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Particulate fouling of sensible heat exchangers Watkinson, Alan Paul 1968

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PARTICULATE FOULING OF SENSIBLE HEAT EXCHANGERS by ALAN PAUL WATKINSON B. Eng., McMaster University, 1962 M.A.Sc, University of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In the Department of CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September,1968 In 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 o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t he 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 r e f e r e n c e and S t udy . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r 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 a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Co lumb ia Vancouve r 8, Canada Date 2.<\ i ABSTRACT Fouling by a petroleum gas o i l and a d i l u t e suspension of sand in water was studied as a function of mass flow rate and wall temperature. The experiments were carried out by c i r c u l a t i n g the l i q u i d through a single tube maintained at constant heat flux by e l e c t r i c a l heating. The change in fouling resistance and pressure drop with time was measured. The fouling resistance of the water and of the o i l at low heat fluxes grows to an asymp-t o t i c value. At higher heat fluxes the o i l fouling resistance increased almost l i n e a r l y with time after an induction period. The asymptotic fouling resistance of both the o i l and the water decreased with increasing mass flow rate. At constant clean tube wall temperature the i n i t i a l f o uling rate of the o i l decreased with increasing mass flow rate. The i n i t i a l fouling rate of the water increased with increasing mass flow rate up to a c r i t i c a l mass flow rate, and then decreased with further increases in mass flow rate. At constant mass flow rate, the i n i t i a l fouling rate of the o i l depended exponentially on the clean tube wall temperature. An activation energy of 29 Kcal/mole was calcu-lated for the o i l fouling process by f i t t i n g the i n i t i a l fouling rate data to an Arrhenius type of equation. The pressure drop increase showed the same general trends with mass flow rate and tube wall temperature as did the fouling resistance. Fouling resistances for heated Kraft cooking liquor, c a l -culated from pulp m i l l operating data and from a single fouling experiment, appeared to follow similar trends to those, followed in common by the gas o i l and the water. The experimental results of this study were compared to the mathematical model of Kern and Seaton. While the shape of most fouling curves was in agreement with that predicted generally by this model, dependence of the i n i t i a l fouling rate and of the asymptotic fouling resistance of the gas o i l on the mass flow rate were both in disagreement with the detailed predictions of the model. For low mass flow rates of the water, however, even "the detailed predictions were borne out. It was, moreover, possible to remove part of the sand deposit by increasing the v e l o c i t y of the water, in accord with the postulated removal mechanism of Kern and Seaton, but the coke-like deposit from the gas o i l could not be s i m i l a r l y removed by increasing the o i l v e l o c i t y . Mathematical models are developed in which the deposition term i s written as the product of a material flux to the wall region and a s t i c k i n g probability, after Parkins, and the removal term depends on the shear stress, after Kern and Seaton, S p e c i f i c cases are considered where deposition is controlled by transfer to the surface, adhesion at the surface, and a combination of both steps.. Where deposition i s controlled partly by transfer and p a r t l y by adhesion, the model predicts mass flow rate and temperature dependence of the i n i t i a l fouling rate in agreement with the experimental results found for the o i l . The observed asymptotic fouling resistance of the o i l , however, depended less strongly on the reciprocal of the mass flow rate than i s predicted by the model. Where transfer alone controls the deposition process, the extended model reduces to a form s i m i l a r to that of Kern and Seaton. i v TABLE OF CONTENTS Page ABSTRACT i LIST OF TABLES v i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS x i :L 1. INTRODUCTION..... 1 2. PERTINENT PRIOR WORK 5 3. SCOPE AND METHOD OF PRESENT WORK 18 4. SELECTION OF WORKING FLUIDS. „, 2 0 5,0 APPARATUS 23 6. EXPERIMENTAL PROCEDURES 3 6 7. RESULTS AND DISCUSSION 39 a) Calculation Methods. 39 b) I n i t i a l Experiments on Gas O i l Fouling 46 c) Eff e c t of Mass Flow Rate on Fouling of O i l . . 48 d) Effect of Wall Temperature on Fouling of O i l 60 e) Combined Effects.of Mass.Flow.Rate.and Wall. Temperature 62 f) Local Fouling Rates 68 g) Nature of Deposits in Gas O i l Fouling „ 69 h) Reproducibility of Gas O i l Results and Somparison with Tabulated.Fouling Factors... 75 i) Sand-Water Fouling................ 76 j) Kraft Liquor Fouling 89 8. EXTENSION OF EXISTING FOULING MODELS 95 9. CONCLUSIONS 124 10, RECOMMENDATION FOR FURTHER WORK.. 12 7 11. LIST OF REFERENCES 12 9 12. NOMENCLATURE 134 Appendix 1. C a l i b r a t i o n of Equipment. 1-1 a) Thermocouple C a l i b r a t i o n 1-1 b) D i f f e r e n t i a l Pressure C e l l C a l i b r a t i o n 1-6 c) O r i f i c e P l a t e C a l i b r a t i o n 1-10 Appendix 2. C a l c u l a t i o n . o f . t h e . H e a t . T r a n s f e r Coef-f i c i e n t 2-1 a) Determination of the Heat Flux 2-1 b) In s i d e Tube Wall Temperature 2-3 c) Determination.of the Mean Temperature D i f f e r e n c e 2-3 d) Sample C a l c u l a t i o n 2-5 e) Dimensions of Test S e c t i o n s I I and I I I 2-10 Appendix 3. Experimental Data 3-1 v i LIST OF TABLES Table Page I, Properties of a Typical Gas O i l Blend 22 I I . Location of Thermocouples on Test Sections 30 i l l . Comparison of Calculated and Measured Water Heat Transfer C o e f f i c i e n t s 47 IV. F i t of Gas O i l Fouling Data to Equation 6 55 V. Linear F i t of I n i t i a l Fouling Rate Data 55 VI. Gas O i l Deposit Weights 71 VII. Approximate Size D i s t r i b u t i o n of Particulates in O i l 72 VIII. Estimated Thermal Conductivity of Gas O i l Deposits from Readings at End of Run 74 IX. Reproducibility of I n i t i a l Fouling Rates 75 X. F i t of Sand-Water Fouling Data to Equation 6 86 XI. Estimated Thermal Conductivity of Sand Deposits 88 XII. Fouling Models for Thin Deposits for W Constant 105 XIII. Fouling Models w'ithil.Bloc&age.'ffo& W Constant 106 XIV. Fouling Models with Blockage for Constant Pressure Gradient 114 XV. Quotient Fouling Models with Blockage for W Constant 119 Appendix 1 Table 1-1 Resistance Thermometer Data 1-3 l - I I Thermocouple Calibrations-Test Section I 1-4 V l l l - I I I Thermocouple C a l i b r a t i o n s - Test Section I I I 1-5 1-IV C a l i b r a t i o n of O r i f i c e D i f f e r e n t i a l Pressure C e l l 1-8 1-V C a l i b r a t i o n of Tube D i f f e r e n t i a l Pres-sure C e l l 1-9 1-VI C a l i b r a t i o n of O r i f i c e Plates 1-12 1-VII F i t of Regression Equations f o r O r i f i c e P lates 1-13 Appendix 3 Table 3-1 Operating Conditions and Clean Tube C o e f f i c i e n t s f o r F o u l i n g Expeximents 3-4 3-II Inside Wall Temperature P r o f i l e s and F o u l i n g Data 3-5 3-I I I Comparison of Clean Tube Heat Transfer C o e f f i c i e n t s w i t h Sieder-Tate Equation 3-10 3-IV Pressure Drop and Deposit Thicknesses 3-11 3-V P a r t i c u l a t e Levels i n F o u l i n g E x p e r i -ments 3 -13 v i i i LIST OF FIGURES Figure Number Page 0 Computed Fouling Curves for Kerris Example 2 12 1 Diagram of Heat Transfer Loop 24 2 O r i f i c e Plates and Flanges 25 3 Diagram of Test Section I 27 4 Pressure Taps and E l e c t r i c a l Terminals 28 5 Photograph of Test Section II 31 6 Outlet Mixing Chamber 3 3 7 Tube Wall Temperature P r o f i l e s and Terminal F l u i d Temperatures 43 8 Comparison of Measured Clean Heat Transfer Coef f i c i e n t s and Predictions of the Sieder-Tate Equation for Gas Oi l s 45 9 Heat Transfer Coefficient versus Time for. T W c « 295°F-Oil A 50 10 Heat Transfer Coefficient versus Time for Tw c« 295°F-Oil B 51 11 Heat Transfer Coefficient versus Time for E . W 346°F-Oil B 53 w c 12 Fouling Resistance of Oi l s versus Time for T w « 2 9 5 (Solid Lines are Least Squares F i t to cEquation 6) 54 13 Fouling Resistance and Pressure Drop Increase versus Time for TT>,« 346°F-Oil "B 57 w c 14 Variation of Parameters of Equation 6 with Mass Flow Rate of O i l (log-log) 58 ix 15 I n i t i a l Fouling Rate of O i l versus Mass 59 Flow Rate (log-log) 16 Fouling Resistance and Pressure Drop Increase versus Time for Varying Heat Fluxes-Oil B 61 17 Log I n i t i a l Fouling Rate versus Reciprocal of Average Clean Tube Wall Temperature-Oils A and B • 63 18 Deviations from I n i t i a l Fouling Rate Correlation:;- 65 19 Thermal Resistance versus Time for Varying Mass Flow Rate at Constant Heat Flux-Oil B 67 20 Local I n i t i a l O i l Fouling Rate versus Recipro-cal of Local Absolute Wall Temperature 70 21. Heat Transfer Coefficient and Pressure Drop Versus Time for I n i t i a l Sand-Water Fouling Experiments 78 22. Heat Transfer Coefficient versus Time for Sand-Water Experiments T W«175°F- 80 23 Fouling Resistance and Deposit Thickness versus Time for Sand-Water 81 24 Fouling Resistance and Deposit Thickness versus time for Sand-Water 82 25 Parameters of Equation 6 versus Mass Flow Rate of Water (log-log) 84 26 I n i t i a l Fouling Rate of Water versus Mass Flow Rate (log-log) 85 27 Fouling Resistance versus Time for M i l l Kraft Liquor Heater 92 28 Heat Transfer C o e f f i c i e n t and Fouling Resistance of Kraft Liquor versus Time 94 X 29 Computed Curves for Constant Mass Flow Rate 108 Fouling with Blockage 30 31 Computed Curves for Constant Mass Flow Rate Fouling with Blockage and Removal Rate Inde-pendent of Thickness 110 Computed Curves for Constant Pressure Gradient Fouling with Blockage 113 32 Computed Curves for ^.Constant Mass Flow Rate Fouling-Quotient Model 117 33 Comparison of Experimental Results with Thin Film Quotient Model Predictions 121 Appendix 1 Figure 1-1 Calibration Curve for O r i f i c e D i f f e r e n t i a l Pressure C e l l 1-7 1-2 Ca l i b r a t i o n Curve for Tube D i f f e r e n t i a l Pressure C e l l 1-16 1-3 Kinematic V i s c o s i t y and S p e c i f i c Gravity of O i l A 1-17 Appendix 2 Figure 2-2 Estimation of Surface Temperature of Insulation 2-2 Heat Loss Through Insulation 2-11 2-12 2-3 Thermal Conductivity Stainless Steel of Type 304 2-12 x i ACKNOWLEDGMENTS I*-.;wish t o t h a n k D r . Norman E p s t e i n , u n d e r whose d i r e c t i o n t h i s i n v e s t i g a t i o n was c o n d u c t e d , f o r h i s g u i d a n c e t h r o u g h o u t t h i s s t u d y . •I' w o u l d l i k e t o t h a n k Mr. R. M u e l c h e n and h i s s t a f f f o r t h e i r a s s i s t a n c e and c o - o p e r a t i o n i n t h e c o n s t r u c t i o n o f t h e a p p a r a t u s . I am g r a t e f u l f o r t h e a s s i s t a n c e o f Mr. F. B e r r y and Mr. A . M a c K e n z i e o f t h e E l e c t r i c a l E n g i n e e r i n g D e p a r t m e n t o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . Thanks a r e due t o S h e l l Canada L t d . f o r d o n a t i o n o f t h e o i l s u s e d i n t h i s work, t o t h e E l e c t r i c S t e e l Company (Esco) L t d . f o r d o n a t i o n o f K r a f t p u l p i n g l i q u o r and some p l a n t o p e r a t i n g d a t a , and t o t h e B r i t i s h C o l u m b i a I n s t i t u t e o f T e c h n o l o g y f o r t h e u s e o f some o f t h e i r e q u i p m e n t . I am i n d e b t e d t o t h e N a t i o n a l R e s e a r c h C o u n c i l , t h e C h e m i c a l E n g i n e e r i n g D e p a r t m e n t o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , and t o Mr. and M r s . M.H. McCurdy f o r f i n a n c i a l s u p p o r t . I am a l s o i n d e b t e d t o my w i f e E l i z a b e t h f o r h e r c o n t i n u a l s u p p o r t t h r o u g h o u t t h i s work. 1 . INTRODUCTION The performance of heat exchangers in service condi-tions often does not l i v e up to design expectations. During operation with many li q u i d s of i n d u s t r i a l importance a fil m gradually builds up on the heat transfer surface due to crys-t a l l i z a t i o n , polymerization, decomposition, sedimentation or b i o l o g i c a l growth. When the deposited f i l m changes the therm-a l resistance or the pressure drop measurably, the condition i s referred to as fouling. The usual' result of fouling i s a de-crease in the o v e r - a l l heat transfer c o e f f i c i e n t . However, roughness or blockage effects can produce an increase in the heat transfer c o e f f i c i e n t under some circumstances, e s p e c i a l l y i f the fou l i n g deposit has a high thermal conductivity. Foul-ing of heat exchangers occurs in many industries, including o i l r e f i n i n g , pulp and paper manufacturing, polymer and f i b e r pro-duction, sea water conversion, and in conventional and nuclear power plants. The causes of fouling are numerous. Rapid fouling of organic-polymer mixtures may be caused by high temperatures that promote polymerization, or the formation of tars, coke, or sludge. Scales may be formed due to an inverse temperature-2 s o l u b i l i t y r e l a t i o n . The presence of a s t i c k y organic f i l m may accelerate the deposition of particulate matter suspended in the l i q u i d as a re s u l t of corrosion or other p r i o r h i s t o r y . D i r t may s e t t l e out in regions of low v e l o c i t y in heat exchangers or slime may grow at hot spots in cooling water systems. In most cases the fouling unit eventually must be shut down and cleaned out. For ease of cleaning the most severely fouling streams are usually carried in the tubes of s h e l l and tube heat exchangers. The amount of fouling that can be t o l e r -ated may be controlled by the allowable increase i n pressure drop across the exchanger as the tubes gradually plug up, or by the a v a i l a b i l i t y of thermal d r i v i n g force to maintain outlet f l u i d temperatures. I f a constant heat flux i s maintained during fouling of a tube, the outside tube wall temperature must be increased with time, and the l i m i t i n g fouled condition may be governed by a maximum tube wall temperature above which cor-rosion rates become excessive or the material becomes susceptible to f a i l u r e . Fouling i s costly as exchangers must be over-designed to provide the extra surface, and then p e r i o d i c a l l y cleaned. Extra fuel or higher pressure condensing vapour may be required to maintain temperatures, or expensive surfactants may be used to keep the fouling material dispersed. The surface area of a heat exchanger may be determined 3 from t h e f o l l o w i n g e q u a t i o n : A = Q (R h. + R h o + R f i + R f o u t + Rw> F o r p r o c e s s h e a t e x c h a n g e r s R ^ and R n a r e u s u a l l y d e t e r m i n e d f r o m d e s i g n c o r r e l a t i o n s o r t h e r m a l and f l u i d m e c h a n i c a l a n a l -y s i s . R w i s a p r o p e r t y o f t h e t u b e m a t e r i a l and geometry. The f o u l i n g r e s i s t a n c e s a r e u s u a l l y o b t a i n e d from p r e v i o u s e x p e r i -e n ce w i t h t h e p r o c e s s f l u i d s o r from a v a i l a b l e t a b l e s ( 1 ) , and a r e u s u a l l y o f t h e o r d e r 0.0005 t o 0.01 ( h r ) ( f t 2 ) ( ° F ) / B T U . I n some c a s e s t h e f o u l i n g r e s i s t a n c e may be t h e c o n t r o l l i n g r e s i s -t a n c e . K e r n and S e a t o n (2) have p o i n t e d o u t t h a t a l t h o u g h methods f o r p r e d i c t i n g Rh^ and R J 1 q a r e f a i r l y r e l i a b l e , methods f o r e s t i m a t i n g t h e f o u l i n g r e s i s t a n c e may be i n c o n s i d e r a b l e e r r o r . Though i t i s r e c o g n i z e d t h a t t u b e m a t e r i a l , v e l o c i t y , f l u i d t e m p e r a t u r e and h e a t f l u x may i n f l u e n c e f o u l i n g , i n many c a s e s p u b l i s h e d f o u l i n g f a c t o r s a r e r e p r e s e n t e d as i n d e p e n d e n t o f t h e s e q u a n t i t i e s . F u r t h e r , t h e f o u l i n g r e s i s t a n c e i s t i m e d e p e n d e n t and t h e t i m e f o r w h i c h t h e f o u l i n g r e s i s t a n c e i s v a l i d i s n o t m e n t i o n e d . K i n e r t ( 3 ) , i n 1949, c a l l e d f o r b a s i c r e s e a r c h i n t o t h e m e c h a n i c s and c h e m i s t r y o f f o u l i n g , p a r t i c u l a r l y as t o t h e e f f e c t o f v e l o c i t y , s u r f a c e t e m p e r a t u r e , and h e a t f l u x on t h e change o f t h e h e a t t r a n s f e r c o e f f i c i e n t w i t h t i m e . R e c e n t l y K n udsen ( 4 ) , i n a l e c t u r e t o t h e N i n t h N a t i o n a l Heat T r a n s f e r 4 Conference, (AICHE-ASME 1967) d i s c u s s e d the p r e d i c t i o n of f o u l -i n g r e s i s t a n c e s as one of the areas i n process heat t r a n s f e r t h a t needs " c o n s i d e r a b l e b a s i c and a p p l i e d study". He suggested t h a t improvements i n a s s i g n i n g f o u l i n g r e s i s t a n c e s "must i n -troduce f o u l i n g as a f u n c t i o n of time, flow v e l o c i t y and tem-perature as b a s i c parameters". He a l s o p o i n t e d out t h a t the behaviour of the f o u l i n g r e s i s t a n c e as a f u n c t i o n of time, ve-l o c i t y and temperature enables one to optimize the d e s i g n and o p e r a t i o n of heat exchangers, i n c l u d i n g the e f f e c t of c l e a n i n g frequency on the decreased s u r f a c e area r e q u i r e d at h i g h e r ve-l o c i t i e s . I t was among the purposes of the present work t o study the e f f e c t s of f l u i d v e l o c i t y and temperature on the time dependence of the f o u l i n g r e s i s t a n c e f o r some f o u l i n g f l u i d s . 5 2. PERTINENT PRIOR WORK There have been a number of attempts to predict f o u l -ing rates, the more successful of which apply to scaling, the formation of crystals on a heat transfer surface due to an i n -verse solubility-temperature relationship. McCabe and Robinson (5) in 1924 proposed that for a sca l i n g isothermal f l u i d in evaporation, the amount of scale formed was proportional to the amount of water evaporated up to time t. This assumption implies that a fixed proportion of scale deposits even though the scale surface temperature drops o f f as scale builds up. Their equation R 2 = R J + a x A A T t (£) has been well v e r i f i e d for scaling in evaporators (5). Hasson (6) considered a scaling non-isothermal l i q u i d . As the scale accumulates, the temperature of the scale surface drops, decreasing the rate of scale formation. The result of his analysis i s A ( T s t - . T i . ) n + 1  R2+n = R2+n + ^ t ( 3 ) (WC p) n 3-5 Hasson found that R-'-(It for three tests at low v e l o c i t i e s in scali n g from hard water in a double pipe heat exchanger with steam in the s h e l l . At the highest v e l o c i t y (4.1 ft/sec) the 6 data did not f i t equation 3. Reitzer (7) considered the rate of scale formation in a tubular exchanger. He assumed a li n e a r inverse tempera-ture s o l u b i l i t y r e l a t i o n and that the rate of c r y s t a l growth was proportional to the supersaturation raised to the power n. His derived results for constant heat flux are R = R Q + a 3 K r ( q | n t (4) where K r i s the o v e r - a l l c r y s t a l l i z a t i o n rate constant. For constant AT, Reitzer obtained Rn+1 = R n + 1 + ^ A j r m t ( 5 ) h i Thus, when reaction at the surface controls the scaling process, K r w i l l be r e l a t i v e l y independent of v e l o c i t y , and high v e l o c i t y with increasing h^ should reduce the rate of scale formation. When mass transfer controls, v e l o c i t y should have l i t t l e e f f e c t as i t then influences h^ and K r s i m i l a r l y . Miyauchi and Mori-yama (8) arrived at a si m i l a r equation independently. Palen and Westwater (9) found that for b o i l i n g CaSO^solutions on a f l a t plate under conditions of uniform heat flux, the fouling rate depended on the square of the heat flux, i . e . n = 2 in equation 4. Similar results have been obtained for deposition of iron oxide scales in b o i l e r s . Man'kina and co-workers (10) found the scaling rate to be uniform with time, and dependent on 7 the square of the l o c a l heat f l u x . I t i s w e l l known that i n many cases high v e l o c i t i e s suppress the growth of the f o u l i n g r e s i s t a n c e (11). Smith (12) measured the f o u l i n g r e s i s t a n c e of exchangers operating on water from the Ri v e r Tees over three-month periods. In the v e l o c i t y range 2 to 6 ft/second, the amount of deposit that formed i n three months was reduced as the v e l o c i t y was increased. Chantry and Church (13) have described the use of high v e l o c i t i e s (10 to 30 f t / s e c ) i n heat exchangers i n f o u l i n g s e r v i c e . Operating times have been increased from s i x days to s i x months on some u n i t s , due to the combined e f f e c t s of the scouring a c t i o n of the l i q u i d and the lower tube w a l l temperatures associated w i t h higher v e l o c i t i e s . Kern and Seaton (2), i n 1959, provided an a n a l y s i s that p r e d i c t e d the e f f e c t of v e l o c i t y on the buildup of the f o u l i n g f i l m . They observed that f o r many d i f f e r e n t f o u l i n g l i q u i d s the f o u l i n g r e s i s t a n c e appeared to increase w i t h time to an asymptotic value. The time dependence of the f o u l i n g r e s i s t a n c e was then approximated by R f = Rf (1 - e" b t) (6) A t h e o r e t i c a l model was developed i n which they as-sumed the net rate of f o u l i n g f i l m formation i n a s i n g l e heat exchanger tube could be w r i t t e n as the d i f f e r e n c e between a con-stant (with time) d e p o s i t i o n rate and a v a r i a b l e removal r a t e . 8 The d e p o s i t i o n r a t e was assumed t o v a r y as t h e d i r t c o n c e n t r a -t i o n C and t h e mass f l o w r a t e , W. The r e m o v a l t e n d e n c y was p i c t u r e d as o c c u r i n g i n chunks a t p l a n e s o f weakness a t random d e p t h i n t h e d e p o s i t , and was assumed p r o p o r t i o n a l t o t h e s h e a r s t r e s s T , and t h e i n s t a n t a n e o u s t h i c k n e s s o f t h e d e p o s i t . The change i n d e p o s i t t h i c k n e s s w i t h t i m e was t h e n w r i t t e n as dx _ K-j^ C'W - K 2 T x (7) At They showed t h a t f o r t h i n d e p o s i t s , where x « p i p e d i a m e t e r D, a n d T r e m a i n s e s s e n t i a l l y c o n s t a n t w i t h t i m e , i n t e g r a t i o n o f e q u a t i o n 7 s t a r t i n g f r o m a c l e a n s u r f a c e y i e l d s e q u a t i o n 6 ( p u t t i n g R f = x / k d , where k d i s t h e t h e r m a l c o n d u c t i v i t y o f t h e d e p o s i t , assumed constant)„ The a s y m p t o t i c f o u l i n g r e s i s t a n c e R f i s o b t a i n e d b y p u t t i n g d x / d t = 0 i n e q u a t i o n 7 so t h a t i f x i s t h e a s y m p t o t i c d e p o s i t t h i c k n e s s , R* = x ^ - KlCVW ( 8 )  c d f k d " K 2 T k d s u b s t i t u t i n g ., 2 T = P_ y b £ :(9) g c 2 and u b = 4 W do) pirn2 i n t o e q u a t i o n 8, i t i s s e e n 'that R* a W"1 (11) a s s u m i n g fchat f i s i n d e p e n d e n t o f R e y n o l d s number. Thus i f a h i g h enough mass f l o w r a t e i s u s e d , an e x c h a n g e r c o u l d t h e o r e t i -9 c a l l y operate i n d e f i n i t e l y w i t h a small, t o l e r a b l e f o u l i n g res i s t a n c e . The parameter b i s obtained from equation 6 and 7 as b •- (dRf/dt) t = 0 = (dx/dt)x=0 _ KiC'W (12) k d R* k d R* Combining equations 8, 9 and 12 b = K 2 T = K2P f u£ a W2 (13) 2 g c I f the d e p o s i t b u i l d s up to a c o n s i d e r a b l e t h i c k n e s s r e l a t i v e to the tube diameter, then T i n equation 7 w i l l v ary w i t h t (at constant W). For t h i s case equation 7 i s not im-m e d i a t e l y i n t e g r a b l e and the f i l m t h i c k n e s s i s a v a i l a b l e only as a s e r i e s of i n t e g r a l s . The asymptotic f i l m t h i c k n e s s can be w r i t t e n i n terms of the asymptotic pressure drop as x* a wO-6 (14) ( A P V D 0 . 8 In a l a t e r p u b l i c a t i o n , Kern (14) considered the a l t e r n a t e case of constant pressure drop and v a r i a b l e mass flow r a t e . No e x p l i c i t data were given i n e i t h e r of the p u b l i c a -t i o n s t o support t h i s t h e o r e t i c a l model. Nor was any mechanism given or p o s t u l a t e d f o r the a t t r a c t i o n of the d i r t p a r t i c l e s to the tube w a l l . The a n a l y s i s was r e s t r i c t e d to the isothermal case, although the s u r f a c e temperature would be expected to p l a y an important r o l e i n many types of f o u l i n g . 10 Kern (2,14) maintained that according to h i s theory, increasing the v e l o c i t y of a d i r t y l i q u i d in the tubes of a heat exchanger would increase the operating time due to suppression of fouling. Equation 8 does indicate that increasing the velo-c i t y and hence W in a tube decreases the ultimate fouling re-•k sistance Rf. D i f f e r e n t i a t i o n of equation 6 yi e l d s , for time zero, dR f -* dt = R f b (15) t=0 Substituting for Rf and b from equations 11 and 13 respectively shows that the i n i t i a l fouling rate increases with mass flow rate: CC W (16) dR f dt t=0 Thus, i t i s conceivable that, in r a i s i n g the design l i q u i d velo-c i t y , the higher i n i t i a l fouling rate may more than offset the lower ultimate resistance, and lead to a shorter operating time. This unexpected facet of the Kern-Seaton model has been pointed out by the present authors to Dr. Kern in connection with numeri-c a l examples Kern c i t e s in his two papers which are there solved erroneously. Kern confuses the mass flow rate per tube, which i s used in the derivation of h i s equations, with the mass flow per exchanger in h i s numerical calculations. Thus, in Example 2 of h i s most recent paper (14), Kern considered a s h e l l and tube heat exchanger with two tube passes that reached a 11 fouling resistance of 0.006(°F)(hr)(ft 2)/BTU in eight months (Figure 0) . By modifying the exchanger to four tube passes for the same heat transfer area and t o t a l mass flow rate, and allowing fouling to 90% of the new asymptotic resistance, he claimed that the operating time could be increased to twenty-two months. This operating time was calculated on the basis that with the change to four tube passes the operating v e l o c i t y would be doubled, while the t o t a l mass flow rate and hence the parameter b would remain constant. It is important to note, however, that the W in Kern'-'-'s derivation i s the mass flow rate per tube rather than the mass flow rate per tube bundle. This interpretation i s e x p l i c i t in the expression = W 7T (D-2x) 2 ^ 4 which underlies subsequent relationships of Kern. In p a r t i c u l a r the d i r e c t proportionality between W and i s b u i l t into subsequent derivations in such a way that W must change when changes, whether or not the number of fixed diameter tubes in p a r a l l e l , and hence the t o t a l mass flow rate per tube bundle, changes. Thus, for example, the wall shear stress T i s taken throughout as varying with W to the same power as i t varies with U-^ , an assumption which does not allow W to be interpreted as the mass flow rate per exchanger when the number of tubes in p a r a l l e l changes. For the new condition of four tube passes, then, the parameter b w i l l quadruple when U, or W doubles 12 0-OIOr 1 1 — 1— r TIME months F i g u r e 0. Computed F o u l i n g C u r v e s f o r K e r n ' s Example 2 13 (equation 13). As a result, the new operating time actually decreases from eight months to five months (Figure 0), rather than increasing to twenty-two months as calculated by Kern. In many i n d u s t r i a l heat exchangers the fouling r e s i s -tance grows almost l i n e a r l y with time u n t i l cleaning out be-comes necessary (15,23). For such cases the i n i t i a l fouling rate i s of primary importance as the asymptotic condition i s never reached. The i n i t i a l rate prediction of the Kern-Seaton model i s that higher v e l o c i t i e s would increase i n i t i a l fouling. The data of Smith (12) do not support this prediction. Gardner (15) stated that in confidential data available to him there i s evidence that the "deposition and removal" rates do not always take the mathematical form suggested by the difference model of Kern and Seaton, and further that the asymptotic resistance i s often not reached u n t i l the tube becomes blocked. In 1961 Parkins (16) proposed that the rate of f i l m formation due to suspended p a r t i c l e s was proportional to the product of the p a r t i c l e concentration, the average v e l o c i t y of p a r t i c l e s towards the surface Uj, and the p r o b a b i l i t y Sj, that a p a r t i c l e contacting the surface would become permanently attached: dx = 7a. C, U. S. (17) dT 3 Parkins then calculated the mass flux for the case of submi-14 cron sized p a r t i c l e s d i f f u s i n g by Brownian motion through the laminar sublayer. He assumed that the s t i c k i n g p r o b a b i l i t y was of the form S = fo e x p ( - E A B T ) (18) U b where S Q i s a constant, since a p a r t i c l e would s t i c k only i f the v e l o c i t y was not large enough to produce mechanical forces on the p a r t i c l e which would counteract the chemical linkages holding the p a r t i c l e to the wall. No attempt was made to integrate equation 17, or to develop equations describing the net e f f e c t of v e l o c i t y , say, on the process. In 1963, Charlesworth (17) in a study of the fouling of organic coolants for nuclear reactors, pointed out that fouling films can be deposited by two mechanisms, which may occur simultaneously. One mechanism involves material soluble in the coolant, and the other involves particulate matter. Further, these two types of fouling showed markedly d i f f e r e n t v e l o c i t y dependence. He found that inorganic material was deposited by a mass transfer mechanism that involved transport of soluble matter to the hot surface where c r y s t a l l i n e deposits formed, presumably due to an inverse temperature-solubility r e l a t i o n . Deposition rates increased with increasing v e l o c i t y to a power between 0.5 and 1.0. Deposition rates depended approximately exponentially on the surface temperature. The 15 deposition of predominantly inorganic material by such a mechanism was termed "mass transfer" fouling. Fouling due to particulate matter suspended in the stream, termed "particulate fouling", showed decreasing rates with increasing v e l o c i t y , an i n l e t e f f e c t , and exponential surface temperature dependence. Charlesworth's results showed that the amount of deposition decreased by a factor of 1.9 when the v e l o c i t y was increased by a factor of 2.3. Data from the United States Atomic Energy Commission (18) showed that for three v e l o c i t i e s , the f i l m formation rate on a f l a t plate was proportional to the r e c i p r o c a l of the v e l o c i t y raised to the power 0.9. Fouling was promoted by increasing the surface temperature and the concentration of p a r t i c u l a t e matter. N i j s i n g (19) i n 1964 explained the v e l o c i t y dependence of the two types of fouling as follows. For p a r t i c l e s below a certain size (including molecules) the deposition process is d i f f u s i o n controlled, and an increase in v e l o c i t y w i l l enhance fouling. For p a r t i c l e s above a certain size, the deposition process i s partly controlled by adhesion of the p a r t i c l e s to the wall, and an increase in v e l o c i t y decreases the adhesion rate due to increased drag on the p a r t i c l e , thereby reducing the fouling rate. N i j s i n g presented equations for material flux to the wall for solute molecules and for the l i m i t i n g case of p a r t i c l e s of zero size, based on a model 1 6 of an alternately growing and collapsing laminar sublayer. He also considered some factors that affect adhesion of par-t i c l e s , but presented no equations describing the net buildup of a fou l i n g f i l m with time. In 1962, Epstein and Evans (20) obtained time dependent mathematical solutions for deposition of radioactive p a r t i -cles from a f l u i d stream as a series of functions. The argu-ments of the functions include a mass transfer c o e f f i c i e n t , and i n e r t i a l transfer c o e f f i c i e n t (describing transfer due to i n e r t i a acquired from v e l o c i t y fluctuations in the turbulent core), a s t i c k i n g c o e f f i c i e n t , an absorption-desorption coef4* f i c i e n t and a removal c o e f f i c i e n t . While t h e i r work presents a good discussion of possible processes occurring in fouling, t h e i r equations are of limited use in predicting fouling rates, since the l a t t e r three c o e f f i c i e n t s cannot be predicted. Recently, Hasson, A v r i e l , Resnick, Rozenmann and Windreich (21) have shown that scaling of solutions of CaC03 in water can be described by a model involving d i f f u s i o n to, and reaction at, the wall. In the Reynolds number range 13,000 to 42,000 the i n i t i a l rate of scale growth i s d i f f u s i o n controlled. Their data were correlated by the equation dm = 0.054 Refif® (19) dt 17 These results substantiate the "mass transfer" fouling results of Charlesworth e£ a l (17), d e f i n i t e l y indicating the increase in i n i t i a l s c a l i n g rate with increasing v e l o c i t y . Matsuda, Akimoto and Taniguchi (22) found that the rate of Mg(0H)2 scale formation from a 8° Be'brine varied as -2.2 Ub " for three tests at v e l o c i t i e s below two meters per second. 