. From the constant head tank, F, MIBK flows through the c o n t r o l v a l v e , K, and rotameter, H, t o the disp e r s e d phase n o z z l e , S, a t the lower end of the column. MIBK r i s e s , i n the form of drops, through the descending water i n the column and coalesces at the i n t e r f a c e , Q, From the "Elgin head MIBK flows d i r e c t l y t o the r e c e i v i n g tank, C. I t i s p o s s i b l e t o  TABLE 1 (Key to Figure 9) Continuous phase feed tank. Continuous phase receiver and storage tank. Dispersed phase r e c e i v e r and storage tank. Dispersed phase feed tank. Continuous phase constant head tank. Dispersed phase constant head "tank. Continuous phase feed rotameter. Dispersed phase feed rotameter. Continuous phase i n l e t sample valve. Continuous phase flowrate c o n t r o l valve. Dispersed phase flowrate c o n t r o l valve. Dispersed phase i n l e t sample valve. E l g i n head. Continuous phase i n l e t pipes. E l g i n head drain valve. C e n t r i f u g a l pump f o r continuous phase. C e n t r i f u g a l pump f o r dispersed phase. Piston-type sampler. Interface. Column proper. Dispersed phase nozzle. Thermometers Bottom c o n i c a l s e c t i o n . Vent to atmosphere. I n t e r f a c e l e v e l c o n t r o l v a l v e . I n t e r f a c e l e v e l c o n t r o l rotameter. Tracer constant head tank. Tracer f l o w r a t e c o n t r o l v a l v e . Tracer feed rotameter. Tracer d i s t r i b u t o r . 22-gauge hypodermic needle sampler take a b u l k sample from the column w i t h the p i s t o n sampler, PTS, d e t a i l s of which are to be found elsewhere (37/ 38). A drawing of the p i s t o n sample c o l l e c t i o n v e s s e l f o r d i s p e r s e d phase hold-ups greater than 12$ i s shown i n Appendix V. The p i s t o n sample c o l l e c t i o n v e s s e l f o r d i s p e r s e d phase hold-ups l e s s than 12$ i s s i m i l a r and i s described elsewhere (37)- Both of the p i s t o n sample c o l l e c t i o n f l a s k s were c a l i b r a t e d by weighing them when they contained v a r i o u s amounts of water. Sodium c h l o r i d e d i s s o l v e d i n MIBK-saturated water was used as t r a c e r . A concentrated s o l u t i o n of t h i s flows from the constant head tank, Z, through the c o n t r o l needle v a l v e , a, and rotameter, b, t o the t r a c e r d i s t r i b u t o r , c, i n the column. Time average p o i n t samples were taken from the column through 22-gauge, 3~in. l o n g hypodermic needles, d. The f l o w r a t e of these samples was r e g u l a t e d by means of simple s t a i n l e s s s t e e l - p o l y e t h y l e n e stopcock v a l v e s . The hypodermic needles were i n s e r t e d through polyethylene gaskets which were between 6 - i n , s e c t i o n s of the Pyrex g l a s s column. (See Appendix V f o r d e t a i l e d drawings of the t r a c e r d i s t r i b u t o r and of the sample v a l v e s . ) Samples c o n t a i n i n g t r a c e r were analysed f o r sodium w i t h a P e r k i n - Elmer 303 atomic a b s o r p t i o n spec t r o - phometer. The major part of the work was c a r r i e d out w i t h a Pyrex glass column of l - | - i n . I.D.' D e t a i l s of the end s e c t i o n s of t h i s column are t o be found elsewhere ( l l 8 , 35). I t s v e r t i c a l dimensions are shown i n Figure 10. The arrangements shown i n F i g u r e 11 and 12 hi CM T — T INTERFACE 6"LONG, 6"I.P. PYREX "DOUBLE TOUGH" PIPE 10" LONG, LV ID. PYREX "DOUBLE TOUGH" PIPE WITH UNFLANGED UPPER END « 3' LONG, l>2" ID. PYREX "DOUBLE TOUGH" PIPE. A 6" LONG, l ' / 2 " I.D. PYREX DOUBLE TOUGH PIPE (SEE T A B L E VI-I FOR MEASURED DIMENSIONS) B V\s" THICK , l!£" I.D. POLYETHY- LENE GASKET THROUGH WHICH SAMPLING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER) STYLE 1-2 (CORNING) TEFLON GASKET '/g THICK, life I.D. TEFLON GASKET THROUGH WHICH THE TRACER INJECTION NEEDLE PASSED I* LONGj'/fc" IO. PYREX "DOUBLE TOUGH" PIPE CUSTOM MADE PYREX "DOUBLE TOUGH" 3" TO I1/a" REDUCER (30) FIGURE 10. l£-IN. I.D. COLUMT were used together with that given in Figure 10 for investigating the effect of column length on the axial eddy d i f f u s i v i t y . Details of the column arragements used for the part of the work concerning sampling techniques are shown in Figures 13 and 14. Two sampling techniques for measuring concentration profiles were investigated. The f i r s t method was the use of the hook and bell-probes.mentioned earlier. Both the hook-shaped probe and the bell-shaped probe were made-from stainless steel. Details of these probes are to be found elsewhere (30, 118), and a diagram is shown in Figure 5« Samples were syphoned out of the column through these probes and through small needle valves and rotameters connected i n series with them. The needle valves were used to control the flows, and the rotameters to measure them. The syphon was started by means of a water aspirator. The second sampling method made use of hypodermic needles as mentioned earlier. The piston sampler, mentioned in the Introduction, was employed in both sampling investigations. The drops were produced at a nozzle similar in design to that of Kreagerand Geankoplis (l6). With this sort of nozzle drops are formed at the ends of jets extending from short tubes press^fitted into a plate forming the end of the spray nozzle. These tubes were chamfered to sharp edges at their delivery ends- The dispersed phase nozzle used with the l-|-in. I.D. column was designed by Choudhury, and a detailed drawing i s to be found fn his thesis (35)? The nozzle tips and nozzle t i p support plate are described elsewhere (30, 35; 118). The average inside diameter of these nozzle tips was measured by the present author and was ^3 INTERFACE 6" LONG, 6" I.D. PYREX "DOUBLE TOUGH" PIPE 10"LONG, l'/2" I.D. PYREX "DOUBLE TOUGH" PIPE WITH UNFLANGED UPPER END 6" LONG, I.D. PYREX "DOUBLE TOUGH" PIPE (SEE TABLE VI-I FOR MEASURED DIMENSIONS) • M N /|€ THICK, |'/2 |.D. POLYETHYLENE GASKET THROUGH WHICH SAMPING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER) l/g THICK, l ' / 2 " |.D. TEFLON GASKET THROUGH WHICH THE TRACER INJECTION NEEDLE PASSED CUSTOM MADE PYREX "DOUBLE TOUGH" 3" TO iVz" REDUCER (30) STYLE 1-2 TEFLON GASKET (CORNING) FIGURE 11. SHORT 1^-IN. I.D. COLUMN kk I N T E R F A C E •6" LONG, 6" I.D. P Y R E X "DOUBLE TOUGH" P I P E 10" LONG, I'/g" I..0. PYREX "DOUBLE TOUGH" PIPE WITH UNFLANGED UPPER END 2' 6" LONG, 1/2 I.D. PYREX "DOUBLE TOUGH" PIPE 3' LONG, I'/g" I.D. PYREX "DOUBLE TOUGH" PIPE A 6" L O N G , V/2. I D . P Y R E X " D O U B L E T O U G H " P I P E ( S E E T A B L E V I - 1 F O R M E A S U R E D D I M E N S I O N S ) B Vi$" T H I C K , I5^ I .D . P O L Y E T H Y L E N E G A S K E T T H R O U G H W H I C H S A M P L I N G N E E D L E S P A S S E D ( E A C H S A M P L I N G P O S I T I O N I S I N D I C A T E D B Y N U M B E R ) S T Y L E 1-2 T E F L O N G A S K E T ( C O R N I N G ) \ / £ T H I C K , .. life" I D . T E F L O N G A S K E T T H R O U G H W H I C H T H E T R A C E R I N J E C T I O N N E E D L E P A S S E D 2' L O N G , l'/2 I D . P Y R E X I D O U B L E T O U G H " P I P E I ' 6" L O N G , l ' / 2 " I.D. P Y R E X " D O U B L E T O U G H " P I P E C U S T O M M A D E P Y R E X " D O U B L E T O U G H " 3 " T O l ' / 2 " R E D U C E R FIGURE 1 2 . LONG l | - I N . I.D. COLUMN 45 CM ^ 4=L r r INTERFACE '6" LONG, 6" I.D. PYREX "DOUBLE TOUGH" PIPE 10" LONG, I.D. PYREX "DOUBLE TOUGH" WITH UNFLANGED UPPER END 3' LONG, l 1 / ^ I.D. PYREX "DOUBLE TOUGH* PIPE I' 6"L0NG, IV 2 I.D. PYREX "DOUBLE TOUGH" PIPE T LONG, l ' / 2 " I.D • PYREX "DOUBLE TOUGH" PIPE CUSTOM MADE PYREX "DOUBLE TOUGH" 3 " TO l!/2" REDUCER D STYLE 1-2 TEFLON GASKET (CORNING) / FIGURE 13. I f - I N . I.D. COLUMN FOR COMPARING HOOK AND BELL-PROBES AND PISTON SAMPLER RESULTS I N T E R F A C E 6" L O N G , 6" I.D. P Y R E X " D O U B L E T O U G H " P I PE 10" L O N G , l ' / 2 M I.D. P Y R E X " D O U B L E T O U G H " P I P E W ITH U N F L A N G E D U P P E R E N D 3' L O N G , l ' / 2 I.D. P Y R E X " D O U B L E T O U G H " P I P E I' L O N G , l ' / 2 I.D. P Y R E X " D O U B L E T O U G H " P I P E A T L O N G , l ' / 2 " P Y R E X " D O U B L E T O U G H " S P A C E R B '/, 6 T H I C K , ||/2H I.D. P O L Y E T H Y L E N E G A S K E T T H R O U G H W H I C H S A M P L I N G N E E D L E S P A S S E D C 2'/2" L O N G , IK/{ I.D. P Y R E X " D O U B L E T O U G H " S P A C E R D S T Y L E 1-2 T E F L O N G A S K E T ( C O R N I N G ) E 3" L O N G , l ' / 2 I.D. P Y R E X " D O U B L E T O U G H " S P A C E R I' L O N G , I.D. P Y R E X " D O U B L E T O U G H " P I P E C U S T O M M A D E P Y R E X " D O U B L E T O U G H " 3" TO l > 2 " R E D U C E R FIGURE Ik. if-IN. I*D. COLUMN FOR COMPARING HYPODERMIC NEEDLE, HOOK, AND BELL-PROBES, AND PISTON SAMPLER RESULTS found t o be 0.103-in. (See Appendix V.) This nozzle and these nozzle t i p s were used f o r much of the work des c r i b e d i n the present t h e s i s i n c l u d i n g a l l the work i n v o l v i n g mass t r a n s f e r between phases. However, the end p l a t e and nozzle t i p assembly wag. replaced f o r c e r t a i n runs so. t h a t the e f f e c t of drop s i z e on the a x i a l eddy" d i f f u s i v i t y , c o u l d be s t u d i e d . Thus sets of nozzle t i p s of average i n s i d e diameter 0.126-in., 0.086-in., and 0-053-in-. r e s p e c t i v e l y were used i n a d d i t i o n t o those of 0.103-in. al r e a d y mentioned. A d i s p e r s e d phase nozzle was designed f o r use i n a 3-in. I.D. Pyrex g l a s s column used f o r part of the work and described l a t e r i n t h i s s e c t i o n of the t h e s i s . D e t a i l e d drawings of the 0.126-in., 0.086-in., and 0.053-in- I.D. nozzle t i p s appear i n Appendix V. The average v e l o c i t y of MIBK In the d i s p e r s e d phase d i s t r i b u t o r nozzle t i p s was maintained constant f o r each set of nozzle t i p s by b l o c k i n g o f f nozzle t i p s w i t h T e f l o n caps or plugs as the MIBK fl o w r a t e was reduced. P a t t e r n s of open nozzle t i p s used i n t h i s work are shown i n F i g u r e s 15, l6, 17, and 18, one f o r each set of nozzle t i p s and f o r the various d i s p e r s e d phase f l o w r a t e s used. Drop s f z e d i s t r i b u t i o n s i n the l§-iri. I.D. column were determined by photographing a 4 ^ i n . l e n g t h of column s i t u a t e d between 7-in. and 11-in..above the top of the p i s t o n sampler b l o c k . The. camera used was an Exacta VX I I a) w i t h a 1.6-in. extension r i n g and a Telemegor 5-5/250 telephoto l e n s . The.camera aperature was set at f22 to give a depth of focus greater than the i n s i d e diameter of the column. Adox KB-14 (20 ASA) f i l m was used- O O P E N # BLOCKED FIGURE 15. NOZZLE TIP PATTERNS. I.D. = 0.126-IN. (lf-IN. I.D,. COLUMN) k9 O O P E N # BLOCKED FIGURE 16. NOZZLE TIP PATTERNS. I.D. - 0.103-IN. (if-IN. I.D. COLUMN) '  1 O O P E N • B L O C K E D FIGURE 17. NOZZLE TIP PATTERNS. I.D. = 0.086-IN. (l^-'IR. I.D. COLUMN) • o • o • • '© o • • o © o ®' o o • • • • * o i i t o i o o • o « « o « « o o • O • • • Oj m o Q o • 4,-73-0 © o ©o© • ® 'o o • • o • c r ® ® o o « o © 0 O o • • • o ® o o © • O O O €) O « • • o • • o • • o L o i » o « o o » o , • o • o n e o « o • o © L -91* o OPEN • B L O C K E D FIGURE 18. NOZZLE TIP PATTERNS. I.D. = 0.053-BT. ( l f - I N . I.D. COLUMN) The s e c t i o n of column photographed was surrounded by a p a r a l l e l - s ided Perspex box f i l l e d , " w i t h d i s t i l l e d water t o reduce the d i s t o r t i n g e f f e c t of the round column. Back l i g h t i n g was e f f e c t e d w i t h a Braun Hobby F 6 0 e l e c t r o n i c f l a s h u n i t w i t h a one m i l l i s e c o n d f l a s h d u r a t i o n . The s e c t i o n of column photographed was s h i e l d e d from extraneous l i g h t w i t h a cardboard box which a l s o supported the e l e c t r o n i c f l a s h head and a l i g h t - d i f f u s i n g screen of e i g h t sheets of t r a c i n g paper. Figure 19 shows the r e l a t i v e p o s i t i o n s of f l a s h , column, and camera. D e t a i l e d drawings of the Perspex box and the cardboard s h i e l d are given i n Appendix V. A few experimental runs were c a r r i e d out w i t h the 3 - i n . I.D. Pyrex g l a s s column shown i n Figure 2 0 . In order t o produce and maintain high continuous phase s u p e r f i c i a l v e l o c i t i e s three continuous phase feed tanks, p r e s s u r i z e d t o about 15 p . s . i . g . w i t h n i t r o g e n , were used. A schematic f l o w diagram i s presented i n Figure 21. D e t a i l e d drawings of the end s e c t i o n s and di s p e r s e d phase d i s t r i b u t o r nozzle are given i n Appendix V. Figure 22 shows the p atterns of open and close d nozzle t i p s used f o r various dispersed phase f l o w r a t e s . Sodium c h l o r i d e t r a c e r was i n j e c t e d i n t o the column through the same t r a c e r d i s t r i b u t o r as used i n the l - ^ - i n . I.D. column. The t r a c e r d i s t r i b u t o r was l o c a t e d on the centre l i n e of the column and t r a c e r flowed i n t o i t through a 3-in- l o n g , l8-gauge hypodermic needle which passed through a l / 8 - i n , t h i c k , 3-in. I.D., and 3 27/32-in. O.D. T e f l o n gasket. Samples were withdrawn as w i t h the l J r - i n . I.D. column except t h a t BACK OF CAMERA II i t f] FLASH DIFFUSING COLUMN PERSPEX LIGHT UNIT SCREEN BOX SHIELD CAMERA FIGURE 19. PHOTOGRAPHIC CONDITIONS 5^ INTERFACE 1—9" LONG, 9" I.D. Q.V. F. PIPE 10-3/4 LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE 6" LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE (SEE TABLE Vl-I FOR MEASURED DIMENSIONS) '/|6 THICK, 3" liD. POLYETHYLENE GASKET THROUGH WHICH SAMPLING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER) 6" LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE WITH BOTH ENDS UNFLANGED (SEE TABLE VI-I FOR MEASURED DIMENSIONS) l/ 8" THICK, 3" i.D. POLYETHYLENE GASKET THROUGH WHICH THE TRACER NEEDLE PASSED CUSTOM MADE PYREX "DOUBLE TOUGH" 6" TO 3" REDUCER F I G U R E 20. 3 - I N . I . D . COLUMN FIGURE 21. SCHEMATIC PLOW DIAGRAM FOR THE 3-E*. I.D. COLUMN TABLE 2 (Key t o Figure 21) .Continuous phase feed tanks. Dispersed phase feed and r e c e i v e r tank. I n t e r f a c e l e v e l c o n t r o l rotameters. I n t e r f a c e l e v e l c o n t r o l v a l v e s . Continuous phase feed rotameters. Dispersed phase feed rotameters. Continuous phase i n l e t sample v a l v e . Continuous phase f l o w r a t e c o n t r o l valves.- Dispersed phase f l o w r a t e c o n t r o l v a l v e s . E l g i n head. Continuous phase i n l e t p i p e s . Nitrogen c y l i n d e r . E l g i n head d r a i n v a l v e . C e n t r i f u g a l pump f o r continuous phase feed. C e n t r i f u g a l pump f o r dis p e r s e d phase feed. C e n t r i f u g a l pump f o r continuous phase o u t l e t . Pre s sure gauge. Pressure r e l i e f v a l v e . I n t e r f a c e . Column proper. Dispersed phase n o z z l e . 57 Thermometers U - Bottom c o n i c a l section. V Vent, to atmosphere. Z ' Tracer constant head tank. a Tracer flowrate c o n t r o l valve. b Tracer feed rotameter. c Tracer d i s t r i b u t o r . . d 22-gauge hypodermic needle samplers. 58 the hypodermic needles, passed through l / l 6 ^ i n . thick, 3-in. I.D., and 3 2'7/32-in. O.D. polyethylene gaskets to the centre line of the column. The eighth 6-rin. section of column above the tracer distributor was cut from a 1-ft. long piece of Pyrex glass pipe. The piece selected was remote from the ends so that i t s bore was reasonably uniform. This section of column was held in place by four aluminum" tie rods, between two large diameter aluminum flanges shown in Appendix V. A flat-sided Perspex box, also shown in Appendix V surrounded this 6-in. long piece of column. The space between the glass and the Perspex was f i l l e d with d i s t i l l e d water. Photographs were taken of the column through the Perspex box with the use of a cardboard light-shield, a tracing paper diffusing screen and an electronic flash as with the l^-.in.. column. Photographic conditions were the same as before except that lighting was by means of a Kakonet - II electronic flash unit with a flash duration of 0.5-millisecond. 6o EXPERIMENTAL PROCEDURE 1. COLUMN OPERATION C i t y water'was passed through a Barnstead Bantam BD-1 mixed bed d e m i n e r a l i z e r t o give b e t t e r than 1 megohm-cm. r e s i s t i v i t y water. In a l l experiments the continuous phase was demineralized water and the disp e r s e d phase was t e c h n i c a l grade methyl i s o b u t y l ketone (MIBK) s u p p l i e d by Chemcell L t d . Each phase was kept saturated w i t h the other by ma i n t a i n i n g a l a y e r of one phase i n the feed tank of the other. The fl o w r a t e s of both phases f e d t o the column were r e g u l a t e d w i t h s t a i n l e s s s t e e l needle valves and metered w i t h rotameters. Four d i f f e r e n t drop s i z e - d i s t r i b u t i o n s were produced i n the i f - i n . I.D. column by means of f o u r sets of nozzle t i p s of r e s p e c t i v e average i n s i d e diameters 0.126-in., 0.103-in., 0 .086-in., and 0 .053-in. Only one set of nozzle t i p s of average i n s i d e diameter 0.102-in. was used w i t h the 3-in. I.D. column. The disp e r s e d phase average v e l o c i t y i n the d i s t r i b u t o r n o z z l e t i p s was held a t 0 . 3 6-ft./sec., 0. ' 3 6 - f t . / s e c , 0 .38-ft./'sec., 0 . 6 8-ft./sec., and 0 - 3 7-ft./sec. f o r the-0 . 1 2 6-in., '0 .103-in., 0 .086-in., 0.053-in., 'and 0.102-in. 1. D. t i p s r e s p e c t i v e l y by u t i l i z i n g only a p o r t i o n of the t o t a l nozzle t i p s a v a i l a b l e w i t h the help of T e f l o n caps or plugs as described under the heading Apparatus. The higher nozzle t i p 61 v e l o c i t y of 0 . 6 8-ft./sec. i n the Q.053-in. I . D . t i p s was found to be necessary i n order t o produce drops of a narrow range of s i z e s . The i n t e r f a c e i n the E l g i n head was maintained steady t o w i t h i n t l / l 6 - i n . by c o n t r o l l i n g the f l o w of continuous phase • " - • . ' • -J l e a v i n g the column by means of a s t a i n l e s s s t e e l needle v a l v e . A rotameter, i n s e r i e s w i t h t h i s v a l v e , i n d i c a t e d the f l o w r a t e . The d i s p e r s e d phase fl o w from the column head t o the r e c e i v i n g tank was u n r e s t r i c t e d . 2. SAMPLING TECHNIQUE STUDIES WITH MASS TRANSFER An attempt was made t o r e l a t e the samples taken by the b e l l and hook-probes to samples taken by means of the p i s t o n . E a r l y i n the-work each of the sampling l i n e s l e a d i n g from the b e l l and hook-probes, r e s p e c t i v e l y , used by e a r l i e r workers (38) was replac e d by 27-ft. of smaller bore (3/32-in. I.D.) Nylon t u b i n g . I t was found t h a t a conservative estimate of the minimum purge time f o r each of these new sampling l i n e s was given by the f o l l o w i n g equation. (See Appendix VI) 120 Purge time, (min. ) = — — :—-—•>—-, / . r D sampling r a t e (ml./min,) In a l l Of the work i n v o l v i n g the hook or b e l l - p r o b e d e s c r i b e d i n t h i s t h e s i s these probes were p o s i t i o n e d as c l o s e l y as p o s s i b l e to the centre l i n e of the column. The times f o r the column t o reach steady s t a t e o p e r a t i n g c o n d i t i o n s a t various f l o w r a t e s of . each phase was taken from the work of Bergeron (38), 6 2 I n a l l experiments a c e t i c a c i d was t r a n s f e r r e d from the continuous aqueous phase t o the d i s p e r s e d MIBK phase. At the end of an experiment the aqueous phase product was t r a n s f e r r e d t o the aqueous phase feed tank and the aqueous phase product tank was f i l l e d w i t h d e - i o n i s e d water. This water was used t o back- wash MIBK from the previous run i n the column i n order t o prepare a feedstock of MIBK low i n a c e t i c a c i d c o n c e n t r a t i o n f o r the next run. " The aqueous phase backwashing product was f e d to the aqueous phase feed tank u n t i l the l i q u i d l e v e l i n that tank was about 6 - i n . from the top and then the remainder was fed to the d r a i n . Reagent grade g l a c i a l a c e t i c a c i d , manufactured by N i c h o l s Chemical Corporation L t d . , was used f o r preparing the aqueous a c e t i c a c i d s o l u t i o n used as continuous phase' feed i n the f o l l o w - i n g manner. I f necessary the aqueous phase feed tank was f i l l e d to w i t h i n about s i x inches from the top by adding d e - i o n i s e d water. The contents, of t h i s tank were pumped up t o the aqueous phase constant' head tank and allowed t o run back i n t o the feed tank u n t i l the s o l u t i o n was homogeneous. Homogeneity was checked by p e r i o d i c a l l y t i t r a t i n g the f l o w from the constant head tank w i t h carbonate-free standard sodium hydroxide s o l u t i o n . (The sodium hydroxide s o l u t i o n was prepared as recommended by S w i f t (119) and' was standardized by t i t r a t i n g a g ainst standard potassium hydrogen phthalate s o l u t i o n . ) From a knowledge of the volume of l i q u i d i n the aqueous phase feed tank and the c o n c e n t r a t i o n of a c e t i c a c i d . i n s o l u t i o n i n t h a t tank the amount of g l a c i a l 63 a c e t i c a c i d to be added i n order to produce a s u i t a b l e a c e t i c a c i d concentration,in the aqueous phase feed was c a l c u l a t e d . This amount of g l a c i a l a c e t i c a c i d was poured i n t o the aqueous phase feed tank. The contents of t h i s tank then were c i r c u l a t e d to give a homogeneous sol u t i o n as before. In t h i s study the set of nozzle t i p s of average in s i d e diameter 0.103-in. was used. In most of these experiments a l l of the dispersed phase d i s t r i b u t o r nozzle t i p s were kept open. Therefore a high ketone flowrate was obtained with the use of an average nozzle t i p v e l o c i t y of 0»36-ft./sec. A high ketone flowrate was required i n order to produce a high dispersed phase hold-up so that the a p p l i c a t i o n of Equation 6 i n connection with the piston sampler would r e s u l t i n a small e r r o r i n the c a l c u l - ated value of c A high aqueous phase flowrate was used so that the column was operating under conditions f a r from e q u i l i - brium i n the v i c i n i t y of the piston sampler. Under these con- d i t i o n s solute concentration gradients which are s u b s t a n t i a l l y d i f f e r e n t from zero i n both phases over the piston height are to be expected. Without t h i s condition a comparison between the various sampling techniques would be meaningless. a) Sampling with hook and bell-probes and piston The apparatus was set up as shown i n Figure 13• Each of the b e l l and hook-probes were positioned so that t h e i r respective entrances were below the centre l i n e of the piston. The desired MIBK flowrate i n t o the empty column was established, and aqueous-feed phase wag pumped in t o the column at the maximum possible r a t e . When the i n t e r f a c e reached the desired l e v e l the flowrate of the aqueous continuous phase was reduced to the operatingivalue and the valve c o n t r o l l i n g the aqueous phase flowrate from the foot of the column was opened and adjusted to maintain the i n t e r f a c e l e v e l . A f t e r allowing the column to reach steady state conditions sampling through the probes was commenced. Samples were c o l l e c t e d i n 50^ml. graduated cylinders which were closed with ground-glass stoppers immediately a f t e r the samples were taken. Samples were c o l l e c t e d with each probe at the l o c a t i o n mentioned above. The probes then were moved 1-in. up the column, and a second set of samples was taken. Sets of samples were c o l l e c t e d at an a d d i t i o n a l four 1-in. i n t e r v a l s up the column, When the probe samples had been taken the probes were r a i s e d above the i n t e r f a c e , and a piston sample was c o l l e c t e d a f t e r a half-hour i n t e r v a l ' i n the c a l i b r a t e d customJmade ve s s e l shown i n Figure V - 1, Appendix V. The volumes of each phase i n samples taken with the bell-probe and with the piston were recorded. Sometime during the course of steady state operation column i n l e t and ou t l e t samples of both phases were taken. A l l of the samples containing two phases were shaken vigorously many times i n order to b r i n g the two phases to equilibrium. The concentration of a c e t i c a c i d i n each phase of 65 each sample was determined hy t i t r a t i n g with standard sodium hydroxide.solution using phenolphthalein as i n d i c a t o r . When t i t r a t i n g the MIBK phase SBAG-1K* was added to render the MIBK and aqueous phases m i s c i b l e . In a d d i t i o n to the experiments described above an experiment was performed with a modification of the hook-probe as shown i n the sketch below. b) Sampling with hook and bell-probes, hypodermic needles, and 1 piston • | Short Pyrex spacers were included i n the column above and below the piston block as shown i n Figure Ik. Hypodermic needles * SDAG-lK.is a mixture of 9 0 $ v/v ethanol and 1 0 $ v/v methanol. 66 were inserted through polyethylene gaskets between the spacers i n a manner s i m i l a r to that shown i n Figure V - 2, Appendix V. The minimum purge time' for these needles was found to be less than 4-5-sec. at a sampling rate of 3A-ml./min. In a l l of the work i n v o l v i n g hypodermic needles described i n t h i s thesis a needle was purged for at least -l§--min. before taking a sample. A hypodermic tneedle sample was taken always with the open end of the needle on the centre l i n e of the column unless otherwise i n d i c a t e d . The column was brought to steady state operating conditions and probe samples were taken as before. Then the probes were ra ised above the interface and the column was allowed to a t t a i n steady state operating condit ions. Samples were co l lec ted by means of the hypodermic needles i n the fo l lowing manner. Two needles, separated by not less than 10 inches, were used concurrently, the other needles being- withdrawn to the column w a l l so as not to protrude i n t o the column. The valves at the end of each of the two needles were opened so as to give sampling rates of about l - m l . / m l n . The samples were c o l l e c t e d i n 10-ml. graduated c y l i n d e r s . Af ter the f i n a l hypodermic needle sample was c o l l e c t e d the column was allowed to reach steady state operating conditions and then a piston sample was taken. The concentration of acet ic ac id i n each phase of each sample was determined by t i t r a t i n g with sodium hydroxide s o l u t i o n as before. \ 3- SEARCH FOR SUITABLE TRACER An i n v e s t i g a t i o n and p r e l i m i n a r y t e s t s were made t o f i n d a t r a c e r f o r use i n the determination of a x i a l eddy d i f f u s i v i t i e s w i t h no mass t r a n s f e r between the d i s p e r s e d and the continuous phases. The necessary t r a c e r p r o p e r t i e s are l i s t e d below: a) high s o l u b i l i t y i n MIBK - saturated water, b) i n s o l u b i l i t y i n water - satura t e d MIBK, c) concentration must be measurable a t low values, d) must not d i s t u r b the f l u i d f l o w patterns when i n j e c t e d i n t o an o p e r a t i n g column, e) must not adsorb a t MIBK - water i n t e r f a c e or at any s o l i d - l i q u i d i n t e r f a c e i n the column, f ) must not r e a c t c h e m i c a l l y w i t h water, MIBK, or any s o l i d surface i n the column, and g) the molecular d i f f u s i v i t y i n MIBK -> saturated water must be n e g l i g i b l e compared w i t h the a x i a l eddy d i f f u s i v i t y . The t r a c e r s considered, the method of q u a n t i t a t i v e a n a l y s i s f o r t h e i r c o n c e n t r a t i o n , and t h e i r shortcomings, i f any, are l i s t e d below. a) F e r r i c n i t r a t e . A n a l y s i s f o r t h i s compound would be by the thiocyanate method making use of c o l o r i m e t r y . F e r r i c n i t r a t e hydrolyses i n MIBK-saturated water, f e r r i c hydroxide p r e c i p i t a t i n g . . b) H y d r o c h l o r i c a c i d . A n a l y s i s would be by t i t r a t i o n , Very low concentrations are not e a s i l y measurable. c) Potassium c h l o r i d e . A n a l y s i s would be c a r r i e d out by means of canductimetry. Very low concentrations are not e a s i l y measurable. d) Water soluble dyes. Solutions of these compounds would be analysed c q l o r i m e t r i c a l l y . Even completely i o n i s e d dyes, such as c r y s t a l v i o l e t , d i s s o l v e i n water-saturated MIBK. e) Cupric sulphate. Analysis would be by the dithizone method making use of colorimetry. Dithizone i s quite unstable. f ) Sodium c h l o r i d e . Analysis would be f o r sodium by means of atomic absorption spectrophotometry. The molecular d i f f u s i v i t y of sodium chloride i n water i s 0.00005-ft./hr. at 65°F f o r concentrations between 0 and 1-molar (128). No data i s a v a i l a b l e f o r t h i s d i f f u s i v i t y i n MIBK-saturated water, but i t i s expected that the value would be c l o s e l y s i m i l a r to that for.pure water and t h i s value has been used. A x i a l eddy d i f f u s i v i t i e s i n t h i s work were found to be 2 always greater than 7-ft./hr. Thus the condition that the molecular d i f f u s i v i t y i s n e g l i g i b l e compared with the a x i a l e d d y . d i f f u s i v i t y i s met. A s o l u t i o n of sodium chloride i n MIBK - saturated water was found to be a sui t a b l e t r a c e r . The d i s t r i b u t i o n c o e f f i c i e n t * f o r sodium chloride between MIBK - saturated water and water - saturated MIBK was found to be 7060. * The d i s t r i b u t i o n c o e f f i c i e n t i s defined here as the concen- - t r a t i o n of sodium chjoride i n the aqueous layer divided by the concentration of that compound i n the ketone layer where concentrations are expressed i n the uni t s of weight per un i t volume of s o l u t i o n . 4. SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER The apparatus was set up as shown i n Figures 9 and 14 w i t h the f o l l o w i n g m o d i f i c a t i o n s . The t h i r d polyethylene gasket below the p i s t o n was exchanged w i t h the T e f l o n gasket f u r t h e r down the column. The hypodermic needle supporting the t r a c e r . d i s t r i b u t o r remained i n t h i s T e f l o n gasket so t h a t there were only two hypodermic needle sampling p o s i t i o n s between the t r a c e r d i s t r i b u t o r and the p i s t o n . The MIBK l e a v i n g the E l g i n head passed d i r e c t l y t o the MIBK feed tank. The aqueous and MIBK feedstocks were f r e e o f " a c e t i c a c i d . The flows of MIBK and aqueous phases were s t a r t e d and the i n t e r f a c e l e v e l was e s t a b l i s h e d as described i n the present s e c t i o n of the t h e s i s under the heading 1: Column Operation. The experiments were performed under the f o l l o w i n g o p e r a t i n g c o n d i t i o n s Continuous, phase Dispersed phase s u p e r f i c i a l v e l o c i t y , s u p e r f i c i a l v e l o c i t y , f t ? / h r . f t ? . f t ? / h r . f t 2 36.5 128 36.5 30.4 27.7 '- 128 A one molar sodium c h l o r i d e t r a c e r feed s o l u t i o n was prepared by d i s s o l v i n g a weighed amount of sodium c h l o r i d e i n MIBK - saturated water (H9)- This s o l u t i o n was s t a r t e d i n t o the column as soon as the i n t e r f a c e , l e v e l had been e s t a b l i s h e d i n the E l g i n head. The column was run f o r one hour t o a l l o w steady s t a t e c o n d i t i o n s t o be a t t a i n e d . (Experiments f o r the study of steady s t a t e times are discussed l a t e r . ) F i v e hook- probe samples were taken from equally spaced positions throughout the height of the piston block. The hook-probe sampling rate was .5-ml./min.• Four hypodermic needle samples were taken, one through each of the gaskets immediately above and below the piston block, and one through each of those approximately s i x inches above and below the piston block. F i n a l l y a piston sample was taken. Half hour time i n t e r v a l s were allowed between taking each probe sample, between taking the l a s t probe sample and the f i r s t hypodermic needle sample, and between taking the l a s t hypodermic needle sample and the piston sample. The aqueous phase of each sample was analysed f o r sodium by means Of a Perkin-Elmer 303 atomic absorption spectrophotometer. 5. AXIAL EDDY DIFFUSIVITY AND DISPERSED PHASE HOLD-UP a) Studies i n the l f - I n . . I.D. column. I n i t i a l l y a few experiments were performed i n order to see whether or not the dispersion model would describe the experimental data adequately and, therefore, whether or not a x i a l eddy d i f f u s i v i t i e s could be determined from t h i s model. These experiments were c a r r i e d out i n a manner i d e n t i c a l to that f o r the main bulk of experiments which i s described below. I t was found that a p l o t of the logarithm of the concentration of t r a c e r versus height up the column was l i n e a r ; accordingly the di s p e r s i o n model was adopted. In addition, before the main bulk of experimental data was c o l l e c t e d some experiments were c a r r i e d out to j u s t i f y some of the experimental techniques used. Since these experi- ments usually were c a r r i e d out i n conjunction with a x i a l eddy, d i f f u s i v i t y determinations t h e i r d e s c r i p t i o n w i l l be given following that of the main experiments. The apparatus used f o r the subsidiary experiments described under i i ) to v i i i ) i n c l u s i v e below was i d e n t i c a l to that used f o r the main experi- ments. i ) A x i a l eddy d i f f u s i v i t y determinations. The column was set up as shown i n Figures 9 and 10 except that the MIBK l i n e from the E l g i n head l e d d i r e c t l y to the MIBK feed tank so that MIBK recycled through the apparatus. As required, some nozzle t i p s of the dispersed phase d i s t r i b - utor were blocked o f f with Teflon caps or plugs according to the. patterns shown i n Figures 15 to 18 to ensure the desired average v e l o c i t y of dispersed phase i n the nozzle t i p s . The flow of MIBK i n t o the column was started, and thereafter maintained at the desired r a t e . Water was pumped i n t o the column at the maximum possible rate u n t i l the int e r f a c e i n the E l g i n head reached a predetermined l e v e l . The flowrate of water was then reduced to the experimental value and water was allowed to leave, the column at such a rate so as to maintain the desired constant i n t e r f a c e l e v e l . The tra c e r (l-molar sodium chloride s o l u t i o n i n MIBK - saturated water) was fed to the column at approximately 1$ of the volumetric flowrate of the aqueous phase. A f t e r allowing the column to reach steady state operating conditions ten aqueous phase samples were taken by means of the hypodermic needles, one at a time. The f i r s t sample was taken with, the lowest needle in the column, the second sample from the next needle up the column, and so on. The samples were withdrawn from the centre of the column and at a rate less than 1-5$ of the volumetric flowrate of aqueous phase though the column. The description of experiments performed to investigate radial concentration gradients and also the effect of sampling rate upon the column operation are discussed later. When a hypodermic needle was not "being used i t was withdrawn to the column wall.. The flowrate of each phase from the column was determined by weighing a sample collected over a suitable time interval. The average of the temperatures of the fluids in the upper and lower sections of the Elgin head, of the fluid at the lower end of the column, and of the ketone phase entering the column was recorded. Finally three piston samples were taken at intervals of ten minutes and the volumes of the two phases in each sample recorded. The tracer concentration in each of the ten hypodermic needle samples and in the aqueous phase leaving the column were measured by means of an atomic absorption, spectrophotometer. (Analysis was for sodium.) The calibration line for the atomic absorption spectrophotometer always was found to be a straight line. The equation for this line was cal- culated by the method of least squares. Samples whose concen- trations were less than 0.05-microgm. sodium/ml. were discarded on the grounds of unreliability. The probable error in the concentration of a sample determined by this method was less than 2 $ . Experiments were performed at a l l p o s s i b l e combinations of the f o l l o w i n g o p erating c o n d i t i o n s . continuous phase d i s p e r s e d phase nozzle t i p s u p e r f i c i a l v e l o c i t y , s u p e r f i c i a l v e l o c i t y , average i n s i d e f t ? / h r . f t 2 f t ? / h r . f t 2 diameter, i n . 9-0 36.5 0.053 18.2 54.7 0.086 27.7 -73-0 0.103 36.5 91.2 0.126 kQ.k ' 110 128 . For each set of nozzle t i p s about 10 photographs of the drops w i t h i n the column were taken as described e a r l i e r under the heading Apparatus a t the o p e r a t i n g c o n d i t i o n s shown i n each l i n e shown i n the f o l l o w i n g t a b l e . continuous phase di s p e r s e d phase s u p e r f i c i a l v e l o c i t y , s u p e r f i c i a l v e l o c i t y , f t ? / h r . f t 2 f t ? / h r . f t 2 9.0 36.5 27.7 36.5 kQ.k 36.5 27.7 54.7 27.7 91-2 Some, but not a l l , of the photographs were taken d u r i n g runs f o r determining a x i a l eddy d i f f u s i v i t i e s . However, those not taken d u r i n g runs were taken under column o p e r a t i n g con- d i t i o n s i d e n t i c a l to those which a p p l i e d d u r i n g runs. The photographic negatives were examined by means of a Recordak model M.P.E. m i c r o f i l m reader. The drop s i z e d i s t r i b u t i o n s were determined by measuring the v e r t i c a l and h o r i z o n t a l dimensions of the p r o j e c t e d images of the' drops. With the photographic Ik conditions described e a r l i e r the depth of focus included the whole of the column cross-section. Only the drops l y i n g within the c e n t r a l U6$> of the column image, as projected on the screen, ware examined, because as determined by experiments described below, the drops f a l l i n g within these l i m i t s were not d i s t o r t e d o p t i c a l l y . Five hundred drops were measured f o r each set of column operating conditions given i n the l a s t t a b l e . i i ) O p t i c a l d i s t o r t i o n of drops. As mentioned e a r l i e r o p t i c a l d i s t o r t i o n was reduced con- siderably by surrounding the round glass column with a f l a t - s i d e d Perspex box. D e t a i l s of the box are presented i n Appendix V. The space between the box and the column was f i l l e d with d i s t i l l e d water. The same photographic conditions were used f o r the c a l i b r a t i o n photographs as f o r the photographs taken to determine drop siz e d i s t r i b u t i o n s as described under the heading Apparatus. The same 6 - i n . long section of column was used f o r the c a l i b - rations as was used f o r the a c t u a l drop size d i s t r i b u t i o n measurements. The Perspex box was not shielded from extraneous l i g h t as i n the drop size d i s t r i b u t i o n studies since the photo- graphs were taken i n a darkroom. Photographs were taken of a 5 / 3 2-in. diameter b a l l bearing s i l v e r soldered to a s t a i n l e s s s t e e l wire. The b a l l ! was photographed at positions shown i n Figure 2 3 f o r each of the h o r i z o n t a l planes located -§-in. above and ^--in. below the centre of the Perspexbox. Two sets 7 5 FIGURE 23. OPTICAL DISTORTION INVESTIGATION, lf-IN. I.D. COLUMN of photographs were taken, one with MIBK - saturated water, and one with a s o l u t i o n of sodium chloride i n MIBK - saturated water i n the column. For t h i s second s o l u t i o n the concentration of sodium was lOO-microgm./ml. i i i ) E f f e c t of t r a c e r feed rate The feed rate of t r a c e r s o l u t i o n i n t o the column should "be low enough so as not to disturb the f l u i d flow patterns within the column. The e f f e c t of t r a c e r feed rate was studied using the s u p e r f i c i a l v e l o c i t i e s of the two phases, and of the tr a c e r feed s o l u t i o n supplied to the column, given i n each l i n e of the following table. Only the nozzle t i p s of 0.103- i n . I. D. were used f o r t h i s study. Continuous phase, Dispersed phase, Tracer s o l u t i o n , f t ? / h r . f t ? ; . f t ? / h r . f t ? f t ? / h r . f t ? 27-7 . ••' 30.4 . , 0.16 27-7 '• 30.4 : 0.31 27.7 - 30.4 0.62 18.2 • . •• . 73 0.10 18.2 73 '. 0.20 18.2 . 73 0.40 i v ) Steady-state time. The experimental conditions f o r sections i v ) to v i i i ) i n c l u s i v e are shown i n each l i n e of the following table Continuous phase - s u p e r f i c i a l v e l o c i t y , Dispersed phase s u p e r f i c i a l v e l o c i t y , f t ? / h r . f t 2 f t ? / h r . f t 2 9 9 27-7 128 30.4 30.4 The time taken f o r the column to reach steady state operating conditions was estimated by taking samples by means of the f i r s t , fourth, seventh, and tenth hypodermic needles above the trace r d i s t r i b u t o r , and also by c o l l e c t i n g aqueous phase leaving the column. One of each of these samples was taken between 3-min. and 21-min. a f t e r start-up and then at i n t e r v a l s varying between 5 _ m i n > and 30-min. u n t i l 2-hr. a f t e r start-up. v) R e p r o d u c i b i l i t y of r e s u l t s . Several of the experiments f o r determining a x i a l eddy d i f f u s i v i t y and hold-up were repeated under i d e n t i c a l operating conditions i n order to te s t the r e p r o d u c i b i l i t y of r e s u l t s . v i ) Cross-sectional homogeneity. In ad d i t i o n to the sample taken from the centre of the column by means of the hypodermic needle immediately above the trace r d i s t r i b u t o r four samples were taken at the same elevation but at posit i o n s on a 1-in. c i r c l e concentric with the column. This experiment was c a r r i e d out f o r each of the runs l i s t e d i n section i v ) above. 78 v i i ) . E f f e c t of sampling r a t e . Samples.of the continuous phase were taken at 0.25-ml./min., 0.'75-ml./min.•, and 1.5-ml./min. f o r the continuous phase s u p e r f i c i a l v e l o c i t y of 9-ft./hr. f t . and at 0.5-ml./min., l.O-ml./min., and 2.O-ml./min.' f o r the continuous phase s u p e r f i c i a l v e l o c i t y of O p • ' 27-7-ft./hr. f t f Only the f i r s t four sampling positions above the tra c e r d i s t r i b u t o r were studied. v i i i ) E f f e c t of order of sampling. •'„ ' . Samples were taken consecutively from the lowest sampling p o s i t i o n up to the highest one. A second set of samples was taken with t h i s sampling order reversed. Both sampling orders were used i n each of the experiments described i n the table given i n section i v ) . i x ) E f f e c t of column length.. In a d d i t i o n to-the standard experiments performed with the column of height 10-ft. 3 l / 8 - i n . , as shown i n Figure 10, a single experiment was performed i n each of two other columns, one of height 6 - f t . ' 3 f - i n . , a n d t h e other of height l 6 - f t . Uf-in. as shown i n Figures 11 and 12 r e s p e c t i v e l y . Each of these l a s t two experiments was c a r r i e d out with a continuous phase s u p e r f i c i a l v e l o c i t y o f \ l 8 , 2 - f t i / h r . f t . , and a dispersed phase o 2 s u p e r f i c i a l v e l o c i t y of 5^-7-ft./hr.: f t . The average I.D. of the nozzle t i p s i n both experiments was 0.103-in. b) Studies i n the 3-in. I.D. column. Although the great bulk of the work described i n t h i s t hesis was c a r r i e d out i n a l ^ - i n . I.D. column, some tracer experiments were c a r r i e d out i n a 3-in. I.D. column. This column i s shown i n Figure 20 and a flowsheet i s given i n Figure 21. In order to produce a continuous phase s u p e r f i c i a l v e l o c i t y i n the column greater than lOO-ft./hr. f t . i t was necessary to pressurize the aqueous phase feed tanks to 15 p . s . i . g . with nitrogen.. Only one set of nozzle t i p s of 0.102-in. average I.D. was used. I t was not possible to measure the dispersed phase hold-up because a piston sampler f o r t h i s column was not a v a i l a b l e . As with the l-jjf-in. I.D. column, experiments were ca r r i e d out i n conjunction with the a x i a l eddy d i f f u s i v i t y experiments to j u s t i f y some of the experimental techniques used f o r the 3-in. I.D. column. The experiments with t h i s column are described below. i ) O p t i c a l d i s t o r t i o n of drops. The photographic t e s t section was a 6-In. long, 3-in. I.D. length of Pyrex Double Tough glass pipe which was cut from a 1-ft. long flanged section as described e a r l i e r . This pipe was surrounded by a f l a t - s i d e d Perspex box and the space between the pipe and the box was f i l l e d with d i s t i l l e d water. The photographic c o n d i t i o n s were s i m i l a r t o those used f o r the l - | - i n . I.D. column* A Kakonet - I I e l e c t r o n i c f l a s h u n i t was used f o r l i g h t i n g purposes. Photographs were taken of a 5/32-in. diameter b a l l b e a r i n g . The b a l l was photographed at p o s i t i o n s shown i n Figure 2k f o r each of the h o r i z o n t a l planes l o c a t e d 1-^-in. above and 1-^-in. below the centre of the Perspex box. Two sets of photographs, were taken, one w i t h MIBK - saturated water, and one w i t h a s o l u t i o n of sodium c h l o r i d e i n MIBK - saturated water i n the column. For t h i s second s o l u t i o n the concentration of sodium was 100-microgin./ml. i i ) Steady-state time. The experimental c o n d i t i o n s f o r s e c t i o n s i i ) and i i i ) are given i n each l i n e of the f o l l o w i n g t a b l e . Column I.D. = 3-in. .Average nozzle t i p I.D. = 0.102-in. Continuous phase s u p e r f i c i a l v e l o c i t y , ft?/hr... f t ? . • 18.2 .100 • 18.2 Samples were taken..by means, of the f i r s t , f o u r t h , seventh, and tenth hypodermic needles above the t r a c e r d i s t r i b u t o r , and a l s o by c o l l e c t i n g aqueous phase l e a v i n g the column. One of each of Dispersed phase s u p e r f i c i a l v e l o c i t y , f t ^ / h r . f t ? , 36.5 36.5 109 , 81 CAMERA FIGURE 2k. OPTICAL DISTORTION INVESTIGATION, 3-IN. I.D. COLUMN 82 these samples was taken between 2-min. and 10-rmin. after start- up and. then. at intervals varying between 5-min- and 30-min. until 1^-hr. after start-up. i i i ) Reproducibility of results. Several of the experiments for. determining axial eddy diffus- ivity were repeated under identical operating conditions in order to test the reproducibility of results. . iv) Cross-sectional homogeneity. In addition to the samples taken from the centre of the column by means of the first and fifth hypodermic needles above the tracer distributor samples were taken, from; positions; 'shown in the following sketch at each of the two above mentioned sampling elevations. These sets of samples were collected for each of the column operating conditions shown in the following table. . Continuous, phase superficial'velocity, . ft-Vhr. f t 2 18.2 100 18.2 100 18.2 100 Dispersed "phase superficial velocity, ft?/hr. f t 2 36.5 • 36.5 73 73 109 109 83 v) A x i a l eddy d i f f u s i v i t y determinations. The experiments performed to determine a x i a l eddy d i f f u s - i v i t i e s were c a r r i e d out i n a manner s i m i l a r to that f o r the l f - i n . I.D. column. . The experimental conditions are given i n Table IV-5, Appendix IV. A sampling rate of 3-nil./min. was used i n a l l experiments i n the 3-in* I«D. column. Photographs were taken of the f l u i d s within the c a l i b r a t e d glass section described e a r l i e r which was i n s t a l l e d as the eighth 6 - i n . section above the t r a c e r d i s t r i b u t o r . This section of column' was surrounded by a f l a t - s i d e d Perspex box as shown i n Appendix V. The photographic conditions were s i m i l a r to those used f o r the i f - i n . I.D. column. A Kakonet - II e l e c t r o n i c f l a s h u n i t was used f o r l i g h t i n g purposes. The column operating c o n d i t i o n s f o r which photographs were taken are shown i n each l i n e of the f o l l o w i n g t a b l e . Continuous phase s u p e r f i c i a l v e l o c i t y , f t ? / h r . f t 2 . 18.2 36.5 75 • 220 6. CONCENTRATION PROFILES WITH MASS TRANSFER The l f - i n . I.D. column was set up as shown i n Figures 9 and 10. The t r a c e r d i s t r i b u t o r , and the T e f l o n gasket through which the t r a c e r supply hypodermic needle passed, were replaced by a standard l / l 6 - i n . t h i c k T e f l o n gasket. A c e t i c a c i d was t r a n s f e r r e d from the continuous phase to the d i s p e r s e d phase. The concentration p r o f i l e i n each phase was measured.by means of the b e l l - p r o b e and hypodermic needles as d e s c r i b e d below. , The column was brought t o the o p e r a t i n g c o n d i t i o n as described under s e c t i o n 2 of Experimental Procedure. The times at which steady s t a t e c o n d i t i o n s were a t t a i n e d were determined by t a k i n g samples by means of the lowest and the highest hypo- dermic needles and of the aqueous phase l e a v i n g the column at various times a f t e r s t a r t - u p . A l l hypodermic needle samples i n t h i s p a r t of the work were taken at S/^-ml./min. During a c t u a l runs samples were taken w i t h the b e l l - p r o b e at the l e v e l s Dispersed phase s u p e r f i c i a l v e l o c i t y , T t J / h r . f t 2 36.5 36.5 36.5 36.5 of the f i r s t , t h i r d , f i f t h , seventh, ninth, and tenth hypo- dermic needles up the column, A bell-probe sampling rate of 5.2-ml./min. was used fori each sample taken. Samples were not taken by means of the bell-probe at a l l l e v e l s of the needles because of the lengthy procedure of sampling with the b e l l - probe. The bell-probe was r a i s e d above the int e r f a c e and a f t e r a half-hour i n t e r v a l aqueous phase samples were taken with the hypodermic needles consecutively s t a r t i n g with the lowest one. Samples of the i n l e t and out l e t streams of the column were taken at the beginning of steady-state operation, a f t e r the b e l l - probe samples had been taken, and a f t e r the hypodermic needle samples had been taken. F i n a l l y a piston sample was taken i n order to measure the dispersed phase hold-up. Each bell-probe sample was shaken, vigorously many times to b r i n g the two phases to equilibrium. Each phase of each sample was analysed f o r ac e t i c a c i d by t i t r a t i n g with standard sodium hydroxide so l u t i o n as described e a r l i e r . The column Operating conditions studied are given i n each l i n e of the fol l o w i n g table. Run Continuous phase Dispersed phase s u p e r f i c i a l v e l o c i t y , • s u p e r f i c i a l v e l o c i t y , , • f t ^ / h r . f t ? ' f t ^ / h r . f t ? J l 36.5 5̂ -7 . J2 ' • 18.2 5U.7 J3 :; 36.5 91.2 jk k&.k 91.2 J5 kQ.k 128 RESULTS AND DISCUSSION An i n i t i a l I n v e s t i g a t i o n was undertaken to assess various methods of removing samples of e i t h e r phase from the o p e r a t i n g spray column. Previous measurements of c o n c e n t r a t i o n p r o f i l e s w i t h i n a l i q u i d - l i q u i d e x t r a c t i o n spray column a t The U n i v e r s i t y of B r i t i s h Columbia, i n v o l v e d the t a k i n g of samples by means of the hook, and the b e l l - p r o b e s mentioned e a r l i e r (35, 37, 38, 39). As discussed under the heading I n t r o d u c t i o n some doubt e x i s t e d as t o whether the s o l u t e concentration i n the Continuous phase e n t e r i n g the hook-probe:was the same as t h a t i n the continuous phase entering, the b e l l - p r o b e along w i t h the drops. A c c o r d i n g l y various methods of sampling of the phases were i n v e s t i g a t e d i n t h i s work. A d i s c u s s i o n of the: r e s u l t s - of the ,. sampling technique s t u d i e s i s presented as a whole a f t e r a l l of these r e s u l t s are given. This procedure' has been adopted i n order t h a t comparisons and c o n t r a s t s between the r e s u l t s of various i n v e s t i g a t i o n s can be seen more e a s i l y . 1 . . RESULTS OF SAMPLING TECHNIQUE STUDIES a) Sampling w i t h hook and b e l l - p r o b e s and p i s t o n w i t h mass t r a n s f e r between the phases. Samples were taken from the o p e r a t i n g spray column w i t h the hook and the b e l l - p r o b e s at v a r i o u s l o c a t i o n s shown f o r a t y p i c a l run i n the abscissa of Figure 2 5 - In each such run a piston sample also was taken. The concentration of a c e t i c a c i d i n the ketone phase of a bell-probe sample was calculated by means.of equation 6 as described e a r l i e r . V a , C / a \ CD = C D + F T ( C C " C C } 6 The value of c^ was taken to be the concentration of a c e t i c a c i d i n the hook-probe sample taken from the same sampling elevation as the bell-probe sample. An average concentration i n each phase over the piston height was determined from the r e s u l t s obtained with each probe by graphical i n t e g r a t i o n of the respective concentration p r o f i l e s of the. sort shown i n Figure 2 5 ' The average concentration of a c e t i c a c i d i n the ketone phase of the piston sample was calculated by means of Equation 6 where c^ was taken to be the average concentration i n the aqueous phase over the piston height calculated from the hook-probe sample r e s u l t s - I t i s assumed that backmixing of the continuous phase can be represented by "packets" of continuous phase r i s i n g with the dispersed phase drops. Presumably these "packets" are, i n f a c t , mainly the wakes of r i s i n g drops*. On t h i s basis i t i s shown i n Appendix I I I that f o r a piston sample the average concentration of a c e t i c . a c i d i n the continuous phase, excluding that i n * Note that the d e r i v a t i o n of Equation III-8 i n Appendix I I I i s general i n that wakes are. not mentioned. In the model used there c^ i s the average concentration of solute i n the descending continuous.phase at the ele v a t i o n under consideration. such wakes, i s given by Equation III-8. c C I I I - 8 The average concentration of a c e t i c . a c i d i n the dispersed phase of each piston sample was calculated a second time by means of Equation 6. However, instead of'using c p from the hook-pro^e sample r e s u l t s as mentioned above, c was determined from Equation - . 111-8.applied to the piston sample. The r e s u l t s of sampling the phases, i n the operating spray column with the hook and the bell-probes and the piston f o r each of several runs are given i n Table 3 - The r e s u l t s of a t y p i c a l experimental run are shown gra p h i c a l l y i n Figure. 2 5 » b) Sampling with hook and'bell-probes, hypodermic needles, and piston with mass t r a n s f e r between the phases. Further runs were made i n which samples were taken as j u s t described under a') but i n which continuous •. phase samples also were withdrawn by means of hypodermic needles i n order to provide an independent check on the hook-probe sample r e s u l t s . In add i t i o n to the average concentrations over the piston height calculated as described under a) a l l c a l c u l a t i o n s Involving the hook-probe were repeated f o r the hypodermic needle r e s u l t s . TABLE 3. SAMPLING STUDIES WITH HOOK AND BELL PROBES AND PISTON Run S u p e r f i c i a l flowrates ft3/hr.ft?- Concentration of a c e t i c a c i d at the time of sampling, .'. . •_ . :• . lb.-moles/ft?- x "1(P" -• • • Hook- probe sampling rate, , ml./min. B e l l - probe sampling rate, ml./min. Q B e l l and hook probes at p o s i t i o n Aver- age i n piston by hook and piston " Average over piston height by hook and b e l l Average i n piston by Equations I I I - 8 and 6 1 2 3 " 4 5 * 6 7 2 a 92.5 90.4 46.8 18.6 48.0 19.I 48 .8 20.4 49.4 ,21.3 50.0 22.3 50.7 21.9 50.7 22.4 49.4 20.9 49.4 21.1 49.5 21.6 8.6 20 4 93-7 12^. 55-1 21.6 " 54.6 2^.5 57-3 2^.4 58.0 23.9 58.6 24.0 59-6 24.2 60.1 25 .0 58.0 : 10.6 i 58.0 2^.8 55.8 P 1 . 6 •8.6 20 5 b . 69.O 7k: k - 60.7 25.8 62.3 2 5 . 5 63.7 26.8 64.5 2 7 . 1 65.1 28.5 65.6 27.5 63.2 13.8 , 63.2 26.6 62.3 23.^ 8.6 17 6 87.5 11^. ^3-9 18.2 45.2 18.7 45.9 1 9 . 5 46.3 1 0 . 7 46.5 IQ . 4 47.2 20.1 46.8 PQ-7 46.1/ 16.0 46 .1 . 45.5 1Q . 0 4 17 7 87.5 11^. 3k.Q ik.6 39-6 Ik.6 40.5 1 5 . 1 40.7 15 . 6 ki.3 16.1 41.7 16.6 42.3 T5.9 40.8 40.8 1 5 . 5 39-5 .15.5 5 20 8 C ' 87.5 113. 4 0 . 1 4 0 . 2 42.2 4 l . 7 43.2 41.7 .41.7 40.4 5 - 9 d 87.5 - i ; L 3 r 33-0 13.2 35.5 .13.2 35-0 14.1 35.7 13.8 36.2 14.4 36.7 .14.6 36.9 14.6. 35.6 12.7 35-6 14.0 35.3 14.2 5 17 For each run the upper number i n each column ref e r s to the continuous phase, the lower number to the dispersed phase. Each run was c a r r i e d out at room temperature. The hook-probe was 0.9 inches above the sampling-.position indicated. The values shown f o r the respective concentrations of a c e t i c a c i d i n the hook probe samples have been taken from a plot of the measured concentrations versus distance up the column. 