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Liquid-liquid extraction in a spray column Rai Choudhury, Prosenjit 1959

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LIQUID-LIQUID EXTRACTION IN A SPRAY COLUMN by PROSENJIT RAI CHOUDHURY B . S c , U n i v e r s i t y o f G a u h a t i , 1956 D i p l . i n Graduate S t u d i e s , U n i v e r s i t y o f Birmingham, 19 57. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF ,MASTER OF APPLIED SCIENCE i n t h e Department o f CHEMICAL ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA September, 1959 i i • ABSTRACT A s t u d y was made on t h e back m i x i n g o r c i r c u l a t i o n i n t h e c o n t i n u o u s phase o f a spray t y p e l i q u i d - l i q u i d e x t r a c t i o n t ower. C o n c e n t r a t i o n p r o f i l e s o f b o t h c o n t i n u o u s and d i s p e r s e d phases were o b t a i n e d by i n t e r n a l s a m p l i n g . Mass t r a n s f e r d a t a a r e p r e s e n t e d f o r t h e t r a n s f e r o f a c e t i c a c i d between wa t e r and m e t h y l i s o b u t y l ketone i n t h e 1.5-i n . I.D. columns o f t h r e e d i f f e r e n t h e i g h t s . C o n s i d e r a b l e c i r -c u l a t i o n i n t h e c o n t i n u o u s w a t e r phase was o b s e r v e d w h i c h r e -s u l t e d i n t h e r e d u c t i o n o f t h e d r i v i n g f o r c e f o r mass t r a n s f e r . A d r i v i n g f o r c e c o r r e c t i o n f a c t o r , F m , was o b t a i n e d f r o m t h e H.T.U. d a t a u s i n g a s i m p l i f i e d p i c t u r e o f b e h a v i o u r a t t h e i n t e r -f a c e . The h e i g h t o f the tower d i d n o t seem t o have any e f f e c t on F m . The o v e r a l l H.T.U. v a l u e s , o b t a i n e d f r o m t h e experimen-t a l p r o f i l e s , were c o r r e l a t e d w i t h t h e f l o w r a t e s . The end e f f e c t due t o t h e a g i t a t i o n and c o a l e s c e n c e o f the drops a t t h e i n t e r f a c e was measured. T h i s end e f f e c t was c o r r e l a t e d w i t h t h e o v e r a l l c a p a c i t y c o e f f i c i e n t s and t h e d i s -p e r s e d phase f l o w r a t e s . 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 t h e r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r 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 purposes may be granted, by t h e 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 . I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be 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 of Chemical Engineering The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver Canada. Date / 3 tic &cA~. iPfA^  TABLE OF CONTENTS page INTRODUCTION 1 EXPERIMENTAL METHODS 6 Apparatus 6 Procedure 21 THEORY . 27 RESULTS 32 DISCUSSION 50 R e p r o d u c i b i l i t y of R e s u l t s 50 J u s t i f i c a t i o n of sampling Technique 54 Appearance of Drops and S t a b i l i t y of J e t s 63 S i m p l i f i e d Model 72 E f f e c t of Concentration 75 O v e r a l l Capacity C o e f f i c i e n t s 81 and Heights of the Transfer U n i t s Holdup and I n t e r f a c i a l Area of Contact 92 Back M i x i n g and End E f f e c t s 96 CONCLUSION JL11 NOMENCLATURE J.13 LIST OF REFERENCES J.16 i v ' L IST OF TABLES page TABLE I Key t o F i g u r e 1 8 & 9 I I C a l i b r a t i o n of Rotameters 13 I I I L o c a t i o n o f S t a i n l e s s S t e e l Sampl ing Tube 20 IV E q u i l i b r i u m Data f o r M e t h y l I s o b u t y l Ketone - 24 A c e t i c A c i d - Water System V Sampl ing Rate and Purge Time 33 VI O v e r a l l T r a n s f e r Data . .34 & 35 VI I O v e r a l l T r a n s f e r Data 36 V I I I C o n c e n t r a t i o n s i n the Water Phase 37 & 38 IX C o n c e n t r a t i o n s i n the Ketone Phase 39 X Average V a l u e s o f K^a , and ( H . T . U . ) k , and End E f f e c t s 40 XI Data f rom Run 68 f o r C a l c u l a t i n g ( H . T . U . ) ^ k by G r a p h i c a l I n t e g r a t i o n 47 XI I R e p r o d u c i b i l i t y of R e s u l t s 51 X I I I Average H . T . U . V a l u e s Over Each F o o t -.89 XIV Average H . T . U . V a l u e s Over F i r s t Foot f rom the Bottom of t h e Column , 93 V LIST OF FIGURES page FIGURE 1. Schematic F l o w Diagram 7 2. Aluminium Tank 10 , 3. C a l i b r a t i o n Curves f o r Rotameters 12 4. F i r s t Change i n N o z z l e Attachment t o t h e Bottom P l a t e 14 5. Second Change i n N o z z l e Attachment t o t h e Bottom P l a t e 16 6. T i p P a t t e r n s f o r Ketone N o z z l e 18 7. Photograph o f S a m p l i n g Tubes i n Column Taken D u r i n g Run 67 19 8. E q u i l i b r i u m Diagram f o r M e t h y l I s o b u t y l Ketone - Water - A c e t i c A c i d System 26 9. C o n c e n t r a t i o n P r o f i l e s f o r Run 68 42 10. G r a p h i c a l I n t e g r a t i o n f o r D e t e r m i n i n g ( H . T . U . . . . 48 11. C o n c e n t r a t i o n P r o f i l e s f o r Runs 67 and 68 52 12. C o n c e n t r a t i o n P r o f i l e s f o r Runs 62 and 69 53 13. C o n c e n t r a t i o n P r o f i l e s f o r Runs 55 and 61 55 14. P l o t o f C o n c e n t r a t i o n o f A c e t i c A c i d i n t h e Water Phase v e r s u s Purge Time 56 15. P l o t o f C o n c e n t r a t i o n o f A c e t i c A c i d i n t h e Ketone Phase v e r s u s Purge Time 57 16. P l o t o f Minimum Purge Time v e r s u s S a m p l i n g r a t e 59 17. Ketone J e t s from N o z z l e d u r i n g Run 65 69 18. Ketone Drops i n Column D u r i n g Run 68 71 19. Ketone Drops a t t h e I n t e r f a c e D u r i n g Run 70 73 20. C o n c e n t r a t i o n P r o f i l e s f o r Run 57 77 21. C o n c e n t r a t i o n P r o f i l e s f o r Run 69 78 VI "'FIGURE page 22. Concentration P r o f i l e s f o r Run 66 79 23. Concentration P r o f i l e s f o r Run 65 80 24. V a r i a t i o n of K^a w i t h I ^ / l ^ ^ 2 24a. V a r i a t i o n of K ka w i t h L w 84 25. V a r i a t i o n of (H.T.U.)/ w i t h L j l ^ . 85 OK 26. V a r i a t i o n of Average H.T.U. Over Each Foot 88 w i t h Mean Height Above Nozzle Tips 27. Ketone Holdup as a Function of L k 94 27a. Ketone Holdup as a Function of L w 95 281 V a r i a t i o n of F m w i t h L ^ A ^ 97 29. V a r i a t i o n of F w i t h L ^ / L i , ,.Based on Runs, where the L i n e a r V e l o c i t y through the Nozzle Tips Was Kept Constant 99 30. V a r i a t i o n of F m w i t h L w i n 7.4 f t . Column 100 31. V a r i a t i o n of F m w i t h L k i n 7.4 f t . Column 101 32. V a r i a t i o n of F m w i t h L^Rf/Lk(1-Hf) 103 33. /} as a Function of K ka 106 34. K, a as a Function of L, 109 y v i i ACKNOWLEDGEMENTS The a u t h o r would l i k e t o ex p r e s s s i n c e r e g r a t i t u d e t o Dr. S.D. Cavers f o r the a s s i s t a n c e , encouragement, and h e l p -f u l c r i t i c i s m s o f f e r e d t h r o u g h o u t the cour s e of t h i s p r o j e c t . A p p r e c i a t i o n i s extended a l s o t o Mr. D i c k Hawrelak f o r h i s a s s i s t a n c e t h r o u g h o u t t h e l a t t e r p a r t o f t h i s i n v e s t i g a t i o n . Thanks a r e due 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 o f Canada f o r f i n a n c i a l a s s i s t a n c e . INTRODUCTION 1 r The u n i t o p e r a t i o n , s o l v e n t e x t r a c t i o n , u t i l i s e s the con-t a c t of two r e l a t i v e l y i mmiscible l i q u i d s , brought about i n v a r i o u s commercial e x t r a c t o r s ( 1 ) . In recent years, s o l v e n t ex-t r a c t i o n has become an important chemical engineering o p e r a t i o n f o r the separation of l i q u i d mixtures, when the conventional methods d i s t i l l a t i o n and evaporation are u n s u i t a b l e owing to un-favourable v a p o u r - l i q u i d e q u i l i b r i a r e l a t i o n s h i p s , thermal i n -s t a b i l i t y of the components, or economic reasons. Furthermore, the separation f a c t o r s f o r d i s t r i b u t i o n between two l i q u i d phases are u s u a l l y considerably l a r g e r than between l i q u i d and vapour. Organic l i q u i d s are most s u i t e d f o r s o l v e n t e x t r a c t i o n by v i r t u e of t h e i r low heats of v a p o r i z a t i o n , r e s u l t i n g i n economical s o l -vent recovery processes. The present i n v e s t i g a t i o n was based on spray towers, a spec-i f i c case of the c l a s s of e x t r a c t o r s which u t i l i z e s countercurrent f l o w