18 3. SCOPE AND METHOD OF THE PRESENT WORK While there are s c a t t e r e d data a v a i l a b l e (23) of f o u l i n g r e s i s t a n c e versus time curves i n which the f o u l i n g was probably due to suspended p a r t i c l e s , no s y s t e m a t i c study of the p e r t i -nent process v a r i a b l e s could be found i n the l i t e r a t u r e . I t was the o b j e c t of the present work, t h e r e f o r e , t o study the e f f e c t s of v e l o c i t y and temperature on the r a t e of f o u l i n g of some l i q u i d s t y p i c a l of i n d u s t r i a l l y important f o u l i n g streams. To study the f o u l i n g process i t would be d e s i r a b l e t o measure the f o u l i n g r e s i s t a n c e , and the t h i c k n e s s and weight of the d e p o s i t , and to observe d i r e c t l y the nature of the d e p o s i t as t o i t s degree of compactness, s u r f a c e roughness, p o r o s i t y , evenness e t c . In most i n d u s t r i a l s h e l l and tube heat exchangers the f o u l i n g streams are pumped through the tubes i f p o s s i b l e , t o f a c i l i t a t e c l e a n i n g . I t was t h e r e f o r e decided t o study f o u l i n g on the i n s i d e r a t h e r than on the o u t s i d e of the tube although t h i s choice has s e v e r a l disadvantages. Because the diameter of the tube i s of n e c e s s i t y s m a l l i n order to achieve h i g h v e l o c i t i e s w i t h reasonable flow r a t e s , the f o u l i n g d e p o s i t could not be observed i n d e t a i l i n s i t u , and d i r e c t measurement of the f i l m t h i c k n e s s had t o be abandoned. Q u a n t i t a t i v e recovery of the d e p o s i t was rendered a l l but i m p o s s i b l e . The amount of f o u l i n g was measured by the change of the heat transfer resistance, and also i n d i r e c t l y by the change in pressure drop. A heat transfer loop was designed and constructed in which fouling of a single heated tube could be studied, and for which pertinent variables could be controlled or mea-sured . The small amount of available data on particulate fouling (12,16,17) appeared to contradict Kern's model as to the e f f e c t of v e l o c i t y on i n i t i a l fouling rate. There was a need for more work on a theory to predict or explain the effects of the important variables i n particulate fouling. An attempt was made therefore to extend the models of Parkins and Kern. 20 4. SELECTION OF WORKING FLUIDS The problems of fouling in o i l refinery equipment is well documented. The American Petroleum Institute Subcommittee on Corrosion reported in 1963 (24) that, based on a survey covering t h i r t y - s i x o i l r e f i n e r i e s , there was general agree-ment on the seriousness of fouling from operational and cost stand-points. Feed preheat exchangers handling crude o i l , and hydrodesulphurizer feed preheat exchangers fouled more than other pieces of equipment. Fouling was most serious at temperatures above 300°F. Nelson (25) says that in determining heat transfer c o e f f i c i e n t s "the d i r t y i n g or fouling that always occurs in petroleum equipment i s such an unknown factor that... the transfer-rate formulas...lose much of t h e i r importance". Crawford and M i l l e r (26) state that "in c a t a l y t i c desulphurizer units p a r t i c u l a r l y the problem of process side fouling has become acute". It thus appeared that some study of a petroleum o i l might be useful. A sour heavy gas o i l was chosen because of i t s convenient range of properties. A straight run o i l was selected because the severe oxidation s u s c e p t i b i l i t y of cracked products might result in rapid changes of the o i l ch a r a c t e r i s t i c s as i t was recirculated„ The s t a b i l i t y of the straight run product was chosen in preference to the more rapid fouling c h a r a c t e r i s t i c s of cracked stock (26) . Properties t y p i c a l of the o i l s used in this s^udy are l i s t e d in Table I. 21 The major part of th i s study i s concerned with gas o i l fouling. Experiments were also conducted with a d i l u t e sus-pension of fine sand p a r t i c l e s in water. Pa r t i c l e s of size 12.8-17.3 microns were used in concentrations of 2 to 5 parts per m i l l i o n . It was hoped that the results of th i s portion of the work might be applicable to some cooling water fouling problems caused by d i r t y water. A single experiment was done on Kraft liquor fouling. TABLE I. PROPERTIES OF A TYPICAL GAS OIL BLEND Kinematic v i s c o s i t y at 210°F. 1.61 centistokes 2 50°F. 1.24 centistokes 300°F. 0.95 centistokes S p e c i f i c gravity at 210°F. 0.797 2 50°F. 0.783 • 300°F. 0.765 Sulphur i n o i l 0.7% Ash 0.006% Prandtl Number at 220°F. tt 20 I n i t i a l B o i l i n g Point 475°F. 10% d i s t i l l e d 537°F. 50% d i s t i l l e d 586°F. 80% d i s t i l l e d 610°F. Sulphur i n particulates 5.4% Ash in particulates 4.6% Particulates retained on 0.8 micron f i l t e r K 15 p.p.m. 5. APPARATUS The change in heat transfer c o e f f i c i e n t for a single heated tube was followed with time. The l i q u i d to be studied was c i r c u l a t e d around a closed heat transfer loop at a measured flow rate. The test section was resistance heated by passing an alternating current d i r e c t l y through the tube wall. Tem-peratures were measured on the outside of the tube wall and around the loop with thermocouples. After passing through the tube of a double pipe cooler the f l u i d was returned to the storage tank. A detailed description of the equipment follows. The apparatus for the study of fouling rates i s shown schematically i n Figure 1. F l u i d i s stored i n a 45 gallon stainless s t e e l drum which i s equipped with an external steam c o i l and insulated. The l i q u i d i s pumped around the closed loop by a Siemen and Hinsch Type CAD Model 3102 stainless s t e e l two-stage self-priming centrifugal pump driven by a 3 HP motor. The flow rate i s controlled manually by a one-h a l f inch Powell stainless s t e e l globe valve with Teflon packing, the excess f l u i d being returned through a F a r r i s No. 1870 spring-loaded bypass valve to the storage tank. The f l u i d i s metered using two calibrated stainless s t e e l sharp-edged o r i f i c e plates (fB~ 0.301, fo = 0.602) supported by o r i f i c e flanges with corner taps (Figure 2). The metering equipment M i x i n g Chamber Cooler ® T-2 T-3 Pressure Gouge Thermocouple AC- Ammeter AC- Voltmeter Flow Control Valve ® :r-<D 0>= Orifice Plate Differential Pressure Cell 220/IIOv IOKVA Transformer IIO/20v I7KVA Variable Transformer 500/5a Current Transformer F i g u r e 1. D i a g r a m o f Heat T r a n s f e r Loop Sewer |4- 0-8750754 \ H-0-75*1 ORIFICE PLATE FLANGE F i g u r e 2. O r i f i c e P l a t e s and F l a n g e s was designed and i n s t a l l e d following recommended procedures (27). The pressure d i f f e r e n t i a l across the o r i f i c e plate i s indicated on a Honeywell d i f f e r e n t i a l pressure meter Model Y227X2-L2 which was previously calibrated (Appendix 1). The pump delivery pressure i s measured at the o r i f i c e with a 0-200 p s i Marsh bourdon gauge. The test section was constructed of 3/8 inch O.D. x 0.016 inch wall thickness Type 304 seamless stainless s t e e l tubing (Figure 3). A 19-% inch (51 inside diameters) hydro-dynamic entrance length was provided upstream of the heated section to s t a b i l i z e the incoming flow. The heated portion of the tube was 23 9/32 inches long and was provided wi'the two heavy brass e l e c t r i c a l terminal bars soldered to the tube wall (Figure 4). (A three-terminal test section in which the two halves of the active length form p a r a l l e l e l e c t r i c a l resistances was f i r s t b u i l t , after the design of Silberburg and Huber (28). This model was abandoned because the drop in wall temperature at the center terminal affected the tem-perature p r o f i l e on a sizeable portion of the tube). Sixteen copper-constantan thermocouples (24 gauge) were soldered along the outside of the tube with 3/8 to 1/2 inch of the thermocouple contacting the tube wall to minimize conduction losses along the thermocouple wires. Thermocouple locations are specified 27 To 1 x i FPT 8 2 Tube fitting Pressure taps Electrical Cabl Size 000 Tube type 304 stainless I 0-D Current Transformer T o $ x £ MPT Tube fitting Detail at Tube Wall Thermocouple Split Teflon ring Solder F i g u r e 3. D i a g r a m o f T e s t S e c t i o n I 28 PRESSURE TAPS Stainless steel Dimensions - inches Two required Drill a tap for 6-32 screw-1 1: i 1 1 4 1 J I I 8 16 II II F i g u r e 4. P r e s s u r e Taps and E l e c t r i c a l T e r m i n a l s TERMINAL BARS Brass Dimensions - inches Two required 2'9 i n Table I I . The thermocouples were c a l i b r a t e d with a platinum r e s i s t a n c e thermometer p r i o r t o mounting on the tube. The c a l i b r a t i o n data are given i n Appendix 1. The thermocouples were supported i n p o s i t i o n w i t h s p l i t T e f l o n r i n g s . A l l s o l d e r i n g on the t e s t s e c t i o n was done wi t h a e u t e c t i c s o l d e r w i t h a 600°F. m e l t i n g temperature and a 750°F. remelt. F i g u r e 5 i s a photograph of a second t e s t s e c t i o n b u i l t towards the end of the water f o u l i n g experiments, when the f i r s t t e s t s e c t i o n f a i l e d . A l l p a r t s are s i I y e r s o l d e r e d oh t h i s tube. Other-wise t h i s t e s t s e c t i o n i s s i m i l a r t o the one used i n most of the work. The dimensions of t e s t s e c t i o n I I and a t h i r d t e s t s e c t i o n are given i n Appendix 2, p a r t e. The a c t i v e p o r t i o n of the t e s t s e c t i o n was i n s u l a t e d w i t h asbestos cement powder packed to the diameter of the Te.fl.oiai r i n g s , and then completely surrounded by one inch t h i c k C a posite pipe i n s u l a t i o n . The t e s t s e c t i o n was mounted v e r t i c a l l y to e l i m i n a t e sedimentation as a cause of f o u l i n g , thereby promoting equal f o u l i n g around the tube r a d i u s . The e l e c t r i c a l power was s u p p l i e d from s i n g l e phase 220 v o l t AC 40 amp l i n e s which passed through a bank of two S u p e r i o r E l e c t r i c , type 1156D v a r i a c s , wired i n p a r a l l e l and mounted on a common s h a f t . The output from the v a r i a c s was 30 TABLE I I : THERMOCOUPLE LOCATIONS i ON TEST SECTIONS* Thermocouple Number Distance from Bottom Edge of Terminal (cm.) Lower E l e c t r i c a l Test Section I Test Section II Test Section III 1 0.0 0.0 59.4 2 0.95 0.9 1.1 3 4.85 5.0 4.55 4 8.55 8.2 8.25 5 12.75 12.3 12.5 6 17.35 16.7 16.4 7 22.05 21.4 20.8 8 26.45 25.4 2 5.5 9 31.05 29.8 29.6 10 35.65 34.3 34.7 11 40.05 38.7 39.7 12 •44.75 43.4 44.0 13 49.25 48.0 49.1 14 53.95 52.5 54.3 15 58.25 1 58.1 58.3 16 59.3 59.1 0.0 * Test Section I used for runs 7 to 43 Test Section II used for fun 44 Test section III used for run 46 31 F i g u r e 5. Photograph of Test S e c t i o n I I 32 fed to a 10 KVA single phase 220/110 vo l t step down trans-former (General E l e c t r i c Cat. 10M36) which fed a 17KVA Bartho-lemew and Montgomery variable transformer 110/20 v o l t s . The output from t h i s transformer was carried in heavy cables to the terminal bars of the test section. The current flowing to the test section was measured on a Weston Model 155 0-2%, 0-5 Amp dual range ammeter (1/2 to 3/4 % accuracy) after re-duction with a 500/5 Amp Instrument Service Laboratory current transformer, Model 4CT15. The ammeter was calibrated in June 1967 by Instrument Service Laboratories, Vancouver. The voltage drop across the test section was registered on a F u j i portable voltmeter (Range 0-15, 0-30 volts AC, Accuracy -0.5% of f u l l s cale). The test section was insulated e l e c t r i -c a l l y from the rest of the heat transfer loop by a Teflon insert (Figure 6). Pressure drop measurements were made across the test section with a calibrated Minneapolis-Honeywell d i f f e r e n t i a l pressure c e l l Model 227X2-C2. Pressure taps (Figure 4) were provided a distance of 26-3/16 inches apart. The downstream pressure tap was followed by an outlet length of 6-1/2 inches. The t o t a l pressure was measured at the down-stream tap with a Marsh 0-200 p s i "Bo,urdon gauge. The i n l e t and outlet bulk l i q u i d temperatures were measured by thermocouples in mixing chambers. The i n l e t chamber was a Jg" pipe "tee". The outlet chamber is shown in 33 D R I L L a T A P N P T T W O H O L E S 2 I N C H S C H E D U L E 4 0 S T A I N L E S S S T E E L P I P E D R I L L S T A P TA I V T W O H O L E S WA A R 6 0 N W E 1 I E N D S O F S T A I N L E S S S T E E L P L A T E T O B E W E L D E D T O P I P E O U T L E T M I X I N G C H A M B E R T E F L O N S H O R T N I P P L E F i g u r e 6 . O u t l e t M i x i n g Chamber Figure 6. After passing through the outlet mixing chamber, the f l u i d was cooled in a double pipe cooler. The test f l u i d flowed within the cooler tube, which was a six foot section of 3/8 inch O.D. x 0.035 inch wall thickness stainless s t e e l tubing. The s h e l l was made of one-half inch galvanized pipe. The cooling water was metered with a Brooks rotameter - Type 12-1110. The cooled f l u i d then returned to the storage tank. The loop was constructed mainly of 1/2 inch Schedule 40 stainl e s s s t e e l pipe, except for the heating and cooling sections (described above) and the pump i n l e t piping which was of one-inch Schedule 40 stainless s t e e l pipe. A l l temperatures were measured by means of calibrated thermocouples (Appendix 1) and a Leeds and Northrup Portable precision Potentiometer (Model 8622, No. 634358, Ch 1648B). The reference junction was an ice-water s l u r r y . A l l thermo-couples i n contact with the test f l u i d were Pyrptenax ir o n -constantan thermocouples with insulated junctions and com-p l e t e l y stainless steel sheathed (Model 122HT7/I-C). As i t was necessary for the apparatus to run unattended, a high temperature alarm and power shutoff system was provided in the event that the pump f a i l e d or the tube wall overheated. A Johnson E l e c t r i c Hot Water Control remote mounting unit (Model 7T674) was used with the bulb mounted in the insulation of the test section. When the temperature exceeded the s point the power to the complete apparatus was cut o f f and buzzer alarm was sounded. 36 6. EXPERIMENTAL PROCEDURES a) Gas O i l Fouling The procedure for carrying out a fouling run was as follows. (Refer to Figure 1 ) . After the l i q u i d was charged to 'the storage tank the steam to the tank c o i l was turned on, bringing the o i l to about 200°F. in 6 to 8 hours. The pump was started and the pressure drop across the o r i f i c e adjusted to and maintained at the desired value by turning the control valve. The power to the test section was turned on tfcc? give the desired heat generation. Once the o i l i n the tank reached the desired temperature ( t y p i c a l l y 1/2 to 3/4 hour) the steam was turned o f f and the cooling water turned on to maintain the i n l e t o i l temperature at the desired value. One-half to 3/4 of an hour l a t e r the test section would reach steady state and the run would commence. Minor adjustments of o i l and water flow rates and of the power input were made to maintain constant flow and constant power d i s s i p a t i o n . M i l l i v o l t readings on the twenty-four thermocouples were taken (after balancing the potentiometer on an external standard c e l l ) as often as was necessary, depending on the fouling rate. Readings were commonly taken every six to eight hours. Pressure drop, voltage drop, and current measurements 37 were made a t t h e same t i m e . The e q u i p m e n t o p e r a t e d c o n t i n u o u s l y u n t i l t h e r u n was c o m p l e t e . Runs l a s t e d f r o m a b o u t e i g h t h o u r s t o s i x t e e n d a y s . O i l samples were w i t h d r a w n from t h e t a n k n e a r t h e b e -g i n n i n g and t h e end o f a r u n . K i n e m a t i c v i s c o s i t i e s were mea-s u r e d a t t h e i n l e t t e m p e r a t u r e . The A.S.T.M. method, D445-53T (2 9 ) , was f o l l o w e d u s i n g two Cannon-Fenske v i s c o m e t e r s ( s i z e 50) t h a t h a d b e e n p r e v i o u s l y c a l i b r a t e d b y de V e r t e u i l ( 3 0 ) . (A r o u g h c h e c k was made on t h e c a l i b r a t i o n u s i n g d i s -t i l l e d w a t e r . The v i s c o m e t e r c o n s t a n t s were w i t h i n 1% o f de V e r t e u i l * s v a l u e s ) . Two measurements were u s u a l l y made on e a c h v i s c o m e t e r . K i n e m a t i c v i s c o s i t i e s were measured o v e r a r a n g e o f t e m p e r a t u r e s on s e l e c t e d o i l samples (see A p p e n d i x 2, F i g u r e 1 - 3 ) . S p e c i f i c g r a v i t y o f t h e o i l samples was d e t e r -m i n e d a c c o r d i n g t o method D287-55 o f t h e A.S.T.M. ( 2 9 ) . The p a r t i c u l a t e m a t t e r was e s t i m a t e d a c c o r d i n g t o t h e A.S.T.M. t e n t a t i v e method ( 2 9 ) , i n w h i c h samples a r e f i l t e r e d t h r o u g h 0.8 m i c r o n p o r e d i a m e t e r M i l l i p o r e f i l t e r s . E n g l e r d i s t i l l a -t i o n s were done on s e l e c t e d o i l samples a f t e r A.S.T.M. method D86-56. S u l p h u r and a s h a n a l y s e s ( T a b l e I ) , were done b y a l o c a l c o m m e r c i a l c h e m i c a l l a b o r a t o r y . The o i l was f a i r l y s t a b l e o v e r t h e 300-400 h o u r s o f t h e l o n g e r r u n s . The k i n e -m a t i c v i s c o s i t y i n c r e a s e d u s u a l l y b y a b o u t one p e r c e n t , and 3 8 there was v i r t u a l l y no change detected in the s p e c i f i c gravity. At the end of each run the piping leading to and from the test section was removed, and the test section was drained and cleaned while remaining in position. Cleaning was accomplished as follows. The tube was rinsed with petroleum ether. A wad of heavy pipe cleaner affixed to a wire was soaked in ether and then drawn through the tube a number of times. The black, sooty deposit was rinsed o f f the wad into an erlenmeyer flask of ether. Vigorous brushing with a long-handled test tube brush and scraping with a sharpened welding rod, combined with the above procedure, was s u f f i c i e n t to clean out the tube. The inside of the test section was inspected v i s u a l l y by shining a l i g h t up from the entrance section. As much of the deposit as possible was recovered for analysis, but i t was not possible to get quantitative recovery. b) Water Fouling The operating procedure was si m i l a r to that described above. Particulate matter was estimated as for the o i l . No v i s c o s i t y or density measurements were made. Pure water pro-perties (31) were assumed v a l i d as the concentration of suspended solids was about fiv e parts per m i l l i o n . 39 7. RESULTS AND DISCUSSION a) C a l c u l a t i o n Methods An o u t l i n e o f t h e c a l c u l a t i o n methods i s h e r e i n p r e s e n t e d , D e t a i l s and sample c a l c u l a t i o n s a p p e a r i n A p p e n d i x 2. The f o u l i n g r e s i s t a n c e a t any i n s t a n t i s g i v e n b y R f = 1 _ 1 (20) h_, h' m m c where t h e i n s t a n t a n e o u s rae.an h e a t t r a n s f e r c o e f f i c i e n t , h m i s g i v e n b y h m = qw (21) A T m The c o e f f i c i e n t i s b a s e d on t h e mean t e m p e r a t u r e d i f f e r e n c e T, • _• T b . / T b , 2 (22) clTb Tw - ^ T h i s mean t e m p e r a t u r e d i f f e r e n c e r e d u c e s t o T w - T^ f o r t h e u n i f o r m h e a t f l u x c o n d i t i o n where T w - T^ i s c o n s t a n t w i t h t u b e l e n g t h , and t o t h e log-mean t e m p e r a t u r e d i f f e r e n c e f o r t h e c o n s t a n t w a l l t e m p e r a t u r e c o n d i t i o n . The h e a t f l u x q w = Q/A was d e t e r m i n e d from t h e power d i s s i p a t e d i n t h e tu b e w a l l . The power was c a l c u l a t e d f r o m 40 the current flowing to the test section and the voltage drop across the test section, assuming a power factor of unity. The power factor was measured at three d i f f e r e n t power levels using a wattmeter, and the voltmeter and ammeter. Within the instrument errors (0.5%) the power factor was found equal to unity* The heat generated in the tube i s then Q = 3.413 x Voltage Drop x Current BTU (23) Most of the heat i s transferred to the l i q u i d but there are losses due to conduction through the insulation and the e l e c t r i c a l terminal bars, and along the tube wall. The losses at the tube ends are d i f f i c u l t to estimate (although t h e o r e t i -been ignored. It was evident from-measured temperature p r o f i l e s along the tube that these losses were quite small. Losses by conduction through the e l e c t r i c a l terminals also have been ignored. The heat loss through the insulation was estimated by measuring the temperatures at two r a d i a l distances in the insulation, and, using the form of the heat conduction equation for cylinders, extrapolating to get the temperature at the outside of the insulation* The heat loss due to natural convection and radiation was then calculated (31), hr cal attempts have been made for simpler geometry (32)), and have (24) 41 where T3 is the temperature at the outside of t h e ; i n s u l a t i o n and TQQ i s the temperature of the a i r in the room. Losses were very small, in a l l cases amounting to less than 3% of the heat generated. The tube wall temperatures were measured on the outside of the tube, and were corrected to•give the inside tube wall temperature by applying the solution of the steady state heat conduction equation for a long hollow cylinder with uniform internal heat generation and an adiabatic outer wall (33): T o - T i .. = Q i l / 2 - r 2out In rout 1 (25) t a l l r 2 .- r 2 r. j v- out 1 1 J 2 TT L K me This correction was usually about 3 or 4 °F. For the o i l experiments the correction was a small fractio n of the mean temperature difference of 80 - 180°F» The temperature d r i v i n g force was calculated by assuming a l i n e a r increase in bulk temperature with length of the heated section, an assumption which i s equivalent to assuming a uniform heat flux with distance. The denominator of the integral of equation 22 was evaluated at eleven thermocouple positions and. then f i t t e d to a quadratic^equation in distance by least squares. The int e -gral was then solved a n a l y t i c a l l y over the central portion of the tube, excluding the thermal entrance and exit regions. In 42 F i g u r e 7 t h e i n s i d e w a l l t e m p e r a t u r e i s shown a l o n g t h e h e a t e d l e n g t h o f t h e t u b e as t h e t u b e became f o u l e d i n a t y p i c a l g a s -o i l e x p e r i m e n t a t a m o d e r a t e l y h i g h h e a t f l u x . The s o l i d l i n e s r e p r e s e n t t h e l e a s t s q u a r e s f i t o v e r t h e s e c t i o n o f t h e t u b e f o r w h i c h t h e mean t e m p e r a t u r e d i f f e r e n c e i s c a l c u l a t e d . The low t e m p e r a t u r e o f t h e t u b e w a l l on e i t h e r s i d e o f t h e h e a t e d s e c t i o n i n d i c a t e s t h a t t h e l o n g i t u d i n a l c o n d u c t i o n l o s s e s were i n d e e d s m a l l . H e a t g e n e r a t e d , h e a t l o s s , a v e r a g e i n s i d e and o u t s i d e t u b e w a l l t e m p e r a t u r e s , A T m and-h^ a r e l i s t e d i n A p p e n d i x 3, T a b l e 3-1, f o r a l l r u n s . A t t i m e z e r o when t h e t u b e i s c l e a n , t h e w a l l t e m p e r a t u r e i s e s s e n t i a l l y p a r a l l e l w i t h t h e l i q u i d b u l k t e m p e r a t u r e . T h i s f a c t i n d i c a t e s t h e n e a r u n i f o r m i t y o f t h e h e a t f l u x w i t h d i s t a n c e . D e v i a t i o n s f r o m u n i f o r m h e a t f l u x a r e p r o b a b l y due t o v a r i a t i o n s i n w a l l t h i c k n e s s o f t h e t u b i n g , and t o t h e i n c r e a s i n g e l e c t r i c a l r e s i s t a n c e and t h u s t h e power d i s s i p a t e d , w i t h t e m p e r a t u r e a l o n g t h e t u b e l e n g t h . T h i s l a t t e r f a c t o r i s a m i n o r one u n d e r c l e a n t u b e c o n d i t i o n s b e c a u s e o f t h e low m a g n i t u d e o f t h e t e m p e r a t u r e c o e f f i c i e n t o f e l e c t r i c a l r e -s i s t a n c e f o r t y p e 304 s t a i n l e s s s t e e l ( 3 4 ) . Thus a t y p i c a l t e m p e r a t u r e r i s e a l o n g t h e c l e a n t u b e i s 20°F., o v e r w h i c h t h e r e s i s t i v i t y i n c r e a s e s b y o n l y a b o u t 1-1/2%. However, u n d e r s e v e r e f o u l i n g c o n d i t i o n s t h i s e f f e c t may be o f g r e a t e r i m p o r t a n c e , 600 e o400| o. £ 200h C 1 Run 27 Q/A=58,250 B T U / H R F T 2 W-0-242 L B / S E C I I 20 40 LENGTH cm 60 g u r e 7. Tube W a l l T e m p e r a t u r e P r o f i l e s and T e r m i n a l F l u i d T e m p e r a t u r e s 44 and may res u l t in a non-uniform heat flux. The clean tube heat transfer c o e f f i c i e n t s for the gas o i l were compared to the values predicted by the Sieder-Tate equation (35), " 1 4 h c a l c D = 0.023 w' (26) V i s c o s i t i e s for the o i l were measured over a range of tempera-tures and were extrapolated i f necessary to get the wall v i s -cosity (Appendix 1, Figure 1-3). The heat capacity was c a l -culated from the heat balance Q = W C_ A T b (27) The thermal conductivity was estimated from data for o i l s (36). Agreement of measured and predicted heat transfer c o e f f i c i e n t s i s shown i n Figure 8. Data are l i s t e d in Appendix 3, Table 3-III. Over the range 182 to 1010 BTU/(hr)(ft 2)(°F), agree-ment was within 6% (standard deviation). The clean tube heat transfer c o e f f i c i e n t s for the water fouling experiments were compared with the si m p l i f i e d dimensional equation for water (35): , 120(1+0.013' T .' ) u g ' 8 , O Q x h = f i l m b (28) m c a l c (D,)U.2 where D1 i s the inside tube diameter in inches, T f i _ m = %( Tw + 4 5 roooh 800 M 600h 400h 200h 200 400 hC0|c 600 800 1000 BTU/hr ft 2 °F F i g u r e 8 C o m p a r i s o n o f M e a s u r e d C l e a n H e a t T r a n s f e r C o e f f i c i e n t s and P r e d i c t i o n s o f t h e S i e d e r - T a t e E q u a t i o n f o r Gas O i l s 46 and i s t h e b u l k v e l o c i t y i n f e e t p e r s e c o n d . The c a l c u l a t e d and measured c o e f f i c i e n t s and t h e h e a t b a l a n c e d e v i a t i o n s a r e l i s t e d i n T a b l e I I I . The agreement o f t h e c o e f f i c i e n t s i s e x c e l l e n t ( 4 . 0 % s t a n d a r d d e v i a t i o n ) , and t h e h e a t b a l a n c e s show a s t a n d a r d d e v i a t i o n o f 4.4%. The h e a t b a l a n c e d e v i a t i o n i s p a r t l y due t o t h e r e l a t i v e l y l a r g e p e r c e n t a g e e r r o r a s s o c i a t e d w i t h t h e c a l c u l a t i o n o f AT^, and p o s s i b l y a l s o due t o e r r o r s i n f l o w measurement and c o n d u c t i o n l o s s e s v i a t h e e l e c t r i c a l t e r m i n a l s . b) I n i t i a l E x p e r i m e n t s on Gas O i l F o u l i n g The most i m p o r t a n t f a c t o r s a f f e c t i n g f o u l i n g o f a g i v e n t u b e w i t h a g i v e n l i q u i d were t h o u g h t t o be t h e f l o w r a t e and t h e h e a t " f l u x (which g o v e r n s t h e t u b e w a l l t e m p e r a t u r e a t a g i v e n f l o w r a t e and i n l e t t e m p e r a t u r e ) . I n o r d e r t o s t u d y t h e e f f e c t o f f l o w r a t e , t h e a v e r a g e c l e a n w a l l t e m p e r a t u r e was h e l d c o n s t a n t t o m i n i m i z e changes i n p o s s i b l e c h e m i c a l a d h e s i o n e f f e c t s . W a l l t e m p e r a t u r e e f f e c t s were s t u d i e d i n a s e p a r a t e s e r i e s o f e x p e r i m e n t s a t c o n s t a n t f l o w r a t e . E x p e r i m e n t s were done i n random o r d e r t o m i n i m i z e p o s s i b l e changes i n t h e o i l w i t h t i m e . S e v e r a l i n i t i a l e x p e r i m e n t s were done t o f i x o p e r a t i n g p r o c e d u r e s and s e l e c t c o n v e n i e n t o p e r a t i n g c o n d i t i o n s . I t was f o u n d t h a t a t c l e a n w a l l t e m p e r a t u r e s o f 4 0 0 ° F . w i t h a TABLE I I I . HEAT BALANCE AND CLEAN HEAT TRANSFER COEFFICIENTS FOR WATER RUN W l b / s e c WC AT* P b BTU/hr Q BTU/hr HEAT BALANCE DEVIATION % h m B T U / h r f t 2 ° F h m c a l c B T U / h r f t 2 ° F HEAT TRANSFER COEFFICIENT DEVIATION % 40 0.1470 5503 6326 -13.1 1343 1302 +3.2 38 . 0.1722 6260 6928 - 9.5 1451 1466 -1.0 34 0.1920 7200 7532 -4.2 1604 1622 -1.1 39 0.2613 9030 9785 -7.6 2072 2061 +0.5 35 0.3866 12,100 12,539 -3.1 2559 2791 -8.3 42 0.3870 12,440 12,207 +2.0 2588 2804 -7.7 36 0.5457 15,600 16,633 -6.1 3427 3667 -6.5 37 0.3105 10,600 10,818 -2.0 2225 2368 -6.1 41 0.1722 12,020 12,718 -5.5 1516 1570 -3.4 * AT-fr-:., a v e r a g e d o v e r f i r s t t h r e e r e a d i n g s o f e a c h r u n 48 sample o f f r e s h o i l , f o u l i n g was e x t r e m e l y r a p i d and s e v e r e . The e x p e r i m e n t h a d t o be s t o p p e d i n about s i x h o u r s b e c a u s e o f e x c e s s i v e w a l l t e m p e r a t u r e s . When t h e r u n was r e p e a t e d w i t h t h e same o i l t h e f o u l i n g r a t e was about h a l f as g r e a t . F o r a t h i r d e x p e r i m e n t t h e f l u x was changed t o g i v e a c l e a n w a l l t e m p e r a t u r e some 50°F. l o w e r . The f o u l i n g r a t e was t h e n s u c h t h a t a r u n o f 100 h o u r s c o u l d be made. R e p e a t i n g t h i s r u n y i e l d e d a s t i l l l o w e r f o u l i n g r a t e , and e v e n t u a l l y no f u r t h e r f o u l i n g o c c u r r e d e v e n u n d e r o p e r a t i n g c o n d i t i o n s t h a t y i e l d e d r a p i d f o u l i n g when t h e o i l was f r e s h . P a r t i c u l a t e s were s t i l l p r e s e n t i n t h e o i l . From t h e s e i n i t i a l e x p e r i m e n t s i t was c o n c l u d e d t h a t f o r r e p r o d u c i b i l i t y , e a c h e x p e r i m e n t s h o u l d h a v e an i d e n t i c a l s t a r t i n g o i l sample. The c l e a n w a l l t e m p e r a t u r e s h o u l d be abo u t 300°F. i n o r d e r t o a l l o w a l a r g e r w a l l t e m p e r a t u r e i n c r e a s e b e f o r e e x c e s s i v e t e m p e r a t u r e s d e v e l o p e d . S i n c e t h e s u p p l y o f f r e s h o i l was l i m i t e d , s t a r t i n g o i l b a t c h e s were made up o f b l e n d s o f f r e s h o i l and r e - c i r c u l a t e d o i l , as men-t i o n e d u n d e r " E x p e r i m e n t a l P r o c e d u r e s " . c) The E f f e c t o f Mass F l o w R a t e a t C o n s t a n t W a l l T e m p e r a t u r e A s e r i e s o f e x p e r i m e n t s was done w i t h c l e a n w a l l t e m p e r a -t u r e s o f ab o u t 2 95°F. F o u r r u n s were made a t c l e a n t u b e 49 Reynolds numbers from 9800 to 42,000 with samples of gas o i l ft, and then two runs with samples of gas o i l B. These o i l s were two samples from the same location in the refinery but were taken some nine months apart. The heat transfer c o e f f i -cients (equation 21) are plotted against time in Figures 9 and 10. Temperature p r o f i l e s , heat transfer c o e f f i c i e n t s and thermal resistances are tabulated in Appendix 3, Table 3-II. The shape of the heat transfer coefficient-time curves are sim i l a r to those reported for some i n d u s t r i a l heat exchangers (23), in that h m i n i t i a l l y drops f a i r l y rapidly from the clean value and then slowly levels out. To check that the l e v e l l i n g out of h m was not due to exhaustion of the fouling material in the closed system, several runs were repeated after cleaning out the tube without changing the gas o i l . The i n i t i a l drop in h m was s t i l l found to occur (Figures 9, 10), but the rate was less rapid and the l e v e l l i n g out appeared sooner. The agreement of the clean c o e f f i c i e n t for the main run and the repeat run indicates that the cleaning procedure was quite reproducible. Gas o i l B fouled to a much lesser extent than gas o i l A. The reason for this was not apparent. O i l B has a s l i g h t l y lower kinematic v i s c o s i t y than o i l A - 1.55 versus 1.62 centistokes, at 210°F. Particulate levels (Appendix 3, Table 3-V) are about the same. Within the accuracy of the 50 9 8 0 9 4 0 7 9 0 K T " x 1 0 2 0 -Sx x ^ X R e c = 4 1 , 8 7 0 I _ Q * R e c = 2 9 , 2 0 0 R e , H 1 6 , 7 5 0 ^ > K ^ U B ^ 9 * 8  4 2 0 W - 0 - 3 1 2 7 5 0 7 1 0 4 6 0 2 4 0 2 0 0 1 6 0 1 2 0 R e c = 9 , 7 9 0 x R e p e o t e d with s o m e oil ^ 3 Q > \ w - n . i 7 « I I 1 0 0 2 0 0 3 0 0 T i m e h o u r s F i g u r e 9. Heat T r a n s f e r C o e f f i c i e n t v e r s u s Time f o r T « 2 9 5 ° F - O i l A 400 380 360 Oil B TWc= 295°F |- x Repeated with same oil R ^ u i Z 5 J 5 Ubc8 7-62 ft/sec O ^ C D Q ) 260 240 220 Rec * 8185 U b c s 4 7 3 W = 0151 c2Q$£x5> O O O C O C O 0 O O O O C P C O Q ) 100 200 300 400 Time hours u r e 10. Heat T r a n s f e r C o e f f i c i e n t v e r s u s Time f o r T W (_« 295°F- 0 i l B 5-2 measurements, the sulphur and ash levels are also the same.;-The fouling data for each o i l were treated separately, that i s , as i f the two samples were two completely d i f f e r e n t l i q u i d s . A second series of experiments with varying mass flow rate was done with the heat flux adjusted to give an average clean tube wall temperature of about 346°F. (Figure 11). Much more severe fouling took place at the higher temperature. A b r i e f induction period at constant h m was followed by a very rapid drop of h m to about 60% of the i n i t i a l value i n less than f i f t y hours. For these conditions i t was necessary to terminate the experiments before h m l e v e l l e d out due to development of excessively high wall temperatures. The fouling resistances (equation 20) corresponding to the data of Figures 9 and 10 are plotted against time in Figure 12. The asymptotic behaviour of Rf with time as sug-gested by Kern and Seaton (2) i s borne out. The s o l i d l i n es in Figure 12 are the least square f i t s of Rf to equation 6. The values of the parameters are l i s t e d i n Table IV. While the curve f i t appears to underestimate the asymptotic fouling re-sistance in some cases, i t i s evident that equation 6 i s f a i r l y good f i t of the experimental data. 53 7 0 0 f£>o 100 W Ibm/sec 0 - 4 7 7 00 7 ^ = 3 4 6 <»F J I L 0 15 3 0 4 5 Time hours F i g u r e 11. Heat T r a n s f e r C o e f f i c i e n t v e r s u s Time f o r T . 346°F-Oil B w 54 3v~" ^ 1  W* 0-178 lbm/sec Oil A Time hours F i g u r e 12. F o u l i n g R e s i s t a n c e o f O i l s v e r s u s Time f o r — ° / T w « 295 F ( S o l i d L i n e s a r e L e a s t S q u a r e s F i t t o E q u a t i o n 6) 55 # TABLE IV; FIT OF GAS OIL FOULING DATA TO EQUATION 6 O i l Run w Re 10 3Rf b 106RfB lb/sec (BTU/hrft 2°F) - i h r - 1 (BTU/ft 2 °I A 17 0.312 15,930 0.4.037 0.01128 4.553 15 0.543 29,200 0.1424 0.01855 2.64 19 0.778 41,870 0.0738 0.0280 2.125 B 22 0.151 8190 0.4125 0.0279 11.52 24 0.242 13,580 0.1256 0.0408 5.13 # T w c « 295 UF TABLE V: LINEAR FIT OF INITIAL FOULING RATES O i l Run W lb/sec Re Op 10 6 Slope A B 14 0. 1784 9, 790 298. 8 8. 77 27 0-2421 14,320 371. 4 124. 5 28 0. 2421 14,120 348. 8 70. 4 29 0. 4770 27,880 345. 4 34. 7 30 0. 1778 10,620 346. 6 •115. 9 31 0. 2419 14,970 402. 7 310. 4 32 0. 2419 14,580 348. 6 83. 0 33 0. 2419 14,480 346. 8 : 8 i : 1 As expected from the heat transfer c o e f f i c i e n t plots, the fouling resistances for the runs at T w « 346°F. do not c l e v e l out to an asymptotic value (Figure 13). After the induction time, Rf ri s e s almost l i n e a r l y with time. Soli d l i n e s are least square f i t s of the l i n e a r portion of these curves. The pressure drop increases are also shown in Figure 13. The pressure drop appears to increase before there i s a measurable change in thermal resistance. This maybe aoroughness e f f e c t . Also the pressure drop increase appears to l e v e l out while the thermal resistance continues to increase. This i s possible due to a packing e f f e c t , or due to a l e v e l l i n g o f f of the deposition l o c a l l y . The v a r i a t i o n of the parameters R^ and b of equation 6 with mass flow rate i s shown in Figure 14. R decreases with mass flow rate, as suggested q u a l i t a -t i v e l y by the theory of Kern and Seaton. The slope of the * log-log plots of Rf vs W i s -2, however, as opposed to the -1 predicted from equation 11. The parameter b increases with W, but to the power 1 as opposed to the power 2 suggested by equation 13. This fundamental difference between the data and the theory i s most strongly emphasized in Figure 15, in which the i n i t i a l f o uling rate is shown to decrease with the mass flow rate. I n i t i a l fouling rates were calculated from the l i n e a r least squares f i t s of R f vs t curves where the 57 0 15 30 45 Time hours F i g u r e 13. F o u l i n g R e s i s t a n c e and P r e s s u r e D r o p I n c r e a s e v e r s u s Time f o r T w 346°F-Oil B 58 i 1 1 r i i i I — 01 0-2 0-5 10 W l b m / sec F i g u r e 14 V a r i a t i o n o f P a r a m e t e r s o f E q u a t i o n 6 w i t h Mass Flow Rate o f O i l ( l o g - l o g ) 59 jL 100 S*2 o 3 o Li. 10 O Oil A A Oil B Least squares fit T W c - 295 «F F i g u r e 15 1 1 01 0-2 W lb 1 m 0-5 /sec 10 I n i t i a l F o u l i n g R ate o f O i l v e r s u s Mass F l o w Rate ( l o g - l o g ) 60 a s y m p t o t i c r e s i s t a n c e c o u l d n o t be e s t i m a t e d ( F i g u r e 1 3 ) . V a l u e s a r e l i s t e d i n T a b l e V. The i n i t i a l f o u l i n g r a t e s f o r gas o i l s A and B a r e v e r y c l o s e ( F i g u r e 1 5 ) , e v e n t h o u g h t h e a s y m p t o t i c r e s i s t a n c e s a r e q u i t e d i f f e r e n t . The s l o p e o f t h e i n i t i a l f o u l i n g r a t e - m a s s f l o w r a t e p l o t i s -1.33 f o r t h e t h r e e d a t a p o i n t s a t T W c « 3 4 6 ° F . ( and -1.02 f o r o i l s A and B a t T W c « 2 9 5 ° F. The b e s t common s l o p e was c a l c u l a t e d b y s t a t i s t i c a l methods (37) t o be -1.07. The K e r n and S e a t o n d i f f e r e n c e model p r e d i c t s a s l o p e o f +1 f o r s u c h c u r v e s ( e q u a t i o n 1 6 ) . T h i s model t h e r e f o r e does n o t d e s c r i b e t h e i n i t i a l f o u l i n g o f t h e s e gas o i l s u n d e r t h e c o n d i t i o n s c o v e r e d . d) The E f f e c t o f W a l l T e m p e r a t u r e on F o u l i n g The e f f e c t o f c l e a n t u b e w a l l t e m p e r a t u r e on t h e b u i l d -up o f t h e f o u l i n g r e s i s t a n c e was s t u d i e d im a s e r i e s o f e x -p e r i m e n t s c a r r i e d o u t a t d i f f e r e n t h e a t f l u x e s , w h i l e m a i n t a i n -i n g t h e i n l e t b u l k t e m p e r a t u r e and mass f l o w r a t e c o n s t a n t . The a v e r a g e c l e a n w a l l t e m p e r a t u r e was v a r i e d o v e r t h e r a n g e 295 t o 4 03°F. The i n l e t b u l k l i q u i d t e m p e r a t u r e was 212°F. and t h e c l e a n t u b e v e l o c i t y was 7.6 f e e t p e r s e c o n d . F o u l i n g r e s i s t a n c e s and p r e s s u r e d r o p i n c r e a s e a r e p l o t t e d a g a i n s t t i m e i n F i g u r e 16. As was a l r e a d y e v i d e n t i n F i g u r e 15, t h e g rowth o f t h e f o u l i n g r e s i s t a n c e i s p r o f o u n d l y a f f e c t e d b y w a l l t e m p e r a t u r e . F o u l i n g becomes much more s e v e r e as t h e 61 003 002 •001 S 20 Q. < 1 Oil B W=0-242 lb m Q/A =69280 BTU/HR T W c =403 °F T Q/A=58 250 T T_ = 371 °F . 