'The b e l l -probe was above the interface throughout the run. ^The hook-probe was modified as shown i n the sketch on page The positions at which samples were taken are indicated by. number i n the abscissa of Figure 25- 90 0 0 5 u. z> <-> 0 0 4 — CO UJ X T • CONTINUOUS PHASE i GO* a o < o o < o z o & or j — z . o z o o 0 0 2 0 0 1 0 0 0 DISPERSED PHASE . RUN 6 - O Q a O A BY BY HOOK-PROBE BELL-PROBE,HOOK-PROBE 8 EQN. 6 AQUEOUS PHASE OF PISTON SAMPLE BY EQN. Ill- 8 KETONE PHASE OF PISTON SAMPLE BY EQNS. III-3 a 6 KETONE PHASE OF RSTON SAMPLE BY HOOK a PISTON 4 ' — 4 2 PISTON SAMPLER 3 4 5 6 SAMPLING POSITION, SCALE FIGURE 25. SAMPLING TECHNIQUE STUDIES WITH HOOK AND BELL-PROBES AND PISTON Table h shows the r e s u l t s of sampling with the hypodermic needles, and fur t h e r r e s u l t s obtained with.the hook and the b e l l - probes and the piston. The r e s u l t s of a t y p i c a l experimental run are shown - g r a p h i c a l l y i n Figure 26. c) Sampling with hook-probes, hypodermic needles; and piston with no mass transfer, between the phases. For each run a s t r a i g h t . l i n e was f i t t e d by the method of l e a s t squares to a p l o t of the natural logarithm of the solute • concentration versus height up the column f o r the hook-probe r e s u l t s and the hypodermic needle, r e s u l t s r e s p e c t i v e l y . The equation f o r t h i s s t r a i g h t l i n e was transformed i n t o the equation f o r the concentration-versus height up the column. Integration of the transformed.equation produced an average concentration-over the piston height. The average concentration of solute i n the continuous phase of a piston sample was determined d i r e c t l y by a n a l y s i s f o r solute. This concentration included the.contribution of. the wakes. The r e s u l t s of sampling technique studies under conditions of no mass t r a n s f e r are presented i n Table 5« The r e s u l t s of a t y p i c a l run are shown gr a p h i c a l l y i n Figure 27• 2. DISCUSSION OF SAMPLING TECHNIQUE STUDIES In order to understand' f u l l y what material enters a sampling device i t would be necessary to know exactly the concentration of solute at every point i n the column and TABL1 3 k. SAMPLING STUDIES WITH HOOK AND BELL-PROBES. HYPODERMIC NEEDLES. AND PISTON Run S u p e r f i c i a l flowrate, „ f t . / h r . f t . Concentration of ac e t i c a c i d at the time of sampling, l b . -moles/ft -?xio ' 3 B e l l and hook probes at p o s i t i o n Hook-probe sampling B e l l -prooe. sampling mS.^Ain. D 1 -3. 5 7 G H 13 a ., 15 16 87.5 113- 87.5 . 113. 87.5 11^. 28.9 9.87 26.8 9.83 27.3 9.6 29.6 10.6 27.3 10.2, 28.1? 1 0 . ? 29.9 10.9 28.2 10.5 b 29-7 b 10.9 30.9 11-3 28.9 i o . a 2 9 . % 10.8 b 31.8 11.9 29.2 11.2 31.0 11.8 32.h 12.U 5 5 5 17 17 17 Concentration of a c e t i c a c i d at the time of sampling, lb.-moles/ft. x 10 Run hypodermic needle at pos i t i o n B D E G H average over piston height by means of hook and b e l l - probes hypod- -ermic needles and b e l l - probe average i n piston by means of hypod- -ermic needles and pi s t o n hook- probe and piston equations I I I - 8 and 6 13= 15 16 26.5 25-3 25-3 27.6 26.O 26.3 27-3 26.3 27.O 28 .h- 26.3 27-3 .28.8 27.0 27.0 30.9 28.9 29-9 31.8 29.U 30.4 31.8 29.J+ 30.4 32.3 29.9 3l>h 33-3 30.7 32.3 30.5 • 11.0 '• 28. k 10.7 29.1 11.7 29.9 11.0 28.0 10.7 28.9 11.7 29-9 11.3 28.0 lo.k 28.9 11.1 30.5 8.3 28. k 8.3 29.1 10.0 30.1 10.5 27.9 10.3' 28.9 10.3 ^For each run the upper number i n each column r e f e r s to the continuous phase, the lower number to the ^dispersed phase. Each run was car r i e d out at room temperature. cSamples were taken 5/8-in. above the p o s i t i o n indicated. * The posi t i o n s at which samples were taken are indicated by number or l e t t e r i n the abscissa of Figure 26. - . 93 CONTINUOUS PHASE 0009 O007 DISPERSED PHASE - RUN 13 - O A 9 • o BY HOOK-PROBE BY HYPODERMIC NEEDLES BY BELL-PROBE, HOOK-PROBE, 8 EQN. 6 AQUEOUS PHASE OF PISTON SAMPLE BY EQN. 111-8 KETONE PHASE OF PISTON SAMPLE BY NEEDLES a KETONE PHASE OF PISTON SAMPLE BY EQNSjIP^a 6 KETONE PHASE OF PISTON SAMPLE BY HOOK 8 PISTON L PISTON _ J ~" A B C D E •SAMPLER'^ F G H j 1 2 3 4 5 6 7 SAMPLING POSITION, SCALE :K-Hl " FIGURE 26. SAMPLING TECHNIQUE STUDIES WITH HOOK AND BELL-PROBES, HYPODERMIC NEEDLES AND PISTON TABLE 5. SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER Sodium concentrations, microgm./ml. Run Hypodermic needle samples Hook-probe samples P i s - ton sam- ple LC> ' f t ? / h r . f t . 3 / h r . 0 Height above piston centre, i n . Aver- age over piston Height above piston centre, i n . Avert- age over piston Temp. °F f t ? f t ? -8.96 -2.90 2.9 8.96 -2.88 - l A 4 0.0 1.44 2.88 ^3 36.5 128. 12.6 2.0 0.25 0.035 6.7k i . 7 1 O.98 0.60 0.39 0.22 O.67' 0.65 Ik 44 36.5 73- 35-2 8.0 1-5 0-33 3.6 7-0 k.7 3-5 2.6 1-7 3.62 3-6 73 44a 36.5 128 15 .8 1.6 0.21 0.03 O.63 I .67 1.03 0.67 O.36 0.24 0.68 O.63 7^ 44b 27-T 128. 47.0 6.6 1.6 0.31 3.72 7 A 5.3 3-6 2.8 1.7 3,9 3.8 73 69 36.5 30.4 110. 61.3 3^.9 19.8 46.8 60.2 54.6 46.0 39,8 3^.2 46,3 46,1 72 VO 50 o o tr ¥ l 0 f - O 0 00 o fee Q: h- 2 UJ z I o o 0-5 •i-J L__J_ RUN 4 4 tr o HOOK-PROBE • HYPODERMIC NEEDL * I »; L — i _ _ J • » -8 -6 - 4 - 2 0 6 8 HEIGHT ABOVE PISTON CENTRE, IN. FIGURE 27. SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER I. from which, point every volume element of the sample originated. Although i t turns out that some conclusions can be drawn f o r the case of no mass transf e r between the phases, s u f f i c i e n t knowledge i s not a v a i l a b l e to do so f o r the case of mass tra n s f e r . Fortunately the bulk of the work described i n t h i s thesis deals with the case where conclusions can be drawn: measurement of a x i a l e d d y . d i f f u s i v i t i e s where no mass transf e r between the phases occured. The comparative s i m p l i c i t y of the sampling techniques i n the absence of mass t r a n s f e r suggests that the r e s u l t s of these studies be discussed f i r s t . Under conditions of no mass tr a n s f e r the measured concentration of solute i n the continuous phase of a piston sample i s the average concentration i n that phase over the piston height at the time of sampling. This average takes into account r a d i a l and a x i a l v a r i a t i o n s i n concentration, and includes the appropriate contributions from the descending continuous phase and from the r i s i n g aqueous phase i n the wakes. I t can be seen from Table 5 that the average solute concentration i n a piston sample i s found to be, to a l l intents and purposes, the same as the average solute concentration over the piston height calculated from the hook-probe or the hypodermic needle r e s u l t s . Therefore e i t h e r the hook-probe or the hypodermic needles can be used to give the average concentration of solute i n the continuous phase of a spray column under conditions applicable when t r a c e r studies are being c a r r i e d out. 97 Although, as mentioned under the heading Theory, the dispersion model envisages no r a d i a l concentration differences i n the continuous phase, presumably such do occur i n operating columns, f o r example i n the wakes of r i s i n g drops. However, i f the dispersion model i s to be applied some average concentration must be used, and that obtained from a piston sample (and also, as shown i n Table 5, hy means of the hook-probe or the hypodermic needles) would seem to be a reasonable choice. Due to the many p r a c t i c a l problems which would be encountered i n incorporating several piston samplers along the length of the column and of the lengthy purge time needed i n taking hook-probe samples hypodermic needles have been used f o r taking samples i n the work in v o l v i n g t r a c e r studies of a x i a l eddy d i f f u s i v i t y . With t h i s r a t i o n a l e f o r the use of the hypodermic needles established, i t i s i n t e r e s t i n g to speculate on the mechanism l y i n g behind the agreement noted i n Table 5 between hypodermic needles, and hook-probe r e s u l t s under conditions of no mass tran s f e r . Among the tenable postulates are the two a l t e r n a t i v e s that e i t h e r the hook-probe and the hypodermic needles both sample the descending continuous phase and the r i s i n g wakes representatively, or the contribution of the wakes to the average solute concentration i n a piston sample i s n e g l i g i b l e . The former explanation perhaps i s possible. However, i t seems un l i k e l y that i t i s true because the physical natures of the hook-probe and of the hypodermic needles are d i f f e r e n t enough that these sampling devices would be expected to withdraw continuous phase i n d i f f e r e n t proportions from the wakes and from the descending aqueous phase. The second a l t e r n a t i v e , then, seems more l i k e l y to be v a l i d than does the f i r s t and i f t h i s i s accepted two p o s s i b i l i t i e s a r i s e . E i t h e r the volume of the wakes i s small r e l a t i v e to the t o t a l volume of the continuous phase, or the concentration of solute i n the bulk of the continuous phase i s almost the same as that i n the wakes. Letan and Kehat ( l 2 l ) suggest that the wakes have almost the. same volume as the drops f o r heat t r a n s f e r studies i n a spray column. The present studies of sampling techniques f o r conditions of no mass transf e r include conditions of dispersed phase hold-up as high as 16$. Therefore, accepting the views of Letan and Kehat, i n tra c e r studies i t would appear l i k e l y that the solute concentration i n the wakes i s almost the same as i n the bulk of the continuous phase. For continuous phase s u p e r f i c i a l v e l o c i t i e s greater than about 36-ft?/hr. f t ? the rate of decrease of tra c e r concentration with height up the column i s so great that the tracer concentration is.measurable only i n the samples taken at the f i r s t two or three sampling points above the t r a c e r d i s t r i b u t o r . Because of t h i s l i m i t a t i o n the work of sampling under conditions of no mass t r a n s f e r was r e s t r i c t e d to low continuous phase s u p e r f i c i a l v e l o c i t i e s . (The work includes both high and low dispersed phase s u p e r f i c i a l v e l o c i t i e s . ) When the studies of sampling techniques f o r runs i n which mass tr a n s f e r took place between the two phases are considered, i t i s found that d e f i n i t e conclusions can not be drawn as to the exact s i g n i f i c a n c e of the r e s u l t s obtained. However, there are i n d i c a t i o n s that the hypodermic needles withdraw continuous phase which i s representative of the descending phase at the sampling elevation. A comparison between the hook-probe and the hypodermic needle r e s u l t s can be made with the help of Figure 26. From t h i s f i g u r e i t can be seen that the solute concentration p r o f i l e i n the continuous phase obtained by means of the hypodermic needles l i e s below that obtained with the hook-probe. The average solute concentration i n the continuous phase over the piston height calculated by graphical i n t e g r a t i o n of the hypodermic needle r e s u l t s l i e s very close to the average solute concentration of the descending continuous phase ( i . e . wakes excluded), i n the piston sample calculated by means of Equation III - 8 . This agreement of the r e s u l t s of the hypodermic needles with those calculated by means of Equation III - 8 shows that, i f the model of Appendix III i s correct, e i t h e r the hypodermic needle samples contain no continuous phase o r i g i n a t i n g In the wakes, or continuous phase from t h i s source i n hypodermic needle samples does not contribute very much to the measured hypodermic needle sample concentrations. Again t h i s small contribution could be the r e s u l t of the wakes being of s i m i l a r solute concentration to that of the bulk of the continuous phase, or the r e s u l t of the i n c l u s i o n of only a small r e l a t i v e volume of wake f l u i d i n the hypodermic needle 100 samples. The f i r s t of these l a s t two a l t e r n a t i v e s seem much less plausible than i t did f o r sampling i n trac e r studies. In the mass transf e r case, f o r t r a n s f e r out of the continuous phase, the wake concentration would be low f o r two reasons: backmixing of d i l u t e material from the lower end of the column, and transfe r out of the wake in t o the dispersed phase. Only the f i r s t of these two factors operates i n the case of the tr a c e r studies. Unfortunately further information i s needed to draw more d e f i n i t e conclusions f o r the runs with mass tra n s f e r . As there was no evidence which indicated that the needles gave erroneous r e s u l t s t h e i r use as sampling devices was adopted i n the f i v e mass t r a n s f e r runs performed i n order to investigate a x i a l eddy d i f f u s i v i t y . However, t h i s procedure perhaps was no worse i n i t s e f f e c t than was the assumption (required f o r the dispersion model) of constant r a d i a l concentration i n the continuous phase at a p a r t i c u l a r a x i a l p o s i t i o n which would not, of course, have been completely v a l i d . The solute concentration p r o f i l e i n the dispersed phase i s su b s t a n t i a l l y the same whether i t i s calculated from hook-probe and bell-probe r e s u l t s by means of Equation 6 or from hypodermic needles and bell-probe r e s u l t s by means of the same equation. (See Table 5-) The reasons f o r t h i s f a c t are that the values of c p from hypodermic needle r e s u l t s and from hook-probe r e s u l t s d i f f e r by roughly two percent only, and — f o r a bell-probe D sample i s of the order of l/7 only. With t h i s r a t i o of V to V a two percent change i n c has only a n e g l i g i b l e e f f e c t on the value of Cp calculated by means of Equation 6. Therefore no conclusions regarding c p can be drawn from the f a c t that c from the bell-probe and the hypodermic needle r e s u l t s agrees with Cp obtained from the bell-probe and the hook-probe r e s u l t s . However, due to the calculated value of c^ f o r a bell-probe • sample being i n s e n s i t i v e to small errors i n i t would be expected that t h i s value of c^ i s the true solute concentration i n the dispersed phase entering the bell-probe i f i t can be assumed that the c used does involve only a small e r r o r . Now, as Table k shows, the average solute concentration i n the dispersed phase of a piston sample calculated from hypodermic needle and piston r e s u l t s agrees with the average solute concentration i n the dispersed phase over the piston height calculated from hypodermic needle and bell-probe r e s u l t s . VC Also, the : average value of — f o r a piston sample i s about D 5, and therefore the value of c^ obtained from Equation 6 applied to a piston sample i s much more s e n s i t i v e to the value of c^ used i n Equation 6 than i t i s f o r a bell-probe sample. Hence the agreement of the values of c^ as noted above implies the correctness of the value of c p used i n the piston case: the concentration given by the hypodermic needles. A l l t h i s r e l i e s , of course, on the assumption that only small errors apply to the concentrations given by the hypodermic needles. Thus one might complain that the argument given here involves an assumption of what i s being proved.. However, although t h i s 102 complaint i s j u s t i f i e d to a degree, i t should be r e a l i z e d that i n presenting the argument the very d i f f e r e n t — ^ - r a t i o i n the piston D sample from that i n the bell-probe sample strenghtens the case f o r the correctness of the hypodermic needle samples. I f these are correct, or even reasonably so, then the value of the dispersed phase concentration from the bell-probe r e s u l t s also i s correct. One further comparison should be made. Table k shows that Cp obtained from the piston r e s u l t s i n conjunction with the hook- probe r e s u l t s i s lower than that obtained from the piston and hypodermic needle r e s u l t s or the piston r e s u l t s and Equation III-8. Table 3 shows s i m i l a r low values of c^ when the hook-probe analyses are used instead of continuous phase concentrations from Equation III-8 i n the c a l c u l a t i o n of c^ f o r the piston. These l a s t observations, of course, are consistent with the f a c t mentioned e a r l i e r , that the value of ĉ , obtained from Equation III-8 agrees with the hypodermic needle r e s u l t s . Now, a low value of c^ i s obtained from a piston sample i f a high value of c^ i s used i n Equation 6. R e c a l l i n g that ĉ , from Equation III-8 assumes the i n c l u s i o n of no wakes, and that i f wakes were included, the value of c^ would be reduced, and, therefore the value of c^ calculated from piston r e s u l t s r a i s e d , we can see that i f i t were postulated that the hook-probe sample included an appreciable and e f f e c t i v e contribution from the wakes, the value of c^ calculated from piston and hook-probe r e s u l t s would be increased i n comparison to the value of c 103 calculated from needle and b e l l , hook and b e l l , and Equation .111-8 and piston, a l l of which are i n reasonable agreement. However, c^ from hook-probe and piston r e s u l t s are lower than the values of c^ obtained by the other methods. Hence i t seems impossible that the low Cp r e s u l t s from hook and piston measurements are due to the hook-probe concentrations r e f l e c t i n g appreciable contributions from drop wakes. In other words c^ f o r the hook-probe i s high, not low. Furthermore i n Run k c^ from the piston sample based on hook-probe analyses i s lower, indeed, than the dispersed phase concentration at the dispersed phase i n l e t nozzle. This r e s u l t , of course, i s impossible, and lends strong support to the hypothesis that c^ from the hook-probe r e s u l t s generally i s too high. I t seems advantageous.to compare hook-probe r e s u l t s with reference to the dispersed phase concentrations, as has been done above, instead of comparing d i r e c t l y the hook-probe and hypodermic needle r e s u l t s . There are two reasons f o r t h i s approach. F i r s t , the d i f f e r e n c e obtained between the values of c^ i s numerically much la r g e r than i s the d i f f e r e n c e between the values of c^ from the hook-probe and. the hypodermic needles r e s p e c t i v e l y , Second, the impossible r e s u l t of c^ being calculated as even lower than that i n the dispersed phase entering the column i s missed when the d i r e c t comparison i s made between c^ from the hook-probe and c^ from the hypodermic needles. The postulate could be put forward that the hook-probe 10k tends to suck i n material from some elev a t i o n higher up the column than i t s a c t u a l p o s i t i o n . However, when an attempt was made to lessen such an e f f e c t h y . d i r e c t i n g the end of the hook h o r i z o n t a l l y , as shown i n the sketch on page,65, no change i n the r e s u l t s were obtained. Perhaps the comparatively large J s i z e of the hook-probe disturbs the flow patterns i n the column to produce high continuous phase concentrations at i t s i n l e t . For example, i f the hook-probe d e f l e c t s drops i n such a way that extraction i s les s complete i n the neighbourhood of the hook-probe i n l e t , then high continuous phase concentrations would be measured by t h i s probe. From plo t s such as that shown i n Figure 26, and assuming that the hypodermic needle samples are representative of the continuous phase, i n the column at the sampling height, i t can be seen that the continuous phase entering the hook-probe appears to be representative of that phase i n the column approximately 1-in. above the probe entrance. As a r e s u l t the continuous phase concentration p r o f i l e s given by Ewanchyna (30, 31) appear to be somewhat i n e r r o r . However, t h i s e r r o r i s only s l i g h t and h i s conclusions mentioned under the heading Introduction regarding the end e f f e c t at the continuous phase i n l e t of the column are s t i l l s u b s t a n t i a l l y v a l i d . 3. AXIAL EDDY DIFFUSIVITY, DEOP SIZE DISTRIBUTION, AND DISPERSED PHASE HOLD-UP STUDIES IN THE l f - I N . I.D. COLUMN The a x i a l eddy d i f f u s i v i t y , E, characterizes the extent to which solute i s backmixed up the column, presumably through the agency of wakes r i s i n g behind dispersed phase drops. In t h i s work values of E have been determined by means of t r a c e r studies with no mass t r a n s f e r between the phases. I f mass t r a n s f e r were present some degree of turbulence at the surfaces of the drops would be expected due to i n t e r f a c i a l phenomena such as the Marangoni e f f e c t . However, the e f f e c t of t h i s i n t e r f a c i a l turbulence on the s i z e of the wakes and on the manner i n which solute i s transferred out of and i n t o the. wakes would be: . expected to be n e g l i g i b l e compared with the e f f e c t of the o s c i l l a t i n g motion of the drops. Consequently the values of E determined by t r a c e r studies would be expected (subject to the li m i t a t i o n s discussed on page 154. ) to be applicable f o r the case of mass, t r a n s f e r . A di s c u s s i o n of the r e s u l t s of the main bulk of experiments precedes that of the preliminary experiments performed i n order to t e s t the a p p l i c a b i l i t y of. the d i s p e r s i o n model and the s u i t - a b i l i t y of the experimental method. a) A x i a l eddy d i f f u s i v i t y , drop' siz e d i s t r i b u t i o n , and hold-up studies. i ) Determination of a x i a l eddy d i f f u s i v i t i e s and Peclet numbers. The c a l c u l a t i o n s to be described here were performed on an IBM 7040 e l e c t r o n i c computer. A data sheet, a hand c a l c u l a t i o n , and a computer output f o r a t y p i c a l run are given i n Appendix IV. These c a l c u l a t i o n s produced the f o l l o w i n g q u a n t i t i e s : s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s , a x i a l eddy d i f f u s i v i t i e s , Peclet numbers, reduced concentrations, and mass balances. The natural logarithms of the concentrations of the samples were plotted versus height down the column. The equation f o r the best s t r a i g h t l i n e through these points was calculated by the method of l e a s t squares. The v a l i d i t y of t h i s method f o r c a l c u l a t i n g the str a i g h t l i n e involved the usual assumptions concerning the normality of the d i s t r i b u t i o n of the natural logarithm of the concentration (125). The s u p e r f i c i a l v e l o c i t y of the continuous phase was divided by the absolute magnitude of the slope of t h i s l i n e to give the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , (Ee). (See -Equation-13•) The a x i a l eddy d i f f u s - i v i t y , E, was.calculated, by d i v i d i n g the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y by the volumetric f r a c t i o n , e, of continuous phase i n the column. The Peclet- number, Pe, was calculated by means of the f o l l o w i n g equation. . 11-18 The i n t e r p r e t a t i o n to be placed on the drop diameter, d^, i s discussed below.. In order that concentration p r o f i l e s could be compared f o r various column operating conditions the reduced concentration at each sampling point was calculated by means of the following expression. reduced concentration = actu a l concentration x 1000 concentration i n the aqueous phase leaving the column Mass balances were calculated f o r the aqueous phase, the ketone phase, and the tracer, r e s p e c t i v e l y , over the column. A set of reduced concentration p r o f i l e s f o r one s u p e r f i c i a l v e l o c i t y of ketone phase and various s u p e r f i c i a l v e l o c i t i e s of aqueous phase i s shown i n Figure 28. The l i n e a r i t y of each p l o t i n Figure 28 indicates that Equation 13, and hence the dispersion model concept, describe, the backmixing of the continuous phase. The reduced concentration p r o f i l e , the dispersed phase hold-up, the a x i a l eddy d i f f u s i v i t y , the Peclet number and the mass balance r e s u l t s f o r each run are given i n Table IV-k, Appendix IV..' As t h i s table shows at the l e v e l of accuracy possible i n the present experiments, there was no dependence of a x i a l eddy d i f f u s i v i t y on the continuous phase s u p e r f i c i a l v e l o c i t y , L^-. „• Continuous phase has been found (21, 22, 23) to move up the column' i n the wakes of r i s i n g dispersed phase drops. The v e l o c i t y of the drops i s n e g l i g i b l y a f f e c t e d by a small change i n the low values of L>£ used i n the trac e r studies. Correspondingly the flowrate of continuous phase up the column i n the wakes of drops i s su b s t a n t i a l l y unaffected by such a change i n the s u p e r f i c i a l v e l o c i t y of the continuous phase. I f the a x i a l mixing of the continuous phase i s caused by the drops and the associated- wakes i t i s not s u r p r i s i n g that the a x i a l eddy d i f f u s i y i t y i s independent of f o r the narrow range of low values of. L Q used i n t h i s work. 1 0 8 FIGURE 2 8 . REDUCED CONCENTRATION PROFILES 109 Figure 29 shows the dependence of a x i a l eddy d i f f u s i v i t y on the dispersed phase flowrate f o r one continuous phase flowrate and various drop s i z e s . The a x i a l eddy d i f f u s i v i t y remained approximately constant as the dispersed phase flowrate was decreased from high values but at low dispersed phase flowrates the a x i a l eddy d i f f u s i v i t y increased r a p i d l y . This e f f e c t i s l e s s pronounced at small drop s i z e s . The e f f e c t of i n c r e a s i n g the drop s i z e f o r a given dispersed phase s u p e r f i c i a l v e l o c i t y was to increase the a x i a l eddy d i f f u s i v i t y . At f i r s t i t was expected that an increase i n the number of drops of a given si z e per unit volume of column would r e s u l t i n a la r g e r volume of continuous phase being c a r r i e d up the column i n t h e i r wakes and hence an increase i n the a x i a l eddy d i f f u s i v i t y , E . However, as mentioned above,, the opposite e f f e c t i s observed at low s u p e r f i c i a l v e l o c i t i e s , L^, of dispersed phase. The reason f o r the decrease i n E with an increase i n the number of drops could be due to the increase i n interference of the wakes of drops by neighbouring drops. This interference would tend to detach the wakes from the drops, r e s u l t i n g i n a lower value of E. Apparently at low values of the decrease i n E due to.interference of wakes predominates over the increase i n E due to the l a r g e r number of drops. At high values of the two.effects on E counterbalance each other. An increase i n the drop s i z e , d^, f o r a given value of would be expected to r e s u l t i n an increase i n E due to an increase i n the size of each wake and also due to l e s s interference of wakes by neighbouring drops. However, the value of E would be expected to decrease due to a smaller 110 FIGURE 29. AXIAL EDDY DIFFUSIVITY' IN THE if-IN. I.D. COLUMN number of drops and hence fewer wakes.. Apparently the e f f e c t s r e s u l t i n g i n ah increase i n E when d^ i s increased predominate over!, those, which.would tend-to decrease E. Figure 30 shows the a x i a l eddy d i f f u s i v i t y , E, p l o t t e d against the s u p e r f i c i a l v e l o c i t y of continuous phase, L^, f o r four, d i f f e r e n t values-of,the.•'superficial -'.velocity of dispersed phase, Lp. The drop s i z e , d^, was 0.135-in. As mentioned e a r l i e r E i s independent of and decreases with an increase i n L^. Also shown i n Figure. 30 are the r e s u l t s of Hazelbeck and Geankoplis (42). They used a l.kl-in. I.D. column, a drop s i z e , d , of 0.134-in. and water and MIBK as the continuous and dispersed phases: r e s p e c t i v e l y . ' They used an aqueous s o l u t i o n of potassium chloride as tr a c e r and the step function method. They found no dependence of E °h. f o r values of between l8.U-ft./h r . f t . and; ̂ 9.5-ft./hr. f t . , but found that E increased l i n e a r l y with L c . As discussed on page 107 of t h i s thesis i t . would be expected that E should be nearly independent of f o r the narrow range of low values of I_ used for. the experiments described i n t h i s thesis and- a l s o those described by Hazelbeck.and Geankoplis. The f a c t that.these workers (42), found a marked increase i n E with i n increase i n -L^ ̂ may have, been due to problems associated with transient response techniques discussed under the heading Introduction. Ee Figure 30a i s a plot of the dispersion number, -y— , against d . P the Reynolds number, . . .This f i g u r e shows a summary, prepared 1 1 2 3 0 T H I S WORK" — — - COLUMN I D . ' 1-5-IN. dp a 0 1 3 5 - IN. L D , C U . F T . / ( H R . SQ.FT.) O 3 0 - 4 Q 36 5 54-7 7 3 _ o H A Z L E B E C K o n d GEANK0PLIS(4gl »-'20 6 co U J 10 COLUMN ID.