under the i n f l u e n c e of g r a v i t y of two mutually i m m i s c i b l e phases i n a v e r t i c a l tower, where the l i g h t e r phase i s dispersed from the bottom end of the column, and the h e a v i e r phase from the top end. This c l a s s of e x t r a c t o r s i n c l u d e s a l s o packed, b a f f l e d , and s i e v e p l a t e towers which are used more f r e q u e n t l y i n indus-t r y than are spray towers(2). However, spray towers are perhaps the cheapest and simplest e x t r a c t o r s . The spray tower i s i n -expensive to c o n s t r u c t , easy t o keep clean, and has l a r g e throughputs, although the height r e q u i r e d f o r a given number of stages w i l l o r d i n a r i l y be greater than f o r other types ( 2 ) . In 2 recent years, spray towers, because of t h e i r inherent q u a l i t i e s , have been subject to s e v e r a l i n v e s t i g a t i o n s ( 3 , 4 , 5 , 6 , 7 , 8 , 9 , 1 0 , 1 1 , 12) . In 1955 Harmathy (13) reviewed a wide range of l i t e r a t u r e on the theory of throughput i n e x t r a c t i o n spray columns. He developed a g r a p h i c a l method to determine the t e r m i n a l v e l o c i t y of drops and suggested a procedure to determine the values of the operating v a r i a b l e a s s o c i a t e d w i t h the c r i t i c a l f l o w r a t e s . He a l s o demonstrated t h a t a t given f l o w r a t e s , the drops of the dispersed phase can t r a v e l a t two d i f f e r e n t v e l o c i t i e s . Most of the l i t e r a t u r e up to 1955, on the subject of back  mixing i n e x t r a c t i o n columns was covered by Ewanchyna (14). Since the present study i s e s s e n t i a l l y a c o n t i n u a t i o n of Ewanchyna's work, the l i t e r a t u r e t h e r e a f t e r w i l l be t r e a t e d i n d e t a i l here. Although c i r c u l a t i o n or back mixing i n the continuous phase can r e s u l t i n considerable r e d u c t i o n i n e x t r a c t i o n e f f i c i e n c y , there was l i t t l e mention of i t i n the l i t e r a t u r e u n t i l 1950. During the l a s t decade the phenomenon of back mixing r a p i d l y became a sub-j e c t of i n v e s t i g a t i o n . Cavers and Ewanchyna (15), and other workers (16,17) measured concentration gradients by i n t e r n a l sampling and reported a p p r e c i a b l e back mixing of the continuous phase. Some e f f e c t s of back mixing were a l s o noted i n a r o t a t i n g d i s c column by Vermijs and Kramers (18). In 1957 Miyauchi (19) analysed t h e o r e t i c a l l y the i n f l u e n c e of l o n g i t u d i n a l d i s p e r s i o n of f l u i d i n continuous counter-current s o l v e n t - e x t r a c t i o n columns, by u s i n g a s i m p l i f i e d model which u t i l i z e s "mean d i f f u s i v i t i e s " and "mean velocities™ f o r both con-3 " t i n u o u s and d i s p e r s e d p h ases. From 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 t h e model, i t has been found t h a t t h e i n f l u e n c e o f l o n g i t u d i n a l d i s p e r s i o n on t h e e x t e n t o f e x t r a c t i o n can be e x p r e s s e d as a f u n c -t i o n o f f o u r d i m e n s i o n l e s s g r o u p s . The r a t e s o f l o n g i t u d i n a l d i s p e r s i o n , t h e o v e r a l l m a s s - t r a n s f e r c o e f f i c i e n t , t h e e q u i l i b r i u m p a r t i t i o n r a t i o , and t h e r a t e s o f f l u i d f l o w a r e t h e v a r i a b l e s i n -c l u d e d i n t h e s e groups. He p r e s e n t e d s o l u t i o n s , w h i c h a p p l y t o s p e c i f i c t y p e s of a p p a r a t u s and t o s p e c i a l c ases o f m i x i n g be-h a v i o u r . He showed t h a t t h e e x t e n t o f e x t r a c t i o n under any g i v e n p a t t e r n o f l o n g i t u d i n a l d i s p e r s i o n i s l i m i t e d , even i f t h e o v e r a l l c o e f f i c i e n t o f mass t r a n s f e r i s i n c r e a s e d t o i n f i n i t y . He a l s o f o u n d i t n e c e s s a r y t o d e f i n e t h r e e k i n d s o f o v e r a l l H.T.U; t h e n t r u e T T v a l u e , w h i c h i s t h e r a t i o o f v o l u m e t r i c f l o w r a t e a c r o s s a u n i t c r o s s s e c t i o n t o t h e " t r u e " o v e r a l l c o e f f i c i e n t of mass t r a n s f e r ; t h e "measured" v a l u e , based on t h e measured c o n c e n t r a t i o n d i s t r i b u -t i o n i n an e x t r a c t o r ; and t h e " p i s t o n f l o w " v a l u e , based on t e r -I * m i n a l c o n c e n t r a t i o n s u s i n g t h e l o g a r i t h m i c - mean d r i v i n g f o r c e . I n g e n e r a l , t h e v a l u e s o f t h e s e H.T.U.s w i l l be suc h , t h a t t h e " p i s t o n f l o w " v a l u e ^ "measured" v a l u e " t r u e " v a l u e . The "measured" and t h e " p i s t o n f l o w " v a l u e s r e f l e c t t h e i n f l u e n c e o f l o n g i t u d i n a l d i s p e r s i o n . The n u m e r i c a l s o l u t i o n s o f M i y a u c h i ' s e q u a t i o n s f o r a l a r g e number of t y p i c a l cases were p r e s e n t e d by McMu l l e n , M i y a u c h i , and Vermeulen (20). Jacques and Vermeulen (21) t r e a t e d t h e performance d a t a o f packed columns, w i t h s i n g l e phase and two phase f l o w systems, u s i n g t h e concept o f l o n g i t u d i n a l d i s p e r s i o n . T h e i r work has a s i m i l a r t h e o r e t i c a l b a s i s t o t h a t o f M i y a u c h i ( 1 9 ) . P e c l e t numbers " I n t h e p r e s e n t t h e s i s the t r u e ( o r a c t u a l ) H.T.U. d e f i n e d l a t e r i s e q u i v a l e n t t o M i y a u c h i ' s measured v a l u e . 4 were used by them to c h a r a c t e r i z e d i s p e r s i o n i n packed beds. Their c a l c u l a t i o n s , based on P e c l e t numbers, show t h a t due to l o n g i t u d i n -a l d i s p e r s i o n the r e a l H.T.U.fs are only 80% to 20% of the c o r r e s -ponding H.T.U.'s based on t e r m i n a l concentrations. The study of back mixing u s i n g the concept of l o n g i t u d i n a l d i s p e r s i o n has an advantage over the use of the H.T.U., si n c e H.T.U. values vary w i t h the types of system, the r a t e s of f l o w , and the co n c e n t r a t i o n , n e c e s s i t a t i n g the use of very s p e c i f i c data. On the other hand the use of P e c l e t numbers r e q u i r e s t r a n s i e n t s t u d i e s i n order t o eval-uate the d i s p e r s i o n c o e f f i c i e n t . However, P e c l e t numbers can be obtained from the r e s u l t s of steady s t a t e s t u d i e s u s i n g c h a r t s developed by Miyauchi (19) and based on s i m p l i f i e d models of l i -quid e x t r a c t i o n cases. S l e i c h e r (22) analysed by means of an i d e a l i z e d d i f f u s -i o n model, the e f f e c t of back mixing of e i t h e r phase i n an e x t r a c -t i o n column on the e x t r a c t i o n e f f i c i e n c y . The d i f f u s i o n model was ch a r a c t e r i z e d by f o u r dimensionless groups, a P e c l e t number of each phase, a mass t r a n s f e r number ( i . e . , number of t r a n s f e r u n i t s ) , and an e x t r a c t i o n f a c t o r ( i . e . the product of the d i s t r i b u t i o n coef-f i c i e n t , and the r a t i o of feed t o sol v e n t s u p e r f i c i a l v e l o c i t y ) . His t h e o r e t i c a l a n a l y s i s was based on assumptions u s u a l l y v a l i d only f o r d i l u t e s o l u t i o n s . The a n a l y s i s y i e l d e d c o r r e l a t i o n s such as height of column versus extent of e x t r a c t i o n f o r various e x t r a c -t i o n f a c t o r s , which showed the amount t h a t the column height must be incr e a s e d , or feed t o solvent r a t i o decreased, to e f f e c t a given change i n e x t r a c t i o n . Transient s t u d i e s on the back mixing of the continuous phase i n spray columns were made r e c e n t l y by Brutvan ( 2 3 ) . He found the l o n g i t u d i n a l mixing of the continuous phase t o i n -crease w i t h column diameter f o r 1, 1.5 and 2- i n c h diameter ,spray columns, t o increase w i t h discontinuous phase f l o w r a t e , to decrease w i t h increased continuous phase f l o w r a t e , and to decrease w i t h increased discontinuous phase p a r t i c l e s i z e f o r 3, 4, 5 and 6 mm s p h e r i c a l p a r t i c l e s . L o n g i t u d i n a l mixing