0 / 1 15 30 Time hours 45 F i g u r e 16 F o u l i n g R e s i s t a n c e and P r e s s u r e D r o p I n c r e a s e v e r s u s Time f o r V a r y i n g Heat F l u x e s - O i l B 62 w a l l t e m p e r a t u r e , o r a l t e r n a t e l y t h e h e a t f l u x (which f o r t h e s e e x p e r i m e n t s v a r i e s a l m o s t l i n e a r l y w i t h w a l l t e m p e r a t u r e ) , i s i n c r e a s e d . The i n i t i a l f o u l i n g r a t e s , c a l c u l a t e d i n most c a s e s f r om t h e l e a s t s q u a r e s f i t o f t h e l i n e a r p o r t i o n o f t h e R f V s t c u r v e , a r e p l o t t e d i n F i g u r e 17 a g a i n s t t h e r e c i p r o c a l o f t h e a v e r a g e c l e a n t u b e w a l l t e m p e r a t u r e i n ° R a n k i n e , a f t e r t h e f o r m o f t h e A r r h e n i u s e q u a t i o n (37) f o r c h e m i c a l r e a c t i o n v e l o c i t y c o n s t a n t s . The i n i t i a l f o u l i n g r a t e d o u b l e s f o r e v e r y i n c r e a s e o f a b o u t 15 °F. o v e r t h e r a n g e c o v e r e d . T h i s s t r o n g t e m p e r a t u r e e f f e c t s u g g e s t s t h a t c h e m i c a l r a t h e r t h a n p h y s i c a l p r o c e s s e s a r e i m p o r t a n t i n t h e d e p o s i t i o n o f m a t e r i a l on t h e w a l l . The a c t i v a t i o n e n e r g y c a l c u l a t e d f r o m t h e a v e r a g e s l o p s i n F i g u r e 17 i s a p p r o x i m a t e l y 29 K c a l / g - m o l e . T h i s h i g h v a l u e i s s u g g e s t i v e o f c h e m i c a l bond f o r m a t i o n . C h a r l e s w o r t h (17) and P a r k i n s (16) h a ve a l s o r e p o r t e d t h a t p a r t i c u l a t e f o u l i n g r a t e s o f o r g a n i c r e a c t o r c o o l a n t s i n c r e a s e d w i t h w a l l t e m p e r a t u r e . e) Combined E f f e c t s o f Mass F l o w Rate and W a l l T e m p e r a t u r e A common p r o b l e m i n h e a t e x c h a n g e r d e s i g n i s t o d e s i g n a u n i t f o r a s p e c i f i e d h e a t l o a d and i n l e t f l u i d t e m p e r a t u r e . F o r s u c h a c a s e an i n c r e a s e d v e l o c i t y w i l l l o w e r t h e s u r f a c e t e m p e r a t u r e . I t was u s e f u l , t h e r e f o r e , t o c o r r e l a t e t h e 6 3 5001 % 100 £ o or 50 V O \ \ \ x O £ x _ 10 A \ \ x N \ v \ \ \ \ \ x v \ W Ibm/sec \ O 0-242 Oil B A 0-1 78 Oil B A V A L V 0-362 Oil A (100 % C» recirculated) M8 _ 1-26 1000/ T W c 1-34 °R "'x I03 F i g u r e 17. L o g I n i t i a l F o u l i n g R a t e v e r s u s R e c i p r o c a l o f A v e r a g e C l e a n Tube W a l l T e m p e r a t u r e - O i l s A and B 64 i n i t i a l f o u l i n g r a t e d a t a i n t o a s i n g l e e q u a t i o n t h a t w o u l d i n d i c a t e t h e combined e f f e c t s o f T w c and W. L e a s t s q u a r e f i t s were made t o g i v e an e q u a t i o n o f t h e f o r m s u g g e s t e d b y F i g u r e s 15 and 17. The e q u a t i o n , where t i m e z e r o i s t a k e n a t t h e end o f any i n d u c t i o n p e r i o d , f i t s t h e d a t a o v e r a 1 5 0 - f o l d range o f i n i t i a l f o u l i n g r a t e s . The d e v i a t i o n s o f t h e d a t a f r o m e q u a t i o n 29 a r e i n d i c a t e d i n F i g u r e 18. T h i s e q u a t i o n t h e n g i v e s t h e combined e f f e c t s o f w a l l t e m p e r a t u r e and mass f l o w r a t e on t h e i n i t i a l f o u l i n g r a t e . F o r t h e gas o i l s t u d i e d t h e e f f e c t o f i n c r e a s i n g W a t c o n s t a n t Q i s more s t r o n g l y f e l t t h r o u g h t h e r e d u c t i o n o f T w t h a n t h r o u g h t h e d i r e c t e f f e c t o f i n c r e a s i n g t h e v e l o c i t y i t s e l f , b e c a u s e o f t h e s t r o n g t e m p e r a t u r e e f f e c t s . T h i s p o i n t was w e l l i l l u s t r a t e d i n an e x p e r i m e n t d e s i g n e d t o see i f m o d e r a t e i n c r e a s e s i n - v e l o c i t y w o u l d remove f o u l i n g f i l m s p r e v i o u s l y d e p o s i t e d a t l o w e r v e l o c i t i e s . The i n i t i a l c o n d i t i o n s o f t h e e x p e r i m e n t were: T W C = 402.7° F W=0.242 l b / s e c ( U b c = 7.6 f t / s e c ) , q w = 69170 BTU/ (hr) ( f t 2 ) e , A f t e r f o u r h o u r s o f f o u l i n g , t h e mass f l o w r a t e was s u d d e n l y i n c r e a s e d t o W = 0.543 l b / s e c , h o l d i n g t h e h e a t f l u x c o n s t a n t . d R f d t -26030 .. 0.1347 x 10 1 6 e T^c (°R) wTTO-T (29) t=o 65 Calculated Initial Fouling Rate (BTU/hr ft2°F)"f/hr x IO6 F i q u r e 18 D e v i a t i o n s f r o m I n i t i a l F o u l i n q R a t e C o r r e l a t i o n 66 I t i s s e e n i n F i g u r e 1.9 t h a t t h e t h e r m a l r e s i s t a n c e d r o p p e d and t h e f o u l i n g r a t e d e c r e a s e d . A f u r t h e r i n c r e a s e i n mass f l o w r a t e t o W = 0.778 l b / s e c , a g a i n w i t h no change i n h e a t f l u x , c a u s e d a f u r t h e r d r o p i n t h e r m a l r e s i s t a n c e and a f u r t h e r d e c r e a s e i n f o u l i n g r a t e . I t a p p e a r s p r o b a b l e t h a t h i g h e r v e l o c i t i e s w o u l d e l i m i n a t e f u r t h e r f o u l i n g . The t h e r m a l r e s i s t a n c e , l / h m , i s t h e sum o f t h e f o u l i n g r e -s i s t a n c e and t h e l i q u i d f i l m r e s i s t a n c e . U s i n g t h e S i e d e r -T a t e e q u a t i o n , w h i c h was p r e v i o u s l y shown t o g i v e good p r e d i c -t i o n o f t h e l i q u i d f i l m r e s i s t a n c e , c a l c u l a t i o n s showed t h a t t h e d r o p s i n l / h m w i t h changes i n mass f l o w r a t e c o u l d be i c o m p l e t e l y a c c o u n t e d f o r b y t h e c o r r e s p o n d i n g d e c r e a s e s i n l i q u i d f i l m r e s i s t a n c e . I n o t h e r words, i n c r e a s i n g t h e mass f l o w r a t e f r o m 0.242 t o 0.778 l b / s e c d i d n o t r e s u l t i n any d e c r e a s e i n t h e f o u l i n g r e s i s t a n c e due t o p o s s i b l e s c o u r i n g b y t h e f l u i d . U n d er t h e c o n d i t i o n s o f c o n s t a n t h e a t l o a d , i n c r e a s i n g t h e mass f l o w r a t e b y a f a c t o r o f 3.2 d e c r e a s e d t h e f o u l i n g r a t e b y a f a c t o r o f 39 from t h e i n i t i a l r a t e . The e x p e c t e d r e d u c t i o n s i n f o u l i n g r a t e w i t h t h e two changes i n mass f l o w r a t e were c a l c u l a t e d f r o m e q u a t i o n 29 u s i n g t h e e s t i m a t e d t e m p e r a t u r e a t t h e edge o f t h e d e p o s i t a f t e r e a c h mass f l o w r a t e change i n p l a c e o f T W ( c , w h i c h i s e q u i v a l e n t t o t h e t e m p e r a t u r e a t t h e 67 Time hours F i g u r e 19. T h e r m a l R e s i s t a n c e v e r s u s Time f o r V a r y i n g Mass F l o w R a t e a t C o n s t a n t H e a t F l u x - O i l B 68 edge o f t h e d e p o s i t o n l y f o r t h e o r i g i n a l f l o w r a t e . (The c o n d i t i o n o f c o n s t a n t h e a t f l u x w i t h t i m e d i c t a t e s t h a t , i n t h e a b s e n c e o f a p p r e c i a b l e b l o c k a g e due t o t h e f o u l i n g d e -p o s i t , t h e t e m p e r a t u r e a t t h e l i q u i d - b o u n d i n g edge o f t h e d e p o s i t r e m a i n s c o n s t a n t w i t h t i m e . ) The c a l c u l a t e d r e d u c t i o n was a b o u t 6% t i m e s t h e o b s e r v e d r e d u c t i o n . The d i s c r e p a n c y i s p o s s i b l y due t o t h e n a t u r e o f t h e d e p o s i t s u r f a c e . The s u r f a c e m a t e r i a l o f a h e a t e x c h a n g e r i s known t o h a v e a s t r o n g i n f l u e n c e on t h e r a t e o f b u i l d u p o f f o u l i n g f i l m s ( 1 1 ) . I t i s n o t u n e x p e c t e d t h a t d e p o s i t i o n o n t o a p r e v i o u s l y d e p o s i t e d f i l m o c c u r s a t a h i g h e r r a t e t h a n d e p o s i t i o n o n t o a c l e a n s t a i n l e s s s t e e l t u b e , u n d e r c o m p a r a b l e v e l o c i t y and t e m p e r a -t u r e c o n d i t i o n s . f ) L o c a l F o u l i n g R a t e s I t i s e v i d e n t f r o m F i g u r e 7 t h a t f o u l i n g i n c r e a s e s w i t h t h e h e a t e d l e n g t h o f t h e t u b e . When c l e a n i n g o u t t h e t u b e i t was o b s e r v e d t h a t t h e d e p o s i t s were h e a v i e s t a t t h e u p p e r o r downstream end. The l o c a l f o u l i n g r e s i s t a n c e i s g i v e n b y R i — T w T z ) - T b ( z ) (30) Q/A V a l u e s o f R^ f o r s e v e r a l v a l u e s o f z were c a l c u l a t e d f o r a number o f f o u l i n g e x p e r i m e n t s . The l o c a l f o u l i n g r e s i s t a n c e 69 v e r s u s t i m e c u r v e s were f o u n d t o be s i m i l a r t o t h o s e f o r t h e mean f o u l i n g r e s i s t a n c e . I n i t i a l f o u l i n g r a t e s , c a l c u l a t e d f r o m t h e s l o p e s o f t h e l i n e a r p o r t i o n s (which u s u a l l y f o l l o w an i n d u c t i o n p e r i o d ) o f R^vs t p l o t s , a r e p l o t t e d i n F i g u r e 20 vs' t h e r e c i p r o c a l o f t h e l o c a l c l e a n t u b e w a l l t e m p e r a t u r e i n d e g r e e s R a n k i n e . The l o c a l f o u l i n g r a t e s f a l l a l o n g t h e same l i n e as t h e mean f o u l i n g r a t e s . P o i n t s f o r some r u n s a t l a r g e v a l u e s o f z o v e r l a p t h o s e f o r s m a l l v a l u e s o f z f o r r u n s a t h i g h e r mean t e m p e r a t u r e . The agreement between t h e t e m p e r a t u r e d ependence o f t h e l o c a l and mean f o u l i n g r a t e s i n d i c a t e s t h a t t h e i n c r e a s e d f o u l i n g w i t h h e a t e d l e n g t h c an be a d e q u a t e l y e x p l a i n e d b y t h e a x i a l t e m p e r a t u r e v a r i a t i o n o f t h e t u b e when c l e a n . g) N a t u r e o f t h e D e p o s i t s The d e p o s i t s f o u n d i n t h e t u b e were a s o f t , powdery, b l a c k , s o o t - l i k e m a t e r i a l . C h e m i c a l a n a l y s i s o f a b l e n d e d sample f r o m s e v e r a l e x p e r i m e n t s i n d i c a t e d t h a t t h e d e p o s i t s were p r i m a r i l y o r g a n i c and c o n t a i n e d 9.9% a s h and 5.5% sulphur*. I t was f o u n d e a r l y i n t h e work t h a t c o n t i n u o u s r e c i r c u l a t i o n o f t h e o i l i n t h e h e a t t r a n s f e r l o o p r e s u l t e d i n no f u r t h e r f o u l i n g on a c l e a n s u r f a c e e v e n t h o u g h i p a r t i c u l a t e s were s t i l l p r e s e n t i n t h e o i l . A s t a t i s t i c a l t e s t on t h e d i f f e r e n c e 70 1000 o M 100 o £ r 10 o o o 1 1 I 1 o o *> o • A — q w BTU/hr ft 2 _ o 402-7 69,168 V 371-4 58,162 A 3488 49,523 Solid points are meon fouling rates 1 l 114 1-20 1-26 I000/T w c (z) • R"'x 1-32 .0* F i g u r e 20, L o c a l I n i t i a l O i l F o u l i n g R ate v e r s u s R e c i p r o c a l o f L o c a l A b s o l u t e W a l l T e m p e r a t u r e between particulate concentrations at the beginning and end of the runs (Appendix 3, Table V) indicated a s t a t i s t i c a l l y -s i g n i f i c a n t decrease. For a few cases a reasonable estimate of the deposit weight could be made, although some losses were unavoidable. Table VI gives these values for several of the more severely fouling runs. TABLE VI. OIL DEPOSIT WEIGHTS Run Rf at end of run Weight of Deposit (BTU/hr-ft 2 °F)~1 grams 25 0.0017 0.32 28 0.0022 0.13 30 0.0026 0.16 31 0.0032 0.42 32 0.0021 0.23 33 0.0017 0.44 The average of these deposit weights i s consistent with a decrease of about 3^ ppm of particulates during a fouling run i f a l l the deposit came from suspended p a r t i c l e s . The observed average decrease for these runs was 5^ ppm. A composite sample of particulates from several experiments analysed 4.6% ash and 5.4% sulphur. Analysis of two o i l samples indicated that in each case there was a s l i g h t drop in sulphur content upon f i l t e r i n g the samples through a 0.8 micron pore size M i l l i p o r e f i l t e r . Since the sulphur content 72 of the deposit and the particulates are e s s e n t i a l l y equal, and are a factor of 8 to 10 times the sulphur content of the o i l (Table I ) , one can i n f e r that the particulate matter which i s r i c h in sulphur is taking part in the fouling process. Presence of particulates did not guarantee that fouling would occur, however. Canapary (39) has discussed the role of sulphur in the formation of high molecular weight material that may lead to fouling. A single o i l sample was analysed for size d i s t r i b u t i o n of particulate matter as follows. The sample was divided into four aliquots of 2.5 l i t e r s each. One aliquot was f i l t e r e d through fine, medium, and coarse f r i t t e d glass f i l t e r s of nominal pore size 4-5//,, 10-15/1, and 40-60/1, respectively, and then the f i l t r a t e s were f i l t e r e d through 0. 8/1 f i l t e r s . An approximate size d i s t r i b u t i o n i s given in Table VII. The results are of course approximate due to the tendency of the f i l t e r pores to plug up and retain p a r t i c l e s smaller than the nominal pore size. TABLE VII. APPROXIMATE SIZE DISTRIBUTION OF PARTICLES Approximate P a r t i c l e Weight % P a r t i c l e s Size 0.8/1 to 4-5/1 17 4-5/1 to 10-15/1 28 10-15/1 to 40-60/1 51 greater than 40-60/1 4 73 Unfortunately no data could be obtained for p a r t i c l e s smaller than 0.8 microns. I t i s believed by some workers (40) that p a r t i c l e s of about 0.5 microns and smaller are responsible for fouling. An attempt was made to remove particulates from the o i l and measure d i r e c t l y the ef f e c t of particulate concentration omfouling. O i l samples were f i l t e r e d through a bed of diatomaceous earth f i l t e r ^ a i d (Hyflo-Supercel supplied by Johns-Manvilie) backed by a f i l t e r paper. Although the p a r t i -culates in the o i l dropped from 39 mg/liter to 0.1 mg/liter, after charging the o i l to the tank and heating to 210°F. in order to commence the fouling run,the particulates had increased again to 19 mg/liter. Further tests indicated that the pre-sence of a i r was aiding particulate formation as the o i l was being heated. Crawford and M i l l e r (26) and Canapary (39) have stressed the importance of excluding a i r from o i l s to minimize fouling due to polymer formation. An attempt to raise the part i c u l a t e concentration by bubbling a i r into the tank as an o i l siample was being heated f a i l e d to increase particulates s i g n i f i c a n t l y . I f the ef f e c t of deposit roughness is ignored, an equivalent deposit thickness can be calculated from the pressure drop 74 i n c r e a s e . The p r e s s u r e g r a d i e n t i s dP 2 f U^yo 3 2 f W2 d l g c D />g c TT 2 D 5 (31) A s s u m i n g t h a t f does n o t change s i g n i f i c a n t l y d u r i n g a r u n , 32fW 2 t h e n _. 2 = a i s a c o n s t a n t w h i c h can be d e t e r m i n e d P y c " from e q u a t i o n (31) a t t i m e z e r o when D i s t h e c l e a n t u b e i n s i d e d i a m e t e r . A t any t i m e , when a d e p o s i t t h i c k n e s s x ha s formed, D-2x = I I (32) L d P / d l J The t h e r m a l c o n d u c t i v i t y o f t h e d e p o s i t c an be e s t i m a t e d b y c a l c u l a t i n g x from e q u a t i o n 32 and m e a s u r i n g R f. Some v a l u e s a r e l i s t e d i n T a b l e V I I I . .TABLE V I I I . THERMAL CONDUCTIVITY OF OIL DEPOSITS FROM READINGS TAKEN AT END OF RUN Run x (mm) x ( f t ) R f k<3 (BTU/(hr) ( f t 2 ) (°F))- 1 B T U / h r ) ( f t ) (°F) 25 0.193 0.00063 0.0017 0.37 27 0.140 0.00046 0.0028 0.17 28 0.107 0.00035 0.0022 0.16 30 0.152 0.00050 0.0026 0.19 31 0.185 0.00060 0.0032 0.19 32 0.103 0.00033 0.0021 0.16 33 0.362 0.00104 0.0017 • 0.61 75 The increased pressure drop with fouling i s doubtless partly due to roughness e f f e c t s . The thermal conductivities w i l l then be overestimated. Most of the values are reasonably close to the value of 0.11 BTU/(hr)(ft)(°P) reported (31) for powdered coke but lower than 0.55, which applies to more compact larger p a r t i c l e s (20-100 mesh) of petroleum coke (31). h) Reproducibility of Gas O i l Results and Comparison with Tabulated Fouling Factors I n i t i a l fouling rates were calculated for the two experiments of section (g) where attempts were made to change par t i c u l a t e l e v e l , and for the control experiment. Since there was no trend of fouling rate with particulate content for these three experiments, they were considered to be r e p l i -cates. The i n i t i a l fouling rates have a range of + 9% of the mean value of 78.1 x 10~ 6 ft 2-°F/BTU. The fouling rates are l i s t e d in Table IX. TABLE IX. REPRODUCIBILITY OF INITIAL FOULING RATES Run I n i t i a l Fouling Rate (ft2)(°F)/BTU x 106 28 70.4 32 83.0 33 81.1 76 The range is probably over-estimated because of minor effects of the pretreatment of the o i l . The fouling factor for heavy gas o i l recommended by the Tubular Exchanger Manufacturers Association i s 0.003 (°F)(hr)(ft2) /BTU (1). In the present work this value was never exceeded in a single run. There are indications that under severe operating conditions (Figures 13 and 16), the fouling r e s i s -tance would have exceeded 0.003 in time. As the heat fluxes in the present work are higher than i s normal for s h e l l and tube heat exchangers, the T.E.M.A. value appears conservatively sound when no other information i s available. i) Sand-Water Fouling A sample of l o c a l beach sand was sieved through a 230 mesh screen (hole size 57 microns), and the fr a c t i o n passing the screen was further c l a s s i f i e d in a Warman "Cyclosizer" at the B r i t i s h Columbia Institute of Technology. From the operating curves of the Cyclosizer, i t was calculated that the smallest p a r t i c l e size f r a c t i o n retained was 12.8 to 17.3 microns (Stokesian diameters). This sand f r a c t i o n was s l u r r i e d in tap water. Thi r t y gallons of 4 ppm s l u r r y was charged to the tank of the heat transfer loop. Particulate concentrations were measured by f i l t e r i n g known volumes through 0.8 micron 77 pore size M i l l i p o r e f i l t e r s . The f i r s t two experiments were done with average clean wall temperatures of 175°F. and an i n l e t water temperature of 140°F. It was found (Figure 21), that as the tube fouled, the heat transfer c o e f f i c i e n t h m actually increased, as did the pressure drop. The pressure drop increase was much greater than had been observed in the o i l experiments or any other subsequent sand-water experiment. The increase in h m was probably due to a combination of surface roughness and increased area e f f e c t s . The increase in h m due to the increase in velo-c i t y caused by blockage has been discussed in the l i t e r a t u r e (41). It was shown that i f h_ • D Nu d _ m c > 2m' (33) K d J m1 where m1 i s defined by the r e l a t i o n Nu = a Re Pr 1 1, then the amount of heat transferred w i l l increase with fouling. For the present case, D = 0.0286 f t and with m' = 0.8, the c r i t i -cal deposit thermal conductivity above which fouling w i l l increase the amount of heat transferred is k d - lw Z 5 6 ( 3 4 ) a c r i t nm<_ For the range of heat transfer c o e f f i c i e n t s covered k^w30 78 2900r -csi !*" 27001 m o c CL < I CL < 2500 1800 1700 1600 16 12 8 4 0 A W =0-387 lb/secA Re c = 56 ,665 I ' _ I O O o W =0192 Re c = 28,570 + O o zP A O A O + - 1 W = 0-387 A A O ° W=0I92 1 AA-10 Time 2 0 hours 30 F i g u r e 21„ Heat T r a n s f e r C o e f f i c i e n t and P r e s s u r e D r o p v e r s u s Time f o r I n i t i a l Sand-Water F o u l i n g E x p e r i m e n t s BTU/(hr)(ft)(°F), a value more t y p i c a l of metals than scale deposits (k d»l-5 BTU/ (hr) (f t) (°F)). According to th i s analysis, then, blockage alone i s u n l i k e l y to cause an increase in h m with time. The deposits for these two runs were found to be contaminated with large chunks of coke-like material from the o i l fouling work, although considerable e f f o r t had been made to clean out the loop. It i s conceivable that t h i s contamina-ti o n contributed to an unusual increase of surface roughness and/or surface area. This would also explain the inordinate pressure drop increase. Fresh sand-water s l u r r y was then added to the tank, and a series of experiments done to study the e f f e c t of the velo-c i t y on fouling at constant T ^ and T W c . After each experiment a small quantity of make-up sand was added to the tank. Particulate levels are l i s t e d in Appendix 3, Table 3-V- In these experiments h m decreased with time for a l l v e l o c i t i e s studied (Figure 22). The fouling resistances and deposit thickness were calculated as before and are plotted versus time in Figures 23 and 24. As expected, fouling of the sand-water system i s much l i g h t e r than for the gas o i l , and the scatter of the data is greater. The fouling factor for un-treated muddy or s i l t y water recommended by T.E.M.A. (1) is 0.003 (°F)(hr)(ft2)/BTU for v e l o c i t i e s less than three feet 80 3500f 3400 330C 2100s — r O 2000 1900 1 5 0 0 ^ 1400 LL o - 1300 JZ r -fJQ 1200 T T o 0 o W = 0-546 lb/sec Re c= 78,534 OQ o o o o o W = 0-261 Rec= 38,388 o ° OO o ° ° O Q ° W = 0-172 Rec= 24,961 ^0 O O O O O W= 0-147 Rec= 21,547 P o .O 20 Ti me 40 hours 60 5> 2600 O 2500 2400 T T W=0-3I O Re r= 45,809 " O o 0 c - Q D o ° o o oo Q o o O 2600 £ 2400k 1500 t 1400 1300 O W = 0-387 Re c = 56,218 " O O ° o O W =0-172 Re c = 2 6 , 4 3 0 O O ° O c- " A M A A A A A A A A A A A A A A A A A 4 0 Ti me 80 hours 120 F i g u r e 22. Heat T r a n s f e r C o e f f i c i e n t v e r s u s Time f o r Sand-Water E x p e r i m e n t s T ^ « I 7 5 ° F # 81 W« 0-261 60 60 TIME hours F i g u r e 23. F o u l i n g R e s i s t a n c e and D e p o s i t T h i c k n e s s v e r s u s Time f o r Sand-Water 82 ' 1 1 1 Time hours F i g u r e 24. F o u l i n g R e s i s t a n c e and D e p o s i t T h i c k n e s s v e r s u s Time f o r Sand- Water 83 p e r s e c o n d , and 0.002 f o r v e l o c i t i e s g r e a t e r t h a n t h r e e f e e t p e r s e c o n d . The maximum f o u l i n g r e s i s t a n c e o f t h e p r e s e n t work i s about 0.00007 ( ° F ) ( h r ) ( f t 2 ) / B T U . The f o u l i n g r e s i s t a n c e - t i m e c u r v e s and t h e d e p o s i t t h i c k -n e s s - t i m e c u r v e s were f i t t e d b y l e a s t s q u a r e s t o e q u a t i o n 6, The v a l u e s o f t h e p a r a m e t e r s o f t h e f o u l i n g r e s i s t a n c e c u r v e s a r e l i s t e d i n T a b l e X„ The i n f l u e n c e o f mass f l o w r a t e , W, •k on t h e p a r a m e t e r s R , b and t h e i n i t i a l f o u l i n g r a t e i s shown i n F i g u r e s 25 and 26. The i n i t i a l f o u l i n g r a t e , t h e a s y m p t o t i c f o u l i n g r e s i s t a n c e and t h e p a r a m e t e r b show v a r i a t i o n s w i t h W i n c l o s e c o n f o r m i t y w i t h t h e p r e d i c t i o n s o f t h e K e r n and S e a t o n model, a t W l e s s t h a n 0.3 l b / s e c . A t h i g h e r mass f l o w r a t e s , however, t h e r e i s a r a p i d d r o p i n i n i t i a l f o u l i n g r a t e . The d e p o s i t s were v e r y l o o s e l y a t t a c h e d t o t h e t u b e w a l l . A t t h e end o f two r u n s t h e v e l o c i t y was t e m p o r a r i l y i n c r e a s e d t o a bout d o u b l e t h e i n i t i a l v e l o c i t y and t h e n b r o u g h t b a c k t o t h e o r i g i n a l c o n d i t i o n . The d e p o s i t s were e s s e n t i a l l y removed by t h e i n c r e a s e i n v e l o c i t y . The r e m o v a l o f t h e d e p o s i t s w i t h t h e i n c r e a s e d s h e a r s t r e s s s u g g e s t s t h a t t h e r e m o v a l mechanism s u g g e s t e d b y K e r n may w e l l ' a p p l y i n t h i s c a s e . U n l i k e t h e p l o t s b a s e d on t h e r m a l f o u l i n g " r e s i s t a n c e , p l o t s o f x* v e r s u s W and b v e r s u s W b a s e d on p r e s s u r e d r o p measurements were b a d l y s c a t t e r e d . No c o n s i s t e n t t r e n d o f t h e s e computed p a r a m e t e r s 84 W lb/sec F i g u r e 25 P a r a m e t e r s o f E q u a t i o n 6 v e r s u s Mass F l o w R a t e o f W a t er ( l o g - l o g ) F i q u r e 26 I n i t i a l F o u l i n g R ate o f Water v e r s u s Mass Flow R a t e ( l o g - l o g ) 86 with W was evident, due, i t is thought, to neglect of roughness in estimating x. TABLE X . FIT OF WATER FOULING DATA TO EQUATION 6 Run W lb/sec Re * 10 4 Rf (BTU/(hr)(ft* )(OP))" 1 b h r " 1 1 0 6 I n i t i a l Rate Rf b (BTU/(ft 2)(°F)) _ 1 40 0.147 21,550 0.668 0.054 3.62 38 0.172 24,960 0. 556 0.067 3.75 39 0.261 38, 390 0.334 0.165 5. 56 44 0.310 43,960 0.375 0.188 7.06 42 0.287 56,220 0.219 0.105 2.30 36 0.546 78,530 0. 58 4i* 0.172 26,430 0.498 0.181 9.01 + = 196°F Kern and Seaton assume that the f i l m begins to b u i l d up, with removal becoming important only after some material has been deposited. It seems reasonable to expect that for d i s -crete p a r t i c l e s as used in the present work, a c r i t i c a l velo-c i t y would exi s t above which the individual p a r t i c l e s would not be able to s t i c k . t o the wall to form any deposit. Under such conditions, i t would be expected that increasing the v e l o c i t y further would result in a lowering of the i n i t i a l 87 f o u l i n g r a t e . T h i s p o i n t i s d i s c u s s e d f u r t h e r i n p a r t 8. One r u n was made a t a h i g h e r c l e a n t u b e w a l l t e m p e r a t u r e — 196°F. compared t o 170°F, , w h i c h was common f o r t h e o t h e r e x p e r i m e n t s . The i n i t i a l f o u l i n g r a t e i n c r e a s e d b y about 2^ t i m e s ( T a b l e X ) , whereas t h e a s y m p t o t i c r e s i s t a n c e remained! about t h e same. An a c t i v a t i o n e n e r g y o f 15.3 K c a l / g - m o l e was c a l c u l a t e d f r o m t h e s e two r e s u l t s , a s s u m i n g t h a t an A r r h e n i u s t y p e o f e q u a t i o n d e s c r i b e d t h e t e m p e r a t u r e dependence o f t h e i n i t i a l f o u l i n g r a t e o f t h e w a t e r . The m a g n i t u d e o f t h i s v a l u e s u g g e s t s t h a t p e r h a p s p h y s i c a l r a t h e r t h a n c h e m i c a l a t t r a c t i o n s a r e o f i m p o r t a n c e , however t h e a c t i v a t i o n e n e r g y i s n o t low enough t o r u l e o u t c h e m i c a l bond f o r m a t i o n . I t i s e v i d e n t f r o m F i g u r e s 23 and 24 t h a t t h e r m a l c o n d u c -t i v i t i e s e s t i m a t e d f r o m d e p o s i t t h i c k n e s s w o u l d i n some c a s e s c o n t i n u a l l y i n c r e a s e w i t h t i m e , where x c o n t i n u e s t o i n c r e a s e a f t e r R f a p p a r e n t l y h a s l e v e l l e d o u t . F o r s u c h c a s e s t h e v a l u e o f x u s e d t o c a l c u l a t e k d was t a k e n a t t h e t i m e t h a t t h e f o u l i n g * r e s i s t a n c e f i r s t a p p e a r e d t o l e v e l o u t . V a l u e s o f k, = x* were a l s o c a l c u l a t e d . T h e r m a l c o n d u c t i v i t i e s f o r t h e w a t e r d e p o s i t s a r e l i s t e d i n T a b l e X I , 88 TABLE XI. THERMAL CONDUCTIVITY ESTIMATES FOR WATER DEPOSITS Run 10 3Rf 10 3x k d Time of k*j (BTU/hr f t 2 O F ) - 1 1 0 3 f t x l O 3 BTU/hr ft°F Run BTU/hr ft°F (Hours) 36 0.012 0.0855 7.1 29.8 37 0.038 0.189 5.0 23.5 38 0.055 0.198 3.6 24.0 4.7 39 0.042 0.136 3.2 30.8 5.3 40 0.056 0.170 3.0 40.8 2.5 41 0.050 0.400 8.0 131.3 9.3 42 0.022 0.14 6.4 72.0 10.3 44 0.035 0.097 3.6 131. 2.5 The values of V, k d in Table XI are about in the s ame range as those reported for scales. Partridge and White (42) report k d for CaS0 4 of 0.95 to 2,1 BEy/(hr)(ft)(°F), while Hasson (21) reports a thermal conductivity of 5 BTU/(hr)-(ft)(°F) for CaCO^ scale. The contribution of roughness to the pressure drop has been ignored in calcul a t i n g k d values in the above table. The deposit thickness calculated from the assumption of smooth surfaces are then probably lower, and the thermal conductivities therefore somewhat higher than the true values. I f the sand Stokejsian diameters are used to calculate a 89 r e l a t i v e roughness for the deposit, i t can be shown that at least a 12 to 40% increase in pressure drop would be expected. The pressure drop increases for these experiments were in the range 3 to 15% (Appendix 3, Table 3-IV). It seems l i k e l y , then, that the individual sand p a r t i c l e s were not deposited in a form si m i l a r to sand grain roughness. j) Scaling of Kraft Liquor Heaters Rapid fouling of liquor heaters on continuous Kraft pulp digesfee>rs; causes a serious maintenance problem (43). In a t y p i c a l operation two liquor heaters are used with one operating while the other is being cleaned out. Operating periods of 120 to 180 hours are t y p i c a l of some i n s t a l l a t i o n s . The cooking liquor i s pumped through the tubes of a s h e l l and tube heat exchanger. Superheated steam in the s h e l l heats the liquo r some 2 5°F. from the i n l e t temperature of 290°F, The liquo r i s under about 110 pounds per square inch pressure. When the tubes begin to foul the steam valve i s opened further to maintain a constant outlet l i q u i d temperature. When the steam valve i s f u l l y "open and the outlet temperature can no longer be maintained, the flow of l i q u i d i s diverted to the spare exchanger. The deposit that forms is predominantly CaC03 (44,45), which is thought to be either carried over in 90 s u s p e n s i o n i n t h e l i q u o r f r o m p r e v i o u s p r o c e s s i n g o r t o o r i g i n a t e i n t h e wood. ESCO L t d . s u p p l i e d t h e f o l l o w i n g o p e r a t i n g d a t a f r o m a West C o a s t K r a f t m i l l : S u p e r h e a t e d steam t e m p e r a t u r e 100 y a r d s f r o m t h e h e a t e r , steam p r e s s u r e i n t h e s h e l l , l i q u o r f l o w r a t e , i n l e t and o u t l e t l i q u o r t e m p e r a t u r e s . The o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t was c a l c u l a t e d b y a s s u m i n g t h a t t h e s h e l l s i d e t e m p e r a t u r e was t h e s a t u r a t i o n t e m p e r a t u r e o f t h e steam a t t h e g i v e n s h e l l - s i d e p r e s s u r e . The f o u l i n g r e s i s t a n c e s a r e p l o t t e d as a f u n c t i o n o f t i m e i n F i g u r e 27. F o r t h e u p p e r h e a t e r t h e f o u l i n g r e s i s t a n c e i n c r e a s e s a l m o s t l i n e a r l y w i t h t i m e a f t e r a f i f t y h o u r i n d u c t i o n p e r i o d . F o r t h e s p a r e h e a t e r t h e a s y m p t o t i c e q u a t i o n f i t s t h e d a t a w e l l , a l t h o u g h shutdown o c c u r s s i g n i f i c a n t l y s h o r t o f t h e a s y m p t o t i c c o n d i t i o n . F o r t h i s r u n i t was n o t e d b y t h e o p e r a t o r t h a t t h e s p a r e e h e a t e r was n o t c l e a n a t t i m e z e r o . T h i s f a c t no d o u b t e x p l a i n s t h e abs e n c e o f t h e i n d u c t i o n p e r i o d . One f o u l i n g e x p e r i m e n t was c a r r i e d o u t on a sample o f K r a f t c o o k i n g l i q u o r s u p p l i e d b y ESCO L t d . The o p e r a t i n g c o n d i t i o n s o f t h e i n d u s t r i a l h e a t e r c o u l d n o t be matched i n t h e l a b o r a t o r y as t h e e x p e r i m e n t a l a p p a r a t u s c o u l d n o t be o p e r a t e d u n d e r h i g h p r e s s u r e . The f o l l o w i n g c o n d i t i o n s were u s e d : T ^ c = 172,3 °F. T b 2 = 152.5 + l O F , W = 0.36 l b / s e c , 91 R e c = 28900, qy, = 41,262 B T U / h r - f t 2 , Ufe_ = 8.3 f t / s e c . Test s e c t i o n I I was used f o r the i n t i a l attempt. I t was damaged when the pump appa r e n t l y became overloaded and the h i g h temperature power c u t - o f f d i d not a c t i v a t e r a p i d l y enough. A t h i r d t e s t s e c t i o n was c o n s t r u c t e d which was i d e n t i c a l t o the second except t h a t new thermocouples without sheathing were used. The T e f l o n supports were t h e r e f o r e unnecessary. Dimensions of t e s t s e c t i o n I I I are given i n Appendix 2, Thermocouple-;, p o s i t i o n s are l i s t e d In Table I I . The mew thermocouples were c a l i b r a t e d over the temperature range 77.5 to 192.1°F. i n a water bath equipped w i t h a C o l o r a U l t r a -Thermostat by means of a thermometer which read t o the nearest 0.2°F. D e t a i l s are given i n Appendix 1. Because o f the danger o f pump overload, the experiment was run under constant a t t e n -t i o n and was shut down each n i g h t . The pufop overloaded s e v e r a l times d u r i n g the course of the experiment, which r e s u l t e d i n f u r t h e r temporary, shut downs. The f o l l o w i n g p r o p e r t i e s o f the l i q u o r were determined i n accordance w i t h accepted methods (51): % S o l i d s = 14.8 2>(150°F). = 0.763CS- NaOH =5.0 g/1 Na 20 />(150°F)= 1.079 g/ml Na 2S = 24.8 g/1 Na 20 , Na 2C0 3 = 8.1 g/lNa 20 The heat t r a n s f e r c o e f f i c i e n t and f o u l i n g r e s i s t a n c e are p l o t t e d 92 • 0 0 8 • 0 0 6 • 0 0 4 u. e CM 3 m • 0 0 2 • 0 1 0 - 0 0 8 • 0 0 6 • 0 0 4 •002P-1 1 A t t i m e z e r o T s t = 5 3 5 ° F P s t = 9 0 p s i g T h . = 2 9 3 ° F U b c = 3 - 8 f t / s e c Q S P A R E H E A T E R R f = 0 0 0 9 9 ( 1 - e - ° ' 0 0 9 , t ) 4 A t t i m e z e r o T s t = 5 2 0 ° F P 8 t = 8 2 p s i g T b i n » 2 8 5 < > F U D e 8 3 - 8 f t / s e c o H Q> U P P E R H E A T E R O a5?o o op o a9 G LQ_ 5 0 1 0 0 1 5 0 T i m e h o u r s F i g u r e 27. F o u l i n g R e s i s t a n c e v e r s u s Time f o r M i l l K r a f t L i q u o r H e a t e r 93 v e r s u s t i m e i n F i g u r e 28, The w ide s c a t t e r o f t h e s e d a t a i s t h o u g h t t o be due p r i m a r i l y t o t h e i n t e r r u p t i o n s o f t h e e x -p e r i m e n t b y pump o v e r l o a d s and t h e n i g h t l y shutdown. F o u l i n g i s much l e s s s e v e r e t h a n i n t h e i n d u s t r i a l h e a t e r s . The c o n d i -t i o n s a r e o f c o u r s e much m i l d e r i n t h e p r e s e n t work. I t i s p o s s i b l e t h a t a l l t h e s e d a t a a r e i n a p r o l o n g e d i n d u c t i o n p e r i o d . I n d o i n g f u r t h e r work on K r a f t l i q u o r f o u l i n g i t w o u l d be b e t t e r t o r u n t h e a p p a r a t u s c o n t i n u a l l y as t h e e x p o s u r e o f t h e d e p o s i t t o c o l d l i q u o r d u r i n g shutdown m i g h t r e s u l t i n i t s p a r t i a l s o l u t i o n , p a r t i c u l a r l y i f t h e d e p o s i t i s an i n v e r s e -s o l u b i l i t y s c a l e . s u c h as a c a l c i u m c a r b o n a t e . The CaCOg c o n t e n t o f t h e l i q u o r s h o u l d be m o n i t o r e d t h r o u g h o u t a r u n . 94 2200 o O J 2 IOOD: 2000 ° ^ ° o o o ° ° ° GO 1900 1800 o CM . o » - 4 CD ^ 2 rr o o o °o o o Kraft liquor h W =0-36 lb/sec Rec = 28,900 O O ° T w c = 172-3 °F 2 q^=4l,262 BTU/hr ft L U]SC= 83 ft/sec O O o o o o ° o o o o -A o o La O D D c5> l o o 1 20 40 TIME hours 60 F i g u r e 28. Heat T r a n s f e r C o e f f i c i e n t and F o u l i n g R e s i s t a n c e o f K r a f t L i q u o r v e r s u s Time 95 8, EXTENSION OF EXISTING FOULING MODELS I t i s o b v i o u s f r om t h e d i f f e r e n t forms o f t h e v e l o c i t y d e p e ndence o f t h e i n i t i a l f o u l i n g r a t e s and a s y m p t o t i c f o u l i n g r e s i s t a n c e s f o r t h e gas o i l and t h e w a t e r s y s t e m s , and from e x p e r i m e n t a l d a t a o f o t h e r w o r k e r s (17) , t h a t f o u l i n g i s e x c e e d i n g l y complex. I t i s u n l i k e l y t h a t one s i m p l e model c o u l d d e s c r i b e a l l t y p e s o f p a r t i c u l a t e f o u l i n g . One a p p a r e n t weakness o f t h e K e r n - S e a t o n model i s t h a t t h e r a t e o f r e m o v a l o f t h e f o u l i n g d e p o s i t i s made t o depend on t h e t h i c k n e s s o f t h e d e p o s i t , so t h a t t h e r e m o v a l t e r m becomes s i g n f i c a n t o n l y a f t e r an a p p r e c i a b l e t h i c k n e s s h as b e e n b u i l t up. I f t h e v e l o c i t y i s g r e a t enough, one m i g h t e x p e c t t h a t d e p o s i t i o n i t s e l f c o u l d be c o m p l e t e l y s u p p r e s s e d and t h a t no d e p o s i t w h a t s o e v e r w o u l d s t a r t t o b u i l d up. I n t h i s r e s p e c t P a r k i n s ' a p p r o a c h g i v e s a more p l a u s i b l e t r e a t m e n t o f t h e d e p o s i t i o n , b u t i t does n o t p r e d i c t b u i l d u p t o a s y m p t o t i c v a l u e s . E x p e r i -m e n t a l e v i d e n c e i n d i c a t e s t h a t a s y m p t o t i c c o n d i t i o n s a r e r e a c h e d , and t h a t t h e a s y m p t o t i c r e s i s t a n c e c o r r e l a t e s w i t h t h e mass f l o w r a t e . An a t t e m p t i s made h e r e t o c a t e g o r i z e t y p e s o f f o u l i n g b a s e d on c o n t r o l l i n g s t e p s i n t h e f o u l i n g p r o c e s s , and t o make p r e d i c t i o n s about t h e e f f e c t s o f p r o c e s s v a r i a b l e s on 96 f o u l i n g r a t e s . The t r e a t m e n t i s b a s e d p a r t l y on t h e i d e a s o f P a r k i n s (16), N i j s i n g ( 1 9 ) , and K e r n and S e a t o n ( 2 ) . The t r e a t m e n t i s f i r s t r e s t r i c t e d t o t h e c a s e o f c o n s t a n t mass f l o w r a t e w i t h t i m e . D e r i v a t i o n s a r e made f o r t h i n f i l m s , where t h e s h e a r s t r e s s T, and t h e v e l o c i t y do n o t i n c r e a s e s i g n i f i c a n t l y w i t h t i m e due t o b l o c k a g e . Once t h e g o v e r n i n g e q u a t i o n s a r e d e r i v e d , t h e y a r e g e n e r a l i z e d t o i n c l u d e b l o c k a g e e f f e c t s . The c a s e o f c o n s t a n t p r e s s u r e g r a d i e n t and v a r i a b l e mass f l o w r a t e i s t h e n c o n s i d e r e d . a) D i f f e r e n c e M o d e l s f o r T h i n D e p o s i t s (W c o n s t a n t ) I t i s assumed t h a t f o u l i n g i s due t o some m a t e r i a l a l -r e a d y p r e s e n t i n t h e l i q u i d , e i t h e r i n s u s p e n s i o n o r i n s o l u -t i o n , i , e , no c o n s i d e r a t i o n i s g i v e n t o t h e g e n e s i s - o f t h e f o u l i n g m a t e r i a l . T h r e e p o s s i b l e p r o c e s s e s i m p o r t a n t i n f o u l i n g a r e ( i ) t r a n s f e r o f m a t e r i a l f r o m t h e b u l k o f t h e l i q u i d t o t h e w a l l r e g i o n ( i i ) a d h e s i o n o f t h e m a t e r i a l t o t h e w a l l o f f i l m ( i i i ) r e m o v a l o f p a r t o f t h e f i l m b y f l a k i n g a t p l a n e s o f weakness i n t h e d e p o s i t as s u g g e s t e d b y K e r n The a p p r o a c h e s o f P a r k i n s , and K e r n and S e a t o n a r e com-b i n e d t o g i v e a g e n e r a l e x p r e s s i o n f o r t h e g r o w t h o f t h e f i l m t h i c k n e s s . F o l l o w i n g P a r k i n s , t h e d e p o s i t i o n t e r m i s f o r m u -l a t e d i n t e r m s o f t h e p r o d u c t o f t h e number o f p a r t i c l e s , n, 97 and t h e i r v e l o c i t i e s n o r m a l t o t h e s u r f a c e , U, w h i c h r e p r e s e n t s a f l u x J = £ n U. and a s t i c k i n g p r o b a b i l i t y , w h i c h 3 3 3 r e p r e s e n t s t h e p r o b a b i l i t y t h a t a p a r t i c l e , once i n c o n t a c t w i t h t h e w a l l , w i l l a d h e r e t o t h e s u r f a c e . U nder c e r t a i n c i r c u m -s t a n c e s a r e m o v a l mechanism may o p e r a t e , and t h e r e m o v a l t e r m o f K e r n and S e a t o n i s u s e d . The n e t r a t e o f f i l m f o r m a t i o n i s t h e n dx = a^ J s - a 2 T x (35) d t The f l u x o f m a t e r i a l t o t h e w a l l i s w r i t t e n i n terms o f t h e mass t r a n s f e r c o e f f i c i e n t , k-,.