« I-4I-IN. dp« 0 -134- IN. L^«l8-4 to 49-5, C U . F T . A H R . SQ.FT.) 0 J [ M i l l l l i i l i i i i i i M j | | l i l | i i i | | | | | | M u L f 0 10 2 0 3 0 4 0 5 0 CU.FTV(Hft. SQ.FT.) FIGURE 3 0 . COMPARISON OF AXIAL EDDY DIFFUSIVITY AS DETERMINED IN THIS WORK WITH THAT OF OTHER WORKERS 20 0-1 0-5 10 5 10 50 100 500 1000 2000 REYNOLDS NUMBER = d p U g FIGURE 30a. COMPARISON OF DISPERSION NUMBER AS : DETERMINED IN THIS WORK WITH THAT FOR PACKED BEDS by L e v e n s p i e l and B i s c h o f f (73), of the data i n the l i t e r a t u r e f o r gas and l i q u i d f l o w through packed beds. A l s o p l o t t e d are the r e s u l t s f o r l i q u i d - l i q u i d spray tower operation determined i n t h i s work.' I t can be seen from F i g u r e 30a t h a t the r e s u l t s f o r spray tower operation more or l e s s c o i n c i d e w i t h those f o r l i q u i d f l o w through packed beds, f o r the l i m i t e d range of Reynolds number i n v e s t i g a t e d . This agreement supports the correctness of the r e s u l t s of a x i a l e d d y . d i f f u s i v i t y i n a spray column presented i n t h i s thesis.. • . In add i t i o n , i t lends support t o the a p p l i c a t i o n of the mixing c e l l -.packed bed analogy to spray column operation described below. P l o t s of drop P e c l e t numbers.versus dispersed phase hold-up f o r the f o u r d i f f e r e n t drop s i z e d i s t r i b u t i o n s s t u d i e d are presented i n F i g u r e s 31, 32, 33, and 3^ r e s p e c t i v e l y . P e c l e t numbers, p r e d i c t e d on the b a s i s of the mixing c e l l - packed bed. analogy (kk, 6k, 90, 92,- 108, 109) were c a l c u l a t e d f o r s i x l a t t i c e arrangements of drops as shown i n Appendix I I . - A l l of the p r e d i c t e d P e c l e t numbers l i e i n the range between those f o r the l a t t i c e arrangements of orthorhombic - 2 and rhombohedral - 1 r e s p e c t i v e l y . The values of the P e c l e t numbers f o r these two cases' are p l o t t e d i n each of F i g u r e s 31, 32:, 33, and 3^ i n order t h a t a comparison between the c a l c u l a t e d and the p r e d i c t e d P e c l e t numbers can be made. The agreement between the experimental Pe and. the p r e d i c t e d Pe i s very good f o r l a r g e drops and becomes p r o g r e s s i v e l y worse 115 116 117 12 0 9 - 0-6 CL 0 3 0 0 A / A • A O EXPERIMENTAL C1 CU.FT./(HR. SQ.FT) 9 0 I I L L o A 18 2 • 27-7 O 36 5 V 48-4 THEORETICAL ORTHORHOMBSC-2 LATTICE r l LATTICE! I 1 L _ J I l - i I 10 15 FIGURE 33. PREDICTED AND CALCULATED PECLET NUMBERS, d = 0.125-IN. 1? 01 0 o o V 0 o O y E X P E R I M E N T A L O A O V c CU.FT./IHR. SQ.F: 9 0 18 2 27 -7 36 -5 4 8 - 4 T H E O R E T I C A L ORTHORHOMB IC - 2 LATT ICE RHOMBOHEDRAL- I L A T T I C E 10 h , % 15 FIGURE 34. PREDICTED AND CALCULATED PECLET NUMBERS, d = 0.095-IN. J? 119 as the drop s i z e i s reduced. A summary of the comparison i s given i n the t a b l e below. However, only by l o o k i n g a t Figur e s 31, 32, 3 3 /and 3̂ - can the trend of the experimental p o i n t s away from the p r e d i c t e d values be seen c l e a r l y . d , i n . P .0.155 0.135 0.125 0.095 Percentage number of experimental points i n the p r e d i c t e d Pe range 7̂ 53 17 Percentage number of experimental points w i t h i n 10$> of the pre- d i c t e d Pe range 87 63 70 ^3 Largest percentage d i f f e r e n c e between the experimental Pe and the nearest side of the p r e - d i c t e d Pe range c a l c u l a t e d along a l i n e of constant h . 20 28 . 30 ! 5̂ The drops, of course,, do. not l i e i n an ordered l a t t i c e arrangement but are p o s i t i o n e d i n a random fashion r e l a t i v e to one another at any.instant i n time. However, the above r e s u l t s i n d i c a t e t h a t the assumption.of a. s i m p l e ; l a t t i c e , arrangement of drops i s of some.limited use i n a p p l y i n g the mixing c e l l - packed bed analogy i n order to make a f i r s t estimate of the P e c l e t number. The mixing c e l l - packed analogy p r e d i c t s a decrease i n E wi t h a decrease i n d at constant h and i t p r e d i c t s a decrease P In E w i t h an increase i n h at constant d^. The experimental r e s u l t s shown i n Figure 29 bear out these p r e d i c t i o n s q u a l i t a t i v e l y . 120 i i ) C a l i b r a t i o n f o r o p t i c a l d i s t o r t i o n and drop s i z e measurements. Figure 23 presented e a r l i e r shows the p o s i t i o n s of the 5/32-In. b a l l bearing.placed i n the column when the o p t i c a l d i s t o r t i o n was being measured. The camera, of course, viewed the column i n e l e v a t i o n from the f r o n t . With the camera lens used the depth of focus was such t h a t a l l the.drops i n the column were i n . f o c u s . D i s t o r t i o n s were s m a l l i n almost a l l cases, and.changed only s l i g h t l y i n most cases when the b a l l was .moved from one p o s i t i o n t o another. Hence i t seemed reasonable t o d i v i d e the c r o s s - s e c t i o n of the column i n t o regions i n each of which the o p t i c a l d i s t o r t i o n ' w a s taken to.be constant. The boundaries between regions are. shown, i n Figure 35' These bound- a r i e s were-placed-equidistant, from adjacent p o s i t i o n s occupied by the b a l l d u r i n g the t a k i n g of the photographs f o r c a l i b r a t i o n f o r o p t i c a l d i s t o r t i o n . The o p t i c a l d i s t o r t i o n of the b a l l was found t o be independent of the height of the b a l l i n the photo- graphic t e s t s e c t i o n of the column and a l s o independent of the concentration of t r a c e r i n the column. By c o n s i d e r i n g only the drops which were l o c a t e d i n the c e n t r a l p o r t i o n s of the photo- graphs i t was p o s s i b l e t o av o i d making d i s t o r t i o n c o r r e c t i o n s , since the c o r r e c t i o n s a p p l i c a b l e t o such drops were only - 1$>. A c c o r d i n g l y only drops i n the r e g i o n shown as "drop s i z e measure- ment f i e l d " i n Figure 35 were measured f o r c a l c u l a t i n g drop s i z e d i s t r i b u t i o n s . The p a r t of the column.shown i n Figure 35 which was used f o r drop s i z e measurements contained the whole of the c e n t r a l 121- I DROP S I ZE l M E A S U R E M E N T F I E L D C A M E R A FIGURE 35. PERCENTAGE ERROR IN THE EQUIVALENT DIAMETER DUE TO OPTICAL DISTORTION IN THE l|-I N . I.D. COLUMN 122 p o r t i o n , but not a l l of the p e r i p h e r a l area of the column c r o s s - s e c t i o n . As a r e s u l t a d i s p r o p o r t i o n a t e number of drops appearing i n the c e n t r a l p o r t i o n of the column c r o s s - s e c t i o n , as opposed to those near the column w a l l , were considered f o r drop s i z e d i s t r i b u t i o n measurements. I f t h e r e were any w a l l e f f e c t on . drop s i z e d i s t r i b u t i o n s i t was not taken i n t o account. With.no l i q u i d i n the photographic t e s t s e c t i o n of the column, the b a l l was p o s i t i o n e d a t the centre of. t h i s t e s t s e c t i o n . The g l a s s column and-Perspex box were removed-without d i s t u r b i n g the b a l l . A photograph of the b a l l i n a i r then was taken i n the u s u a l way. The diameter of the p r o j e c t e d image of the b a l l i n : t h i s photograph was measured. The enlargement f a c t o r f o r c a l - c u l a t i n g the ;,apparertt .dimensions, of the b a l l d u r i n g c a l i b r a t i o n s t u d i e s and of drops d u r i n g drop s i z e - d i s t r i b u t i o n measurements was determined, by d i v i d i n g the;measured.diameter of the pro- j e c t e d image of the b a l l photographed i n a i r by the a c t u a l diameter of the b a l l . The v e r t i c a l and h o r i z o n t a l dimensions of the images of 500 drops were measured f o r each run i n which drop s i z e d i s t r i b u - t i o n s were determined. Each drop was assumed t o be an oblate spheroid.- This assumption has bgen found t o be reasonably good f o r drops i s s u i n g from the 0.103-in. I.D. nozzl e t i p s (39)* The measured drop dimensions were c o r r e c t e d f o r o p t i c a l m a g n i f i - c a t i o n , but no c o r r e c t i o n for- o p t i c a l d i s t o r t i o n was a p p l i e d . The equ i v a l e n t drop diameter, d , was c a l c u l a t e d f o r each drop by means of the f o l l o w i n g equation h^ = the v e r t i c a l dimension of the drop image, and -p̂ ,. = ' the h o r i z o n t a l dimension of the drop image. Out of 13,000 drops measured only one drop was found to have an equivalent drop diameter of greater than 0 . 2 5-in. This drop was not considered t o be t y p i c a l and was not considered i n drop s i z e d i s t r i b u t i o n ...calculations,.:. The range of d from O.OO-in. t o 0 . 2 5-in. was d i v i d e d up i n t o increments of 0 . 0 1-in. An IBM - "(OkO e l e c t r o n i c computer was used t o c a l c u l a t e ' t h e percentage of the t o t a l number of drops, and the percentage of t o t a l drop,volume found i n each of these increments. T h e s e . c a l c u l a t i o n s were performed f o r the f i r s t 100 drops measured, the f i r s t 200 drops measured, the f i r s t 300, the f i r s t kOO, and the f i r s t 500 drops measured i n each set of data. I t was found that the c a l c u l a t e d drop s i z e d i s t r i b u t i o n s for . 4 0 0 and 500 drops r e s p e c t i v e l y were almost the same f o r each of the sets of data. E v i d e n t l y a.sample s i z e of 500 drops i s s u f f i c i e n t l y l a r g e t o be r e p r e s e n t a t i v e of the whole po p u l a t i o n of drops i n the column. A c c o r d i n g l y a l l subsequent d i s c u s s i o n i n v o l v i n g drop s i z e i s based on a t o t a l of 500 drops f o r each set of data. A t y p i c a l set of r e s u l t s ' f o r the drop s i z e d i s t r i b - 124 u t i o n c a l c u l a t i o n s i s given i n Table IV - 6 and p l o t t e d i n F i g u r e 36. A summary of a l l of the r e s u l t s i s presented i n Table IV - 7 - In each case there was a peak between 0 . 0 1-in. and 0 . 0 3-in. i n the equ i v a l e n t diameter on the drop s i z e d i s t r i b u t i o n plots.. In a d d i t i o n a second peak appeared at a higher drop diameter. The mean of the two l i m i t s of the eq u i v a l e n t drop diameter range, of width 0 .01-in., i n which the second peak o.ccured was taken to be the drop diameter, d^, used i n the P e c l e t number c a l c u l - a t i o n s . For example, from F i g u r e 36 the drop diameter of 0.135- i n . was used t o c a l c u l a t e Pe f o r Run 50. R o c c h i n i (39) took close-up photographs of a l f - i n . I.D. spray column u s i n g the 0.103-in. I.D. nozzle t i p s and w i t h the t r a n s f e r of a c e t i c a c i d from the continuous phase t o the d i s p e r s e d phase. His photographic c o n d i t i o n s r e s u l t e d i n a very short depth of focus i n which drops were examined. R o c c h i n i d i d not use any means f o r reducing o p t i c a l d i s t o r t i o n but he c o r r e c t e d the drop s i z e measurements f o r o p t i c a l d i s t o r t i o n by means of a c a l i b r a t i o n graph. The drop s i z e d i s t r i b u t i o n s which he presents (39) have peaks a t e x a c t l y the same equivalent-drop diameter as shown i n F i g u r e 36. In the present work the second peak, was very high and narrow f o r drops produced from the 0.053-in-. I.D. nozzle t i p s and very low and broad f o r the 0.126-in. I.D. t i p s . Obviously the pro- d u c t i o n of i r r e g u l a r l y s i z e d drops at the nozzle t i p s would r e s u l t i n a broad peak. However, i t i s f e l t t h a t the main reason f o r the change i n the shape of t h e peaks i s the i n v a l i d i t y of the assumption t h a t the l a r g e r drops are of oblate spheroid shape. 20 EQUIVALENT DROP DIAMETER, IM. FIGURE 36. DROP SIZE DISTRIBUTION FOR RUN 50, AVERAGE NOZZLE TIP DIAMETER = 0.103-IN. 126 T y p i c a l photographs of drop's produced i n the. l f - i n . I.D. column by the f o u r d i f f e r e n t s i z e s of nozzle t i p s are shown i n Figure 37- From photographs .such as these i t can be seen t h a t l a r g e r drops are more i r r e g u l a r i n shape than smaller drops. T y p i c a l drop s i z e d i s t r i b u t i o n histograms f o r the 0.103-in. I.D. and the 0,126-in. ;T.D.- nozzle t i p s are presented i n F i g u r e s 36 and 38 r e s p e c t i v e l y . For each of the three s m a l l e s t nozzle t i p diameters .the second peak i n the drop s i z e d i s t r i b u t i o n p l o t was not i n f l u e n c e d by run c o n d i t i o n s . In the case pf the.nozzle t i p s of average I.D., 0.126-in. the. l o c a t i o n of the- peak was i n f l u e n c e d s l i g h t l y by run conditions... The drop diameter, dp, f o r these n o z z l e t i p s was taken as 0.155-in. Garwin and Smith (43) r e p o r t t h a t the drop s i z e . i s independent-of the continuous phase f l o w r a t e . This c o n c l u s i o n i s c o n s i s t e n t w i t h the above observations. Figure 39 i s a t y p i c a l example of p l o t s made t o show the percent of t o t a l drop volume versus e q u i v a l e n t drop diameter. There was no n o t i c e a b l e peak f o r the very s m a l l d r o p s - i n t h i s s o r t of p l o t since the c o n t r i b u t i o n of these t o the t o t a l volume was n e g l i g i b l e . i i i ) Hold-up s t u d i e s . P l o t s are given i n F i g u r e s 40, 4 l , 42, and 43 f o r the d i s p e r s e d phase hold-up•(measured by means of the p i s t o n ) versus the d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y f o r each of the f o u r nozzle t i p s i z e s s t u d i e d . Weaver, Lapidus, and E l g i n (41) • ' . . ' ' ' / • • • AVERAGE NOZZLE TIP DIA. = 0.053-IN. (RUN 148) 127 AVERAGE NOZZLE TIP DIA. = 0 . 0 8 6-IN. (RUN 9 6 ) AVERAGE NOZZLE TIP DIA. = 0.103-IN. (RUN 65) AVERAGE NOZZLE TIP DIA. = 0.126-IN. (RUN 126) FIGURE 37. PHOTOGRAPHS OF DROPS AT OPERATING CONDITIONS CORRESPONDING TO RUNS INDICATED. MAGNIFICATION FACTOR = 3. 0 0 0 015 0 2 0 0 0 5 010 EQUIVALENT DROP DIAMETER, IN. FIGURE 38. DROP SIZE DISTRIBUTION FOR RUN 130, AVERAGE NOZZLE TIP DIAMETER = 0.126-IN. 0-25 0 0 5 010 0 85 E Q U I V A L E N T DROP D I A M E T E R , 0*5 FIGURE 3 9 . DISTRIBUTION OF TOTAL PERCENT OF VOLUME OF DROPS FOR RUN 5 0 , AVERAGE NOZZLE TIP DIAMETER = 0 . 1 0 3 - I N . FIGURE kO. DISPERSED PHASE HOLD-UP, d = 0.155-IEF. 131 FIGURE bl. .DISPERSED PHASE HOLD-UP, d- = 0 . 1 3 5 - I f f i 132 FIGURE 42. DISPERSED PHASE HOLD-UP, d = 0.125-IN. 133 o / FIGURE 43. DISPERSED PHASE HOLD-UP, d = 0.095-IN. extended the theory r e l a t i n g s l i p v e l o c i t y and hold-up i n f l u i d i z e d beds t o spray column op e r a t i o n . They show t h a t the s l i p v e l o c i t y i s expected t o decrease with i n c r e a s i n g hold-up. As a r e s u l t a p l o t of hold-up versus dispersed phase s u p e r f i c i a l v e l o c i t y , L^, i s expected t o be curved, concave upwards. Figu r e s 40, 41, 42, and 43 bear out t h i s p r e d i c t i o n f o r values of l e s s than 60-ft?/hr. f t ? However, no explanation, could be found f o r the l i n e a r i t y of the hold-up curves f o r values of greater than 60-ft./hr. f t . . The v e l o c i t y , u, of r i s e of the di s p e r s e d phase drops;was of the order of lOOO-ft./hr. and experiments were c a r r i e d o u t . f o r continuous phase s u p e r f i c i a l v e l o c i t i e s , L , between 9 - f t ? / h r . f t ? and 48.4-ft?/hr. f t ? I n c r e a s i n g L w i t h i n t h i s narrow range would be expected t o r e s u l t i n only a small decrease i n u and t h e r e f o r e only a s l i g h t increase i n the hold-up. Although Figures 40, 4l,. 42, and 43 show no r e g u l a r dependence of the hold-up on L there i s a s l i g h t tendency f o r the hold-up t o be somewhat higher at higher continuous phase f l o w r a t e s . For a given d i s p e r s e d phase f l o w r a t e decreasing the drop s i z e should r e s u l t i n an i n - creased hold-up since u s u a l l y s maller drops have a smaller t e r m i n a l v e l o c i t y . However, no e f f e c t of t h i s s o r t was n o t i c e d i n going from a drop diameter, d^, of 0.155-in. t o one of 0.135-in. as can be seen by comparing F i g u r e s 40 and 4 l . The reason f o r t h i s might be t h a t drops of about 0.155-in. eq u i v a l e n t diameter are so l a r g e that they are much d i s t o r t e d from the oblate spheroid shape. The d i s t o r t i o n u s u a l l y r e s u l t s i n a large frontal area of each drop ( l l 4 ) which in turn increases the drag and lowers the terminal velocity. Comparison of Figures 4 l , h2, and 43, however, shows an increase in the hold- up as the drop size is decreased. b) Results of the preliminary experiments. The sampling positions 1 to 10 inclusive mentioned below are shown in the abscissa of Figure 28. i) Time to reach steady-state. . The solute concentrations in samples taken by means of the first,.fourth, seventh, and tenth hypodermic needles, shown in Figure 9, above the tracer distributor, and in the aqueous phase leaving the column were, plotted versus time after start-up. Table 6 shows the time to reach steady-state at the last sampling position to do so. TABLE 6. TIME TO REACH STEADY-STATE IN THE if-IN. I.D. COLUMN UNDER CONDITIONS OF NO MASS TRANSFER. Run 32 33 3^ L c, ft?/hr. ft? 9 -0. 9-0 27-7 L D, ft?/hr. ft? 128 30.4 30.4 time to reach steadyestate, min. 100 115 ^5 Temperature, °F 71 68 69 Table 6 shows that the time to reach steady state varies l i t t l e when L is varied over a wide range. Hence the effect of 1̂ . on 136 the time t o reach steady s t a t e was not taken i n t o account. Table 6 a l s o shows t h a t the time t o reach steady s t a t e decreases r a p i d l y w i t h an increase i n L^. Co n s i d e r a t i o n of Table 6 suggested t h a t 1-hr. would be. a conservative estimate of the time r e q u i r e d t o reach steady, s t a t e when was greater .than 3 0-ft./hr. f t . and t h a t 2-hr. would be a conservative estimate of t h i s time o 2 *3 2 f o r values of L c between 9 - f t . / h r . f t . and 30-f.t./hr. f t . These steady s t a t e times f o r v a r i o u s values of were adopted f o r a l l the . s t u d i e s i n v o l v i n g t r a c e r i n the l f - i n . column. i i ) E f f e c t . o f t r a c e r feed r a t e . Table :7 shows the r e s u l t s of t e s t s performed t o i n v e s t i g a t e any e f f e c t s of t r a c e r feed r a t e on the reduced c o n c e n t r a t i o n p r o f i l e s or on the a x i a l eddy d i f f u s i v i t y values. TABLE 7, EFFECT OF TRACER FEED RATE ON REDUCED CONCENTRATION . PROFILES AND AXIAL' EDDY DIFFUSIVITY IN THE i f - I N . I.D. COLUMN. Run ¥ f t ? / hr. f t ? ,. ¥ f t ? / 'nr. f t ? f t ? / hr.. . f t ? , , Reduced sampling c o n c e n t r a t i o n a t p o s i t i o n s E. • f t ? / hr. Temp. °F 1 .2 .3 -. 4 • 5 6 7 8~ - 9 10. 35 27-7 30.4 0.16 599 411 271 l62 98' 67 42 32 19 12 32.5 69 4o . 27.7 30.4 0.31 557 380 246 152 9^ 60 40 27 18 11 32.6 70 36 27.7. 30.4 •0.62 621 389 251 160 104 66 42 29 20 12 32.8 71 67 18.2 73 ' 0.10 350 157 50 24 • 8 2.8 1-3 - - - 10.3 72 57 18.2 73: 0.20 '^33 166 76 35 11 .5 2.1 0.85 0.35 - 11.0 74 68 18.2- '73 ' . 0.40 307 142 48 18 8 3.3 1 .4 0.51 0.20 - 10.7 73 • The reduced con c e n t r a t i o n a t a given sampling p o i n t v a r i e s c o n s i d e r a b l y f o r various t r a c e r feed r a t e s i n many cases. 137 However, the resulting overall concentration profile and axial eddy diffusivity are not affected appreciably by tracer-feed rate. It is concluded that the effect of tracer feed rate on the value of the axial eddy diffusivity is negligible for tracer fLowrates of less than 2$ of the continuous phase superficial velocity. ....>• i i i ) Reproducibility of results. Three runs were duplicated to provide a check on reproduci- bi l i t y of results. The reduced concentration profiles and the calculated values:of.the axial eddy diffusivity for these experiments are given in Table 8. TABLE 8. REPRODUCIBILITY OF RESULTS FOR AXIAL EDDY DIFFUSIVITY IN THE 1-|-IN. I.D. COLUMN. ' • . . Run ft?/ hr. ft? ft?/ hr. ft? V Reduced concentration at position sampling r hr. Temp. °F .1 2 3 ' 4 5 6 7 8 9 10 32 9,0. 128 575 256 155 79 48 28 14 9 3.8 2.0 8.6 71 47 9.0 128., 529 308. 157 .86, 46 28 14 7-8 5-3 2.9 8.9 71 33 9,0 30.4 755 644 566 487 391 330 297 259 223 179 29.3 68 42 9.0 30.4 : 75^ 668 571 492 397 252 288 250 221 179 28.7 73 3^ 27-7 30.4 523 408 257 166 93 58 38 28 19 12 33-0 69 40 27-7 30.4 . 557 380 246 152 9k 60 40 27 18 11 32.6 70 The reproducibility of the calculated value of the axial eddy diffusivity is good although point reduced concentrations are not exactly the same in duplicate runs. iv) Cross-sectional homogeneity. The dispersion model requires that .at any elevation in the column the concentrations of solute in the continuous phase be uniform. A c c o r d i n g l y i t was necessary t o check on whether or not c r o s s - s e c t i o n a l homogeneity e x i s t e d . Samples were withdrawn at the l e v e l of the f i r s t hypodermic needle above the t r a c e r d i s t r i b u t o r (Figure 9) f o r each of the three runs l i s t e d i n Table 9« This l o c a t i o n was chosen because of a l l the sampling • l o c a t i o n s i t would be the one most l i k e l y t o e x h i b i t non- u n i f o r m i t y of .solute c o n c e n t r a t i o n . Samples were taken i n each run a t the p o s i t i o n s shown i n the sketch below: The corresponding reduced concentrations appear i n Table 9. A l s o shown i s the reduced c o n c e n t r a t i o n at p o s i t i o n 1 f o r a sample taken i n each run about kO minutes before the f i v e samples mentioned above. / Although the c o n c e n t r a t i o n of s o l u t e i s not e x a c t l y uniform over the c r o s s - s e c t i o n of the column, the v a r i a - t i o n i s not l a r g e compared w i t h the v a r i a t i o n of c o n c e n t r a t i o n w i t h time at the centre of the c r o s s - s e c t i o n . . P o s i t i o n 1 was the f i r s t sampling p o s i t i o n above the t r a c e r d i s t r i b u t o r . The small v a r i a t i o n i n c o n c e n t r a t i o n over the c r o s s - s e c t i o n a t t h i s 139 TABLE 9. CROSS-SECTIONAL HOMOGENEITY IN THE l f - I N . I.D.. COLUMN Run LC> f t ? / h r . f t . f t ? / 2 h r . f t . . Reduced con c e n t r a t i o n a t sampling p o s i t i o n . . remp. a F l a l b l ' i c I d 1, sample taken e a r l i e r 32 9-0 127-7 . 578 575 568 • 577 573 575 71 33 9-0 30.4 754 723, 7̂ 5 751 755 755 68 34 27.7 •30. V. •: 532-. 525 526 . 537 519 523 69 sampling e l e v a t i o n i n d i c a t e s t h a t t r a c e r l e a v i n g the d i s t r i b u t o r spreads over the c r o s s - s e c t i o n i n a s m a l l incremental column height. Hawrelak (37) s t u d i e d a l f - i n . I.D. spray column w i t h the t r a n s f e r of .acetic a c i d from the continuous, phase t o the dispe r s e d phase. He took samples from v a r i o u s p o s i t i o n s a t a given c r o s s - s e c t i o n by means of hypodermic,needles and. found no r a d i a l c o n c e n t r a t i o n g r a d i e n t s . v) Sampling r a t e . Table 10 shows the reduced concentrations of s o l u t e i n .samples taken from the f i r s t f o u r sampling p o s i t i o n s above the t r a c e r d i s t r i b u t o r a t various sampling r a t e s . Sampling r a t e s of l.O-ml./min. f o r s u p e r f i c i a l v e l o c i t i e s of, continuous phase gre a t e r than 3 2 27.7 f t . / n r . f t . and of 0.75 ml./min. f o r s u p e r f i c i a l v e l o c i t i e s of continuous phase, between . 9 . .O-ft./hr. f t . and 2 7 . 7-ft./hr. f t . appear t o be sm a l l enough so as not t o d i s t u r b the operation of the column. A c c o r d i n g l y these sampling r a t e s were used f o r a l l TABLE 10. EFFECT OF :SAMPLING BATE ON THE REDUCED CONCENTRATION PROFILE IN THE l | - I N . I.D. COLUMN Run L '• f t ? / p h r . f t . LD f t ? / h r . f t . Reduced concentration at sampling p o s i t i o n Temp. °F Sampling r a t e = 0.5 ml./min. Sampling r a t e = 1.0 ml./min. . Sampling'rate = 2.0 ml./min. P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 3^ 27-7 30.4 523 388 255 158 523 4o8 257 166 522 387 25^ 155 69 Run LC . h r . f t . h r . f t . - Reduced concentration at sampling p o s i t i o n Temp. °F Sampling r a t e . .= 0.25 ml./min. Sampling r a t e = 0-75 ml;/min. Sampling r a t e = 1.5 ml./min. P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 P o s i - t i o n 1 P o s i - t i o n 2 P o s i - t i o n 3 P o s i - t i o n 4 . 33 32 9-0 9.0 30.4 128 749 575 642 257 566 155 485 . 80 755 575 644 256 566 155 487 79 751 573 644 255 568 155 488, 79 68 71 of the t r a c e r s t u d i e s i n the Tg-in. I.D. column. v i ) Order of sampling. The. u s u a l order of sampling was t o take a sample by means of the f i r s t hypodermic needle above the t r a c e r d i s t r i b u t o r , then by means of the next higher needle, and so on. (See Figure s 9 and 10 f o r sampling p o s i t i o n s . ) For three runs samples were taken i n the reverse order, t h a t i s s t a r t i n g w i t h the highest hypodermic needle. As w e l l i n these same runs samples were taken i n the u s u a l order. The r e s u l t s are given i n Table 11. I t i s evident from Table 11 t h a t the order i n which samples are taken does not a f f e c t the measured co n c e n t r a t i o n p r o f i l e . v i i ) E f f e c t of column height. For one set of column op e r a t i n g c o n d i t i o n s three experiments were performed w i t h three d i f f e r e n t lengths of column. (See Figure s 10, 11, and 12.) Table 12 shows the reduced c o n c e n t r a t i o n p r o f i l e of s o l u t e i n the t e s t s e c t i o n and the c a l c u l a t e d value of the a x i a l eddy d i f f u s i v i t y f o r each run. The l e n g t h of the column appears to have no s i g n i f i c a n t e f f e c t upon the a x i a l eddy d i f f u s i v i t y . TABLE 11. EFFECT OF THE ORDER OF SAMPLING ON THE MEASURED CONCENTRATION PROFILE IN THE 1^-IN. I.D. COLUMN Run LC ' f t 3 / h r . f t . LD f t ? / h r . f t . Order of sampling Reduced con c e n t r a t i o n a t sampling p o s i t i o n Temp. °F 1 2 3 4 5 6 7 8 9 10 33 9-0 30.4 • usual ( l t o 10) 755 644 566 487 391 330 297 259 223 179 68 reverse (10 t o l ) 7̂ 7 642 564 485 389 327 297 258 215 178 32 9-0 128 usual ( l t o 10) 57H.-. 256 155. 79 •48 28 14. 9.0 3-0 ' 2.0 71 " reverse (10 to l ) 572 253. 155 79 48 28 14 8.9 3-8 2.0 3^ 27-7 30.4 usual ( l t o 10) 523 4o8 257 166 93 . 5 8 38 28 19 . 12 69 reverse (10 to l ) 526 374 254 153 ' 97 61 40 27 18 11 TABLE 12..EFFECT OF COLUMN HEIGHT ON THE MEASURED CONCENTRATION PROFILE AND AXIAL EDDY DIFFUSIVITY IN. THE T|-IN. I.D. COLUMN Run Column length (nozzle t i p s t o i n t e r f a c e ) L f t ? / h ' tt.ft. f t ? / h r . f t f Reduced concer L t r a t i o n at sampling p o s i t i o n s E f t ? / h r . Temp. °F 1 2 ' 3 4. 5 6 7 8 9 ' 10 174 51 175 6-ft.' 3 l / 8 - i n . 1 0-ft. 3?-in. 1 6-ft. 4|-in. 18.2 18.2 18.2 54.7 54.7 54.7 426 561 562 286 298 299 136 138 146 81-. 83 73 39 37 45 20 18 23 9.9 11 9-9 5-7 5.8 5.2 3-0 2.7 2.7 1.4 T-5 1-5 14.9 14.5 • 14.5. . 68 . 71 68 1 4 3 4. AXIAL EDDY DIFFUSIVITY AND DROP SIZE DISTRIBUTION STUDIES IN THE 3-IN. I.D. COLUMN. The r e s u l t s of the preliminary experiments concerning steady- state time, r e p r o d u c i b i l i t y of r e s u l t s , and cross-sectionalvhomo- geneity are discussed a f t e r those of the main experiments. a) Main Experiments. • • . The value of-the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , Ee, f o r each run.- was ca l c u l a t e d in- a manner s i m i l a r to that already described f o r the 1-|—in. I.D... column. . A summary of the r e s u l t s • f o r the 3-in. I.D. column i s given i n Table IV-5. Figure 44 shows the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y p l o t t e d against dispersed phase s u p e r f i c i a l v e l o c i t y . The curve shown i n t h i s f i g u r e was drawn through the points by eye.. As with the l f - i n . I.D. column, the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y decreases with in c r e a s i n g dispersed phase flowrate. However, there appears to be some tendency, f o r higher s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y values' f o r the. 3-in.'I..D. column to be associated with higher s u p e r f i c i a l v e l o c i t i e s of the.continuous phase. Comparison of the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y r e s u l t s f o r the 3~in. I.D. column with those f o r the i f - I n . I.D. column shows that at a drop s i z e , d̂ > of 0.135-in. and f o r a given s u p e r f i c i a l v e l o c i t y of each phase the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y i n the 3-in. I.D. column was between 6.3 and 17•3 times that i n the l f - i n . I.D. column. I t was evident that the continuous phase underwent channelling. (See later.) This f a c t , no doubt, r e s u l t e d i n an increase i n a x i a l mixing of the continuous phase In the 3 - i n . I.D. FldURE kk. SUPERFICIAL AXIAL EDDY DIFFUSIVITY IN THE 3-IN. I.D. COLUMN 145 column. G i e r and Hougen ( 2 8 ) s a y t h a t the "... b u l k mixing e f f e c t would be expected t o be most se r i o u s i n spray columns of high diameter t o height r a t i o . " However, the r e s u l t s of the experiments des c r i b e d i n t h i s t h e s i s show t h a t the diameter, but not the height, of the column i s important i n a s s e s s i n g the extent of the a x i a l mixing of the continuous phase. A c t u a l eddy d i f f u s i v i t i e s were not c a l c u l a t e d from the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s because the d i s p e r s e d phase hold-up, h, was not measured i n the 3 _ i u . I.D. column.. Previous, workers (3, .6, 30, 31, ^3) have estimated the hold-up/ h, by means of - Equation 7• . 