i n pulsed e x t r a c t i o n column was st u d i e d r e c e n t l y by Mar (24). The present i n v e s t i g a t i o n was undertaken as an attempt to provide a b e t t e r understanding of the phenomenon of back mix-i n g or c i r c u l a t i o n i n the continuous phase of spray columns. A steady s t a t e study of the phenomenon was made u s i n g a pro-cedure s i m i l a r to t h a t of Ewan.chyna(14). The system a c e t i c acid-methyl i s o b u t y l ketone - water was chosen so t h a t the r e s u l t s could be compared w i t h those of other r e s e a r c h e r s . Ewanchyna's work was based on a 3.8 f t . column. I n the pres-ent i n v e s t i g a t i o n three heights of column were s t u d i e d . EXPERIMENTAL METHODS Apparatus A schematic flow diagram of the apparatus i s shown i n Figure 1, which i s reproduced from Wiginton's thesis (25). A key-to Figure 1, i s presented in Table I. Most of the construction details are as described by LeCPage (26). The 12 U.S. gallon tanks, A, B, C and D in the flow diagram, were replaced by alum-inium tanks shown in Figure 2. The continuous water phase i s discharged through two 1/8 -inch Schedule 40 Type 304 stainless steel pipes, N, into the bottom of a 6-inch I.D. Pyrex pipe sec-tion, M, flows through the column, R, and out to a storage tank, B. The nozzle, S, disperses the ketone phase into drops which rise countercurrently to the descending water phase, coalesce in the upper expanded section, M, and are removed from the top of the column to a storage tank, C. The position of the interface, Q, was controlled origin-a l l y as in References 14 and 25, by varying the height of the water phase product line which was vented to atmosphere, and was constructed entirely out of Saran tubing. Due to the f l e x i b i l i t y of the Saran tubing control of the interface was poor, and siphoning in the line was observed. Therefore, i t was replaced by a constant head tank, constructed entirely from glass, and of the same general type as described by Dean (275. The details of the nozzle were shown by Ewanchyna (14) in his Figure 9. The nozzle was connected in Ewanchynafs work, and at the beginning of this study, to the bottom plate by means of a FIGURE 1. SCHEMATIC FLOW DIAGRAM TABLE I.' KEY' TO FIGURE 1 A - Co n t i n u o u s phase f e e d t a n k B - C o n t i n u o u s phase r e c e i v e r and s t o r a g e t a n k C - D i s p e r s e d phase r e c e i v e r and s t o r a g e t a n k D - D i s p e r s e d phase f e e d tank E - Continuous phase c o n s t a n t head tank F - D i s p e r s e d phase c o n s t a n t head t a n k G - Continuous phase r o t a m e t e r H - D i s p e r s e d phase r o t a m e t e r I - Continuous phase i n l e t sample v a l v e J1,J2 - C o n t i n u o u s phase f l o w r a t e c o n t r o l v a l v e s K1,K2 - D i s p e r s e d phase f l o w r a t e c o n t r o l v a l v e s L - D i s p e r s e d phase i n l e t sample v a l v e M - 6 i n c h I.D. t o p end s e c t i o n N - Co n t i n u o u s phase i n l e t p i p e s 0 - D r a i n v a l v e f o r t o p end s e c t i o n P1,P2 - C e n t r i f u g a l f e e d pumps f o r c o n t i n u o u s and d i s p e r s e d phases r e p s e c t i v e l y Q - L e v e l of I n t e r f a c e R - Column p r o p e r l j i n c h I.D. S - D i s p e r s e d phase n o z z l e T1,T2,T3,T4 - Thermometers U - Bottom end s e c t i o n V - Vent t o atmosphere W - P r e s s u r e e q u a l i z i n g v e n t X - C o n t r o l f o r i n t e r f a c e l e v e l TABLE I . CONTINUED. Y - V a l v e f o r d r a i n i n g column Z1,Z2 - O u t l e t sample v a l v e s f o r c o n t i n u o u s and d i s p e r s e d phases r e s p e c t i v e l y a - D i s p e r s e d phase sample probe b - Continuous phase sample probe c - T r a v e l l i n g b l o c k from w h i c h s a m p l i n g probes a r e suspended d - Guide on framework f o r b l o c k C e - C o n t i n u o u s phase s a m p l i n g r a t e c o n t r o l v a l v e f - D i s p e r s e d phase s a m p l i n g r a t e c o n t r o l v a l v e h - C o n t i n u o u s phase sample c o l l e c t o r k - D i s p e r s e d phase sample c o l l e c t o r m - Mercury manometer n - Water a s p i r a t o r (Vacuum c o n t r o l l e d by a i r v e n t a t t h e bottom o f a, mercury column.) r - V a l v e f o r r e l e a s i n g vacuum 10 SPACED N O T E : ALL SHEET IS ALUMINUM, l / ) 6 " THICK FIGURE 2. ALUMINIUM TANK. 11 stainless steel pipe coupling and a pipe nipple. The centrifugal pumps used at f i r s t were Eastern, Type E - 1, with a Type 316 stainless steel housing and Teflon pack-ing. These pumps were later replaced by sparkprobf Eastern pumps, Type D - l l , with a Type 316 stainless steel housing and Teflon packing. Flow rates were measured by rotameters (26). Calibration curves are presented in Figure 3, and the data in Table II. Although in Runs 47 and 48 the apparatus operated satis-factorily, in Runs 49 and 50 i t was found that the jets from the nozzle tips were very unstable."'" Some of the nozzle tips pro-duced long sinuous streams of f l u i d and i n others drops formed right at the nozzle tips. Also a change of behaviour from one sort to the other was observed at individual nozzle tips. Various attempts were made to get uniform jets, some of these involving apparatus modification. At f i r s t , the 3-in. I.E. Pyrex spacer(15), used at the bottom end of the column, was removed. Also, the nozzle was redesigned as shown in Figure 4, to remove the pos-s i b i l i t y of pipe threads throwing the nozzle off the v e r t i c a l . The annular space between the distributor nozzle and the walls of the expanded bottom section should be sufficiently large so that the ratio of the area of the column proper to the area of the annulus i s between 0.2 and 0.9 (2). From Run 47 to 53 i n -elusive this ratio was 0.48 and the nozzle used was that of Figure 4. With this ratio, and a vertical nozzle, i t was hoped that drop An e a r l i e r t r i a l r u n - Run 46 p r e s e n t e d s i m i l a r d i f f i c u l t i e s .24 ROTAMETER READING FIGURE 3. CALIBRATION CURVES FOR ROTAMETERS 13 TABLE II CALIBRATION OF ROTAMETERS Ketone Rotameter Room Temperature - 71°F Liquid = Ketone saturated twith water Rotameter reading Rate of flow cu.ft/hr. 0.02 0.04 0.06 0.08 0.12 0.16 0.20 0.217 0.400 0.593 0.774 1.164 1.541 1.896 Water Rotameter Room Temperature = 71°F. Liquid - Water saturated "with Ketone Rotameter reading Rate of flow cu.ft./hr. 0.02 0.04 0.06 0.08 0.12 0.14 0.150 0.325 0.493 0.648 0.967 1.115 14 FIGURE 4 , FIGURE 4. FIRST CHANGE IN NOZZLE ATTACHMENT TO THE BOTTOM PLATE 15 formation would take place with a minimum of disturbance. Un-fortunately Run 50 had to be discarded since i t was s t i l l not pos-sible to obtain stable jets. Runs 49, 51, 52, and 53 were dis-carded for this reason and others. It was f e l t that i t would be advantageous to construct the nozzle i n such a way that the annular space between i t and the expanded bottom section of the column could be adjusted. Accordingly, the attachment of the nozzle to the bottom plate was redesigned after Run 53 as shown in Figure 5. Consequently, the annular space could be varied through a wide range by raising or lowering the nozzle, and tightening the gland-packing nut. From Run 54 to 70 inclusive this last design was used, and the ratio of the column proper to the area of the annulus was 0.64, which was the same as that used by Ewanchyna (14). However, this value of 0.64 for Ewanchyna's work was determined by the author from a photograph of his column and i s consequently rather approximate. The inside diameter of the nozzle tips should have been O.lOOin according to specification (26), but measurements with a travelling microscope showed that the average inside diameter of the tips was 0.1024 - i n . (When these measurements were made a range of tip diameter from 0.1023 - to 0.1074-in. was obtained. A test using d r i l l s of various sizes showed that, a number of the nozzle tips were tapered from top to bottom of the tips. Hence, the value of 0.1023-in. was used as an working average after allowing for the effect of this taper. A similar statement i s also true for the tip diameter of 0.1029-in. described below). This dia-meter of 0.1024-in. was used for calculations in Runs 47 to 60 16 FIGURE 5 if D. CIRCLE 4 2" D. CIRCLE I CLEARANCE HOLE FOR i " STD. PIPE ,1 N C - T A P 4 H O L E S EQUALLY SPACED 3 C L E A R A N C E HOLES FOR i " 8 STD. PIPE II w II PLAN VIEW OF PLATE X 7 t ml® TEFLON SEAL RING I" D. NUT -Ire -I* roi^ r roioo fO KETONE N O Z Z L E (FIG. 9 IN REF. 14 ) 5 - 26 MACHINE TWO HOLES - g D. i " DEEP FOR WRENCH COLUMN BOTTOM P L A T E ( 2 6 ) P L A T E . " X " - 2 g D, TEFLON PACKING TEFLON S E A L RING THREADED TO FIT -SARAN COUPLING NUT CHAMFERED FOR | TUBING FLARE FIGURE 5. SECOND CHANGE IN NOZZLE ATTACHMENT TO THE BOTTOM PLATE 17 inclusive. Due to non uniformity of the nozzle tips they had to be d r i l l e d to a larger size, so that the average inside diameter was changed to 0.1029-in.j again found from measurements with a travelling microscope. This diameter of 0.1029-in. was used for calculations from Rttsn 61 to 70 inclusive. The distributor plate within the nozzle (Fig. 9 in Ref. 14) was removed from Run 61 to 70 inclusive. Observations showed that this plate has l i t t l e effect on jet formation or jet s t a b i l i t y in this apparatus. The nozzle tips used by Ewanchyna (14) were also measured by the author with a travelling microscope. The average inside diameter was found to be 0.09#9-in. From the above measurements the average velocity through the nozzle tips used by Ewanchyna (14) was 0.279 ft/sec. In order to keep the linear velocity of the dispersed phase through the tips constant with varying total ketone flow rates through the column, some of the tips were blocked out by using Teflon caps (15). Accordingly, the number of open tips changed with ketone flow rate. Figure 6 shows the various t i p -patterns used. The sampling tubes used were V 8 inch O.D. by 0.020 inch wall thickness, Type 304 stainless steel seamless tubing (26). Figure 7 i s a photograph of a section of the column showing the sampling tubes in operation under conditions of Run 67 • The two tubes were clamped to a wooden block, and their various posi-tions with respect to the nozzle tips were calibrated. The re-sults are presented in Table III. To get better control of the sampling rates than that obtained by Ewanchyna, glass capilary Actually two constant ketone velocities were used, approximately 0.271 and 0.357 ft./sec. (Fig.6). 18 FIGURE 6 . • BLOCKED OUT L K ». 36.6 v = 0.272 FT/SEO. L K • 51.5 v = 0.270 FT/SEC. L K = 36.5 v = 0.357 FT/SEC. /•••••••*\ P • 0 • O /precox p • o • o L K = 54.7 v = 0.357 FT/SEC. L K = 72.9 v = 0.357 FT/SEC. FIGURE 6. TIP PATTERNS FOR KETONE NOZZLE. 'fi v = L i n e a r v e l o c i t y t h r o u g h t i p s i n ketone n o z z l e , f t . / s e c . FIGURE 7 FIGURE 7. PHOTOGRAPH OF SAMPLING TUBES IN COLUMN TAKEN DURING RUN 67. TABLE I I I LOCATION OF STAINLESS STEEL SAMPLING TUBES P o i n t Number D i s t a n c e above n o z z l e t i p s , f t . 1 0.078 1A 0.161 2 0.445 2A • 1.161 2B 0.911 3 0.755 3A 2.161 3B 1.661 4 1.060 4A 3.161 4B 2.411 5 1.379 5A 1.355 5B 4.161 5C 3.786 6 5.161 7 6.161 8 7.286 2 1 ' tubes were used between the sample valves and the sample collectors, i.e., between e and hy. and f and k, respectively in Figure 1. These were the sampling arrangements used in Runs l i s t e d i n Tables V to X. Temperatures were measured as shown in the flow diagram in Figure 1, and the thermometers used were as specified by Le -Page (26). Procedure . The required flow rates were obtained by making use of the rotameter calibration curves and then adjusting the control valves, before the rotameters, to give the required rotameter readings. The height of the interface was adjusted by raising or lowering the interface level controller, X, in Figure 1. Transient studies were made by taking outlet samples at frequent intervals from the beginning of a run and i t was found that steady state conditions were attained in the tower after i t s contents had changed two to three times. The flow rates were checked at fre-quent intervals and average values were used. During the course of a run inlet and outlet samples were taken intermittently and the results were averaged. Outlet samples remained quite constant throughout the course of a run. For example in Run 68 the out-- I * l e t samples had the following concentrations. Water phase: 0.01485, 0.01497, 0.01497, and 0.01491 lb.moles/ft^ Ketone phase: 0.01580, 0.01568, 0.01562, and 0.01568 lb.moles/ft3 Experiments were performed on sampling rate and purging time for internal sampling of the phases. The results are pres-Samples taken over the course of. the run 22 ented in Figures 14, 15, and 16 under"Discussion" The rate of sampling used in the present investigation, as seen from Table V (under"Treatment of Data), were quite low percentages of the respective phase flow rates as compared to 15% for the worst case reported by Cavers and Ewanchyna(15). The analysis of the acetic acid in the samples i s des-cribed elsewhere (14). Because of the v o l a t i l i t y of the ketone were a l l analyses^carried out within a day or two from the time the samples were obtained. As a precaution, the cork stoppers used on the sample bottles were covered with aluminium f o i l s at an early stage of this investigation. However, with both plain cork stoppers, and with stoppers covered with aluminium f o i l s , the concentrations of acetic acid in the ketone samples were found to remain constant even i f the samples were l e f t for a week. Sometimes wetting of the sample probes by the ketone was observed. This was avoided by keeping the probes clean. There was no noticeable entrainment of the ketone phase in the water phase samples obtained by internal sampling. The ketone phase samples contained up to approximately 10% by volume of the water phase. Therefore, after collection of the samples, (and before analysis) mass transfer continued so that correction was necessary of the measured concentration of acetic acid in the ketone samples. This correction was made by using Equation 1,' the derivation of which was treated in detail by Ewanchyna(14). / / / 23 fA table of nomenclature appears at the end of this Thesis). The concentrations of the acetic acid in the feed streams were kept approximately the same for a l l runs, since the aim of this investigation was to study variables other than concentra-tion. Johnson and Bliss (9) have shown that the mass transfer coefficient increases only slightly with increased solute con-centration. After a l l the feed solutions had been used up the acetic acid concentration in the outlet water phase was adjusted by adding glacial acetic acid. This solution then served as the feed in subsequent runs. The concentration of acetic acid in the outlet ketone phase was adjusted by washing i t with d i s t i l l e d water in the column. The product of these "reverse" runs then formed the feed for following runs. The phases were kept always mutually saturated i n order that the extraction of only acid occurred in the column. Mutual saturation was achieved by main-taining a thin layer of water at the bottom of the ketone feed tank and a thin layer of ketone at the top of the water feed tank. The distribution data for the MIBK-water-acetic acid sys-tem were obtained mainly from Ewanchyna (14), and Fleming and Johnson(6). A few data obtained as part of the present work, as a check on the previous data used (14, 16), are presented in Table IV. Table IV over y 24 , Table IV Equilibrium Data for the Methyl Isobutyl Ketone -water - Acetic Acid System Temp. Acetic Acid Acetic Acid Distribution Ratio cone, in Ketone cone, in water n F phase _ phase , m - ^ ^ . . ^ w ^ w w / ^ v , . lb.moles/ft.^ 'Gw 70 0.0125 0 . 0 2 6 0 0.481 70 0.0191 0 . 