__, and t h e c o n c e n t r a t i o n d i f f e r e n c e : O l f f J = k d i f f ( C b " ° w ) ( 3 6 ) S i n c e t h e f o u l i n g m a t e r i a l i s assumed t o be f i n e p a r t i c u l a t e m a t t e r , o r p o l y m e r i z e d m o l e c u l e s , t h e S c h m i d t number Sc= -j^ i s l a r g e . The M e t z n e r - F r i e n d e q u a t i o n (46) i s u s e d t o a p p r o x i m a t e t h e mass t r a n s f e r c o e f f i c i e n t : U b f / 2 , ^ k,. = — (37a) 1.2 + 1 1 . 8 ( S c - l ) S c " 1 / 3 J~0~2 w h i c h i n t h e l i m i t o f Sc » 1 becomes a p p r o x i m a t e l y ub-/f72 k » TTa (37b) d i f f 11.8 Sc 3 98 An e x p r e s s i o n f o r s t i c k i n g p r o b a b i l i t y , S, i s d e v e l o p e d b y a s s u m i n g t h a t a p a r t i c l e w i l l adhere t o t h e w a l l i f t h e p h y s i c o - c h e m i c a l a d h e s i v e f o r c e b etween t h e p a r t i c l e and t h e w a l l o r f i l m e x c e e d s t h e o p p o s i n g h y d r o d y n a m i c f o r c e s on t h e p a r t i c l e a t t h e i n s t a n t t h a t t h e p a r t i c l e r e a c h e s t h e w a l l . A s s u m i n g t h a t t h e l a t t e r f o r c e s a r e p r o p o r t i o n a l t o t h e d r a g f o r c e on t h e p a r t i c l e , S = So F a d h e s i o n . (38) F d r a g where S;Q i s a c o n s t a n t . I f t h e p a r t i c l e a d h e r e s b e c a u s e o f c h e m i c a l o r p h y s i c a l b o n d i n g , i t m i g h t be e x p e c t e d t h a t t h e number o f bonds formed i n t h e p r o c e s s w o u l d depend on t h e s u r f a c e t e m p e r a t u r e T s , and w o u l d be c h a r a c t e r i z e d b y an a c t i v a -t i o n e n e r g y E. The a d h e s i v e f o r c e on a p a r t i c l e i s assumed p r o p o r t i o n a l t o t h e number o f bonds formed: F a d h e s i o n = F o e ~ E / R g T s (39) where Rg i s t h e u n i v e r s a l gas c o n s t a n t and F Q i s a c o n s t a n t . The d r a g f o r c e on t h e p a r t i c l e i s g i v e n b y (47) F d r a g = A p I^L C D (40) \ where A i s t h e c r o s s s e c t i o n a l a r e a o f t h e p a r t i c l e n o r m a l ir t o t h e f l o w . 99 I f the transfer of material to the surface controls the deposition process, i . e . i f the s t i c k i n g p r o b a b i l i t y is very high and independent of vel o c i t y , then the concentration of p a r t i c l e s at the surface is very low. The fouling rate is found by combining equations 35, 36 and 37b, taking'C_-w = 0: dx _ a i S Cb Ub ^/f/2 - a 2 T x (41) dt " 11.8 ' . 2/3 Sc In the absence of a removal mechanism for the p a r t i a l l y deposited film, the fouling rate is simply dx = a i S Ch Ub ^ 172 (42) dt 11.8 g-^ : 2/3 which i s also the i n t i a l fouling rate in the presence of a removal mechanism. Thus the i n i t i a l fouling rate increases with ve l o c i t y , as i s expected for a mass transfer controlled deposition process. The asymptotic fouling resistance is found by setting dx _ 0 in equation 41: dt R f = x ai, S Ch Ub Vf/2 Cy, k d a 2 11.8 @c 2/3 k d k d U b Jf (43) This result d i f f e r s from the Kern-Seaton case only in the power on f, being % here as opposed to unity in the Kern-Seaton derivation., Since f is p r a c t i c a l l y constant for turbulent flow through a given rough pipe, the difference i s only a 100 m i n o r one. I f t h e t r a n s f e r o f f o u l i n g m a t e r i a l t o t h e s u r f a c e i s v e r y f a s t and t h e d e p o s i t i o n r a t e i s c o n t r o l l e d b y t h e chemis-t r y o f t h e a d h e s i o n p r o c e s s , i . e . t h e s t i c k i n g p r o b a b i l i t y i s v e r y low and i s i n d e p e n d e n t o f v e l o c i t y , t h e C w a p p r o a c h e s C and t h e f o u l i n g r a t e can be w r i t t e n as b y dx a e -E/RgT s _ a T x (44) d t 5 2 where a,, i s a c o n s t a n t w h i c h depends upon Cj_ and t h e r e a c t i o n mechanism. The i n i t i a l f o u l i n g r a t e i s t h e n c o n s t a n t w i t h r e s p e c t t o v e l o c i t y , and depends o n l y on t h e r e a c t i o n k i n e t i c s o f t h e a d h e s I o n . p r o c e s s : dx d t t=0 a 5 ( C b ) e - E / R g T s (45) T h i s t y p e o f b e h a v i o u r was o b s e r v e d b y M c A l l i s t e r and c o -w o r k e r s (48), who f o u n d t h a t t h e r a t e o f f o u l i n g o f c o n d e n s e r s u r f a c e s b y r i v e r w a t e r was i n i t i a l l y n o t a f u n c t i o n o f v e l o -c i t y , b u t depended on t h e c h l o r i d e i o n c o n c e n t r a t i o n . I f a f i l m r e m o v a l mechanism i s a l s o o p e r a t i v e , t h e a s y m p t o t i c f o u l i n g r e s i s t a n c e p r e d i c t e d f r o m e q u a t i o n 44 w o u l d v a r y w i t h t h e r e c i p r o c a l o f t h e s h e a r s t r e s s . 101 x* e ~ E / R g T s e - E / R g T s R-f' = — a cc — (46) d k_ k d T k d u b f I n t h e s i t u a t i o n where t r a n s f e r o f f o u l i n g m a t e r i a l t o t h e s u r f a c e and a d h e s i o n a r e b o t h i m p o r t a n t , t h e i m p o r t a n t v a r i a b l e s a f f e c t i n g t h e s t i c k i n g p r o b a b i l i t y ( e q u a t i o n 38) must be c o n s i d e r e d . E q u a t i o n 40 i s r e w r i t t e n a s s u m i n g t h a t t h e p a r t i c l e s c a u s i n g f o u l i n g a r e s p h e r e s o f d i a m e t e r D^, and a r e s m a l l compared t o t h e t h i c k n e s s o f t h e v i s c o u s s u b l a y e r . The v e l o c i t y u s e d i n t h e d r a g f o r c e c a l c u l a t i o n i s t h e a p p r o a c h v e l o -c i t y a t t h g m i d - p o i n t o f t h e p a r t i c l e , w h i c h i s j u s t t o u c h i n g t h e w a l l . I n t h e v i s c o u s s u b l a y e r , t h e v e l o c i t y d i s t r i b u t i o n i s g i v e n b y ( 4 7 ) . 0 Y U b f U (Y) = (47) y 2 Where Y i s t h e d i s t a n c e f r o m t h e w a l l . Then U D „ U? f P o no = — (48) The d r a g c o e f f i c i e n t i s assumed t o depend on t h e p a r t i c l e R e y n o l d s number, i n w h i c h t h e v e l o c i t y i s g i v e n b y e q u a t i o n 48: cD l _ a 6 (49) C j ) ~ , ,n ~ 2n , 2 x n ( R e p ) n D p ( U b f ) where n l i e s b e tween z e r o (Newton regime) and u n i t y ( S t o k e s r e g i m e ) . The d r a g f o r c e i s g i v e n b y s u b s t i t u t i n g e q u a t i o n s 102 48 and 49 i n t o 40: F d r a g = ? D P P- i ? p j % _ 2 *6 (50a) 4 2 l 6 y ^ D 2 n ( u g f ) n P D = a 7 D 4 ~ 2 n (u2f)2-n ( 5 0 b ) where a-j i s a c o n s t a n t w h i c h i n c l u d e s t h e l i q u i d p r o p e r t i e s p and V. E q u a t i o n 39 f o r t h e a d h e s i v e f o r c e d s ^ m b d i f i e d s l i g h t l y t o i n c l u d e i n t h e t e r m F Q t h e e f f e c t o f p a r t i c l e s i z e . A s s u m i n g t h a t t h e a d h e s i v e f o r c e i s p r o p o r t i o n a l t o t h e s u r -f a c e a r e a o f t h e p a r t i c l e , and t h e r e f o r e r e p l a c i n g F D b y ag Dp, g i v e s F ^ . = a 8 D 2 e"-E/R T s ( 5 1 ) a d h e s i o n p S u b s t i t u t i n g e q u a t i o n s 50b and 51 i n t o e q u a t i o n 38 y i e l d s S = a.q e - E / R g T s (52) * D p ^ n (Ugf)^-n • The n e t r a t e o f f o u l i n g f i l m f o r m a t i o n i s f o u n d b y i n s e r t i n g e q u a t i o n s 52, 36 and 37b i n t o e q u a t i o n 35: dx = a 1 0 (Gb-C w) e - E / R g T s -a 2 T x d t S c 2 / 3 D _ 2 - 2 n ( u 2 f ) 3 / 2 - n (53) F o r s l o w f l o w , as w o u l d u s u a l l y be e x p e c t e d w i t h i n t h e v i s c o u s 103 1 s u b l a y e r , n = 1 i . e . C n CC . The i n i t i a l f o u l i n g r a t e w i l l R e P t h e n d e c r e a s e w i t h v e l o c i t y i n t h e manner dx d t e - E / R g T s e > - E / R g T s CC, CC (54) u b y f w t=o f o r f c o n s t a n t . T h i s e x p r e s s i o n i s s i m i l a r t o t h e e q u a t i o n d e s c r i b i n g t h e i n i t i a l f o u l i n g r a t e d a t a f o r t h e o i l ( e q u a t i o n 2 9 ) . The c o r r e s p o n d i n g v e l o c i t y dependence o f t h e a s y m p t o t i c f o u l i n g r e s i s t a n c e , o b t a i n e d from e q u a t i o n 53, i s t h e n * * x 1 1 1 R = — cc c c — ; — - cc — (55) k d u T f T u 3 f 3 / 2 w3 A l l t h e models c o n s i d e r e d t o t h i s p o i n t a r e r e s t r i c t e d t h i n d e p o s i t s i . e . x<<D. F o r s u c h c a s e s t h e b u l k v e l o c i t y and t h e s h e a r s t r e s s a r e e s s e n t i a l l y i n d e p e n d e n t o f t i m e . The b a s i c d i f f e r e n t i a l e q u a t i o n s a r e a l l o f t h e form — = a - b x (56) d t where a' and b' a r e c o n s t a n t s . The s o l u t i o n o f e q u a t i o n 56 i s i a i x = —7 (1 - e " b t ) b i . * -b r 2 = x T (1 - e ) (57) 104 The p a r t i c u l a r equations for each proposed c o n t r o l l i n g mechanism of deposition are summarized in Table XII, along with * the predicted expressions for x , b and the i n i t i a l fouling rate. b) Difference models with blockage e f f e c t s (W constant) Where the deposits become thick r e l a t i v e to the tube diameter, the v e l o c i t y and shear stress are no longer constant for a constant mass flow rate. Following Kern, expressions for Ub andTTwhich take into account the decreasing e f f e c t i v e diameter of the tube are substituted into the previously derived equations. Substitute U b = _W_ (58) yr,7T(D-2x) 2and . , ..... . . .  T = P U 2 f _ 8f W2^ (59) 2g c <3cpTTZ (D-2x) 4 into equations 41, 44 and 53. The re s u l t i n g equations are l i s t e d in Table XIII i n terms of the dimensionless deposit thickness X=x/D.. The fouling rate in the absence of any removal mechanism can be determined as before by ignoring the removal term. The i n i t i a l fouling rate i s determined by setting X=0, TABLE X I I . FOULING MODELS WITHOUT BLOCKAGE FOR W = CONSTANT Model Differential Equation Asymptotic Resistance Rf Parameter b Initial Fouling Rate R* b Kern-Seoton = K,C'W - Kg TX , X « _ K , C ' W b = K 2 r R«b . Transfer Controlling Deposition dx _ a , S c b L H ^ dt - MS S c 2 ' 3 " Q 2 T X a,Sc b U b f ~4~ 2/3 f II-8Q2SC%T b = a 2 T o * L _ Q I s cbivfie 118 Sc \ Adhesion Controlling Deposition ^ - = a 5 e - E / R « T » - a 2 T X b = a 2 T R * b = _9JL e - E / R g T 8 Transfer a Adhesion Controlling dx _ q < f c b - c j e rf _ oJc^-c^Je b = a 2 T <" ' s<?/W"B(uff?/*-" * K * I ^ S c ^ ^ T < / > = E / R C J T S sc2/3kdubvr TABLE X I I I . FOULING MODELS WITH BLOCKAGE FOR W=CONSTANT M o d e l D i f f e r e n t i a l Equat ion i C o n s t a n t s A s y m p t o t i c Th ickness Approx i mat e Asymptotic Thickness Kern -Seaton j £ = A,W - A g W V ^ - T * dt 1 " « (|-2X)4 A, = K,C7D A - 8K2f A2= *4 ' % I 2 3 A + 2 4 X * - 3 2 X % l 6 X * = ^ - 3 + 8 X * « A 2 A.WD3 +8 T r a n s f e r Control l ing Deposi t ion dX dt 2± - AW, _ AoVI^ X (1-2 X)2 (I-2X)4 . = 4o,Scff/2 ' 118 Sc , r e/>trD 3 A 2 as above v* . I . A 2W. * + 4 X - 4~AT + ' A2W ~AV + 4 A d h e s i o n Contro l l ing Depos i t i o n dX dt = A, -(I-2X) 4 .. _ Qge ~ » A 2 os above £ * + 2 4 X - 3 2 X + I6X = ^ r £ + 8 X A, X * - I A2W2 — + 8 T r a n s f e r & A d h e s i o n Control l ing Deposit ion dX AJ(I-2X)2 A 2W 2X dt W ( I -2X) 4 „ o J [ c h - c j D e - E / R » T » A 2 as above I 2 3 , 4 5 +60X*-I60X"+240X*-I92X +60X* A 2 W3 .+ 12 ± + 6 0 x ^ M ? 3 + . 2 X A i 1 Refer to equations for thin deposits for 0 | a £ OJQ K| Kg 2 Approximation ignores terms In complete expression contributing less than 3-6% at 25% blockage 107 When b l o c k a g e i s i m p o r t a n t , t h e t r a n s f e r c o n t r o l l e d d e p o s i t i o n model p r e d i c t s d i f f e r e n t f o u l i n g r a t e b e h a v i o u r i n t h e a b s e n c e o f r e m o v a l t h a n does t h e K e r n - S e a t o n model, whereas f o r t h i n f i l m s b o t h models p r e d i c t v i j i t t r a l l y t h e same t y p e o f f o u l i n g b e h a v i o u r u n d e r s u c h c o n d i t i o n s . The d i f f e r e n t i a l e q u a t i o n s o f T a b l e X I I I a r e d i f f i c u l t t o s o l v e a n a l y t i c a l l y , and so n u m e r i c a l s o l u t i o n s have b e e n o b t a i n e d b y t h e e i g h t p o i n t Gauss method. T y p i c a l r e s u l t s a r e p l o t t e d i n F i g u r e 29 f o r a f i x e d v a l u e o f , and f o r d i f f e r e n t v a l u e s o f t h e p a r a m e t e r s A 2 and W. A l l e q u a t i o n s g i v e r e s u l t s o f t h e same g e n e r a l shape, b u t t h e i n f l u e n c e o f t h e p a r a m e t e r s o f c o u r s e v a r i e s . F o r t h e K e r n - S e a t o n model and t h e t r a n s f e r c o n t r o l l e d d e p o s i t i o n model, i n c r e a s i n g W p r o d u c e s a c r o s s - o v e r e f f e c t , as t h e i n i t i a l r a t e s a r e h i g h e r and t h e f i n a l a s y m p t o t e s a r e l o w e r f o r i n c r e a s i n g W. Asymp-t o t i c d e p o s i t t h i c k n e s s e s were d e t e r m i n e d f o r t h e d i f f e r e n t •k models b y s e t t i n g dX 0., E x p l i c i t s o l u t i o n s f o r X were d t n o t p o s s i b l e . However, a p p r o x i m a t i o n s were made f o r c a s e s where t h e d e p o s i t s a r e n o t t o o t h i c k . The c o m p l e t e e x p r e s s i o n s * f o r X and a p p r o x i m a t i o n s v a l i d f o r c a s e s where t h e f l o w a r e a i s a t l e a s t 7 5 % o f t h e o r i g i n a l a r e a a r e l i s t e d i n T a b l e X I I I . O t h e r d i f f e r e n c e models f o r c o n s t a n t W can be c o n s i d e r e d . 108 TIME (arbitrary) F i g u r e 29. Computed C u r v e s f o r C o n s t a n t Mass F l o w Rate F o u l i n g w i t h B l o c k a g e 109 One r e a s o n a b l e a s s u m p t i o n w o u l d be t h a t t h e r e m o v a l r a t e m i g h t d epend o n l y on t h e s h e a r s t r e s s , and be i n d e p e n d e n t o f t h e d e p o s i t t h i c k n e s s . Where b l o c k a g e i s n o t i m p o r t a n t , t h e assump-t i o n o f r e m o v a l r a t e i n d e p e n d e n t o f x r e s u l t s i n p r e d i c t i o n s o f l i n e a r g r o w t h o f t h e f o u l i n g r e s i s t a n c e . T h e r e i s t h e n no a s y m p t o t i c c o n d i t i o n p r e d i c t e d . The e q u a t i o n f o r t h e d i f f e r e n t c o n t r o l l i n g s t e p s i n t h e d e p o s i t i o n p r o c e s s i s dX _ fij_ Wra - A 2W 2 = c o n s t a n t d t (60) where m=-l, 0, o r +1. When b l o c k a g e e f f e c t s a r e c o n s i d e r e d , t h e c o n t r o l l i n g d i f f e r e n t i a l e q u a t i o n s a r e as l i s t e d i n T a b l e X I I I , e x c e p t t h a t t h e v a r i a b l e X does n o t a p p e a r as a m u l t i p l i e r 2 i n t h e r e m o v a l term, w h i c h becomes A2W r a t h e r t h a n Hl2X)4 A 2 W 2 X. ( 1 - 2 X ) 4 N u m e r i c a l s o l u t i o n s were o b t a i n e d f o r t h e l a t t e r s i t u a -t i o n , and some t y p i c a l r e s u l t s a r e p l o t t e d i n F i g u r e 30. A p p r o x i m a t e v a l u e s f o r t h e a s y m p t o t i c d e p o s i t t h i c k n e s s e s p r e d i c t e d f o r e a c h model were o b t a i n e d b y a p p r o x i m a t i n g t h e s e r i e s ( l - 2 X ) i b y l - 2 i x ; M o d i f i e d K e r n - S e a t o n T r a n s f e r c o n t r o l l i n g d epos i t i o n * X » 1-A.2W A l 8 X* w (l-A2_W)/4 A' 110 - A , = 250 W =0-5 W = I Kern-Seoton =--W=0-5 —W= I Transfer Controlling Deposition 10 15 A, = 250 A^O W=0-5 W= I Adhesion Controlling Deposition T W = 0-5 W= I /f,- 250 Transfer 8 Adhesion Controlling Deposition TIME (arbitrary) F i g u r e 30. Computed C u r v e s f o r C o n s t a n t Mass Flow Rate F o u l i n g w i t h B l o c k a g e and Removal R a t e I n d e p e n d e n t o f T h i c k n e s s I l l ,2. Adhesion c o n t r o l l i n g ^ (1-A2W^) /8 I deposition X » >^ (61) 3 Transfer and Adhesion * (1-A2W )/12 co n t r o l l i n g deposition X * A"' 1 These approximations are v a l i d only at low blockages, say X < 0.05. c) Constant pressure drop operation Many heat exchangers are operated at constant pressure drop, and the mass flow rate decreases as the deposit builds up. Kern (14) applied these conditions to his difference model. Introducing equation 58 into the Fanning expression for pressure gradient in the presence of blockage. 2 f U b P dP = (62) d l gn (D-2x) / S e p " r d p i yields W = IT / (D-2x) D / / (63) V 32f LdlJ Substituting this l a t t e r expression for W into the d i f f e r e n t i a l equations of Table XIII results in the equations of Table XIV (which are also written in terms of the dimensionless thickness X), which are v a l i d for constant pressure drop and variable mass flow rate conditions. Kern has siolved the equation for his model a n a l y t i c a l l y for X< 0.1 by approximating the binomial e x p a n s i o n o f (D-2x) b y i t s f i r s t two t e r m s . A p p r o x i m a t e e x p r e s s i o n s f o r X a r e l i s t e d i n T a b l e XIV. T h e s e e x p r e s s i o n s a l s o depend on a t r u n c a t i o n o f t h e b i n o m i a l e x p a n s i o n s a f t e r two t e r m s , e x c e p t f o r t h e a d h e s i o n c o n t r o l l i n g c a s e where no e x p a n s i o n i s n e c e s s a r y . The d i f f e r e n t i a l e q u a t i o n s o f T a b l e XIV h a v e b e e n i n t e g r a t e d n u m e r i c a l l y b y the' e i g h t r i p o i n t Gauss method. P l o t s o f X v e r s u s t i m e a r e shown i n F i g u r e 31. The r e m o v a l t e r m f o r a l l models goes t h r o u g h a maximum w i t h i n -c r e a s i n g X a t x = D/4. I t i s e v i d e n t from T a b l e XIV t h a t f o r t h e K e r n - S e a t o n and t h e t r a n s f e r c o n t r o l c a s e s , t h e d e p o s i t i o n t e r m d e c r e a s e s w i t h i n c r e a s i n g X o r t i m e , whereas f o r t h e c a s e where b o t h t r a n s f e r and a d h e s i o n c o n t r o l , t h e d e p o s i t i o n t e r m i n c r e a s e s w i t h t i m e . ( F o r t h i n f i l m c o n d i t i o n s a l l d e p o s i t i o n terms a r e c o n s t a n t w i t h t i m e . ) Thus as X — 0 . 5 f o r t h e l a t t e r c a s e , t h e d e p o s i t i o n s - r a t e i n c r e a s e s r a p i d l y whereas t h e r e -m o val r a t e a p p r a o c h e s z e r o . T h i s s i t u a t i o n i s n o t ^ r e f l e c t e d i n t h e a s y m p t o t i c t h i c k n e s s e q u a t i o n s b e c a u s e t h e a p p r o x i m a t i o n u s e d i s v a l i d o n l y f o r r e l a t i v e l y s m a l l X, d) Q u o t i e n t models K e r n t r i e d a s e c o n d a p p r o a c h t o m o d e l l i n g t h e f o u l i n g p r o c e s s . R a t h e r t h a n e x p r e s s t h e n e t f o u l i n g r a t e as a d i f f e r e n c e between d e p o s i t i o n and r e m o v a l t e r m s , a r a t i o o f 113 0 1 2 3 TIME (arbitrary) F i g u r e 31. Computed C u r v e s f o r C o n s t a n t P r e s s u r e G r a d i e n t F o u l i n g w i t h B l o c k a g e TABLE XIV. FOULING MODELS WITH BLOCKAGE FOR CONSTANT PRESSURE GRADIENT Model Differential Equation 1 Constants 2 Approximation for X* Ke rn — Seaton ^ = A 3 a S ( l - 2 X ) - A4c/>(I-2X)X A 3 = K , C ' D t ^ A 4 = K2D/4 aS = dP/d 1 Transfer Controlling Deposition -ly i 1/2 1/2 •2^ = AsaS (I -2X) - A 4 a M l - 2 X ) X A 4 , ab as above Adhesion Controlling Deposition A'3 - A 4 < £ ( I - 2 X ) X A ' ; = A ; / D A 4 ,aS as above Y * _ 1 + / l A 3 * 4 A^»2 Transfer 8t Adhesion Controlling A" ^ = ^ ( i - 2 X r 2 X ) X A'" r A" •» 3 A , V 3 2 f D^2 A4.0S as obove 6 V 36 3 A 4 D l / 2 ^ z 1 R e f e r to Toble XIII for A', , Aj" 2 Based on ( l - 2 X ) ' « I- 2i X ( i= 3/2 for K-S 8 T+Ad , i= 1/2 for Tr control) 115 d e p o s i t i o n and r e m o v a l terms was u s e d : „ , . _ . D e p o s i t i o n Terms F o u l i n g R a t e = — E :— .... . " : - Removal Terms (64) He t h e n s t a t e d t h a t t h e d e p o s i t i o n terms must i m p a r t t h e asymp-t o t i c b e h a v i o u r t h a t h a d b e e n o b s e r v e d i n many s y s t e m s . He assumed t h a t t h e d r i v i n g f o r c e f o r d e p o s i t i o n was o f t h e form Xe _ b t , where X and b a r e c o n s t a n t s . The r e m o v a l p o t e n t i a l ' J -was assumed t o be t h e s h e a r s t r e s s . Thus d R f = X e ~ b t (65) d t T I n t e g r a t i n g , R f = 2 g ^ X ( l - e _ b t ) (66) PH U b f A s s u m i n g t h a t X i s i n d e p e n d e n t o f v e l o c i t y , R* = 2gr X ^ 1 (67) f Z>b U2 f * f ^ b and t h e i n t i a l r a t e i s g i v e n b y dRf d t « — L — cc - U — ( 6 8 ) \52 f U2 f t=o b b No comment was made on t h e c o n t r a s t i n g v e l o c i t y dependence o f t h e i n t i a l f o u l i n g r a t e i n t h e q u o t i e n t and d i f f e r e n c e models, 116 n o r was any t h e o r e t i c a l r a t i o n a l e g i v e n f o r t h e f o r m o f t h e c h o s e n d e p o s i t i o n d r i v i n g f o r c e . K e r n abandoned t h i s a p p r o a c h b e c a u s e t h e v a r i a b l e s t e n d e d t o " c a n c e l o u t and l o s e i d e n t i t y as f l u i d d y n a m i c e n t i t i e s " . A s e t o f q u o t i e n t models can be d e v e l o p e d b y u s i n g t h e d e p o s i t i o n t e r m s o f t h e p r e v i o u s l y d e r i v e d d i f f e r e n c e models as t h e n u m e r a t o r s i n s t e a d o f K e r n ' s a r b i t r a r y d e p o s i t i o n t e r m ~Y e ""k^ ", and t h e c o r r e s p o n d i n g r e m o v a l t e r m as t h e d e n o m i n a t o r . The r e s u l t i n g d i f f e r e n c i a l e q u a t i o n s a r e e a s i l y s o l v e d a n a l y t i c a l l y . E q u a t i o n s and s o l u t i o n s a r e l i s t e d i n T a b l e XV. F o r t h e t h i n f i l m c a s e t h e d i f f e r e n t i a l e q u a t i o n s r e d u c e t o dX _ £ D 3 d t ' Wm X (69) where £, a, and m a r e constants.. T h i s e q u a t i o n y i e l d s a s q u a r e r o o t dependence o f t h e d e p o s i t t h i c k n e s s on t i m e i . e . X CC ft . S o l u t i o n s f o r c a s e s w i t h b l o c k a g e a r e p l o t t e d i n F i g u r e 32. e) L i m i t a t i o n s o f p r o p o s e d models The models c o n s i d e r e d have a l l assumed a c o n s t a n t d e p o s i t s u r f a c e t e m p e r a t u r e w i t h t i m e i . e . a c o n s t a n t h e a t f l u x . The s u r f a c e t e m p e r a t u r e i s most i m p o r t a n t f o r t h e c a s e s where t h e 117 D D D Adhesion Controlling i Deposition 4 8 TIME (arbitrary) F i g u r e 32. Computed C u r v e s f o r C o n s t a n t Mass Flow R a t e F o u l i n g - Q u o t i e n t M o d e l 118 r e a c t i o n a t t h e s u r f a c e i s i m p o r t a n t . I f t h e w a l l t e m p e r a t u r e i s c o n s t a n t t h e n t h e d e p o s i t s u r f a c e t e m p e r a t u r e w i l l d e c r e a s e w i t h t i m e as t h e d e p o s i t b u i l d s up and t h e t h e r m a l r e s i s t a n c e i n c r e a s e s . The t e m p e r a t u r e T i n e q u a t i o n s 44 and 53 w i l l t h e n s no l o n g e r be c o n s t a n t . I f t h e f o u l i n g f i l m i s n o t t o o t h i c k and t h e h e a t l o a d does n o t change t o o much, T g c o u l d be a p p r o x i -mated b y T s = T s | -a x (70) |t=o where a i s t a k e n t o be c o n s t a n t . I n t e g r a t i o n o f e q u a t i o n s 44 and 53 becomes more d i f f i c u l t , and a n u m e r i c a l t e c h n i q u e must p r o b a b l y be u s e d . The r a t e o f f o u l i n g w i l l o f c o u r s e d e c r e a s e more r a p i d l y w i t h t i m e t h a n t h e c o r r e s p o n d i n g c o n s t a n t h e a t f l u x c a s e . The m o d els c o n s i d e r e d a r e o f n e c e s s i t y s i m p l i f i e d and i n some c a s e s h i g h l y s p e c u l a t i v e . C o m p l i c a t i n g e f f e c t s t h a t have b e e n i g n o r e d i n c l u d e : v a r i a t i o n o f t h e r m a l c o n d u c t i v i t y w i t h d e p o s i t t h i c k n e s s , e f f e c t o f s u r f a c e r o u g h n e s s , d i s t r i b u t i o n o f s i z e o f f o u l i n g p a r t i c l e s , shape o f f o u l i n g p a r t i c l e s . The n a t u r e o f t h e a d h e s i v e f o r c e s i s l a r g e l y unknown. I t i s h o p e d t h a t c o n s i d e r a t i o n o f t h e p r o p o s e d f o u l i n g models w i l l h e l p t o r a t i o n a l i z e f o u l i n g b e h a v i o u r and p r e d i c t e f f e c t s and t r e n d s o when more o p e r a t i n g i n f o r m a t i o n i s a v a i l a b l e . TABLE XV. QUOTIENT FOULING MODELS WITH BLOCKAGE FOR W CONSTANT Mode Differentia I Equation Analyt ical Solution K e r n - S e o t o n dX A, D4 (I-2X) 4 dt A 2 W t _ A 2W [ I I , _Ll " 4A, D 4 L3 ( I -2X) 3 2(I-2X) 2 * 6 j Transfer Controlled Deposition dX A',D2 ( I -2X) 2 dt A 2 W A 2 W  4A', D 2 U - 2 X [ - I + ln( l -2X) ] Adhesion Controlled Deposition dX A'j D 4 ( I - 2 X ) 4 dt * A 2 W 2 X 4 A >w2 r i i _ L ] L3( I -2X) 3 " 2U -2X) 2 6 J Transfer ft Adhesion Controlled Deposition dX dt Al"D 6 ( I -2X) 6 A , W 3 X t * A 2 w3 r 5 0 - 2 X ) 5 4(1-2X)4 20 . 120 f ) I n t e r p r e t a t i o n o f p r e s e n t e x p e r i m e n t a l r e s u l t s i n terms o f p r o p o s e d models A l l e x p e r i m e n t s were c a r r i e d o u t at c o n s t a n t mass f l o w r a t e and c o n s t a n t h e a t f l u x w i t h t i m e . The maximum e s t i m a t e d d e p o s i t t h i c k n e s s e s f o r w h i c h d a t a were f i t t e d b y t h e asymp-t o t i c e q u a t i o n were (Appendix 3, T a b l e IV) 0.00013 f t . f o r t h e o i l and 0.0002 f t f o r t h e w a t e r f o u l i n g e x p e r i m e n t s . These d a t a y i e l d x/D v a l u e s o f 0.0045 and 0.007 r e s p e c t i v e l y . The p e r c e n t b l o c k a g e , 100 l b 2 - (D-2X) 2 1 , was 0.9% and 1.4% L 52 J r e s p e c t i v e l y . The use o f t h e t h i n f i l m models i s t h e n j u s t i f i e d . S i n c e i t was f o u n d t h a t a s y m p t o t i c c o n d i t i o n s were o f t e n r e a c h e d f o r b o t h t h e o i l and w a t e r e x p e r i m e n t s , i t a p p e a r s t h a t t h e d i f f e r e n c e model w i t h r e m o v a l i n d e p e n d e n t o f t h i c k n e s s does n o t a p p l y t o t h e p r e s e n t r e s u l t s , as t h i s model p r e d i c t s a c o n s t a n t f o u l i n g r a t e f o r t h i n f i l m s . The q u o t i e n t model d e r i v e d b y K e r n does n o t a p p e a r t o f i t t h e p r e s e n t d a t a as t h e i n i t i a l f o u l i n g r a t e s were n o t p r o p o r t i o n a l t o W~2, and b e c a u s e t h e p a r a m e t e r b was f o u n d t o be d e p e n d e n t on W whereas t h e model assumes b i n d e p e n d e n t o f W. The q u o t i e n t models p r o p o s e d b y t h e p r e s e n t a u t h o r a l l p r e d i c t j , RfCC t 2 f o r t h i n d e p o s i t s . F i g u r e 33 shows t h a t t h e r e a r e s e v e r e d e v i a t i o n s from t h e s q u a r e r o o t t i m e dependence f o r b o t h o i l and w a t e r . Some o f t h e e x p e r i m e n t a l d a t a c o u l d be f i t t e d 121 O X e 1-5 1-0 0-5 CM Z 0-4 3 I-ffi 1 I 1 A A A a A ^ A " A -A Oil-Run 15 W « 0 - 5 4 3 lb/ sec ~" TWc= 296 °F " o b ° o < * < p * ° o o o o - o o , ° 1 Water-Run 44 W = 0-311 lb/sec T W c a "70°F 1 1 5 , 10 ± (TIME)2 (hours)2 15 F i g u r e 33 C o m p a r i s o n o f E x p e r i m e n t a l R e s u l t s w i t h T h i n F i l m Q u o t i e n t M o d e l P r e d i c t i o n s 122 f a i r l y w e l l w i t h t h i s t y p e o f e q u a t i o n , however. F o r t h i n f i l m s , t h e a s y m p t o t i c e q u a t i o n r e s u l t s f r o m t h e i n t e g r a t i o n o f a l l t h e d i f f e r e n c e models a t c o n s t a n t W ( T a b l e X I I ) . C o r r e l a t i o n o f t h e i n i t i a l f o u l i n g r a t e d a t a o f t h e o i l showed t h a t a good f i t was a c h i e v e d o v e r a wide r a n g e o f c o n d i -t i o n s b y t h e f o r m o f e q u a t i o n 54. W h i l e t h i s f a c t does n o t i i m p l y t h a t t h e a s s u m p t i o n s made i n t h e t r a n s f e r p l u s a d h e s i o n c o n t r o l l i n g d e p o s i t i o n model a r e e n t i . r e l y c o r r e c t , i t does l e n d s u p p o r t t o t h e m a t h e m a t i c a l t r e a t m e n t o f f o u l i n g as a combina-t i o n o f t h e two p r o c e s s e s . F u r t h e r e v i d e n c e o f t h e i m p o r t a n c e o f a d h e s i o n i n f o u l i n g i s t h e s u c c e s s f u l a p p l i c a t i o n o f s u r f a c e a c t i v e a g e n t s t o r e d u c e f o u l i n g f r o m p e t r o l e u m s t r e a m s (39,49) b y h i n d e r i n g s t i c k i n g , and t h e u s e o f T e f l o n h e a t e x c h a n g e r t u b e s w h i c h h i n d e r s t i c k i n g and promote f l a k i n g o f d e p o s i t s ( 5 0 ) . The a s y m p t o t i c f o u l i n g r e s i s t a n c e was f o u n d t o v a r y as W*"2, r a t h e r t h a n W-^ as p r e d i c t e d b y t h e t r a n s f e r and a d h e s i o n model ( e q u a t i o n 55)„ The f o r m o f t h e f o u l i n g r e s i s t a n c e e q u a t i o n f o r t h e o i l d a t a i s R f = A;|- (1 - e _ B W t ) (71) w2" where A' and B a r e c o n s t a n t w i t h r e s p e c t t o mass f l o w r a t e . I f t h e g o v e r n i n g d i f f e r e n t i a l e q u a t i o n i s 123 dx _ d e p o s i t i o n t e r m - r e m o v a l t e r m (72a) d t t h e n dx d t BWx (72b) whe r e A-^  = A' B k d , and we see t h a t t h e r e m o v a l t e r m v a r i e s as W 1 r a t h e r t h a n as T o r W2 . More work c o u l d be done on o t h e r p o s s i b l e forms o f t h e r e m o v a l t e r m . F o r t h e w a t e r f o u l i n g , t h e e x p e r i m e n t a l d a t a i n d i c a t e t h a t up t o a c r i t i c a l v a l u e o f t h e mass f l o w r a t e , t h e K e r n - S e a t o n model o r t h e t r a n s f e r c o n t r o l l e d d e p o s i t i o n model i s a p p l i c a b l e . B o t h i n i t i a l r a t e and a s y m p t o t i c r e s i s t a n c e f o l l o w t h e p r e d i c t i o n s o f t h i s m o d e l . Above t h e c r i t i c a l v a l u e o f W, o t h e r p r o c e s s e s e v i d e n t l y a r e i m p o r t a n t . C o n s i d e r a t i o n o f t h e f o u l i n g p r o c e s s as i n v o l v i n g t r a n s f e r , a d h e s i o n and r e m o v a l l e a d s one t o e x p e c t t h a t as v e l o c i t i e s become v e r y h i g h , t r a n s f e r w o u l d c e a s e t o c o n t r o l t h e d e p o s i t i o n p r o c e s s and a d h e s i o n w o u l d be e x p e c t e d t o be i m p o r t a n t . I f t h e d e p o s i t i o n p r o c e s s i s c o n t r o l l e d b y t r a n s f e r t o s u r f a c e , w a l l t e m p e r a t u r e s h o u l d have a r e l a t i v e l y m i n o r e f f e c t on t h e d e p o s i t i o n r a t e . A s i n g l e e x p e r i m e n t w i t h t h e w a t e r s y s t e m was r u n a t a w a l l t e m p e r a t u r e 26°F. h i g h e r t h a n t h e o t h e r s . The i n i t i a l f o u l i n g r a t e i n c r e a s e d b y 2% t i m e s a l -t h o u g h t h e a s y m p t o t i c r e s i s t a n c e d i d n o t change. F u r t h e r i n v e s t i g a t i o n o f t h e t e m p e r a t u r e e f f e c t may be w a r r a n t e d . 124 9. CONCLUSIONS F o u l i n g o f a h e a t e d t u b e b y a s o u r s t r a i g h t - r u n h e a v y gas o i l , and b y a s a n d - w a t e r m i x t u r e , h a s b e e n s t u d i e d e x p e r i -m e n t a l l y as a f u n c t i o n o f mass f l o w irate and h e a t f l u x . The f o u l i n g r e s i s t a n c e o f t h e o i l a t low h e a t f l u x e s , and o f t h e w a t e r , b u i l d s up t o an a s y m p t o t i c v a l u e as s u g g e s t e d b y K e r n and S e a t o n . A t h i g h e r h e a t f l u x e s i n o i l f o u l i n g , t h e asymp-t o t i c c o n d i t i o n was n o t r e a c h e d b e f o r e t h e e x p e r i m e n t s h a d t o be t e r m i n a t e d due t o d e v e l o p m e n t o f e x c e s s i v e w a l l t e m p e r a t u r e s . The d e p o s i t s f r o m t h e o i l were a b l a c k , c o k e - l i k e powder t h a t was about 9 0 % c o m b u s t i b l e , and c o n t a i n e d about 5.5% sulphur.. C o n t r a r y t o t h e more d e t a i l e d p r e d i c t i o n s o f t h e K e r n -S e a t o n d i f f e r e n c e model o f t h e f o u l i n g p r o c e s s , t h e i n i t i a l f o u l i n g r a t e o f t h e o i l d e c r e a s e d w i t h i n c r e a s i n g mass f l o w r a t e , and t h e a s y m p t o t i c f o u l i n g r e s i s t a n c e v a r i e d as t h e r e c i p r o c a l o f t h e mass f l o w r a t e s q u a r e d . A t c o n s t a n t mass f l o w rate., t h e i n i t i a l f o u l i n g r a t e o f t h e o i l depended e x p o n e n -t i a l l y on t h e c l e a n t u b e w a l l t e m p e r a t u r e , i n t h e f o r m o f t h e A r r h e n i u s e q u a t i o n . The v a l u e o f 29 K c a l / g m o l e f o u n d f o r t h e a c t i v a t i o n e n e r g y i n t h e l a t t e r e q u a t i o n s u g g e s t e d t h a t c h e m i c a l b o n d i n g was i m p o r t a n t i n t h e f o u l i n g p r o c e s s . O ver a 1 5 0 - f o l d r a n g e o f i n i t i a l f o u l i n g r a t e s , t h e f o l l o w i n g e q u a t i o n c o r r e l a t e d t h e d a t a f o r t h e gas o i l : 125 d R f 0.1347x10 w 1 . 0 / -26,030 d t e Tw c (°R) t=o F o u l i n g o f t h e o i l i n c r e a s e d w i t h d i s t a n c e a l o n g t h e h e a t e d t u b e . L o c a l f o u l i n g r a t e s depended on t h e l o c a l c l e a n t u b e w a l l . t e m p e r a t u r e . The a s y m p t o t i c f o u l i n g r e s i s t a n c e o f t h e sand d e p o s i t s d e c r e a s e d w i t h i n c r e a s i n g mass f l o w r a t e . The i n i t i a l f o u l i n g r a t e s i n c r e a s e d w i t h mass f l o w r a t e , f o l l o w i n g t h e p r e d i c t i o n s o f t h e K e r n - S e a t o n model, up t o a c r i t i c a l v a l u e o f t h e mass f l o w r a t e . H i g h e r mass f l o w r a t e s r e s u l t e d i n l o w e r i n i t i a l f o u l i n g r a t e s . The p r e s s u r e d r o p i n c r e a s e f o l l o w e d a p p r o x i m a t e l y t h e same t y p e o f t r e n d s w i t h t i m e as d i d t h e f o u l i n g r e s i s t a n c e f o r b o t h t h e w a t e r and t h e o i l f o u l i n g e x p e r i m e n t s . I g n o r i n g t h e e f f e c t s o f r o u g h n e s s , d e p o s i t t h i c k n e s s e s were b a c k c a l c u l a t e d f r o m p r e s s u r e d r o p d a t a . T h e r m a l c o n d u c t i v i t i e s , c a l c u l a t e d f r o m t h e e s t i m a t e d t h i c k n e s s e s , were i n r e a s o n a b l e agreement w i t h v a l u e s r e p o r t e d f o r s i m i l a r d e p o s i t s . E x t e n s i o n s were made t o t h e m a t h e m a t i c a l m o d els o f K e r n and S e a t o n , and o f P a r k i n s . A model i n w h i c h t h e d e p o s i t i o n was assumed t o be c o n t r o l l e d p a r t l y b y t r a n s f e r o f t h e m a t e r i a l t o t h e s u r f a c e , and p a r t l y b y a d h e s i o n o f m a t e r i a l t o t h e s u r f a c e , y i e l d e d an e x p r e s s i o n f o r t h e i n i t i a l f o u l i n g r a t e v i r t u a l l y i d e n t i c a l i n f o r m t o t h a t f o u n d e x p e r i m e n t a l l y f o r t h e gas o i l . M o d e l s were a l s o p r o p o s e d f o r t h e l i m i t i n g c a s e s o f t r a n s f e r c o n t r o l l i n g d e p o s i t i o n , w h i c h i s s i m i l a r t o t h e K e r n - S e a t o n model, and a d h e s i o n c o n t r o l l i n g d e p o s i t i o n . 127 10. RECOMMENDATIONS FOR FURTHER WORK F u r t h e r work on h e a t e x c h a n g e r f o u l i n g s h o u l d e n t a i l g a t h e r i n g more d a t a o f t h e t y p e p r e s e n t e d h e r e , b u t f o r o t h e r l i q u i d s . O t h e r o p e r a t i n g c o n d i t i o n s s u c h as c o n s t a n t p r e s s u r e d r o p and c o n s t a n t w a l l t e m p e r a t u r e a l s o c o u l d be i n v e s t i g a t e d . R e l i a b l e d a t a a r e needed t o e v a l u a t e t h e m a t h e m a t i c a l m o d e l s . The work o f Ha s s o n and c o - w o r k e r s on s e a w a t e r s c a l i n g c o u l d be e x t e n d e d t o l o n g e r o p e r a t i n g t i m e s t o see w h e t h e r a s y m p t o t i c c o n d i t o n s a r e r e a c h e d . I t has n o t been d e m o n s t r a t e d t h a t u n d e r c o n s t a n t h e a t f l u x c o n d i t i o n s an a s y m p t o t i c t h i c k -n e s s i s r e a c h e d w i t h a compact s c a l e . K r a f t c o o k i n g l i q u o r s c a l i n g a l s o m i g h t be s t u d i e d . I t h a s b e e n p o s t u l a t e d t h a t t h e CaC03 s c a l e t h a t forms i s due t o p a r t i c u l a t e CaC03. The i n i t i a l r a t e may t h e r e f o r e be a d h e s i o n c o n t r o l l e d o r i t may be d i f f u s i o n c o n t r o l l e d as i n s e a w a t e r s c a l i n g . The v e l o c i t y dependence o f t h e s c a l i n g r a t e i s t h e r e f o r e open t o q u e s t i o n . I f a s y m p t o t i c c o n d i t i o n s c o u l d be r e a c h e d a t r e a s o n a b l e v e l o c i t i e s some s a v i n g s i n m a i n t e n a n c e e f f o r t w o u l d be p o s s i b l e . F o r p a r t i c u l a t e f o u l i n g i n g e n e r a l , t h e q u e s t i o n o f t h e t y p e and m a g n i t u d e o f f o r c e s i n v o l v e d i n a d h e s i o n o f s m a l l p a r t i c l e s t o smooth and ro u g h s u r f a c e s i s open. The e f f e c t 128 o f p a r t i c l e s i z e and c o n c e n t r a t i o n on f o u l i n g r a t e s r e q u i r e s some work. E f f o r t m i g h t be p u t i n t o i m p r o v i n g t h e m a t h e m a t i c a l a p p r o a c h t o f o u l i n g . The d i f f e r e n c e a p p r o a c h , w h i l e i t a p p e a r s s u c c e s s f u l i n some r e s p e c t s i s b a s e d on a h y p o t h e t i c a l " r e m o v a l " p r o c e s s t h a t h a s n o t b e e n d i r e c t l y d e m o n s t r a t e d t o e x i s t . O p t i m i z a t i o n o f h e a t e x c h a n g e r d e s i g n f o r f o u l i n g s e r v i c e , i n c l u d i n g t h e e f f e c t o f v e l o c i t y on t h e o p e r a t i n g t i m e , c an be a t t e m p t e d u s i n g some o f t h e p r o p o s e d e x p r e s s i o n s f o r t h e f o u l i n g r a t e „ The whole q u e s t i o n o f s h e l l s i d e f o u l i n g o f s h e l l and tu b e h e a t e x c h a n g e r s , i n c l u d i n g t h e i n f l u e n c e o f p r o c e s s v a r i a b l e s and geometry, has h a d l i t t l e e x p o s u r e i n t h e open l i t e r a t u r e . 