100 h h _ . • u 7 However, i n the.present work i t was not p o s s i b l e t o measure the v e l o c i t y of r i s e of t h e d i s p e r s e d phase drops w i t h any accuracy due t o the s w i r l i n g motion of the drops (described l a t e r ) . As a r e s u l t Equation 7 c o u l d not be used t o estimate the hold-up, h. The percentage e r r o r i n the e q u i v a l e n t diameter of drops due to o p t i c a l ^ d i s t o r t i o n was determined i n a manner s i m i l a r t o t h a t used f o r the , l f - i n . I.D. column. The o p t i c a l d i s t o r t i o n was independent of the v e r t i c a l p o s i t i o n of the b a l l and of the c o n c e n t r a t i o n of t r a c e r i n . the column. F i g u r e 45 shows t h i s . percentage e r r o r a t v a r i o u s p o s i t i o n s i n the c r o s s - s e c t i o n of the column. A l s o s h o w n i n Figure 45 i s the p o r t i o n of the c r o s s - s e c t i o n i n which drop s i z e measurements were made. J u s t as f o r the l f - i n . I.D. column r e s t r i c t i n g the drop s i z e measurements t o . the f i e l d shown i n . t h i s f i g u r e made i t unnecessary t o apply any c o r r e c t i o n f o r " o p t i c a l d i s t o r t i o n . A summary of the drop IDROP SIZE] M E A S U R E M E N T F I E L D C A M E R A FIGUEE if-5. PERCENTAGE ERROR IN THE EQUIVALENT DIAMETER DUE TO OPTICAL DISTORTION IN THE 3-IN. I.D. COLUMN Ikl s i z e d i s t r i b u t i o n s measured appears i n Table IV - 8 . The second peak i n each drop s i z e d i s t r i b u t i o n p l o t appeared between 0 .13-in. and 0 . I k - i n . . e q u i v a l e n t drop diameter. b) P r e l i m i n a r y Experiments. i ) Steady-state time. _ The c o n c e n t r a t i o n o f . t r a c e r i n samples taken by means of the. f i r s t , . t h i r d , seventh, and t e n t h hypodermic needles above the t r a c e r d i s t r i b u t o r (Figures 20 and 2 l ) and i n the aqueous phase l e a v i n g the column were p l o t t e d versus time a f t e r s t a r t - u p . Table 13 shows the time t o reach steady-state a t the l a s t sampling p o s i t i o n t o do. so. TABLE' 13. STEADY-STATE TIMES FOR THE 3-IN. I.D. 'COLUMN. Run • • •.' 177 ISO 203 L c , f t ? / h r . f t ? 18.2 100 18.2 Lp, f t ? / h r . f t ? , 36.5 36.5 109 time t o reach, steady-state?, min.. 55 25 57 Temperature, °F 70 70 69 Although the time t o reach, steady-state v a r i e d l i t t l e f o r a wide range of dis p e r s e d phase s u p e r f i c i a l v e l o c i t i e s i t decreased markedly for. an i n c r e a s e i n the s u p e r f i c i a l v e l o c i t y of con- tinuous phase. The time f o r the.column t o reach a steady- s t a t e c o n d i t i o n was.taken t o be 1-hr. f o r continuous phase s u p e r f i c i a l v e l o c i t i e s of l e s s than l O O - f t . / h r . f t . and 30-min. o 2 f o r continuous phase s u p e r f i c i a l v e l o c i t i e s of IGO-ft./hr. f t . 148 and greater. i i ) R e p r o d u c i b i l i t y of r e s u l t s . The reduced con c e n t r a t i o n p r o f i l e s and the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s f o r d u p l i c a t e runs are presented i n " Table 14. TABLE 14. REPRODUCIBILITY OF RESULTS FOR THE 3-IN. I.D.. COLUMN Run f t ? / h r 2 f t . f t ? / f t T . Reduced co n c e n t r a t i o n at sampling p o i n t s ft2./ hr. Temp. °F .1 . 2 3 4 5 6 • 7 8 9 10 177 18.2 36.5 933 863 844 8 l l 777 707 680 656 636 593 188 70 186 18.. 2 36.5 921 888 819 785 761 731 689 656 620 595 190 70 191 48 .4 54.7 1080 933 780 701 .546 457 395 317 273 257 •145 70 207 48 .4 54.7 1077 892 731 608 532 444 367 310 249 218 138' 69 201 100 109 1118 613 167 101 40 18.8 6.03 1.09 - - 53-6 67 208 100 109 ' 1131 565 193 109 37 13-7 5.17 2.13 1.14 - 56.5 68 Table l 4 shows t h a t , although p o i n t concentrations are not e x a c t l y r e p r o d u c i b l e , the reduced con c e n t r a t i o n p r o f i l e s and s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s f o r d u p l i c a t e runs are qui t e s i m i l a r . i i i ) C r o s s - s e c t i o n a l homogeneity. The reduced concentrations of so l u t e a t the p o s i t i o n s shown i n the f o l l o w i n g sketch are given i n Table 15 f o r the l e v e l s of 149 the f i r s t and f i f t h hypodermic needles above the t r a c e r d i s t r i - b u t o r . (See Figure s 20 and 21.) TABLE 15.- CROSS-SECTIONAL HOMOGENEITY IN THE 3-IN. I.D. COLUMN Run l L c f t ? / 2 hr.ftf LD f t ? / 2 hKftr Reduced con c e n t r a t i o n a t sampling p o i n t s Temp.. °F l a . l b . 1. l c I d l e . I f l h . 177 l 8 . 2 36.5 937 •933 937 917 901 939 936 933 919 70 180 100 36.5 838 833 816 784 737 791 811 847 855 70 197 18.-2 73 980 988 960 972 968 958 958 966 968 67 • 195 100 73 . 1290 1263 1097 947 889 913 1019 1021 1034 68 203 18.2 109 916 911 909 897 893 903 903 907 907 69 201 100 ' 109 1277 1198 1120 990 895 893 920 1008 1034 67 Run L c f t ? / hr.ft. V f t.?/ hr.ft. Reduced con c e n t r a t i o n a t sampling p o i n t s Temp.. °F 5a 5b 5 5c 5d 5e 5f 5g 5h 177 18.2 36.5 807 798 733 773 762 776 760 751 742 70 180 100. 36.5 230 225 218 206 196 223 225 220 208 70 197 18.2 73 664 682 69k 672 724 696' 684 698 708 67 :i95 100 73 194 184 169 151 144 161 163 170 176 68 .203 18.2~- 109 611 599 603 576 553 591 601 609 611 69 201 100 109 41 4o 4o 39 38 41 41 40 39 67 •'1 150 Table 15 shows that the assumption of radial homogeneity is less valid for the I.D. column than for the 1-jjr-in. I.D. column. Visual observations of the very small dispersed phase drops during experimental runs showed that large scale axial swirling motions occurred in the continuous phase of the 3-in. I.D. column as mentioned later. . However, the plot of the natural logarithm of the tracer concentration versus column height is straight for the runs in the 3-in. I.D. column as required by the dispersion model equation (Equation 13). Therefore a lack of cross-sectional homogeneity in the 3-in. I . D . column seems not to be too serious as far as the determination of superficial axial eddy diffusivities is concerned. 5. VISUAL OBSERVATIONS OF THE MOTION OF THE DROPS The motion of the drops in the Tg-in. I.D. column was very erratic but always.in an upwardly direction. There was no evidence of drops ever taking a downward course. The very small drops of about 0".02-in. diameter moved up the column very slowly. Due to the small size of these drops their motion would have reflected any.large scale turbulence or channelling in the main bulk of the continuous phase. However no such effects were observed. These general flow characteristics were the same for the various' flow- t rates of the"two phases and for the four different 'drop size distributions studied in the T§-in. I.D. column. Evidently the drops moved up the column in effective plug flow. Thus the 151 assumption of no a x i a l eddy d i f f u s i o n i n the dispersed phase (28, 31, 35) i s v a l i d . In contrast to the observations of the drop motion i n the T§-in. I.D. column the drop behaviour i n the 3-in. I.DI column was quite d i f f e r e n t . Not only d i d the very small drops e x h i b i t an a x i a l s w i r l i n g motion but la r g e r drops often took a downward course f o r a short distance along the column. Obviously the continuous phase underwent channelling. As discussed e a r l i e r t h i s phenomenon re s u l t e d i n r a d i a l inhomogeneity of the continuous phase Due to the s w i r l i n g motion of the drops the assumption of no backmixing of" the dispersed phase i s i n v a l i d . 6.' CONCENTRATION PROFILES WITH MASS TRANSFER Five runs were performed with the t r a n s f e r of a c e t i c a c i d from the continuous aqueous phase to the dispersed ketone phase i n the T§-in. I.D. column as described under'Experimental Procedure. Samples' were taken from within the operating column by means of the hypodermic needle samplers and also by means of the b e l l - probe. The concentration, c^, of a c e t i c a c i d i n the 'ketone phase of each bell-probe sample at the time of sampling was cal c u l a t e d by means of Equation 6 and the concentration, c^, of a c e t i c a c i d i n the hypodermic needle sample at the sampling elevation-. CD = CD + "̂ C ( c C " C C } . VD For each run the concentration p r o f i l e s of solute i n both phases over the tes t sect ion were p l o t t e d . Smoothed values of the con- centrations of solute i n each phase at the sampling posi t ions were read from these p l o t s . The value of the d i s t r i b u t i o n c o e f f i c i e n t , m, at each of the ten. hypodermic needle sampling pos i t ions was calculated from the equi l ibr ium curve for acet ic a c i d d i s t r i b - uted between MIBK - saturated water and water - saturated MIBK at 70°F. The ari thmetic average of these ten values of m was calculated and used i n subsequent c a l c u l a t i o n s . The e q u i l i b r i u m curve i s shown i n Figure k6 and the equi l ibr ium data used to prepare t h i s p lot appear i n Table IV-13, Appendix IV. The capacity c o e f f i c i e n t , K^a, was calculated by means of the smoothed concen- t r a t i o n s and Equation 20. Integrat ion was c a r r i e d out over the test sect ion only. The dispers ion model characterizes the extent of backmixing of the continuous phase. I t i s l i k e l y that the continuous phase which i s backmixe'd enters the wakes of drops and i s transported some distance up the column as wake mater ia l before passing back i n t o the main bulk of the continuous phase. In the tracer experiments described e a r l i e r t h i s backmixing was studied by measuring the extent to which a solute t r a c e r , soluble only i n the continuous phase, was carr ied up the column. 20 The experimental r e s u l t s are presented i n Table IV-9, Appendix IV. 153 0 0 0 FIGURE k6. 0 0 0 0 02 0 04 0 0 6 ACETIC ACID CONC. IN MIBK PHASE, LB.-MOLES/CU.FT. EQUILIBRIUM CURVE FOR ACETIC ACID DISTRIBUTED BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK AT 70°F 154 When mass t r a n s f e r can take place the simple c o n d i t i o n s of the t r a c e r work no longer o b t a i n and c a u t i o n must be e x e r c i s e d i n u s i n g the t r a c e r r e s u l t s and the d i s p e r s i o n model. The d i f f e r e n c e s which can a r i s e are t h a t the wakes are no longer t y p i c a l of the l o c a t i o n from which they were drawn,.and mass t r a n s f e r can s t i l l occur from a wake wh i l e i t i s t r a v e l l i n g w i t h the drop. : I n the case o f mass t r a n s f e r from the continuous t o the d i s p e r s e d phase, s o l u t e , i n t h i s case s o l u b l e i n both phases, i s t r a n s p o r t e d along with.continuous phase up the column i n the wakes of the r i s i n g drops as was the case i n the t r a c e r s t u d i e s . However, i t i s probable t h a t the continuous phase, immediately p r i o r t o e n t e r i n g a wake, had been i n the near v i c i n i t y of the a s s o c i a t e d drop. Consequently t h i s continuous phase would be lower i n s o l u t e c o n c e n t r a t i o n than the b u l k of t h a t phase at, t h e same e l e v a t i o n . Therefore the amount of s o l u t e c a r r i e d up the .'column .in the rising.wakes would be l e s s than t h a t p r e d i c t e d from the t r a c e r s t u d i e s wherein no such d e p l e t i o n of t r a c e r could have taken p l a c e . • In a d d i t i o n t o t h e above e f f e c t there i s the d i s s i m i l a r i t y of the d i f f u s i o n p a t t e r n of s o l u t e between the wake and the surrounding ( •continuous phase. In the case of the n o n - p a r t i t i o n e d t r a c e r d i f f u s i o n must i n e v i t a b l y be from the wake t o the continuous phase i n which the c o n c e n t r a t i o n of t r a c e r i s l e s s . However, i n the case of mass t r a n s f e r , as d e s c r i b e d i n the present work, the wakes are moving towards a r e g i o n of higher c o n c e n t r a t i o n of s o l u t e and t h e r e - f o r e molecular . d i f f u s i o n of s o l u t e i s from the continuous phase towards the wake. As- has been discussed elsewhere i n t h i s t h e s i s 155 molecular d i f f u s i o n can be neglected w i t h respect t o eddy d i f f u s i o n , and hence i t i s f e l t t h a t t h i s p a r t i c u l a r d i s t o r t i o n of the wake composition can be neglected. There i s y e t , however, one more f a c t o r t o be considered. Mass t r a n s f e r i n e v i t a b l y w i l l occur between the wake and the drop i t s e l f by the t r a n s f e r of the p a r t i t i o n a b l e s o l u t e from the wake t o the drop. For the moment bur concern i s w i t h the wake i t s e l f and such mass t r a n s f e r .would s t i l l f u r t h e r . d e p l e t e the s o l u t e i n the wake and so when p a r t s of t h i s wake are cast o f f at higher l e v e l s the amount,of s o l u t e t r a n s f e r r e d by the backmixing method w i l l be lower than that had mass t r a n s f e r not taken p l a c e . In passing one might mention t h a t because pa r t of the drop i s exposed t o the wake r a t h e r than t o the. surrounding continuous phase mass t r a n s f e r t o the drop w i l l be:lower than would.have been true i f ' t h e wake had not e x i s t e d . E v i d e n t l y the d i s p e r s i o n model.should be used w i t h c a u t i o n f o r the case of mass t r a n s f e r between the phases. In s p i t e of the above mentioned d e f i c i e n c e s of the d i s p e r s i o n model i t was used i n t h i s work t o analyse the r e s u l t s of f i v e runs i n v o l v i n g mass t r a n s f e r . For each run Equation iki • C c = Aexp. ( A XZ) + Bexp ( A 2 Z ) ~ Q iU was f i t t e d t o the measured co n c e n t r a t i o n p r o f i l e of a c e t i c a c i d i n the continuous phase over the t e s t s e c t i o n f o r a value of 2 6 0-ft./hr. for' the a x i a l eddy d i f f u s i v i t y , E. Values of A and B were estimated by means, of the l e a s t squares technique as l$6 described under Theory. These c a l c u l a t i o n s were performed on an IBM-7040 e l e c t r o n i c computer. The f l u x of solute, J, down the column was calculated by means of Equation 21: L D C 21 The curve f i t t i n g was repeated f o r values of E decreased by one f o r each successive t r i a l ( i . e . 59, 58, 57, etc.) u n t i l . e i t h e r ) i l 0 r X 2 r e a c l i e ^ a v a l u e °f 10^- Numbers greater than 10^ could not be handled by the IBM-7040 e l e c t r o n i c computer. The lower l i m i t of E was between 5 and 9- The value of E which resu l t e d i n the smallest sum of squares, A , of the deviations between the calculated and measured values of c^, was taken to be the estimate of E. The values of E calculated by t h i s method and the values of E ca l c u l a t e d by means of tra c e r studies f o r s i m i l a r column operating conditions are given i n table l6. TABLE 16. COMPARISON OF AXIAL EDDY DIFFUSIVITY BY MASS TRANSFER AND TRACER STUDIES. Mass t r a n s f e r studies Tracer studies Run ftV/hr..ftT f t ? / h r . f t ? E, f t ? / h r . Run f t ? / h r . J l J2 J3 J4 J5. 36.5 18.2 36.5 48 A 48.4 54.T 5U.7 91.2 91.2 127 16, 4 2 31 39 53 k9 51 138 139 lk3 15 15 l l l l 9 Table IV-10 shows the point values of and E f o r the estimation 1-57 of E i n each of the f i v e runs. In each run the value of the a x i a l eddy d i f f u s i v i t y , E, determined from concentration p r o f i l e s with mass t r a n s f e r was l e s s than E calculated from t r a c e r studies f o r the same column operating conditions. The estimation of E f o r each run was repeated several times. ' The f i r s t r e p e t i t i o n involved the replacement i n the c a l c u l a t i o n s of J as given by Equation 21 by J as given by Equation 25: J = ( L c c'J - L D c°) . 2 5 The second r e p e t i t i o n consisted of repla c i n g the value of J used by that given by Equation 26: . J = ( LC CC " LD C C } Further r e p e t i t i o n s involved the use of various a r b i t r a r i l y chosen values of m and K^a. Tables IV-11 and IV-12, Appendix IV show the values' of E calculated f o r each of the three values of J used and also f o r the various values of m and K^a used f o r each run. T y p i c a l sets of r e s u l t s are shown g r a p h i c a l l y i n Figures 47, 48, 49, and 50 Figure'47 shows how passes through a minimum value as E i s varied a r b i t r a r i l y . However, the minimum value of £ i s not pronounced enough to enable E to be estimated with any great accuracy. In addition, the true value of E i n any case may not correspond exactly with the minimum value of & because of  159 FIGURE 1+8. THE EFFECT ON E OF VARYING THE METHOD OF-FLUX CALCULATION AND OF VARYING K^a FOR RUN J I i6o ' I 84 188 1-92 196 m FIGURE 4 9 . THE EFFECT ON E OF VARIATIONS IN m FOR RUN J l l 6 l O MEASURED CONCENTRATION EQUATION 14 F ITTED TO THE EXPERIMENTAL POINTS ' i I | i l i ; j ; — i _ _ L _ 1 2 3 4 5 6 7 8 9 10 SAMPLING POSITION, S C A L E : K6 U-H FIGURE 5 0 , MEASURED AND FITTED CONCENTRATION PROFILES FOR RUN J l 162- the f a c t t h a t the u n d e r l y i n g assumptions on which the l e a s t squares f i t t i n g technique i s based have no sound b a s i s as a p p l i e d i n t h i s case. These assumptions are t h a t the c o n c e n t r a t i o n of s o l u t e i n the continuous phase at each sampling p o i n t comes from a normal d i s t r i b u t i o n and t h a t each such d i s t r i b u t i o n has the same variance a t a l l sampling p o i n t s (125)« Figu r e 48 shows the e f f e c t on E of c a l c u l a t i n g J by the v a r i o u s methods. This f i g u r e a l s o shows the e f f e c t of a r b i t r a r y changes i n the value of K^a-used i n the c a l c u l a t i o n . The d i f f e r e n c e s i n the values of J used a r i s e because the f l u x of s o l u t e down the column as c a l c u l a t e d a t the upper and a t the lower ends of the column are not equal. These d i f f e r e n c e s are due s o l e l y to experimental e r r o r . Large d i f f e r e n c e s r e s u l t between the values of E c a l c u l a t e d from the various values of J . The e r r o r i n the value of K^a c a l c u l a t e d by means of Equation 20 may be 'quite l a r g e due t o the d i f f e r e n c e ( c Q - C D ) b e i n g m s m a l l compared w i t h ^ c ^ o r c^. Figure 48 shows t h a t the c a l c u l a t e d value of E is'highly mdependent upon the value of K^a used. Hence s m a l l e r r o r s i n c^, m, or c^ r e s u l t i n a l a r g e e r r o r i n E. " The e f f e c t on the c a l c u l a t e d value of E of the value of m used i s shown- i n Figure 49• E v i d e n t l y t h i s e f f e c t i s q u i t e s u b s t a n t i a l . As mentioned e a r l i e r the value of m used i n i t i a l l y (Table IV-9) was the a r i t h m e t i c average of m a t the ten hypodermic 163 needle sampling p o s i t i o n s . The values of m a t the highest and lowest hypodermic needles f o r Run J I were 1.86 and 1.99 r e s p e c t - i v e l y . The assumption of constancy of m over the t e s t s e c t i o n o b v i o u s l y i s not v a l i d . Furthermore there are no t h e o r e t i c a l grounds f o r t a k i n g the a r i t h m e t i c average of m as t h a t value of m which should be used. In the l i g h t of Figure 4-9 and these f a c t s the c a l c u l a t e d value of E can be conside r a b l y i n e r r o r . F i g ure 50 shows the measured concentrations f o r Run J I . Superimposed'is the curve c a l c u l a t e d from Equation Ik using.the value of K^a c a l c u l a t e d by means of Equation 20, the value of J c a l c u l a t e d from Equation 21, and the value of m-calculated as the a r i t h m e t i c mean of m at the ten hypodermic needle sampling p o s i t i o n s A l t h o u g h the value of E corresponding t o t h i s curve may be i n e r r o r , the agreement between the-curve and the e x p e r i - mental p o i n t s i s good. 164 CONCLUSIONS A b e t t e r understanding of sampling methods has r e s u l t e d from the work described i n t h i s t h e s i s . At low continuous phase f l o w r a t e s a hook-probe sample i s r e p r e s e n t a t i v e of the continuous.phase i n the column a t the sampling e l e v a t i o n . However, a t high f l o w r a t e s of the phases such a sample appears t o be r e p r e s e n t a t i v e of continuous phase i n the column at some height above the sampling e l e v a t i o n . . Hypodermic needles (22-gauge) do, however, withdraw continuous phase which i s r e p r e s e n t a t i v e of that, i n the. column at the sampling height. The d i s p e r s e d phase s o l u t e c o n c e n t r a t i o n obtained from the b e l l - p r o b e sample i s r e p r e s e n t a t i v e of the di s p e r s e d phase i n the '• column a t the sampling e l e v a t i o n . Equation I I I - 8 i n conjunction with' the r e s u l t s of a p i s t o n sample and the t e r m i n a l c o n d i t i o n s of the column gives the average s o l u t e c o n c e n t r a t i o n i n the continuous phase, e x c l u d i n g the c o n t r i b u t i o n from the wakes, of the p i s t o n sample at the time of sampling. This c a l c u l a t e d value of the s o l u t e c o n c e n t r a t i o n i n the continuous phase together w i t h Equation,-6 r e s u l t s i n the average s o l u t e c o n c e n t r a t i o n i n the disp e r s e d phase of the p i s t o n sample a t the time of sampling. This work has t e s t e d the' d i s p e r s i o n model as a means of d e s c r i b i n g a x i a l mixing of the continuous phase of a spray column. The p r e d i c t i o n by t h i s model of an e x p o n e n t i a l decay of s o l u t e c o n c e n t r a t i o n upstream, w i t h respect t o continuous phase f l o w , 165 from the i n j e c t i o n p o i n t of a t r a c e r s o l u b l e only i n the continuous phase, i s i n agreement w i t h experimental r e s u l t s . The a x i a l eddy d i f f u s i v i t y , which c h a r a c t e r i z e s the a x i a l mixing of the c o n t i n - uous phase, was c a l c u l a t e d from such r e s u l t s . In a d d i t i o n the e f f e c t s of column diameter, column height, drop s i z e , and fl o w - r a t e s of the two. phases have been measured e x p e r i m e n t a l l y . The a x i a l eddy d i f f u s i v i t y of the continuous phase i s independent of the s u p e r f i c i a l v e l o c i t y of the continuous phase and of the column height and remains approximately constant as the d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y i s decreased from high values. However, the a x i a l eddy d i f f u s i v i t y i n c r e a s e s r a p i d l y as the dispe r s e d phase s u p e r f i c i a l v e l o c i t y i s decreased to low values. This e f f e c t i s less.pronounced a t sm a l l drop s i z e s . The e f f e c t of i n c r e a s i n g the drop s i z e f o r a given d i s p e r s e d phase super- f i c i a l v e l o c i t y i s t o in c r e a s e the a x i a l eddy d i f f u s i v i t y . The e f f e c t of i n c r e a s i n g the column diameter i s t o increase the a x i a l eddy d i f f u s i v i t y . For the same f l o w r a t e s of r e s p e c t i v e phases i n each of the two columns the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y f o r the continuous phase i s between 6.3 and 17-3 times greater i n the 3 ~ i n . I.D. column than i n the l§ r - i n . I.D. column f o r the s i n g l e value of d (0.135-in.) i n v e s t i g a t e d . The mixing c e l l - p a c k e d bed analogy, when a p p l i e d t o a spray column, p r e d i c t s the P e c l e t number adequately f o r dis p e r s e d phase drops of about 0.155-in. d^. For drops of smaller e q u i v a l e n t diameter the agreement between the p r e d i c t e d P e c l e t 166 number and the measured P e c l e t number becomes worse. In the present work drop s i z e d i s t r i b u t i o n s were measured i n order t o de f i n e the p h y s i c a l systems e x i s t i n g i n the v a r i o u s backmixing s t u d i e s . This was an a u x i l l i a r y study and not a complete i n v e s t i g a t i o n of drop s i z e d i s t r i b u t i o n s f o r v a r i o u s n o z z l e t i p s i z e s , n o z z l e t i p v e l o c i t i e s , and the l i k e . . For the r e s t r i c t e d c o n d i t i o n s i n v e s t i g a t e d drop s i z e d i s t r i b u t i o n p l o t s show two peaks. For a l l the drop formation c o n d i t i o n s i n v e s t i g a t e d i n t h i s work the f i r s t peak occurs a t an eq u i v a l e n t drop diameter of about 0 . 0 2-in. and i n d i c a t e s a l a r g e number of drops of t h i s s i z e . The second peak i s high and narrow f o r drops of about 0.095-in. e q u i v a l e n t diameter (formed at. 0 .053~in. I.D. nozzle t i p s ) and becomes p r o g r e s s i v e l y f l a t t e r and broader as the equi v a l e n t diameter i s increased t o about 0.155'-in. (formed a t 0.126-in. I.D. nozzle t i p s ) . The p i s t o n sampler proved t o be an e x c e l l e n t device f o r use i n measuring the di s p e r s e d phase hold-up. This hold-up was found t o be almost independent of the continuous phase super- f i c i a l v e l o c i t y as, indeed, would be expected. The hold-up i n c r e a s e s approximately l i n e a r l y w i t h d i s p e r s e d phase f l o w r a t e s above 6 0-ft./hr. f t . For a given d i s p e r s e d phase f l o w r a t e the • hold-up inc r e a s e s w i t h decreasing drop s i z e except when d^ i s greater than about O.lU-in. 167 A x i a l eddy d i f f u s i v i t i e s can be c a l c u l a t e d from runs i n v o l v i n g mass t r a n s f e r by f i t t i n g the d i s p e r s i o n model equation t o e x p e r i - mental c o n c e n t r a t i o n p r o f i l e s . However, the eddy d i f f u s i v i t y values obtained were very s e n s i t i v e t o s m a l l changes i n the f l u x of s o l u t e down the column, the value of the mass t r a n s f e r c a p a c i t y c o e f f i c i e n t , and the value of the d i s t r i b u t i o n c o e f f i c i e n t . The e f f e c t of small.changes i n other parameters such as s u p e r f i c i a l v e l o c i t i e s and disp e r s e d phase hold-up on the c a l c u l a t e d values of the a x i a l eddy d i f f u s i v i t y were not i n v e s t i g a t e d . I n v e s t i g a t i o n s i n t o the v a l i d i t y of the boundary c o n d i t i o n s proposed by Danckwerts (60) as a p p l i e d t o an experimental column might l e a d t o the accurate p r e d i c t i o n of s o l u t e c o n c e n t r a t i o n p r o f i l e s by means of the d i s p e r s i o n model equation and. a x i a l eddy d i f f u s i v i t y values measured i n t h i s work by t r a c e r experiments w i t h no mass t r a n s f e r . NOMENCLATURE Constant of i n t e g r a t i o n . i I n t e r f a c i a l area per u n i t volume of column, f t ? / f t ? Constant of i n t e g r a t i o n . Average s o l u t e c o n c e n t r a t i o n i n the continuous phase backmixing stream, l b . - m o l e s / f t . Reduced co n c e n t r a t i o n i n the continuous phase. Solute c o n c e n t r a t i o n i n the continuous phase, l b . - m o l e s / f t . or microgm./ml. Solute c o n c e n t r a t i o n i n the continuous phase of a be l l - p r o b e sample or a p i s t o n sample a t the time of a n a l y s i s , l b . - m o l e s / f t . Value of when z = 0, microgm./ml. Solute c o n c e n t r a t i o n .in the continuous phase i n the j'k*1 c e l l of a s e r i e s of p e r f e c t mixers, lb.-moles/ "Tt? or microgm./ml. Solute c o n c e n t r a t i o n i n the continuous phase i n l e t , l b . - m o l e s / f t ? Solute c o n c e n t r a t i o n i n the continuous phase o u t l e t , Tb.-moles/ft? Solute c o n c e n t r a t i o n i n the d i s p e r s e d phase, l b . - m o l e s / f t ? 