0 3 7 3 0.512 70 0.0243 0.0464 0.524 Using the data of Fleming and Johnson (6) and Ewanchyna (14) an equation was developed by the least-mean-square method for the equilibrium relationship. This equation i s G w = 2.02168 Ck + 0.00021. where i s in equilibrium with C^. The values of G w cal-culated from this equation were found to be within Z. 4% of the measured value for concentrations in the ketone phase be-tween 2.0x10"^ lb.moleycu.ft. and 19.0X10"-3 lb.moles /cu.ft. The equation presented by Seltzer (28) for the present system was also tested using the same data (6,14). The calculated values of C w again were within £ k% of the measured values. . (In one case where the concentration in the ketone phase was 1.87xl0~3lbjnQles/cu.ft. the calculated value of C w differed by about 10% from the measured value. This statement applied to calculations made with either the foregoing equation or the 25 S e l t z e r equation (28). This poor agreement could e a s i l y be due to the e r r o r s i n measurement because of the low concentra-t i o n s i n v o l v e d i n t h i s p a r t i c u l a r c a s e ) . However, only F i g u r e 8 was used i n the present work. Sodium hydroxide and g l a c i a l a c e t i c a c i d were reagent A.C.S., and were obtained from N i c h o l s Chemical Co., L t d . , Montreal. Laboratory d i s t i l l e d water was used f o r a l l of the runs reported i n Tables V to X except i n Runs 47 and 48, where deionized water from the chemistry l a b o r a t o r y was used. Tap water was used i n Run 50 o n l y which was d i s c a r d e d . The MIBK used was t e c h n i c a l grade mainly obtained from theCanadian Chemical Co., Edmonton, w i t h smaller amounts i n the e a r l y stages of the work from George C. Henderson Co.Ltd., Vancouver. The f o l l o w i n g are the r e f r a c t i v e i n d i c e s as measured by the author,of the MIBK used Source of MIBK R e f r a c t i v e Index Temperature George C. Henderson Order No.l 1.3935 25 Co.Ltd. Order No.2 1.3935 25 Canadian Chemical B a r r e l No.l 1.3940 25 Company B a r r e l No.2 1.3941 25 The r e f r a c t i v e index of MIBK of 99% p u r i t y i s 1.3958 a t 20°C (29). 26 FIGURE & 0 0.01 0.02 0.03 0.04 0.05 0.06 ACETIC ACID CONCENTRATION IN KETONE P H A S E , LB . M O L E S / C U . FT. FIGURE 8. EQUILIBRIUM DIAGRAM FOR METHYL ISQBUTYL KETONE - WATER -ACETIC ACID SYSTEM. 27 THEORY In order to describe the operation of a liquid-liquid extraction spray column the following differential equation can be used as a starting point: The general theory of diffusional operations i s treated in detail elsewhere (14). Hence a very brief description of the theory i s given in the present thesis. 1. The partition coefficient i s constant with changing concent-rations, 2. the two liquids involved, in this case ketone and water, are relatively immiscible, 3. the solutions are sufficiently dilute so that the volume change is negligible when solute transfer occurs, then Equation 2 can be integrated to give the following result dN = KkdS (C k - C k) 2. where dS = aAdh. When the following assumptions are valid: (H): N = KkaAh (C k - C k) 3. Also, N = I^A ( C ^ - C K 2 ) = VUCW-L " 4. Since (H.T.U.) o k = L kA KkaA & 28 then f rom equations 3 and 4, ( H . T . U . ) = h « k - Vl.m. also, K K a - L k A ( c k ; L - C k 2 ) A h < < " C J l . m . 7. I t i s o b v i o u s , t h a t E q u a t i o n 4, b e i n g a t o t a l mass b a l a n c e e q u -a t i o n , i s v a l i d r e g a r d l e s s o f the mechanism of mass t r a n s f e r i n the co lumn. However, E q u a t i o n 3 i s v a l i d o n l y f o r t r u e c o u n t e r c u r r e n t f l o w and i n t h e absence o f end e f f e c t s . But i n a s p r a y co lumn, due t o l o n g i t u d i n a l m i x i n g i n t h e c o n t i n u o u s  phase the r a t e o f mass t r a n s f e r a c r o s s the i n t e r f a c e between the two phases i s lower than t h a t c a l c u l a t e d by E q u a t i o n 3» Consequent l y e q u a t i o n 3 was m o d i f i e d t o B = K k a A h ( C k - C s ) 1 < m / m . g > The f a c t o r , F m , c o r r e c t s f o r the r e d u c t i o n i n d r i v i n g f o r c e due t o back m i x i n g i n t h e c o n t i n u o u s phase and i t s v a l u e cannot ex -c e e d u n i t y , which i s r e a c h e d f o r t r u e c o u n t e r c u r r e n t f l o w . The ketone drops on moving upwards c a r r y w i t h them an "a tmosphere" (16) o f c o n t i n u o u s phase f rom a r e g i o n o f lower to one o f h i g h -e r c o n c e n t r a t i o n , so t h a t the mean d r i v i n g f o r c e i s r e d u c e d . E x c e p t perhaps f o r a few s m a l l d r o p s , t h e ketone p a r t i c l e s move upward i n a z i g - z a g manner and s i g n i f i c a n t back m i x i n g o f m a t e r i a l s o f d i f f e r e n t c o n c e n t r a t i o n s does not o c c u r f o r the 29 dispersed phase. Hence the dimensionless correction factor, F m, essentially accounts for the back mixing in the continuous phase. The same correction factor for longitudinal mixing was also used by Gayler and Pratt(30) for packed columns. From equations 4, 5 and 8 the corrected H.T.U., designated by a prime is (H.T.U.)/ - Fm h (G k - C k ) i . m . 9. Ok : (ck - ck ) . 1 K 2 From equations 9 and 6 we get Fm = (H.T.U.)Zok 10. '(H.T.U.)ok The true height of a transfer unit, (H.T.U.)^, can be obtained by graphical integration from the following equation (14. , 31): .(H.T.U.)/k = h 11. dC k The right hand side of equation 11 may be integrated only i f both concentration profiles are known and i f the concentrations of the phase mentioned in the equation result only from mass transfer across the interface. Due to back mixing in the continuous phase, dN # LwAdCw 30' and hence, an equation corresponding to equation 11, based on water phase concentrations cannot be obtained. Therefore a true value of the H.T.U. based on the water phase cannot be ob-tained by graphical integration. Consequently a l l calculations in the present investigation were based on the dispersed ketone phase only The interfacial area of contact per unit volume, a, i s a variable depending on the shape and size of the drops, num-ber of drops passing a given point per unit time, and the linear velocities at which the phases move in the column. Elgin and Browning (5) derived an expression for the specific area per unit volume using "equivalent drop diameter". However, ex-act measurements of drop size are f a i r l y d i f f i c u l t , and theoret-i c a l calculations in terms of known constants and physical properties are impractical at the present time. Usually the quantity, a, i s incorporated with the overall mass-transfer co-the product efficient and^is called the capacity coefficient, K ka, which i s given by equation 7 under true countercurrent conditions. The fractional holdup, H^ , i s another variable in spray column operation and i s given by the following equation ( 1 4 ) : L kAh H f = _ ^ - Lk 1 2 . hA * The quantity, v , i s the velocity of the dispersed phase re-lative to the laboratory, which velocity i s much larger than the continuous phase velocity relative to the laboratory, and hence, Hf mainly depends on the dispersed phase flow rate, L K , 31 as long as the drop size i s maintained constant. i s also a weak function of the water phase flow rate since v i s af-fected, to a small extent by L . 1> RESULTS The data obtained in the operation of the spray tower are presented in Tables V to X inclusive. The treatment of Run 68 is presented below as a sample calculation: The total rates of mass transfer were: N w = I^A ( C W 1 - C W 2) = 18.235 x 0.01227(0.05043 - 0.01492) = 7.944 x 10""3 l b . moles/ h r and % = v ( c k X - v - 72.94 x 0.01227 (0.01570 - 0.00659) = 8.153 x 10"3 l b . moles/ h r > i N = Nw + Nk = 8.049 x 10-3 lb.moles/hj 2 Thus N w - % Percent deviation = X IOO N S 2.5^07« The acetic acid mass balance was calculated as follows: Acetic acid entering column = I^AG^ + ^ kA^k =0.017179 l b . moles/ h r i TABLE V SAMPLING RATE AND PURGE TIME D i r e c t i o n D i r e c t i o n S a m p l i n g r a t e S a mpling r a t e . . P u r g i n g . R u n o f e x t r a c t i o n o f i n t e r n a l mls/min. as a % o f phase time,mins. No; o f a c i d . s a m p l i n g . f l o w r a t e Water Ketone Water Ketone phase phase phase phase 47 R n 6.0 6.0 2.44 2.76 6.7 48 N n 6.0 6.0 2.48 2.99 6.7 54 N P 9.7 14.5 3.99 6.75 -55 N P » r 7.0 7.2 2.88 3.36 10.0 56 N i 7.0 7.0 3.44 3.26 13.0 57 N r 4.7 5.2 4.86 2.46 16.0 58 N i 9.0 8.6 2.98 4.07 9.0 60 N n 11.0 10.2 3.69 3.25 8.5 6 1 * N 4.8 5.1 1.98 2.42 18.0 62* N n 8.8 9.4 8.33 2.97 8.0 63 N r 8.8 9.4 4.17 2.97 8.0 65 N r 8.8 9.8 2.78 2.32 8.0 66 N r 8.8 9.8 4.17 2.32 8.0 67 N r 4.2 6.0 3.88 1.42 18.0 68 N r 4.2 6.0 3.88 1.42 18.0 69 N r 4.2 6.0 3.88 1.90 18.0 70 N r 6.0 8.0 2.44 3.78 12.0 R - E x t r a c t i o n of a c e t i c a c i d f r om t h e ketone phase t o t h e w a t e r phase, i . e . a r e v e r s e r u n . N - E x t r a c t i o n of a c e t i c a c i d f r o m t h e w a t e r phase t o t h e ketone phase, i - Sampling from t h e i n t e r f a c e t o t h e n o z z l e t i p s , n - Sampling f r o m t h e n o z z l e t i p s t o