129 11. REFERENCES 1. T.E.M.A. S t a n d a r d s , F o u r t h E d i t i o n , T u b u l a r E x c h a n g e r s M a n u f a c t u r e r s A s s o c i a t i o n , New Y o r k ( 1 9 5 9 ) . 2. K e r n , D. Q. and S e a t o n , R. E. , B r i t . Chem. Eng. 4., 258 (1959) 3. K i n e r t , C., T r a n s . A.S.M.E. 7 1, 876 (1949). 4. 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P e r r y , J . H., ( E d i t o r - i n - C h i e f ) " C h e m i c a l E n g i n e e r s ' Handbook" T h i r d E d i t i o n , M c G r a w - H i l l Book Co., New Y o r k ( 1 9 5 0 ) . 32. Rotem, Z,, Pa p e r P r e s e n t e d t o F i r s t W e s t e r n C a n a d i a n Heat T r a n s f e r C o n f e r e n c e , R e g i n a , 1966. 33. McAdams, W. H., "Heat T r a n s m i s s i o n " T h i r d E d i t i o n , McGraw-H i l l Book Co., New Y o r k (1958). 34. S m i t h e l l s , C. J . , ( E d i t o r ) , " M e t a l s R e f e r e n c e . B o o k " , V o l . 2, T h i r d E d i t i o n , B u t t e r w o r t h s , London ( 1 9 6 2 ) . 35. Knudsen, J . G. and K a t z , D. L . , " F l u i d Dynamics and Heat T r a n s f e r " , M c G r a w - H i l l Book Co., New Y o r k (1958)„ 36..' M a x w e l l , J . B., "Data Book on H y d r o c a r b o n s " , D. Van N o s t r a n d Co., New Y o r k (1950). 37. B e n n e t t , C, A,, and F r a n k l i n , N. 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C h a l k , R., C o l u m b i a C e l l u l o s e Co., R e s e a r c h and De v e l o p m e n t D i v i s i o n , P e r s o n a l c o m m u n i c a t i o n . 46. M e t z n e r , A,. B. and F r i e n d , W. L. , Can, J . Chem. Eng. 36, 235 ( 1 9 5 8 ) . 133 47. B i r d , R. B., S t e w a r t , W. E. and L i g h t f o o t , E. N., " T r a n s p o r t Phenomena" J o h n W i l e y and Sons, New Y o r k (1960). 48. M c A l l i s t e r , . R. A., E as tham, D. H. D o u g h a r t y , .N. A. and H o l l i e r , M., C o r r o s i o n 1?, "579t ( 1 9 6 1 ) . 49. F r a z i e r , A. W.,, Huddle, J . G. and Power, W. R. , O i l and Gas j o u r n a l 63_, No. 18, 117 (1965). 50. M i n o r , W. R., Petro/Chem E n g i n e e r , F e b r u a r y 1966. 51. S t e p h e n s o n , J . N., ( E d i t o r - o n - C h i e f ) , " P u l p and P a p e r M a n u f a c t u r e " , V o l . 1, " P r e p a r a t i o n and T r e a t m e n t o f Wood P u l p " , M c G r a w - H i l l Book Co., New Y o r k ( 1 9 5 0 ) . . 134 12. NOMENCLATURE T y p i c a l u n i t s a / aj < A j , c o n s t a n t . T'"..r:.-1 L A a r e a f t 2 b p a r a m e t e r o f e q u a t i o n 6 h r " ^ C c o n c e n t r a t i o n l b m o l e s / f t 3 C c o n c e n t r a t i o n o f d i r t i n l i q u i d l b / f t 3 On d r a g c o e f f i c i e n t d i m e n s i o n l e s s Cp h e a t c a p a c i t y a t c o n s t a n t p r e s s u r e B T U / ( l b ) ( ° F ) D i n s i d e d i a m t e r o f t u b e f t D' i n s i d e d i a m e t e r o f t u b e i n ; . i n c h e s i n c h e s D p a r t i c l e d i a m e t e r f e e t .tr ^ d i f f u s i o n c o e f f i c i e n t f t 2 / s e c e b a s e f o r n a t u r a l l o g a r i t h m = 2,71828 d i m e n s i o n l e s s E a c t i v a t i o n e n e r g y K c a l / g - m o l e f F a n n i n g f r i c t i o n f a c t o r d i m e n s i o n l e s s F f o r c e l b f g c g r a v i t a t i o n a l c o n s t a n t h h e a t t r a n s f e r c o e f f i c i e n t B T U / ( h r ) ( f t 2 ) ( ° F . ) h m i n s t a n t a n e o u s mean h e a t t r a n s f e r c o e f f i c i e n t f o r combined f o u l i n g r e s i s t a n c e and l i q u i d f i l m B T U/(hr) ( f t 2 ) (°F) J f l u x o f m a t e r i a l l b / ( h r ) - ( f t 2 ) 135 k t h e r m a l c o n d u c t i v i t y o f l i q u i d k g B o l t z m a n n ' s c o n s t a n t k^ t h e r m a l c o n d u c t i v i t y o f d e p o s i t k - d i f f m a s s t r a n s f e r c o e f f i c i e n t k r r e a c t i o n r a t e c o n s t a n t K c o n s t a n t K r o v e r a l l c r y s t a l l i z a t i o n r a t e c o n s t a n t 1 l e n g t h LLI. l e n g t h o f tu b e m mass n number p,P p r e s s u r e q h e a t f l u x Q h e a t f l o w r r a d i u s R t h e r m a l r e s i s t a n c e R f f o u l i n g f i l m r e s i s t a n c e = R-R Q Rg u n i v e r s a l gas c o n s t a n t S s t i c k i n g p r o b a b i l i t y t t i m e T t e m p e r a t u r e U v e l o c i t y TT v e l o c i t y o f p a r t i c l e s n o r m a l t o s u r f a c e u ^ b u l k v e l o c i t y B T U /(hr) ( f t ) ((>°F) B T U / ( l b m o l e ) ( ° R ) B T U / ( h r ) ( f t ) ( ° F ) f t / s e c f t f t l b l b f / f t 2 B T U / ( h r ) ( f t 2 ) BTU/hr f t ( B T U / ( h r ) ( f t 2 ) ( ° F ) ) (BTU/(hr)(ftl)(°F)) B\'.V/ '.'! ,.:) [ft , B T U / ( l b mole)!(j°R) h r °F f t / s e c f t / s e c f t / s e c 136 W mass f l o w r a t e x d e p o s i t t h i c k n e s s X d i m e n s i o n l e s s d e p o s i t t h i c k n e s s = x/D Y d i s t a n c e f r o m t u b e w a l l z l e n g t h a l o n g t u b e l b / s e c f t f t f t D i m e n s i o n l e s s Groups Nu N u s s e l t number Pr P r a n d t l n n u m b e r Re R e y n o l d s number Sc S c h m i d t number h D/k C p / X / k U b D/l/ G r e e k - L e t t e r s O r a t i o o f i n s i d e o r i f i c e d i a m e t e r r* t o i n s i d e p i p e d i a m e t e r O" S t e f a n - B o l t z m a n n c o n s t a n t € e m i s s i v i t y /\ d i f f e r e n c e (^) power f a c t o r p d e n s i t y d i m e n s i o n l e s s B T U / ( h r ) ( f t 2 ) ( ° R ) 4 arime'ns!Lohle'ss).( 'R) 4 d i m e n s i o n l e s s l b / f t 3 137 T k i n e m a t i c v i s c o s i t y v i s c o s i t y o r m i c r o n s h e a r s t r e s s a t w a l l f t V s e c l b / ( f t ) ( s e c ) l b / ( f t ) ( s e c ) 2 S u b s c r i p t s i n l e t 2 . o u t l e t 3 o u t s i d e o f i n s u l a t i o n b b u l k c c l e a n c a l c c a l c u l a t e d c r i t c r i t i c a l v a l u e d d e p o s i t f f o u l i n g f i l m f i l m l i q u i d f i l m h o u t s i d e f i l m o h ^ i n s i d e f i l m i i n s i d e H l o c a l l o s s l o s t t o s u r r o n d o u n d i n g s mean v a l u e m n * OR o u t P s St w CO j S u p e r s c r i p t s a t t i m e z e r o o r i f i c e v a l u e o u t s i d e p a r t i c l e s u r f a c e steam w a l l f a r f r o m s o u r c e o v e r a l l p a r t i c l e s power a s y m p t o t i c v a l u e a v e r a g e v a l u e 1-1 APPENDIX 1: CALIBRATION OF EQUIPMENT a) Thermocouple Calibration A l l thermocouples were calibrated in an o i l bath equipped with an Instrument Co, Ltd. thermoregulator (Model 7530) for temperatures above 200°F„ and in a water bath equipped with a Colura U l t r a thermostat for temperatures below 200°F. The temperature in the bath was measured with a Platinum resistance thermometer (Leeds & Northrup No. 169314). A Leeds & Northrup Muel&er temperature bridge No. 83429 was used to measure the resistance of the thermometer. A u x i l i a r y equipment included a Scalamp Galvanometer, an Eppley Standard C e l l No. 737516 and a Leeds & Northrup Mercury commutator. The resistance readings were corrected for resistance of the lead wires, and were converted to temperature v i a the Callender equation for the resistance thermometer. The constants for this resistance thermometer were determined by the National Research Council of Canada in October 1959: T (°C) = 1 ["Jr ll +1.5 I" T j T T x" 0.0038748 [ !R T " J |_10oJ [lOO (1-1) This equation was solved by t r i a l and error for the various values of Rrp measured using the measured value of the resistance 1-2 a t t h e i c e p o i n t (2,5128 ohms). T a b l e 1-1 g i v e s t h e v a l u e s o f t h e r e s i s t a n c e and t h e t e m p e r a t u r e s i n °G and °F. The m i l l i v o l t r e a d i n g s o f t h e t h e r m o c o u p l e s were f i t t e d b y l e a s t s q u a r e s t o a q u a d r a t i c e q u a t i o n o f t h e f o r m T = a + b x M i l l i v o l t s + c x M i l l i v o l t s 2 1. I I •• :;vl " L ' - C M • ''. -II b I n T a b l e 1-1-1 t h e c o n s t a n t s f o r t h e t h e r m o c o u p l e s a r e g i v e n a l o n g w i t h d e v i a t i o n s o f t h e c a l c u l a t e d v a l u e s from measured v a l u e s a t two t e m p e r a t u r e s n e a r t h e range t h a t t h e i n d i v i d u a l t h e r m o-c o u p l e was u s e d . T h e r m o c o u p l e s 1 t o 16 were mounted on t h e t u b e w a l l ( T a b l e I I ) T h e r m o c o u p l e s 17 and 18 measured i n l e t and o u t l e t c o o l i n g w a t e r t e m p e r a t u r e s r e s p e c t i v e l y . T h e r m o c o u p l e s 19 t o 24 a r e s h e a t h e d i r o n - c o n s t a n t a n t h e r m o c o u p l e s . Thermo-c o u p l e 19 measures t h e f o u l i n g l i q u i d t e m p e r a t u r e a t t h e h e a t e r i n l e t . T h e r m o c o u p l e s 21 and 22 measure t h e t e m p e r a t u r e i n t h e o u t l e t m i x i n g chamber. T h e r m o c o u p l e s 23 and 24 measure t h e i n l e t and o u t l e t f o u l i n g l i q u i d t e m p e r a t u r e s on t h e c o o l e r . T h e r m o c o u p l e 20 i n d i c a t e s t h e l i q u i d t e m p e r a t u r e i n t h e t a n k . TABLE 1-1: RESISTANCE THERMOMETER DATA R e s i s t a n c e T e m p e r a t u r e T e m p e r a t u r e (ohms) °C. °F. 2.593000 8.15 46.66 2.65340 14.26 57.66 2.68210 17.17 62.91 2.72070 21.10/ 69.98 2.80790 29.99 85.99 2,91470 40.91 105.65 3,05210 55.02 131.03 3,20795 71,09 159.96 3,37953 88.87 191.96 3.46700 97.97 208.35 3.63580 1.15.61 240.09 3.74035. 126.58 259.84 3.91578 145.07 293.13 4.11656 166.37 331.47 4.28806 184.67 364.41 4.35363 191.70 377.06 4.59115 217.28 423.10 4.74292 233.73 452.72 4,89970 250.82 483.48 1-4 TABLE 1 - I I a . THERMOCOUPLE CALIBRATION TEST SECTION I AND I I # T h e r m o c o u p l e Number D e v i a t i o n °F T'eale - T me as 192.0 °F 483. 1 43. 088 41.501 -0.40063 -0.3 -0.4 2 49. 3d6 40.405 -0.34253 -1.3 -0.8 3 42, 9l'5 41.557 -0.40932 -0.2 -0.6 4 41. 517 41.854 -0.41836 -0.3 -0.2 5 42 , 331 41.636 -0.40749 -0.4 -0.4 6 43, 565 41,317 -0.38472 -0.5 -0.4 7 43. 185 41,404 -0,39123 +0.1 -0.5 8 43. 078 41.361 -0.39282 +0.4 -0.6 9 47, 872 40.377 -0.33106 + 0,4 -0.5 10 43, 102 41,365 -0.38766 + 0.1 -0.4 11 43. 394 41.359 -0,38945 +0.2 -0.4 12 43, 080 41,497 -0.40308 +0.3 -0.6 13 41, 519 41.906 -0,42814 -0.3 -0.6 14 40. 961 42.062 -0.4367 -0.4 -0.3 15 42. 959 41.423 -0,3979 + 0.1 -0.5 16 46, 292 40.272 -0.34193 -1.0 -0.2 17 34. 363 44.191 -0.0000 + 0...4* +0.6 18 32. 227 46.560 -0.92456 : . o . 6 * -0.1 19 38. 055 32.939 -0.04098 0.0** -0.5 20 37. 106 33.258 -0.05664 +0.3** -0.3 21 35. 712 33.248 -0.06034 0. ** -0.4 22 36, 611 33.203 -0.053612 +0.1** -0.5 23 36, 842 33.109 -0.048376 +0.2** -0.6 24 36. 982 33.101 -0.04755 +0.2** -0.6 ** *** * a t 47°F. ** a t 131QF, *** a t 160°F. # T°F = a + b ( m i l l i v o l t s ) + c ( m i l l i v o l t s ) 2 1-5 TABLE 1 - I I b . THERMOCOUPLE CALIBRATION FOR TEST SECTION I I I T h e r m o c o u p l e a b c .; D e v i a t i o n O F ( C a l c -number O b s e r v e d ) a t 7 7 . 5 5°F 192.1°P 1 3 1 . 8 3 8 46 .642 - 1 . 0 4 8 8 - 0 . 0 7 0 . 0 9 2 29 .192 4 8 . 4 7 3 " - 1 . 3 4 6 2 *0„~23 - 0 . 1 4 3 3 2 . 6 7 9 45 .852 - 0 . 8 9 3 2 5 : o ? o o 0 .00 4 32 .651 4 5 . 7 7 8 - 0 . 8 4 0 9 6 -0 . '05 0 .08 5 32 .502 45 .903 - 0 . 8 7 2 3 8 - 0 . 0 2 0 .03 6 30 .713 47 ,612 - 1 , 0 5 6 3 0 .00 0 . 0 8 7 31 ,939 46 ,512 - 1 . 0 0 7 6 - 0 . 1 1 0 .13 8 32 .255 4 6 . 0 5 9 - 0 , 8 5 6 4 1 - 0 . 0 9 0 .12 9 32 .255 4 6 , 0 5 9 - 0 . 8 5 6 4 1 - 0 . 0 9 0 .12 10 31 .901 46 .491 - 0 . 9 9 9 3 7 - 0 . 0 7 0 . 0 9 11 32 .311 46 .101 - 0 . 9 4 4 5 8 0 .01 0 .00 12 31 ,580 4 6 . 7 9 0 - 1 . 0 7 9 7 - 0 . 0 4 0 .07 13 31 ,178 46 .760 - 0 . 7 6 9 3 8 - 0 . 0 2 0 .08 14 31 ,577 4 6 . 8 9 9 - 1 . 1 0 3 5 0 .00 0 .06 15 32 .130 46 .367 - 0 . 9 7 4 0 - 0 . 0 3 0.. 01 16 3 2 , 7 8 8 4 5 . 7 0 9 - 0 . 8 6 3 2 2 0 .04 90?04 + T e m p e r a t u r e °F = a + b ( M i l l i v o l t s ) + c ( M i l l i v o l t s ) 1-6 b) D i f f e r e n t i a l P r e s s u r e C e l l C a l i b r a t i o n i ) O r i f i c e DP I n d i c a t o r The i n s t r u m e n t u s e d was a H o n e y w e l l M o d e l 292D11 No. K678 5429001, w h i c h i s n o r m a l l y u s e d t o i n d i c a t e l i q u i d l e v e l s i n t a n k s and t h e r e f o r e i n d i c a t e s 100% when t h e t a n k i s empty and t h e d i f f e r e n t i a l p r e s s u r e i s z e r o . F o r t h e p r e s e n t p u r p o s e t h e n e e d l e was s e t on z e r o a t z e r o d i f f e r e n t i a l p r e s s u r e and t h e h i g h and low p r e s s u r e t a p s r e v e r s e d . C a l i b r a t i o n wascdone w i t h a m e r c u r y manometer u t i l i z i n g t h e l a b a i r s u p p l y . The d a t a a r e g i v e n i n T a b l e l - I I I and a r e p l o t t e d i n F i g u r e 1-1. F o r r e a d i n g s b e l o w 70 t h e p l o t o f DP C e l l R e a d i n g v e r s u s A P w a s u s e d w h i l e above 70 t h e i n v e r s e p l o t was u s e d . i i ) T e s t S e c t i o n P r e s s u r e D r o p I n d i c a t o r The i n s t r u m e n t u s e d was a H o n e y w e l l M o d e l 227X2-C2 No. B466 7102002 w i t h t h r e e r a n g e s p r i n g s , 0-50" "water, 0-100" w a t e r , and 0-150" w a t e r . W i t h no r a n g e s p r i n g i n , t h e i n s t r u m e n t r a n g e i s 0-20" w a t e r . The m e t e r was c a l i b r a t e d w i t h a w a t e r column as reccpmmended i n S e c t i o n 195-F o f t h e H o n e y w e l l I n s t r u c t i o n book r e c e i v e d w i t h t h e i n s t r u m e n t , f o r t h e 0-20" w a t e r , span and d r y c a l i b r a t e d w i t h a m e r c u r y manometer f o r t h e 0-50" w a t e r , t h e 0- 100" w a t e r and t h e 0-150" w a t e r r a n g e s p r i n g s . The c a l i b r a t i o n c u r v e s a r e p l o t t e d i n F i g u r e 1-2 and t h e d a t a a r e l i s t e d i n T a b l e 1- IV. 1-7 100/DP Cell Reading DP Cell Reading F i g u r e 1-1. C a l i b r a t i o n C u r v e s f o r O r i f i c e D i f f e r e n t i a l P r e s s u r e C e l l 1-8 TABLE l - I I I . CALIBRATION OF ORIFICE DIFFERENTIAL PRESSURE CELL Manometer R e a d i n g ( I n c h e s Hg) DP C e l l R e a d i n g Manometer ( I n c h e s R e a d i n g Hg) DP C e l l R e a d i n g . 13.15 84.0 11.01 81.0 15. 92 86.7 12.45 83.0 20.08 90.1 14.46 85.1 25.06 94.5 19.0 89.8 27.12 96.1 1.48 19.5 3. 50 38.0 1.78 22.0 3.33 35.5 3.07 33.5 5. 78 57, 8 3. 90 41. 8 7.13 69.0 5.13 52. 5 8.05 74,3 5. 50 56.0 8.33 75,1 6„40 63.2 8. 89 76.5 7.26 69.5 9. 70 78,5 8, 32 75.2 7.68 72.0 TABLE 1-IV. CALIBRATION OF TUBE DIFFERENTIAL PRESSURE CELL Range S p r i n g j N o n e + 0-50 i n c h e s H 2 0 0-100 i n c h e s H 2 0 0-150 i n c h e s H 2 0 S c a l e R e a d i n g A P TSrcale..-.Read-.i' ng A P S c a l e R e a d i n g A P S c a l e R e a d i n g AP i n c h e s H 2 0 i n c h e s E^O i n c h e s H 2 0 i n c h e s H 2 0 30.2 6. 06 28.0 14.00 16.0 16.33 15. 5 23.37 40.8 "8". 14 37.0 18. 22 23.8 23.11 26.4 40.39 57. 2 10. 82 74.0 38.07 34.0 33. 58 44. 6 66.87 76.2 14. 93 87. 5 44.19 45. 5 45.28 58. 8 89.57 97,3 19.16 86,5 44.19 .S.6..-2 35^ 74 71.2 107.40 89.6 17,49 96,0 48,94 63.54 . 63 ..36 82. 3 124.42 82,9 16.10 98,0 49. 63 78.0 77. 09 93.2 141.31 76.0 14. 71 9.9 5.17 86.2 86. 06 96.0 144.56 70.0 13.68 20,9 10.06 94.0 ' 92. 86 87,0 131.59 59. 9 11, 70 39„5 19. 85 95.4 95.04 76,0 114.65 45-9 9,06 61.1 31,41 96.0 96. 53 64. 5 96.46 38,7 7.-64 62.0 31. 95 82.2 81.57 56.3 -83-362 30. 9 •"613)0 78, 1 40, 79 76.3 74. 92 48. 5 72.68 24. 9 4. 90- 77. 5 39.16 67. 5 62.13 37.5 55.79 20.0 4.02 87.0 44. 87 60.5 59. 28 28.5 42.5 15.0 3.09 99.0 50.03 53.3 52. 89 20. 9 30.80 10.1 2.11 68.0 34. 81 41.8 41.33 15.0 21.62 7.8 1.54 53.0 26.78 30.8 31.00 9.4 13.51 5.6 1.12 45.0 23.11 27.0 26.10 5.9 7.43 3.6 0. 71 38.5 20.8 9.0 19. 71 9. 93 4.08 20.0 10.1 18. 76 9. 65 Range 0-2O i n c h e s H 2 0 1-10 c) O r i f i c e P l a t e C a l i b r a t i o n Two s h a r p - e d g e d o r i f i c e p l a t e s ( F i g u r e 2) were c a l i b r a t e d b y n o t i n g t h e t i m e f o r s u c c e s s i v e i n c r e m e n t s o f w e i g h t o f w a t e r t o c o l l e c t i n a 45 g a l l o n drum. The t e m p e r a t u r e was measured, and t h e d i f f e r e n t i a l p r e s s u r e a c r o s s t h e o r i f i c e r e a d on t h e p r e v i o u s l y c a l i b r a t e d d i f f e r e n t i a l p r e s s u r e c e l l . The o r i f i c e d i s c h a r g e c o e f f i c i e n t C was c a l c u l a t e d (31) from W = C S 2 / 2 g c A P /O " 1-2 w h e r e = o r i f i c e d i a m e t e r / p i p e d i a m e t e r S 2 = a r e a o f d i s c h a r g e o p e n i n g E q u a t i o n 1-2 i s g e n e r a l i z e d f o r use w i t h t h e gas o i l t o ReOR = 4W = D2 / 2 g c A.P pS 1-3 C 7TD2yU.C l*. A l o g - l o g p l o t o f R S Q R V S ReQ^/c was made and t h e d a t a f i t t e d b y l e a s t s q u a r e s y i e l d i n g : 0 Q71R2 F o r ft = 0.301 Re O R = 0.80564 ( R e 0 R / C ) * 1-4 F o r ft = 0.602 R e Q R = 0.925069 ( R e 0 R / C ) 0 • 9 6 3 0 6 1-5 T a b l e 1-V g i v e s t h e d a t a f o r c a l c u l a t i n g t h e d i s c h a r g e c o e f f i -c i e n t s and T a b l e 1-VI l i s t s t h e d e v i a t i o n s o f e x p e r i m e n t a l p o i n t s 1-11 from the f i t t e d equations. For the o i l experiments Re Q R/C i s calculated from equation 1-3 knowing p and p. at the temperature of the o i l at the o r i f i c e , and then ReQR i s calculted from equation 1-4 or 1-5. W, and Re in the test section are then calculated knowing the physical properties at the average temperature in the test section. Kinematic v i s c o s i t i e s and densities were measured at the o r i f i e e temperature, 210°F. Sample Calculation i) O r i f i c e C o e f f i c i e n t For the o r i f i c e with = 0.301 the following data were measured: W = 0.1538 lb/sec DP c e l l reading =60. Water Temperature = 18.5°C. From Figure 1-1, DP c e l l reading of 60 corresponds to A P = 6.0 in . Hg At 18.5°C, p. = 1.04 cp p = 0.99853 g/ml (Reference 31) = 0.301, 0^ = 0.008285 1-^g4 = 0.9917915 D 2 = 0.187S.;in. S 2 = 1.91748 x 10~ 4 f t 2 From equation 1-2 C = W ., , . ,QJ-153;8 . ... .. . , . S 2 /2gr&Pff~ = 1, 91748 x J-Q.y7x32.174x (6x7Q. 727) (-9983: V 1-^4 -v/9917915 ~ 62.' TABLE 1-V. CALIBRATION OF ORIFICE PLATES i>=0.301 0.602 DP C e l l R e a d i n g (P1-P2) i n c h e s Hg A v e r a g e W e i g h t R a t e l b / s e c Temp °C Re OR g/ml cp 30 2 , 68 0. 1014 21. 4 0. 9994 0. 97 0. 605 12, 696 30 2. 68 0, 1019 19. 0 0. 9984 1. 03 0. 608 12, 015 50 4. 91 0. 1377 19. 8 0. 99847 1. 033 0. 608 16, 189 60 6. 0 0. 1538 18, 5 0. 99853 1. 04 0. 614 IV, 960 75 8., 30 0. 1772 17. 5 0, 9987 1. 07 0. 585 19, 544 80 10, 4 0. 1965 18. 0 0, 9986 1, 056 0. 596 22, 599 85 14. 2 0. 2293 17 , 0 0. 9988 1. 083 0. 595 25, 713 90 19. 55 0. 2680 18. 0 0, 9986 1. 056 0. 594 -30, 822 95 25. 7 0. 3088 19. 0 0. 99843 1. 030 0. 590 36, 410 .100 32. 9 0. 3451 18. 0 0. 9986 1. 056 0. 588 39, 688 70 7. 33 0. 1689 20. 8 0. 99806 0. 988 0. 610 20, 761 25 2. 13 0. 3975 18. 0 0. 9986 1. 0559 0. 623 22, 857 40 3. 77 0. 5306 14. 2 0. 9992 * 1. 170 0. 625 27, 538 50 4. 90 0. 6066 17. 0 0. 9988 1. 083 0. 627 34, 012 60 :"6C 0 0. 6709 14. 0 0. 9993 1. 171 0. 626 34, 790 70 7. 33 0. 7353 17. 0 0. 9988 1. 083 0. 621 41, 228 80 10. 4 0. 8750 17. 0 0. 9988 1. 083 0. 614 48, 500 80 10. 4 0. 8637 13. 5 0. 9993 1. 185 0. 613 44, 258 85 14. 25 1. 000 14. 8 0. 9991 1. 15 0. 606 52, 802 90 19. 55 1. 1580 16. 5 0. 9989 1. 095 0. 599 64, 217 95 25. 7 1. 3389 17. 2 0. 9988 1. 077 0. 604 75, 489 100 32. 9 1. 5017 16. 5 0. 9989 1. 095 0. 599 83, 277 I I—' TABLE 1-VI. F I T OF REGRESSION EQUATIONS FOR ORIFICES A. S m a l l O r i f i c e = 0.301 RE/C RE(OBS) R e ( C A L C ) * % D e v i a t i o n 20983. 12696. 12771. 0.6 26637. 16189, 16103. -0.5 34034. 20761. 20434. -1.6 51852. 30822, 30764, -0.2 61712. 36410. 36435, 0.1 67451. 39689. 39724, 0.1 37925,. 22599. 22700. 0.4 43214. 25713. 25771, 0.2 29251. 17960, 17637, -1.8 33437, 19545, 20085. 2.8 19772, 12015, 12054, 0.3 * R E C a l c b y E q u a t i o n 1-4 B. L a r g e O r i f i c e = 0.602 RE/C RE.(OBS) R E ( C A L C ) * % D e v i a t i o n 34736. 21700. 21838.„ 0.6 51476. 32000, 31896. -0.3 65827. 40500. 40419. -0.2 74546. 45800. 45563. -0.5 77175. 47100. 47109. 0.0 87531. 53300. 53183. -0.2 110506. 67000. 66567. -0.6 121181. 72000. 72749. 1.0 131451. 78500, 78678. 0.2 * R e c a ^ c b y e q u a t i o n 1-5 1-14 = 802.128 _ . 802128 = 0.6123 (1.71635xl06)*S 1.31 (Program y i e l d s .614) Then, Re = 4 W = 4( 1538) 17,933 7TD2fjL 3 ,, 14x ( . 1875/12)x (1. 04x6. 7 1 9 7 x l 0 _ 4 7 (Program y i e l d s 17,960) where 1 cp = 6 7197 x 1 0 - 4 l b m / f t - s e c R e 0 R / C = 17933 = 29,288 (Program y i e l d s 29,251) 0 6123 These c o - o r d i n a t e s g i v e one p o i n t f o r t h e c o r r e l a t i o n ( T a b l e 1 - V I ) . i i ) Mass F l o w R a t e and V e l o c i t y f o r O i l F l o w D a t a : P = 0.301 D 2 = 0.1875 i n c h e s ( F i g u r e 2 ) . Run 2 7 DP c e l l r e a d i n g = 9 0 . ( A P = 19.6 i n . Hg.) V i s c o s i t y and D e n s i t y m e a s u r e d a t 210°F /JL = 1.231 cp p = 0.795 g/ml C a l c u l a t e R C Q R / C f r o m e q u a t i o n 1-3 Re O R _ D_2 / 2 g c A P 7 ^ _ 0,1875/12 /64. 348x19. 6x70 . 727x62 . 43x . 795 C p- 1-^g4 1 231x6 7 1 9 7 x l O - 4 V 0.9917915 = 3 9 90 7 From e q u a t i o n 1-4, R eO R = 0 80564 (39,907)° 9 7 1 8 2 = 0 80564 (29,606) = 23,852 W - Rep 7T D2H- _. 23,852 x 3 1416 x '1875/12 x 1.231 x 6 7197 x 1 0 " 4 4 4 = 0.24209 l b n / s e c 1-15 A v e r a g e b u l k t e m p e r a t u r e i n t e s t s e c t i o n ( T a b l e 3 - I I , A p p e n d i x 3) Tb = T b i n + T o u t = 221.. °F. p= 0 - 7 9 1 r g/ml ^  = 1.415 cs 2 ( F i g u r e 1-3) U b = _W _ 0.2421 _ 7.63 f t / s e c p A 0.. 7 9 1x62.,43x6.425xl0 - 4 Re = U^D = 7. ...633?043,43 2:1,2 = 14,319 ~V~ 1.415x.03875 3600 Th e s e d a t a a r e l i s t e d i n T a b l e 3-1 (Appendix 3) =-- 1 ?':• I.. 1-16 Scale Reading F i g u r e 1-2. C a l i b r a t i o n C u r v e s f o r Tube D i f f e r e n t i a l P r e s s u r e C e l l ( 0-20, 0-50, 0-100 and 0-150 i n c h e s w a t e r r a n g e ) . I - i / F i g u r e 1-3. K i n e m a t i c V i s c o s i t y and S p e c i f i c G r a v i t y o f O i l A. 2-1 APPENDIX 2: CALCULATION OF THE HEAT TRANSFER COEFFICIENT a) D e t e r m i n a t i o n o f t h e h e a t f l u x The power d i s s i p a t e d b y an a l t e r n a t i n g c u r r e n t i s Power = V o l t s x Amps x cos(|j) w a t t s ( 2 - l a ) where <J) i s t h e power f a c t o r , t h e a n g l e b y w h i c h t h e c u r r e n t l e a d s t h e v o l t a g e . T e s t s a t t h r e e power l e v e l s showed t h a t w i t h i n t h e a c c u r a c y o f t h e m e a s u r i n g i n s t r u m e n t s (0.5%) t h e c i r c u i t was p u r e l y r e s i s t i v e (cOsC|) = 1) . The h e a t g e n e r a t e d i n t h e t u b e i s t h e n g i v e n b y Q t o t a l = 3.413 x V o l t s x Amps BTU/hr ( 2 - l b ) A p o r t i o n o f t h e h e a t w i l l be c o n d u c t e d t h r o u g h t h e i n s u l a t i o n and l o s t t o t h e s u r r o u n d i n g s b y n a t u r a l c o n v e c t i o n and r a d i a t i o n . T h i s h e a t l o s s i s g i v e n b y Q l o s s = 2 T R L { ^ ( T a - T ^ ) +€CT [ [ 1 3 _ ] 4 - [ ^ ] 4 ] } (2"2> where t i s t h e t e m p e r a t u r e i n °R, and R i s t h e r a d i u s i n f e e t . The o u t s i d e i n s u l a t i o n t e m p e r a t u r e T^ was d e t e r m i n e d b y mea-s u r i n g t h e t e m p e r a t u r e a t two r a d i i i n t h e p i p e i n s u l a t i o n , and e x t r a p o l a t i n g a p l o t o f l o g ( r / R ) v s T t o r/R = 1 ( F i g u r e 2 - 1 ) . The o u t s i d e f i l m c o e f f i c i e n t f o r n a t u r a l c o n v e c t i o n was c a l c u l a t e d 2-2 b y (31) h Q = 0.5 |~ T 3 - Top j ° - 2 5 (2-3) where Dp i s t h e o u t s i d e p i p e d i a m e t e r i n i n c h e s (Dp = 3 . 0 ) . I n s e r t i n g <T = 0.1713, R = 0.12 5 F t , L = .1.932 f t . and € = 0.93 f o r a s b e s t o s ( r e f e r e n c e 31, p. 484) i n t o e q u a t i o n 2-2, one ob-t a i n s Q l o s s = 12-135 | (0.0475) ^ - T ^ J 1 ' 2 5 * 0 . 0 1 9 9 9 5 ^ 3 ] 4 - [ t 0 0 ] 4jj (2-4) H e a t l o s s e s a t f o u r power l e v e l s were p l o t t e d v e r s u s t u b e w a l l t e m p e r a t u r e measured i n t h e same h o r i z o n t a l p l a n e a t w h i c h t h e i n s u l a t i o n t h e r m o c o u p l e s were s i t u a t e d ( F i g u r e 2-2), and an e q u a t i o n f i t t e d t o e s t i m a t e t h e h e a t l o s s : Q l o s s = ° - 6 2 5 Tw " 1 5 6 < 2~ 5) The h e a t t h a t p a s s e s t o t h e l i q u i d i n t h e p o r t i o n o f t h e tu b e f o r w h i c h A T i s c a l c u l a t e d i s t h e n m Q l i q = 49.1 ( Q t o t a l _ Q l o s s ) (2-6) 58.95 ' and t h e h e a t f l u x i s q w = Qua B T U < 2-7) A ( h r ) ( f t 2 ) 2-3 where t h e i n s i d e a r e a o f t h e t u b e , 0.1742 f t 2 , must a l s o be c o r r e c t e d b y t h e f a c t o r 49.1/58.95 i n o r d e r t o y i e l d A f o r e q u a t i o n 2-7. b) I n s i d e Tube W a l l T e m p e r a t u r e The i n s i d e w a l l t e m p e r a t u r e was c a l c u l a t e d f r o m t h e measured o u t s i d e v a l u e s u s i n g t h e s o l u t i o n o f t h e h e a t c o n d u c t i o n e q u a t i o n f o r a l o n g h o l l o w c y l i n d e r w i t h u n i f o r m i n t e r n a l h e a t g e n e r a t i o n and an a d i a b a t i c o u t e r s u r f a c e ( e q u a t i o n 2-14d o f r e f e r e n c e 3 3 ) : f o r r i n = 0.1715 i n , , r Q u t = 0.1875 i n . , L ,= 1.945 f t . , and r e p r e s e n t i n g t h e t h e r m a l c o n d u c t i v i t y d a t a (34) o f t y p e 304 S t a i n l e s s s t e e l b y t h e l i n e a r e q u a t i o n ( F i g u r e 2-3) l n (2-8) k w a l l = 8.45 + 0 . 0 0 4 5 5 T BTU h r ft°F (2-9) The t e m p e r a t u r e d r o p a c r o s s t h e t u b e w a l l t h e n becomes. T, o u t - T-i n = Q L I O U I D x 0 . 0 0 3 3 8 8 4 8.45 + 0 . 0 0 4 5 5 T (2-10) c) D e t e r m i n a t i o n o f t h e Mean T e m p e r a t u r e D i f f e r e n c e The a p p r o p r i a t e A T m i s g i v e n b y 2-4 AT, m (22) dTb The i n t e g r a l was s o l v e d b y e v a l u a t i n g T w a t e a c h t h e r m o c o u p l e l o c a t i o n , c o r r e c t i n g f o r t h e d r o p a c r o s s t h e t u b e w a l l , b y a s -s uming a l i n e a r i n c r e a s e i n T-^  w i t h h e a t e d l e n g t h , and b y f i t t i n g T w - T^ t o a q u a d r a t i c e q u a t i o n i n l e n g t h b y l e a s t s q u a r e s and t h e n i n t e g r a t i n g a n a l y t i c a l l y between t h e r m o c o u p l e s 3 and 14 ( F i g u r e 7 ) . Thus .dTb. Tw - T b T b o u t - T b i n E " x 2 i'-n C d X i n / n / ax^ + bx + i X -(2-11) where a, b, and c a r e t h e l e a s t s q u a r e f i t c o e f f i c i e n t s F o r b 2 < 4ae, I n t e g r a l = _2 t a n ^ 2ax +b I . / l a c - b 2 </4ac - b 2 J X *2 (2-12) F o r b• > 4ac, I n t e g r a l = 1 y b 2 - 4 a c I n 2 ax + b - A/b 2-4ac 2ax + b 4-,/b^-4ac x 2 X n (2-13) d) Sample C a l c u l a t i o n The computer program t h a t was u s e d r o u t i n e l y f o r t h e s e c a l c u l a t i o n s i s appended. The sample c a l c u l a t i o n i s done f o r r u n 27. i ) C a l c u l a t i o n o f Heat F l u x V o l t m e t e r r e a d i n g = 11.2 v o l t s Ammeter r e a d i n g = 2.675 amps. C o r r e c t i n g t h e ammeter r e a d i n g f o r t h e 500/5 amp c u r r e n t t r a n s f o r m e r , a c t u a l c u r r e n t = 500/5 x 2.675 = 267.5 amps. From e q u a t i o n 2-1, t h e h e a t g e n e r a t e d i s Q = 3.413 x 11,2 x 267.5 = 10,225.4 BTU (2-15) h r The a v e r a g e w a l l t e m p e r a t u r e i s c a l c u l a t e d between t h e r m o c o u p l e s 3 and 14, e x c l u d i n g t h e r m o c o u p l e 12 w h i c h gave c o n s i s t e n t l y low v a l u e s , T A V = (354,4 + 3 6 7 8 + 369,6 + 365,5 + 375,2 + 373.2 + 377,6 + 385.7 + 380.1 + 381.3 + 3 8 5 . 9 ) / l l . = 374,2 °F, (2-16) The h e a t l o s t t h r o u g h t h e i n s u l a t i o n between t h e r m o c o u p l e s 3 and 14 i s g i v e n b y e q u a t i o n 2-5.-Heat l o s s = 0.625 (274.2) - 156 = 233.9 - 156 = 77.9 BTU h r (2-17) The h e a t t r a n s f e r r e d t o t h e l i q u i d i s t h e n Heat t o l i q u i d = 49,1 (10225.4 - 77.9) = 8451.9 BTU 58.95 h r (2-18) The h e a t f l u x t h e n becomes = 8451.9 . = 58,254 BTU (2-19) 0.1742 ( 4 9 . 1 ) / ( | 8 . 9 5 ) ~ h r f t 2 i i ) C a l c u l a t i o n o f T e m p e r a t u r e D r o p T h r o u g h Tube W a l l The sample c a l c u l a t i o n i s done f o r t h e r m o c o u p l e 3. P o t e n t i o m e t e r r e a d i n g = 8.15 m i l l i v o l t s , . From T a b l e I - I I a , A p p e n d i x 1 t h e e q u a t i o n f o r t h e r m o c o u p l e 3 i s T ^ = 42,915 + m i l l i v o l t s x 41.557 - 0.40932 ( m i l l i v o l t s ) 2 o u t = 42.915 + 338.69 - 27.19 = 354.42 °F. (2-20) The t h e r m a l c o n d u c t i v i t y o f t h e t u b e w a l l i s c a l c u l a t e d from e q u a t i o n 2-9. ^ w a l l = ^ ' 4 5 + ° - 0 0 4 5 5 (354.4) = 10.06 BTU (2-21) h r ft°F The t e m p e r a t u r e d r o p a c r o s s t h e t u b e w a l l i s t h e n f o u n d f r o m equation 2-10 as, Tout " T i n = Q l 1 Q U I D X 0.0033884 _ 8451.9 (0.0033884) _ 2.87 °F. 10.06 10.06 (2-22) T i n = 354.4 - 2.9 = 351.5 °F. (2-23) Calculations are repeated for each of the eleven thermocouples, i i i ) Calculation of A.Tm The equation for the bulk l i q u i d temperature is,,assuming a l i n e a r increase with heated length, T = ^ o u t l e t T b i n l e t x + T 58.95 i n l e t (2-24a) = 231.9 - 210.7 x + 210.7 58.95 = 0.359627 x + 210.7 (2;-24b) where x i s the heated length of the tube in centimeters. Values of Tb outlet and T^ i n l e t are taken from Table 3-1, Appendix 3. A T x _ 4 > 8 5 c m w _ 1 . 7 4 4 + 210.7 = 212.44 °F. The measured l o c a l temperature difference i s then, (T w - Tt,) measured = 351.-56 = 212.44 = 139.12 °F. The least square f i t of T w - T^ with length is found to be 2-8 (T w - Tb) calculated = -0.010389 x 2 + 0.76306 x + 140.15 (2-25) At x = 4.85, the calculated l o c a l temperature difference is (T w - T b) calculated = -0.24437 + 3.7008 + 140.15 = 143.61°F. The integral in equation 2-11 is then, .x2 53. 95 Integral = t dx _ C J ax2+bx+c J dx -0.010389 x2 + 0.76306 x + 140.15 x i 4.85 (2-26) The discriminant, b 2-4ac = 0.763062 - 4(140.15)(-0.010389) = 6.40633 Since the discriminant i s greater than zero, the integral is given by equation 2-13. The square root of the discriminant i s ^/ b 2 - 4ac = 2.53106. At x = 53.95, Numerator = -2.88896, Denominator: = 2.17314. The upper l i m i t of equation 2-13 is then, Upper l i m i t = 1 l n 1-2.888961 = 0.39509 l n (1.3239) = 0.112383 2.53106 I 2.173141 At x = 4.85, Numerator = -1.86876, Denominator = 3.19334 The lower l i m i t of equation 2-13 is then, Lower l i m i t = 1 l n -1.86876 _ 0.39509 l n (0.585205)=-0.211689 2.53106 | 3.19334 The t o t a l integral is the upper l i m i t minus the lower l i m i t , Total Integral = 0,112383 - (-0.211689) = 0.32407. The computer program yielded a value of 0.32416. The bulk 2-9 l i q u i d temperatures at the upper and lower l i m i t s are found from equation 2-24b. (x = 53,95) = 0,359627 (53,95) + 210.7 = 230.10 °F. T b (x = 4.85) = 212.44 °F., calculated above. The mean temperature difference i s then found by substituting the necessary values into equation 22, A T m - 230.10 - 212.44 = 17.66 = 151.53°F. The computer program yields A.Tm = 151.47°F. An independent check of the integration was made by determining the area under a plot of 1 versus T^ by counting the squares. This graphi-0.359627 (0.32407) Tw"Tb cal method yielded AT m = 152.5°F„ The mean heat transfer c o e f f i c i e n t is then calculated by equation 21, 58,254 _ 384,4 BTU/hr-ft 2 - °F, 151.53 These data appear in Appendix 3, Table 3-III, 2-10 e) T e s t S e c t i o n s I I and I I I Runs 44 and 46 were made w i t h t e s t s e c t i o n s I I and I I I r e s p e c t i v e l y , w h i c h had s l i g h t l y d i f f e r e n t a r e a s and d i f f e r e n t t h e r m o c o u p l e p o s i t i o n s ( T a b l e II)., The u p p e r and l o w e r l i m i t s on t h e i n t e g r a l were a l s o d i f f e r e n t . T e s t S e c t i o n I I T e s t S e c t i o n I I I Lower L i m i t 5.0 4.55 Upper L i m i t 58.1 58.3 The d i m e n s i o n s o f t e s t s e c t i o n s I I and I I I a r e g i v e n b e l o w r -Hg K-D i m e n s i o n (cm) T e s t S e c t i o n I I T e s t S e c t i o n I I I a b c d e f I n s i d e a r e a ( f t 2 ) 66.4 59.1 46, 9 5,7 2.0 2,1 3.2 0.1740 67.1 59.4 46.2 5.7 ,2.3 2.2 3.2 0.1750 2-11 F i g u r e 2-1. E s t i m a t i o n o f S u r f a c e T e m p e r a t u r e o f I n s u l a t i o n 2-12 F i g u r e 2-3 T h e r m a l C o n d u c t i v i t y S t a i n l e s s S t e e l o f Type 304 2 -13 COMPUTER PROGRAM TO CALCULATE HEAT TRANSFER COEFFICIENTS C CORRECTED P R O F I L E S AND C O E F F I C I E N T S 1 DIMENSION Z ( 2 0 0 ) , T ( 2 0 0 ) , T C O N ( 2 0 0 > , C O R ( 2 0 0 ) , T C ( 2 0 0 ) 2 DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) , Y F ( 2 0 0 ) , T B ( 2 0 0 ) 3 READ(5 f 223) ( X ( I ) ,1 = 1, 11) 4 223 F 0 R M A K 8 F 1 0 . 5 ) 5 R E A D ( 5 , 1 0 ) N , M , N I 6 10 FORMAT(315) 7 149 R E A D ( 5 t l l l ) R U N » F N P I 10 111 F O R M A T ( 2 F 1 0 . 5 ) I 11 NP=FNP 12 DO 484 L = 1 , N P 13 3 R E A D ( 5 , 7 ) T I M E , V O L T S , A M P S , D P T 14 7 F 0 R M A T K F 1 0 . 5 ) 15 A T E S T = 0 . 1 7 4 2 * 4 9 . 1 / 5 8 . 9 5 16 I F I R U N . L T . 1 3 . 8 ) GO TO 444 17 AMP=AMPS*100. 20 GO TO 555 21 444 AMP=AMPS*240 . 22 555 CONTINUE 23 Q = 3 . 4 1 3 * V 0 L T S * A M P 24 Q D I S = 4 9 . 1 / 5 8 . 9 5 * Q 2 5 R E A D ( 5 , 1 ) ( Z ( I ) , 1 = 1 , 2 4 ) 26 1 F 0 R M A K 8 F 1 0 . 5 ) 27 T( 1 ) = 4 3 . 0 8 8 + Z { 1 ) * ( 4 1 . 5 0 1 - . 4 0 0 6 3 * Z ( 1 ) ) 30 T ( 2 ) = 4 9 . 3 8 6 + Z ( 2 ) * ( 4 0 . 4 0 5 - . 3 4 2 5 3 * Z ( 2 ) ) 31 T ( 3 ) = 4 2 . 9 1 5 + Z ( 3 ) * ( 4 1 . 5 5 7 - . 4 0 9 3 2 * Z ( 3 ) ) 32 T ( 4 ) = 4 1 . 5 1 7 + Z ( 4 ) * ( 4 1 . 8 5 4 - . 4 1 8 3 6 * Z ( 4 ) ) 3 3 T ( 5 ) = 4 2 . 3 3 1 + Z ( 5 ) * ( 4 1 . 6 3 6 - . 4 0 7 4 9 * Z ( 5 ) ) 34 T ( 6 ) = 4 3 . 5 6 5 + Z ( 6 ) * ( 4 1 . 3 1 7 - . 3 8 5 7 ? * Z ( 6 ) ) 35 T ( 7 ) = 4 3 . 1 8 5 + Z ( 7 ) * ( 4 1 . 4 0 4 - . 3 9 1 2 2 * Z ( 7 ) ) 36 T ( 8 ) = 4 3 . 0 7 8 + Z ( 8 ) * ( 4 1 . 3 6 1 - . 3 9 2 8 2 * Z ( 8 ) ) 37 T ( 9 ) = 4 7 . 8 7 2 + Z ( 9 ) * ( 4 0 . 3 7 7 - . 3 3 1 0 6 * Z ( 9 ) ) 40 T ( 1 0 ) = 4 3 . 1 0 2 + Z ( 1 0 ) * ( 4 1 . 3 6 5 - . 3 8 7 6 6 * Z ( 1 0 ) ) 41 T ( l l ) = 4 3 . 3 9 4 + Z ( 1 1 ) * ( 4 1 . 3 5 9 - . 3 8 ^ 4 5 * Z ( 1 1 ) ) 42 T ( 1 2 ) = 4 3 . 0 8 0 + Z ( 1 2 ) * ( 4 1 . 4 9 7 - . 4 0 3 0 8 * Z ( 1 2 ) ) 43 T ( 1 3 ) = 4 1 . 5 1 9 + Z ( 1 3 ) * ( 4 1 . 9 0 6 - . 4 2 8 1 4 * Z ( 1 3 ) ) 44 T ( 1 4 ) = 4 0 . 9 6 1 + Z ( 1 4 ) * ( 4 2 . 0 6 2 - 0 . 4 3 6 7 * Z ( 1 4 ) ) 45 T ( 1 5 ) = 4 2 . 9 5 9 + Z ( 1 5 ) * ( 4 1 . 4 2 3 - . 3 9 7 9 * Z ( 1 5 ) ) 46 T ( 1 6 ) = 4 6 . 2 9 2 + Z ( 1 6 ) * ( 4 0 . 2 7 2 - . 3 4 1 9 3 * Z ( 1 6 ) ) 47 T ( 1 2 ) = T ( 1 3 ) 50 T ( 1 3 ) = T ( 1 4 ) 51 T ( 1 4 ) = T ( 1 5 ) 52 T ( 1 5 ) = T ( 1 6 ) 53 T ( 1 7 ) = 3 4 . 3 6 3 + 4 4 . 1 9 1 * Z ( 1 7 ) 54 T ( 1 8 ) = 3 2 . 2 2 7 + Z ( 1 8 ) * ( 4 6 . 5 6 0 - . 9 2 4 5 6 * Z ( 1 8 ) ) 55 T ( 1 9 ) = 3 8 . 0 5 5 + Z ( 1 9 ) * ( 3 2 . 9 3 9 - . 0 4 0 9 8 * Z ( 1 9 ) ) 56 T' (20)=37. 1 0 6 + Z ( 2 0 ) * ( 3 3 . 2 5 8 - . 0 5 6 6 4 4 * Z ( 2 0 ) ) —• 57 T ( 2 1 ) = 3 5 . 7 1 2 + Z ( 2 1 ) * ( 3 3 . 2 4 8 - . 0 6 C 3 4 * Z ( 2 1 ) ) 60 T ( 2 2 ) = 3 6 . 6 1 1 + Z ( 2 2 ) * ( 3 3 . 2 0 3 - . 0 5 3 6 1 2 * Z ( 2 2 ) ) 61 T ( 2 3 ) = 3 6 . 8 4 2 + Z ( 2 3 ) * ( 3 3 . 1 0 9 - . 0 4 8 3 7 6 * Z ( 2 3 ) ) 62 T ( 2 4 ) = 3 6 . 9 8 2 + Z ( 2 4 ) * ( 3 3 . 1 0 1 - . 0 4 7 5 5 * Z ( 2 4 ) ) 2-14 C CORRECTION FOR LOSS THRU I N S U L A T I O N 63 ST=0. 64 DO 456 1=3,13 65 ST=ST+T<I) 66 456 CONTINUE 67 T A V = S T / 1 1 . 70 Q L 0 S S = 0 . 6 2 5 * T A V - 1 5 6 . 71 Q F = Q D I S - ( Q L 0 S S * 4 9 . 1 / 5 8 . 9 5 ) 72 QW=QF/ATEST 73 T C ( 1 ) = T ( 1 ) C CORRECTION FOR DROP THROUGH TU EE WALL 74 DO 157 1=2,15 75 T C O N ( I ) = 8 . 4 5 + 0 . 0 0 4 5 5 * T ( I ) 76 C O R ( I ) = Q D I S * 0 . 0 4 1 1 7 5 5 / ( 2 . * 3 . 1 4 1 6 * 1 . 9 4 0 * T C O N ( I ) ) 77 T C U )=T( I ) - C O R ( I ) ICO 157 CONTINUE 101 DO 751 1=1,11 102 TB( I ) = ( T ( 2 2 ) - T ( 1 9 ) ) / 5 8 . 9 5 * X ( I ) + T ( 1 9 )  103 K=2+I 104 Y ( I ) = T C ( K ) - T B ( I ) 105 751 CONTINUE 106 SY=0. 107 SX1=0. 110 SX2=0. 111 SX1Y=0. 112 SX2Y=0. 113 " SX1X2=0. 114 SSX1=0 . 115 , SSX2=0. 116 DO 47 1=1,N 117 SY=SY+Y(I) 120 SX1=SX1+X(I) 121 S S X I = S S X 1 + X ( I ) * X ( I ) 122 S S X 2 = S S X 2 + X ( I ) * * 4 123 SX1X2 = SX1X2 + X{I )**3 124 S X 1 Y = S X 1 Y + X ( I ) * Y ( I ) 125 S X 2 Y = S X 2 Y + X ( I ) * X { I ) * Y { I ) 126 47 CONTINUE 127 FN=N 130 SX2=SSX1 131 B = S S X l - ( ( S X 1 * * 2 ) / F N ) 132 C = S X 1 X 2 - S X 1 * S X 2 / F N 133 D = S X 1 Y - S X 1 * S Y / F N 134 F = S S X 2 - ( ( S X 2 * * 2 ) / F N ) 135 G = S X 2 Y - S X 2 * S Y / F N 136 B 2 = ( D * C - G * B ) / ( C * C - F * B ) 137 B 1 = ( D - B 2 # C ) / B 140 B 0 = { S Y - B 1 * S X 1 - B 2 * S X 2 ) / F N 141 AA=B2 142 BB=B1 143 CC=BO 144 V V 1 = 2 . * A A * 5 3 . 9 5 + B B 145 V V 2 = 2 . * A A * 4 . 8 5 + B B 146 D I S C = B B * * 2 - 4 . * A A * C C 2-15 f 147 IF ( D I S C . G T . 0 . 0 ) GO TO 373 150 R M D I S = S Q R T ( - 1 . * D I S C ) 151 A R E A 1 = 2 . / R M D I S * ( A T A N ( V V 1 / R M D I S ) ) 152 AREA2 = 2 . / R M D I S # ( A T A N ( V V 2 / R M D I S )) 153 GO TO 374 154 373 CONTINUE 155 R D I S = S Q R T ( D I S C ) . ' . . 156 VV3=ABS( { V V 1 - R D I S ) / {.VVl+RDIS ) ) 157 V V 4 = A B S { ( V V 2 - R D I S ) / ( V V 2 + R D I S ) ) 160 A R E A 1 = 1 . / R D I S * A L 0 G ! V V 3 ) 161 A R E A 2 = 1 . / R D I S * A L O G ( V V 4 ) 162 374 A R E A = A R E A 1 - A R E A 2 163 D T M = 5 8 . 9 5 / A R E A * ( T B ( 1 1 ) - T B ( 1 ) ) / { T ( 2 2 ) - T ( 1 9 ) ) 164 H=QW/DTM 165 R = 1 0 0 0 . / H 166 W R I T E ( 6 , 7 2 7 ) ( T C ( I ) , 1 = 1 1 1 5 ) , T ( 1 9 ) , T I 2 2 ) , H , R , T I M E 167 727 F O R M A T ( I X , 1 7 F 6 . 1 , 1 X , F 8 . I t l X t F 8 . 3 , I X , F 6 . 