169 Solute c o n c e n t r a t i o n i n the dispersed phase i n the c e l l of a .series of p e r f e c t mixers, l b . - m o l e s / f t ? or microgm./ml. Solute c o n c e n t r a t i o n i n the dispersed phase of a b e l l - p r o b e sample or a p i s t o n sample at the time of• a n a l y s i s , l b . - m o l e s / f t . Solute c o n c e n t r a t i o n i n the dispersed phase i n l e t , l b . - m o l e s / f t . Solute c o n c e n t r a t i o n i n the dispersed phase o u t l e t , l b . - m o l e s / f t ? Constant of i n t e g r a t i o n . Height of a mixing c e l l , f t . Value of d g at the second peak of a drop s i z e , d i s t r i b u t i o n p l o t , i n . or f t . ' E q u i v a l e n t drop diameter = the diameter of a sphere whose volume i s the same as t h a t of the drop, f t . Continuous phase a x i a l eddy d i f f u s i v i t y f o r the case of the dis p e r s e d phase moving r e l a t i v e t o the co-ordinate axes, f t . / h r . Continuous phase a x i a l eddy d i f f u s i v i t y f o r the case o f the d i s p e r s e d phase s t a t i o n a r y r e l a t i v e t o the 2 co-ordinate axes, f t . / h r . Volumetric f r a c t i o n of continuous phase i n the column. Test s e c t i o n height, " f t . Volume percentage of dispersed phase i n the column, °jo. 170 V e r t i c a l dimension of a drop image correct e d f o r m a g n i f i c a t i o n , f t . 2 J Wet f l u x of s o l u t e down the column, l b . - m o l e s / ( h r . f t . ) . Mass t r a n s f e r c o e f f i c i e n t based on lb.-moles m " °D d r i v i n g f o r c e , ( . h r . ) ( f t ? ) ( l b . - m o l e s / f t ^ ) S u p e r f i c i a l v e l o c i t y of the continuous phase back- 's 2 mixing stream r e l a t i v e t o the l a b o r a t o r y , f t . / ( h r . f t . ) . S u p e r f i c i a l v e l o c i t y . o f the continuous phase f o r the case of.the d i s p e r s e d phase moving r e l a t i v e t o co-ordinate axes f i x e d w i t h respect t o the l a b o r a - t o r y , , f t ? / ( h r . f t ? ) . S u p e r f i c i a l v e l o c i t y of the continuous phase f o r the case of the dispersed phase s t a t i o n a r y r e l a t i v e t o co-ordinate axes. These may be e i t h e r f i x e d or o 2 moving r e l a t i v e t o the l a b o r a t o r y , f t . / ( h r . f t . ) . Lp S u p e r f i c i a l v e l o c i t y of the dis p e r s e d phase r e l a t i v e o 2 to the l a b o r a t o r y , f t . / ( h r . f t . ) . L„p S u p e r f i c i a l v e l o c i t y of the t r a c e r feed r e l a t i v e o 2 t o the l a b o r a t o r y , f t . / ( h r . f t . ) . (Cp\ D i s t r i b u t i o n c o e f f i c i e n t f o r the s o l u t e between the — C / GQ D' * c o n t i nuous phase and the dispersed phase, (lb.-mole s / f t ?)/(lb.-mole s / f t ? ) . (Ud \ P e c l e t number f o r two phase, f l o w (L^d \ P e c l e t number f o r s i n g l e phase flow . p^ H o r i z o n t a l dimension of a drop image c o r r e c t e d f o r m a g n i f i c a t i o n , f t . 2 S C r o s s - s e c t i o n a l area of the column, f t . t . Time, hr. (L^+L \ 'Continuous phase i n t e r s t i t i a l v e l o c i t y r e l a t i v e t o e 1—e/ / ' the r i s i n g drops, f t . / h r . \ '• Average l i n e a r v e l o c i t y of the dis p e r s e d phase drops r e l a t i v e t o the l a b o r a t o r y , f t . / h r . U -I n 11-e, AL, Volume of the continuous phase backmixing stream 3 i n a p i s t o n sample, f t . V Volume of the continuous phase i n a b e l l - p r o b e • 3 sample or. a p i s t o n sample, f t . V^ Volume of .the.dispersed phase i n a b e l l - p r o b e sample' 3 or a p i s t o n sample-, f t . VT-, Average volume of a continuous phase backmixing "packet" a s s o c i a t e d w i t h each d i s p e r s e d phase 3 drop, f t . . 3 Vp- Average volume of a dis p e r s e d phase drop, f t . 172 y=z + ut Distance along the column, i n the d i r e c t i o n of the continuous phase f l o w , r e l a t i v e t o co-ordinate axes s t a t i o n a r y w i t h respect t o the disp e r s e d phase drops, f t . Z = z/H Dimensionless distance along the column i n the d i r e c t i o n of the continuous phase f l o w , z Distance along the column, i n the d i r e c t i o n of the ' continuous phase f l o w , r e l a t i v e t o co-ordinate axes s t a t i o n a r y w i t h respect t o the l a b o r a t o r y , f t . o < = H 2 - E e L D J f t : 1 P = ( LD - aH f t T 1 mL^Ee LD E e CCO 3N2 ^=2[Cc ' A e x p ( \ Z ) - B e x P ( ^ 2 Z ) + Q ] ' ( l b . - m o l e s / f t ? ) X= °< + v / ^ P > f t T l X = p < - y S f , f t : 1 £> Density of the continuous phase, l b . / f t . V i s c o s i t y of the continuous phase, l b . / h r . f t . 173, LITERATURE CITED 1. Geankoplis, C. J . and Hixson, A. N., Ind. Eng. Chem. 42, 1141 (1950) 2. B l a n d i n g , F. H. and E l g i n , J.C., Trans. Am. I n s t . Chem. Engrs. 3§_, 305 (1942) 3. Johnson, H.F. and B l i s s , " H., Trans. Am. I n s t . Chem. Engrs..42, 331 (1946) 4. Hayworth, C. B. and Trey b a l , R. E., Ind. Eng. Chem. 42, 1174 (1950) 5. 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A., Chem. Eng. Progr. 5£, 79 (1963) 128. J o s t , W., D i f f u s i o n , p. 477, Academic Press Inc., New York, i960 183 APPENDIX I DISPERSION MODEL THEORY The assumptions upon which the mathematical model i s based are given under the heading of Theory. Consider the c o n t r o l zone i n the C-phase, shown i n F i g u r e I - l , d u r i n g the incremental time d t . The case considered i s one i n which mass t r a n s f e r i s t a k i n g place between the continuous phase and the d i s p e r s e d phase. A so l u t e mass balance over the c o n t r o l zone gives the f o l l o w i n g terms. i ) Solute out due t o mass t r a n s f e r . Kp/c^ - c D \ S a ( d z ) ( d t ) \ m I i i ) Solute out due t o C-phase f l o w . L c S ^ c c + | b c c y d z ) j ( d t ) i i i ) Solute i n due t o C-phase flow. L c S c c ( d t ) i v ) Solute i n due to eddy d i f f u s i o n . , E ( ^ - . ( C C + ^ c c j d Z ^ S e ( d t ) = E e S ( d z ) ( d t HEeSpfc^ (dz) ( d t ) C - P H A S E , D-PHASl CONTROL ZONE FIGURE I - T . SOLUTE MASS BALANCE IN THE CONTINUOUS PHASE 185 v) Solute out due to eddy d i f f u s i o n . E/))c c\(dz')eS(dt) Terms i ) to v) i n c l u s i v e have "been shown on Figure I - l as arrows with the corresponding numbers as given here indicated beside them. v i ) Accumulation of solute. / V c \ S e ( d z ) ( d t ) These terms'combine in t o the following mass balance. KJJ / c c - c D\ Sa (dz) ( dt ) + L c S c c (dt ) + L c S A c A (dz) (dt )+E A C ( A Se (dz) (dt) / c c - c D j Sa (dz) ( dt )+L cSc c (dt )+ csp c ^ (dz) (dt ) + E ^ C c J fey +Ac c\Se(dz)(dt)=L cSc c(dt)+E/^c c\Se(dz)(dt)+E/^c c\(dz)Se(dt) The above equation can be rearranged to give At- steady state Equation I - l reduces to 2 \ Ee/d c p \ - L p / d c ^ - K^a/Cp - c ^ = 0 I - l dz / > V m / d z 2 ; v Equation 1-2 can be rearranged to give 1-2 186-- M l ? / v U z / ~ 1-3 The net f l u x , J , of s o l u t e down the column at the e l e v a t i o n z i s given by Equation I-k. J = L c c c - E/dc c\e - L D c D I-k The s u b s t i t u t i o n of c^ from'Equation 1-3 i n t o Equation. --I-k y i e l d s ,2 J = L c c G - Ee/dc^-f L DEe^d cQ\ - /dc c\ -/L Dc cN V d z 1 V d z 2 / a dz y \ m / 1-5 Equation 1-5 can be rearranged t o give , 2 c c l - / v W - /M/ d ccY + / V c V ^ -f^v l L D E e / , 2 / ' I L_. A d z / \Ee/\dz / V L^Ee / \ mEe , . _lV. , d z / \ D / V / • » i \ I \ D ' N ' \ D 1-6 Concentrations and di s t a n c e s can be put on a dimensionless b a s i s by means of Equations 1-7 and 1-8. °C = c c o c c 1-7 z = ZH .. 1-8 These two equations now can be used t o transform Equation 1-6 i n t o Equation 1-9. d Z 2 I \dZ 1-9 187 where o i , p ; and. Y are given by Equation 1-10, 1-11, and 1-12. 1-10 1-11 (Lp - mL^KpaH 2 P ml^Ee L Eec D L ° 1-12 I f p ^ 0 I-12a) and ( c * 2 + p) > 0 I-12b) the s o l u t i o n of Equation 1-9 i s given by Equation 1-13. C c = Aexp Q XZ) + Bexp fo2Z) - Q 1-13 A and B are constants of i n t e g r a t i o n and and Q are given by Equations 1-14, 1-15, and I - l 6 r e s p e c t i v e l y . ^2 = cc-JJ7$ 1-14 1-15 P ." CCO ( LD " m L C ) 1-16 Other s o l u t i o n s of Equation 1-9. are appropriate when the c o n d i t i o n s given by Equation I-12a) and I-12b) are not met. However, the a p p l i c a b i l i t y of these other s o l u t i o n s i s more l i m i t e d than t h a t of Equation 1-13 and no e x t r a i n f o r m a t i o n can be obtained by t h e i r use. When the c o n d i t i o n given by Equation I-12b) i s not s a t i s f i e d problems i n v o l v i n g i n s t a b i l i t y may a r i s e . For a s o l u t e which d i s s o l v e s only in- the continuous phase CD = °> ' . ' 188 and Equation I-k reduces to J = L G c c - Ee 1-17 If, i n addition, continuous phase samples are withdrawn from the portion of the column which, f o r the continuous phase, i s upstream from the feed point of t r a c e r then J = 0. Then Equation 1-17 becomes 1-18 The s o l u t i o n of Equation I - l 8 i s 1-19 where D i s a constant of i n t e g r a t i o n . But c C = c CO when z = 0. Therefore, 1-20 Equation 1-20 can be rearranged . to give 1-21 189 APPENDIX I I A. MIXING CELL - PACKED BED ANALOGYj(kk, 6k, 90, 92, 10Q, 109) Consider a s e r i e s of p e r f e c t mixers as shown i n the sketch below. Suppose t h a t a s o l u t e i s e x t r a c t e d from a moving continuous phase by a s t a t i o n a r y d i s p e r s e d phase. L et the i n t e r - } f j - 2 • 1 1 j ) J-H \ j + 2 V 1 9 0 stage s u p e r f i c i a l v e l o c i t y of the continuous phase be L p , the solute concentration f o r the continuous phase i n the mixer be c ., and the solute concentration f o r the dispersed phase i n o,j th the j mixer be c^ y Let the mass tr a n s f e r c o e f f i c i e n t , K^; the i n t e r f a c i a l area per unit, volume of mixer, a; and the height of a mixing c e l l , . d ^ , , be the same f o r each mixer. At steady t h state a solute, mass balance f o r the continuous phase of the j mixer r e s u l t s I n the following equation. n - 1 Equation I I - l can be rearranged to give 'C , j - 1 " " C j ' ... m C V. / 1 1 - 2 I f E i s replaced by E and L n i s replaced by L Equation u o 1-2 becomes Equation II-3 which i s applicable to the continuous phase of a packed bed with solute t r a n s f e r r e d from the f l u i d phase to the packing. •••(SK®-v I t i s assumed that the solute concentration i n each packing piece i s uniform throughout the piece at the value c^. Sub- s t i t u t i o n pf the c e n t r a l d i f f e r e n c e equivalents of d i f f e r e n t i a l s , as given i n Equations II - U and T l - 5 , i n t o Equation II-3 leads to Equation II-6 (8). 191 ( cC,j+i " c c > j - i ) 2d. 1 Il-k 'dCc\ ( CC„H1 - 2 cC„j + CC„j-l) ,dz ( C c ^ - 1 " C c ^ M ^ " i + - ) + • ( c c , j + i 1 - c c , j ) I I - 5 V i C m J), j II-6 c„ .1=0 B y • c o n s i d e r i n g the i n t e r s t i c e s between the packing pieces of a packed bed as p e r f e c t mixing c e l l s ' an analogy can be drawn between a s e r i e s of perfect,mixers and a packed bed. For Equations II - 2 and I I - 6 t o be : c o n s i s t e n t the f o l l o w i n g e q u a l i t y must be s a t i s f i e d . where 2 P 4 1 , E II-7 II-8 The r i g h t hand side of Equation II-7 d e f i n e s the P e c l e t number Pe »4 i/ i E II-9 192 The mixing c e l l l e n g t h , cL, i s supposed (112) t o be the v e r t i c a l c e n t r e-to-centre d i s tance between the l a y e r s of packing pieces i n an ordered packing system. Although exact values f o r d^ can be c a l c u l a t e d f o r ordered packings, i t would be expected t h a t only an average value f o r d^ could be c a l c u l a t e d f o r random packings. .For a packed bed the value of X'is approximately one. Thus f o r t h i s case Equations I I - 7 and I I - 9 y i e l d the f o l l o w i n g w e l l known" r e l a t i o n s h i p (kk, 6k, 92, 108, 109, 122, 123). Pe'' = 2 B. SPRAY COLUMN - PACKED BED ANALOGY. For a spray column o p e r a t i n g a t steady s t a t e and w i t h a . s o l u t e which d i s s o l v e s only i n the continuous phase Equation.1-2 reduces t o Ee//d 2c cj = L c / d c c | 11-10 Consider a spray column o p e r a t i n g a t steady s t a t e w i t h axes of reference moving a t the same v e l o c i t y , u, as the r i s i n g d ispersed phase drops. The drops appear s t a t i o n a r y , on a time-average b a s i s , r e l a t i v e t o the co-ordinate system.. That i s , the system appears as a packed bed w i t h the packing pieces not touching" each other. Let y be the a x i a l p o s i t i o n r e l a t i v e t o the moving co-ordinate axes. Thus, y = z + ut 11-11 1 9 3 Let the a x i a l mixing of the continuous phase be c h a r a c t e r i z e d by an a x i a l eddy d i f f u s i v i t y , E , r e l a t i v e t o the moving -co-ordinate axes. Consider the c o n t r o l zone i n the continuous phase as shown i n the f o l l o w i n g sketch. L et the c o n t r o l zone be f i x e d r e l a t i v e t o the moving co-ordinate system and be of incremental height (dy), CONTROL. ZONE y + dy CONTINUOUS PHASE D ISPERSED P H A S E A s o l u t e mass balance over the c o n t r o l zone f o r u n i t area of column and f o r an incremental time i n t e r v a l ( d t ) gives j^(L c+ue)c e+ E ' ^ C C ^ P c\(dy)) (dt)= (Lp+ue) ( c c + | V c y d y ) + E e ^ j !(dt) + 'uecc-ue /c c +/^ c \(dy) (dt) 11-12 The l e f t - h a n d s i d e of Equation 11-12 represents the amount of so l u t e entering'the c o n t r o l zone. The terms i n the f i r s t set of square br a c k e t s on the right-hand side of Equation 11-12 represent the amount of so l u t e l e a v i n g the c o n t r o l zone. The terms' i n the second set of square br a c k e t s on the right-hand side of Equation 11-12 represent the accumulation of s o l u t e i n the c o n t r o l zone. Equation 11-12 s i m p l i f i e s to E e 19k- H-13 But ccY = / d c c : dz (12^) and C \ = / * % dz Therefore Equation 11-13 becomes , 2 E e/d c C\ C ,dz dc^ dz (12M 11-14- A comparison o f Equations 11-10 and I I - l h shows t h a t E ' = E 11-15 The i d e n t i t i e s given i n Equations II-15 above, and i n I I - 1 6 , and 11-17 below: 1-e II - 1 6 L c = L c + ue 11-17 can be used w i t h the f o l l o w i n g d e f i n i t i o n of Pe : Pe = / L„ n - 1 8 195 and w i t h Equation I I - 7 t o produce Equation H - 1 9 . Pe - 2- 11-19 For simple ordered l a t t i c e " arragements of uniform s p h e r i c a l drops the v e r t i c a l d i s t a nce "between l a y e r s of drops, d^, i s a f u n c t i o n of the hold-up, h, and the drop diameter, d^. The P e c l e t number, Pe, c a l c u l a t e d from Equation 11-19, i s a f u n c t i o n of h only, The f u n c t i o n g i v i n g d^ and Pe are presented i n the f o l l o w i n g t a b l e f o r s i x simple l a t t i c e arrangements of drops. Each drop i s supposed t o be c o n c e n t r i c w i t h an imaginary l a r g e r sphere whose diameter i s - e q u a l to the centre - t o - centre .distance between neighbouring, drops. In the s i x l a t t i c e arrangements considered each imaginary sphere touches each of i t s nearest neighbours. These l a t t i c e arrangements represent the s t a b l e systems f o r beds of packed spheres and i t i s suggested by the author o f . t h i s t h e s i s t h a t they are the ones most, l i k e l y t o be a p p l i c a b l e .for use i n a p p l y i n g the mixing c e l l - packed bed analogy t o a spray column. I t can be seen from the f o l l o w i n g t a b l e t h a t f o r a given value of h a l l of the p r e d i c t e d Pe values l i e i n the range between the Pe values f o r the. l a t t i c e arrangements of orthorhombic - 2 and rhombohedral - 1. 1 9 6 L A T T I C E Pe NUMBER OF NEAREST NEIGHBOURS DIAGRAM LAYERS 1,3,5 O LAYERS 2,4,6 (ONLY 2 LAYERS SHOWN) CUBIC u J 6 h 3 \ 48 h 7T 6 O O O P L A N O O O O O O Fd FRONT o o o — 1 1 V 1 E W ORTHO- RHOMBIC- 1 w J 8 h 3 64 h 7T 8 O O O O O PLAN o o o c o V , E W O O F R O N T I ' VIEW o o o - 1 RHOMBO- HEDRAL-I J 12 h 3 \ 96 h 7T 12 OrPrP PLAN o ° o " ' o V , E W O O —~rA F R 0 N T O O * O — 1 ' VIEW ORTHO- RHOMBIC-2 J 3fT h 3 24/3 h 7T 8 O O O PLAN O O O V , E W O O O - — - X J FRONT o o o — J 1 V , E W TETRAGONAL 3 \ 3 10 C «000»-0 PLAN O O O O O VIEW O O O - rX FRONT o o O — * ' V I E W 12 h 32/3" h RHOMBO- HEDRAL-2 J 9^3 h 3 36/3" h 7T 12 O'PfO PLAN W " n c n ± 3 d . FRONT O <J y—* i VIEW APPENDIX I I I ANALYSIS OF PISTON SAMPLE RESULTS TO PRODUCE THE AVERAGE CONTIN- UOUS PHASE CONCENTRATION, EXCLUDING THE CONTRIBUTION FROM THE WAKES, IN THE PISTON SAMPLE.AT THE TIME OF SAMPLING continuous phase c o n c e n t r a t i o n , e x c l u d i n g the c o n t r i b u t i o n from the .wakes, i n the p i s t o n a t the time of sampling i s based on a model i n which i t i s p i c t u r e d t h a t each drop c a r r i e s some continuous phase w i t h i t , f o r example i n i t s wake (21, 22, 23, 2k, 26, 1 2 l ) . I t i s assumed t h a t on the average a volume v^ of continuous phase of average s o l u t e c o n c e n t r a t i o n c^ is - c a r r i e d up the column past a given e l e v a t i o n by each r i s i n g d i s p e r s e d . . . h phase drop. Thus the f r e q u e n c y , — , of drops passing through VD Lg u n i t area a t a given e l e v a t i o n i s equal t o the frequency, — , VB of passage of volumes, v^, of continuous phase i n the form of a backmixing stream. The a n a l y s i s of p i s t o n sample . r e s u l t s t o produce the average i . e . V. D V-B Thus I I I - l 198* The number of dis p e r s e d phase drops i n a p i s t o n sample i s VD • and the number of packets of backmixed continuous phase i n a p i s t o n sample i s Therefore, or IP_ = I B v = V _p_ J D v V B B From Equations I I I - l and I I I - 2 , or V B h B LD I I I - 2 I I I - 3 Consider the lower p o r t i o n of a spray column as shown i n Fig u r e I I I - l . I t i s assumed.that the descending continuous phase i s f u l l y mixed a t any given e l e v a t i o n . A mass balance on so l u t e over the s e c t i o n of column shown i n Figure I I I - l y i e l d s 199 V B + V D + L C C C = L C C C + V c + L D C D The above equation can be rearranged to give Os . „ / i - Cc) = L C V D ( C C " C C } + V C D " BD> I I I - l * Now consider a piston sample. Figure III-2a represents t h i s sample at the instant of sampling. Figure III-2b. represents the same sample but l a t e r i n time: when the sample i s analysed. A mass balance on solute i n the pi s t o n sample over the time between sampling and a n a l y s i s y i e l d s V D C D V V B + <vc - V c c = V S + V c " - III-5 Substituting."for Vg from Equation H I - 3 i n Equation III-5 and then rearranging gives ' V D . ( C B - V g . V C S - C D> + V c c - cc> III-6 Equating- ¥ D ( C E - c c ) L D , as given by each of Equations III-l*- a n d III-6 r e s u l t s i n : V c ( C C - C C ) + V C D " C D> = V C D " C D ' ) + \ ( C & C ~ CC) - I I I - T 200 Equation III-7 can be rearranged to give D LC VC + V D III-8 The concentration, c^, given By Equation III-8 i s the average solute concentration:in a piston sample, excluding the contribution from the wakes, at the time of sampling. I t L C CC L D CD BOTTOM OF COLUMN FIGURE I I I - l . LOWER PORTION OF A SPRAY COLUMN 202 V D C D V B PISTON S A M P L E PISTON S A M P L E A T T H E T I M E A T T H E T I M E OF S A M P L I N G O F A N A L Y S I S ( a ) ( b ) FIGURE I I I - 2 . THE EFFECT OF TIME ON A PISTON SAMPLE ) 203 APPENDIX IV CALCULATIONS AND TABULATED RESULTS FOR AXIAL EDDY DIFFUSIVITY DETERMINATIONS AND DROP SIZE DISTRIBUTIONS a) CALCULATIONS. • A specimen hand c a l c u l a t i o n i s presented s t a r t i n g from a data sheet shown i n Table IV-1 . ( A c t u a l data sheets were more . abbreviated than the one shown . i n Table IV-1.) RUN 50 Water f l o w r a t e = 27.7 f t ? / h r . . f t ? Ketone f l o w r a t e = 5U.7 f t . / h r . f t . 3 / 2 Tracer f l o w r a t e = 0.310 f t r / h r . f t . 2 Column I.D. = 1.5 i n . C r o s s - s e c t i o n a l area of column = 0.01227 f t . Sampling r a t e = 1 ml./min. = 0.002119 f t ? / h r . = 0.1727 f t ? / h r . f t ? Ketone hold-up = U.7# .• .204 TABLE IV-1. DATA SHEET. RUN NO. 50 DATE: 25 AUG. 1966 Column' I.D. = 1.5-in. Tracer feed cone.=23,OOO-microgm./ml. Nozzle t i p average I.D.=0.103-in. Water rotameter reading = 86-mm. *Ketone rotameter reading=108-mm. Tracer rotameter reading=7«5- m m « 9 open nozzle t i p s L =27-7-ft? A i r . f t ? L r = 5 k . 7^-ft|/hr.ft| I^=0.310-ftv/hr.ft. Average temperature of the f l u i d s i n the column = 72°F Steady state time=l-hr. Sampling rate = 1-ml./min. ANALYSIS.OF SAMPLES (See fi g u r e 10 f o r sampling po s i t i o n s ) Sampling Sample D i l u t i o n Absorption p o s i t i o n c o l l e c t i o n f a c t o r reading on / / - ' - tube spectropho- meter, 1 GI 25 54.7 2 G2 10 58.0 3 03 ' 5 48.3 k G4 5 31.8 • > 5 G5 • 1 4o.6 6 • G6 • 1 20 .6 •7 07 1 • . 8.1 8 G8 1 " 3 A . 9 G9 ' 1 1.6 10 G10 1 0.9 aqueous phase G i l 100 41.7 leaving column CALIBRATION OF ATOMIC ABSORP- TION SPECTRO- PHOTOMETER ' PISTON SAMPLE Sample Absorp- cone., t i o n , microgr. 1o " /ml. 0 0.0 1 I8.7 3 46.7 5 64.3 7 76.2 9 84.3 T r i - a l A B C D E F G 1 0.9.5 6.45 0.95 6.25 116.4 5-3 4.55 2 0.95 6.85 0.95 6.65 116.4 5-7 4.90 . 3 1.0 6.60 1.0 6.40 116.4 5-4 4.64 A=reading of ketone/air i n t e r f a c e level,'ml.- B=reading of water/ketone i n t e r f a c e l e v e l , ml. C=corrected A from c a l i b r a t i o n curve, ml. D=corrected B from c a l i b r a t i o n curve, ml. E=total volume in' sample, ml. F=volume of ketone i n sample, ml. G=hold-up of dispersed phase, # AQUEOUS PHASE OUTLET SAMPLE C o l l e c t i o n tfme=40-min. Weight of c o l l e c t i o n flask= 1-lb. 15-oz. Weight of f l a s k + sample= 16-lb.' 2-oz. Weight of sample=l4-lb.3-oz. KETONE PHASE OUTLET SAMPLE C o l l e c t i o n time=10-min-i • " Weight of c o l l . f l a s k = l - l b . 5 - o z . Weight of f l a s k + sample=6-lb . l4-oz. Weight of sample=5-lb.'9-oz.'. C a l i b r a t i o n of atomic absorption spectrophotometer 205 Sodium cone. Absorption Absorbance (Absorbance)' (Cone.) (Absorbance) 0 1 3 5 7 9 0.0 . 1&..7 46.7 64.3 76.2 84.3 0.0000 0.0899 0.2733 0.4473 0.6234 0 .804 - 1 0.0000 0.0081 0.074-7 0.2001 0.3886 0.6466 .0.0000 0.0899 0.8199 2.2365 4.3638 .7.2369 T o t a l 25 2.2380 1.3181 14.7470 Let t h e : c a l i b r a t i o n l i n e be - -cone. = (m^)(absorbance) + By l e a s t squares f i t (2.,2380)(25) - (6)(l4.7^70) m l = (2.2380) 2 - ( 6)(l . 3 l 8 0 ) ( 2 5)(l . 3 l 8 l ) - (2.238o)(l4.7470) and k± =-( 6)( 1 < 3 1ei) . (2.2380) 2 = 11.22 = -0.018 Therefore, cone. = (11.22)(absorbance) - 0.018 Table IV-2 shows the c a l c u l a t i o n of the solute concentration at the sampling posi t i o n s i n the column. Also shown i n Table IV-2 are quantities required'for f u r t h e r computations. The dimensions of each piece of Pyrex pipe i n the t e s t section of the column are given i n Table VI - 1 , Appendix VI. Water balance Density of MIBK-saturated water = 0.996 gm./ml. (Measured by means of s p e c i f i c g r a v i t y b o t t l e ) Aqueous phase l e a v i n g the lower end of the column = 14 l b . 3 oz. i n 1*0 min. = 27.897 f t ? / h r . f t 2 n p Sampling r a t e = 1 ml./min. = 0.1727 f t r / h r . f t . O p Tracer feed r a t e = 0.310 f t . / h r . f t . ' Aqueous phase f e d t o the column =27-7 f t . / h r . f t . Apparent l o s s = 27.7 + 0.310 - 0.1727 - 27.897 27.7 (100)$ = -0.22$ Ketone balance Density of water-saturated MIBK = O.806 gm./ml. (Measured by means of s p e c i f i c g r a v i t y b o t t l e ) Ketone phase l e a v i n g the E l g i n head of the column = 5 l b . 9 oz. i n 10 min. = 54.07 f t . / h r . f t . Ketone phase f ed t o the column = 54.74 f t . / h r . f t . Apparent l o s s = Tracer balance 54.74 - 54.07 54.74 (100) $ = 1.22$ The amount of t r a c e r l e a v i n g the column due t o sampling i s neglected. TABLE IV-2. CALCULATION OF QUANTITIES USED FOR THE CALCULATION OF E. sampling p o s i t i o n ( F i g s . 9 and 10) Height above t r a c e r d i s t r - i b u t o r =w,ft, D i l u - t i o n f a c t o r Absor- p t i o n * Absor- bance Measured cone., microgm. per ml. Sample cone. =cc> microgm. per ml. Log e(C c.) = q 2 w 2 q 1 0.5115 25 54.7 0.3439 3.8406 96.015 4.564 0.2616 2.3345 20.8301 2 1.014 10 58.0 0.3768 4.2097 42.097 3-740 1.0282 3.7924 13^9876 3 1.517 5 48.3 0.2865 3.1965 15.9825 2.771 2.3013 4.2036 7.6784 4 2.020 "5 31.8 0.1662 1.8468 9.2340 2.223 4.0804 4.4905 4.9417 5 2.527 1 40.6 0.2262 2.5200 2.2500 0.9423 6.3857 2.3812 0.8543 6 3-015 1 20.6 0.1002 1.1062 I..IO62 0.1008 9.0902 0.3039 0.0102 7 3.518 1 8.1 0.0367 0.3938 0.3938 -0.9319 12.3763 -3.2784 0.8684 •8 4.028 l - 3.4 0.0150 O.1503 0.1503 -1.895 16.2248 -7.633I 3.5910 9 4-537 1 1.6 0.0070 O.0605 0.0605 -2.805 20.5844 -12.7263 7.8680 10 5.045 1 0.9 0.0039 0.0258 0.0258 il*» 100 41.7 0.2343 2.6108 261.08 . T o t a l * 22.6875 167.559 8.709 72.3329 -6.1317 1 60.6297 * For p o s i t i o n s 1 to 9 ( i n c l . ) only. (Sample cone, a t p o s i t i o n 10 i s l e s s than 0.05 microgm./ml.) * * P o s i t i o n 11 r e f e r s t o the aqueous phase l e a v i n g the column. 208 Tracer l e a v i n g the lower end of the column = (27'.897)(26l.08)=7,283 (microgm./ml. ) ( f t ? ) / ( h r . ) ( f t ? of column) Tracer f e d t o the column = (0.310)(23,000).= 7,130 (microgm./ml.) • . ( ' f t ? ) / ( h r . ) ( f t ? of column) Apparent l o s s =[7,130 - 7,283"] (100) $ = -2.15$ L T A 3 0 J A x i a l eddy d i f f u s i v i t y The f o l l o w i n g s t a t i s t i c a l computations are based on the methods described by Bennett and F r a n k l i n (125). n = the number of sample concentrations l e s s than 0.05-microgm./ ml.. = 9 S(q,w)= g ( q ) ( v ) - S(q )5(w) = -6.1317-(22.6875)(8.709) = -28.0856 n 9 S ( q 2 ) =^( (1 2) " H a l 2 . ' = 60.6297 - 8.709 2 = 52.2023 • ' n ' . 9 . S(w 2) =^(w 2) - ( $ w ) 2 = 72.3329 - 22.6875 2 = 15.1415 • n . 9 v/s(.w2) = 3.8912 - S 2 [ r = ( S ( q 2 ) ) ( S ( w 2 ) - ( S ( q , w ) ) 2 = (52.2023) (15. lkX5) - ( -28.0856 )2=0.01529 *'w 'U^(sU)) ( 7 ) ( l 5 . l f l 5 ) : Sq,w = ° ' ^ 6 A l e a s t squares f i t (125) of the data t o the equation q = (M)(w) + K y i e l d s . . • K = ( 5 q ) ( 5 w 2 ) - S((g)(w))£w = (8.709)(72.3329)-(-6.1317)(22.6875) ( n ) ( ^ ( w 2 ) ) - ( ^ w ) 2 (9)(72.3329) - (22.6S75) 2 = 5.640 209 and M = S(q,w) = -1.8549 = -I.8549 S"(w2) 15.1415 i confidence l i m i t s on M are (125) M + ( t o . ) (S ) - v n-2,g<. q,v / S T Y where t 0 , , = the value of the t - d i s t r i b u t i o n f o r (n-2) degrees of freedom and (l00)(l-©<) $ confidence l i m i t s . Y o . 0 5 = 2 ' 3 6 k 6 ( 1 2 5 ) 95$ confidence l i m i t s on M are -I.8549 t- (2.3646)(0.1236) = -I.8549 t 0.07511 3-8912 = -1.9300 t o -1.7798 ( I t should be noted t h a t f o r runs where n = 2 no s t a t i s t i c a l t e s t r e g arding the confidence of r e s u l t s can be performed. For runs where n = 3 the 95$ confidence l i m i t s on M are l i k e l y t o be wide since ^ , 0 . 0 5 = 1 2 ' 7 1 - ' In f a c t the 95$ confidence l i m i t s c a l c u l a t e d f o r runs where n = 3 are not l i k e l y t o represent the tr u e s i t u a t i o n because i t i s not p o s s i b l e t o i n c l u d e n o n - s t a t i s t i c a l reasoning i n the s t a t - i s t i c a l a n a l y s i s . For example, there i s no reason t o doubt the l i n e a r i t y of the r e l a t i o n s h i p between and UJ f o r runs where n i s greater than 3•) The s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , (Ee), i s given by the f o l l o w i n g equation. 210 (Ee) = - L c ~M~ (Ee) = -27.7 = 14.93 f t ? / h r . -1.8549 The f l o w r a t e , L^, of aqueous phase f e d t o the column can be measured and kept constant t o w i t h i n approximately 1$ of L^. On the assumption: t h a t the recorded value of comes from a normal d i s t r i b u t i o n an estimate of the standard d e v i a t i o n , cT~r, of L c i s given by (125) CT^C = (L c/100) . Therefore (J- = 27.7 = 0.09233 L C 300 An estimate of the v a r i a n c e , C J ^ , of M i s given by c r M = s = 0.01529 = 0.001010 15.1415 S(w 2) The v a r i a n c e , C 7 E e , of (Ee) i s given by the f o l l o w i n g equation (125) ''Ee (Be) £ m t M J = (14.93T o. 09233 \ + /.o. 00101 27.7 J 13.4407 0.06791 Therefore 0 ~ = 0.2606 Ee In c a l c u l a t i n g 95$ confidence l i m i t s f o r (Ee) i t must be remembered t h a t M was determined from n data p o i n t s . A reasonable approximation i s t o assume t h a t (Ee) comes from a t - d i s t r i b u t i o n 211 with (n-2) degrees of freedom. Therefore the 95$ confidence limits on (Ee) are ( E e) " ^n - 2 , O ^ ^ =-14.93 - (2.3646)(o.26o6) = 14.93 t 0.62 = 14.31 to 15.55 Now l~hold-up 100 • The three values of e calculated from hold-up measurements are e = 1 - 4.55 = 0.9545 100 e = 1 - 4.90 = O.95IO 100 e = 1 - 4.64 = 0.9536 100 The arithmetic average of e = 0.9545 + O.9510 + O.9536 = O.953O 3 The best estimate, O" , of the variance of e is given by gf = (n)(Se2) - (ge)2 = (3)(2.72482421) - (2.8591) 2 (n)(n-l) (3,(2) = 0.000003303 The axial eddy diffusivity, E, is given by E = (Ee) = 14.93 = 15.67 ' e 0.9530 2 The variance, o~n,, of E is given by 'E 'Sit + K Ee/ I e / = (15.67 2 ) r 70.2606^ 2 + 0. U ^ . 9 3 7 000003303 (0.9530) 2 = 0.0748 212' Therefore . <TK= 0.2735 On the assumption t h a t E comes from a t - d i s t r i b u t i o n w i t h (n-2) degrees of freedom the 95$ confidence l i m i t s f o r E are taken to be E t ( t n _ 2 , 0 . 