t h e i n t e r f a c e , r - random s a m p l i n g . p - Purge t i m e s t u d y when s a m p l i n g probes were moved back and f o r t h between two p o s i t i o n s i n column. * - S i n c e r u n 62 had a h i g h s a m p l i n g r a t e , r u n 69 was made which had t h e same f l o w r a t e s as r u n 62 b u t a l o w e r s a m p l i n g r a t e was u s e d . TABLE VI OVERALL TRANSFER DATA Run Inlet and Outlet Concentrations Lb.Moles Acid/cu.ft x 10 3 Flow Rates Cu.ft/hr./sq. f t . Overall Acetic Acid Transfer Rates Lb.Mbles/hr.xl03 Per cent Deviation Nw~Nk xlOO N No. Water Ketone Water Ketone Water Ketone Average In C W 1 0 u t c w 2 Out C, k l V \ Nw N k N 47 0.02 4.0 9.9 5.4 42.6 37.7 2.07 2.02 2.05 + 2.20 48 50.2 39.9 7*2 19.6 42 .0 24.7 5.25 5.21 5.23 + 0.75 54 50.3 34.4 6.8 25 .6 42 .0 37.1 8.21 8.55 8.38 - 4.02 55 ' 50.3 33.9 6.8 25.6 42.0 37.2 8.45 8.59 8.52 - 1.57 56 50.3 30.6 6.9 25.0 35.1 37.2 8.46 8.25 8.36 + 2.51 57 45.5 19.2 6.7 18.1 16.5 36.5 5.33 5.13 5.23 + 3.82 58 45.7 34.2 6.8 22.6 52.2 36.5 7.35 7.03 7.19 4 4.45 60 45.4 28.3 6.6 22.0 51.5 54.3 10.84 10.27 10.56 + 5.40 61 50.2 33.4 6.4 25 .4 42.0 36.5 8.64 8.54 8.59 + 1.15 62 50.3 15.7 6.4 17.6 18.2 54.8 7.72 7.53 7.63 4 2.49 63 50.3 23 .8 6.4 23 .7 36 .5 54.7 11.85 11.63 11.74 4 1.94 TABLE VI CONTINUED. Run Inlet and Outlet Concentrations Lb.Moles Acid/cu.ft x 10 3 Flow Rates Gu.ft/hr./sq. f t . Overall Acetic Acid Transfer Rates Lb.Moles/hr.xl03 Per Cent Deviation Nw-Nk xlOO N No: Water Ketone Water Ketone Water Ketone Average In C r w l Out C„ w2 In C k  K2 Out C, K l \ N„ w \ N 65 50.4 26.3 6.5 24.7 54.7 72.9 16.22 16.26 16.24 - 0.27 66 50.3 19.9 6.7 22.1 36.5 72.9 13.58 13.81 13.69 - 1.69 67 50.5 14.6 6.5 15.6 18.2 72.9 8.04 8.14 8.09 - 1.20 68 50.4 14.9 6.6 15.7 18.2 72.9 7.94 8.15 8.05 - 2.60 69 50.2 16.6 6.8 17.9 18.2 54.7 7.53 7.50 7.52 + 0.33 70 50.2 36.2 7.1 23.5 42.5 36.5 7.28 7.35 7.32 - 1.025 TABLE V I I OVERALL TRANSFER DATA No. o f Open T i p s i n -L i n e a r V e l o c - A c t u a l Drop A c e t i c A c i d Run Temper-a t u r e a , c i t y t h r o u g h T i p s i n Ke- V e l o c i t y , Holdup Column H e i g h t 0 , M a t e r i a l B a l a n c e No: ?F k e t o n e N o z z l e . tone n o z z l e , f t / s e c . f t . / h r . % f t . fo D i f f e r e n c e 47 73 8 0.277 882.4 4.3 1.39 - 1.02 48 74 8 0.255 875.9 4.0 1.36 + 0.14 54 68 8 0.276 1036.2 3.6 7.34 -;.1.18 55 69 8 0.277 1078.9 3.4 7.37 - 0.48 56 70 8 0.277 1055.2 3.5 7.39 4 0.86 57 74 8 0.272 1200.0 3.0 7.36 + I . 6 4 58 72 8 0.272 1098.5 3.3 7.36 +, 0.98 60 72 12 0.270 841.6 6.5 7.37 + 1.79 61 76 6 0.357 1030.9 3.5 7.36 ? 0.34 62 74 9 0.357 1097.5 5.0 7.35 + 1.74 63 72 9 0.357 1008.2 5.4 7.34 + 0.85 65 69 12 0.357 899.6 8.1 7.35 - 0.11 66 75 12 0.357 969.9 7.5 7.35 - 0.85 67 71 12 0.357 950.3 7.7 7.35 - 0.57 68 74 12 0.357 980.4 7.4 7.34 - 1.22 69 75 9 0.357 1041.8 5.3 7.34 + 0.16 70 74 6 0.357 1001.7 3.6 3.83 - 0.25 a - Average Temperature o f aqueous phase, ketone phase, and room. b - V e l o c i t y = h£ 3600 (No. of T i p s open) ( Area o f 1 T i p ) c - D i s t a n c e from n o z z l e t i p s t o i n t e r f a c e . TABLE VIII : CONCENTRATIONS IN THE WATER PHASE1 (SMOOTHED.VALUES) Outlet Concentration Acetic Acid in Water Phase, lb.moles/ft3xl0-* at Inlet Water^ •a watpr lb.moles/ft3 Run ^ G 1 > Distance from Nozzle Tips, f t . lb.moles/ -; , : No. ft3 _ 0.1 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 h d 48 56 58 60 Point "E" Point »D" 4.0 4.0 3.6 2.8 0.02 47 3 3.5 1*8 0*7 39.9 40.4 42.4 45.0 46.3 - 50.2 40.9 43.9 47.4 " 49.5 33.9 34.8 37.1 39.1 42.6 45.2 46.9 47.9 48.6 49.3 49.6 - 50.3 5 5 34.8 38.2 40.8 44.2 46.4 48.0 48.9 49.6 50.1 - 50.3 30.6 31.6 34.4 37.0 40.5 43.1 45.0 46.5 47.6 48.5 48.8 - 50.3 31 .8 35.0 37.7 41.3 43.9 45 .8 47.4 48.5 49.3 - 49.6 19.2 19.6 20.6 21.9 24.6 27.2 29.9 32.5 35.2 37.8 38.8 - 45.5 5 7 19.6 20.8 22.4 25.8 29.0 32.2 35.4 38.7 42.0 - 43.2 34.2 35.2 37.6 39.3 41.5 42.9 43.9 44.6 44.8 45.2 45.6 - 45.7 35.2 37.6 39.3 41.5 42.9 43.9 44.6 44.8 45.2 - 45.6 28.3 28.8 30.6 32.6 36.0 38.4 40.2 41.8 43.1 44.7 45.4 - 45.4 29.2 31.6 33.9 36.8 39.1 41.0 42.5 43.5 44.2 - 45.4 33.4 34.0 36.0 38.3 42.2 45.2 47.4 48.5 49.2 49.7 49.9 - 50.2 6 1 34.4 37.2 39.7 43.2 45.8 47.8 48.6 49.2 49.8 50.0 TABLE VILT CONTINUED Outlet Concentration Acetic Acid in Water Phase, lb.moles/ft-^xlOJ* at Inlet Water2 Run W a t e r » lb.moles/ft3 lb.moles/ Distance from Nozzle Tips, f t . No. ft3 ~ 0.1 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 h 2 Point "E'» Point nD" 62 63 65 66 67 68 69 70 15.7 15.8 16.6 17.6 20.4 23.8 27.3 31.1 35.0 39.0 40.4 - 50.3 16.0 17.0 18.4 21.7 25.3 28.9 33.2 38.1 43.9 - 47.3 23.8 24.2 26.1 28.7 33.2 37.3 40.9 44.0 46.4 47.9 48.2 - 50.3 24.4 26.6 29.3 34.0 37.8 41.2 44.4 47.2 49.3 - 49.8 26.3 27.0 29.6 32.5 36.9 40.4 43.6 46.2 47.7 49.1 49.5 - 50.4 2 7 . 0 2 9 . 8 3 2 . 8 3 7 . 6 4 1 . 1 4 4 . 2 4 6 . 5 4 8 . 1 4 9 . 6 - 50.1 19.9 2 0 . 3 2 1 . 7 2 3 . 5 2 7 . 2 3 O . 8 3 4 . 5 3 8 . 2 4 1 . 8 4 5 . 7 47.1 - 50.3 20.4 22.4 24.4 28.4 32.1 35.6 39.3 43.0 47.0 - 48.4 14.6 14.6 14.9 15.2 16.0 17.8 20.2 23.2 27.7 35.4 38.2 - 50.5 14.6 15.0 15.4 16.7 18.6 21.6 26.5 33.0 42.3 - 46.0 14.9 15.0 15.3 15.7 16.5 18.0 20.2 23.2 28.0 35.5 38.5 - 50.4 15.0 15.4 15.9 17.2 19.2 22.0 26.0 32.3 42.4 - 46.0 16.6 16.7 17.2 18.0 20.0 23.4 27.2 31.2 35.1 38.9 40.2 - 50.2 16.7 17.4 18.6 21.7 25.5 29.2 33.0 38.0 45.1 - 47.6 36.2 36.8 38.6 41.0 45.2 47.8 48.8 - 50.2 37.2 40.0 42.6 46.5 48.6 " 49.8 l l n the Table the upper figure i s the value measured. The lower figure i s calculated by 2material balance on the basis of true countercurrent flow. ^Distance from nozzle tips equal to column height (Table VII). ^Reverse Run.Concentration just below interface i s 2.1x10-3 lb.moles/ft3. ON TABLE IX CONCENTRATIONS IN THE KETONE PHASE (SMOOTHED VALUES) Inlet ketone lb.moles/ ft3 Concentration of acetic acid in ketone phase, lb.moles/ft3xl03 Outlet Run at distance from nozzle tips, f t . ketone 0.1 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 hi lb.moles, ft-No; Point MB" 4 7 2 9.9 9.3 7.5 6.0 5.4 48 7.2 8.3 12.0 16.8 - - .- - - - 18.9 19.6 55 6.8 8.1 10.8 14.6 18.7 21.1 22.8 23.9 24.6 25.2 25.4 25.6 56 6.9 7.8 10.5 13.0 16.6 19.2 21.2 22.7 23.8 24.6 24.8 25.0 57 6.7 6.8 7.4 8.1 9.6 11.1 12.5 14.0 15.5 16.9 17.4 18.1 58 6.8 7.5 10.3 13.1 17.2 19.4 20.7 21.4 21.8 22.3 22.6 22.6 60 6.6 7.4 9.9 12.0 14.8 17.0 18.7 19.8 20.6 21.3 21.6 22.0 61 6.4 7.4 10.9 13.7 17.6 20.7 22.9 24.1 24.7 25.2 25.4 25.4 62 6.4 6.5 6.9 7.2 8.5 9.6 10.8 12.0 13.8 15.9 16.7 17.6 63 6.4 6.9 8.6 10.3 13.2 15.6 18.0 20.2 22.1 23.5 23.7 23.7 65 6.5 7.1 9.3 11.4 15.0 17.8 19.9 21.6 22.9 24.0 24.3 24.7 66 6.7 7.0 8.0 9.0 10.9 12.7 14.4 16.2 18.2 20.2 20.9 22.1 67 6.5 6.6 6.7 6.8 7.1 7.7 8.4 9.2 10.8 13.4 14.3 15.6 68 6.6 6.6 6.7 6.9 7.2 7.7 8.4 9.4 10.9 13.3 14.4 15.7 69 6.8 6.9 7.2 7.5 8.5 9.7 11.0 12.3 14.0 16.2 17.2 17.9 70 7.1 8.2 11.4 14.6 19.0 21.6 — — 22.8 23.5 1 1 Distance from nozzle tips equal to column height (Table VII). 2 Reverse Run. Concentration just below interface i s 5.5 x 10""3 l b . moles/ft3. TABLE X AVERAGE VALUES OF K k a , AND ( H . T . U . ) o k , AND END EFFECT ft Run P e r c e n t flj/ D e v i a t i o n l b . m o l e s 7 N ^ - N^ No: n r 7 x 10? x 100 4 7 3 -48 4.98 55 8.47 56 8.17 57 4.84 58 7.17 60 10.43 61 8.55 62 6.99 63 11.64 65 15.96 66 12.74 67 7.01 68 6.96 69 6.98 70 7.06 Average v a l u e s o f K k a and ( H . T . U . ) o k R e s u l t u s i n g l o g mean + 0 . 4 6 - 0 . 4 6 + 0 . 1 6 + 0 . 8 5 3 . 9 7 7.82 0 . 2 0 2.21 0 . 2 4 • 0 . 4 0 - 0 . 2 1 + 0 . 7 7 + 0.25 - 0 . 7 6 + 0 . 5 4 R e s u l t o f g r a p h i c a l i n t e g r a t i o n K k a 2 (H.T.U. ) o k K ^ 1 ' 2 (H.T.U. ) ^ c o l u m f t . f t . K k a 18.333 3 0 . 8 7 24.98 21.16 14.80 1 8 . 9 6 28.34 25.79 21.70 36.51 4 8 . 6 2 3 8 . 4 9 25.39 24.02 22.52 23.50 2.053 1.12 1.49 1.76 2.47 1.92 1.92 1.41 2.52 1 .50 1.50 1 .90 2.87 3 . 0 4 2.43 1.55 35.09 34.00 32.31 23.14 20.02 36.98 29.70 32.37 44.26 56.11 50.90 49.87 41.78 35.80 26.70 1.813 0.99 1.09 1.15 1.58 1.82 1.47 1.23 1.69 1.24 1 .30 1.43 1.46 1.75 1.53 1.37 20.81 37.78 35.46 32.97 23.82 20.02 38.72 29.70 33.21 44.26 58.21 53.71 51.08 43.08 36.49 28.94 m o k col n /. ir _ O -A H TH .T.U.) .T.U.j / 0.8813 0.879 0.735 0.655 0 . 6 4 0 0.947 0 . 7 6 6 0 . 8 6 8 0.670 0.825 0 . 8 6 7 0.756 O.509 0.575 0.629 0 . 8 8 0 End E f f e c t l b . m o l e s / h r x 105 3 0 . 