1 ) 170 484 CONTINUE 171 GO TO 149 172 234 STOP 173 END $ENTRY 3-1 APPENDIX 3: EXPERIMENTAL DATA T a b l e 3-1 c o n t a i n s t h e o p e r a t i n g c o n d i t i o n s f o r e a c h r u n and c a l c u l a t e d v a l u e s o f R e y n o l d s number, mass f l o w r a t e s , v e l o c i t y , h e a t g e n e r a t i o n , h e a t l o s s e s , h e a t f l u x and i n i t i a l h e a t t r a n s f e r c o e f f i c i e n t , t h e r m a l r e s i s t a n c e and a v e r a g e t u b e w a l l t e m p e r a t u r e . T a b l e 3 - I I l i s t s t h e i n s i d e w a l l t e m p e r a t u r e p r o f i l e s f o r e a c h s e t o f measurements f o r e a c h r u n , a l o n g w i t h t h e h e a t t r a n s f e r c o e f f i c i e n t s and r e s i s t a n c e s . Runs 5 t h r o u g h 13 a r e t h e p r e l i m i n a r y e x p e r i m e n t s done on the two t e r m i n a l t e s t s e c t i o n s . R e s u l t s f r o m t h e s e r u n s were no t u s e d i n t h e t h e s i s p r o p e r , e x c e p t f o r i n i t i a l f o u l i n g r a t e s f o r f u n s 6 and 7, w h i c h a p p e a r i n F i g u r e 17. Runs 14 t h r o u g h 20 were done on b l e n d s o f o i l A, r u n s 22 t h o u g h 33 on o i l B, and r u n s 34 t o 44 on t h e san d w a t e r s y s t e m . Run 46 was done on K r a f t l i q u o r . Run 21 was d i s c a r d e d b e c a u s e o f t r o u b l e a t t h e l o w e r e l e c t r i c a l t e r m i n a l w h i c h l e d t o o v e r h e a t i n g and shutdown. Run 43 was o n l y p a r t i a l l y done when t h e t e s t s e c t i o n was d e s t r o y e d , due ( i t i s t h o u g h t ) t o pump shutdown f o l l o w e d b y b u r n o u t . T e s t s e c t i o n I I was u s e d f o r r u n 44, t h e n i t was damaged d u r i n g t h e n e x t r u n . T e s t s e c t i o n I I I was u s e d f o r r u n 46. A l e g e n d f o r t h e h e a d i n g s o f T a b l e s 3-1 and 3 - I I i s g i v e n b e l o w . TB=average b u l k l i q u i d t e m p e r a t u r e , °F 3-2 VISK = "kinematic v i s c o s i t y at TB, centistokes RHO = s p e c i f i c gravity at TB RE = Reynolds number W = mass flow rate, lb/second UBULK = bulk ve l o c i t y , ft/second Q = heat generated, BTU/hr QLOSS = heat l o s t through insulation, BTU/hr QW = heat flux to l i q u i d , BTU/hr-ft 2 TWOUT = outside average wall temperature, °F TWIN = inside average wall temperature, °F DTM = A.T m HC = clean tube-heat transfer c o e f f i c i e n t , BTU/hr-ft 2 °F ^ 1000 RO = 1000/HC TWC = clean tube inside average wall temperature, °F DTMC = T m c TIN = l i q u i d i n l e t temperature, °F HM = mean heat transfer c o e f f i c i e n t , BTU/hr-ft °F 1000 R = 1000/HM TIME = time from start of run, hours Table 3-III i s a comparison of the clean tube o i l heat transfer c o e f f i c i e n t s with values predicted by the Sieder-Tate equation. 3-3 T a b l e 3-IV c o n t a i n s t h e p r e s s u r e d r o p d a t a f o r t h e f o u l i n g e x p e r i m e n t s , and t h e d e p o s i t t h i c k n e s s e s e s t i m a t e d from e q u a t i o n 32. D a t a f r o m a few r u n s a r e m i s s i n g b e c a u s e r a n g e s p r i n g s f o r t h e d i f f e r e n t i a l p r e s s u r e c e l l were n o t y e t a v a i l a b l e . I n T a b l e 3-IV, DELP = p r e s s u r e d r o p i n i n c h e s o f w a t e r , and X = d e p o s i t t h i c k n e s s i n m i l l i m e t e r s . T a b l e 3-V c o n t a i n s t h e d a t a on p a r t i c u l a t e l e v e l s o f t h e l i q u i d s . TABLE 3-1. OPERATING CONDITIONS AND CLEAN TUBE HEAT TRANSFER COEFFICIENTS RUN VI SCK RHO W UBULK RE 0 QLOSS ow TWOUT TWINS DTK HC 1000RO Oi 1 A "5. 2 2.0. 5 1.49 0. 794 0.3621 11.37 20263. 15543. 89. 88711. 393. 388.2 168.5 526. 6 1.8991 6. 2 21.3 1.49 0. 794 0.3621 11.37 20263. 15260. 89. 87093. 391. 387.2 166 .9 522. n 1.9159 7. 218.0 • 1.50 0.793 0.3621 11.38 20153. 12324. 61. 70391. 348. 344.5 124.8 563. 9 1.7733 8. 218.0 1.50 0. 793 0.3621 I 1 . 38 20153. 12 324. 63. 70382. 350. 347.0 131.0 537. 3 1.8612 9. 219.0 1.50. 0.793 0.1781 5.60 9914. 5942. 60 . "'33764. "346. 343.9 127.0 265. 8 3 .7623 10. 217.0 1. 50 0.793 0.5413 17.02 30125. 16112. 63. 92132. 350. 345.5 127.0 725. 7 1 .37 8 0 11. 220.0 1.54 0. 794 0.0922 ?.90 4993. 4176. 63. .23611. 350. 348.7 129.3 182. 6 5.4763 12. 219.3 1.50 0. 794 0.17R4 5.60 9951.1 6877. 71. 39070. 362. 360.5 142 .6 273. 5 .3.6562 13. 216.0 1.52 0. 794 0.1781 5.59 9768.1 4216. 31. 24025. 300.. 298.5 85.9 2 79. 7 3 .5747 14. 215.8 1. 52 0.794 0.1784 5.60 9787. 4180. 31. 23815. 300. 298.8 32.5 288. 8 3 .46 24 15. 215.3 1 .55 0. 795 0.54^2 17.04 29200. " 10578." 29. 60557. ?96. 29P.6 78. 1 775. 8 1 . ?G90 16. 214.4 1.57 0.796 0.5421 16.97 28699. 10587. 28. 60615. 294. 291.4 77.1 7S6. 1 1.2721 17. 216.0 1.55 0. 796 0.3123 9.77 16746. 6948. 31. 3 9709. 299-. 29^.3 81.9 485. 0 2.0617 18. 215.6 1.58 0.795 0.31?4 9.80 16468. 6948. 30. 39713. 298. 296.4 81.2 439. 0 2 . 04 5 1 19. 214.5 1. 55 0. 794 0.77P4 24.44 41874. 1392 2. 30. 79751 .. 297. 293.5 78 .9 1010. 3 0.9898 Oil B 20. 215.3 1 .58 0.795 0.77^1 24.43 41061. 13922. 29. 7^758. 295. 291.4 76. 1 1048. 3 0.9539 22. 216.4 1 .49 0. 79 5 0. 1503 4.72 8185. 3744.' 31. 21314. 299. 297.6 82 .2 259. 3 3. 8564 23. 216.0 1.49 0.795 0.1503 4.71 7841. 3744. 31. 21312. 299. 29?.2 8 3 . 0 256. 8 3 .8937 24. 216.3 1 .49 0.793 0.?4?4 7.62 13575. 5541. 30. 31636. 298. 296.6 -81 .2 389. 5 2.5672 25. 222.0 1.41 0.793 0.24'5 7.62 14356. 12048. 94. 68624. 400. 396.6 176 .4 389. u 2.5707 26. 217.0 1.46 0.794 0.2424 7.61 13845. 7654. 49. 43655. 329. 32* .6 I'lO .7 394. 2 2.5369 27. 221.0 1.42 0. 791 0.24 21 7.63 14322. 10225. 78. 58252. 374. 37!.4 151.5 384. 6 2.6002 28. 219.0 1.44 0.79 1 0.2421 7.63 14122. 8703. 64. 49596. 351. 348.8 131 . 1 378. 3 2.6435 29. 21 7.0 1.43 0.79? 0.4770 15.02 27883. 15364. 63. 87838. 350. 34 5.4 129 .6 677. 8 1.47 54 30. 218.0 1.40 0. 792 0.17 78 5.60 10617. 6681. 62. 3 799 7. 348. 346.6 129. 1 294. 2 3.39 8 8 31. 223.5 1.36 0.789 0.2419 7.64 " 14968. 12166. 48. 69281. 406. 402.7 131.0 382. 8 2.6124 32. 220-2 1.39 0. 790 0.2419 7.63 14581. 8763. 63. 49940. 351. 348.6 1 29 . 7 385. I 2.5970 33. 219.2 1 .40 0.790 0.24 19 7.63 14481. 8746. 62. 49848. 349. 34f .8 128 .9 386. 8 2.58 55 Wftter 34. 146.0 0.45 0.962 0.1920 4.87 28570. 7532. 0. 43236. 176. 173.7 26 .9 1604. 4 0.62 3 3 35. 144. 5 0.46 0.982 0.3866 . 9.82 56665. 12539. 0. . 71979. 173. 169.6 28 . 1 2 5 59. 1 0.3908 36. 142. 2 0.47 C.983 0 .54 c 7 13.84 78534. 16633. 0. 95484. 174. 169.3 27.9 3426. 6 0.2918 37. 144.7 0.46 0.98? 0.3105 7.88 45809. 10818. 0. 62102. 175. 17?.2 27 .9 2224. 8 0.4495 38. 143. 1 0.46 0. 982 0.1722 4.37 24961. 6928. 0. 39773. 172. 17C.0 27.4 1451. 3 0.6890 39. 144.7 . 0.46 0.98? 0.2613 6.64 38388. 9785. 0. 56170. 174. 171.4 27.. 1 2071. 5 0.48 27 40. 144.3 0,46 0.98 2 0 . 1 4 70 3.73 21547." 6326, 0. 36313. 173. 171.5 27 .0 1343. 0 0.7446 41 . 149.1 0.44 0. 980 0. 1722 4.38 26430. 12718. 0. 73010. 200. 196.3 48 .2 1516. 2 0.6595 42. 143.5 0.46 0.98? 0.3870 9.82 56218. 12207. 0. 70072. 174. 170.2 27. 1 2588. 1 0.38 64 44. 144. 7 0.46 Q.9S2 0.3105 7.88 45809. lOTSS. 0. 61657. 1.70. 166.0 23.5 2626. 0.38 07 Kraft 46. 155.2 0.76 1.080 0.35S8 8.31 28909. 6500. 0. 41262. 175. 172.3 19.4 212 8 . 6 0.4700 Liquor 3-5 TABLE 3- I I . INSIDE WALL TEMPERATURES AND FOULING DATA RUN 5. M 0.362 RE 20263. OW 88711. TWC .388.2 OTMC 168.5 T(l) TI21 T(3) TI4) T<5> TI6) TI7) TIB) T (91 TI10) T(U) TI12J T1131 THAI TU5I TIN TOUT HM 1000 R 2 6 6 . 5 206.0 208.0 207.3 207.3 206.1 2 3 5 . 7 315.6 316.7 324.9 335.5 338.5 375.3 374.0 373. 7 381.9 406.0 413.4 396.1 397.1 398.8 415.0 442.2 450. 364.2 384.9 3B5.4 401.9 430.7 440.0 3 7 3 . 6 373.3 373.0 369.7 422.0 433.4 0 3'9"l'; C 391, 0 393. 5 413. 0 446. 7 456, 5 460. 8 399, 2 404. 0 426 2 463 7 475 6 392. 9 391, 0 393. 5 417, 2 456. 1 467. 8.391.1 8 391.6 2 395.4 0 425.6 1 467.5 9 480.4 3*9.4 399.5 404.0 433.2 474.8 488. 551.6 363.0 384.0 401.7 424.1 429, 1 208.7 7 210.6 4_210.8 1 210.2 8 209.9 7 209.9 232.3 234.6 234.9 232.4 " 231.9 231.9 526.6 533.2 528.9 468.5 394.6 376.6 1.899 1.676 2.134, 2.534 2.655 0.0 0.6 !•>_ 3.1 4.6 512 T o r 205.7 206.5 205.0 205.4 384.7 384384.8 384, 385.3 384399.5 401. 426.5 43643*.B 445 444.2 456 450.8 465 457.0 473 464.8 483 469.5 489. B 467 .6 4 74. 0 482. 5 492, 0 497. 8 487. T 497, 3 505. 0 515. 1 521. 0 495.5 2 507.Z 6 515.5 4 528.1 8 535.6 504.7 516.4 525.8 539. 1 547.8 438.3 442.4 445.9 446.6 449.9 2 . 8 l B 5 T 7 -2.910 6.2 2.99*_ 6.8 " 3^100 "" " 7.3" 3.171 7.9 342.3 345.0 347.3 349.5 352,3 423.2 429.7 435.3 443.4 448.3 459.6 466.5 471.5 480.4 486.1 450.2 456. 1 462.8 471.6 476.1 445.0 452.8 461.0 470.1 475.2 8 48) 0 491, 1 499 5 511, 4 517. 1 209.3 1 209.9 7 210.2 4 209.1 4 206.9 231.3 231.5 231.'3 230.3 229.7 354.9 343. 7 334. 0_ 322.6 315.4 TWC 367.2 DTMC 166.9 TH) TI2) T<3) T(41 T!5) T16) TIT) Tl a 1 T(9) T110) T(ll) T(t2) T(13> TI14) T115) TIN TOUT HM 1000 R 206.9 314.5 207.7 314.8 208.0 315.7 208.3 316,8 207.7 317.1 205.7 321.4 206.8 329.2 206.5 333.B 369.4 394.8 382.0 372.4 385.1 383.1 392.3 397.7 393.4 390.1 370.3 396.2 383.7 373.2 386. 1 384.C 392.6 398.1 393.2 389.8 371.3 396.5 383.1 373.5 385.9 383.1 393.2 397.9 392.9 391.4 371.0 396.2 383.3 372.2 386.1 383.6 394.0 398.7 392.7 392.4 369.9 395.2 363.3 372.0 385.8 383.4 394.9 399.3 393.2 394.5 374.1 398.2 384.1 378.2' 391.9 392.3 405.2 414.8 409.2 387.8 412.1 406.1 397.4 406.9 411.2 423.5 437.2 433.3 405.7 431.1 426.2 419.4 <.25.3 434.7 445.6 461.2 458.6 417.8 443.6 472.Q 39 3 382.4 245.7 210.0 232.5 522.0 1.916 399.7 383.1 246.6 210.5 233.0 521.5 _1.917_ 4002 383.1 247.1 210.3 232.9 ~'526.6~ 1.921 401.5 384.3 245.8 210.4 233.1 520.2 1.923 404.  387.4 244.5 209.6 232.3 516.5 1.936 430.0 403.8 241.8 208.2 229.8 457.7 417.7 241.9 210.5 231.6 487. 1 432.9 239.8_207.9 228.7_ 477.8 435.2 3B5.7 2.693 2.298 2.593 TWC 344.2 Till T12) T(3I T(4) TI5) T(6) T(7J T18) TI9) T(10> T(ll) ril2I TI13I TI14) TU5) TIN 206.1 289.3 331.4 350.0 206. 206. 205, 207. 207. 289.' 287.' 290. 7 290.1 1 ,290.' 1 291.! 3 3 1 . 0 330.9 332.7 331.6 332.0 333.3 5^ 346.1 350.8 352.2 350.7 351. 342.9 341.7 : . 0 352.1 348.9 347.1 354. 350. 352. 353. 4 352. 355. 7 345, 6 344. 3 347. 6 349. 3 348. 4 351. ,8 351. .3 353.' ,7 355-' ,0 356.1 .1 358.! .7 365.' ! 211.8 228.9 20fl\9 226.1 208.9 225.4 210.5 227.7 209.1 226.2 210.8 227.B 210.3 227. D TIME 0.0 ~T5T 205. 205, 206, 206. 206, 5 292. 7 292, 8 29?, 9 291. 9 290. 1 290. 338.7 330.0 341.0 332.4 341.0 333.0 340.2 331.5 342.4 333.9 343.7 3 3 3 . 2 349.0 338.1 349.2 337.5 348.5 335.7 349.0 336.4 350.0 336.6 341.0 341.0 343.5 344.9 343.1 346.3 5 345, 0 347, C 350. 1 351 7 355 7 359. 6 367. 6 369. 6 369, 9 368, 3 371 7 357. 8 364, 2 364. 4 365. 8 365, 2 367. 9 343 9 345 6 347 8 347 7 349 3 354 340.5 344.8 347.4 351.2 357. 9 365.1 6 374.7 9 375.7 6 375.3 375.7 37B.4 243.2 243.2 244. 1 242.8 242.8 243.2 242.6 243 242.8 243.2 243.2 2 1 0 . f i 2 2 7 . 5 209.5 226.1 209.2 226.6 210.8 22B.3 209.5 226.1 209.7 226.2 559.4 557. B 547.4 555.8 ' 538.: 5 2 4 . 3 494.5 492.9 499,4 491.9 467.2 1.788 1.793 1.827 1.799 1.858 1.907 2.022 2.029 2.003 2.033 2.052 11.8 20.3 24.5 26.6 28.9 30.3 33.4 -2TT 206. 206. 205, 207. 205. 208. 208. 206. 206, 207, 334.5 9 337.3 2 338.1 5 337.6 9 336.6 9 337.4 ,5 339.3 ,3 341.9 ,8 344.8 ,7 345.3 ,7 343.1 ,7 345.4 3 346.8 3 348.5 .7 350.3 5 352.7 4 349.9 355.2 360.5 359.9 359.5 360.5 360.8 3 6 3 T T 368.8 372.0 373.0 372.6 374.4 377.1 380.5 363.0 366.7 384 3 5 3 . 0 339.4 356.9 342.4 359.6 345.6 •360.2 346.0 360.2 346.0 361.5 347.9 364.1 35019 366.9 354.4 366.9 355.4 372.0 360.7 366.9 357.9 349.8 356.1 355.1 354.2 355.6 355.4 3*5" 363. 1 366. 1 366.3 366.8 367.3 371.6 372.8 371.8 178.7 373.8 4 361 8 366 0 366 1 366 6 366 370 5 373, 7 3 79 2 382, 9 384, 7 385, 3 386, 0 392. 3 396, f 396, 8 403. 7 400, 1 361, 1 371, 5 373, 5 374 8 375, 9 379. 3 375 8 387. 8 390, 9 392. 392 397 2t0 .2 227.0 209.5 225.9 210.3 227 .1 ' 209.7 226.6 209.7 226..5 209.5 225.9 478.3 456.5 447.3 440.9 436.0 429.0 2.091 2.191 2.236 2.268 2.283 2.331 36.3 43.8 52.5 55.6 1 290 5 293 9 295 7 294 2 294 9 294 4 298. 0 298 9-298 300 299. 374. 0 381. 3 386. 1 387. 1 369. 3 391, 4 399. 1 405. 8 409. 417. 415. 5 37T 0 379 4 365. 7 337, 0 389. 7 393. 1 403. 2 416. 2 421. 7 432. 7 433 I 385. 6 397. 0 404.. 0 410. 6 414. 1 421. 4 0 3 . ; 416.' 423.! 430.1 435.' 444.' 376.5 389.4 393.1 396.7 398.3 399.4 243.2 243.2 235-1 234.7 233.6 233.3 6 436. 0 455, 9 464. 4 477. 6 481 3 460. 3 488. 2 497. 2 513. 0 517. 1 406.0 4 418.6 0 416.7 2 423.1 5 422.1 233.6 233.6 233.3 232.6 232.2 209.5 226.1 210.2 226-8 209.9 226.2 210.3 226.T 210.0 225.7 210.3 226.2 209.3 225.0 210.5 225-_B_ 210.5 226.8 413.8 401.0 394.6 380.2 383.6 377. 366.2 _ 356-B 346.7 2.416 2.494 2.534 2.630 2.607 2.649 .2.716 _2iB03_ 2.884 59.3 66.1 69.9 73.5 75.9 79.7 83. 6 206. 207, 206, 206, 1 298, 5 300. 7 299. 3 301. 351.0 8 354.1 4 353.1 7 357.6 384.5 385.2 390.5 393.6 369.6 359.6 369.4 360.9 373.8 366.6 378.6 370.6 374.6 376.5 378.5 380.6 1 403, 5 406. 0 412, 1 418. 1 422. 4 426. 8 <>3a. 4 446. 5 443. 7 452. 5 466. 9 476. 2 496. 7 508. 2 528. 5 543. 537, 550. 5 573, 7 592, 2 429.4 9 431.7 5 439.8 0 447.5 231.B 231.0 231.4 231.8 HUN 8. W 0.362 KE 20153. OH 70382. TWC 347.0 DTMC 131.0 fill T<2) T(3) T(4) TI5) T16) TI7I U8) T(9) TUOJ Till) 7(12) T ( 131 TI 14) T(15) TIN TOUT " T o ? ; 207. 206. 206. 208. 207. ~2OT: 207. 206. 206. 207. 207. 207. 207. 206. 205. 0 284. 1 288. 3 284. 9 286. 0 269.1 1 286. 7 287. 6 2B7.i 7 286. 1 2B7.< 3 267. 6 287. 7 286. 5 287. 3 266. I 267. 7 286.' . 326.0 330.7 325.6 329.2 331.3 329.2 330.4 330.7 331.3 332.7 .331.8 331.6 331.3 332.7 332.3 333.8 334.1 347.1 350.8 348.9 349.3 351.6 349.6 352.0 351.7 352. I 353.3 353.5 354.2 354.? 356.5 357.1 359.4 359.1 338.7 34?. 7 341.7 341.8 343.4 342.4 344.7 344. 7 345.2 347.0 347.3 348. 1 He.4 351.0 351.2 352.0 351.5 328.0 332.4 329.4 330.0 332.2 330.9 332.4 332.2 332.3 332.4 333.2 333.6 334.5 336.4 335. 3 335.7 336.6 341.0 345.6 342.6 344. 1 345.9 344.3 347.3 347.2 346.8 346.7 350.2 352.2 353.3 355.4 354.7 355.1 356.3 340. 1 344.7 342.? 342.3 344.9 342.6 344.2 344.fi 345.0 345.4 346.2 347.2 346.9 350.6 350.3 351.0 352.7 353.6 359.6 355.5 356.6 359.7 35B.7 365.5 367.3 367.0 369.0 371.5 373.2 375.9 360.6 382.4 382.1 384.0 356.1 362.0 358.8 360.0 363.1 3 62.2 368.9 373.2 373.0 375.9 376.8 379.6 393.3 368.6 390.5 390.5 393.1 355.0 347. 361.3 354, 357.1 346. 358.4 349. 361.6 354, 361.6 352. 368.9 355. 372.5 357. 372.5 356. 375.7 357, 378.3 356, 363.4 358. 386.5 354 . 393.7 364. 396.4 363, 396.6 360, 399.5 .363. 8 383. 1 391. 4 388. 2 390, 0 394. 2 394. 3 403. 0-407. 3 407. 5 411. 4 412. 4 417. 9 420, 8 430. 0 429, 9 429, 2 431. 6 346. 3 352, 1 350. 0 352. 7 356. 9 357. B" 366. 369 369 372 372 375 4 230, 4 233. 3 232. 3 232. 6 234. 3 232. 2 233. .5 37B, 2 386, .8 384, .5 384, 8 385. .1 80 5 233 4 233 1 232 6 232 9 232 4 234 9 232 9 233 5 233 7 208, 3 211, 0 209. 9 210, 0 210. 7 209. 3 210. 1 211, 3 210. 2 210. 5 210. 9 210, .9 209. ,2 211, .9 209, ,0 209, .0 209, 4 224.8 0 226.3 l_225.7 1 227.3 9 227.5 9 226.4 8 tir;o~ 2 227.7 2 227.0 0 226.5 2 226.7 7 227.4 6 226.4 1 227.6 7 226.2 3 225.9 2 226.0 HM 537.3 528.0 533.2 533.2 523.8 524.9 511.9 508.8 505.5 496.4 494.0 490.0 480.9 •473.4 467. 5 465.2 460.9 1000 R 1.861 1.894 1.675 1.876 1.909 1.905 1.953 1.965 1.976 2.015 2.024 2.041 2.079 2.112 2.139. 2.150! 2.170 0 . 0 1.9 7.4 20.B 23.6 37.7 4 4 . 9 TWC 343.9 DTMC. 127.0.„ TIU TI2) T < 3 > TI41 TI5) TI6) TI7) T(8) T(9) TUO) Till) TU2] TI13) T(l'4) T (15) TIN 205.4 205.8 205.4 205.7 204.2 2 6 6 . 5 205.4 206.2 205.8 205.0 205.7 5 6 6 . 5 205.9 206.1 204.8 206.5 205.8 206.9 205.4 206.5 206.5 206.1 264.2 204.6 205.7 20S, 205, 205. 8 318. 6 318. B 318. 9 316. 9 317, 7 3 2 0 . 5 318. 8 319. 6 319. 5 320. 9 320. 1 3 2 2 . 3 321. 5 322. 9 321. 6 322. 6 321. 3 320, 2 320. 6 321, 8 320, .4 319, .7 320, 9 321, 9 321, 0 321, 1 322. 321 8 337.! 2 336.: 0 334.' 4 337.: 4'338.' 2 334. 7 338. .4 337, .9 338. ,3 339, 6 340. 6 341. 0 340. 4 340. 0 342. 0 345, 5 347. ,7 347, ,5 348. ,8 355. .3 356. ,9 357. .3 356, ,5 35B, .8 360. 360, 364, 363, 338. 336. 334. 337. 337, 7 340. 1 338. 8 338. 6 339. 0 340, 0 340. 6 342. 1 340. 1 343. 6 349. 6 355. 2 359. 2 362. 4 363. 1 379. 9 384. 2 386. 5 389. 390. 394. 395. 399. 400. 7 331.! 7 3 30.] 5 330.1 1 332.' 6 331.E 2 3 3 3 . ^ 6 333.J 5 332.< 7 335.( 5 335.' 1 334.' 6 3 3 7 . ! 6 336.< 6 343.! 1 349.3 7 361.1 2 366.t .0 372.1 ,8 374.' .2 394.: ,7 404.' 5 407.1 206.1 265.7 322.1 364.7 400, i 402 405 409 1 Ml 416 418 ,1 .341. 3 340. 4 341. 5 343. 7 342. 2 3 4 5 . 4 344. .7 344. 1 345. 4 346. .6 346. 4 346. 8 347. 7 337. 5 365. 1 381. 5 391. .9 399. .0 403. ,9 431, .2 449, •6 453. F T T T 8 413 7 419 7 421 9 427 1 429  5 427.4 418.B 485 7 4 5 8 . 8 462, 4 469, 3 473. 8 461, 0 484, 9 350. 4 349. 5 349. 6 351. * 350. 6 352. 3 350. 7 350. 7 351. 6 352. 3 352. 6 354. S 353. 5 355. 0 365. 2 376. 4 385. ,3 390. .9 395. 8 425, ,6 444, 2 448. 3 453, .9 456. , * 464, 1 468. ,7 475, •'6 477. ,4 477, 352. 350.1 351. : 352.1 352. ! .7 353.' ,6 351.' ,5 352.1 ,7 352.1 ,3 353. ,6 354.1 0 355.i 6 354. 6 355. 0" 363. 6 377. 2 386. .3 395. 3 401. ,7 437, ,5 458, .4 465, ,9 4 7 1 , . f l 476. .9 483. .5 488, .2 496, .6 499, .8 560, 352. 351. 351. 353. 354. 356. 354. 356. 357. 357. 357. 6 360. 6 359, 6 372. 1 365. 6 409. 8 423. .5 434. 2 443. 7 462, 4 504, ,1 '512, ,4 526 ,3 525 2 534 ,0 541 .4 551 .2 552 .6 354. 2 353.1 .4 354.' , 1 359., 5 361. 5 367.1 9 366.: 1 366.: ,7 372. ,6 373, .1 373, 4 380. 9 379. .3 413. 9 432, 0 458. .6 472. .8 462. .1 489, .0 526, .4 548, 557. 362.6 362.0 362.0 367.8 370.1 0 373.9 2 372.3 3 373:9 2 376.5 5 378.7 8 379.4 1 363.6 3 383.3 3 414.0 6~429,9 2 454.9 0 465.1 ,4 473.2 5 478.7 .3 505.7 ,4 516.6 0 524.5 330.7 330. 2_ 329.2 333.3 332.9 335.9 333.6 332. 8_ 333.2 334.9 334.6 338.5 337.7 343.1 345.5" 354.6 357.2 360.0 361.6 370.5 372.5 373.6 0 209. 0 210. ,3 209. ,6 206. .1 207. ,4 2 1 6 . ,1 209. 5 210. 6 209. ,6 209, ,5 209. 6 210. 6 211. > 209. .2 209. 4 210. 5 210. ,1 210. .1 210. .0 209, .3 210. 5 209. .1 567.9 533.3 376.6 232.6 216, 7 569.9 537.9 375.9 232.6 210. 9 579.2 544.5 377.8 232.6.210, 5 584.7 548.7 377.1 233.2 210. 4 395.0 556.9 379.4 232.6 211, 2 597.2 557.2 379.5 232.0 20?. 7 599.8 539.0 380.5 233.1 211, TDUT 5 227.0 .5 227.3 2 225-7 " .9 225.4 9 224.4 ,6 2 2 7 . 4 ,3 226.1 5 227.3_ ,9 226.8 .6 226.8 ,6 226.6 ,2 22>.l"-,2 227.4 ,9^226.7 ,1 225.6 " 0 226.8 2 227.3 .4 227.6 ,5 227.1 ,4 225.8 .2 226.7 .5 225.7 ,5 '226^7 .1 226.7 • 2_22_6.7 ,7 226.7 .1 227.7 •2 223.8 .6 2 2 V . 1 HM 265.8 270. 2_ 267.1 261.9 259.1 260.1 260.2 -2*1.3-257.3 253. B 254. '9 231.5 254i4 _238.3 ' 224.6 207.8 199.6 193.5. 189.3 166.7 159.0 155.a "153.6 ' 151.3 _147.B 146.4 142.9 141. 1000 R TIME 3.762 3.700 3.744 3.819 3.860 3.644 3.844' -3.827_ 3.687 3.909 . 3.922 3.976 3.931 4.193 4.465 4.812 i . o i t .5.167 5.263 5.999 6.290 6.419 "6.509 6.609 6.765 6.833 6.996' 7.089 6.1 13.5 16.7 19.4 23.6 26.1 29.6 29.6 33.2 36.5 38.7 >5.2. 63.1 85.6 . 9 7 . S 69.6 96.1 101.9 104.1 1 4 1 . 6 7 . 6 6 1 1 0 4 . 6 3 RUN 10. W 0.541 RE 30125. OH 92132. TWC 3*5.5 DTMC 127.0 Til) T12) Tl 3) TC) T(5) T(6) T(7) TI8 » T(9) Tt 10) T C11 > T( 12) T(13) Tl 14) Tl 15) TIN TOUT HM 1000 R TIME 206.4 206.2 207.3 296.0 295.6 295.1 330.6 330.2 330. 1 354.A 353.3 354.0 340.5 340.3 340.2 325.8 325.9 325.1 344.3 343.5 343.5 340.4 340.1 340. ? 352.4 352.6 353.2 351.0 350.1 349.1 346.6 346.5 346.5 351.2 351.7 351. 1 363.5 363.2 363.0 338.4 339.1 338.6 233.2 23?. 1 232.2 210.8 21Q.5 2L0. 7 227.2 226.5 226.3 725.6 724.3 725.0 1.378 1.361 1.379 0.0 0.9 2.4 209.2 295.8 329.8 354.0 340.7 325.4 342.3 341.0 354.2 349.8 346.0 351.1 362.7 337.5 231.7 210.7 226.1 723.8 1.382 7.1 207.3 295.4 328.4 354.4 340.2 325.0 343.7 341.7 355.4 350.4 346.9 351.5 362.8 338.6 232.0 210.1 225.7 718.6 1.392 9.9 208.5 294.7 329.7 353.6 339.6 325.6 343.3 341.f 355.3 349.7 346.0 350.8 3&3.2 337.6 232.1 210.3 725.3 719.6 1.390 17.7 206.5 294.0 328.6 353.1 .338.8 324.7 343.3 340.'8 355.4 349.3 346.2 350.2 362.5 337.2 231.4 208.6 224.3 714.5 1.400 20.9 207.2 295.3 330.6 353.7 339.7 325.8 344.5 343.0 357.4 350.9 348.2 351.8 364.3 339.3 231.9 209.8 225.1 711.3 1.406 23.9 207.6 293.B 328. 7 352. 3 330.6 325.1 343.1 341.3 355.4 549. 1 346.3 549.5 362.8 338.0 236.2 209.5 224.8 718.7 VTW[ 36.4 207.3 294.3 329.2 353.1 338.5 325.1 343.2 341.? 355.9 349.7 346.4 350.4 362.9 338.1 230.7 209.6 224.8 716.7 1.395 29.9 207. 3 293.B 329.1 352.4 33B.B 324.7 343.3 342.1 356.3 349.6 346.3 351.0 362.8 338.0 231.7 210.7 226.5 724.5 1.380 33.9 208.0 294.4 329.4 353. 1 330.8 324.9 342.7 341.8 356.4—349.0 345.9 350.2 362.5 337.7 231.7 210.5 226.0 723.7 1.3B2 41.2 209.4 295.5 329.6 353.5 339.2 325.4 343.5 342.2 356.7 350.0 347.1 351.1 363.4 339.1 231.8 210.3 225.7 718.4 1.392 45.2 206.5 294.7 329.9 353.3 338.7 325.6 343.8 342.'- 356.8 350. 1 347.5 351.6 363.7 339.4 232.5 210.0 225.3 715.4 1.39B 49.2 207.6 294.8 330.3 353.9 330. 7 325.0 343.5 343.4 357.9 351.0 347. <) 351.8 364.1 '339. "6-2"32.2 2t0.3 225.7 715.3 1 .398 5275"" 207.6 294.0 328.8 353.2 340.5 325.2 343.1 343.3 358.1 350.3 347.6 351.3 364.1 338.3 231.9 711.1 226.6 720.9 1.387 57.5 20B.0 295.6 330.6 353.2 340.0 324.4 344.9 343.7 358.? 351.0 348.7 351.3 363.7 338;9' 230.8 209.4 224.5 708.2 1.412 64.9 207.7 295.1 330.2 353.7 339.7 325.2 344.3 343.1 358.1 351.0 348.3 352.0 364.2 339.4 231.4 209.B 225.1 711.0 1.407 69.1 208.6 294.9 330.6 353.9 339.5 325.4 344.4 343.3 357.4 350.2 347.9 351.1 363.5 339.8 231.3 209.7 224.8 708.9 1.411 73.1 V±*ml- ?!9,Z 3?7.6 33B. 1 324.1 342.8 341.1 357. 1 349.6 347. 3 350.5 362.5 338.0 230.7 208.6 223.B 708.6. 1.411 77.3 205.7 293.3 329.7 353.0 339.0 323.6 343.8 343.1 356.3 349.6 346.4 350.1 363.5 339.4 229.9 208.8 224.2 709.5 '• I'.Vto Bl.9 205.9 293.1 329.fl 353.0 339.7 324.5 343.4 343.? 357.4 .349.8 347.0 350.8 364.0 339.5 230.5 209.4 224.9 710.6 1.407 B9.1 206.7 293.9 329.7 354.4 339.6 325.1 343.8 343.4 358.8 350.8 347.8 351.5 364.4 339.5 230.7 209.0 225.0 706.5 1.412 93.6 207.6 293.9 329.8 353.3 330.4 324.1 343.1 342.5 357.5 349.7 347.3 350.4 363.2 339.2 230.9 209.7 224.9 713.0 208.0 294.7 330.5 354.6 340.0 325.8 344.8 343.6 358.2 349.6 348.7 352.5 365.0 340.4 231.7 210.2 225.4 709.2 . 402 1.410 103. 106. £UO.U * T t . ( J . J J i J t . O 3 1 V . <J 9£ 1 • O 3*t*».d J t j . O J f f . O 3 7 1 . 3 3*t-VJ . £31*1 £ 1 M . I d d 3 . *t I VI t £ 1 • <t 1 U 208.0 294.7 329.9 353.2 338.5 324.5 343.5 342.9 357.6 350.1 347.7 351.2 363.7 339.5 231.2 2p9.9 225.3 712.8 1.403  206.7 294.2 330.2 354.0 339.4 325.3 344.5 343.3 358.7 350.3 348.7 351.9 365.2 340.9 236.9 209.9 22S.2 708.2 f".4'12 TTTTv 207.7 294.3 330.3 353.1'338.6 324.1 343.5 342.9 358.5 349.7 348.1 351.2 364.2 340.2 230.7 209.4 224.7 709.2 1.410 116.9 208.0 294.3 330.3 353.8 339.8 325.0 344.5 343.6 359.7 351.9 350.1 352.9 366.0 341.5 232.5 210.7 225.9 711.4 1.406 120.4 "RUN TT. V) 0.092 RE. 4993. QW 23611. fwC 348.7 DTMC 129.3 Till T12) T13) T14) T15) T16) T(7) T(8) T(9) T I 10} Till) TI 12) T113) T114) TU5) TIN TUUT HM 1000 R 202.7 261.9 330.4 351.9 359.7 347.2347.7 344.n 346.9 345.9 348.8 353.4 359.5 331.6 245.6 209.3 230.1 102.6 5.476 203.4 262.4 330.4 352.1 359.7 348.2 347.9 344.0 348.9346.6 348.5 353.5 359.6 333.2 246.7 211.4 232.2 185.0 5.404 202.9 263.3 333.3 354.4 362.6 340.9 348.7 344.3 349.6 340.0 349.0 354.3 360.5 331.5 246.3 210.1 231.4 181.9 5.49B 202.5 261.0 331.3 353.7 360.8 347.9 348.9 344.*? 347.8 346.6 348.3 354.1 360.6 332.9 246.0 209.5 230.7 182.1 5.491 202.7 261.4 331.8 354.2 359.7'346.8 348.6 344.9 347.1 348.2 348.7 354.1 361.4 333.8 246.7 210.8 232.2 1B4.0 5.435 201.0 262.0 330.7 354.0 359.5 346.5 347.9 343.4 347.1 345.9 348.3 354.2 359.9 332.7 246.3 209.6 230.B 183.2 5.460 203.4 262.4 331.5 353.3 35B.7 346.4 346.8 343. P 347.1 347.0 346.2 353.1 360.6 332. 2 247.3 210.1 231.1 183.9 5.437 9.7 203.3 262.9 331.8 352.6 359.9 346.8 347.2 343.7 347.1 346.6 347.9 354.5 361. 3 332. 4 247.3 210.1 231.7 184.0 5.435 12.8 202.7 262.2 332.5 353.0 359.7 346.9 346.8 344. 7 347.4 346.7 348.5 355. 1 362. 7 332, .7 747.6 210.2 231.2 183.2 5.459 20.9 201.8 262.4 333.0 354.9 361.3 346.1 347.5 344.5 346.9 346.6 348.9 355.0 362. 5 333. 8 247. 1 210.3 231.6 183.2 5.458 24.7 201.9 263.0 333.3 355.a 361.5 345.8 347.6 344. •» 3 47.6 347.3 349.2 355.2 363. 0 334.6 247.7 210.0 231.6 182.5 5.478 27.4 201.7 262.6 333.2 356.3 .360.8 345.8 347.9 344. 1 346.8 346.3 348.9 356.0 363. a 335, .7 247.4 209.2 231 .3 182.0 5.495 30.6 3.4 264.1 3.5 357.3 361.9 346.8 347.5 3 .3." 347.9 347.0 34 .8 357.2 363.7 35.4 247.6 209.9 231.7 181.9 5.498 4.2 202.5 264.4 334.1 357.2 360.B 347.5 347.5 344.7 348.2 347.4 349.8 357.6 364.5 336.4 247.7 209.5 231.4 181.0 5.524 37.8 203.3 264.4 335.0 356.8 361.1 347.2 347.8 345.5 348.4 347.4 349.6 357.1 364.4 335.0 247.4.208.9 230.2 179.6 5.568 202.7 263.1 333.2 356.3.361.5 347.4 347.3 345.7 347.5 347.0 350.2 356.6 364.0 333.6 247.4 209.5 231.0 161.0 5.524 180.9 5.528 _ . . 181.7 5.504 204. 203. 203. 202. 203. . . 203. 1 264.0 333.4 357.1 362.2 348.2 348. . :  203.8 264.2 334.3 357.0 361.8 348.6 348.2 344.347.8 347.3 349.6 357.2 364.0 333.8 247.8 210.9 237.4 182.6 5.476 95.9 202.1 263.3 333.6 357.2 360.4 348.2 348.6 344.1 346.1 347.7 350.2 356.2 363.3 337.7 247.0 210.3 231.9 182.4 5.482 102.6 203.8 263.7 333.2 358.2 359.7 348.6 347.9 344.8 348.5 348.0 348.5 357.3 362.9 333.3 247.5 211.0 232.5 1B3.0 5.465 108.1 204.2 265.1 334.8 358.2 359.5 348.6 347.9 344.1 347.5 348.0 350.5 356.2 363.3 333.3 247.4 211.1 232.9 1B3.3 5.455 112.4 206.5 342.8 452.9 444.5 421.7 401.7 416.5 416.B 418. 1 439.4 451.0 480.2 455.4 420.8 206.6 208.6 259.1 267.7 3.735 123.2 207.3 343.0 460.9 451.0 424.1 401.7 415.9 417.5 419.0 441.9 452.9 484.3 466.0 423.2 288.4 210.4 260.1 266.1 3.758 124.8 205. 207. 205 205 204 205.. ..^.^ ^ w . ^ J ^ , , J — ^ . . . . . . . . . . . . . ~ . - c 206. 1 278.3 337.2"358-9 350.1 348.6 354.9 352.9 356.9 354.7 355.5 360.9 369.5 343.4 252.0 "209^V 22.9 285.6 3.502 205.7 278.2 337.8 359.0 357.9 349.7 356.1 353.6 356.5 355.5 356.7 362.L 371.0 344.7 252.3 209.9 229.2 284.5 3.515 160.3 206.9 279.5 338.8 360.3 358.6 351.4 356.2 355.0 358.6 357.0 357.3 362.5 370.6 344.5 252.0 210-1 229.6 203.1 3.532 167.3 206.9 279.3 338.1 359.2 357.9 349.7 355.2 353.£ 35B.1 356.1 357.2 361.4 370.3 344.2 252.5 210";5 229.5 285.1 3.507 170.1 RUN 12. W 0.178 RE 9951. OH 39070. TWC 360.5 OTMC 142.8 Ttl), T12) T13) TI4) T15) T[6) T17) TtB) TI9) TUOI Till! T(12) T113) T(14> T1 15) TIN TOUT HM 1000 R TIME 205.7 276.0 334.3 357.5 357.7 351.4 361.5 362.3 369.8 366,2 365.6 365.4 374.3 351.2 331.7 209.6 228.9 273.5 3.656 0.0 205.8 277.9 336.5 357.8 357.2 550.9 361.2 362.3 369.6 366.8 365.6 366.6 376.7 356.1 266.4 209.4 228.8 272.5 3.669 1.3 206.3 278.4 337.8 358.9 358.6 352.B 362.2 362.1 369.4 367.3 364.9 367.fl 377.8 356.3 267.8 210.6 230.B 274.4 3.644 3.9 207.3 279.5 337.B 359.0 35T.6 351.7 360.8 362.3 405.1 367.0 368.0 360.9 378.B 358.8 268.8 209.B 230.6 265.B 3.762 7.7 206.0 279.8 342.6 363.0 361.1 358.0 363.3 367.g 379.8 378.0 380.3 387.5 411.4 367.8 265.9 210.3 230.1 255.3 3.917 U.7 276.1 1st I? 395:i 412.1 427> 40!*.8 452.6 462.7 492.1 4I3U 519.8 541.9 407.1 2S5,V 265.9 22H.2 TCTTl 57977 TBTTT 207.3 277.5 350.7 410.1 431.8 452.5 420.3 478.fi 484.9 515.4 514.4 525.8 554.fl 416.9 258.4 210.3 229.4 155.3 6.440 19.9 205.4 275.3 358.4 418.3 441.8 463.5 427.8 491.4 493.0 513.3 527.5 533.2 570.7 422.2 259.1 209.0 228.1 148.0 6.758 21.0 204.2 276.3 364.4.430.7 453.0 477,8 437.0 510.4 501.2 524.I 536.9 550.0 589.3 428.7 259.1 208.4 227.5 139.9 7.150 22.0 206.3 276,8 366.1 435.3457.1 482.8 440,6 513.3 503.7 525.1 537.9 554.3 595.6 430,2 259.1 209.6 228.9 138.8 7.205 22.5 3-7 RUN 1 3 . W 0 .178 RE 9 7 6 B . QW 24025 . TWC * 2 9 8 . 5 DTMC 8 5 . 9 T i l ) T l ? ) T131 T t 41 T 1 5 ) T (6) T t 7) T IB) Tt 9) T 1 10 ) T i l l ) TI 12) T113) T ( 14) T t 1 5 ) TIN 2 6 4 . 4 3 . 5 1 6 46.1 2 0 5 . 7 276 .6 333 .5 3 5 5 . 4 3 5 6 . 9 344 .3 3 5 7 . 4 3 6 0 . ^ 3 6 5 . 2 361 .8 362 .5 362 .9 370 .9 351 .5 261 -3 209 .7 229 .4 2 8 0 . 8 3.562 4 6 . 4 2 0 6 . 3 2 7 7 . 5 333 .2 358 .3 3 5 9 . 8 3 4 4 . 3 359 .4 359 . f l 366-1 364 .4 364-.3 3 6 4 . 9 3 7 3 . 5 351 .9 261 .3 210 .4 23D.2 279 .2 3 .582 49 .1 206 .1 2 7 7 . 9 3 3 5 . 3 358-2 3 5 9 . 3 3 4 4 . 0 3 5 B . 7 3 5 8 . 4 3 6 5 . 6 364.1 362 .8 364 .3 372 .9 3 5 2 . 4 26D .2 2 1 1 . ? 230 .7 2 8 1 . 6 3.551 5 2 . 9 2 0 7 . 5 2 7 8 . 6 335 .5 350.2 3 5 0 . 7 3 4 4 . 0 358 .4 356^7 3 6 5 . 8 363 .7 363 .0 364 .5 373 .1 351 .5 2 6 0 . 0 209 ,5 2 2 9 . 0 278 .2 3 .595 5 6 . 9 2 0 5 . 4 2 7 6 . 6 334 .9 357 .6 3 5 9 . 0 3 4 3 . 6 358 .4 3 5 6 . 7 3 6 6 . 9 3 6 5 . 0 3 6 4 . 4 365 .9 373 .8 351.2 2 5 9 . 8 210.2 23Q.Q 27B.8 3 .5B6 6 0 . 9 -2 0 5 . 7 2 7 6 . 8 3 3 4 . 9 358 .3 359 .1 344 .0 358 .7 3 5 8 . 7 3 6 5 - 9 363 .7 361 .8 365 .6 3 7 3 . 3 351 .5 244.1 2 1 0 . 7 230 .3 2 8 0 . 5 3 .565 6 9 . 4 2 0 6 . 9 2 7 6 . 0 3 3 4 . 8 358 .2 359.1 344 ,6 359 .7 359.= 3 6 6 . 7 365 .7 365 .4 366 .6 375.2 352.2 260 .5 2 1 3 . 4 233.1 283 .8 3 .524 7 2 . 4 2 0 6 . 9 3 1 8 . 6 4 0 9 . 3 4 5 0 . 2 4 4 6 . 4 416.1 437.1 4 3 4 . 7 4 3 4 . 6 4 3 3 . 6 4 3 8 . 6 4 4 8 . 0 4 5 5 . 9 4 2 4 . 7 2 8 6 . 4 2 1 0 . 0 2 4 2 . 0 303 .9 3 .290 7 3 . 4 207 .2 3 1 9 . 8 4 0 9 . 8 450.1 4 4 6 . 7 414 .8 4 3 5 . 7 4 3 7 . 6 4 3 7 . 3 436 .5 4 4 0 . 6 4 4 9 . 0 4 6 0 . 7 4 2 7 . 0 2 8 5 . 7 210 .2 242-1 302.1 3 .310 74 .8 2 0 7 . 3 320.2 4 1 3 . 5 4 5 3 . 4 4 4 9 . 0 418.1 4 3 6 . 6 4 3 7 . B 4 3 9 . 5 4 3 9 . 6 4 4 3 . 4 4 5 2 . 4 4 6 6 . 6 4 2 7 . 8 2 3 4 . 6 210.1 742 .7 298 .7 3 .348 77 .1 2 0 7 . 3 320.4 412 .6 . 454.1 4 4 9 . 0 417-8 4 3 7 . 2 438 .4 4 4 0 . 6 4 4 0 . 3 443 .1 4 4 9 . 0 465 .5 4 2 7 . 6 2 8 4 . 3 210 -3 2 4 3 . 0 299 .2 3 . 3 4 ? 7B .6 2 0 8 . 4 320 .4 4 1 2 . 6 4b3 .2 4 4 9 . 0 4 1 * . 9 434.?. 4 3 6 . 6 441 .1 439 .1 444 .4 4 4 9 . 3 4 6 4 . 7 4 2 7 . S 2 9 1 . 9 209.1 241 .8 2 3 8 . 5 3 .350 B0 .5 2 0 9 . 2 3 2 0 . 5 4 1 0 . 8 4 5 1 . 7 4 4 9 . 0 41&.9 4 3 5 . 9 436 .R 4 3 9 . 6 437 .1 4 4 4 . 4 450.1 4 6 4 . 8 4 2 7 . 7 281 .7 209 .B 241 .6 299 .2 3 .343 84.1 2 0 7 . 7 3 1 9 . 7 4 1 1 . B 4 5 3 . 7 4 4 B . 6 416 .8 436.1 4 3 6 . 6 4 3 9 . 0 4 3 6 . 5 4 4 3 . 3 4 5 1 . 5 467.1 4 2 B . 0 2 8 1 . 4 209 .3 241 .6 2 9 B . 6 3 .349 8 6 . 9 2 0 8 . 4 3 2 0 . 0 4 1 2 . 5 4 5 5 . 9 4 4 B . 6 4*17.8 4 3 6 . 5 4 3 6 . 6 44D.8 4 3 7 . 6 4 4 4 . 9 4 5 2 . 6 4 6 8 . 4 4 2 7 . 0 2 8 0 . 6 209 .2 241.1 296-B 3 .37D 92 ,9 2 0 8 . 2 320 .4 4 1 2 . 6 4 5 6 , 9 4 4 9 . 0 418 .8 4 3 6 . 7 4 3 5 . 6 4 4 0 . 6 4 3 8 . 4 4 4 5 . 2 453 -0 471 .7 4 2 8 . 0 2 6 0 , 3 209.1 241.1 2 9 5 . 9 3 .380 9 6 . 4 2 0 6 . 9 3 1 9 . 3 4 1 3 . 7 457.1 4 4 9 . 5 410 .8 4 3 8 . 4 4 3 6 . 6 4 4 0 . 3 4 4 Q . 3 4 4 6 . 4 4 5 5 . 6 4 7 3 . 5 42B .3 2 8 0 . 5 2 0 9 . 9 247 .3 295 .B 3 .380 100.1 2 0 9 . 3 320 .5 4 1 5 , 8 4 5 9 . 0 4 5 0 . 9 419.1 4 3 8 . 4 4 3 7 . 3 4 4 0 . 6 4 3 9 . 3 4 4 6 . 2 456.1 475 -2 4 2 8 . 0 2 8 0 . 3 2 1 6 . 0 2 4 ? . 5 2 9 5 . 4 TTTe"?—103 .0 2 0 8 . 2 3 2 0 . 9 4 1 4 . 8 4 5 9 . 0 4 5 0 . 0 4 2 0 - 0 438 .6 436 .8 4 4 0 . 6 4 3 9 . 4 4 4 6 . 9 4 5 6 . 1 4 7 5 . 9 4 2 6 . 0 2 7 8 . 8 209.1 241.2 293 .8 3 .404 106 .0 2 0 8 . 8 3 2 0 . 7 4 L 6 . 1 4 6 0 . 7 4 5 0 . 0 420 .3 4 3 9 . 0 436 . f i 4 4 0 . 6 4 4 0 . 6 4 4 7 . 7 4 5 6 . 8 4 7 8 . 4 4 2 9 . 0 2 7 9 . 6 210 .7 743 .5 7 9 5 . 4 3 .3B5 l 'OB.8 2 0 9 . 3 321 .1 4 1 5 . B 461 .3 4 5 6 . 4 4 2 5 . 8 4 4 3 . 3 4 4 0 . 3 4 4 9 . 3 4 4 5 . 9 4 5 4 . 5 4 6 4 . 3 4 8 3 . 3 433 .5 2 8 1 . 4 2 0 9 . g 242 .7 287 .3 3.481 115.8 2 0 6 . 0 3 2 0 . 6 4 1 5 . 8 463 .9 4 5 7 . 7 4 2 5 . 0 4 4 5 . 0 4-43.5 4 5 2 . 0 4 4 6 . 8 4 5 8 . 4 4 6 7 . 0 488 -3 4 3 6 . 0 2 8 2 . 4 210 .7 2 4 2 . 8 2 8 4 . 7 3 .512 119.1 2 0 5 . 9 3 1 8 . 6 4 1 6 . 1 4 6 4 . 3 4 5 7 . 1 425 .8 4 4 4 . 3 4 4 3 . 6 4 5 ? . 6 4 4 9 . 2 4 5 9 . 6 4 6 6 . 7 4 8 7 . ? 4 3 2 . 6 2 6 0 . 8 7 0 9 . 0 241 .4 2 8 2 , 7 3 .538 123. 1 _ 2 0 5 . 0 2 4 8 . 0 785 .4 3 0 2 . 0 303 .7 290 .4 7 9 9 . 9 2 9 9 . 9 305 .1 303 .2 3 0 5 . 4 307 .9 317.1 3 0 1 . 4 2 4 3 . 8 210.1 221 .7 277 .5 3 .603 124 .4 2 0 4 . 6 246 .2 2R5 .8 302 .5 3 0 4 . 0 2 9 0 . 6 2 9 9 . 3 2 9 9 . 9 305.1 3 0 3 . 0 3 0 5 . 7 307 .9 316 .7 3 0 1 . 2 2 4 3 . 6 208 -4 2 2 0 . 1 272 .4 3.671 127 .0 2 0 5 . 0 2 4 9 . 0 2 8 6 . 9 303.1 3 0 5 . 0 2R9.7 301.1 3 0 0 . 3 3 0 4 . 9 3 0 3 . 4 3 0 6 . 0 3 0 9 . 6 317 .6 301 .1 2 4 2 . 6 2 1 0 . 6 222.8 278.2 3 .594 132 .6 2 0 5 . 3 2 4 9 . 0 2 8 7 . 6 303.1 304 .2 2 9 1 . 0 301 .3 3 0 1 . n 3 0 6 . 3 304 .4 307 .4 310 .5 3 1 8 . 9 300 .4 7 4 0 . 4 210 .3 722 .5 2 7 4 . 6 3 .639 140 .8 205 .1 2 4 9 . 0 2 8 7 . 7 304.1 304 .7 2 0 1 . 4 301 .5 301.1 3 0 6 . 3 304.5 3 0 6 . 6 310 .2 319 .2 3 0 0 . 0 240.1 210 .5 222 .5 2 7 4 . 7 3 .640 145 .5 2 0 5 . 7 250 .8 2 8 8 . 2 304 .7 306 . 1 292 . 1 301 .8 3 0 2 . C 3 0 7 . 4 305 .7 3 0 7 . 9 310 .2 319.2 300 .4 2 3 9 . 7 2 t 0 . Q 221 .8 2 7 0 . 4 3 .-6"9'8 151.2 " 205.2- 249.'5 28G.1 303. 1 305 .4 2 9 1 . 5 3 0 L . 1 3 0 1 . 5 3 0 6 . 8 305 .3 307 .5 3 0 9 . 6 313 .5 2 9 9 . 6 2 3 7 . 9 209 . j 220 ,6 2 6 9 . 2 3 .715 156 .5 2 0 5 . 4 2 4 9 . 7 2 8 7 . 3 303 .8 305-1 2 9 1 . 7 301 .5 3 0 1 . ? 3 0 7 . 0 105 .0 307 .4 310.2 318 .7 299 .9 2 3 7 . 5 210-1 221 .9 272 .5 3 .670 164 .8 206 .1 315.1 4 1 1 . 8 4 6 0 . 0 4 5 5 . 8 424 .5 4 4 5 . 0 449 .1 4 5 3 . 2 4 4 6 . 4 4 5 9 . 8 4 6 6 . 5 4 9 0 . 5 4 3 8 . 6 2 8 4 . 6 2 0 9 . 3 241 .3 2 8 2 . 9 3 .535 1 6 5 . 1 \ 2 0 9 . 4 3 1 9 . 5 4 1 5 . 8 4 6 4 . 3 4 6 0 . 5 427 .8 4 4 7 . 6 4 4 9 . 3 4 5 3 . 9 4 5 0 . 9 4 6 0 . 3 4 6 8 . 6 4 9 3 . 9 4 3 5 . 6 283 .2 2 1 0 . 8 2 4 2 . 9 281-5 3 .553 168 .5 .fl 4 6 7 . 2 473.1 495 .7 435 .8 280 .1 2 0 8 . 9 241.2 277. . 2 0 8 . 4 3 1 8 . 6 4 2 0 . 8 473 .8 4 6 5 . 7 4 3 0 . 8 4 4 8 . 3 4 4 8 . 5 4 5 6 . 9 4 5 5 . 7 4 6 6 . 0 4 7 5 . 3 506 .0 4 3 9 . 0 2 8 0 . 0 2 1 0 . 5 242 .3 2 7 5 , 4 3.631 179 .0 2 0 8 . 0 2 7 9 . 2 3 4 2 . 6 375 .2 3 7 6 . 8 351 . 4 363 .9 3 6 5 . 4 3 7 4 . 6 372 . 1 3 7 7 . 4 380 . 8 403 .9 363. .0 2 5 8 . 9 209 .2 2 7 8 . 6 251 .6 3 .974 179.1 2 0 8 . 4 278 .2 342 . 7 372. R 376 . 7 3 5 1 . 4 362 .9 3 6 4 . 9 3 7 5 . 0 372 .1 378 .3 3 8 1 . 1 402 . B 362. .3 2 5 9 . 1 210 . 7 229 .3 255 .7 3. 91 l 188 .9 2 0 6 . 5 2 7 7 . 5 3 4 1 . 6 372.8 376. 7 352 . 0 363.2 3 6 5 . 0 3 7 4 . 6 372 . 1 377 .5 381 . 2 4 0 3 . 5 362. .0 25H.9 209 .5 22B .7 253 .6 3.94D . 193 .4 2 0 6 . 1 2 7 7 . 5 3 4 3 . 9 3 7 3 . 6 376 .4 3 5 2 . 8 3 6 4 . 4 3 6 5 . 4 3 7 4 . 6 373.1 37B.4 382 . 5 404 .5 362, .0 2 5 B . 7 210 .4 229 .7 253-B 3.941 1 9 B . 4 2 0 7 . 3 2 7 6 . 4 343. 1 3 74. 7 3 7 8 . 0 352. 4 363 .6 365 . 3 3 7 4 . 6 372 .3 3 7 8 . 4 3 8 1 . a 4 0 3 . 7 362. , 7 258 .7 2 1 0 . 8 2 30 .0 255 .0 3 .922 2 0 3 . 4 252 .5 3 .960 2 5 0 . 4 3 .993 250 .6 3 .990 249 .1 4 .014 248 .2 4 .030 9797 . GW 23(115. TWC 29F1.4 Tt 1 ) T 1 2 ) Tt 31 rt4) i I T (6] T i n t (8) T (9 ) T i l l ] T i l l ) T( 12) n i - •) n 14) T( 11) r i N ruur HM i o o o q TIME 204 . 2 249 .4 784 . 3 294 . 5 ? s e . ,0 2 fl 9. 7 299 . 7 299 . 2 3 0 2 . 7 302 . 7 302. , 3 304 .0 109. 1 3G2.8 250 .7 2 1 1 . 6 722 .3 28 P. 5 3.4 67 0 .0 204 . 6 2 4 3 . 4 2 8 5 . 3 296. 1 299. . 3 2"30. 4 290 .6 2^9. 9 3 04 .1 301 . 5 301. . 1 303 . 1 308. 4 30 3 .9 2 5 4 . 4 7 .'i A . i 71 a . f> 2 76 .3 3 .619 0 .5 20 3. 4 248 .3 284 . 7 293 .9 293. , •) 2 9 1 . 0 ?OB.O 299 . ? 3 0 3 . 1 301 .6 301. , 3 303 .4 3 C 0 . 1 305 .6 257 .2 70 ' . 9 ? l o . 6 2 7 0 .0 3. 597 1.2 ? 0 3 . 6 248 .2 264 . 7 2 i 5 . 2 296 . . 5 289 .2 ? 9 8 . 9 2 9 B . 5 303 .6 302 .0 307. .2 303 . 6 309 . 4 304. 1 254 . 9 2 0 9 . 5 221 .5 203. 3 3 .5 29 3 .3 2 0 4 . 6 2 4 9 . C 384 .9 2 96 .0 793, , 9 239 .2 7 9 7 . 1 2 18. 303 .4 3 02 .4 303. ,6 304 . 2 309 . 7 303 .6 250 . 9 7 0 9 . R ?? 1 .9 2^3.7 3 .525 7 .7 2 C 4 . 3 24-9.6 2 B 5 . 3 2 96 . 3 •tit. .? 2P.9.9 298.4 2 9 9 . r 304 . ' , 301 . 3 304. , 8 305 .6 3 l 2 . £• 303 .8 251 . I 7'19 .4 721 . 3 2 79 .7 3.581 lfa.O 205 . 2 2 4 9 . 6 2 8 0 . 1 ?97 . 7 •i C 0. . 7 790 .6 ? 9 B . 9 3 9 0 . 7 3 0 4 . 5 302 .4 304 , ,0 305 .9 314. 3 303 .5 257 .0 210 .4 772 .3 780 . 7 3 . 562 1 9 . 5 204 . 4 249 .4 2 P 6 . 6 2 ?P. 1 302. . 2 2 31 . 1 300.2 300. 9 3 0 5 . ? 30 3. 5 304. .9 306. 7 317. 3 312 .2 759 . 1 2 09 .8 2 7 1.9 275 .7 3 , 6 ? 7 74 .1 704 . 5 2 4 9 . 9 ?8fc . 7 ?^f i . 3 107, . 5 291 .7 3CO.0 3 0 1 . 0 3 36 . 5 315 .3 306. . 5 307. 7 319 , . ^ 312.6 259 . 2 2 10.7 2 2 5. 0 776 .6 3 .616 2 6 . 3 2 0 6 . 9 2 5 2 . 5 280 .4 300. 3 304 . . 7 29 ). 3 301 .5 3 0 3 . ? 3 OB. 4 30 5 .6 30P. .0 310 .7 323 . .2 315.1 25B.4 2 1 0 . 0 2 2 2 . 9 2>,h.7 3.721 2 9 .4 7 C 6 . 2 5 1 . S 788 . 9 3 C 0 . B 301. , ? 2 9 4 . 0 S12.0 303 . •> 10 7.7 3 05 . 6 309, .4 317 .3 376 . .3 116.5 2 5 7 . 0 2 1 i i . 1 77? . 5 266 .4 3 . 753 3 3 . 5 206 .4 25 1 . 8 290 . 2 307. P 398 .4 796 , I 305 . 4 306 . 1 111.7 307 .0 313 .4 316 .0 3 13.6 329 .0 267 .9 2 1 1 . 1 223. 1 259,?. 3 .859 4 4 . 3 2 0 5 . 2 251 .6 2 b 9 . 3 302 .3 308 . 7 295 .7 3.05.5 305 . 0 3 1 1 . 7 307. ' - 314 .0 316. 6 334 ,9 330.1 266 .4 209 ,B 221 .3 254 .0 3 .038 4 8 . 3 207 .5 753 .4 2 9 1 . 3 304.1 310 .5 2^7.4 308 .7 3 0 6 . " 312 .4 30A .9 317.2 317 .7 136.9 330.4 2 6 5 . 3 2 0 9 . 5 2 2 0 . 9 74^ .5 4 . 0 5 7 53 .2 207 .5 253 .4 2 9 1 . 3 304.1 310 .5 297 ,7 308 .7 306 .1 3 1 0 . 6 308 .5 315 .9 313 .5 337 .6 329 .7 2 6 4 . 6 209.Q 222.1 25^ .6 3 .990 5 7 . 5 204 .2 2 5 2 . 0 290 . 5 303 .P 309..9 297 . 7 3 10 . 1 3 0 6 . '• 3 13. 1 308 . 2 316 .0 319 . 7 341 . 3 331 .6 2 6 1 . 7 299 .6 22.1 .7 248 .5 4 . 0 2 5 6 5 . 3 2 C 5 . 4 Z b Z . ' i J 9 J . 4 Wb.tt H I . . q 29 j . r . 307 .3 3 0 6 . " 309 .6 3 l i j . 9 321 .0 343 .4 332 .2 ? 6 l . O 2 U . 3 722. 2 2~4~7TT 4 .04Q 6 9 . 6 2 0 5 . 4 252 .3 792.4 304.4 312 .3 2^3.0 S07.3 307.1 3 1 3 . 1 309 .6 319 .0 321.1 344 .0 332 .6 2 5 9 . 9 210 .6 272.8 2 4 " . 3 4 .028 7 4 . 0 2 0 5 . 9 252 .C 292 .4 305.4 31 3. 3 291.2 3^7.3 3 0 7 . 7 31 5 .0 310 . 2 320 . 3 321 . 7 345 .0 335 .0 76.3.9 210 . 4 222. 7 2 4 S . 4 4 . 0 7 5 8 0 . 8 2 0 6 . 0 2 5 2 . 9 292 .4 306.2 313 .7 299 .7 307 .3 307.h 3 1 5 . ? 310 .9 321 .9 3 2 ? . 4 346.2 340 .7 7 7 0 . 8 2 1 0 . 0 721.fc 243.1 4 .113 8 9 . 6 2 0 8 . B 257 .1 2 9 5 . 7 31C.1 317 .5 303.4 30*7.3 3 1 7 . 0 3 1 9 . 9 314 .6 323 .9 376 .9 351 .G 336.B 761 .7 209 .6 771.8 234.1 4.271 101.1 2 0 6 . 3 254 .5 295.8 310.2 319.4 303.9 307 .3 312 .0 319.1 314 .6 325.2 328.1 352.2 343 .5 267 .2 2 t 0 . 2 227 .0 - 234 .0 4 . 2 7 3 105.1 2 0 b . / * ! ; b . 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TC 11 ) T I 12 ) TI13I TI14) TI15) TIN 205.6 265.1 285.8 295.6 287.1 281.1 290.5 288.7 292.9 299.1 294.5 293.1 296.5 301.4 206.7 266.8 286.3 296.5 268.0 281.4 292.0 289.0 293.3 299.4 295.2 293.5 298.1 301.8 Z06.1 266.6 2H6.b ^ 96.4 2UH.0 781.8 291.3 289.? 293.7 299.9 295.3 293.5. 