0 5 ) ( = 1 5 ' 6 t +- (2.3646)(0.2735) = 15.67 t 0.65 = 15.02 t o 16.32 The P e c l e t number, Pe, i s c a l c u l a t e d from the f o l l o w i n g equation. (d ) r \ 1 - e e / Pe = 11-18 where d^ i s the dispersed phase drop diameter. Pe = /Q.I35^ /54.74 + 27.7 V = O.857 /0.135) / 54.74 + 27.7 ^ [ 12 J [ 0T0W 0.953/ 15-67 . Table IV - 3 shows the r e s u l t s of the above c a l c u l a t i o n s as c a r r i e d out on 'an IBM-7040 e l e c t r o n i c computer. b) TABULATED RESULTS Table IV -4 "gives the reduced con c e n t r a t i o n p r o f i l e s , the dispe r s e d phase hold-up, the number of experimental p o i n t s used f o r the e s t i m a t i o n of the a x i a l eddy d i f f u s i v i t y , the a x i a l eddy d i f f u s i v i t y , and the P e c l e t number f o r each run c a r r i e d out wi t h the 1-^-in. I.D. column. The reduced con c e n t r a t i o n p r o f i l e , the number of experimental p o i n t s used f o r the e s t i m a t i o n of the TABLE IV-3. TYPICAL COMPUTER RESULTS RUN 50 HATER FLOWRATE • 27.70 CU.FT./IHR. SO.FT.) KETONE FLOWRATE • 54.74 CU.FT./INR. SO.FT.I TRACER FLOWRATE - 0.510 CU.FT./IHR. SQ.FT.> _ 1 _ NOZZLE TIP AVERAGE DIA. • 0.10) IN. EQUIVALENT. DROP OIA. « 0.135 IN. AVERAGE VELOCITY OF OISPERSEO PHASE IN NOZZLE TIPS • 0.56 FT./SEC. COLUNN I.D. • 1.5 IN. COLUMN HEIGHT INOZZLE TIPS TO INTERFACE 1 • lO^FT. 3 1/0-IN. TEMPERATURE » 72 »F CALIBRATION OF ATOMIC ABSORPTION SPECTROPHOTOMETER SOO.CONC. PER CENT ABSDRBANCE CONCENTRATIONS ARE M ABSORPTION MICROGN./NL. 0 0.0 0.000 t 18.7 0.090 3 46.7 0.273 5 • 64.1 0.447 7 76.2 0.623 9 84.3 0.804 CONCENTRATION • U.219*ABSORBANCE-0.018 POSITION OILUTION PER CENT ABSORBANCE MEASURED SAMPLE LOG.E REOUCEO ISEE FIG. FACTOR ABSORPTION CONC. CONC. CONC. CONC. 101 25 1 54.7 0. 344 3.840 96.004 4.564 367.705 2 10 58.0 0.377 4.209 42.087 3.740 161.197 i 5 48.3 0.287 3.196 15.981 2.771 61.210 4 5 31.8 0. 166 1.847 9.233 2.223 35.365 » 1 40.6 0.226 2.520 2.320 ' 0.924 9.651 * 1 20.6 0.100 1.106 1.106 0.101 4.236 1 1 B.l 0.037 0.393 0.393 -0.933 1.507 • 1 3.4 0.015 0.150 0.150 -1.894 0.576 9 1 1.6 0.007 0.061 0.061 -2.805 0.232 10 1 0.9 0.004 0.026 0.026 -3.650 0.100 11 100 41.7 0.234 2.611 261.089 5.565 1000.000 •POSITION 11 REFERS TO THE AQUEOUS PHASE LEAVING THE COLUMN) HATER MASS BALANCE APPARENT LOSS • -0.201 PER CENT KETONE MASS BALANCE APPARENT LOSS » 1.257 PER CENT TRACER MASS 8ALANCE APPARENT LOSS • -2.139 PER CENT KETONE HOLD-UP - 4.70 PER CENT tOO.EICONC)" -1.8549«IHE1GHT ABOVE TRACER INJECTION)**.6414 95 PC CONFIDENCE LIMITS ON SLOPE ARE -1.9404 TO -1.7693 LOG.IOICQNC). -4.2718*IHEIGHT ABOVE TRACER INJECTI0NI.LOG.101281.86) : " : NUMBER OF POINTS FOR ESTIMATION OF EOOY DIFFUSIVITY » 9 SUPERFICIAL AXIAL EOOY DIFFUSIVITY '14.93 SO.FT./HR. 95 PC CONFIDENCE LIMITS ARE 14.23 SO.FT./HR. TO 13.63 SQ.FT./HR. AXIAL EOOY OIFFUSIVITY -15.67 SQ.FT./HR. 95 PC CONFIDENCE LIMITS ARE 14.93 SQ.FT./HR. TO 16.41 SQ.FT./HR. PECLET NUMBER • 0.858 TABLE IV-k. AXIAL EDDY DIFFUSIVITY RESULTS FOR THE l | - I N . I.D. COLUMN AVERAGE INSIDE DIAMETER Of HOI til TIPS - 0.126 IN. C1SPERSED PHASE EOUIVALENT OA CP DIAMETER - 0. IS* IN. AVERAGE VELOCITY OF 0I3PERSE0 PHASE IN 101lit TIPS • 0.36 PT./SEC. COLUMN INSIDE DIAMETER • 1.5 IN. COLUMN HEIGHT IN022LE TIPS TO INTERFACE I • 10-FT. 1 l/>-IN. I5EE FIG. 10 FOR OIAC. OP APPARATUS) IX • CONTINUOUS PHASE SUPERFICIAL VSLOCir/, CU.FT./IHR. SO.FI.I : LK . OISPERSED PHASE SUPERFICIAL VeioclTY, CU.FT./IHR. SU.FT.I IT • TRACER FEEO SUPERFICIAL V£LOCI*Yi CU.FT./IHR. SO.FT.I HnlD-UP • VOLUMETRIC PERCENTAGE OF OISPFRSED PHASE IN COLUMN PP • NUMBER OF SAMPLE C01CENTRATIONS USED FOR ESTIMATION OF AXIAL EOOV OIFFUMVIIT f » AKIAL EODT OIFFUSIYITT MlTH 93 PER CENT CONFIOENCF LIMITS. SO.FT./HR. PE • PECLET NUMBER BASED ON OISPERSED PHASE DROP OIAMETER tm • WATER BALANCE APPARENT LOSS. PER CENT ER? • KETONE BALANCE APPARENT LOSS. PER CENT ER) • TRACER BALANCE APPARENT LOSS. PER CENT IM LK LT TEMP wENTRAT If lN AT SA MPLING P OINTS IS FE FIG. 101 HOLO PP E Pt ERI ER2 ER) *F « r * ' 3 4 5 & 7 ll y 16 -UP 126 9.0 >6.3 0.112 71 837.33 720.74 631.46 530.62 405.09 359.35 318.5? 282.61 254.1)7 215 . 17 2 . 7 10 3 0 . 4 9 1 2 . 6 6 0 . 5 s 1.08 -l .o : 2. 35 12T 18.2 36.5 0.200 71 760.53 576.77 417.22 304.01 198.41 147.83 105.04 7 6 . 4 9 6 c 75 4 6 . 5 1 2 . 5 10 2 ' ( . 6 1 1 1 . 7 3 0.64 2.65 0.14 -1. 35 12a 27. T 36.3 0.310 70 694.03 532.74 328.25 184.81 89.88 56.47 34.84 ? 6 . 2 2 1 9 . 74 1 1 . 5 9 7 . 6 10 3C.26t2.71 0.62 1.23 -1.05 6. 11 i ? ) 36. 3 36.3 0.350 72 612.47 357.07 200.93 108.89 47.00 24.43 14.15 7.92 5 . 2 f 2 . 4 6 2 . 6 10 3 0 . 4 6 * 1 . 4 6 0.62 1.45 0. l< 3. 02 no 48.4 36.5 0.680 72 520.28 206.90 93.9) 32.37 12.59 5.74 i . l l 1.37 0 . 6 2 0 . 2 7 2 . 9 10 3 0 . 0 4 H . 34 0.56 -1.45 1. 33 -0. 45 TT 9.0 34.7 0.112 72 707.79 549.90 4)9.74 342.22 238.2? 201.20 146.76 124.30 9 3 . 9 2 73.79 4.7 10 18.77*0.76 0.82 -1.77 -0.9« -5. 91 76 18.2 54.7 0.200 T2 624.01 413.69 742.01 169.91 87.33 52.99 31.38 ??.71 1 4 . 3 8 8 . 2 3 4 . 7 10 19.8510.86 0. 77 1.37 1.26 -3. 62 75 27.7 54.7 0.310 70 407.72 188.50 102.32 40.93 16.77 10.24 4.91 ?.47 U . 9 2 0.45 4 . 7 10 19.4710 .69 0.79 -1.21 1.2« ). 36 T9 36.5 54.7 0.350 71 335.61 168.54 47.38 22.79 9.55 3.18 1.36 0.46 a.in 0 . 0 8 4 . 6 8 20.2710.96 0.78 1.29 1.2C 1. 25 TS 48.4 54.7 0.682 71 312.21 85.19 25.34 7.08 1.73 0.49 0.14 9.05 0.03 0.03 4.8 6 19.7410.57 0.78 0.54 I.2C 0. 44 82 9.0 73.0 0.112 71 742.70 584.97 386.07 280.12 163.41 133.78 83.59 61.69 49.10 28.76 6 . 8 10 13.4410.73 1.05 2.28 1.71 9. 13 01 18.2 73.0 0.200 70 469.37 200.41 102.20 48.95 22.06 11.41 6.13 ?.86 1.23 0 . 6 1 6.7 10 13.4810.29 1.06 1.37 0.15 4. 04 80 27.7 73.0 0.310 70 247.88 18.00 26.40 11.08 3.51 1.10 0.41 - 0.16 0.04 0.00 6 . 7 7 13.8810.51 1.04 1.13 -0.37 3. 4) 1)1 36.3 73.0 0.350 71 400.42 123.95 27.75 4.28 0.94 0.27 0.11 0.02 0.00 0 . 0 0 7.0 6 13.0011.10 1.07 -1.41 0.67 -3. 64 132 48.4 73.0 0.680 70 235.96 98.01 7.16 0.64 0.20 0.03 0.01 0.02 0.01 o.oi 7 . 2 5 13.7 )14.03 1 . 0 0 1.94 1.19 9t 96 83 9.0 91.2 0.112 71 643.46 442.38 263.43 190.87 108.02 77157 52.92 33.13 20.43 11.54 9.) 10 11.3910.46 1.13 -0.56 0.36 0. 29 a* 18.2 91.2 0.200 70 322.17 127.69 53.90 16.60 7.49 3.24 1.31 0.45 0.09 0.00 9 . 2 8 10.8010.42 1.21 1.37 0.98 -1. 99 86 27.7 91.2 0.310 72 169.13 49.23 8.32 2.39 0.64 0.16 0.06 0.02 0 . 0 0 0.01 9.4 5 1 0 . 8 7 l l . 2 ) 1.19 -1.04 0.14 -11. 01 85 36.5 91.2 0.350 72 111.50 18.66 2.28 0.S2 0.16 0.13 0.04 0 . 0 0 0.00 0.00 9 . 6 4 11.1512.18 1.14 1.17 1.39 I. 40 133 48.4 91.2 0.680 70 101.15 11.64 0.93 0.09 0.02 0.01 0.00 0 . 0 0 0.01 0.00 9 . 8 3 11.5516.27 1.10 0.48 1.39 Of 34 88 9.0 109.5 0.112 71 477.46 321.83 182. » 116.59 64.74 51.7) 26.18 18.38 10.31 6.24 12 .0 10 10.7110.44 l . l l 0.91 1.00 1. 71 87 18.2 109.3 0.200 T3 293.73 123.06 36.80 12.68 3.74 2.13 0.46 0.14 0.00 0.00 12.1 7 9.7510.82 1.23 -0.74 1.00 1. 46 90 27.7 109.5 0.310 74 153.20 38.37 6.12 2.92 0.82 0.24 0.10 0 . 0 3 o.ov 0.03 11 .8 6 12.3411.74 1 . 0 0 -1.53 1.43 0. 20 89 36.5 109.5 0.330 73 101.39 13.85 1.69 0.43 0.14 0.07 0.05 0.03 0.03 0 . 0 5 12 .1 4 11.2712.98 1.09 -0.06 0.57 -1. 05 134 48.4 109.3 0.610 TO 86.18 7.53 0.27 0.02 0.01 0.00 0.00 0.01 o.oo 0.02 12.1 3 9.63110.7 1.29 -0.48 l.OC -3. 24 9* 9.0 127.7 0.112 73. 393.54 354.25 189.80 121.78 60.06 45.56 23.91 13.67 10.33 5.57 13.7 10 10.2510.46 1.19 1.96 0.13 -3. 9) 93 18.2 127.7 0.200 75 304.16 145.78 29.3) 9.84 3.26 1.28 0.37 0.13 0.11 0 . 1 1 13.6 7 9.3110.71 1 . 3 ) -0.88 -1.17 1. 6) 92 27.7 127.7 0.310 73 136.22 31.81 4.30 1.10 0.31 0.15 0.11 0.09 0.11 0.09 13.7 5 10.4311.61 1.19 -1.98 -0.31 -0. 39 91 36.3 127.7 0.350 75 80.62 8.82 0.94 0.10 0.06 0.06 0.04 0.04 0.08 0.04 13.8 3 9.5610.62 1.31 1.01 0 . 9 9 3. 67 133 48.4 127 .7 0.680 71 73.37 6.30 0.16 0.04 0.01 0.02 0.00 0.01 0.00 0.00 14 .8 3 10. 7416 .04 1.10 1.04 -111'1 -1. 69 215 o o -4- t t> M ii m 3 5 2 5 3 *TTT- 32225 •?•?•?•?• 2 Jo'-o- - i i i 52222 0--0- ? 5 2 2 2 ---00 S.T--?«- 777?" ? 3 2 2 2 3SC55 t 77?7° ... a ooooo 00̂ 00 ̂ 0000 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 333s s s s s s liili l-Stif is*;; III <; 0 ^ - i i : o o o c « Oil tM N CM IHi <NJ M fx IMft ; 2 2 ^ *• - - 0 0 0 •»> -SS3S ooooo mi sggss •^o'ooo SSoSS 0 0 0 c SSSSg j ~ o o o s s s g s je'doo S23SS Voooo 5SISS i d d d D KS5SS ; d o d c SCSSg •*~o'o'o' 53133 3 S 2 S S 2SSSS S5SS5 f~ O O O O •3S2-- IS22 | 3 3 S ! 2 2 2 2 2 It!..- |SS = ~ p i ! 15533 S52SS J--000 2 2 2 2 2 rg 2S3SS S3"" SSSE2 I s - - 51533 13333 j;ddo 2 2 2 2 2 p i n $« IJS25 SUSS 8 ^000 SS2« I1S55 IPs SSSSJ SSJ25-; iiiii S2SS- 3315? SS2S5 "ESSSS usees SSS22 im HE!* 552§S 2 2 C E s o^oo^l oooo'c ?!!H IB!! !!!!! 2 i i i i l 2 2 J 2 <j| Villi nm «n «c* v* m «n sssss Mil ma || 5?SSS| SS33SJ SKS5?| 3SS27 TABLE IV-4. CONTINUED (2) AVERAGE INSIOE DIAMETER OF NO H i t TIPS • 0.066 IN. DISPERSED PHASE EQUIVALENT DROP DIAMETER • 0.US IH. AVERAGE VELOCITY OF DISPERSED PHASE IN NOZILE TIPS • 0.38 FT./SEC. COLUMN INSIOE OIAMETER • US IN. COLUMN HEIGHT INOHLE TIPS TO INTERFACE) • 10-FT. 1 1/8-IN. ISCE FIG. ID FOR 01AG. OF APPARATUS) LM • CONTINUOUS PHASE SUPERFICIAL VELOCOy, CU.PT./IHA. SO.FT.) LK • DISPERSEO PHASE SUPERFICIAL VfLOCITY, CU.FT./IHA. SO.FT.I IT • TRACER FEED SUPERFICIAL VftOCiry, CU.FT./IHR. SO.FT.) HOLD-UP • VOLUMETRIC PERCENTAGE OF OISPERSEO PHASE IN COLUMN PP • NUMBER OF SAMPLE CONCENTRATIONS USED FOR ESTIMATION OF AXIAL EOUY DIFFUSIVITY t - AXIAL EOOY 0IFFUS1YITY WITH 9* PER CENT CONFIDENCE LIMITS. SO.FT./HR. PE • PECLET NUMBER BASED ON DISPERSED PHASE DROP DIAMETER EKI • WATER BALANCE APPARENT LOSS. PER CENT EA2 • KETONE BALANCE APPARENT LOSS. PER CENT ER1 • TRACER BALANCE APPARENT LOSS. PER CENT RUN LM LK IT TEMP REDUCED CONCENTRAT1 ON AT SAMPLING POINTS ISFE FIG. 10) HOLD PP E PE ERI ER2 ERS 'f 1 2 3 4 9 6 1 8 •* lo -UP 96 9.6 "SSTV srm "To- J96.J9" 49i.4» 433.99 282.IS 254.6} 184. K KV:J* 94.43 77.43 1.0 15 17.3511.16 V4 -1.62 1.25 -0.71 n 18.2 34.* 0.200 69 961.82 271.11 147.93 98.41 49.02 30.50 17.67 7.9* 5.19 2.75 2.9 10 16.2310.66 0.83 -0.88 0.14 -1.82 98 2T.T 36.* 0.310 70 314.14 149.29 80.0* 31.96 10.11 3.4* 2.00 1.20 0.66 0.31 2.8 10 18.17*1.17 0.76 0.62 1.25 2.8* 99 36.* 36.* 0.3*0 TO 23*.63 74.26 20.27 10.93 2.09 1.38 0.44 0.18 0.10 0.07 2.9 7 1B.1U2.14 0.7* 1.45 0.14 4.9* 100 48.4 36. 5 0.6S0 A9 97.90 42.26 7.46 2.11 0.29 0.07 0.0* 0.00 0.03 0.00 2.9 5 17.1413.91 0.80 -0.97 1.25 -0.97 101 9.0 S4.7 0.112 72 961.61 4*3.17 260.53 181.61 120.17 81.66 46.47 36.83 23.38 13.69 4.9 10 11.4710.56 1.03 -0.80 1.26 1.71 102 18.2 *4.7 0.200 73 389.16 177.99 58.66 34.56 8.83 ».19 1.95 0.67 0.21 0.00 4.8 9 10.1710.63 1.16 1.59 1.26 0.77 103 27.7 94.7 0.310 73 146.91 67.11 12.29 5.92 2.80 0.47 0.00 0.00 0.00 0.00 4.8 6 13.1112.61 0.93 0^79 1.26 0.0* 10* 36.5 54.7 0.3*0 73 93.48 23.61 4.12 1.51 0.39 0.04 0.00 0.00 0.00 0.00 4.8 5 14.1112.06 0.87 0.19 2.37 1.25 10* 48.4 *4.7 0.680 73 34.4* 6.92 0.72 0.15 0.00 0.00 0.00 0.00 0.00 0.00 9.0 4 13.7713.03 0.87 0.84 2.37 -4. 54 106 9.0 73.0 0.112 73 410.67 28S.08 161.50 107.92 57.S2 42.32 24.20 16.80 10.63 9.81 7.7 10 10.3910.39 1.03 -0.8S 0.67 1.67 ior 18.2 73.0 0.200 73 303.97 129.34 36.06 16.99 4.5) 1.6* 0.4* 0.20 0.00 0.00 7.0 7 9.0610.60 1.23 0.92 1.19 2.69 108 27.7 73.0 0.310 74 136.8* 3*.29 6.1* 1.67 0.3* 0.11 0.07 0.07 0.09 0.1* 7.2 5 10.0210.74 1.08 -0.64 -0.89 1.44 109 36.5 73.0 0.3*0 74 80.32 13.16 0.94 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7.9 3 8.92112.2 1.19 -0.51 1.19 3.57 no 48.4 73.0 0.480 74 22.19 2.29 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 7.3 2 11.56 0.95 2.48 0.67 2.78 111 9.0 91.2 0.112 72 422.19 2*6.99 12*. 99 74.49 36.49 24.99 14.94 7.89 4.29 ?.*7 9.6 10 8.8210.30 1.13 0.41 0.96 I'll 112 18.2 91.2 0.200 72 22*.76 78.04 21.44 7.87 2.30 0.66 0.20 0.03 0.00 0.00 9.6 7 8.6110.29 1.18 -0.71 0.S6 -2.49 11) 27.7 91.2 0.310 71 128.84 28.08 9.16 0.90 0.22 0.00 0.00 0.00 o.oo 0.00 10.1 * 9.9910.61 1.01 -0.64 0.98 2.80 114 16.* 91.2 0.350 71 *9.68 8.57 0.70 0.1) 0.08 0.06 0.03 0.01 0.~06 0.06 9.8 3 9.1518.49 l.ll 0.96 0.14 -0.11 11* 48.4 91.2 0.680 70 36.61 2.42 0.21 0.04 -0.02 0.02 0.04 0.06 0.04 0.02 10.5 3 10.5114.03 0.92 -0.02 0.56 4.14 116 9.0 109. 5 0.112 69 S74.78 343.98 168.56 96.93 46.44 31.44 17.23 10.07 5.64 2.89 12.6 10 8.9010.31 1.03 0.22 1.43 -1.16 LIT 18.2 109.* 0.200 70 287.24 97.2* 2».5l 9.15 2.29 0.76 0.22 0.00 0.00 0.00 12.3 7 3.6610.32 1.09 .1.12 1.00 6.34 118 21.7 109.5 0.310 70 117.37 24.99 2.56 0.40 0.00 0.00 0.00 0.00 0.00 0.00 12.2 4 8.2211.74 1.18 -0.79 1.00 2.81 119 36. » 109.* 0.3*0 70 69.88 6.72 0.48 0.00 U.OD 0.00 0.00 0.00 0.00 0.00 12.7 3 8.9114.42 1.1* 0.16 1.4) 3.42 120 48.4 109.* 0.680 70 27.62 1.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.9 2 10.08 0.96 1.0* 1 .4) 1.89 121 9.0 127.7 0.112 70 463.18 246.69 128.48 73.25 37.99 21.43 10.57 6.*0 3.57 2.07 19.4 10 8.8*10.24 0.'<9 2.57 -0.31 -1.36 122 18.2 127.7 0.200 70 243.02 74.94 17.54 6.79 1.93 0.70 0.12 0.00 0.00 0.00 14.9 6 9.1210.6a 1.00 1.76 0.1) 3.06 123 27.7 127.7 0.310 69 107.13 18.12 1.98 0.28 0.00 0.00 0.00 3.00 0.00 0.00 19.0 4 8.1811.0b 1.1) 0.2* -1.17 4.04 124 36. S 127.7 0.3*0 ri 41.99 4.13 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.6 2 9.40 0.96 1.17 -0.31 3.98 12* 48.4 127.7 0.680 71 22.83 1.16 0.00 0.00 0.00 0.00 0.00 0.00 o.oo 0.00 iv.n 2 9.71 0.93 0.53 1-42 4.26 ro V-1 ON TABLE IV - U . CONTINUED ( 3 ) AVERAGE INSIDE DIAMETER OF NO/HE TIPS • 0.0*1 IN. DISPERSED PHASE EOUIVALENT ORUP DIAMETER • 0.04* IN. AVERAGE- VELOCITY OF OISPERSED PHASE IN N022LE TIPS • 0.68 FT./SEC. COLUMN INSIDE DIAMETER • I . * IN. LULUMN HEIGHT I H O m t TIPS TO INTERFACE! « 10-FT. 1 1/8-IN. ISEE FIG. 10 FOR DIAG. OF APPARATUS! LU •CONTINUOUS PHASE SUPERFICIAL VELOCITY, CU.FI./IHR.' SO.FT.I IK • DISPERSED PttASE SUPERFICIAL Ml LOC IT Y, CU.FT./IHR. SQ.FT. I LT • TRACER FEED SUPERFICIAL </««.o«IT7*, CU.FT./IHR. SO.FT.I HOLD-UP • VOLUMETRIC PERCENTAGE OF DISPERSED PHASE IN COLUMN PP • NUMBER OF SAMPLE CONCENT'AT IONS USED FOR ESTIMATION OF AXIAL EDDY DIFFUSIVITY E_« AXIAL EDDY DIFFUSIVITY WITH 9* PER CENT CONFIOENCE LIMITS. SC.FT./HR. PE • PECLET' N i m E R ~BASE0 ON DISPERSEO PHASE DROP DIAMETER CHI • MATFR BALANCE APPARENT LOSS, PER CENT ER2 - KFTONE BALANCE APPARENT LOSS. PER CENT tR) • TRACER BALANCE APPARENT LOSS. PER CENT RUN LU L« IT TEMP RED JCEO CON CENTRA!IC N Al SAMPLING POINTS ISEE FIG. 10) HCILO PP E Pt 6«« EK2 ER) ^F 1 2 1 * * 6 7 8 9 10 -UP IAS 9.0 16.* 0.112 68 498.46 400.76 211.71 146.04 71.48 59.88 34.14 22.98 l i . * 7 6 . 0 ) 2.7 10 9.6610.71 1.10 1.96 -0.97 4. 14 147 18.2 16.* 0.200 68 28*. 99 107.67 48.81 12.7* 5.25 2.27 0.90 0.41 0.1* 0.09 2 .11 8 9.89l0.*l> 1.05 0.92 1.25 1.42 1*6 27.7 36.* 9 11  68 161.17 48.48 6.57 1.82 0.62 0.25 0.09 0.05 0.05 0.07 2 . 9 6 10.70tl.79 0.95 0.62 1.25 2.01 1*5 36.* 36.* 0 .1*0 68 89.06 16.72 1.67 0.11 0.08 0.06 0.06 0.08 0.11 0.06 3 . U 4 9.82*1.97 1.02 1.12 2.16 2.7) l*» 48.4 36.* D.680 68 21.28 1.94 0.20 0.08 0.07 0.05 0.0* 0.07 0.05 O.OI 1.0 1 10.78A2.3* 0.92 1.04 1.25 1.68 1*1 9.0 **.7 8.112 68 *60.75 192.12 213.61 12*.96 54.10 31.41 17.16 1.57 4.17 1.97 4 . 8 10 7.4*t0.18 1.21 -1.62 2.17 0.51 1*2 18.2 3*.7 0.200 68 287.1* 122.05 24.81 7.81 1.84 0.48 0.13 0.04 0.02 0.01 5.1 6' 7.3710.66 1.17 -0.27 2.17 1.24 1 * 1 27.7 **.7 310 68 118.93 25.34 3.44 0.23 0.03 0.01 0.01 0.00 fi.Ot! 0.C1 5.3 4 7.0712.71 1.11 1.13 -0.96 2.89 1*0 16.* *A.T 0 . 1*0 68 70.68 5.54 0.41 0.04 0.04 0.02 0.02 0.04 0.02 0.02 5.2 3 7.5910.32 1.15 -0.06 1.26 0 . 1 1 1*9 48.4 SA.7 0.6AO 68 26.6* 1.30 0.01 0.01 0.00 u.00 0.01 0.00 O.00 0.01 4 . 9 2 8.69 1.07 1.04 1.26 1.16 1*8 9.0 73.0 0.112 66 76*.71 465.25 245.89 161.00 61.10 41.98 19.29 If.16 6.71 i./r 8.2 10 S.1110.34 0.6-1 -0.80 0.69 ).*5 1*7 1 0 . 2 13.4 D.200 67 127.39 113.56 21.42 5.11 1.22 0.24 0.0* 0.01 0.01 J . u l n . i 6 6.8210.51 l . o ; 2.6* 1.21 5.19 1*6 27.7 73.0 0.110 67 104.00 26.37 2 . 1 * 0.44 0.0* 0.03 o.oi 0.02 0.02 0.01 8.0 4 8.0412.41 0.41 0.12 1.21 6.16 1** 16.* 73.0 0.1*0 68 72.49 *.S0 0.18 0.04 0.04 0.02 0.02 0.0* 0.02 0.02 7 . 9 3 7.5812.15 1.01 -1.41 1.21 4.26 1*4 48.4 68 68 _ 28.74 0.97 0.06 0.0* 0.0* 0.04 0.04 0.0* 0.06 0.0* 8.3 2 7.84 0 . 9 * 0.03 0.69 -0.51 161 9.0 91.2 0.112 69 474.10 297.44 171.87 97.69 44.40 21.90 15.58 6.11 3.52 1.91 10.* 10 8.0610.18 0.S7 -1.45 -1.14 1.62 162 18.2 91.2 O.200 68 329.94 109.41 28.** 8 . 8 * 1.84 0.47 0.1* 0.07 U.U3 o.oi 10.7 6 7.7*10.57 0.89 -0.74 0.51 0.66 161 27 . 1 91.2 0.110 68 127.40 25.41 2.10 0.42 0.06 0.02 0.04 ".02 0.02 0.02 11 . 2 * H.0111.86 O . i * -1.53 0.53 0.48 160 16.* 91.2 0.1*0 68 81.24 8.5* 0.5* 0.03 0.00 0.00 0.00 0.00 o.oo 0.00 10 . 9 1 8.1715.80 0.85 0.61 1.78 1.57 1*9 .**•*. 91.2 0.690 _69 18.66 0.11 0.02 0.00 0.01 0.01 0.01 0.00 0.01 O.Uti 11 . 2 2 8.18 0.82 0.48 1.16 0.07 168 9.0 109.* 0.112 68 451.70 129 . 1 1 171.77 104.22 51.12 11.65 19.00 10.7* 6.tiO l . r t l 13.1 10 >.3910.17 0.70 0.91 0.59 3.75 167 IB.2 109.* 0.200 68 244.*9 77.40 19.36 4.87 1.13 0.17 0.16 0.09 0.09 0.07 13 . 2 6 7.9U0.38 0.85 -0.88 1.4* 1.66 166 77.7 109.* 31  68 119.48 20.52 1 . 8 8 0.12 0.11 0.09 0.09 0.09 0.11 0.11 13 . 9 * t l . 0011.5.* 0.81 -1.09 1.02 1.29 16* 16.* 109.* 0.1*0 69 **.97 6.71 0.*7 0.11 0.09 0.09 0.11 0.11 0.09 0. 1 1 13.8 1 9.2915.0* 0. 71 0.65 1.02 1.08 164 46.4 109.* 0.680 67 . 12.70 0.69 0.07 0.07 0.0* 0.05 0.0* 0.07 0.0* 0.07 l * . l 2 9 . 7 * 0.6" 1.04 1.4* 1.26 171 9.0 127.7 0.112 68 482.44 141.44 118.97 76.14 29.4) 20.21 9.51 5.48 2.57 I.II 16 . 2 10 7.9810.41 0.79 -1.62 -0.74 l . H 172 18.2 127.7 0.200 69 1*2.27 94.91 17.96 4.83 1.2* 0.28 0.12 0.0* 0.0* 0.0* U.* 6 7.6610.34 0.0 1 -1.11 1.42 1 . 1 1 III 27.7 127.7 0.110 69 97.27 16.67 1.19 0.18 0.115 0.03 0.01 0.05 0.05 J.Oft 16.4 1 7.56111.0 0 . 6 5 -1.09 0.11 -1.7* 170 16.* 127.7 0.1*0 69 41.41 2.79 0.2* 0.07 0.07 0.07 0.04 0.0* 0.04 0.07 16 . 6 1 P.5411.49 0. 75 1.01 -1.17 1.14 16 1 Aft.A 127.7 0.680 68 18.71 .0.65 0.0* 0.01 0.01 0.03 0.0* 0.0* 0.01 0.01 17 . 2 ? n. 75 0. 72 0.51 - 2 . 0 * 0.41 218 s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , and the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y f o r each run- w i t h the 3-in- I.D. column are given i n Table IV-5. Dispersed phase hold-ups i n the 3 _ i n . I.D. column were not measured. Consequently i t was not p o s s i b l e to reduce s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s t o tru e a x i a l eddy d i f f u s i v i t i e s or to c a l c u l a t e P e c l e t numbers. Measurements of the dispersed phase drop s i z e s were analysed on an IBM-7040 e l e c t r o n i c computer. No hand c a l c u l a t i o n s are presented due t o t h e i r voluminous nature. However, the a l g e b r a i c equation used, to process the data i s given below. Let r = the v e r t i c a l • d i m e n s i o n of the drop image as measured by means of the m i c r o f i l m reader, mm., x =. the. h o r i z o n t a l dimension of the drop image as measured, by means of the m i c r o f i l m reader, mm. f^= the conversion f a c t o r f o r mm. to i n . = 0,.03937> f = the enlargement f a c t o r = a . l i n e a r dimension of the observed image d i v i d e d by the same l i n e a r dimension of the a c t u a l object - 4-309, and d g= the e q u i v a l e n t diameter of the drop = the diameter of a sphere having the same volume as the drop. Then., - d g= (fjX^r/Xx^)) . f 2 The range of d between 0.00 and 0.25-in. was d i v i d e d up i n t o TABLE IV-5. SUPERFICIAL AXIAL EDDY DIFFUSIVITY RESULTS FOR THE 3-IN. I.D. COLUMN AVERAGE INSIOE OIAMETER OF NOZZLE TIPS • 0.102 IN. OISPERSEO PHASE EQUIVALENT DROP DIAMETER • 0.135 IN. AVERAGE VELOCITY OF OISPERSEO PHASE IN NOZZLE TIPS • 0.37 FT./SEC. COLUMN INSIDE DIAMETER • 1.0 IN. COLUMN HEIGHT [NOZZLE TIPS TO INTERFACE) • 10-FT. 9 T/B-IN. (SEE FIG. 20 FOR DUG. OF APPARATUS! LU • CONTINUOUS PHASE SUPERFICIAL MBLOCITY, CU.FT./IHR. SQ.FT.) LK • DISPERSED PHASE SUPERFICIAL VCLOCIT^ CU.FT./IHR. SO.FT.) LT - TRACER FEED SUPERFICIAL V£i.OeiTjf, CU.FT./(HR._ SQ.FT.I _ PP • NUMBER OF SAMPLE CONCENTRATIONS USED FOR ESTIMATION OF SUPERFICIAL AXIAL EDDY DIFFUSIVITY SE > SUPERFICIAL AXIAL EDDY DIFFUSIVITY MITH 99 PER CENT CONFIDENCE LIMITS. SO.FT./HR. ER1 . MtTFR BALANCE APPARENT LOSS. PER CENT • : ER2 - TRACER BALANCE APPARENT LOSS. PER CENT RUN LM LK LT TEMP REDUCED CON CENTRATI ON AT SA MPLING P DINTS IS EE FIG. 201 PP SE ER1 ER2 *F 1 2 3 * 3 6 7 -8 . 9 10 177 18.2 36.9 0.090 70 933.27 863.08 843.83 810.9* 776.76 707.25 680.2) 655.87 6)3.98 593.46 10 187.9116.* -1.28 -0.29 181 27.7 36.9 0.100 69 939.04 877.36 842.38 759.66 693.78 676.66 604.4* 568.8* 471.59 470.11 10 17*.7120.1 -1.83 -0.48 182 36.9 36.9 0.150 68 972.18 949.34 846.63 7*1.07 623.71 998.60 383.77 525.69 435.07 389.08 10 181.3121.8 0.75 2.06 181 *8.4 36.5 0.190 66 923.97 799.06 718.67 602.38 316.67 490.81 *33.57 327.9* 312.99 273.32 10 179.811*.6 1.40 0.19 ISA 79.0 36.3 0.200 69 938.87 717.49 606.97 451.6* 330.10 283.24 236 . 7 9 192.38 150.23 123.07 10 169 . 0 1 9.5 -0.03 -3.00 180 100.0 36.3 0.290 70 816.43 644.68 440.33 337.34 218.3* 171.58 133.89 97.49 75.67 53. 16 10 168.OllO.3 -0.94 -1.09 179 220.0 36.5 0.410 67 991.99 282.48 142.48 49.30 33.00 21.28 11.30 6.10 3.75 2.19 10 181.4114.5 -0.78 3.51 185 285.0 36.5 0.410 70 487.7* 274.18 109.02 93.78 28.72 16.72 9.16 *. 1* 1.88 0.87 8 21*.0113.6 0.76 -1.26 19* 18.2 94.7 0.090 6B 1028.76 974.63 936.07 864.67 816.98 767.73 711.99 672.35 634.91 583.14 10 146 . 1 1 6.5 -1.70 1.52 193 27.7 54.7 0.100 69 1022.09 973.11 909.10 853.8B 78*.30 735.85 662.86 620 . 2 2 577.73 502.74 10 181.211*.5 -1.2* -6.18 I 9 ? 36.9 94.7 0.190 71 1011.09 938.87 782.22 724.39 639.31 574.92 499.13 *22.79 368.37 334.76 10 146 . 7 1 8.0 1.59 1.68 191 48.* 94.7 0.150 70 1079.77 933.1* 780.03 700.88 5*5.95 456.55 39*.37 317.39 272.97 257.38 10 144.91 9.5 -0.72 -0.63 178 75.0 94.7 0.200 71 999.69 756.42 993.69 428.97 319.98 273.73 210.35 170.16 134.21 96.94 10 152 . 0 1 6.9 -0.25 -4.12 190 100.0 94.7 0.290 71 1123.63 7*8.37 949.14 366.41 23*.51 179.48 149.88 80.05 54.91 40.04 10 137 . 2 1 8.1 -1.75 -2.62 189 190.0 54.7 0.410 70 1163.87 731.16 491.99 299. 36 143.42 76.33 *7.72 27.65 17.87 9.48 10 140.91 4.1 -0.16 -4.76 188 220.0 54.7 0.410 70 1081.40 623.83 320.26 149.96 72.90 32.54 11.63 9.67 2.76 1.32 9 1*4 .81 8.2 0.0* 1.9* 187 262.0 94.7 0.410 70 1199.62 540.40 166.24 46.87 12.97 3.4* 2.31 1.12 0.17 0 . 0 0 7 121.6110.7 -0.** -0.91 197 18.2 73.0 0.090 67 996.99 882.90 783.93 730.68 692.97 623.84 608.65 5*1.26 486.45 495.21 10 113 . 7 1 7.7 -0.58 *.71 196 48.4 73.0 0.190 70 1089.17 896.39 700.69 914.79 400.69 396.02 287.76 211.93 161.29 132.63 10 104.21 5.4 0.61 -2.20 195 100.0 73.6 0.290 68 1286.97 I0T1.40 634.73 400.63 166.89 122.51 61.29 37.89 23.20 12.09 10 94.01 6.4 -1.05 0.19 200 18.2 91.2 0.050 70 894.06 768.91 692.29 610.94 537.10 486.32 *32.12 383.60 360.91 323.60 10 82.81 4.5 1.00 2.78 199 48.4 91.2 0.190 67 1036.04 7*8.89 606.34 412.92 288.99 220.71 181.26 114.90 •87.42 74.25 10 81.21 *.* -1.51 -1.99 198 100.0 91.2 0.290 69 1195.97 683.49 276.73 160.0* 89.92 38.56 19.68 10.34 5.35 3.5* 10 76.21 3.2 -1.46 1.01 203 18.2 109.0 0.090 69 903.74 822.91 798.86 718.11 603.11 328.61 491.67 428.69 387.63 336.02 10 81.91 6.8 1.00 1.6* 202 48.4 109.0 0.190 68 1064.79 851.97. 630.43 459.27 272.23 202.34 1)8.32 94.93 65.80 52.66 10 69.51 3.* 0.4) *.98 201 100.0 109.0 0.290 67 1117.61 613.37 167.42 100.89 40.26 18.79 6.03 1.09 0.18 0.00 8 53.71 7.* -0.91 -0.90 206 18.2 128.0 0.040 69 996.89 879.33 744.99 392.89 471.32 408.91 323.8* 279.32 23*.*B 190.85 10 49 . 0 1 2.0 0.12 7.27 205 48.4 128.0 0.190 69 934.09 700.19 471.77 289.27 157.78 115.89 6*. 79 38.37 2 * . 82 18.17 10 52.91 2.6 1 .46 -0.33 20* 100.0 128.0 0.290 70 980.29 291.22 83.91 31.47 17.03 4.63 2.06 0 . / 2 0 . 5 7 0.28 7 52.91 *.* -0.64 -1 .*6 220 0 . 0 1-in. increments. The number,of drops, and the t o t a l drop . volume a s s o c i a t e d w i t h the drops, appearing i n each of these increments were c a l c u l a t e d . For each increment the number of drops was converted i n t o the percentage of the t o t a l number of drops measured. S i m i l a r l y the sum of the volumes of the drops i n each increment was converted i n t o a percentage of the t o t a l drop volume a s s o c i a t e d w i t h a l l of the drops. These c a l c u l a t i o n s were performed f o r the f i r s t 100 drops examined and were extended to the f i r s t 200, 300, 400, and 500 drops examined. A t y p i c a l set of r e s u l t s appears i n Table IV - 6 . The r e s u l t s f o r the 500 drops examined f o r each.run . i n which drop s i z e s were measured appear i n Table IV-7 f o r the l§--in. I.D. column and i n Table IV-8 f o r the 3-in. I.D. column. Due t o the o v e r l a p p i n g of the drops i n the photographs i t was not p o s s i b l e t o measure the drop s i z e s f o r runs when was l a r g e . Therefore i t was assumed t h a t the drop s i z e d i s t r i b u t i o n s were the same a t high and low values of L^. Table IV - 9 shows the s u p e r f i c i a l - f l o w r a t e s , the measured co n c e n t r a t i o n s , the c a l c u l a t e d c a p a c i t y c o e f f i c i e n t , the hold-up, and the e r r o r i n the mass balance f o r each run i n v o l v i n g mass t r a n s f e r . Table IV-10 shows, the r e l a t i o n between £ & n c l E f o r the e s t i m a t i o n of E. The values of K^a and m were taken from Table IV -9 and the values of J were c a l c u l a t e d by means of Equation 21. Tables IV-11 and IV-12 show the e f f e c t on E of v a r y i n g K^a, m, and the method of c a l c u l a t i o n of J . Table IV-13 gives the e q u i l i b r i u m c o n c e n t r a t i o n of a c e t i c a c i d i n MIBK - saturated water and water - saturat e d MIBK at 70°F as determined i n t h i s work. 221 TABLE IV-6. TYPICAL DROP SIZE DISTRIBUTION RESULTS WATER S U P E R F I C I A L V E L O C I T Y = 27*70 C U . F I . / ( H R . S Q . F T . ) K E T O N E S U P E R F I C I A L V E L O C I T Y = 54.74 C U . F T . / M H R . S Q . F T . ) N O Z Z L E T I P A V E R A G E D I A M E T E R = 0.103 I N . COLUMN D I A M E T E R = 1.5 I N . C O N D I T I O N S C O R R E S P O N D TO RUN 50 RANGE OF P E R C E N T A G E OF DROPS IN P E R C E N T A G E OF T O T A L DROP E Q U I V A L E N T G I V E N S I Z E RANGE FOR VOLUME C O N T R I B U T E D BY DROP D I A . T O T A L NUMBER OF DROPS DROPS IN G I V E N S I Z E RANGE IN I N C H E S SHOWN AT HEAD OF L I S T FOR T O T A L NUMBER OF DROPS SHOWN AT HEAD OF L I S T 100 200 300 400 500 100 200 300 400 500 0.00-0.01 0.0 0.0 0.0 0. 0 0.0 0.0 0.0 0.0 0.0 0.0 0.01-0.02 15.0 15.5 15.7 16.0 16.6 0. 1 0.1 0. 1 0.1 0.1 0.02-0.03 25.0 24.5 25.0 24.2 23.0 0.4 0.4 0.4 0.4 0.3 0.03-0.04 6.0 7.0 5.3 6.3 7.4 0.2 0.3 0.2 0.2 0.3 0.04-0.05 5.0 4.0 3.3 3.5 3.0 0.4 0.4 0.3 0.3 0.3 0.05-0.06 3.0 3.0 2.7 2.2 1.8 0.5 0.5 0.4 0.3 0.3 0.06-0.07 0.0 0.5 0.7 0.5 0.4 6.0 0.1 0.2 0.1 0.1 0.07-0.08 1.0 2.0 1.7 1.2 1.6 0.4 0.8 0.7 0.5 0.6 0.08-0.09 0.0 2.0 2.3 2. 2 2.2 0.0 1.1 1.2 1.2 l . l 0.09-0.10 2.0 2.0 2.3 2.0 2.0 1.6 1.7 1.9 1.6 t . 6 0.10-0.11 3.0 3.5 4.3 3.7 3.0 3.1 3.9 4.6 4.0 3.1 0. 11-0.12 4.0 2.5 3.0 3.0 3*6 5.4 3.6 4.3 4.2 5.0 0.12-0.13 3.0 5.0 6.3 7.0 7.2 5.0 9.4 11.6 12.7 12.8 0. 13-0.14 16.0 13.5 12.3 13. 2 13.8 33.7 31.0 27.8 29.5 30.0 0.14-0.15 9.0 9.5 10.0 10. 0 9.2 23.2 26.9 27.7 27.3 24.5 0.15-0.16 6.0 4*0 3.7 3.5 3.6 18.3 13.3 11.8 11*3 11*6 0.16-0.17 2.0 1.5 1.0 0. 7 0.6 7.7 6.4 4.1 3. i 2.4 0.17-0.18 0.0 0.0 0.0 0.2 0.6 0.0 0.0 0.0 1.3 2.8 0.18-0.19 0.0 0.0 0.0 0.6 6.0 0.0 6.6 0.0 0.0 0.0 0.19-0.20 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.20-0.21 0.0 0.0 0.3 0.2 0.4 0.0 0.0 2.7 2.0 3.0 0.21-0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.22-0.23 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.23-0.24 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.24-0.25 o.o| b.o 0.0 o. 6 6.6 0.6 6.6 6.6 0.0 0.0 TABLE I V - 7 . DROP SIZE DISTRIBUTIONS IN THE l|-IN.. I.D. COLUMN RANGE OF EOUIVALENT DROP DIA. PERCENTAGE OF DROPS IN GIVEN SIZE RANGE FOR A TOTAL OF 500 OROPS. CONDITIONS CORRESPOND T3 RUN AT HEAD OF LIST AVERAGE NOZZLE AVERAGE NOZZLE IN INCHES TIP 1.0. » 0.126-1N. TIP I.D. •» 0.103- IN. TIP I .0. * 0.086-1N. TIP 1.0. » 0.053-14. 126 128 130 75 86 92 65 63 66 50 55 45 96 99 100 103 113 148 146 144 151 144 0.00-0.01 0.2 0.0 0.0 0.4 0.2 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 a.2 0.0 0.0 0.8 0.2 0.2 0.2 0.01-0.02 22.4 29.4 28.2 21.6 21.6 19.0 9.6 18.6 22.0 16.6 9.0 6.4 19.8 20.3 25.4 18.4 10.8 11.4 10.4 13.2 13.2 7.0 0.02-0.03 16.6 17.4 16.2 16.0 17.8 19.4 16.0 20.0 23.4 23.0 16.8 12.2 22.0 23.^ 19.6 20.2 20.0 9.6 10.0 8.6 10.2 13.0 0.03-0.0* 6.0 5.4 4.8 8.2 5.6 8.2 10.3 6.6 6.2 7.4 11.4 7.8 6.8 8.2 5.4 8.8 8.2 1.2. 2.4 1.6 1.2 3.6 0.04-0.0$ 1.6 2.0 3.0 5.0 3.0 2.0 4.6 4.0 3.-4 3.0 4.0 4.4 1.8 2.6 3.0 2.4 2.4 0.4 0.6 0.4 0.0 0.2 0.05-0.06 0.6 3.2 2.4 1.8 3.2 2.2 2.2 2.2 0.6 1.8 1.8 3.0 0.8 1.2 1.4 0.0 2.2 0.2 0.4 0.4 0.2 0.2 0.06-0.07 2.0 2.4 1.2 1.6 2.8 2.2 1.0 1.6 0.8 0.4 1.6 0.8 1.8 1.0 1 .2 0.8 0.6 1.0 0.4 0.8 0.0 0.0 0.07-0.08 1.6 2.2 3.0 2.4 1.8 1.0 1.4 2.2 1.0 1.6 1.4 1.4 0.6 1.8 1.2 0.8 1.0 1.2 2.0 1.2 1.0 3.8 0.08-0.09 2.8 2.2 3.0 2.4 2.0 1.6 3.2 1.8 1.2 2.2 1.0 1.4 0.8 0.4 1.6 2.2 1.8 18.4' 17.8 14.0 18.0 16.4 0.09-0.10 3.2 2.2 2.0 2.2 2.4 2.0 3.2 1.8 2.4 2.0 2.2 2.4 2.8 2.2 1.4 2.0 4.0 44.2 42.8 43.4 45.0 47.4 0.10-0.11 3.6 3.0 2.8 3.0 2.4 3.0 4.0 2.4 2.4 3.0 2.4 3.8 3.0 3.0 4.6 3.8 4.8 9.4 7.6 11.4 7.4 8.6 0.11-0.12 3.4 2.6 3.0 2.0 3.4 3.4 5.4 5.2 3.6 3.6 4.6 5.6 8.4 8.2 9.6 11.4 15.0 2.4 4.4 3.2 2.6 4.4 0.12-0.13 6.0 3.4 2.4 2.6 3.2 4.0 8.2 10.0 6.0 7.2 6.4 11.2 21.4 13.8 14.8 17.8 16.6 0. 