6 9 . 6 6 . 8 31.4 0 . 0 2 6 . 6 0 . 0 62.5 0 . 0 3 3 . 1 107.4 112.8 120.8 5 0 . 0 31.3 •'•Integrated f r o m bottom o f t h e column t o p o i n t ! B f i n t h e ketone phase, and p o i n t 'D' i n t h e wa t e r phase. 2 U n i t s : l b . m o l e s / ( h r ) ( f t 3 ) ( l b . m o l e s p e r f t 3 ) . 3Reverse Run. The v a l u e s o f K k a , ( H . T . U . ) Q k , and ( H . T . U . w e r e c a l c u l a t e d u s i n g t h e whole e x p e r i m e n t a l p r o f i l e s , i . e . from i n l e t t o o u t l e t . F m h e r e has t h e same meaning as i n normal r u n s j s i n c e = 0 f o r a r e v e r s e r u n i n t h i s i n v e s t i g a t i o n , 'A' and »B { c o i n c i d e and so do 'C 1 and 'D1 i n t h e t y p i c a l p r o f i l e s . 41 Acetic acid leaving column = I^AC^ * L ^ A 0 ^ = 0.017389 l b . moles/ h r # % difference = 0-Q17179 - 0.017389 x 1 0 0 0.017179 - - 1.222% The plan was to discard runs in which this per cent difference was over +_ 2.0% (14). However none actually had to be discarded for this cause. Graphical integration was used to obtain (H.T.U.)^, and the logarithmic mean driving force was used to obtain (H.T.U.) o k. However, before proceeding further with the sample calculation i t i s desirable to show a typical concentration profile which appears in Figure 9. The true situation at the interface i s rep-resented by a simplified model: Water phase enters the column at the interface just above a bed of agitating and coalescing drops. At entry the water phase has a concentration which w i l l be labelled point n C n in concentration profiles, e.g., as in Figure 9. At this point the driving force i s ^ ckjp "" ^ k p}' Drops agitate and coalesce at the interface (14), their concentration changing from that of "B" to that of "A". As a result, the con-centration of the water phase f a l l s to nDtt, and the driving force to - c k ^ ; the f a l l "CD" in the water phase profile being related to the rise "BA" i n the ketone phase profile by the equa-tion Iv A/CD/ = L kA /AB7, 42 FIGURE 9 CONCENTRATION PROFILES FOR RUN 68, 43 where /~CD__7 and /~AB_7 represent the differences in concentration as obtained from the concentration profiles, e.g., Figure 9. Then the back mixing causes C w to f a l l from MD n to "E", infinitesim-a l l y below the interface, resulting in a further reduction in driving force to - C k • However, this last reduction in IE IB driving force does not contribute to the value of H.T.U. obtained by the graphical integration method since the abscissa of the curve of l/C£ - C k versus C k i s unchanged. Hence, in graphical integration to obtain ( H . T . U . a s in Figure 10, the limits used were from the bottom of the column, designated by " 2 " to point B. By stopping at point B and not proceeding to point A, the extraction due to drop agitation and coalescence i s eliminated. In order to calculate the H.T.U. using the logarithmic - mean driving force, point " D " was used together with points "B", "L n, and nM". By this procedure the effects of drop agitation and coalescence were eliminated, but, the effect of back mixing i s included.(Point nE" would coincide with point " D " i f there were no back mixing in the continuous phase). Point "Dtt was calculated by extrapolating to interface the calculated water phase profile represented by the dotted line in Figure 9« The calculated water phase profile was obtained, on the basis of true countercurrent flow, from the measured ketone phase profile using the outlet concentration of the water phase, . Thus, to calculate any point, C w , ^n the dotted line, the following mass balance equation was used: 44 P o i n t "D" was found by t h e e x t r a p o l a t i o n method r a t h e r t h a n by a mass b a l a n c e a t t h e i n t e r f a c e , as shown p r e v i o u s l y , s i m p l y be-cause t h e forme r method uses t h e e n t i r e k e t o n e p r o f i l e whereas t h e l a t t e r method uses t h e jump "AB n a l o n e . O v e r a l l mass t r a n s f e r c o e f f i c i e n t s and H.T.U. v a l u e s were c a l c u l a t e d by u s i n g e q u a t i o n s 4, 6, and 7 m o d i f i e d as f o l l o w s - , where t h e d a t a i s a g a i n t h a t o f Run 68: = L k A ( C ^ - C ^ ) - 6.936 x 1 0 ~ 3 l b . m o l e s / h r . N / = L A (G - C ) w w 1 D w 2 = 6.953 x 10*3 i b . m o l e s / h r . 2 l / = Nw + N k = 6.94 x 1 0 " 3 l b . m o l e s / h r . N / - N / P e r c e n t d e v i a t i o n ; - w * x 100 N / = 0.245% The o v e r a l l c a p a c i t y c o e f f i c i e n t based on4C k is l.m. K a L k A ( C k " C k } * = k l B K 2 Ah (C* - C K ) K K l.m. where ( C ? - C k ) = A C k 4« # (CT, -CT, . ) - (CT, - C v ) K 1 D K1B K2 K2 2.3 log ( c r - C k ) *1D K1B < 2 - c k 2 ) The values of C£ were obtained from Figure £. Then,for Run 68, (0.02380 - 0.01435) - (0.00720 - 0.00660) l.m, And K ka 2.3 log (0.02380 - 0.01435) (0.00720 - 0.00660) 3.21 x 10~3 l b . moles/ cu.ft. N/ hA ^ C k ±.m 6.945 x 10"3 7.34 x 0.01227 x 3.21 x 10""3 2 4 . 0 ^ j . Hence, (H.T.U.)ok = Lk = 72.9 K ka 24.0 - 3.04 f t . 46 . • The true H.T.U. values were obtained by graphical integrat-ion using equation 11, modified to eliminate drop agitation effect as mentioned earlier, so that the limits of integration are as shown below. (H.T.U.)/ ok = f d C k J Ck - Ck 2 As an example, calculations for Run 68 are shown in Table XI, and the plot in Figure 10. The area under the curve up to point "B" in Figure 10 i s 4.20, and, hence, (8.T.U.)/ = h _ = 7.34 4.20 4.20 1.75 f t . and the true capacity coefficient is Kk* = L k , - JbL = 4 i . . h - i (H.T.U.)J k 1.75 n r * The driving force correction factor, F , i s the ratio of (H.T.U.)^. to (H.T.U.)Qk, i.e., Fm = 1 , 7 5 = 0.575 3.04 The correction for the entrained water in the ketone phase sample was made using equation 1. Thus, for sample point number 7, in Run 68, the ketone sample collected consisted of 1.5 mis. of TABLE X I DATA FROM RUN 68 FOR CALCULATING (H.T.U.)/, BY GRAPHICAL INTEGRATION P o i n t n a C b eg c eg - Ck o 1 l b . m o l e s / f t 3 l b . m o l e s / f t 3 l b . m o l e s / f t 3 l b . m o l e s / f t 3 eg - c k ft3/lb.moles, No: x K)3 x 103 x 103 x 103 Bottom o f Column. 6.60 13.90 7.20 0.60 1666.7 1A 6.62 15.20 7.25 0.63 1587.3 2A 6.95 15.80 7.60 0.65 1538.5 3A 7.10 16.60 8.00 0.90 1111.1 LA 7.80 18.21 8.75 0.95 1052.6 5B 8.58 20.65 10.00 1.42 704.2 6 9.55 23.85 11.65 2.10 476.2 7 11.25 28.95 14.25 3.00 333.3 8 14.24 38.00 19.25 5.01 199.6 P o i n t "B" and "E» 14.35 38.45 19.45 5.10 196.1 P o i n t "B" and "D» 14.35 46.00 23.80 9.45 105.8 Top o f 26.35 10.65 column 15.70 50.43 93.9 a - C o n c e n t r a t i o n o f a c e t i c a c i d i n t h e ketone phase, o b t a i n e d as smoothed v a l u e s f rom ketone phase c o n c e n t r a t i o n p r o f i l e i n F i g u r e 9 . b - C o n c e n t r a t i o n o f a c e t i c a c i d i n the wat e r phase, o b t a i n e d as smoothed v a l u e s f rom w a t e r phase c o n c e n t r a t i o n p r o f i l e i n F i g u r e 9 . c - C o n c e n t r a t i o n o f a c e t i c a c i d i n ketone phase i n e q u i l i b r i u m w i t h C w, o b t a i n e d f rom e q u i l i b r i u m diagram, F i g u r e 8. 48 o o UJ _i o z m _i o o o o 00 o I o o RUN 68 AREA UNDER CURVE UP TO C K IB = 4 2 0 'KIA 4.34 o KIA 8 ACID 10 12 CONCENTRATION 14 16 IN KETONE 18 PHASE 20 LB. MOLES/ F T . 3 X I 0 3 FIGURE 1 0 . GRAPHICAL INTEGRATION FOR DETERMINING (H.T.U.)/ i". OK 49' "water and 30.0 mis of ketone, which on analysis gave the following results: cl - 0.01152 lb . moles/cu.ft., K2 c / 2 = 0.0236 lb. moles/cu.ft.