298.3 .302 .M. 208.3 268.8 288.7 297.9 289.1 283.6 292.4 289.7 295.1,300.9 297.1 294.8 298.7 303.7 208.6 267.5 268.7 298.5 289.0 283.4 293.3 290.f 295.6 302.2 297.8 296.1 300.1 304.6 208.6 266.2 288.8 298.6 290.0 2B4.1 292.8 291.? 296.5 302.4 298.0 296.5 300.2.305.2 208.0 268.4 288.0 298.3 289.1 284.0 292.4 290.5 295.9 302.4 298.2 296.8 300.1 305.4 207.3 266.6 288.0 298.3 289.1 284.8 293.5 291.5 296.4 303.5 298.2 297.1 301.6 306.2 242.6 209.4 219.8 241.1 209.5 219.9 .244.» 209.3 219.7. 245.9 209.6 219.9. 246.3 210.6 220.9 246.3 210.3 220.4 247.4, 209.9 220.5 245.9 210.5 221.2 786.1 781.6 77S.5 ' 766.3 771.3 76 4.0 764.9 765.4 • 1000 R TIME .272 0. 1.279 0.7 1.285 1.302 1.297 1.309 1.307 1.306 ~TT4— 3.'8 9.0 17.3 21.4 33.4 3-9 4UN 17. . W 0.312 .HE 16746. OW 39709. TWC 297.3 0TKC 81.9 v T i n— r m—T m— f r o — r r n — m n — r m — m n—T I M T t IO> T i m TI 121 T J U J r n o TI 15) mr TUTT? HM 1000 « TTM? 206.8 262.2 289.7 ?97.R 292,8 269.6 297.1 294,P 299.6 304.5 301.0 300.9 302.8 309.1 261.3 210.0 222.1 485.0 2.062 0.0 208.3 262.5 290.3 258.6 293.6 290.0 206.9 295.* 300.4 305.3 301.8 301.3 303.5 310.0 261.7 210.6 222.9 485.7 2.069 1.0 206.9 261.8 289.4 298.?. 294,1 209.6 207.0 295.f 299.6 304.6 299.9 301.4 303.8 310.7 261.6 210.7 222.2 485.8 2.059 4^0 207.1 261.8 289.0 29R.1 293.4 288.4 ?96.0 294.? 298.3 304.3 299.7 300.0 302.5 308.0 260.2 209.6 2 2 1 . 6 487.2 2.053 7.0 2UU.0 263.1 9^0.1 294./ 290.2 2-W.7. 2 .^6 301.5 305.9 301.8 301.3 303.5 312.6 264.9 210.2 221.6 479.5 2.086 1576" 209.2 264.5 291.6 299.9 ?<5.3 290.7 297.4 296.2 302.2 306.0 301.8 301.3 303.0 313.8 264.9 210.1 221.6 476.6 2.09B 19.0 208 .6 264 . 7 292.3 3C0.4 ?oh.7 201.3 298.1 296. *l 303.9 307.4 302. 7 302.2 303.2 315-3 264.0 209.7 2 2 1 . 4 469.8 2. 129 24.3 207.7 262.9 293.2 301.0 2^ 7.0 200.9 298.7 297.^  304.0 308.6 302.8 302.3 303.5 316.1 263.1 209.8 221.7 468.3 2.135 29.8 2C8.0 264 .4 29*.5 302.1 79H.1 290.9 2°R.9.208.? 306.2 310.8 303.5 303.0 303.0 319.1 265.1 209.7 2 2 1 . 6 462.9 2. 160 39.0 208.8 264.0 295.2 3C&.1 299.4 29V.2 301.1 300.2 3C7.7 311.3 303.6 3D4.5 303.4 320.7 267.1 210.9 222.5 461.6 2.165 42.1 ZCB,:0"~2'5Vn~,795V2 3Ci.? 7^",/ 7m.2 1301.3 300. * i 09 .'9 "TIT.- 5~37fc". 1 30571~30~372~ 322 - 2 269.6 ZIO.b Z7.2.1 4 b b . I z. l95 43.0-208.4 264. 5 295.6 303. f, 3C0. 3 294.2 302 . 1 301-» 310.2 312.0 305.4 305.6 304. 1 320.7 262.0 211.2 222.4 456. 1 2. 192 44.5 205.4 262.2 294.9 3C3.3 30n.4 292.0 303.0 301.1 309.7 313.1 305.4 304.9 304.2 319.3 257.1 209.5 2 2 1 . 3 4 4 9 . 6 2.223 49,0 207.3 264.0 296.4 305.7 301.7 794.0 303.6 302.7 312.? 315.3 307.6 307.7 304.9-323.6 262.9 209.B 221.3 .441.6 2.264 59.8 208.4 ¥64, 4 797 .C 305.9 3G2 . 2 204.0 304.4 304.C 313.1 316.5 300.6 308.8 304.9 323.2 262.0 210.0 271.4 438.4 2.281 68.5 209.1 266,5 298.6 307.7 303.2 296.1 305.2 305.2 314.1 317.7 3Q0.9 309.4 305.6 326.6 267.1 210.3 221.6 434.0 .2.304 75.8 208.0 266.3 2W'.0 307.3 307.5 29b. 4'"30574~305; 4 314. 3 3 18. 3 3 10.1 308.3 305.5 326.9 271. 1 209.2 "22075 479.8 2. 327 8~475 207.7 265.8 20b.3 307.5 303.4 796.6 305.9 306.' 313.6 310.8 30O.7 309.0 305.6 326.6 264.5 210.6 221.9 434.1 2,303 90.5 207.3 266.5 209.5 307.? 303,o 297.1 306.3 306.9 315.7 319.6 311.3 310.5 306.3 325.2 261.1 210.7 222.0 430.1 2,325 97.8 207.3 266.5 299.C 309.0 305.7 297.3 307.0 308,1 316.7 321.2 313.1 311.5 3Q7.3 327.8 266.7 210.3 221.8 424.2 - 2.358 108.4 207. 1 265.« 299. 4 308. 1 304 .6 297. 1 306.7 307. 4 3 15 .5 319.6 31 1 .9 31 1 .2 307. 3 326.5 763. 1 209. 7 221 .2 421 . 5 2. 372 1 12.8 205. 4 264 . 8 7 9 9 . 5 307.7 303. S _2_9b. 0 _3Q6,8_i9_7 , 4 3 14 ,8_ 3 70 . 4 31 1.4 311.5 307.3 327.2 265.6 209.2 220.7 422.6 2.366 116.8 208. 1 267.5 300.4 309.0 305 .'0 297. 2 307. 2 307 .8 316.8 321.5 313.5 311.4 307.5 330.3 269.6 210.4 221.9 423.8 2.360 122.8 208.4 267.6 300.3 309.5 305.7 298.5 308.3 303.9 317.8 322.3 314.3 312.7 308.3 332.3 272.2 211.2 222.7 427.2 2.368 132.1 2C6.5 265,5 798.8 310.7 30^ .8 297.4 308.4 308.5 317.4 321.7 313.7 313.1 306.5 330.7 263.2 210.6 222.3 421.4 2.373 138.3 207.7 267.6 300.3 30O.9 305.7 298.7 308.1 308.7 317.6 322.0 313.8 312.6 308.1 329.3 266.4 210.1 221 .7' 417.9 2.393 144.7 208.6 266.4 301 .6 309.-1 3C6.0 293.4 306.2 308.T 317.7 322.4 314.7 313.0 308.2 330.3 268.2 210.5 221.3 417.6 2. 393 156.2 267. 3 267. 1 3G1 . 3 309.9 3C0.ti 298.6 308.6 309.5 3 17.3 322.4 313.6 313.3 308.6 331 .5 269.3 210.9 222.2 419.3 2.335 162.7 208.e 269.1 302.0 311.3 306.4 290.0 309.0 309.0 318.0 323.2 314.7 314.0 309.2 330.0 264.4 210.fi 222.1 416.3 2.402 170.3 207.7 267.6 30C.8 310.7 306.5 298./. 307.4 309.' 317.9 322.4 314.5 313.3 306.2 331.2 266.9 210.1 221.2 415.5 2.406 180.6 2C7.7 267.6 3C1 . 4 310.6 305.9 790.6 308.0 309.? 316.6 323. 5 314.4 31 3. 5 308.9 .332.2 26B.~9 210.2 222.2 417.8 2.394 186.6 208.4 268.7 301.5 310.0 305.° 29B.8 308.3 309.? 317.6 323.5 315.0 314.0 309.1 333.3 271.1 210.8 222.3 417.8 2.394 193.8 208.9 26H.9 302.1 311.1 306.1 299.6 308.3 309.8 3IB.4 324.1 315.4 314.2 308.8 333.3 270.9 210.9 222.3 416.4 .2.401 205.1 268.9 269.1 301.9 311.7 306.1 290.3 308.7 309.1 316.8 324.2 315.4 314.0 308.1 332.6 267.1 210.4 221.7 413.9 2,416 219.8 208.9 269, 8 307 . 3 .31 1 .7 306,P 299.,6 308.3 310.1 318.7 324.7 315.6 314. 1 308.8 332.3 268.5 210.8 222.3 415.2 2.408 229.7 208 .0 260. H 302 .8 31 1 .3 307, 1 299.5 308.6 310.7 318.4 324.4 315.4 314.4 306.9 333.3 271.4 210.7 222.4 414.7 2.412 236.7 208.0 269. 1 3C2.1 311.6 3C.2 3C0.4 308.3 310.4 310.4 324.2 315.6 314.4 308.8 332.8 269.6 210.4 22l\7 412. B 2.423 242.8 208.4 269,1 307.4 311.7 307,7 3C0.4 303.6 310.5 318.6 324.4 315.8 314.6 308.8 332.3 267.8 210.6 222.2 413.7 2.417 252.6 20B.4 768.4 301.3 317.1 307.3 208.2 308.7 310.7 318.4 323.9 315.7 314.1 303.4 332.3 267.8 209.7 221.1 410.7 2.435 7.56.8 206. 4 269.b 302.6 312.6 307,2 2?9.? 309.6 311.? 3 19. 5 324 .3 3 l6.2 314.6 369.0 332.5 268.2 210. 2 221.6 4T677 2.438 266.6 . 2C8.0 266.8 302.3 312.4 307.7 3C0.4 308.6 311.4 318.4 374.9 315.8 314.9 309.1 3*3.6 269.0 210.0 221.1 408.B 2.446 27t>.6 2C7.3 268.4 302.1 312.2 307.0 3C0.3 309.4 311.4 318.4 324.7 316.6 314.8 30B.4 3 3 5 . 3 271.4 210.6 222.8 414.3 2.414 284.1 208.0 270.0 302.9 312.8 307.4 3C0.9 309.2 311.9 319.0 325.4 317.0 315.6 309.5 335.7 271.1 210.8 222.3 410.7 2.435 291.1 206.5 270.5 303.9 313.1 307.7 301.0 308.6 311.? 318.6 325.4 316.6 314.8 308.9 335.9 274.3 209.9 221.2 407.5 2.454 300.£ | 208.2 270.3 304.2 312.0 307.5 301.5 309.3 311.7 318.2 326.5 316.3 315.1' 309.5 335.6 275.1 210.5 221.B 409.1 2.444 308.7 208.6 270.4 361.5 312.7 3o7.7 306.5 368.7 311 .8 318.3 325.5 316.9 315.3 510.6 334.4 2/1.1 210. 3 221 .U 47J9T3 27T4~1—3T470" 208.1 270.0 303.3 313.0 307.4 3C0.5 308.2 312.0 318.1 325.3 316.9 314.9 309.7 333.5 268.5 210.3 221.8 409.8 2.440 324.5 HUN IB. W 0.312 RE 16468. QW 39713. TWC 296.4 DTWC 81.2 Till Tl?) TI3> T(4) T(5) T<6) T{7) TIB) T(9) TIIO) Till) T112) T(13> Tl14) TI IS) TIN TOUT HM 1000 R TIME 207. 8 261 .? 288.0 296. f, 297 . 6 2PR.3 296.1 204.7 299.4 303.0 300,3 300. 1 301 . 0 311 .4 262.7 209.9 221.6 489.0 2.045 0.0 207.6 261 .4 288.4 296.b 293.3 289. 0 797. 1 295. 1 299.5 304. 5 30 1 . 2 301 .2 303. 5 312.8 265. 1 21 1 . 1 223. 1 490.9 2.037 0.6 207.6261 .4 289.4 799.7 2^4.ii 290.3 297.8 235. 7 299.3 364.3 301.6 362 .2 304. 1 315.2 267.4 209.5 2 2 o . 9 476.4 2.099 276" 209.0 262. 7 2 O 0 . 4 239.7 2^ 5.8 240.6 298.9 291.0 300.5 306.0 302.5 303.3 306.2 316.2 269.3 211.3 22?.8 480.6 2.081 4 . 0 208.9 263.6 20Q. 1 290. fj 29<-.0 2-.0.7 297.9 296.c 301 .2 305.7 302. 1 302.7 305.6 316.5 269.4 210.8 222.6 490.3 2.082 6.0 2C9.3 262.9 289.0 29d.0 294.7 2 0 0 . 0 298.4 296.r 301.7 304.9 303.0 303.0 305.2 317.2 269.2 210.2 221.8 476,5 7.099 11.0 206.4 2ft?.7 ?89.3 290.3 294.6 290.1 708.1 297. * 302.3 306.5 303.5 302.9 305.3 317.7 ?66.3 210.0 221.6 473.3 2.113 23.0 207.8 2bi.fi. 208. 5 300. 2 295.6 ?89.fl 297.3 297.0 301.9 305.9 303.2 302.9 305.6 316.2 264.5 210.2 221.9 475.2 2.104 29.0 208.0 262.3 289.2 299.7 2*5. 2 290.0 297.8 296. 6 301 . 5 365.9 303 .2 303. 1 305.6 319.3 266.3 2 6 9 . 2 221 .2 47077 77174 3T7o" 208.8 263.0 ? ; o . l 300.3 295.6 290.6 298.3 297.r 301.7 306.3 303.8 303.6 305.3 320.0 268.0 209.7 221.4 470.3 2.126 45.8 RUN 19. W 0.770 RE 41874. OW 79751. THC 293.5 DTMl 78.9 Til) T12) T13) T(4) T(5) T16) T(71 TIB) T(9) T(101 TIU) T(12) T (13) Tll4> TI15) TIN T PUT HM 1000 ft TI ME 209.1 273.6 287.7 301.0 289.2 282.0 292.7 268.1 295.7 302.7 296.1 294.9 297.4 300.0 234.6 211.9 221.5 1036.1 0.965 0.0 208.8 273.3 28B.3 301.9 28B.6 2-81.6 ?92.6 288.9 295.2 302.9 296.2 296.3 298.6 300.3 234.4 209.9 219.3 1004.4 0.996 0.5 208.8 273.6 289.I 301.o 28B.9 281.6 292. 1 289. 1 295.3 303.2 296.6 296.7 299.8 301.2 235.7 209.9 219.4 1002, 5 0.997 1.3 209.2 273.9 288.9 301.5 289.1 2-81.6 292.6 289.1 294.5 303.4 295.3 296.5 300.2 301.9 236.4 209.9 219.5 1004.6 0.995 3.3 IZ5,0 3g ?-B 289. 3 282.5 292.7 289.6 296.3 304.0 296.5 297.3 300.9 303.2 237.2 210.3 220.1 1001.6 0.998 6.5 208.8 274.4 289.9 302.9 289.9 282.6 293.9 290.7 296.5 304.7 296.5 29B.0 301.2 364.6 '237.0 210.0 71978 991.2 1.009 T T T T 208.0 274.3 290.6 304.6 291.6 283.1 295.1 291.« 299.6 305.3 298.3 298.4 301.5 305.3 236.2 209.6 219.1 969.6 1.031 21.8 209.5 275.7 292.1 305.4 29?.8 284.2 296,1 291,? 300.2 305.B 298.5 298.9 301.2 307.4 738.3 210.0 219.7 968.5 1.033 26.9 209.9 276.3 292.4 306.6 292.8 284.7 295.8 291.5 300.3 306.2 299.4 299.2 302.3 306.9 237.2 210.1 219.2 962.0 1.039 31.9 208.4 273.7 292.5 306.5 292.5 284.3 295.9 291.5 300.3 305.7 298.7 299.9 302.6 308.4 233.2 210.0 219.B 966.5 (1.035 36.4 209.7 275.8 292.8 307.0 292.9 2-65.5 296.4 292.1 301.1 307.5 299.2 300.1 303.1 309.1 236.7 209.8 ?19.4 954.4 1.048 46.6 209.1 274.7 291.7 307.1 3 0 3 . 5 284,2 296.5 291.3 299.8 307.0 298.7 300.2 307.9 309.6 239.8 209.3 219.1 955.3 1.047 53;1 209.3 276.0 293.0 307.1 294.4 285.6 296.5 292.5 301.0 307.6 300.4 300.7 303.7 310.3 240.6 210.0 220.0 953.4 1.049 59.6 209.6 276.0 293,6 307.1 294.2 265.9 ?9?.2 292.7 301.8 308.1 300.8 301.1 303,8 311.6 243.B 210.3 219.7 949.9 1.053 69.6 209.1 275.5 293.0 307.3 295.0 285.2 297.7 292.8 301.8 307.6 300.1 300.5 304.0 309.8 236.7 210.5 219.9 953.4 1.049 75.9 210.0 276.7 294.4 308.0 295.0 287.1 297.9-293.5 302.3 308.6 301.5 302.0 304.7 311.6 239.6 210.5 220.1 944.2 1.059 83.4 210.1 276.6 293.6 307.5 294.8 286.8 298.0 293.3 302.4 308.6 301.2 301.8 304.7 311.3 239.4 210.6 270.0 945.9 1.Q57 93.9 209.6 275.5 292. 5 307,8 295.4 286.0 297.8 292. * 301.7 307.9 300.5 300.9 303.9 3l LVo 239.8 209;7"Tl"97l 9"42".'8 1.061 99~79~ 209.0 276.1 293.2 307.5 295.0 286.0 297.2 293.1 301.9 308.6 301.0 301.0 304.3 311.8 241.6 209.8 219.4 942.3 1.061 137.1 209.5 277.3 293.9 307.5 295.'3 286.2 297.2 293. 1 302.4 308.3 301,2 301 .4 304.3 311.3 240.2 210. 1 219.7 944.3 1.059 117.9 209.7 276.2 293.6 308.2 2^ 5.3 2B6.0 298.1 293.0 302.1 307.7 301.9 301.4 303.5 311.4 240.2 210.6 Z20.3 949.9 1.053 123.9 209.9 276.9 293.9 308.? 295.5 286.2 297.2 293.0 302.8 307.9 301.0 301.3 303.9 311.2 240.7 210.0 219.1 940.1 1.064 132.9 209.9 276.9 294.5 30B.2 295.0 286.0 297.6 293.1 303.0 3Q8.4 301.4 301.6 304.1 312.5 243.8 209.9 219.2 938.3 1.066 U1.9 209.2 276.3 293.2 308.2 294.7 285.9 297.7 293.' 302.7 308.0 301.6 301.6 303.6 311.3 237.6 210.5 220.1 : 948.4 1.054 148.1 209.8 276.3 293.6 308.4 295.0 286.5 297.7 293. <* 302-2 308.4 301- 3 301.6 303.8 311.3 235.0 209.6 219, 1 938.7 1.065 155.1 209.4 276.9 293.6 307.9 294.7 286.0 296.9 292.5 302.2 308.0 300.8 301.6 304.3 311.3 236.1 209.6 218.9 ' 939.5 1.064 157.2 209.6 276.5 293.2 308.6 295.0 285.6 297.4 292." 302.6 307.9 301.6 301.3 303.9 310.9 238.3 210.1 219.6 944.5 1.059 173.1 209.3 275.9 294.1 307.9 294,7 285.6 296.9 293.1 302.4 306.9 301.2 301.1 303.9 311.3 236.1 210.2 219.7 945.8 1,057 179.9 209.1 276.4 293.6 308.2 294.7 286.0 297.2 293.0 302. 7 308.3 300.8 301.3 303.5 311.3 235.7 209.5 219. 1 938.5 0^65 . 191.1 210.0 277.2 294.6 308.3 296.1 287.5 297.4 293.6 302.4 308.5 301.3 302.0 304.3 311.2 235.0 210.4 219.9 942.3 1.061 2D2.4 209.6 277.1 294.4 307.9 295.3 267.5 296.9 293.1 302.8 308.4 301.8 301.4, 303.9 311.3 235.7 210.0 219.4 939.4 1.065 214.2 210.1 276.3 294.4 308.2 295.5 266.7 296.0 293.9 303.9 308.3 301.5 302.2 304.4 310.9 236.3 210.3 220.1 941.5 1.062 220.0 209.4 276.6 293.7 308.2 295.7 286.6 298.1 293.1 302.9 308.5 301.2 302.0 304.4 310.9 235.7 209.9 219.2 936.0 1.068 226.0 210.1 277.6 295.0 30B.3 295.4 286.5 298.2 293.5 303.3 308.5 300.9 301.6 304.5 310.8 237.3 210.3 219.6 941.3 1.062 237.7 209.3 276.9 293.6 308.8 295.8 286.6 297.8 2 q 3 . 3 302.6 309.3 366 .8 303.6 364 .3 3 1 1 . 4 238,5 2 0 9 . 9 219 .2 935.0 TTo&T 244 .2 209.5 276.6 293.9 307.9 295.1 2-B6.V 297.4 292.6 302.0 309.0 300.8 302.0 303.9 311.4 237.9 209.4 218.9 936.0 1.068 250.4 209.6 277.4 293.6 308.3 295.4 286.3 297.5 293.6 303.1 306.2 300,7 302.2 304.1 310.9 237.4 209.7 219.1 936.4 1.068 252.4 209.2 277.1 293.0 308.0 295.1 285.9 297.3 293.5 302.2 308.3 300.8 302.2 304.1 311.2 236.8 209.5 219.2 938.5 1,066 269.0 209.6 278.0 294.6 306.4 295.2 287.1 298.4 293.8 303.0 308.9 301,2 301.7 304.1 311.1 238.7 210.4 220.1 942-1 1.061 297.0 209.9 276.9 294.6 308.6 295.4 286.4 298.0 293.6 303.6 309.3 301.9 302.6 305.3 312.3 239.8 210.7 220.0 940.0 1.064 294.0 208.8 277.3 293.9 308.6 294.7 2-86.4 29T-.7 292.ft 302.5 308.6 301. 1 30?.3 304.9 311.3 239.4 210.1 219.6 941.3 1.06'2 29B.2 208.8 276.9 294.2 30B.8 295.0 286.3 296.3 293.9 303.5 309.3 301.9 302.7,304.5 311.4 237.9 209.7 219.3 931.5 1.073 338.5 3-10 QH 7 9 7 5 8 : DTMC 7 6 . 1 T i l ) . 712) T131 T I M T l 51 TT 6) T I 7 ) . T(8> T I 9 ) H I D ] T i l l ) T I1Z ) T113) T I14 ) T I15) TIN 2 0 6 . 4 2 0 9 . 4 2 0 8 . 6 2 0 9 . 6 2 0 9 . 1 2 0 9 . 6 2 0 9 . 5 2 0 8 . 8 2 0 9 . 8 2 0 9 . 9 2 7 2 . 0 2 8 5 . 9 2 7 3 . 3 2 8 7 . 3 2 T 1 . 5 161.6 2 7 2 . 5 2 8 7 . 0 2 7 2 . 9 2 8 7 . 1 2 7 3 . 3 2 8 6 . 9 .273.6 2 8 8 . 2 2 7 2 . 9 2 8 6 . 9 2 7 4 . T 2 6 6 . 6 2 7 4 . 2 2 8 7 . 7 2 9 7 . 7 2 9 8 . 2 2 9 8 . 6 2 9 9 . 9 2 9 9 . 4 3 0 0 . 0 3 0 0 . 0 2 9 9 . 8 3 0 6 . 6 3 0 0 . 7 2 8 6 . 3 2 8 0 . 5 2 8 5 . 9 2 8 0 . 6 2 4 6 . 3 2-S6.7 2 8 6 . 6 2 6 0 . 9 2 8 6 . 5 2 6 1 . 2 2 8 7 . 3 2 8 1 . 4 2 8 6 . 2 2 8 1 . 7 2 8 7 . 7 2 8 2 . 1 "2T8T4~~58"276~ 3 2 8 2 . 3 2 9 1 . 4 - 2 8 7 . 2 9 1 . 2 2 8 8 . 2 9 1 . 2 5 6 7 . 2 9 2 . 1 288 . 2 9 2 . 4 288 , 2 9 3 . 3 289 , 2 9 3 . 0 289 , 2931.2 289 . 2 9 3 . 5 269. 2 9 7 . 9 289 . 4 2 9 3 . 1 2 9 3 . 4 2 9 3 . 4 2 9 4 . C 2 9 3 . 0 2 9 5 . 1 2 9 5 . 1 2 9 5 . 5 2 9 5 . 5 2 9 6 . 3 0 0 . 3 0 1 . 3 0 0 . 0 3 0 1 . 8 3 0 1 . 0 3 0 1 . 4 3 0 2 . 2 3 0 3 . 2 3 0 3 . 0 3 0 3 . 9 2 9 4 . 0 0 2 9 4 . 0 V 2 9 4 . 1 4 2 9 4 . 9 5 2 9 5 . 5 4 2 9 5 . 0 2 9 6 . 6 296 .1 2 9 6 . 5 2 9 2 . 7 2 9 3 . 5 2 9 3 . 6 2 9 4 . 7 2 9 4 . 5 2 9 5 . 3 2 9 5 . 3 2 9 5 . 6 295 .1 2 9 5 . 2 2 9 5 . 0 2 9 7 . 3 2 9 7 . 9 2 9 7 . 9 298 .1 2 9 7 . 4 2 9 8 . 2 2 9 9 . 4 2 9 9 . 0 2 9 8 . 6 2 9 9 . 0 299 .1 300 .1 300 .1 3 0 0 . 5 301 .1 3 0 1 . 5 3 0 2 . 0 3 o 2 . 4 2 3 4 . 3 2 3 4 . 3 2 3 1 . 9 2 3 4 . 1 2 3 4 . 3 236 . 1 2 3 4 . 6 2 3 5 . 9 2 3 8 . 3 2 1 0 . 8 2 2 0 . 5 2 1 0 . 5 2 1 9 . 9 2 0 9 . 5 219.1 2 0 9 . 6 2 1 8 . 9 2 0 9 . 9 2 1 9 . 5 2 0 9 . 9 2 2 0 . 0 2 0 9 . 9 2 1 9 . 4 2 1 0 . 2 220 .1 2 1 0 . 3 2 2 0 . 0 10,48.3 0 . 9 5 4 0 . 0 1 0 3 7 . 0 0 . 9 6 4 0 .0 3 0 2 . 6 2 3 8 . 3 2 1 0 . 2 2 1 9 . 2 1024 .5 1015 .5 1 0 2 0 . 5 1 0 1 8 . 3 1007 .2 1012 .9 1 0 1 0 . 0 1 0 0 3 . 9 0 . 9 7 6 0 .985 0 . 9 8 0 0. 962. 0 . 9 9 3 0 . 9 B 7  0 . 9 9 0 4 5 . 4 D .996 5 1 . 0 1.5 3 . 5 5 .5 11 .3 2 1 . 8 3 0 . 5 TWC 2 9 7 . 6 DTMC 82 .2 . , T i t ) . TI21 T I3 I T14) T I 5 ) TI6I T I7 ] T I B ) T I 9 ) T I10 ) T i l l ) TC12) T I13 I T1141 T l 1 5 ) TIN 2 0 6 . ' 2 0 8 . , " T o X 2 0 6 . 2 1 0 . 2 1 1 . 2 1 1 . 2 1 0 . 2 5 8 . 0 2 5 9 . 9 2 6 0 . ! 2 6 0 . 6 2 6 2 . 9 2 6 2 . 4 2 6 4 . 1 2 6 2 . 0 2 8 3 . 1 2 6 4 . 8 2 8 5 . 1 2 6 4 . 4 2 6 8 . 3 2 8 8 . 6 2 9 0 . 7 2 9 1 . 0 2 4 0 . 7 2 9 0 . 7 2 9 2 . 5 2 9 1 . 9 2 9 2 . 5 2 9 2 . 9 2 9 3 . 2 2 9 2 . 5 2 9 2 . 1 293 .1 2 9 2 . 9 2 9 2 . 1 2 9 3 . 6 2 9 5 . 6 2 9 5 . 0 2 9 5 . 4 2 9 2 . 9 2 9 5 . 2 2 9 5 . 8 2 9 4 . 7 2 9 3 . 9 2 9 7 . 2 2 9 5 . 4 2 9 7 . 2 2 9 6 . 5 2 9 6 . 8 2 9 6 . 5 2 9 7 . 9 2 9 7 . 9 • 2 9 9 . 1 2 9 4 . 5 2 9 5 . 6 2 9 6 . 4 2 9 5 . 7 2 9 7 . 5 2 9 8 . 3 P 9 9 . 1 3 0 0 . 2 E 9 9 . 9 2 9 9 . 9 3 0 0 . 8 300 .1 3 0 0 . 3 3 0 1 . 7 3 0 1 . 2 2 9 9 . 6 3 0 0 . 6 2 9 9 . 9 3 0 0 . 5 3 0 1 . 9 2 9 5 . 2 2 9 6 . 2 2 9 6 . 2 2 9 6 . 6 2 9 7 . 9 2 9 6 . 3 2 9 9 . 4 3 0 0 . 5 3 0 0 . 8 3 0 0 . 5 3 0 1 . 6 3 0 1 . 2 3 0 1 . 2 3 0 1 . 2 3 0 1 . 4 3 0 0 . 5 3 0 1 . 6 3 0 1 . 4 3 0 1 . 2 3 0 2 . 3 3 0 2 . 5 3 0 6 . 0 3 0 2 . 7 3 0 2 . 5 3 0 2 . 3 3 0 3 . 1 304 .1 3 0 3 . 6 3 0 3 . 6 3 0 4 . 3 3 0 8 . 2 3 0 4 . 8 304 .1 3 0 4 . 6 304 .1 3 0 5 . 0 3 0 4 . 5 3 0 4 . 5 2 9 2 . 2 2 9 8 . 2 2 9 2 . 9 2 9 9 . 4 293.3 2 9 9 . 6 2 9 2 . 4 296 .1 2 9 5 . 5 3 0 1 . 3 2 9 5 . 8 3 0 1 . 4 2 9 7 . 0 3 0 2 . 4 2 9 7 . 4 3 0 3 . 0 E H . 7 3 0 3 . 0 2 9 6 . 4 3 0 3 . 8 2 9 9 . 2 304.1 299 .1 304 .1 299 .1 304 .1 299 .1 304 .1 2 9 8 . 2 3 0 1 . 2 299.3 3 0 2 . 5 2 9 6 . 6 3 0 1 . 4 2 9 8 . 2 3 0 1 . 0 2 9 9 . 7 3 0 3 . 1 3 0 0 . 6 3 0 3 . 2 301.9 3 0 4 . 6 3 0 2 . 6 3 0 5 . 2 3 0 3 . ! 3 0 5 . 0 3 0 3 . 7 3 0 5 . 3 3 0 4 . ? 306 .1 3 0 3 . 7 3 0 5 . 7 3 0 4 . 4 3 0 5 . 7 3 0 4 . 4 3 0 5 . 7 3 0 3 . 6 3 0 4 . T 3 0 4 . 0 3 0 3 . 9 3 0 6 . 5 3 0 7 . 6 3 0 7 . 7 3 0 8 . 8 3 0 8 . 7 3 0 9 . 3 3 0 9 . 9 3 0 9 . 4 3 1 0 . 6 310 .1 3 0 4 . 1 3 0 3 . 9 3 0 3 . 2 3 0 2 . 7 3 0 4 . 4 3 0 5 . 2 3 0 6 . 9 3 0 6 . 6 3 0 T . 4 3 0 7 . 5 3 0 8 . 3 3 0 7 . 7 3 0 8 . 8 3 0 9 . 2 3 0 9 . 2 3 0 B . 4 3 0 8 . 9 3 0 6 . 4 3 0 9 . 2 3 0 8 . 8 3 0 0 . 9 3 0 1 , 9 3 6 3 . 4 303.1 3 0 6 . 3 3 0 6 . 7 3 0 8 . 3 3 0 9 . 4 3 0 9 . 6 3 0 9 . 2 3 1 0 . 5 3 1 0 . 8 3 1 1 . 4 3 1 L . 4 T n r t r 3 1 0 . 7 3 1 1 . 4 3 1 1 . 4 3 1 1 . 6 3 1 1 . 4 3 0 2 . 5 3 0 8 . 9 3 0 3 . 5 3 0 9 . 6 3 0 3 . 5 3 0 9 . 8 3 0 3 . 5 3 1 2 . 7 306 .1 3 1 4 . 6 3 0 6 . 8 317.1 308 .1 318 .2 3 0 6 . 5 3 2 1 . 3 2 6 3 . 8 2 1 0 . 2 6 3 . 5 2 1 0 . 2 6 4 . 0 2 1 0 . 2 6 8 . 7 2 0 9 . 2 7 0 . 5 2 0 9 . 2 7 3 . 8 2 0 9 . 2 7 2 . 9 2 1 0 . 2 7 7 . 8 2 0 9 . 2 7 6 . 6 2 0 9 . 2 7 7 . 4 2D8. 2 7 9 . 9 2 0 9 . 277 .1 210 . 2 7 3 . 4 2 1 0 . 273 .1 2 0 9 . 2 7 7 . 4 2 0 9 . 2.80.0 209 2 7 3 . 8 210 2 7 3 . 8 209 2 7 4 . 5 209 2 7 4 . 2 210 0 2 2 2 . 8 3 223 .2 0 2 2 2 . 5 9 2 2 2 . 6 5 2 2 2 . 3 8 2 2 2 . 3 2 223 .1 6 2 2 2 . 9 9 2 2 2 . 9 2 2 2 0 . 9 6 2 2 2 . 0 2 2 2 2 . 8 3 223 .1 9 2 2 2 . 2 HM 2 5 9 . 3 2 5 7 . 3 2 5 6 . 2 2 5 7 . 5 249 .1 2 4 7 . 8 2 4 6 . 4 2 4 3 . 3 3 . 8 5 6 • 3 . 8 B 6 3 . 903 3 . 6 8 4 4 . 0 1 5 4 . 0 3 6 4 . 0 5 8 4 . 1 1 0 4 .121 4 . 2 1 3 4 . 1 9 4 4 . 1 4 8 4 .161 4 . 1 9 6 4 . 2 0 6 4 . 2 3 0 4 . 1 7 7 4 .212 4 . 2 2 3 . 4 . 1 B 4 0 . 0 0 . 6 2 1 0 . 7 2 1 0 . 3 2 1 1 . 2 2 1 0 . 7 2 1 1 . 1 ill 2 4 1 . 6 2 6 2 . 0 2 6 4 . 7 2 6 4 . 2 2 6 4 . 9 2 6 4 . 9 2 6 5 . 3 2 6 2 . 8 2 6 4 . 8 2 6 6 . 0 266..7 C 6 B . 6 3 0 9 . 0 3 2 1 . 7 3 0 9 . 0 3 2 2 . 0 310 .1 3 2 4 . 2 310 .1 3 2 3 . 8 3 1 0 . 8 323 .1 310.B 323 .1 2 4 2 . : 2 3 7 . 4 2 3 8 . 4 241 .1 2 4 0 . 3 2 3 8 . 3 1.6 i . 3 7 .3 11 .8 2 2 . 8 2 9 . 5 3 5 . 8 4 8 . 5 5 4 . 5 6 0 . 3 7 1 . 0 7 8 . 0 2 1 1 . 1 2 0 9 . 9 2 1 1 . 2 2 1 1 . 1 2 1 1 . 1 2 1 1 . 2 2 1 S . 4 I l » . 9 2 1 4 . 1 2 1 4 . 9 2 1 4 . 9 2 9 9 . 8 304 .1 299 .1 3 0 3 . 0 2 9 8 . 7 3 0 4 . 3 299 .1 304 .1 299 .1 3 0 3 . 8 2 9 9 . 4 304 .1 3 0 4 . 0 3 0 5 . 7 3 0 3 . 7 3 0 5 . 3 3 0 4 . 4 3 0 6 . 2 3 0 3 . 7 3 0 5 . 7 3 0 4 . 0 3 0 6 . 1 3 0 4 . 0 3 0 7 . 1 3 1 0 . 4 310 .1 3 1 0 . 3 3 0 9 . 9 3 1 0 . 6 3 1 0 . 8 3 1 1 . 5 3 2 4 . 5 310 .1 3 2 4 . 9 3 1 1 . 5 323 .1 3 1 0 . 4 3 2 3 . 4 311 .1 3 2 4 . 2 311 .1 3 2 3 . 4 238 .1 2 3 6 . 4 2 3 9 . 4 2 3 7 . 4 2 3 6 . 6 2 3 9 . 0 2 7 1 . 9 2 7 4 . 4 2 7 4 . 0 2 7 4 . 8 2175.1 3 0 2 . 3 3 0 2 . 8 302 .1 302 .1 3 0 1 . 7 3 0 3 . 5 3 0 3 . 5 3 0 3 . 5 3 0 2 . 8 3 0 3 . 6 7 0 2 . 4 3 0 3 . 2 3 0 2 . 8 3 0 3 . 4 3 0 3 . 2 3 0 5 . 2 3 0 4 . 4 3 0 4 . 6 2 9 9 . 8 3 0 7 . 8 3 0 0 . 7 3 0 5 . 6 2 9 9 . 8 304 .1 301 .1 3 0 4 . 7 7 0 0 . 2 3 0 4 . 3 2 9 9 . 8 304 .8 301 .1 3 0 5 . 6 3 0 1 . 3 3 0 5 . 2 3 0 1 . 3 3 0 5 . 6 3 0 2 . 4 3 0 6 . 3 3 0 0 . 2 3 0 5 . 2 3 0 4 . C 3 0 6 . 8 3 0 5 . 1 3 0 7 . 1 3 0 4 . 6 3 0 6 . 4 3 0 5 . 1 3 0 6 . 4 3 0 4 . 7 3 0 6 . 4 3 1 0 . 4 3 1 1 . 0 3 1 1 . 2 3 1 1 . 3 3 1 0 . 4 3 0 9 . 2 3 0 9 . 5 3 0 9 . 2 3 0 9 . 2 3 0 9 . 5 3 1 1 . 4 312 .1 3 1 2 . 6 3 1 3 . 2 3 1 2 . 5 3 1 0 . 8 3 2 3 . 4 3 1 2 . 6 3 2 4 . 2 3 1 1 . 9 3 2 3 . 8 3 1 2 . 9 3 2 3 . 4 3 1 2 . 2 3 2 2 . 7 3 1 2 . 9 3 2 4 . 5 3 1 2 . 6 3 2 4 . 5 3 1 6 . 3 3 2 5 . 9 3 1 3 . 6 3 2 6 . 3 3 1 3 . 5 3 2 6 . 8 3 1 2 . 2 3 2 5 . 9 2 7 2 . 4 209 . 2 7 2 . 7 211 . 2 7 4 . 3 210 . 2 7 4 . 7 210, 2 7 4 . 2 209 . 2 7 4 . 9 209 , 2 7 5 . 3 209 . 2 7 6 . 0 208, 2 7 6 . 1 208. 2 7 9 . 8 210. 2 7 3 . 8 206, 2 7 5 . 6 210, 277 .1 209 , 2 7 6 . 9 210. 2 7 7 . 4 209. 2 7 6 . 7 211. 275 .6 . 210, 2 7 5 . 6 209, 2 2 2 . 4 2 2 1 . 4 2 2 2 . 5 2 2 1 . 6 2 2 1 . 6 2 2 2 . 8 9 2 2 2 . 7 2 2 2 3 . 6 3 2 2 2 . 7 2 2 2 2 . 6 1 2 2 1 . 3 236 .1 2 3 8 . 5 2 3 7 . 4 2 3 6 . 2 2 3 4 . 4 2 3 5 . 8 2 3 4 . 8 2 3 2 . 2 231 .1 2 3 3 . 6 2 3 1 - 5 B 4 . 3 9 5 . 0 1 0 1 . 5 109 .5 1 2 1 . 3 1 2 8 . 3 4 . 1 9 9 4 . 1 9 2 4 .212 4 . 2 3 3 4 . 2 6 6 146 .3 156 .3 170 .5 182 .3 192 .0 2 1 6 . 4 2 1 6 . 0 2 1 3 . 8 2 1 4 . 1 2 1 7 . 2 2 1 4 . 1 B 7 6 . S S76. '6 2 7 2 . 9 2 7 3 . 7 2 7 7 . 9 2 7 5 . 9 3 0 1 . 6 3 0 5 . 6 3 0 2 ; 0 3 0 5 . 9 7 0 2 . 0 3 0 6 . 3 3 0 2 . 0 3 0 5 . 9 7 0 3 . 2 3 0 6 . 5 7 0 2 . 4 3 0 6 . 3 3 0 2 . 4 3 0 5 . 9 3 0 4 . 7 3 0 6 . 6 305 .1 3 0 6 . 4 3 0 4 . 7 3 0 7 . 1 3 0 4 . 7 3 0 6 . 8 3 0 6 . 5 3 0 8 . 6 3 0 4 . 7 3 0 6 . 4 3 1 0 . 6 3 1 1 . 3 3 1 1 . 2 3 1 0 . 8 3 1 2 . 2 3 1 0 . 8 3 0 9 . 5 309 . 5 3 0 9 . 2 3 0 9 . 2 3 1 0 . 6 3 0 9 . 2 312 .1 3 1 2 . 5 3 1 2 . 5 3 1 2 . 5 3 1 4 . > 312.1 3 1 3 . 5 3 2 6 . 6 3 1 2 . 9 3 2 6 . 3 3 1 4 . 3 3 2 7 . 7 3 1 3 . 8 328 .1 3 1 4 . 4 3 2 7 . 7 3 1 4 . 5 3 2 7 . 0 2 2 2 . 4 9 2 2 2 . 5 6 2 2 1 . 6 1 2 2 0 . 7 8 2 2 2 . 8 5 220 .2 2 2 3 . 5 2 2 2 1 . 8 2 2 2 2 . 9 8 2 2 2 . 2 1 2 2 3 . 8 2 223 .2 6 2 2 2 . 3 4 .241 4 . 2 5 9 4 . 3 0 7 4 . 3 2 6 4 .281 4 . 3 2 0 2 0 6 . 5 2 1 6 . 3 2 2 9 . 0 2 4 3 . 3 2 5 4 . 5 2 b 8 . 3 2 1 6 . 6 1 1 5 . 7 1 1 5 . 3 2 1 6 . 5 2 1 7 . 9 2 2 0 . 2 2 7 9 . 1 2 7 8 . 8 2 7 7 . 3 2 8 0 . 2 2 6 3 . 4 2 8 6 . 4 3 0 5 . 5 3 0 7 . 6 3 0 5 . 8 3 0 7 . 9 3 0 5 . 8 3 0 7 . 5 3 0 5 . 8 3 0 7 . 1 3 0 7 . 2 3 0 8 . 9 3 0 5 . 8 306 3 1 1 . 9 3 1 1 . 5 3 1 2 . 6 3 1 1 . 5 3 1 3 . 0 3 1 2 . 6 3 1 0 . 2 3 0 9 . 5 3 1 1 . 3 3 1 0 . 2 3 1 1 . 3 3 1 1 . 3 3 1 3 . 5 313 .2 3 1 3 . 5 3 1 3 . 4 3 1 4 . 8 3 1 3 . 5 3 6 6 . 5 3 0 6 . 9 312 .3 3 1 1 . 7 3 1 4 . 3 3 1 4 . 6 3 2 6 . 3 2 3 5 . 5 2 3 2 . 0 2 3 3 . 2 2 3 2 . 9 2 3 3 . 4 2 3 2 . 7 2 3 0 . 6 4 . 2 4 6 4 .311 4 . 2 6 8 4 . 2 9 4 4 . 2 8 5 4 . 2 9 7 4 . 3 3 6 2 8 0 . 0 2 9 3 . 3 3 0 2 . 5 3 1 5 . 0 3 2 6 . 3 3 3 9 . 3 3 4 3 . 5 TWC 2 9 8 . 2 DTMC 8 3 . 0 J l 1). T I 2 J T l 31 TC4) T I 5 ) T16) T I7) T ( 8 ) T<9) T-l 101 T i l l ) T 112 1 T l 131 Tl 14) T I15I TIN TOUT HM 1000 8 TIME 2 1 5 . 3 2 1 6 . 0 2 1 8 . 3 2 7 2 . 6 2 7 4 . 2 2 7 5 . 7 2 8 6 . 7 2 9 4 . 5 2 8 7 . 1 J95 . .9 2 6 8 . 6 299 .1 2 9 4 . 5 2 9 S . 4 2 9 8 . 0 2 9 5 . L 2 9 4 . 2 2 9 6 . 6 2 9 7 . 7 2 9 9 . 4 3 0 1 . 3 2 9 8 . 1 2 9 8 . 6 2 9 B . 9 3 0 1 . 2 3 0 2 . 0 3 0 2 . 2 3 0 4 . 4 3 0 4 . 4 3 0 6 . 5 3 0 3 . 0 302 .1 3 0 6 . 3 3 0 2 . 7 303 .1 3 0 5 . 6 • 3 0 2 . 9 3 0 3 . 0 3 0 5 . 9 3 1 0 . 2 3 1 1 . 5 3 1 4 . 7 2 7 1 . 6 2 7 2 . 4 2 7 4 . 5 210-1 2 0 9 . 9 2 1 0 . 2 2 2 2 . 2 2 2 2 . 9 2 2 3 . 4 2 5 6 . 6 2 5 6 . 4 ' 2 5 1 . 2 3 . 8 9 4 3 . 9 0 0 3 .961 0 . 0 0 . 5 3 . 3 2 1 8 . 7 2 6 0 . 6 2 9 0 . 4 2 9 9 . 7 2 1 5 - 5 2 6 4 . 9 2 9 0 . 9 2 9 9 . 5 2 9 9 . 0 2 9 5 . B 3 0 1 . 2 3 0 0 . 6 3 0 3 . 5 3 0 6 . 8 3 0 5 . 2 3 0 6 . 7 3 0 6 . 1 313..4 2 7 5 . 6 2 1 0 . 4 2 2 3 . 4 2 9 B . 7 2 9 6 . 2 3 0 1 . 2 3 0 0 . 4 3 0 3 . 2 3 0 7 . 6 3 0 5 . 6 3 0 6 . 0 3 0 5 . 7 3 1 2 . 7 2 7 4 . 2 209 .1 2 2 1 . 8 250 .1 2.45.8 3 . 9 9 9 4 . 0 6 9 6 . 3 1 1 . 0 2 2 . 0 3-11 RUN 24. W 0.242 RE 13575. QW 31601. TWC 296.6 DTMC B1.2 T ( l l TI21 T O ! TI41 T15I T ( 6 ) T(7I TIB! t ! 9 l Tl tOI M i l l T(12) T1131 T t 14) T U S I TIN TOUT HM 1000 R T I HE 205.0 253.0 289.3 296 .1 293.0 2B9.0 296.4 296 .1 298.5 302.9 300.2 300.9 3 0 1 . * 307.6 260.9 201.1 222.2 389.5 2.567 0.0 205.0 253.0 288.3 296.1 294.2 290.8 297.6 295.= 299.7 304.0 301.7 301.9 302.3 308.6 262.9 210.2 222.1 385.7 2.593 0.8 205.0 253.0 268.3 296.1 295.2 291.7 298.5 296.1 300.7 304.7 301.6 303.1 303.4 311.1 264.2 210.9 223 .1 386.3 2.589 l.a 205.0 253.0 288.3 296.1 294.2 291.3 29B.2 296.1 300.2 304.7 301.8 302.9 3Q3.4 309.7 262.4 209.9 222.5 393.5 2.608 4 .0 205.0 253.0 268.3 296.1 294.5 291-0 298.2 296 .6 300.2 304.5 301.4 302.6 302.7 310.0 261.7 206.8 221.2 378.6 2.641 7.3 205.0 253.0 288.3 296.1 294.5 291.0 297.5 296.6 300.3 304.9 301.4 302.6 303.6 310.4 262.4 208.6 220.8 376.9 2.654 12.3 205.0 253.0 28B.3 296.1 296.3 292.4 299.3 2 9 7 . 3 0 1 . 6 306.0 303.2 303.3 304.3 310.4 263.1 210.5 222.8 380.5 2.628 23.0 205.0 253.0 288.3 296.1 296.3 292.1 299.6 298.6 101.6 306.3 304.4 304.4 304.8 311.3 264.6 210.6 223.2 379.9 2.63? 29.0 205.0 253.0 288.3 296.1 295.6 292.1 299.6 298.4 301.2 305.6 303.2 303.7 304.5 311.2 262.4 208.2 221.2 371.9 2.6B9 37.7 205.0 253.0 288.3 296.1 296.0 292.4 299.3 29B.4 301.2 306.3 302.9 303.7 304.5 312.2 263.1 209.2 221.5 372.9 2.682 47.7 205.0 253.0 2B8.3 296.1 296.7 293.1 299.6 299.9 301.7 306.7 304.3 305.5 304.B 312.2 263.5 210-2 222.9 376.5 g.b56 51.7 205.0 253.0 288.3 296. 1 296.3 293"."l ' 300.0 299.5 361.6 307,0 304.3 305.5 305.2 312.6 264.2 210.5 222.9 376. 7 2.654 59.7 205.0 253.0 288.3 296.1 297.1 293.5 299.6 299.5 301.6 306.7 303.6 304.7 304.8 317.2 262.4 210.3 222.8 377.0 ?.652 70.7 205.0 253.0 288.3 296.1 296.3 292.8 299.6 298 .4 301.2 305.2 303.2 304.0 304.7 311.1 262.0 208.4 221.1 371.4 2.692 91.1 205.0 253.0 288.3 296.1 297.4 293.5 300.4 299.2 302.3 306.7 305.0 304.7 305.7 113.5 264.6 210.0 222.7 374.3 2.672 94.1 205.0 253.0 288.3 296.1 297.5 292.8 299.3 298.1 302.1 306.7 304.0 304.4 305.6 312.7 263.5 2o<).4 221.9 373.3 2.679 101.1 241.3-335 .B 295.6 299.B 296.3 29?.1 298.9 297.7 301.? 305.2 303.2 303.7 304.5 311.8 259.5 208.3 221.4 370.6 2.699 106.1 „ „ — ~ - - " = ^-TTS 106.T RUN 25. . W C .2' .2 1 14156. OW &86?*. TWC 396.6 DTMC. 1 76.4 - I l l ) j m H I ) T<4) ri51 T I 6 ) TI7) TIB) T |9) T 1 10 ) T i l l ) Tl 12) r i 131 II 14) 1115) TIN TUMI 1000 * TIME 206.5 305.2 371.5 392.3 391 .0 3B6.7 1 9 7 . 2 194.9 *01 .3 * 12.0 404.6 403.6 407.3 407 . 1 799. 1 209. ? 2 3 ' . 6 369.0 7. 571 0.0 205.' . 301.5 3 7 ? . * 392.7 390. 7 3?6.3 397.9 396.7 4C? . * * 1 2 . ' *05 .8 404 . 4 407. E 407.? 797. 7 2L'E.9 734. 5 367.2 2.563 1.0 2C5.4 30* . 1 174.3 397.3 391. 3 367.2 198.9 395.'> 402.4 *12 .7 *05 .3 403,8 407.6 4 0 7 . i ?98.0 2.'8. 7 734. ' . 3P5. 5 2. 587 2 .0 206. 1 3 0 * . 9 3 75.5 193, 7 393.1 307.7 399.6 317.1 ' .04. 1 413.7 407. 3 405.4 *09 .6 415.S 305.2 21C.5 235, •) 3E6.8 2. 585 5.0 205 .0 304,9 3 7 6 . 0 1S3.3 39?.0 3E7.7 398..1 397.3 *03 . 1 M O . * *06 .0 4 0 * . 1 4QB.6 417.8 798. 1 2 C.<i. 2 735.4 334. 5 7.601 7.8 208 .9 328 .5 * 5 * . 6 * 7 * . 7 495.8 *70 .5 469.1 * 8 * . 6 * 9 * . 9 5*4 .5 514. 7 523 .2 5 71.0 424.5 308 . * 3l2 .1 736.6 2 3 7 . * * . 2 l ? 14.3 RUN 26. W 0.242 RE 11E45. QW 43655. TWC 326.6 UT^C 110.7 H I ! T (? l TI31 TI4) T15) T(6) T{7) TI81 T<9) TI 10) T i l l ) T112) T i l l ] TI14) T115) T I \ TOOT HM 1000 R TIME 204.2 269.0 312.3 323 . 3 323.1 12C.7 126.5 37.5.8 329.0 335. 1 331 .6 331 .3 333.2 3*0.8 279. 7 209.6 225. 1 394.2 2.517 0.0 2C3.e 769.4 313.5 37*.0 323.5 319.2 3?6.7 3 2 5 . 3 2 9 . ? 335.2 312.4 337.0 334.5 319.0 271.0 ?09.9 275.3 395.5 2.529 0.3 205.1 270.7 114.6 324.4 323.0 321.2 328.5 327 . * 331.9 317.5 314.3 313.5 335.0 3*1.2 273.4 210.2 277.1 195.0 2.532 0.5 :JO4.6 g&q.a s u . f e 32T,e 324.5 120.3 126.2 nt.} 332.0 337.7 333.8 334.6 136.4 v . i . i an.4 200.9 225.3 VFJ7% r r s n TTT 20* .8 77C.0 114.4 3?4.7 375.2 370.7 378.8 329.3 132.0 3 IE.2 335. 7 31*.9'337.8 .119. 1 269.0 709.9 225.3 337.0 2.58* 4.0 206. 5 271 .5 315.5 375.? 325.6 371. f. 120.6 120. 1 3 ,1 .7 339.6 335.5 135.2 337. 1 319.7 271 .2 209. 5 ' 24 .9 31-5.0 2.598 5.5 206.5 271 . 1 314.4 325.3 375. 2 321 .9 179.6 379.5 331.7 HP.6 315.9 336.3 337.fi 319.7 270.5 ?rr».5 275. 7 19 / . 4 2. 582 6.5 206.5 271 .8 315.5 325 . * 125.6 3 ? ' . I 379.9 3?.). 7 ,33.4 133.6 116.1 135.') 339. 1 342.5 775. 2 7J-J.9 776.2 19 I. 1 7. 582 15.3 ?05.7 271 .3 114.4 325.9 125.^ 371.0 111.0 1?B.7 l j t . , 0 119.7 .317.5 336.1 318.6 3*3.9 276.5 210.Z ??6.7 387.6 7. 580 18.5 204.6 270.0 31 3.7 125.4 326. 1 370.7 3 *P .? 33 3 .T~3 34. ? 1*"-. 9 336.6 336.5 339.6 341.6 773^6 ?0>*.2 ?25\ 7 TgTTl 5TTT" 2C5.4 271 .4 31 5.9 325 . * l?5.fc 320.7 130.2 329.2 1 3*.5 33-7.5 336.3 337.0 340. 1 147.9 271 .9 709.8 2?b.I '39^.6 2.594 24.5 2C5.4 27?.0 315.5 175.4 325.6 3'?..4 131.0 3?<>.7 314.5 339.7 335.9 336.5 139.1 343.? 277.7 209.9 226,1 385.4 2.594 30.3 207.7 271 . * 114.8 3 ? 5 . * 325.2 327.1 3 1 C ? 3? .^C 3 ) * . 5 340.0 117.3 337 . * 338.7 3*4.6 275.9 ?uv.B 226.0 165.1 2.596 39.5 205.0 270. 7 314 .B 325.) 325.4 -21.4 179.5 32S.C 3 33 .3 319.7 116.6 336.6 337. 5 346.4 279.9 209.6 ??4,6 382.8 2.61? 48.5 2 0 3 . 8 2 7 0 . 3 314 3 I J25 6 • . J I . • 33B. 7 3 1 4 •J K.C 0 3 3 7 . 7 3 5 7 . 4 3 4 0 . 0 3 4 7 9 ?0O. i 225 .0 •Mil. 1 2 . 6 1 7 6 4 . 8 2 0 5 . 7 2 7 0 . 7 3 1 5 5 3 2 6 0 125 3 ? ? . * 1 3 0 . ? 3 2 9 . 4 3 3 4 9 3 4 C 7 1 1 7 . 7 1 1 7 . 7 3 4 0 . 3 3 * 7 1 2 7 6 . 8 2 0 8 . 9 2 2 5 . 2 3 9 0 . 5 2 . 6 2 B 7 3 . 3 2 0 5 . 4 2 7 0 . 7 3 1 5 5 3 2 6 6 1 2 6 0 1 2 2 . 4 3 3 0 . 2 3 7 8 . 7 3 1 3 * 1 3 9 3 3 3 6 . 6 3 3 7 . * l l f i . 9 3*5 3 2 7 6 . 1 208.0 7 2 * . 5 3 7 9 . 8 2 . 6 3 3 7 B . 5 - ' 2 0 5 . 1 2 7 0 . 3 316 ? 3 7 5 R 326 1 1 2 7 . 3 131.0 1 3 0 . 6 3 35 7 3*C 7 3 3 8 - 6 3 3 7 . 4 3 4 1 . 0 348 6 2 8 6 . * 2 1 0 . e 2 2 6 . 7 3 8 * . 7 ' 2 . 5 9 9 9 0 . 8 t 2 0 6 . 1 2 7 1 . 6 316 9 3 2 6 5 176 ? 3 ? I-i 331.0 3 1 0 . 4 3 3 5 6 140 0 3 3 6 . 0 3 3 7 . 4 341 .0 3 4 9 5 ? 6 5 . 3 20*5 .2 7 2 5 . * 3 7 9 . 5 2 . 6 3 5 1 0 2 . 3 i 2 C 6 . 1 2 7 3 . 1 3 1 7 7 1 2 6 5 3 2 6 7 1 2 1 . •> 331.0 310. e 3 36 6 141 4 3 1 8 . 4 3 3 8 . 1 3 4 0 . 7 3 * 8 8 2 7 5 . 6 2 1 0 . 8 27 7 . 5 3 8 * . 2 2 . 6 0 3 115.0 - • - • — - - - - • - — J J P . . t . . . . . , u , . , j . , 179.5 2 C * . 6 270.7 316. 6 126.9 326. 7 371.5 330.2 110. 4' 3 35,9 3*1 .0 338. 7 337.0 340-7 354. 1 294.6 208 . * 224.9 377.1 203.8 270.3 116.6 126.5 3 26.7 373.2 310.2 330.4 335,2 140.0 137.7 337.0 340.0 351.6 781.7 20G.1 224.7 " 2C5.0 271.1 117.1 326.9 177.2 322.8 310.6 330.4 335.7 140.5 337.7 337.0 3*0.3 352.0 283.1 2H6.8 2?4.9 2C5.7 277.7 317.3 527.7 327.4 323.2 111.6 330.P 135.9 341.1 339.1 118.4 340.e 352.0 281.0 ?10.2 226.7 204.6 272.2 117.7 327.5 328.1 324.1 317.0 330.6 138.0 1*1.3 340.1 339.1 3*1.7 351.6 785.7 709.? ? ? 5 . 5 652 377.7 2.647 373.2 2.644 161.8 381.6 2.620 17*.5 *1 .3   1 . 1 1 .  .  .  .  .  375.4 7 .66* 185.8 "'^Ub.O 27?.4 117. 7 326.1 327.4 3 2 31 ^ n z T O T J ' U T H ~i IB ."4 " 3 4? . 5 340. 1 330.4 341 .C 359.3 299.3 2 0 7 . 2 2 4 . 1 TTTTS 2T5TI 1'99". 3 " 7C 5 . 6 2 77 . 7 JIB.4 327.tS 178'.* 1 ? * . 7 333. 1 3 33. 1 3 38. 7 343.4 341 -2 339.5 342.4 360.7 295. 7 710.? 276. 1 375.1 37";.ft 117.7 l * n t a TA I n s t n r> i n c u i /. ioi a ir\n -, i c n -i-, -t -> - - - - - - - - - - - • - ?.666 213.3 205.1 273.0 319.1 326.1 128.o 325-6 312.7 332.1 338.4 3*2.8 141.2 140.2 3*3.5 361.4 292.8 209.7 275.8 377.2 2.687 223.5 205.1 273.3 31B.9 328.4 128.9 324.3 331.0 312 . * 319.5 343.4 3*2.6 342.3 344.5 369;7 305.7 710.2 226 .7 , 373.5 2.677 CVJJ.J t p j . j J I U . T j £ c . j £ n , - i .-tct. .i j j i, a a i i . i : j • y , a ^ j . i 31^.0 i*tc . J ini i I au->,f * IU. { i.i.b. t , fJ.5 205.1 273.3 319.6 327.9 329.2 324.8 333.4 332.9 319.1 3*7.1 3*3.0 347.1 3*3.7 398.1 .151.0 ?09.? 226.0^ 171.2 lll'l ^-'^ ll1"'7. . j - ' 4 ^ 1 9 ' f ' 342.5 342. 3 3*1 .9 343. 1 331.9 2 ? 8 . o ' ? H . 6 ? ? 7 . 7 ; 378.7 236.8 2.694 248.8 2.05.0 272. „ SLU.J J £ J . n J E , . < , „ . - ^H^.H ,H*.W 2C2.7 27?.? 315.2 125.8 3?9.2 324.6 333.9 317.2 341.7 3*1.1 ?C2.7 271 .S 115,'5 375. 1 327.7 324.2 113.<* 13 1.9 3*0.7 3*2.8 203.4 272.7 316.3 325.6 378 . * 125.0 3 3 * . 3 - 3 3 2 . F 3*1.7 , 4 * . 6 7C3.8 776.0 117.7 326.8 330.6 326.2 336.5 334.1 3 * 2 , ° 346.0 2C5.0 275.J5 112.1 J77.7 330.^2 3?6. 1 316.4 3 3 * . ! 343.5 346. 1 204.6 275.0 319.3 3?6 ." 311.1 32S.6 337.1 31* .7 3*3 .2 3 * 6 . * 342.9 341 . 9 34313 331.9 226 1 200 5 >,>* 9 371.6 2.691 257.0 343.0 341 .6 343.6 311.7 2?5 5 ?oe ? ??3 6 366.5 2. 728 270. 5 342.6 342 1 143.6 332.3 ?24 3 208 4 223 9 368.? 2.716 276.5 344.0 .14* 1 345.2 334.0 226 6 208 ? ??3 5 36.3.8 2.749 2B<!. 0 345. e 345 .6 347.7 335.8 227 6 209 5 ??4 B- 363.0 2.755 293.8 3*6.0 146 3 347.8 336.7 227 6 210 5 276 2 165.8 2. 734 307.8 347.0 3*7 .6 149.3 337.3 228 O 210 2 225 9 363.3 2. 753' RUN 27 . W 0.2*2 HE 1*322. QW 5B252. TWC 3 7 1 . * UTMC 151.5 j T(2) K l ) T<4) T(5) 7(6) T(7I T(8) TI91 T(t01 T i l l ) TI121 T1131 TI14) T115) f[N TOUT HM 1000 R TIME 378.4 383.0 363.8 2*41. 1 2 10.7 231.9 384.6 2.600 0.0 _ ^ '380 .3 392.7 364.8 242.2 211 .6 233.3 384.7 2.599 1.0 204.6 292.8 353. 7 365.2 367. 3 362.8 373.3 371.C 378.2 365.5 380.6 380. 1 383.5 365.9 240.6 210.5 737. 3 3B0.8 2.626 4.0' 2C5.4 ?92.8 352.6 367.3 366 . * 362.7 373.0 371.C 378.5 385.3 379.9 380.5 384.0 365.2 239.4 210.0 231.6 379.3 2.636 5.5 205.4 297.5 352.6 365.9 367. 1 362.3 372.7 371 . r 378. 2 385.3 379.9 380.8 385.1 366. 1 241.4 210. 1 231.7 379.6 2.634 6.8 204.6 293.7 355.2 367.7 368.4 363 . * 374.6 372.4 37B.9 385.6 381.1 380.8 385.3 364.8 240.7 20".9 231.6 376.7 2.654 ., 10.I 206. 1 296. 1 356.8 367.3 36S.8 362. 7 376. 1 373.(S 3B2.7 387.? 384.1 3B2.4 384.1 365.5 237.6 ?09.9 231 .5 373.3 • 2.679 13.3 207. 3 31 2.5 394.9 398.2 402. 7 393.7 408.6' 411. *- * 1 9 . 1 4*0.2 435. 3 431.9 443.8 392.3 236. 1 210.5 232.3 295.3 3.386 21 .6 273.B 3.653 23.4 264.9 3.775 24.7 207.   .  .  .  .  .  .   1 . *- * . 1 * .  .  .  .  .1 .1 £\0.t Z3Z.J 207.3 316.1 468.6 411.7 416.2 468.6 422.0 427.9 434.6 45B.8 454.1 451.7 466.4 402.2 236.) 211.8 233.2 206.1 316.1 413,1 416.4 421.9 414.5 4?7.0 433.3 440.4 466.4 459.9 458.0 473.8 403.5 234.2 210.8 232.0 205.0 316.7 *17 .0 421.8 426.8 421.8 *31.7 441.7 446.9 475.8 469.0 467.9 484.9 406.9 232.4 208.5 230.3 253.b 1 .^*0 dt..u 205.4 31B.7 426.2 431.9 436.9 431.9 447.4 452 . * 457.7 488.1 480.7 480.4 49B.7 414.0 ?34.7 210.5 231.9 736.0 4.237 27.5 2C5.0 320.1 438. ' . 4 * 1 . * 446.7 444.B 453.? 46*.1 464.2 501.1 *92 .2 496.2 517.5 421.6 235.1 208.6 229.8 222.6 4.493 29.5 207.3 370.1 446.9 4*9.2 457.0 454.7 462.1 475.5 475.3 514.7 505.8 505.8 529.1 423.6 234.4 208.0 228.4 209.4 * - 7 ? 5 31.7 234.2 323.0 455.1 45e.? 465. 8 465.6 471.fl 486.e 481 .5 528.6 513.0 517.2 541 .4 42A.I 235.5 308.6 210. 1 20276^ 479T7 33.8 205.0 324,8 463.0 *67 .2 475.0 476.1 480.8 498 . * 491.9 542.5 525.5 530.0 556.5 431.7 235.5 210.2 231.3 195.4 5.117 36.1 3-12 RUN 26. W 0.242 1412>. QW 49596. TWC 348.6 DTMC 131.1 ; T i l l T<2) T(31 TI4) T (5) T(6) T (7) T181 TI91 T (10) T i l l ) H I ? ) T (13)"T (141 T115) TIN TOUT HM 1000 R 2C5.1 2 M . 1 333.7 342.9 144,0 340.2 346.9 346.4 351.6 360.2 355.3 156.0 357.9 340.5 43.5 209.6 228.1 178.3 2.643 204.7 281.0 333.7 344.3 345.1 340.6 349.9 348.7 353.5 360.8 356.5 356.9 359.3 342.2 43.5 210.5 ??9 .3 377.B 2.647 205.7 382.0 334.5"345.0 346.3 342. 1" 3~5T.2 346.B 354.6 361.1 356.5 357.4 359.7 34?T4 43.5 211.1 229.B 37772 2.651 204.4 281.0 332.7 344.3 345.5 341.0 350.1 348.8 353.6 359.7 356.0 356.7 359.0 339.8 43.5 208.7 227.3 372.8 2.682 204.4 281.1 333.4 344.3 345.8 341.0 349.8 348.= 352.9 361.1 356.0 356.4 358.6 340.5 43.5 208.6 227.4 372.7 2.683 2C5.0 281.1 334.1 344.8 345.5 341.0 349.9 34B.5 353.9 361.1 357.1 358.5 360.7 347.6 43.5 210.1 22B.9 375.2 2.665 2C5.0 281.3 334. 1 345.4 345.7 340.6 349.9 34B. 1 353.6 362.0 356.7 356. 1 361 .4 340.5 43.5 209.3 226.2 373.0 2.681 .205.4 285.0 341.0 349.8 359.9 351.2 366.6 364.0 374.1 386.6 380.7 390.6 415.9 359.4 43 .5 ,210 .6 279.4 320.8 3.117 206.9 287.0 345.0 3"5T:?"365".fl 357.2 371 . ! 370. 5 380.5 396.5 389.6 400.7 429.9 365.0 43. 5 211.2 229.9 30671S 37260 25,0 > 403.8 396.1 408.4 441.3 367.0 43.5 209.5 278.0 796.0 3.379 27.0 • - 1.8 369. 1 43.5 209.7 22B.0 267.7 3.476 29.0 6.2 375.7 43.5 209.7 22S.2 273.8 3.587 31.0 t v „ u * a , . , . J U . . . , , , . 8 . 6 378.8 43.5 209.9 228.7 768.6 3.723 206.2 289.7 350.0 368.8 366.3 380.3 390.3 396.7 4C4.5 436.4 424.1 441.2 4B7.2 382.6 43.5 211.3 229.2 260.0 3.846 itJO.^ £Of.U 3*t?.<J 331. * 3(1.1 JOU.J 3-JO • :> jqi.O t u u . l 1C1.-» 204.2 285.0 345.9 351.5 366.7 358.6 173.8 374.2 384.2 403.8 396.1 408.4 441.3 205.4 2B5.7 346.B 357.4 370.7 363.2 376.9 37B.4 388.2 409.9 401.5 416.1 451.8 204.7 287.2 351.1 361.2 375.1 369.0 3B2.4 384.( 394.1 418.5 40B.3 424.1 466.2 204.6 287.5 354.8 365.7 391.7 376.3 386.9 391.4 399.6 428.7 41B.0 435.0 478.6 s n * . ? ?flo_7 * t ; n n ^mn.fl ion •x n o n . * 3 0 * . ? 4f:4.5 436.4 424 . i 441.2 407.? 206 3 291.0 360.4 371.6 390.6 3 8 5 . i 395.1 401.6 409.a 445.3 426.9 449.4 497.8 38?.9 43.5 210.2 226.4 751.1 3 982 37.8 206 1 290.4 366.6 3 77.B 401 . 1 4C0.3 404.6 418. 1 423.0 468.2 445.6 463.9 516.3 389.7 43.5 210.2 229.3 234. 7 4.260 40.0 2C4 6 289.0 368.9 381.7 404.2 404.4 406.3 422.4 424.0 477.7 448.6 468. 1 518.5 3<)0.4 43. 5 ?oo .e 228.4 230.4 4 340 41.7 1 204 6 2B9.7 374.6 389.5 416.3 417.9 416.5 436.4 434.7 484.9 459.7 478.0 525.5 395.2 43.5 210.P 228.7 219.0 4 .565 43, 7 202 7 290.B 377.3 311 .9 4L9. 7 473.9 419.2 439. * 438.7 487.8 464.5 483.4 532.8 397.6 43.6 208.9 227.0 71 1.6 4 727 45. 7 205 0 291.9 381. 1 397.7 424; 7 427.9 422.9 444.7 443.1 494.5 471.7 491.9 543.9 400.6 43.6 2 09.9 227.9 207.2 4 826 48.2 TWC 345.4 DTKC 129.6 T i l l T(2) T'131 TI4) . T15J T<6) T(7) T (8 ! TI9) T110) T i l l ) T(12) TI131 T ( 1 -41 1(151 TIN TOUT HM 1000 R TIME 205.8 296.0 337.1 344.4 340.1 313.8 344.4 341.4 346.? 356.5 350.0 349.1 354.3 341.1 227.5 208.5 224.5 677.7 1.476 0.0 205.8 297.2 338.5 345.6 341.3 334.2 345.4 342,^ 348.9 358.2 351.8 351.2 357.9 343.2 229.0 209.2 226.1 6 7 6 . 0 1.477 0.5 205.6 296.4 337.9 345.6 340.1 333.5 344.4 341.0 34B.2 357.9 350.3 351.4 358.5 345.3 229.4 209.1 226.4 677.7 1.475 2.0 206.9 2o8.5 340.3 346.7 340.8 333.2 344.5 341 .4 .34T .9 359.3 35077 '351.7 "3"5"8.6 344.2 230. 5 ? 107?" 227.4 &B3.4 T776T T T S -2C6.3 2«-9.6 341.4 348.1 344.0 335.2 349.3 344.2 352.4 361.7 354.9 354.2 361.6 349.1 230.1 210.6 227.9 669.6 1.493 7.0 207.3 303.0 348.0 351.7 352i4 341.2 359.1 351.2 365.B 375.1 365.7 370.5 395.2 363.1 729.4 210.8 227.3 614.2 1.628 12.0 207.7 304.7 350.2 352.7 355.3 342.7 362.6 355.1 369.4 379.5 370.2 377.1 404.7 36B.0 229.8 711.2 228.0 592.3 1.688 13.0 2C5.4 3C6.5 358.2 359.8 359.4 346.0 368.5 361.0 376.4 391.8 378.5 391.7 437.9 377.3 727.6 203,9 225.B 551.9 ' ~ ~ " ' " ' " " " " " " " " ' " " " 515.6 RUN 3C. W C.176 HE 10617. Ow 37097, TwC 146.6 0TMC 129.1 T i l ) T(2) T131 TI41 T|51 T<6) TI71 TI8) T(9) T110) T i l l ) T U 2 ) T f 13 > TI14) T1151 TIN TOUT HM 203.8 271.4 327 . 