6 0.4 1.2 0.8 1.0 0.13-0.14 5.2 3.4 4.6 4.2 3.4 4.0 15.0 11.8 14.0 13.8 16.4 15.2 8.2 11.0 9.0 7.4 H.6 0.0 0.0 0.4 0.2 0.0 0.14-0.15 6.4 6.2 6.2 5.8 6.0 7.0 10. 9 7.8 8.4 9.2 12.0 13.8 1.6 2.2 1.2 3.6 2.2 0.0 0.3 0.0 0.0 0.0 0.15-0.16 8.2 5.2 6.6 8.6 5.6 5.6 2.2 3.6 4.2 3.6 5.8 6.0 " 0.2 1.0 0.4 0.2 1.4 0.0 0.0 0.0 0.0 0.0 0.16-0.17 5.6 2.6 5.4 5.8 6.4 7.6 1.4 0.2 0.2 0.6 1.8 3.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.2 0.17-0.18 2.4 4.2 2.8 2.8 4.6 2.8 0.2 0.2 0.2 0.6 0.2 0.6 0.0 0.0 0.0 0.0 3.2 0.0 0.0 0.0 0.0 0.0 0.18-0.19 0.6 0.8 1.2 1.2 1.8 3.2 0.2 0.0 0.0 0.0 0.6 0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19-0.20 1.2 1.0 0.8 0.6 1.8 0.4 0.2 0.0 0.0 0.0 0.4 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.20-0.21 0.4 0.8 0.2 1.2 0.4 0.4 0.2 0.0 0.0 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.21-0.22 0.0 0.2 0.2 0.2 0.4 0.6 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 O.O 0.0 0.0 0.0 0.0 0.22-0.23 0.0 0.0 0.0 0.2 0.0 0.2 0.0 ' 0.0 0.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.23-0.24 0.0 0.2 0.0 0.2 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.24-0.25 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0" 0.0 0.0 0.0 Q.O 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 AVERAGE NOZZLE AVERAGE NOZZLE TABLE IV-7.. CONTINUED PERCENTAGE OF TOTAL OROP VOLUME CONTRIBUTED BY OROPS IN GIVEN SIZE RANGE F0« A TOTAL OF 500 OROPS. RANGE OF CONDITIONS CORRFSPOND TO RUM AT HEAO OF LIST EQUIVALENT DROP OIA. AVERAGE NOZZLE AVERAGE NOZZLE AVERAGE NOZZLE AVERAGE NOZZLE IN INCHES TIP I.D. » 0.126-1N. TIP I.D. « 0.103- IN. TIP I.D. = C.086-IN. TIP 1.0. = 0. 053-IN. 126 128 130 75 86 92 65 63 66 50 55 45 96 98 100 103 113 148 146 144 151 149 O.OO-O.Ol 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 CO 0.0 0.0 0.0 3.0 0.0 0.0 0.0 "To" 6.0 0.01-0.02 0.1 0.1 0.1 0.1 O.I 0.1 0.0 0.1 0.1 0.1 0.0 0.0 0. 1 0.1 0.2 0. 1 3.1 0.1 0. 1 0.1 0.1 0. 1 0.02-0.03 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.4 0.3 0.2 0. 1 0.4 0.4 0.4 0.4 0.3 0.2 0.2 0.2 0.2 3.4 0.03-0.04 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.3 0.3 0.4 0.2 0.4 0.4 0.3 0.4 C.4 C. 1 0.2 C. 1 0.1 0.0 Oo04-0.05 0.1 0.1 0.2 0.3 0.2 0.1 0.3 0.4 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.3 0.2 o.o 0. 1 0.1 0.0 0.0 0.05-0.06 0.1 0.4 0.3 0.2 0.3 0.2 0.3 0.3 0.1 O.J 0.2 0.3 0.1 0.2 0.3 0.0 3.4 0.1 0.1 0.1 0.1 O.U 0.06-0.07 0.4 0.6 0.3 0.3 0.5 0.4 0.2 0.4 0.2 0.1 0.3 0.1 0.6 O.J 0.3 0.2 3.2 0.4. 0.2 0.4 u.o 0.0 0.07-0.08 0.4 0.7 1.0 0.7 0.5 0.3 0.5 0.9 0.4 0.6 0.4 0.4 0.3 1.0 0.6 0.4 0.4 C.d I .5 0.7 0.7 0.5 0.08-0.09 1.2 1.1 1.5 1.0 0.8 0.6 1.6 1.1 0.7 1.1 0.4 0.5 0.6 0.3 1.2 1.6 l . l 1 b.8-18.3 13.8 lfl.5 15.7 0.09-0.10 1.9 1.6 1.2 1.3 1.3 1.1 2.2 1.5 2.1 1.6 1.3 1.2 2.7 2.3 1.5 2.0 3.4 56.2 54.9 54.8 58. 3 56.3 0.10-0.11 2.8 2.9 2.5 2.4 1.8 2.1 3.6 2.8 2.7 3.1 1.9 2.7 4.1 4.2 6.B 5.0 5.5 16. 3 13.3 18.3 12.7 13.5 0.11-0.12 3.6 3.2 3.6 2.1 3.4 3.3 6.6 7.8 5.4 5.0 4.9 5.2 14.8 15.1 IB.9 10.3 22.9 5.3 10.3 6.9 6.3 9.1 0.12-0.13 8.2 5.3 3.5 3.5 4.2 4.9 12.9 19.0 11.5 12.') 8.8 13.2 47.2 31.* 35.9 3d.4 31.7 1 .& 1.2 3.4 2.3 2.7 0.13-0.14 8.9 6.6 8.6 7.0 5.5 6.2 29.5 27.6 34.0 30.0 28.3 23.0 22. 1 31.3 26.* IV. 4 23.2 0.0 0.0 1.3 0.7 0.0 0.14-0.15 13.6 15.3 14.6 12.0 11.8 13.3 25.8 22.6 24.8 24.5 25.2 25.2 5.5 7.9 4.5 11.7 6.5 0.0 0.0 0.0 0.0 3.0 0.15-0.16 21.2 15.7 18.9 21.5 13.3 12.9 6.4 13.0 15.1 11.6 14.8 13.5 0.8 4.2 1.7 T.8 4.9 CO 0.0 0.0 0.0 0.0 0.16-0.17 17.2 9.2 18.6 17.4 18.4 21.3 5.1 0.8 0.8 2.4 5.8 a.2 0.0 0.0 0.0 0.0 3.8 0.0 0.0 0.0 0.0 1.3 0.17-0.18 8.9 17.9 11.3 10.2 15.4 9.2 0.3 1.1 1.0 2.8 0.7 1.9 0.0 0.3 0.0 0.0 l.C 0.0 0.3 0.0 0.0 0.0 0.18-0.19 2.7 4.0 5.9 5.2 7.3 12.5 1.0 0.0 0.0 0.0 2.6 3.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19-0.20 6.0 6.0 4. 7 3.0 8.S 1.9 l . l 0.0 0.0 0.0 2.1 3.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.20-0.21 2.2 5.5 1.3 6.8 2.2 . 2.2 1.4 0.0 0.0 3.3 0.3 0.0 0.0 3.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.21-0.22 0.0 1.5 1.6 1.4 2.4 3.8 0.0 0.0 0.0 0.3 1.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 O.U 0.0 3.0 0.22-0.23 0.0 0.0 0.0 1.5 0.0 1.4 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.23-0.24 0.0 2.0 0.0 1.7 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 o-.:) 0.0 0.0 0.0 o.o 0.0 0.3 0.0 0.0 0.24-0.25 0.0 0.0 0.0 0.0 0.0 1.9 0.3 0.0 0.0 0.3 3.3 0.0 0.0 0.3 0.0 o.o . 3.0 o.o 0.0 0.0 0.0 0.3 22k TABLE I V - 8 . DROP SIZE DISTRIBUTIONS IN THE 3-IN. I.D. COLUMN A V E R A G E N O Z Z L E T I P I . D . = 0 . 1 0 2 -• I N . C O N D I T I O N S C O R R E S P O N D T O R U N A T H E A D O F L I S T R A N G E O F P E R C E N T A G E O F T H E E Q U I V A L E N T P E R C E N T A G E O F T H E D R O P S T O T A L D R O P V O L U M E DROP 0 1 A . I N G I V E N S I Z E R A N G E C O N T R I B U T E D B Y DROPS I N I N C H E S I N G I V E N S I Z E R A N G E 1 7 7 1 8 2 1 8 4 1 7 9 1 7 7 1 8 2 1 8 4 1 7 9 0 . 0 0 - 0 . 0 1 8 . 4 2 . 4 1 . 0 0 . 6 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1 - 0 . 0 2 1 2 9 . 8 3 2 . 8 3 2 . 2 1 3 . 0 0 . 1 0 . 1 0 . 1 0 . 0 0 . 0 2 - 0 . 0 3 5 . 6 1 2 . 4 1 0 . 8 1 3 . 6 0 . 1 0 . 2 0 . 2 0 . 2 0 . 0 3 - 0 . O A 3 . 6 2 . 2 2 . 8 4 . 8 0 . 2 0 . 1 0 . 1 0 . 2 0 . 0 4 - 0 . 0 5 1 . 8 1 . 0 1 . 6 4 . 0 0 . 2 0 . 1 0 . 1 0 . 3 0 . 0 5 - 0 . 0 6 1 . 2 1 . 4 1 . 8 1 . 0 0 . 2 0 . 2 0 . 3 0 . 1 0 . 0 6 - 0 . 0 7 1 . 4 2 . 4 0 . 8 2 . 6 0 . 4 0 . 7 0 . 2 0 . 4 0 . 0 7 - 0 . 0 8 1 . 6 0 . 8 0 . 8 2 . 4 0 . 6 0 . 3 0 . 4 0 . 9 0 . 0 8 - 0 . 0 9 3 . 2 2 . 8 1 . 4 2 . 6 2 . 1 1 . 7 0 . 8 1 . 3 0 . 0 9 - 0 . 1 0 2 . 8 2 . 6 1 . 8 3 . 8 2 . 6 2 . 3 1 . 5 2 . 7 0 . 1 0 - 0 . 1 1 2 . 8 1 . 4 4 . 0 4 . 2 3 . 2 1 . 7 4 . 4 4 . 1 0 . 1 1 - 0 . 1 2 5 . 4 4 . 0 5 . 8 8 . 6 8 . 5 6 . 2 8 . 5 1 0 . 8 0 . 1 2 - 0 . 1 3 1 1 . 2 1 0 . 0 1 0 . 2 1 2 . 4 2 2 . 4 1 9 . 4 1 9 . 2 1 9 . 4 0 . 1 3 - 0 . 1 4 1 2 . 2 1 3 . 2 1 6 . 6 1 6 . 4 3 0 . 5 3 2 . 5 3 8 * 4 3 2 . 1 0 . 1 4 - 0 . 1 5 7 . 4 7 . 8 6 . 6 7 . 0 2 2 . 3 2 3 . 3 1 9 . 0 1 6 . 7 0 . 1 5 - 0 . 1 6 0 . 8 2 . 0 0 . 8 3 . 2 2 . 9 7 . 2 2 . 8 9 . 3 0 . 1 6 - 0 . 1 7 0 . 6 0 . 6 1 . 0 0 . 4 2 . 7 2 . 6 4 . 1 1 . 4 0 . 1 7 - 0 . 1 8 0 . 2 0 . 0 0 . 0 0 . 0 1 . 0 0 . 0 0 . 0 0 . 0 0 . 1 8 - 0 . 1 9 0 . 0 0 . 2 0 . 0 0 . 0 0 . 0 1 . 3 0 . 0 0 . 0 0 . 1 9 - 0 . 2 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 2 0 - 0 . 2 1 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 2 1 - 0 . 2 2 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 2 2 - 0 . 2 3 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 2 3 - 0 . 2 4 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 2 4 - 0 . 2 5 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 TABLE I V - 9 . . CONCENTRATION STUDIES WITH MASS TRANSFER IN THE l | - I N . I.D. COLUMN tvm h h Concentration at stapling points* (See Figure 10), ld'x lb.-seles/ft? and and V Average • h % K.B? Tlaw to reach steady etate adn. Tea* °r ' 1 2 3 4 5 6 7 8 9 10 n 36.5 54.7 30.66 9.11 34.30 ,40.37 15.2 43.70 47.71 19.88 '49.47 53.72 23.3 55.24 5 7 . a 25.95 58.82 27.2 81.37 0.00 19.28 40.06 42.54 1.92 4.6 3.3 65 71 J2 18.2 54.7 9.04 2.91 10.05 11.84 4.21 13.96 15.33 5.72 17.00 19.43 7.50 22.31 24.25 9.82 27.32 11.1 83.32 0.00 54.63 25-19 56.24 2.04 4.5 2.75 122 71 n 36.5 91.2 15.49 6.1 16.69 18.27 7.4 19.73 21.43 8.76 23.07 25.50 10.81 27.59 30.41 12.40 32.54 13.55 80.75 3.64 11.53 31.23 79.03 2.02 9.3 0.39 90 *». Jk 48.4 91.2 25.25 9.16 27.71 30.35 12.2 32.7* 35.42 15.0 37.51 40.06 17.9 42.49 45.25 20.9 48.02 22.7 80.43 4.02 16.39 37.03 94.63 1.96 9.8 3.22 101 72 n 48.4 127.7 14.63 6.1 15.48 16.39 7.04 17.36 18.85 8.1 20.21 21.73 9.70 23.43 25.40 11.1 27.59 12.2 82.93 4.74 13.72 31.87 141.1 2.04 14.8 -3.42 85 70 the upper matter refer* to the continuous phase, the lover matter to the dispersed phase. K.B. i s the error la the aass balance. This ease balance traa calculated according to the following equation. ro TABLE IV - 1 0 . THE RELATION BETWEEN E AND A . (The values of K^a, and m were taken from Table I V - 9 . The values of J were c a l c u l a t e d from. Equation 21.) The numbers l i s t e d under the various values of E t e s t e d = 10 ^ • Run J V m E 60 59 58 57 56 ' 55 54 53 52 51 50 49 48 47 J I 0.743 •42.54 1.92 2800 2800 2700 2700 2600 2600 2500 2500 2400 2400 2300 2300 2200 2200 J2 0.119 56.24 2.0k 820 760 690 . 630 570 510 46o 4oo 350 300 250 210 170 140 J3 0.09k': 79.03 2.02 1300 1200 1200 1100 1000 990 930 880 820' 770 720 660 610 560 J4 0.477 94.63 I.96 920 860 800 74o 680 620 560 500 450 4oo 350 300 260 210 J5 0.0017 L41.1 2.04 58 47 38 31 25 20 ' 18 18 19 23 29 38 50 .65 Run J m E 46 45 44 4 3 42 4 i 4o 39 3b1 37 36 35 34 33 J I 0.743 42.54 1.92 2100 2100 2000 2000 1900 1800 1800 1700 1700 1600 1600 1500 i4oo i4oo J2 0.119 56.24 2.04 110 89 73 64 63 71 89 120 160 220 290 380 490 620 J3 0.09k: 79.03 2.02 510 46o 410 370 320 280 240 200 170 i4o 110 85 65 51 J4 O.U77 94.63 I.96 180 i4o 110 88 6a 53 .44 41 45 57 78 110 150 200 J5 0.0017 L4I.I 2.04 83 100 130 160 190 230 • 270 320 370 430 500 570 650 74o Run J V m E 32 31 30 29 28 27 26. 25 24 23 22 21 20 19 JI 0.743 42.54 1.92 1300 1300 1200 1100 1100 1000 970 920 870 840 790 750 720 690 J2 0.119 56.24 2.04 770 960 1200 i4oo 1700 2000 2400 2900 3400 4000 46oo 54oo 6300 7300 J3' O.09J+: 79.03 2.02 42 39 43 55 76 110 150 200 270 350 44o 560 700 850 J4 0.477 94.63 I.96 260 330 420 530 650 790 950 1100 1300 1600 1800 2100 2400 2800 J5 0.0017 L4I.I 2.04 840 94o 1100 1200 1300, 1500 1600 1800 2000. 2200 2500 2700 3000 3300 Run J V m E 18 17 16 15 14 13 12 11 10 9 8 7 6 5 • J I 0.7^3 42.54 1-92 670 660 660 660 • 680 720 770 84o 920 1000 1200 1300 1500 J2 0.119 56.24 2.04 8500 9800 11000 13000 150001 17000 20000 23000 27000 31000 36000 42000 49000 57000 J3 0.094; 79.03 2.02 1000 1300 1500 1800 2100 2500 2900 3300 3800 44oo 5100 5800 6600 Jk 0.477 94.63 I .96 3200 3600 4ioo 4700 5200 5900 66OQ 1 74oo. 8200 9100 10000 J5 0.0017 L4I.I 2.04 3600 4000 4300 4800 5200 5700 6200; 68oo' 7400 8000 TABLE IV-11 . CALCULATED VALUES OF E FOR VARIOUS1 VALUES OF K^a AND J . (The values of m were taken from Table IV-9) . " ' Run J m 25 30 35 4 0 42 . 5 4 45 50 55 ~ 60 65 0.743^ 1.92 E .60 5 5 12 16 20 25 29 33 35 J I 0.782 b 1.92 E 60 5 12 22 26 29 34 38 4 l .43 . 0.704° I . 9 2 E . 60 60 5 6- 6 10 16 21 24 27 Run J m '35 4o 45 50 55 56.24 60 65 70 75 .80 o . l l 9 a 2.04 E 30. 34 37. 4o 42 .42 44 . 5̂ 47 4 8 49 • J 2 0.138 b 2.04 •E 34 38 4 l 44 46 47 4 8 50 51 53 54 0.0994° 2.04 E . 26 30 33 35 38 38 39 • 4 l 42 44 45 Run J m V 65 70 75. 79-03 80 : 85 90 95 100 105 0.0943 a 2.02 E 22 26 29 31 32 34 37 39 41 42 J3 0.0992 b 2.02 E 23 27 30 32 33 35 38 40 '42 44 0.0893° 2.02 E 21 24 28 30 .30 .3.3 35 - S7 39 4 l Run J m V 70 75 80 85 90 94.63 .95 100 105 110 115 0.477^ I . 9 6 E 21 26 30 • 33 36 39 39 42 44 46 48 J4 0.527 b 1.96 E 32 37 4 l 44 48 50 50. 53 • 55 57 59 0.427° I . 9 6 E 10 14 19 22 25 28 28 31 33 35 37 Run J m V 120 125 130 135 140 14.1.1' 145 150 155 160 165 0.0017" 2.04 E '44 47 49 51 53 53 55 56 . 58 60 60 J5 -0.056o b 2.04 E 26 28 30 32 34 34 35 37 38 40 4 l 0.0594° 2.04 E 60 60 60 60 60 60 60 60 60 60 60 a The f l u x of sol u t e down the column, J = \ ^c°C " ̂ D°D^ + ^C°C " ̂ D°D^ b The f l u x of sol u t e down the column, J = (LQ CQ - kj) cj)) ° The f l u x of sol u t e down the column, J = (L^c^ - L_ cn) TABLE I V - 1 2 . CALCULATED VALUES OF E FOR VARIOUS VALUES OF m. (The values of J and K^a were taken from Table IV - 9 ' ) Run J m 1 .82 l.6k 1 .66 1.88 1 .90 1 .92 1 .94 1 .96 I . 9 8 2 . 0 0 2 . 0 2 J l 0,7^3 k2.$k E 36 32 28 2k 2 0 16 12 9 6 6 6 Run J m I .9U 1 .96 1 .98 2 . 0 0 2 . 0 2 2 . 0 ^ 2 . 0 6 2 . 0 8 2 . 1 0 2 . 1 2 J 2 0.119 56.2h E kQ k6 k5 kk : k3 k2 L l ^ 0 ko 39 Run J m 1 .92 1.9k 1.96 I . 9 8 2 . 0 0 2 . 0 2 2.0L 2 .06 2 . 0 8 2 . 1 0 2 . 1 2 J3 0 . 0 9 L 3 79.03 E kk ki 39 36 3^ 31 29 26 2k 2 2 19 Run J m •1.86 1 .88 I . 9 0 1 .92 I . 9 L I . 9 6 I . 9 8 2 . 0 0 2 . 0 2 2 . 0 4 2 .06 Jk 0.^77 E 59 ' ' 55 51 L T ^3 39 .35 32 28 2L 2 1 Run J m I.9L I .96 1 .98 2 . 0 0 2 . 0 2 2.0*f 2 . 0 6 2 . 0 8 2 . 1 0 2 . 1 2 2.1U J5 0.0017 l L l . l E 60 - 60 60 60 58 53 k9 h5 : L l 37 3^ 229 "TABLE IV -13 . EQUILIBRIUM DATA FOR ACETIC ACID DISTRIBUTED BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK AT 70°F. (MEASURED IN THIS WORK.) .Concentration of a c e t i c a c i d , D i s t r i b u t i o n l b . - m o l e s / f t ? c o e f f i c i e n t , Water phase' MIBK phase' m 0 . 0 0 1 0 1 0 • 0 . 0 0 0 5 5 4 5 1 . 8 2 1 4 0.002218 . 0.001099 2.0180 O.OOM-089 •0.001990 2 . 0 5 4 7 . . o.006307 0 . 0 0 3 0 7 9 2 . 0 4 8 2 O .OO6743 . 0 . 0 0 3 2 8 7 2.0512 O . O I I 2 7 ' 0 . 0 0 5 4 8 5 2.0542 O . O I 3 8 5 0 . 0 0 6 7 7 2 2 . 0 4 5 3 O . O I 7 6 3 0 . 0 0 8 6 1 9 2 . 0 4 6 0 0 . 0 2 5 6 4 0 . 0 1 2 6 2 2 . 0 3 1 4 0.02109 . 0.01040. 2.0286• 0.02802 0.01412 1.9846 . 0.03728 O.OI9OI 1.9609 0.04663 .... 0.02446 1.9069 0.05794 0.03111 1.8622 0.06683 0.03614 1.8493 O.06802 0.03738 . . I.8199 0,07376 . 0.04059 I .8171 O.07891 0.04368 1.8064 0.08381 0.04733 . 1.7709 0.08807 O.05050 1.7441 O.09625 • 0.05564 1.7297 0.1008 O.05881 1.7146 0.1051 0.0.6188 1.6978 0.1104 O.06569 1.6812 0.1150 ' O.06901 I .6671 230 APPENDIX V DETAILS OF THE APPARATUS Fig u r e s V - l t o V-23 i n c l u s i v e show the d e t a i l s of v arious p o r t i o n s of the l g r - i n . I.D." and 3-in. I.D. spray columns and t h e i r a c c e s s o r i e s . A H s t a i n l e s s s t e e l p a r t s were made from Type.304 s t a i n l e s s s t e e l . . The p i s t o n sample c o l l e c t i o n f l a s k shown In F i g u r e V - l was used f o r d i s p e r s e d phase hold-ups greater than 12$. The c o l l e c t i o n f l a s k f o r hold-ups l e s s than 12$ i s described e l s e - where (37)' F i g u r e V-2 i s a diagram of the hypodermic needle sampling system and F i g u r e V-3 gives, d e t a i l s of the sampling v a l v e . The t r a c e r i n j e c t i o n arrangement i s given i n Figure V-4 and d e t a i l s of the t r a c e r d i s t r i b u t o r are shown i n Figure V-§. F i g u r e s V - 6 , V-7, and V-8 show the 0.126-in. I.D., 0.086- i n . I.D., and the 0.053-in« I.D. no z z l e t i p s together w i t h the r e s p e c t i v e nozzle t i p support p l a t e s and nozzle t i p caps or plugs f o r use i n the 1^-in. I.D. spray, column. The n o z z l e t i p support p l a t e s were press f i t t e d i n t o the nozzle designed by Choudhury (35)* The f l o w s t r a i g h t e n e r i n the n o z z l e designed by Choudhury was not used i n the present work. The 0 .103-in. I.D. nozzle t i p s , the corresponding n o z z l e t i p support p l a t e and n o z z l e t i p caps are described elsewhere (30, 35)- The i n s i d e diameter of each nozzle t i p i n each set of nozzles was measured by means of a t r a v e l l i n g microscope. Two such diameters at r i g h t angles to each other were measured f o r each nozzle t i p . The a r i t h m e t i c average of the nozzle t i p i n s i d e diameter was c a l c u l a t e d f o r each set of t i p s . The Perspex box used t o reduce o p t i c a l d i s t o r t i o n i n the 1-g-in, I.D. column i s shown i n Figure V-9- An 0-ring was press f i t t e d i n each of the top and bottom of the box t o prevent the l o s s of water from between the. box. and the column. The cardboard l i g h t s h i e l d / which f i t t e d over the Perspex box, i s shown i n Figure V-10. . The i n s i d e surfaces of the l i g h t s h i e l d were painted w i t h b l a c k . i n k t o reduce, unwanted l i g h t r e f l e c t i o n s . The e i g h t sheets of t r a c i n g paper i n . t h e l i g h t s h i e l d served as a d i f f u s i n g screen f o r the l i g h t . F igure V - l l shows the nozzle and nozzle t i p s assembled i n the lower p o r t i o n . o f the 3-in. I.D. column. D e t a i l s of the various p a r t s of the.assembly are given i n F i g u r e s V-12 t o V-17 i n c l u s i v e . The d i a m e t r i c a l l y opposite holes l a b e l l e d B i n Figure V-17 were o u t l e t s f o r the aqueous phase. The t h i r d hole l a b e l l e d B was f o r a thermometer w e l l . The nozzle support f i t t e d i n t o E. C was f o r a d r a i n v a l v e . F i g u r e V - l 8 shows the E l g i n head f o r the 3-in- I'D. column and Fi g u r e s V-19, V-20, and V-21 give d e t a i l s of v a r i o u s component p a r t s . The aqueous phase i n l e t p i p e s , shown as A i n Figure V - l 8 , •were screwed i n t o the' holes marked C i n Figure V-19- The two holes l a b e l l e d B i n Figure V-19 were the dispersed phase e x i t s and E i n the same Figure accommodated a thermometer w e l l . F i n F i g ure V-20 accommodated another thermometer w e l l . The s i x holes, C, i n Figure V-20 were f o r b o l t s which held a standard f l a n g e . This f l a n g e compressed the polyethylene packing shown i n F i gure V-21. E i n Figure V-20 was f o r a d r a i n v a l v e . F i g u r e V-22 shows the Perspex box used t o reduce o p t i c a l d i s t o r t i o n i n the 3~in. I.D. column. O-rings were press f i t t e d i n t o the te>p and the bottom of the box. t o prevent the escape of water from between the .box and the- column. Drop photographs were taken through a • 6-in... l o n g . s e c t i o n of 3 - i n . I.D. g l a s s pipe cut from a longer p i e c e . This 6 - i n . piece used f o r photography t h e r e f o r e had unflanged ends. . I t was held i n p l a c e , c o n c e n t r i c w i t h the r e s t of the column, by means of two f l a n g e s , one of which i s shown i n F i g u r e V-23« Four 9 ~ i n ' l o n g aluminum t i e - rods held the f l a n g e s i n p o s i t i o n . . Each end of these was threaded and c a r r i e d a nut f o r - t i g h t e n i n g ' p u r p o s e s . 233 O E O c\l O §14-35 F U L L L E N G T H P Y R E X G R O U N D G L A S S J O I N T ,0'Z m l . D IV IS IONS ( A P P R O X . 2 m l 8 . / c m . ) 2 5 mm. DIA. 0 - 2 ml. D IV IS IONS ( A P P R O X . 2 m l s . / c m . ) H O O K S F O R S P R I N G S 4 0 mm. DIA. T E F L O N S T O P C O C K ( W I T H L A R G E D I A . H O L E FOR PAST D E L I V E R Y ) FIGURE V - l . PISTON SAMPLE COLLECTION FLASK FOR LARGE HOLD-UPS S A M P L I N G V A L V E C O L U M N W A L L 3 L O N G 2 2 G A U G E H Y P O D E R M I C N E E D L E !{g T H I C K , ijfg I.D.', II 2 ^ 3 2 O D . P O L Y E T H Y L E N E G A S K E T W I T H 0 0 2 5 " DIA. H O L E F O R N E E D L E 1 FIGURE V-2. HYPODERMIC NEEDLE INSTALLED FOR SAMPLING 0-7 II * 0-5" • •0-25j—j L _ : 0 1 2 5 " D i r Q lO CD SECTION ON A - A BODY M A T E R I A L : P O L Y E T H Y L E N E 0 0 8 9 " D. 0 0 6 2 5 " R. o L O STEM MATER IAL : S T A I N L E S S S T E E L v F I G U R E V-3- S A M P L I N G V A L V E F O R H Y P O D E R M I C N E E D L E "A" N Y L O N C O M P R E S S I O N NUT •A" N Y L O N U N I O N VTZZZA zzzzzzzi W w w 2 L O N G 18 G A U G E H Y P O D E R M I C N E E D L E T R A C E R D I S T R I B U T O R L O N G . V Q D ! 0 0 5 7 " I D . P O L Y E T H Y L E N E iV'O.D., Ve" L D . P O L Y E T H Y L E N E T U B E V T H I C K , Ifc" i . D ; , 2 W O.D. T E F L O N G A S K E T W I T H 0 0 5 7 " D IA . H O L E F O R N E E D L E C O L U M N W A L L FIGURE V-4. TRACER INJECTION SYSTEM ro u> 2 3 7 in 6 \ • \ \ i \ \ s \ \ \ M>25'tH o o 6 GLASS—* POLYETHYLENE 2 ^ ^ O cO ro 7 6 6 SECTION ON A - A • — A I HOLE 0 043 " D 4 H O L E S 0 0 6 3 " D . 0157" D SECTION ON B-B F I G U R E V - 5 . TRACER DISTRIBUTOR 2 3 8 10 HOLES 3 / j 6 " D ON »V RC.D. 4 HOLES 3/,6 D. ON 3/8" RC.D. STAINLESS STEEL NOZZLE TIP SUPPORT Vs D. h 3 / l6 D. to\45° t CHAMFER SECTION ON A-A STAINLESS STEEL NOZZLE TIP \ i -1 f \ \ N t \ s '/4" D. II TEFLON NOZZLE CAP FIGURE V-6. 0.126-IN. I.D. NOZZLE TIPS, NOZZLE TIP SUPPORT PLATE AND NOZZLE TIP CAPS ' 239 9 HOLE'S '/e" 0. ON V P.C.D. 16 HOLES •/s" D. ON I" RC.I5 3 HOLES '/a" D. ON V PC.D. STA INLESS S T E E L N O Z Z L E TIP SUPPORT N fK45° r CHAMFER M/e" D. 0 0 8 6 " D. S E C T I O N ON A-A S T A I N L E S S S T E E L NOZZLE TIP 0 086 "D. T E F L O N NOZZLE TIP PLUG FIGURE V-7. 0.086-IN. I.D. NOZZLE TIPS, NOZZLE TIP SUPPORT PLATE, AND NOZZLE TIP PLUGS 73 HOLES 3 / 3 2 " D. ON V TRIANGULAR PITCH STAINLESS STEEL NOZZLE TIP SUPPORT * \ \ 4 5 ° y v vCHAMFER -a,| J3. K0052 D. II 3/3 2" D. ^-0052nD. S E C T I O N O N A - A STAINLESS STEEL NOZZLE TIP TEFLON NOZZLE TIP PLUG FIGURE V-8. 0.053-IN. I.D. NOZZLE TIPS, NOZZLE TIP SUPPORT PLATE, AND NOZZLE TIP PLUGS 2hi „ A*1 ^ ' / < " D R I L L AND T A P '/„ D. V E N T T ! CM CM A • ill — — r T R A N S L U S C E N T '/8" P E R S P E X S E C T I O N ON A - A f ftp / / / / * / / h-7/ ' 3 2 S E C T I O N O N B-B M A T E R I A L - T R A N S P A R E N T V P E R S P E X U N L E S S O T H E R W I S E S P E C I F I E D FIGURE V-9. PERSPEX BOX FOR THE 1^-IN. I.D. COLUMN PHOTOGRAPHS „ PHOTOGRAPHIC SECTION M A T E R I A L 1 ' / 3 2 P U L P B O A R D OF COLUMN FITS HERE 'IGUBE V-10. LIGHT SHIELD FOR THE 1±-IN? I.D. COLUMN PHOTOGRAPHS 243 NOZZLE TIPS NOZZLE TIP SUPPORT SPECIAL PYREX REDUCER NOZZLE TIP PLUGS NOZZLE FLOW STRAIGHTENER T E F L O N ^ G A S K E T 777771 END P L A T E P O L Y E T H Y L E N E GASKET N O Z Z L E RETAINING NUT NOZZLE SECURING P L A T E FIGURE V - l l . LOWER END OF THE 3-IN. I.D. COLUMN 3 " DIA.* FIGURE V-12. SPECIAL PYREX REDUCER FOR THE 3-IN. I.D. COLUMN 24-5 o i o r o r o 1 o IO OJ 6 JL T 2-875 n D; 2-719" D: 2-657" D. / / / ( 2-469" D / / / / / / / / / / MATERIAL: STAINLESS S T E E L 2jfe" I.D/I6T.RI FIGURE V - 1 3 . NOZZLE SHELL FOR THE 3-IN. I.D. COLUMN 85 HOLES Vs D. ON V TRIANGULAR PITCH STA INLESS S T E E L N O Z Z L E TIP SUPPORT i 45° f CHAMFER II M/ 8 H D. l - O - I O f D . SECTION ON A-A STAINLESS STEEL NOZZLE TIP 1 I 1 1 K M O f ' D . TEFLON N O Z Z L E TIP PLUG FIGURE V-lk. NOZZLE TIPS, NOZZLE TIP SUPPORT PLATE, AND NOZZLE TIP PLUGS FOR THE 3-IN. I.D. COLUMN MATERIAL: STAINLESS S T E E L FIGURE V-15. FLOW STRAIGHTENER FOR THE 3-IN. I.D. COLUMN NOZZLE 2k8 .2 9 /i6 M0.D./l6 T.PI. I K W W N - o r .9 JL _ •/a" N.P.T. 3 - '• / 4 0.D./I6T.PI SECTION ON B-B 'I I II I 'I II I " I II I " • •' • B I SECTION ON A-A STAINLESS S T E E L N O Z Z L E SECURING PLATE % 0.D./I6 T.P.I II SECTION ON C-C STAINLESS S T E E L RETAINING NUT FIGURE V-16. NOZZLE SECURING PLATE AND RETAINING NUT FOR THE 3-IN I D COLUMN 2k9 8 HOLES WITH CLEARANCE FOR % " BOLTS ON 9 V 2 RC.D. 4'/ " RC D B, B,B, 3 HOLES DRILL AND TAP-V*" N.P.T. C, 1 H O L E DRILL AND T A P !V' N.P.T. E , l HOLE V D. 1 " IO'/2 D. 1 \ A ^ \ V lkV VM kA VV] I\ \ \ S N r « , MACHINE F L A T S E C T I O N ON A - A M A T E R I A L : S T A I N L E S S S T E E L FIGURE V - l ? . END PLATE FOR THE BOTTOM OF THE 3-IN. I.D. COLUMN 250 A W STAINLESS S T E E L PIPES (AQUEOUS PHASE INLET). B UPPER END P L A T E OF ELGIN HEAD. C TEFLON COVERED GASKETS. D 9" LONG, 9" I.D. Q.V.F. GLASS SECTION. E LOWER END P L A T E O F ELGIN HEAD. F LOWER END PLATE PACKING. G 10 LONG, 3" I.D. PYREX " D O U B L E TOUGH" PIPE WITH F L A T U N F L A R E D UPPER END. FIGURE V-18. ELGIN HEAD FOR THE 3-IN. I.D. COLUMN B,B, 2 HOLES DRILL AND TAP 'A" N.P.T. b,C, 2 HOLES DRILL AND TAP %" N.P.T. ! FROM BOTH SIDES £, I HOLE DRILL AND TAP '/2" N.P.T. MACHINE FLAT SECTION ON A-A MATERIAL-STAINLESS STEEL FIGURE V-19..' UPPER END PLATE FOR THE ELGIN HEAD OF THE 3-IN. I.D. COLUMN . ...... .252 B 8 HOLES 7 / . 6 U D. ON 12VRC.D. C 6 HOLES DRILL. AND T A P '/a" DEEP FOR Vie" B O L T S ON 5%" P.CD. E I HOLE DRILL AND T A P VA" N.P.T. ON 7Vz" P.C.D. F I HOLE DRILL AND T A P '/a" N.P.T. ON 7'/ 2" P.C.D. T A P E AND F F R O M THIS SIDE MACHINE FLAT / - ^ h — — 133/4 D.— * SECTION ON A - A MATERIAL^ STAINLESS S T E E L FIGURE V - 2 0 . LOWER END PLATE FOR THE ELGIN HEAD OF THE 3-IN. I.D. COLUMN 253 4 V D ; SECT ION ON A - A MATERIAL^ P O L Y E T H Y L E N E FIGURE V-21. LOWER END PLATE PACKING FOR THE ELGIN HEAD OF THE 3-IN. I.D. COLUMN' 25k u D R I L L '/2" D. D R I L L A N D T A P % N.PT. \ \ \ \ foo r 2 in A - 1 S E C T I O N ON A - A r -3 l 3 / i6 D p-3'/2 P." / / \ =1 2 W / / in ' — 5 ' / a " — S E C T I O N O N B - B M A T E R I A L : T R A N S P A R E N T V i i ' P E R S P E X FIGURE V-22. PERSPEX BOX FOR THE 3-IN. I.D. COLUMN PHOTOGRAPHS 255 4 H O L E S ? /32 H Q . O N 9 " P C D . ^ — - 9 V D . S E C T I O N O N A - A M A T E R I A L : A L U M I N U M FIGURE V - 2 3 . FLANGE FOR THE PHOTOGRAPHIC SECTION OF THE 3-IN. I.D. COLUMN • •• 256 APPENDIX VI DIMENSIONS OF THE GLASS PORTIONS IN THE COLUMN TEST SECTIONS AND MEASUREMENT OF PURGE TIMES. a) Dimensions of the glass p o r t i o n s i n the column t e s t s e c t i o n s . .The. l e n g t h and i n s i d e diameter of each piece of Pyrex "Double Tough" glass pipe i n the t e s t s e c t i o n s of the 1-g-in. I.D. and 3 -In.. •I.D. columns, were measured by means of v e r n i e r c a l i p e r s . The,I.D. was taken to be the average of s i x readings e q u a l l y spaced along the le n g t h of the gl a s s p i e c e . These measurements" are given i n Table VI - 1 . TABLE VI - 1 . DIMENSIONS' OF THE GLASS PORTIONS IN THE COLUMN TEST SECTIONS.: Sec t i o n of . column between : p o s i t i o n s (See d i a g s . . 10 and 20) Length ( 1^-ln. I.D.column) in . . I.D. (l§--in. I.D. c o l - umn) i n . Length (3-in.I.D. column) i n . I.D. (3-in. I.D. column ) i n . Tracer d i s t r r i b u t o r and I 6.044 • 1.500 5.983 2.992 1 and 2 5.967 .1.500 6.022 3.026 2 and 3 5.969. 1.497 . 6.020 2.985 ' 3 and 4 5.978 1.503 5.975 2.989 4 and 5 . 6.024 ' . I .492 6.020 3.008 5 and 6 5.793* 1.497 a • 6.014 3*009 6 and 7 5.975. 1.504 6.008 2.992 7 and 8 6.050 1.595 6.044 b 3.020 b 8 and 9 6.0^9 I .508 6.018 2.998 9 and 10 6.032 1.500 5.996 2.995 9 The p i s t o n sampler b l o c k replaced a glass s e c t i o n . This piece of g l a s s was used as the photographic t e s t s e c t i o n . I t was cut from a longer piece of Pyrex "Double Tough" pipe. The th i c k n e s s of each polyethylene gasket was measured and . was found t o be l / l 6 - i n . This measurement d i d not change when the gasket was compressed between two pieces of g l a s s . b) Measurement of purge times. i ) Hook and b e l l - p r o b e s sampling l i n e s . The column was brought t o steady s t a t e operating c o n d i t i o n s w i t h the t r a n s f e r o £ a c e t i c a c i d from the continuous phase t o the d i s p e r s e d phase as described under Experimental Procedure. With the probes a few inches below the i n t e r f a c e the f l o w of samples i n t o the probes and along the sampling l i n e s was s t a r t e d and maintained f o r about 2-hr. Without a l t e r i n g the sampling r a t e s the probes were lowered t o about 1 - f t . above the nozzle t i p s . Samples from each probe were c o l l e c t e d a t time i n t e r v a l s of about 1-min. u n t i l 30-min. a f t e r moving the probes. The b e l l - p r o b e samples were.shaken v i g o r o u s l y many times t o b r i n g the two phases t o e q u i l i b r i u m . . The hook-probe samples and the ketone phase of the b e l l - p r o b e samples were analysed f o r a c e t i c a c i d as de s c r i b e d e a r l i e r . For each probe a p l o t was made of the c o n c e n t r a t i o n of a c e t i c a c i d i n each sample versus the time a f t e r moving the probes. •The purge time was taken t o be t h a t time when there was' no change i n c o n c e n t r a t i o n w i t h i n c r e a s i n g time. . Purge times were determined f o r v a r i o u s sampling r a t e s 258 between 4-ml./min. and 20/-ml./min. I t was found t h a t a conserv- a t i v e estimate of the minimum purge time f o r each of the sampling l i n e s was given by the f o l l o w i n g equation. 120 Purge time (min.) = — >—r—7—: R • ,sampling r a t e (ml./mm.J i i ) Hypodermic needles. The i n s i d e diameter of a 22-gauge hypodermic needle i s so s m a l l t h a t the purge time f o r such a sampling device i s very s m a l l . A"conservative: estimate of the minimum purge time was estimated- i n the f o l l o w i n g manner. A hypodermic needle sampler was i n s e r t e d through one. of the l§-in. I.D. polyethylene gaskets de s c r i b e d e a r l i e r . This gasket was sandwiched between one end of a 3 - f t . l e n g t h of l§-in. I.D. Pyrex pipe and a l§-in. d i a . d i s k of l / l 6 - i n . t h i c k p o l y e t h y l e n e . The gasket and d i s k were clamped t o the end of the pipe by means of an aluminum end p l a t e and f l a n g e . The pipe was f i l l e d w i t h water and a sampling r a t e of 3/4-ml./min. through the needle was e s t a b l i s h e d . The water was poured out of the pipe and then the pipe was f i l l e d w i t h an aqueous s o l u t i o n of potassium permanganate. The f l o w of l i q u i d through the hypodermic needle recommenced at 3A-ml./min. The colour of the potassium permanganate showed up i n the sample i s s u i n g from the needle i n l e s s than 45-sec. The change i n colour was so r a p i d t h a t the time between t h a t when the c o l o u r f i r s t appeared and t h a t when i t reached f u l l s t r e n g t h was considered to be n e g l i g i b l e . A purge time of l-g-min. was considered t o be conservative f o r sampling r a t e s of at l e a s t 3A-ml./min.

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