9 337.5 3 4 3 . 0 340.1 347.2 347.0 351.0 356.5 353.4 353 . 3 355.0 ,333.6 234.9 209.6 228.2 294.2 3.399 0.0 202.7 270.3 327.2 336.6 342.9 338.7 345.7 345.2 349.6 354.7 350.6 352.0 354.6 334.0 234.2 203.6 227 . 4 295.1 3.388 0.3 2C3.8 273.0 328.8 3 3 9 . 4 3 4 4 . 3 340,8 346.4 346.6 351.7 357.0 353.3 354.0 356.9 335.7 234.7 208.2 226.7 290.1 . 3.447 1.3 2C3.4 271.0 376.7 330.7 343.1 3 3 9 . 1 347 . 9 346 . 3 350.6 357.2 353.8 354.8 356.4 334.7 236.4 210.3 229.2 295.8 3.381 2,9 203.5 271.4 326 . 3 3 ) 7 . 1 343.3 330.7 346.5 345.0 3 4 9 . 6 354.7 352.4 352.4 355.0 333.3 236.4 209.5 227.9 295.2 3.387 5.4 21:5.4 2 M . 4 IZg,C 338.7 343.5 339.3 346.5 346.3 3b0.b 356.5^352.0 3S3.4 3 5 7 . i 334.7 237. 1 21 1.2 229.2 ?9T72 3736"4" 7 7 V 2C5.9 217.2 332.2 33E.9 345.4 341.9 351.4 348.4 351.0 361.7 358.0 361.8 374.1 337.9 233.4 211.3 229 . 4 287.4 3.480 11.2 205.7 278.7 337.B 342.1 351.7 340.6 361.5 3 5 7 . 1 3 5 8 . 3 373.4 371.2 377.0 395.3 344.2 231.6 209.5 227 . 4 261.3 3.819 14.5 205.7 281.6 346.3 349.5 360.4 361.9 374.9 374.6 372.6 391.8 390.8 398.8 421.1 355.1 231.6 211.8 229.7 239.4 4.177 18.5 205.7 282.0 350.8 355.4 368.8 371.3 3B3.0 385.E 382.6 403.7 402.7 412.3 444.1 362.4 231.2 209.3 227.1 220 . 3 4.538 21.2 2C5.4 284.0 357.5 360.8 375.3 3 7 0 . 2 3 0 2 . 9 397.C 3 4 3 . 3 417.9 417.9 425.1 461.0 368.3 232.0 209.8 227.5 208.0 4.807 23.3 205.7 2Bb.9 364.4 36b.6 3S5.0 390.3 403.2 409.2 404.2 430.3 429.3 43B. 1 476.0 3 7 4 . 9 232.0 21 1.0 229.4 YWTX STToTJ 25.3 2C5.4 268.4 371.C 373.5 393.2 4C0.5 414.3 421.3 415.7 445.5 443.5 452.5 496.1 381.7 232.3 210.0 220.6 1B6.1 5.375 27.3 204.6 2B7.7 372.7 376.3 396.2 4C6.3 417.0 427.? 419.8 453.4 447.8 458.5 504,8 381.0 232.7 210.2 228.2 179.B 5.562 29.3 2C3.B 285.9 376.5 380.1 403.0 412.7 423.7 435. f 427.9 -.60.b 454.7 467.6 513.2 383.8 232.7 209.2 227.4 173,3 5.770 31.6 203^8 287.0 381.9 387.3 41 1 . 1 423.4 432.0 444. 1 438.2 472.6 464.B 47B.8 521.7 306.8 232.0 208.5 226.6 167. 5 5 .972 34.6 RUN 31. W C.242 * E 14968. OW 69281. TWC 402.7 DTKC 181.0 I l l l T(2) T13) T<41 T15) T16) TI7) T O ) TI01 TI10) T i l l ) T i m T1131 U 1 4 ) T H 5 ) '1*4 IQUT 205,7*311.3 37B.0 39).6 400.8 393.5 406.0 399.3 410.5 412.7 410.4 410.1 416.6 394.2 245. 204.6 312.0 360.4 393.5 403.0 396.2 413.5 404.7 470,6 422.1 420.8 419.3 427.6 390.9 244. 205.7 31 1.5 383.7 355-3 405.9 397.6 419.2 407.4 427 ." ' " ' ' " " " 1 312.7 385.6 306.4 410.6 402.4 424.5 411.B 434. _ _ _ 203.8 314-9 383.3 4C2.5 4 19. 7 413.5 431 .5 422. f 445.2 456.5 461 .7 471 .6 504.0 419.5 240.0 21)0.1 234.5 207.3 260.7 298.7 319.5 330.2 341.0 3SS.8 362.5 382.8 433.4 432. 7 472.5 542.9 374.7 216. 1 211.2 219.6 • 415,9 2.294 15.7 RUN 32. W C'. 242 HE 14501. OW 40040. TWC 34B.6 DTMC 129. 7 T( 11 T<2) Tl 3) Tl 4) 1(51 T<6) T(7) TI8) TIO) T (10) T< 1 U T(12) TI131 T( 14) T( 151 TIN TOUT HM 1000 R TIME 205.4 205.4 270.7 279.7 33 3 .7 331.9 341. 3 340.4 345.1 344.6 340.3 34,9.7 346.4 338.5 349.4 345.0 354.6 351-5 360.1 158.9 353.6 352.5 354.3 355.1 352.9 354.5 337.6 336.2 234.7 234.3 210.7 210.2 229.6 228.8 385. 1 3B6.2 2.597 2.589 0.0 2.3 2C5.2 202.5 332.3 340.B 344.4 338.9 349.6 344.4 352.7 362.9 355.0 357.8 371.4 335.5 231.4 210.1 228.3 377.7 2.647 57T~ . . w . * «.„«.. ^ j j i . j , - . .  .1 .  .  .  .  .  .B  .  .  1 .  t . u . . c t o t J 204.6 2B4.0 334.4 339.4 347.4 341.1 357.7 349.5 360.0 370.0 363.5 369.9 388.9 342.9 229.1 2J9 .4 228.0 J U U . V < . . . , u 207.3 287.8 337.6 340.1 351.1 347.0 355.4 354.1 365.4 376.4 370.6 376.4 399.4 348.5 231.0 211.3 229.6 352.6 2.836 202.7 289.6 350.2 349.9 362.6 360.B 370.3 369.4 382.7 393.2 389.6 400.3 427.5 359.0 227.3 208.2 226.1 307.0 3.257 2C5.1 295.0 363.8 359.1 377.2 376.9 386.2 386.6 401.7 416 .0 -413 .0 426.2 459.5 375.3 230.3 208.8 226.5 275.1 3.635 1 7QZ 1 iT/s i ifcfc n i a -a 7 io*. *. l a c a i m e A 1 1 i A I A I. . /. T I.J,*> a i. • 1 c l a i i n A i ^t\r\ -* tt-r i ien -i i o -»-i 360.0 2.77B 8.8 10.9 205.1 294.3 370.6 365.0 383.7 3B6.6 395.8 397.5 4 3.3 430.4 426.7 442.8 48 .5 383.2 230.6 209.2 227.2 258.2 3.873 203.4 296.1 .380.7 374.7 395.3 390,i 408.3 412.0 429.3 448.2 447.6 469.3 509.5 394.5 22B.4 207,0 225.2 2 36.7 4.225 203.1 298.3 389.9 381.2 4C3.6 400.1 417.1 420.0 437.7 460.2 459.7 480.1 523.0 400.6 229.9 208.0 226.1 225.4 4.436 204.4 3CO.0 4CC.5 366.8 413.6 417.4 426.2 430.8 443.2 463.5 464.3 486.2 530.0 402.0 2 3 \ . \ 209.5 227.0 214,6 4.654 204.4 300.8 402.8 392.9 416.8 422.4 430.8 435.4 449.0 468.5 470.1 493.0 537.1 405.3 200.4 208.7 226.9 213.8 4.677 RUN 33. W 0.242 RE 14481. QW 49848. TWC 346.8 DTMC 128.9 T i l l T(2) T(3> TI4) T t 51 T(6) T I 7) TI8) T(9) TI10) T | U | TI12) TI13) T I M ) T 1.15» TIN TOUT HM 1000 R TIME 204.6 279.5 332.I 341.7 342.3 338.9 346.6 346.4 346.3 359.2 352.9 352.5 353.9 335.9 232.8 2 0 9 . 9 2 2 8 . 4 386.8 2.565 070~ 205.0 280.2 332.6 341.7 341.3 339.6 346.6 345.0 34B.3 360.6 352.2 353.4 356.9 337.6 233.6 209.1 227.8 384.2 2.603 1.3 204.8 280.6 333.7 340.8 340.9 339.2 348.0 346.4 349.7 360.4 353.6 354.3 356.2 336.9 234.7 209.5 228.4 3B3.9 2.6p5 3.8 203.B 282.6 330.5 334.1 334.0 325.0 333.5 331.2 332.8 34S.9 340.9 343.8 369.0 323.8 230.6 211.0 229.5 418.3 2.391 • U . O 202.7 281.7 328.4 328.7 332.4 325.0 332.8 332. ( 337:0 348.5 346.9 350. 1 384.0 328. 1 227.3 207.4 226.6 404.5- 2.472 15.2 205.4 289.6 363.5 345.0 359.6 349.1 367.2 373.9 375.8 401.4 39B.B 409.0 479.9 355.5 229.1 210.9 2 2 9 . * 306.2 3.266 21.0 2C5.'6 29 l . f l 381.4 355.9 376.5 363.8 383.1 391.7 391.3 421.0 417.7 428.7 502.4 364.2-228.4 210.8 229.1 277.4 3.605 24.3 2C5.4 290.7 385.1 356.6 379.3 367.6 386.2 397.5 395.8 429.7 424.1 435.9 507.4 365.3 229.2 210.6 228.9' 267.3 3.741 27.3 205.1 294.0 3S5.0 362.2 369.2 3 7 6 . 3 3 9 5 . 3 406.3 407.4 444.6 435.4 450.0 518.4 369.4 228.0 210,1 228.0 251.7 3.973 30.5 2C6.3 296.5 399.4 366.4 394.3 381.8 400.5 414.0 412.B 452.2 439.7 457. 1 523.9 372.2 229.9 21 1 .2 229. 1 246.0 4.065 34.-3 3-13 Tt'll T<2) TI3I T(4) J15) T(6) T I 7 J T18) T(9) T I 10 ) Till) T (12 ) TI13) T114) T 115) OUT HM 1000 R TIME 168.9 168.8 168.2 166-5 168.0 169.3 166.5 167.7 165.7 164.2 167.7 141.2 141.0 _1*0-P_ 140.4 139.6 141.2 137.2 141.2 140.8 136. 8 140.6 164.3 165.6 165.2 165.2 165.9 167.5 165.2 166.4 164.1 162.5 165.6 168.2 168.2 167.1 168.6 168.4 166.9 167.5 166.6 166.0 164. 3 167.5 165.2 166.0 166.3 166.4 165.2 '164.9 165.2 164.9 165.1 164.4 164.0 164.5 162.4 162.9 163.6 162.5 162.4 160.9 160.1 159.0 162.4 162.1 168.6 168.2 166.6 166.7 166.6 166. 7 163.q 164.4 163.5 160.8 163.5 169.9 173 170.2 173 168.3 171 168.1 171 167.5 171 167. r, 1 70 165.6 169. 164.8 166. 164.0 168. 161.7 164. 164.6 167. 175.0 .7 174.6 .0 174,3 175.4 .0 173.8 6 173.5 1 171.9 7 171.7 3 170.3 9 169.2 9 171.2 176.8 176.8 176.8 175.7 175.2 174.9 173.3 172.8 171.6 169.5 173.0 180.7 198.0 179.8 201.5 179.7 202.3 179.5 202.9 179.4 204.9 180.1 203.4 179.1 205.0 179.8 205.0 177.5 203.8 175.2 201.1 177.9 202.9 178.8 179.0 178.5 176.9 178.6 176.9 177.7 176.7 173.8 173.4 175.9 153.3 154.4 152.9 152.1 152. 7 154. 1 152. 5 152.9 150.2 149.1 152.5. I 39.9 140.4 139.4 141.0 151.1 151.8 150.4 150.6 149.6 150.9 140.1 150.2 140.8 150.6 139.1 149.1 136.5 146.5 140.5 150.2 1614.2 0.620 0.0 1655.0 0.604 0.8 1625.2 0.615 1.6 1627.6 0.614 3.1 1637.5 0.611 5,8 1692.0 0.591 8.5 1775.4 0.563 12.5 1798.8 0.556 15.0 1794.0 D.557 18.3 1757.7 0.569 22.5 1828.9 0.547 27.5 TWC 169.6 DTMC 28.1 Hi) TTT) tTT) TTT) TTT) T T m fm TW) T(9) t i i o i Till) Tim t m i TU4i t i i s T TIN OUT HM 1000 R T I MET 138.0 140.8 138.8 138.0 138.0 139.6 139.6 141.6 136.4 141.6 139.J 162.2 164.5 164.5 164.8 165.1 167.5 168.0 171.4 166.3 173.4 171.4 3 170.7 8 173.2 3 173.2 3 171.6 7 171.7 5 174.0 7 173.7 3 175.0 7 170.1 8 171,9 8 171.3 164.8 168. 1 167.6 164.4 164.5 166.6 166.1 164.1 163.8 165. 1 165.5 167.3 162.9 165.4 164.5 169.6 171.8 170.3 169.4 167.6 170. 1 169.7 167. 7 172.7 1 75.8 176-0 172.9 173.5 176.6 176.6 175.0 173.4 171.1 176.1 175.1 175.5 174.1 173.4 172. 172.4 175.5 172^8 172.3 173.4 176.2 174.0 173.0 147.9 150.2 148. 7 146.3 137.5 146.3 140.2 148.9 139.4 148.2 138.0 146. 2568.8 0.389 2540.0 0.394 2558.7 0.391 2618.8 0.382 164.1 165.2 165.7 166.8 164.0 166. 1 164.5 168.0 170. 1 168.4 169.8 166.3 167.5 166. I 167.2 166. 7 168.4 163.3 166. 1 171.1 172.5 173. 1 174.3 169.8 172.3 172.9 175.3 174.7 175.9 171.2 1 73.6 170.5 169.1 172.2 171.4 171.9 170.0 174.2 171.6 170.2 167.1 173.9 169.9 170.5 172.8 172.' 174.0 171.0 173.6 170.0 172.2 171.2 174.6 170. 173.5 146.4 147.9 147.9 149.5 145.6 147.6 l3fl.l 146.4 139.6 148.5 139.1 148.0 142.5 151.2 •137.4 146.2 139.7 148.0 26ft2. 2739.7 2699.9 2892.9 2834.3 2706.4 0.373 0.365 0.370 0.346 0. 353 0. 369 166.8 165.5 1 7 1 . 2 173 .2 171 . 1 170.2 172.2 172.0 146.8 139.9 H A . 3 2 A 9 O . T " 0.346 TWC 169.3 DTMC 27.9 HI) TI2) TI3) T(4) T151 T(6) T(7) T(9) T(10) Till) Tl12) TI13) T114) T115) TIN TDUT-136.6 138.4 139.2 138.4 138.7 138.2 140.0 138.8 138.0 164.0 164.0 164.8 163.9 164.6 164.8 165.5 165.5 165.2 165.2 165.5 166.5 165.0 166.2 165.6 167.2 166.0 166.7 173.5 173.4 174.7 173.5 174.4 173.9 174,7 175.4 174.7 164.8 164.8 165.6 U 4 . 7 165.3 164.5 165.8 165.2 165.7 164.0 163.9 164.8 162.4 163.6 163.3 163.9 164.6 163.7 169.3 169.3 169.7 168.5 169.3 166.6 169.8 169.8 169.8 166.3 172.6 166.7 172.7 167.3 173.2 173.8 174.7 175.9 172.3 173.0 174.3 170.6 170.9 171.7 171.7 171.7 171.7 172.9 173.0 171.3 169.6 170.0 171.7 170.7 171.5 171.1 173. 1 173.1 172.3 172.6 172.7 174.0 146.6 145.9 146.7 13B.1 145.3 138.2 146. 1-139.1 147.1 13d.1 146.1 138.5 146.0 137.6 145.3 139.2 146.7 138.6 146.2 137.8 145.3 3436.3 0.291 3450.3 0.290 3448.3 0.290 166.0 172.4 166.7 172.8 166.7 172.1 167.6 173.5 167.3 173.6 166.6 172.5 174.0 174.4 173.8 175.3 175.4 175.2 172.5 173.0 172-3 174.2 173.3 172.7 172.5 173.9 173.1 173.9 174.5 173.9 144.9 146. 3 145.9 146.3 146. 3 146. 3 3504." 1 3433.3 3393.7 3383.7 3376.4 3 3Q6-2 0.285 0.291 0.295 0.296 0.296 0. 302 14.6 20.8 TWC 172.2 DTMC 27.9 " T i l l TT21 TTTT T P D TT51 TTT" TT7T rTFJ fl") TIIOI T'111 T ( 1 2 , T I B ) T ( 1 4 1 T t T 5 1 TTW rnur 139.2 140.6 141.1 141.0 134.6 139.0 137.2 137.2 138.0 163.4 167.0 165.3 167.4 167.0 167.6 166.9 168.0 165.8 166.1 166.2 165.9 165.8 165.3 165.0 163.7 165.6 165.3 172.2 173.7 174.3 175.3 173.6 174.2 173.2 171.5 173.0 168.5 166.6 169.5 167.4 169.7 168.1 170.3 168.2 148.1 166.6 169.3 167.1 168.5 166.3 166.5 165.5 166.1 165.8 171.5 172.7 173.5 173.1 172.3 172.7 170.8 170.3 170.7 170.1 170.5 171.2 171.4 176. * 172.1 170. 169.] 169.: 176.1 176.4 176.9 177.7 176.8 177.7 176-9 178.7 176.5 178.3 175.9 178-3 174.7 177.2 173.3 175.0 173.5 175.8 176.6 176.9 176.8 177.4 177.4 177.0 175.9 174.7 175.5 175.0 174.1 174.7 175.6 176.2 176.8 176.6 177.1. 176.2 176.2 175.2 175.7 173.8 174.1 173.8 172.5 173.4 173.7 176.3 176.3 176.7 176.6 151.1 1 50.8 151.5 151.5 151.5 150.0 149.? 146. 5 149.? 139.9 149.5 139.2 1<>B.6 140.4 149.5 140.1 148.6 13B.7 U 8 . 2 138.9 148.2 136.1 147.3 137.5 146.5 137.8 147,2 HM 1000 R 1 I ME 2234.3 0.448 0.0 2)00.8 0.476 3.B 2140.4 . 0.467 10.3 2074.2 0.482 13.0 2073.3 0.482 19.0 2062.5 0.485 23.5 2100.3 0.476 30.3 2141.9 0.467 36.5 2132. 1 . 0.469 36.5 176.2 173.6 173.9 170.9 173 TWC 170.0 DTMC 27.4 Till) T(2) TO) T14) T15) T161 T17) T I 8 ) T(9) T 110 ) Till) T112) T 113 ) T (14) T115) T|N TOUT HM 1000 R 138.4 162.7 136.4 162.7 140.4 164.6 136.4 163.9 166.5 166. 1 167.2 166.5 170.4 170.6 172.2 172.2 166.9 164.3 167.3 165.4 169.3 166.6 168.5 166.2 169.0 169.6 171.5 170.0 168.7 173.7 169.1 173.7 169.I 175.0 170.1 174.7 173.3 173.7 174.6 174.6 173.1 172.6 173.5 173.0 174.8 173.9 175,5 174.0 171.7 172.9 174.5 174.1 174.4 150.1 175.2 150.: 175,2 152. 175.5 152. 138.0 147.9 138.7 149^3 139.8 149.6 139.3 149.4 1461.5 0.684 1496.0 0.668 1463.7 0.683 1458.3 0.686 6.1 139.6 165, 138.4 164. 140.8 166.5 140.4 167.3 137.6 165.0 139.6 166.2 165.3 164.9 165.7 166.5 163.7 164.9 171.8 171.0 172.2 172.4 169.8 170.6 168.5 166.2 167.7 166.2 169.5 167.5 170.9 168.2 168.5 166.2 169.3 167.0 170.2 170.3 171.5 171.7 169.9 171.1 170.1 174.3 169.6 173.9 172.1 176.5 171.8 176.9 169.7 174.3 170.9 175.0 1 74.5 174.8 176.4 177.4 176.0 1 76.4 174.7 175.0 173.9 175.0 176.6 175.8 177.0 175.7 174.7 174.2 175.1 175.0 175.4 175.3 177.2 176.0 174.5 175.4 177.3 152. 175.9 151. 176.7 157. 177.1 15?. 175.5 151. 175.9 151. 139.1 149.1' 138.5 148.4 140.1 150.2 139.9 149.7 137.5 147.6 139.3 146.6 1443.9 1418.1 0.705 1424.0 0.702 13B3.6 0.723 1381.8 0.724 1412.5 0.708 Q.693 10.6 15.8 20. 1 24.1 2t>. 1 33.6 TWC 171.4 DTMC 27.1 Tin f m TTT) t T v ) t T s T TTT) f m Tie) Ti9) t u o ) t u d t< 12> n m tu4) t u s j U N -140.4 163.8 136.0 161.5 136.0 160.7 138.1 160.7 166.8 165.0 164.0 164.2 171.3 169.4 169.8 169.2 168. 165.9 166.3 165.9 166.8 165.1 164.6 164.6 171.1 169.1 169.2 169.2 169.( 174.9 167.S 173,8 166.2 173.7 169.2 173.7 175.3 174.0 174.0 174.0 175.4 175.9 175-2 174.0 175.6 175.3 175.9 175.2 173.8 173.0 173.5 174.i 174.2 174.4 174.8 175.2 174.6 T t T T o " 172.6 171.1 171.4 171.6 174.1 173.7 172.6 172.2 174.2 173.0 173.6 172.8 171.8 171.2 171.6 174.4 173.8 173.1 172.9 172.B 174.0 173.7 176.6 152. 175.3 150. 174.7 150. 174.7 150. 177.4 150. 176.2 150. 175.9 150. 175.2 149. 175.2 149, 175.1 149. 175.5 149. 2 140, 3 138. 3 137. 3 137. 7 138 7 137 9 137 6 139 3 137 TUUT 0 149.3 1 148.1 5 147.3 9 147.3 147.9 • HM 2081.5 2082.9 2043.0 2048.1 1970.8 1959.4 1963.5 1985.1 1981.5 1912.4 0.460 0,480 0.489 0.468 136.8 161.5 139.6 163.6 136.4 163.4 137.6 163.4 136.4 163.0 138.0 164.0 165.8 166.6 166.5 165.6 166.6 166.4 176.6 172.0 170.7 171.0 171.2 171.3 167.6 167.9 167.3 166.9 166.9 167.3 165.6, 165.7 165.3 165.0 165.8 165.7 TTOTS" 170.6 170.8 169.7 172.0 171.2 170.0 174.5 170.0 174.9 166.8 174.5 168.'' 173.9 170.0 175.4 169.2 174.9 1 147.9 6 147.4 .9 147.6 0 148.5 6 146.6 7 147.1 0.507 0.510 0.509 0.504 0.505 0.523 10.0 17.0 21.0 25-5 30.8 138.3 164.1 139.0 164.5 139.5 165.2 166.6 167.2 167.8 171.3 171.6 173.1 167.6 167.4 168.4 166.1 165.7 166.9 171.2 171,0 171.8 169.2 174.5 169.2 175.3 170.4 175.6 9 137 0 136 1 139 1926.1 1934.8 1961.5 0.519 0.517 0.510 34.0 40 .8 4 T . 0 TWC 171.5 OTMC 27.0 " T i l l " T m T(3) Tt4) T15) T16) T(7( T(8) T19) TUO) Till) TI 12 ) T I 13 ) T ( 14) T 115 ) TIN 136.8 159.8 165.3 166.5 167.5 166.5 17Q.9 171.0 175.3 175.9 139.4 137.6 138 138 139 138 16l.i 159. 165.9 165. 160.5 165.8 159.6 164.8 134.6 139.4 139.4. iti.b 167.6 162.5 167.5 163.7 168.0 163.9 168.1 TS9TT 168.1 168.9 166.8 169.6 169.4 170.2 170.2 170.4 170.8 16?.0 166.2 166.8 165.2 166.8 _ 166.6 ,0 167.0 .7 167.2 ,3 167.6_ 5 168.2 172.6 171.2 172.1 169.7 171.8 172.2 171.5 171.5 173.0 172.9 5 176. o 175. 7 176.2 7 174,4 0 176.0 9 175.6 0 176.2 7 176.9 1 177.5_ 6 177.1 176.4 174.4 .175.6 175.0 176.8 177.0 177.0 177.1 177.7 177.4 174.5 176.4 174.1 176.6 176.9 176.0 177.2 178.2 177.4 174.5 175.1 174.0 175.6 174.8 175.3 175.8 176.3 174.8 173.5 175.4 172.7 176.6 175.5 175.8 175.8 175.5 175.5 176.1 176.5 175.3 178.1 177.0 178.4 177.7 177.0 178.0 153.7 153.7 151.7 153.3 152.5 152.9 153.3 153.3 152.5 138.7 149.0 139.3 150.0 137.7 147.9 139.2 149.6 136.2i146.9 138.5 149.0 138.6 149.2 139.4 149.8 138.7 149.2 1353.1 0.739 1328. 1325. 1312.7 1301.0 1281.7 1257.2 1259.7 1257.S 1253.3 1236.8 0.752 0.755 0.762 0.769 0.780 0.795 0.794 0.795 0.796 0.809 3-RUN 41. W 0.172 RE 26430. OH 73010. TWC 196.3 DTMC 48.2 Til) Tl 2) TI3I T(4) T(5> TI6) TI7) TI81 TI9) T 1 10) T(ll) TU2) Tl 131 TI14) T(15) TIN TOUT • HM 1000 R TI HE 139.6 174.2 1B6.1 194.1 188.9 187.7 195.5 194.7 201.3 204.7 203.0 201.9 201.5 205.4 163.2 139.4 156.7 1519.9 0.65B 0.0 139.3 174.7 186.2 194.2 169.1 188.1 195.6 194.4 201.8 205.5 203.6 201.6 201.5 204.5 163.6 139.3 158.7 1509.0 0.663 0.7 138.0 175.1 185.4 193.4' 1B9.3 188.3 195.7 195.? 202.2 205.8 204.1 200.0 199.9 203.4 163.6 137.8 157.3 1470.2 0.680 3.0 137.6 176.3 186.4 194.9 190.1 189.2 197.2 196.1 203.1 207.3 205.4 200.7 201.4 204.6 163.6 139.2 158.6 1477.1 . 0.677 • 5.0 136.4 175.9 169.1 196.1 190.B 192.3 199.5 198.C 204.2 210.2 206.8 203.8 202.8 205.B 163.2 139.2 158.7 1428.2 0.700 139.4 183.1 189.9 196."/ 191.2 lsl.2 197.6 196.9 202.6"20871"205."5~202.3 262.3 205.0 161.7 138.9 158.1 1436.8 o76"9"5 84.3 139.8 182.4 1B9.9 196.4 191.8 191.2 198.0 196.9 202.6 207.4 205.1 202.7 202.8 205.0 162.1 138.6 157.9 1425.8 0.701 91.5 139.8 182.0 189.9 196.1 192.0 191.2 197.8 197.3 202.5 207.3 205.3 203.7 203.8 205.3 162.2 138.5 157.9 1423.8 0.702 97.B 140.6 183.9.191.1 197.6 192.0 191.5 198.3 197.3 202.9 207.3.205.3 204.4 204.0 206.9 162.4 137.9 157.3 1398.9 0.715 102.5 139.2 183.5 190.3 196.5 191.6 190.8 197.2 196.5 202.5 206.9 205.3 203.5 201.9 205.3 161.3 137.6 156-9 1412.9 0.708 107.8 139.8 183.2 191.1 197.4 193.7 191.9 198.7 197.8 203.3 206.3 206.4 203.3 203.4 207.6 163.1 139.2 158.6 1430.4 0.699 115.0 138.4 193.9 196.7 198.6""[VS" 1 191.6 19871" 197.7 203.7 207.3 206.6 202.7 203.0 205.3 161.7 138.B 158-1 1415.1 07707—13075-1.38.8 184.3 190.3 196.5 192.0 191.6 198.3 196." 202.9 206.6 205.9 202.7 202.5 205.7 161.7 137.8 157.3 1407.9 0.710 125.5 139.0 183.5 191.1 '196.9 192.8 191.9 19B.7 197.7 203.1 207.3 205.7 203.7 202.6 705.3 161.7 138.7 157.3 1400.2 0.714 131.3 136.4 171.6 187.2 193.8 1B9.7 186.4 194.5 193.8 199.9 205.0 204.1 202-7 202.3 203.8 163.6 139.B 158.8 1529.2 0.654 131.5 RE 56216. TWC 170.2 DTMC 27.1 Til) T(2I T131 T14] T(5) TI6) T(7) TIB) T19) TI101 Till) TI12) TI13) TI14) T(15) TIN TOUT 139.8 139.0 139.8 140.4 140.2 140.4 140.0 140.8 139.6 13B.B 139.2 139.7 140.0 140.0 140.9 140.1 139.2 138.8 139.2 139.1 163.8 163.4 162.9 163.4 163.9 163.9 163. 2 164.9 164.9 163.4 164.6 163.8 164.9 164.4 165.5 165.4 165.5 159.2 159.3 163.0 165.3 165.3 165.4 166.0 166.2 166.4 166,4 167.2 166.4 166.0 166.4 166.0 1 6 5 . 8 165.6 166.4 166.4 166.2 158.2 159.0 165.3 171.4 171.7 172.0 171.4 171.6 172.5 172.3 172.3 171.9 171.0 172.7 171.8 172.1 171.8 17219 172.5 172.5 164.1 164.0 171.6 1 6 5 . 8 165.7 166.2 166.5 166. 1 167. 1 167.9 167. 3 166.9 166. 1 166.5 166. 1 166.5 166. 1 166.3 165.5 165.3 157.9 15B.3 165.7 164.6 164.2 164.9 164.6 165.1 165.6 165.4 165.6 165.4 164.6 164.6 164.6 165.0 164.6 165.6 164.6 164.4 1 56. B 157.3 163.8 169.5 170.0 169.9 169.5 170.7 171.0 171.8 171.1 170.3 170.3 170.7 169.9 170.3 170.3 171. 1 170.7 170.9 160.9 161.2 170.2 16"B'.1 173. 16B.1 174. 168.1 173. 169.2 173. 169.2 174. 169.1 173. 1 6 9 . 4 1 7 3 . 169.2 174. 168.9 174. 168.5 173. 169.2 174. 169.1 173. 169 .h 173-168.9 173. 169.8 173. 169.7 173. 169.f 173. 159.1 163. 159.5 163. 16B.4 172. 2. 174.6 0 174.7 B 175.0 5 175.1 2 175.6 8 175.9 6 175.9 6 175.9 2 175.9 4 175.2 3 175.9 4 175.6 B 177-3 2 176.3 6 177.3 2 176.3 0 175.9 8 165.4 8 165.2 7 174.8 173.5 173.6 174.0 174.6 174.6 174.6 174.8 174.8 174.2 173.5 174.3 173.9 174. 1 174.3 175.7 175.0 174.6 164. 1 163.9 172-7 173.1 173.0 173.0 173.5 173.8 173.2 1'74.4 173.6 173.8 173.1 173.1 173.0 173.2 173.3 173.B 173.6 173.6 162.0 162.B 171.5 172.8 172.1 172.5 172.3 172.5 173.5 173.3 172.7 171.7 172.1 173.3 172.5 173.3 172.6 173.3 172.9 172.9 161.8 162.2 171.5 175.1 175.1 175.1 175.2 175.9 176.0 175.5 175.1 175.1 174.5 174.7 173.6 175.2 173.9 175.2 174.3 174.3 163.0 163.4 173.9 149.5 150.3 150.3 149. 5 149.2 150.3 149.5 149.5 149.2 149.2 149.5 149.5 149.2 148.4 149.5 150.3 149.5 144.5 144.2 149.5 139.4 147.6 138.9 148.2 139.0 147.6 138.9 147.2 138.8 147.3 139.2 147.7 139.6 148.4 136-8 147.6 13B.5 146.9 137.B 146.2 138.9 147.5 137.7 146.0 138.6 146.8 138.3 146.4 139.3 147.8 138.3 146.6 138.1 146.5 138.3 143.6 139.0 144.1 13B.9 147.5 HM 2598.1 2594.9 2554.2 2516.9 2487.3 2501.1 2530.4 2466.9 2464.0 2448.2 2496.4 2 4 i e . 9 2443.4 2447.3 2462.5 2433.1 2433.7 3416.2 3475.6 2601.4 1000 R TIME 0 . 3 6 5 0.385 0.392 0.397 0.402 .400 6.395 0.405 0. 406 0.408 0.401 0.413 0.409 0.409 0.403 0.411 0.411 0.793 0.288 0.3B4 15.8 19.8 24.1 27.5 32.4 39.4 45.4 56.4 102.1 102.4 102.5 102.6 RE 45809. TWC 166.0 DTM: 23.5 Till T12) T(31 T14) TI5) TI6) T(7) TI81 T|9) TUP) Till) T<12) TI131 TI14) TI15) TIN T JUT 135.9 136.4 135.8 135.4 136.8 137.6 136.4 136.8 136.4 138.0 137.6 136.2 138.0 136.4 136.0 137.6 138.0 137.6 136.0 137.6 137.6 136.8 138.0 136.& 138.0 138.0 156.2 156.4 156.0 156.0 157.8 157.5 158.2 158.2 157.6 157.8 159.2 157.4 157.fl 157.6 156.7 158.0 158.3 159.3 158.2 158.2 158.2 157.4 158.2 15B.6 159.5 ISP.8 15B.0 160.7 160.7 159.6 160. 1 159.6 161.1 160.9 160.3 161. 1 161.7 160.0 160.4 160.3 160.3 160.6 159.5 159.8 161.7 161.6 162.6 162.6 162.0 161.7 162.0 161.9 162.9 163.3 161.7 163.3 163. (. 161 . 1 163.6 163.(1 161.3 163. 1 162.0 160.9 162.6 162.B 161.4 163.7 163.6 161.9 164.3 162.B 163.4 162.9 164.3 164.9 164.9 164.4 165.5 165.7 165.0 i65.o : 165.6 : 166.7 161. 1 161'.7 162.2 160. 165.2 169.5 165.7 169.5 166.0 168.6 166.0 168.0 166.3 169.6 166. f. 169.7 165.9 169.7 165.3 169.9 165.t 170.3 167. ? 170.3 166.0 166.T 170.7 164.3 163.2 164.3 163.6 163.0 163.6 161.9 163.9 164.2 161.5 163.1 163.4 161.9 164.5 1 6 4 . 6 161.1 160.8 160. 7 163.9 163 164.7 163 164.3 163 164.3 163 164.3 163... 161.7 164. fi 163.6 161.9 164.4 163.B 161.4 162.2 162.7 167.3 162.5 160.4 161.7 165.3 166.2 166.9 165.6 166.8 165.4 167.1. 166.4 166.9 166.8 166.9 166.6 166.4 166.B 166.*) 178.1 179. 4 178.8 179.4 179.4 179.3 179.9 179.3 1B0.4 1H0.B 180.6 172. 5 171.4 172.0 172.6 172.8 172.8 172.2 173.4 173.9 1 73.5 166.0 169.9 179.7 166.7 170.5 1B0.1 167. ' 171.1 165.*- 170.3 167.1 171.4 165.* 170.7 181.0 172.6 181.6 179.9 101.0 173. 1 73.7 174.6 173. 1 174. 1 166.9 171.5 166.3 170.8 167. ? 171.6 167.7 171.5 167.5 171.1 167.3 171.1 167.1 171.1 167.3 171.4 166.'' 171.1 : 174.2 173.7 174. 1 174.3 174. 1 174.4 174.1 174.6 170.8 161.8 170.9 162.2 170.1 161.7 170.2 161.3 170.8 163.2 171.6 163.6 171.0 163.2 170.8 163.2 171.6 163.2 172.6 164.2 171.9 164.7 171.2 163.6 172.4 164.0 172.9 165.2 171.4 163.8 172.6 164.9 171.6 164.1 173.2 165.0 172.0 164.4 172.6 165.4 172.1 165.0 172.4 164.4 172.2 164.6 172.8 164.B 173.4 164.6 172.8 164.0 167.5 167.6 16B.7 170.1 170.0 170. I 170.2 169.7 169.3 169.7 169.3 170. 1 143.6 143.6 142.8 143.2 1 43. B 143.9 143.9 143.2 141.2 1 44. 5 144.0 143.2 143. 2 144.3 144. I 144.4 143.6 143.6 144. 3 143.7 144.D 144.5 143.6 144.4 143.6 143.6 13E.1 147.9 138.8 148.6 13B.1 148.2 1 17.3 147.2 136.4 147.7 138.1 146.6 137.9 147.3 1)6.9 H6.3 137.7 146.6 139.4 144. 1 13B.7 14B.3 l3?.3 U 7 . 1 139.6 14B.3-138.6 US.2 137.3 146.B 138.8 148.? 137.5 147.3 13B.7 147.7 133.0 147.5 138.7 143.) 139.9 147.9 138.7 148.2 13B.1 147.5 139.5 147.3 130.0 147.7 138. 3 1 47. 7 2626.5 2643.7 2663.9 2596.9 2526.4 2434.5 2485.1 2417.3 2411.2 2556. •) 2497.3 2436.2 2478.7 2418.? 2425.1 2441.4 2435.7 23B8.1 2417.1 242B.6 2416.2 2441.8 2396.7 "TTTBTT"" 241B.0 2402.2 0.378 0.375 3. 3B5 0.396 0.411 0.402 0.403 0.413 0.412 0.410 0.414 0.412 0.414 0.410 0.417 5.0 7 . 3 9.D - 5 7 4 1 7 — 1 1 1 . 5 0.413 123.3 0.416 131.0 TWC 172.3 • T H : 19.4 "TTTI TTD TTO TT51 TTTi TI6) ' TI7) ITB7 T|9) TtlO) Till) H12J TU31 TI14) IMS) TT3 TUOT-149.6 151.0 152.7 150. B 151.6 149.8 149.8 151.8 152.2 150.2 150.9 151.4 150.2 150.2 151.4 152.7 lt>l .6 150.4 151. B 151.8 151.0 151.2 151';'2" 151.4 149.8 150.2 152.2 ISO.2 151.0 ISO. 2 151.4 151.4 151.4 150.6 151.4 151.0 156.6 157.6 158. B 158.1 1 5 7 . 1 157.1 157.1 158.8 159.1 157.9 158.7 158.7 158.9 158.1 157.9 15B.3 T5T7T" L57.5 158.7 157.9 158.7 156.5 "15877-158.7 157.9 157.5 159.1 157.9 157.9 158.7 156.3 157.9 157.9 157.9 171.3 171.9 172.2 172.5 172.5 171.9 172.7 172.9 173.3 171.7 172/9 " 174.3 172.3 173.3 172.5" 172.1 173.5 172.3 173.3 173.3 172.9 172.9 1 72.3 172.9 173.5 172.1 173.1 172.7 173.3 174. 1 173.7 174. 1 173.7 173.3 169.1 170.3 171.2 170.3 170.4 171.2 172.5 171.6 170.fl 1 170.0 171.1 171.7 171.3 172.0 170.7 172.0 171.1 169.5 L71.6 170.7 1'72.4 171.1 171.6 170.7 171.6 171.5 17179" 171.1 171.7 171. 1 1 70.5 170.9 170.5 171. 5 170.9 170.7 171.6 170. 7 T7TTT 171.5 170.7 172.6 171.6 172.0 172.3 172.0 172.4 171.5 177.4 172.2 171.6 171.6 171.8 172.4 172.9 172.2 172.4 172.2 172.3 ~ T T o T T " 171.1 172. : 17 3.1 174.; 173.1 T737i 173. ' 174. ' 174.1 173.1 1 73.1 173.1 173. ' 1 7.3. ( 174. ( T747J 1 74.( 174.1 174.' 1 73.1 174. ( 1737' 174.1 173.' 1 73.; 173.' 173. : T7TT 175. i 174. : 174.1 174.1 174.1 T747 I 73.1 171.1 1 7 1 . 1 169-5 169.9 170.1 169.9 169.5 169.9 169.5 169.5 169.5 169.9 171.1 172.1 171.1 172.0 171.7 171.1 170.7 1 70.5 170.6 170.3 170.3 170.9 170.1 170.7 • 171.5 170.7 171.1 171.3 170.7 "77077" 169.9 : 171.9 173. ' 174.8 174. C 173.A 172. 8 174.0 172.9 173.2 172. B 17 3.2'' 173.2 173. 7 173.B 174 175 165-5 176.0 167.3. 177.2 167.7 178.5 167.5 170.7 167.1 178.4 166.3 178.8 166.1 17B.4 167.3 178.1 167.9 178.4 166.3 177.7 T&7.I 177.5 167.5 178.0 166.9 177.6 166.9 177.6 160.1 170.2 167.9 179.6 167.7 "17976™ L 7 5 - 1 174.2 175.4 174. 3 173.6 174.6 167.4 178.9 173.1 1 74.5 174.6 173.8 174.7 173.8 174". V 1 75.2 174.6 175.2 175.2 1 74.5 1 6 7 . 0 1 7 8 - 4 168.1 178.5 167.7 178.9 167.3 177.9 167.5 178.9 167.7 178.3 T67."5-17B.3 167.8 178.7 167.6 178.3 167.8 178.5 167.6 178.7 167.5 178.8 176. 1 176.8 178.4 178.0 177.6" 177.2 177.6 177.4 177.6 177.2 177. B 178.0 177. B 177.6 17B.B 180.4 ISO.2 179.8 180.0 179.2 17B.4 17B.2 176.4 178.2 179.4 178.6 179.2 178.0 178. B 179.2 17B.4 179.2 178.8 178.8 178.4 177. 1 177.3 179.2 178.7 178.7 178.3 178.7 177.9 178.3 177.1 1 77.9 176.3 178.5 178. B 179.1 181.6 180.8 179.5 180.6 179.9 179.9 179.6 179.4 179,5 178.7 178.1 179.7 178.7 17B.7 180.3 179.5 160.3 179.9 179.1 179.3 174.0 175.0 175.6 174.3 173.6 173.8 174.6 174.1 174.5 173.B TT4TTT 175.0 174.6 175.1 175.4 177.7 176.9 175.9 176. 1 176.1 175.7 175.7 175.7 175.3 175.3 174.1 174.6 174.7 175.3 176.1 175.7 175.9 175.7 174.8 177.B 178.7 181 .6 181.4 180.5 181.7 181.9 181.5 181.9 180.8 181 .b IB1.9 1B2.7 182.3 182.7 1B2.7 162.5" 182.9 183.9 183.9 182.7 182.5 182.9 182.5 1B3.3 1B2.1 183.3 182.5 182." 7" 183.1 162.3 182.7 182.5 182.7 182.7 183.1 151.0 149.8 149.8 15! .B 1 52.2 150.2 150.9 151.4 150.2 150.2 151.4 152.7 152.5 156.8 153.2 157.9 153.8 158.6 153.2 158.4 153-3 1 5 8 . 8 153.6 15B.4 152.7 157.4 152.2 157.2 152.5 157.7 151.7 155.7 152.5 15 7. 7 : 152.8 158.1 152.5 157.8 151.9 157.2 152.8 159.7 153.2 158.7 fSlTB-lW.l 159.5 150.4 151.6 151.B 151.0 151.2 152.2 157.4 153.5 159.1 152.8 158.3 152.2 157.7 152.3 157.3 151.2 T"52".l 157.6 151.4 149.6 150.2 152.2 150.2 T5T7TJ-150.2 151.4 151.4 151.4 150.6 T5T 152.8 158.1 152.6 158.4 151.9 157.4 153.1 15B.7 152-2 157.8 152.8 158". 4"" 151.9 157.1 151.3 157.3 152-3 157.3 152.3 157.5 152-5 156.6 T5775—TTT77-2128.6 2103.6 2024.4 2078.8 "2TT9T3 2132.2 1978.1 19B6.1 2003.5 1932.2 "TTJTtJTB 2015.4 2015-7 1961.5 2031-1 1937.3 1889.9 1975.8 1975.4 1961.2 1934.0 197678" 1985.9 2019.9 1984.9 2044.7 2008.1 1653.5 1890.8 1895.9 1923.5 1681-9 "195673-0.470 0.475 0.494 0.4B1 "D'.472"' 0.469 0.506 0.504 0.499 0.518 C7T77 0. 496 0.496 0.510 0.492 0.516 .529 0-506 0.506 0.510 0.517 ""0.'5D"f" 0.504 0.495 0.504 0.489 0.498 16.1 17.6 19.4 20.7 21.6 ' 202BT6 074()3 2T78-22.5 23.5 26.7 2B.7 29.5 30.4 33.4 34.4 35.B 38.8 40.9 -2 03X73 D7T9T 42.2 0.540 0.529 0.527 0.520 0.531 D.511 49.4 50.0 52.5 151.0 151.3 155.9 1862.6 0.537 3s-15 TABLE 3 - I I I : COMPARISON OF CLEAN TUBE HEAT TRANSFER COEFFICIENTS WITH THE SIEDER-TATE EQUATION RE PR V I S R CP H HC AL HR NU I 5203. 25. 7 2 .27 0 .656 183. 193. 1.06 67. 65 ! 8209. 24. 4 1 .82 0 .598 259. 266. 1.02 95. 71 t 9914. 25. 0 2 .16 0 .672 266. 3 19. 1.20 98. 18 9766. 25. 5 1 .68 0 .677 280. 306. 1.10 103. 24 9594. 25. 5 1 .71 0 .663 289. 303. 1.05 106. 58 10622. 23. 0 2 .03 0 .660 294. 3 25. 1.10 108. 65 14119. 22. 6 ' 2 .07 0 .635 378. 407. 1 .08 139. 7 5 14472. 22. 4 2 .17 0 .600 387. 416. 1.08 142. 90 ! 14577. 21. 8 2 .17 0 .585 385. 415. 1.08 142. 32 ! 13580. 23. 4 1 .71 0 .633 390." 3 88. 1.00 143. 7 6 i 14319. 23. 3 2 .49 0 .665 385. 4 26. 1.1L 142. 18 14351. 23. 1 2 .79 0 .659 389. 432. 1.11 143. 85 14918. 21. 5 2 .99 0 .573 383. 439. 1.15 141. 63 13841. 23. 0 1 .90 0 .635 394. 398. 1.01 145. 53 16738. 25. 0 1 .71 0 .650 485. 4 70. 0.97 178. 99 20146. 25. 3 2 .31 0 .639 564. 570. 1.01 208. 25 27892. 23. 7 2 .07 0 .667 678. 7 12. 1.05 250. 23 30131. 23. 9 2 .16 0 .643 726. 765. 1.05 267. 92 29193. 23. 5 1 .71 0 .612 776. 718. 0.93 286. 25 28342. 25. 7 1 . 75 0 .653 786. 725. 0.92 290. 00 ' 41871. 22. 9 1 .71 0 .595 1010. 9 50. 0.94 372. 68 ; RE = R e y n o l d s number NU = N u s s e l t number PR = P r a n d t l number VISR = 'fJL/ /Aw CP = h e a t c a p a c i t y , B T U / l b °F H = measured h e a t t r a n s f e r c o e f f i c i e n t , B T U / h r - f t 2 °F HCAL = 0.023 Re ° ' 8 p r 0 - 3 3 3 (U/LL) ° > ' 1 4 D ~ nv HR = HCAL/H 3-16 TABLE 3-IV. PRESSURE DROP AND DEPOSIT THICKNESS 0. ! 9. 10 0.03B2 ' 1.2 8.90 a.coon 3.3 8.9U O.COQO 7.7 9.25 0.0135 . 16.0 a.90 D'.OOQO 19.5 9 . 10 0.0193 24.1 9.00 0.0097 26.3 B.90 • 0.OOQO 29.4 9 . Ill 0.0193 31.5 9.CO 0.0097 41.2 9.CO 0.0097 44.3 9.00 0.C097 *e.a 9.00 0.0097 53. 2 9. IQ 0.0193 57. 5 9.00 6.C097 65.1 9.00 0.0097 69.fi 9.00 0.0097 74.0 9.00 O.C097 60.8 9.00 0.0097 89.6 9.10 0,0191 l O l , I 9.10 0.0191 10). 1 9.20 0.0288 113.8 9.20 0.02BB 119,6 9. 10 0.0302 123.1 9.30 D.0387 127.3 9.25 0.0135 1?S.6 9.2? 0.03i5 137.6 9.25 0.0315 143.-) 9.20 0.02B8 1*7.1 O.0302 152.5 9.25 0.0135 16L.G 9 . * 5 0.0520 145. 1 9 . 5 5 0.0610 169. 5 9.55 0.0610 LT5.2 9.60 0.0655 185.4 9.60 0.0655' 189. 6 9.65 0.0700 194.4 9.90 0.0918 200. 0 9.90 0.0918 209.0 10. IS 0.1 111 213.5 10. 10 0.1009 216.7 10. 10 0.1089 219.0 LO. 10 0. 1089 224.3 10. 10 0.1089 • 233.1 10.35 0.1596 238.5 10..)5 0.1296 243.5 10.50 0.1416 248, 10.50 0.1418 257.a 10.35 0.1296 262.4 10.7fi 0.15 76 261.9 10. "Cl 0.1576 271.S 10.65 0.1537 2B0.7 10.65 0.1537 2B5.1 10.70 0.1576 290.4 10.70 1>. 1576 295.6 10.75 0. 1616 304.7 10.95 ti. 1770 301.0 u . c o o.ieo8 314,7 11.15 0.1921 311,7 11.00 0.1808 32fl.3 11.10 0.1SB4 3)3.6 l l . l O 0.1884 336. 3 11.10 0. IB84 3*4.6 11.05 0.1046 352.B 11.15 0. 1921 356.4 11.20 0.1958 362.4 11.30 0.203Z 368.4 11.25 0.1995 374.2 11.20 0.195R 377.4 11.20 0.1958 382.6 11.35 0.2069 38B.fi 11.70 D.195B RUN 15. TIME DELP X 1.5 69.00 a.cooo 3.7 68.70 o.cooo 6.2 69.00 o.oooo IS. 4 69.00 6.0606 19.3 69.CO o.cooo 23.4 69.00 o.cooo 25.9 69.00 O.COOO 31.4 69.00 o.aooo 39.9 69.00 o.ccao 44, 7 69.00 0 .0000 *9.6 69.00 o.oaoa 5) .* 69.CO o.ccco 63.8 69. 00 o.cooo 6B.6 69.00 o.aooo 73,8 69.00 o.cooo 74.0 64.00 O.COOO SB.8 69.00 0 .0000 92.5 69.CO a.coco 9B.3 69.00 o.cooo 103.B 69.00 o.aooo 112.4 69.00 o.aooo 111.8 69. CO fl.CCCfl 122.2 69.00 'O.COOO 132.7 69.00 O.cono 140.3 69.00 o.cooo 14B.7 69.CO o.coco 137.2 69.00 o.cooo 1*4.1 69.00 0.0000 170.2 69.CO o.cooo 181,* 69.00 o.caoo 1 187.9 69.00 o.oooo 18).* 69.00 O.COOO 1 20 5.4 69.15 0.CO19 j 312.4 64.14 0.0014 ; 219.2 69.15 0.0019 229.1 69.30. 0.0018 237.1 69, 38 0.0048 2*2.1 69.15 0.0019 2S2.3 69,15 . . 0.0019 165.2 69. 15 0.0019 176.5 69,15 0.0019 287,0 69.30 O.OOJB SOO.T 69.45 0.0057 RUN 16. TIME DELP X 0.7 69.00 0.0000 1.4 69.CO o.caoo 3.8 69.00 o.coco 9.0 69.00 0 .0000 17.3 69.00 o.ccoo 21.* 69.00 o.cooo 33.* 69.00 0.oonn RUN 17. TIME DELP X 1.0 21.85 0 0334 4.0 21.85 • 0 0134 7.0 23.85 0 0334 15.0 21.85 0 0314 14.0 24.00 3 oifla 2*. 3 24.00 0 0180 29.8 24.00 0 0388 39.0 24,15 0 0442 42.1 24. 15 0 0442 43.0 23.70 0 02 79 ** . ! 21.85 0 0334 49.0 23.70 0 59.8 21.85 0 (1314 6B.5 21.85 0 0334 75. 8 21.85 0 0114 8*.5 24.00 0 03B8 ' 90.S 24.00 0 0388 97.8 24.CO 0 0388 108.4 24.00 0 0388 112.8 23.85 0 0314 116.8 21.85 0 0134 122.B 23, 70 0 0279 139.1 23.70 02 ?9 138.3 21 . 70 0 0279 1*4. 7 2 1 . 70 0 0279 156.2 24.00 0 03BB 162.7 23.85 0114 170.3 2.1. it 5 0 0314 1H6.6 ii. 115 0 0414 186.6 2 1.05 0 0334 193.8 23.85 0 0134 205.0 2 (.85 0 219. B 23. 85 0134 229.7 23.B5 0 0114 . 2 3 6 . r 24.CO 0 03BB 2*2.8 21.B5 0 0314 252.6 24.00 0188 258.B 24.CO 0 0388 266.6 21.85 0 0334 276.6 24.00 0 0388 28*. 1 2*.CO 0386 291.1 24. CO 0 03BB 300. e 24.CO 0 03BB 308.7 23.85 0 0134 314.0 24.CO 0 0188 324.5 24.00 0 0181 RUN 18. TIME OELP X 0.6 24.00 0276 t 2.0 23.0$ 0 0272 4.0 23.40 0 C056 6.0 21.25 0 ccao 11.0 23.25 ccao 23.0 23.25 0 0000 29.0 21.55 0 0112 ! 36.0 23.55 0112 46.0 23.55 • 0 o n ? RUN 22. TIME HELP X 0.5 b.OO 0 COOO 1.0 6.CO 0 caoo 3.3 6.00 o.cooo 7.3 6 . 10 0 0144 11.8 b. 10 0.0144 22.8 6. 10 0 0144 S4.5 6. 1ft ti 0144 35.8 6 . 10 0 0144 1 46,5 6.10 0.0144 54.5 6.10 0.0144 60.3 6.10 0.0144 71.0 6 . 10 0 0144 | Tfi.O 6.10 0 0144 1 84.3 6.10 0.0144 95.0 6.10 0.0144 . 10L.5 6.10 0 0144 109.5 6.10 0144 , 121.3 6.10 0 0144 1 128.3 6 . ID 0  . 146.3 6.10 0 0144 1 156.3 6 . 10 0144 170.5 6.10 0 0144 187. 3 6. 10 0.0144 192.0 6. 10 0 0144 204.•> 6. Ill U.U144 216.J 6. 10 0.0144 229.0 6.10 0.0144 243.3 6.10 0 0144 254. 5 6. 10 0 263.3 6.10 0.0144 1 200.0 6.10 0 0144 243.3 6. 10 0.0144 102.5 6. 10 0.0144 315,0 6.10 0.0144 326.1 6.10 0.01*4 339.3 6.10 0 0144 1 3*3.5 6.10 0.0144 RUN 23. ' TIME DELP X . 0.5 6.10 0 0000 3.3 6.10 0 0000 . . 6.3 . 6.10 0. 0000 11.0 6,10 0 coco 22.0 6.10 0 COOO BUN 24. TINE DELP X 1 O.B 14.55 0 0060 1.8 14.45 0 COOO 1 4.0 14.45 0 0000 7.3 i * . * i ft COOO 12.3 14.4! o.cooo 13.0 14.60 0.C090 29.5 14.45 o.aooo • 37.7 14,50 0 0030 47.7 14.45 0 caoo i l . 7 14.50 0 OOifl 1 54.7 14.45 0.0000 70.7 14.S5 0.C060 81.1 14.50 0.00)0 94.1 lit.50 0.0030 101.1 14.50 0 0030 1 166.1 14.6J 0.0120 ! 106.1 14.60 0 C090 113.1 14.60 0.0209 124.1 14.80 0 0208 I 137.4 14,90 0.0267 1*8.4 15.10 0 0382 114.4 14.40 , 0 0247 171.4 14.90 0.0267 IS*.9 14.90 0 0267 196.9 15.00 0 0324 209.4 14.90 0.0267 220.4 14.80 0 0208 132.4 14.40 0.0267 145.* 15.05 0 0153 156.7 15.00 0 0124 m . « 15.10 0.0382 240.0 14.95 0.0296 ' 303.5 15.00 0 0324 TIME DELP X 1.0 13.20 •.0111 2.0 0.0192 5.0 13.40 0.O243 7.8 13.40 0.0261 14.3 15.10 0.192B RUN 27 TINE DELP X 4.0 11.85 0.0158 6.8 13.65 0.0017 10.4 13.60 0.COOO 13.3 14. 10 0.0114 S l . 6 15.9? 0.1168 23.4 16.00 0.1394 24.7 16.05 0.1420 26.0 16. 15 0. 1473 27.5 16.00 0.1194 29.5 16. 10 0.1446 31.7 15,95 0.1368 33.B 15.95 0.1168 36.3 16.CO 0.1394 RUN 28 YIHE DElP 2.3 11.50 O.COOO 3.7 13.60 0.0064 11.60 0.0064 6.8 13.60 0.006* 23.0 14.BO 0.0794 25.0 14. 0.067.3 27.0 14.90 0.0857 29.0 15.10 0.0966 11.0 14.90 3 3 . 5 15.CO 0.0909 35.5 0.0852 37.8 14.90 0.065" 40.0 14,90 0.0852 41.7 15. )J0 0.1078 43.7 15.30 0.107B 45.7 15.20 0. 1022 48.2 15.30 0.1078 12.5 13.45 0.0096 RUN 29 TIME DELP 2.0 9.60 0.C091 T.O g.iti 0.0091 12.0 9 . 7 5 0.0226 13.0 9 . 7 5 0.0226 17.0 9.90 0.0358 21.3 10.10 0.0511 24.3 10.00 0.0445 <f/.U 10,00 0.0445 29.0 10.oa 0.0445 31.0 10.00 0.0445 33.0 10.00 0.04*5 RUN 36. TIME OELP 2.9 7.70 O.COOO 5.4 7.80 7.4 7.90 0.0221 11.2 8.25 0.0597 14.5 8.45 0.0B03 18.5 • 8.80 0. 1149 I 21.2 8.85 0.1197 1 23.3 9.00 0.1119 25.3 9.^0 0.1524 27.3 9.20 0.1524 1 29.6 9.20 0.1524 31.6 9 . 10 0. 1432 RUN 31 Tint DELP 1.1 14. CO 0.0510 1.9 14.50 0.0B11 2.4 15.30 0.1268 2.9 15.70 0. 14B6 3.6 15.70 0.I486 4.2 16.40 6.1652 RUN 32. » TINE OELP ' X 2.3 14.20 o.caoo 5.8 15.Oo 0.0475 B.8 15.40 0.07Q1 10.9 15.60 0.0812 17.4 16.40 0.1238 20.9 16.00 0. 1028 23.4 16.00 0.1028 26.9 14.00 0.102B 29.4 16.00 0.1028 32.4 16,00 0.1028 33.4 16.CO 0.1028 RUN 33. TIME OELP 1 1.3 14.20 0.0000 11.0 16.90 0.1491 15.3 17. 70 0.1879 21.0 19.60 0.2721 24.3 20.20 0.2967 < 27.3 20.70 0.3165 30.5 20.70 0.3165 34.3 20.70 0.3165 HUM 14. TIME OELP 0.8 13.00 O.0692 1.8 13.BO 0.1201 3.1 14.20 0,1443'' 5.8 13.00 0.1902 8.S [5.20 0.2013 12.5 16.00 0,2437 19.0 17.00 0.2913 18.1 17.30 0.3073 22.5 18.10 0.3440 27.5 18.50 0.3615 1 RUN 33. 1 TIME OELP t ' 3 31.30 0.0111 4.3 Si.10 0.0275 T.B JS. so O.0T2O 11.B 36.00 0.1Z5T 13.3 37.70 0.1646 18.3 39,90 0.2119 22. B 42,00 0.2542 23.6 43.40 o. 'ALo 30.8 46.60 0.3366 32.8 * 7 .CO, 0.3455 TIME OELP 'X 1.3 46. 10 0.C019 2.5 46.00 0 .0000 5.0 46.30 0.0057 8.3 46.50 0 0094 11.5 46.70 0 0131 14.4 46.40 0 0149 20. B 47.00 0.0187 26.3 47.10 0 0206 29.8 47.40 0.0261 37.1 47.50 0.0279 . RUN 37. ' TIKE DELP X 3.8 16.30 0 0162 10.3 16.80 0 0423 13.0 16.95 0 0500 14.0 17,00 0 0525 23.5 17.10 0 0576 30.3 17.25 a 0651 36.5 17.70 0 0B71 38.5 17.BO 0 0920 RUN 38 TIME DELP O.B 6.30 0 C069 2.B 6. 32 0 C097 6. 1 6.45 0 02 74 10.4 4.50 0 0341 15.8 6.60 0 0472 20. 1 6.65 0517 24.1 6.70 0 0602 28.1 6. 75 0 0666 33.6 6.75 0 0666 1 RUN 19 TIME OELP 0.8 12.70 0014 1.8 12.80 0082 3.0 12.95 0 0183 7.8 13.00 0 0217 10.0' 12.90 0150 17.0 11.05 0 0250 21.0 11.15 0 0316 25.5 13,25 0 0382 30.8 13. 10 0 . 041* 34.0 11.40 0 04T9 40.8 13.35 0 0*47 RUN 40 TIME DELP X. 1.2 4.75 0.C092 3 .0 4.85 0.0271 6.8 0.0367 10.6 4.45 0 . 0449 1 16. B 4.95 0 . 044 9 20.8 4.9B 0.050? 25.8 4.98 0.0507 31.3 4.99 0 . 0519 34.0 4,99 0.0519 40.8 0 . 0519 45.0 5.00 0. 0516 51. B 5.Q0 0 . 053(S RUN 41. TIME DEL P o.t 5.95 0.0O73 3.0 5.95 0 . 0073 5.0 6.CO 0. 0146 6.8 6.00 0.0146 10.5 6.10 a. 0290 13.3 6.05 0. 0218 20.5 6.15 0360 25.3 6.25 0.0499 30. B 0. 0S6B 36.3 6.45 0.0770 43.5 0 . 0703 48.3 6.45 0 . 53.0 6.50 0.0B34 60.3 6. 50 0.0S36 67.3 6.60 0. 0966 73. B 6.70 0 . 1094 8 4 . 3 6.BO 0 . 1220 91.5 6.80 0 . 1220 9 7 . 8 4.80 0. 1220 102.5 6.80 0.1220 107.8 6.60 0. 1220 115.0 6.75 0 . 1159 . 120.B 6.75 0 . 1158 125.5 6.80 0 . 1220 .1S1.1 6.80 6. 1170 RLJN * 2 . TIME OELP X ' 1.1 22.10 0. C040 2.1 21.20 0.C079 4 . 8 22.30 • 0 . o n e 6 .8 2 2 . 3 3 0.0137 9.0 22.50 0.0195 15.8 22.60 0 . 0234 19 . B 2 2 . 4 ! 0. OZSJ 24.1 22.65 0. 0253 Z7.5 22.75 0. 0291 3 2 . 4 22.75 0. 029L 3 9 . * 23.CO 0.0386 4 5 . 4 23.00 0. 0386 63.7 . 71.9 79.9 87.7 93.9 •?:!-9.0 ' u.o '"16.0 23.3 _*7..l. 29.5 S2.fi  36.0 42.0 30.0 . 93.3 60. S 67.3 72.3 65.5 93.5 100.5 113.5 120.5 111.0 23.00 23.15 23.60 21.30 23.75 23.40 OELP 16,00 —II. « .. 1ft.00 16.00 _ 16.25 16.19 16.20 14.15 16.19 16.25 16.40 16.90 —M. 45 16.40 16.49 _ 16.40 16.40 16.33 — 16.43 16.49 16.90 16.90 16.90 0.0386 0.0442 0.0608 0.0371 0.0662 0.040S 0.0027 o.caoo— 0.C027 O.COZT 0.016Z 0.010a 0.0133 0.Oioa 0.0108 0.010a 0.0162 0.0242 0.0295 0 . S 2 4 5 — . 0.0242 ' . 0.0268 ' _ .0.0242 0.0242 0.02H O.OSil 0.0260 „O.0IM_ 0.0293 0.0299 0.0295 , 3-1:7 TABLE 3-V: PARTICULATE CONCENTRATIONS O i l F o u l i n g Run P a r t i c u l a t e C o n c e n t r a t i o n ( m g / l i t e r ) B e g i n n i n g o f Run End o f Run 14 22. 6 24.0 15 15. 8 6.5 17 13.4 18.4 19 25. 5 28.6 25 25. 8 14.8 27 37.6 24.1 28 21.8 21.5 29 22.2 20.7 30 18. 8 18. 5 32 22.7 17.7 Water F o u l i n g Run P a r t i c u l a t e C o n c e n t r a t i o n ( m g / l i t e r ) 34 3.47 35 3.1 36 8.7 37 3.0 38 2.6 39 2.1 40 5.1 41 4.3 42 4.4 44 4.0 

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