*, V - 30.0 mis, V w = 1.5 mis, and Cwi = 0.02899 lb . moles/cu.ft. i s obtained as a smooth value from Figure 9. Hence, C ^ _ 1.5(0.0236 - 0.02899) + 30.0 x 0.01152 30.0 = 0.01125 lb. moles/cu.ft. Not an analytical value in this case, although ordinarily i t would be. The volume of entrained water being very small i t was assumed that the water phase reached equilibrium with the ketone phase by the time the analysis was .carried out. ^ence an equilibrium value corresponding to C£ 2 was used. This was obtained from Figure 8. Checks on this showed a maximum d i f -ference of 2f0 between the measured value and the value obtained by assuming equilibrium with Cfo2> f ° r samples containing as much as 30 to 40%. water and with analysis carried out at least 12 hours from the time the run was made. x DISCUSSION 50 , Reproducibility of Results. Run 68 was a replicate of Run 67. The reproducibility of the results may be seen by comparing the figures for the two runs li s t e d in Table XII. Figure 11 shows the concentration profiles of these two runs. The large deviation in the reproducibility of (H.T.U. is due to the fact that the phases approach equilibrium near the bottom of the column, which results in the possibility of large errors in computing the driving force, and consequent large errors in the graphical integration. ^ i s an agitation end effect and w i l l be discussed in detail under "Back Mixing and End Effects". Run 62 had a high sampling rate (see Table V), and so, Run 69 was made as a repeat run at a lower sampling rate. Figure 12 shows the concentration profiles of the two runs. For further comparison, results obtained are presented in Table XII. As seen from Table XII the use of a high sampling rate in Run 62 did not seem to have any noticeable effect on the reproducibility. Run 70 was a replicate of Ewanchyna's (14) Run 23, with approximately the same flow rates and column height. However, a higher linear velocity through the nozzle tips was used in Run 70. Table XII shows that these two runs agree almost equally as well as do the replicate Runs 67 and 68. TABLE X I I REPRODUCIBILITY OF RESULTS Run No: N l b . m o l e s / X1O!T' ( H . T . U . ) Q k from l.m. f t . (H.T.U.)/ k from g r a p h i c a l i n t e g r a t i o n , f t . F Am % holdup l b . m o l e s / h r t x 1 0 ? . -L i n e a r v e l o c -i t y o f ketone i n t h e n o z z l e t i p s , f t / s e c . 67 8 . 0 9 2 .873 1 .463 0 . 5 0 9 7 . 6 8 1 1 2 . 8 0 . 3 5 7 68 8 . 0 5 3 . 0 3 6 1 .746 0 . 5 7 5 7 .44 1 2 0 . 8 0 . 3 5 7 62 7 . 5 1 2 . 5 2 4 1 .692 0 . 6 7 0 4 . 9 9 6 2 . 5 0 . 3 5 7 69 7 .63 2.430 1 .528 0 . 6 2 9 5 . 2 5 5 0 . 0 0 . 3 5 7 70 7.32 1.552 1.366 0 . 8 8 0 3 . 6 3 1 . 3 0 . 3 5 7 23 7 . 3 8 1 .760 1 . 5 1 8 0 .863 3 . 4 3 3 . 0 0 . 2 8 0 55 8 . 5 2 1 .487 1 .093 0 . 7 3 5 3 . 4 9 . 6 0 . 2 7 7 61 8 . 5 9 1 . 4 1 4 1 .228 0 . 8 6 8 3 . 5 0 . 0 0.3.57 5 2 10 L K = 7 2 . 9 F T . / ' t H R . K F T . 2 ) L w = 18.2 FT.//(HR )( FT . 2 ) O RUN 67 X RUN 68 • C|/* VALUES FOR RUN 67 C A L C U L A T E D WATER PHASE PROFILE FOR RUN 67 INTERFACE 4 WATER PHASE PROFILE FOR RUN 67 • K E T O N E PHASE PROFILE FOR RUN 6 7 BTM. I 4 5 HEIGHT , FT FIGURE 11. CONCENTRATION PROFILES FOR RUNS 67 AND 68 53 6 0 ro O x ro H 50 it. </> UJ _J O C O z o 2 30 H Z 1U o z o u o <• L K B 5 4 . 8 F T . y i H R . M F T . 2 ) L w • 18.2 F T . ^ H R . K F T . 2 ) o x RUN 62 RUN 69 6 C A L C U L A T E D WATER PHASE PROFILE FOR RUN 62 KETONE P H A S E PROFILE FOR RUN 6 2 BTM. I FIGURE 12. 2 3 4 5 6 HEIGHT , F T . CONCENTRATION PROFILES FOR RUNS 62 and 69 Runs 55 and 6 1 had approximately the same flow rates, but a higher velocity through the nozzle tips was used in Run 6 1 . Figure 13 shows the concentration profiles of these two Runs. The large difference in the values of (H.T.U.)/ here i s partly ok due to the fact that the phases approach equilibrium near the top of the column which results in the possibility of large errors in the graphical integration. Justification of Sampling Technique. It was shown by Ewanchyna (14) that the presence of the sampling tubes in the column, direction of sampling (top to bottom or bottom to top), and the location of the tubes in the cross section of the column at a given distance from the nozzle, had no effect on the concentrations of the samples withdrawn. One of the important factors in internal sampling i s to purge lines thoroughly when sampling tubes are changed from one position to another. The rate of sampling i s another important factor to be considered both from the point of view of possible effects on the concentration of the drops entering the dispersed phase sampling probe due to possible effects of drop coalescence there, and also from the point of view of possible disturbances i n the steady state operation of the column by removing too large a percentage of the flowing phases. Figures 1 4 and 1 5 show the change in concentration of acetic acid in the water and the ketone phases respectively with purge time for various rates of sampling. These figures are based on Runs 5 4 , 5 5 , and 6 1 . The conditions under which these runs were performed appear in Table V, VI, and VII. The procedure was briefly as follows: 55 60 •°o 50 ro UJ -I o 4 0 30 < CL Z UJ o 20 z o o < 10 CALCULATED WATER PHASE PROFILE FOR RUN 55 6 WATER PHASE PROFILE FOR RUN 55 INTERFACE 6 KETONE PHASE P R O F I L E FOR RUN 55 O RUN 55 , L K • 37.2 , L w = 4 2 . 0 X RUN 61 , L K » 36 .5 , l _ w = 4 2 . 0 <b C K * » VALUrLS- FOR RUN 55 01 I I I I I I L B T M . I 2 3 4 5 6 7 HEIGHT , F T . FIGURE 13. CONCENTRATION PROFILES FOR RUNS 55 AND 61 I I I I I I I 1 1 — .1 I 0 2 4 6 8 10 12 14 16 18 20 P U R G E TIME , MINS. FIGURE 14. PLOT OF CONCENTRATION OF ACETIC ACID IN THE WATER PHASE VERSUS PURGE TIME U i CO < I 0 . 2 5 . 0 UJlO z o o ~ r- „ l l j X ro _ I— £ u. \ z w O _ J Z O 2 4 . 5 < 2 or S 3 Ul U Z o o < 2 4 . 0 O o o 9 D A T A F R O M R U N 5 4 S A M P L I N G R A T E = 1 4 . 5 M L S . / M I N . D A T A F R O M R U N 5 5 S A M P L I N G R A T E = 7 . 2 M L S . / M I N . D A T A F R O M R U N 6 1 S A M P L I N G R A T E « 5 . 1 M L S . / M I N . 9 — - < ? • 9 1 6 1 8 2 0 0 2 4 6 8 1 0 1 2 1 4 P U R G E T I M E , M I N S . FIGURE 15. PLOT OF CONCENTRATION OF ACETIC ACID IN THE KETONE PHASE VERSUS PURGE TIME . . . Samples were taken at sample point number 7. In each run several samples were taken at one sampling rate. The time of purging varied from sample to sample. Between any two consecu-tive samples at point 7 the sampling probes were moved down to sample point number 2A, where purging was carried out for a sufficiently long time to change the acid concentrations of the phases from the previous values to those corresponding to point number 2A. The concentrations of the samples obtained after sufficient purging in these runs (54, 55, and 61) check within approximately 0.5% at the worst in the respective phases. The sampling rates used for each run i n the present work appear in Table V which also shows the sampling rates as percentages of the respective phase flow rates. In a l l the runs the sampling rates were kept quite low so that the steady state in the column was not disturbed. Figure 16 shows roughly the minimum purge time to obtain uniform concentration at various sampling rates. To be on the safe side at least 2 to 3 mins. should be allowed beyond the value of the purge time obtained from Figure 16. The results obtained from internal samples of the phases during the course of a run, using the necessary precautions as discussed in the foregoing section, gave the experimental con-centration profiles (e.g., shown as solid lines in Figure 9 ) . The calculated water phase profile (e.g., shown dotted in Figure 9) was obtained on the basis of true countercurrent flow as ex-plained previously. Thus, •> *Extra 2 to 3 min. purge time not always used in this work. 59 O DATA FROM FIG. 14 t ) DATA FROM FIG. 15 6 P H A S E WATER PHASE ~6 i i 1_— 1 «— 2 4 6 8 10 12 SAMPLING R A T E , MLS ./MIN 14 FIGURE 16. PLOT OF MINIMUM PURGE TIME VERSUS SAMPLING 60 L (C - C ) s L, (C. - G. ) w w w0 k k k ' C c c. where C i s a point on the calculated water phase profile cor-w c responding to C k on the ketone profile. In the presence of back mixing l e t (1^ + R) ft}/ft2.hr.be the incoming water phase flowing downward, to a section of the column shown in the ac-companying sketch. Here R i s the recirculating stream. Let the concentration of the ( L w + R) stream be x l b . moles/ft3. The out-going water phase from the bottom of the column, i s 1^ with acid concentration C w 2 and, from the top of the section, R with acid concentration y. In addition, a ketone stream enters the bottom of the column at concentration C k£ and leaves the top of the section at concentration C k. The material balance on this section of the column gives ( I ^ t R) x - Ry. - L ^ a L k (C k - C^) = L (C - C ) - w , w c w 2 or ( L w + R) x _ Ry V w For truecountercurrent flow, by i t s very nature and R = 0 In the presence of back mixing c w c > x > c w > y 62 where G w i s the experimentally measured water phase c o n c e n t r a t i o n . x exceeds G w because the stream + R comes from a r e g i o n of comparatively high c o n c e n t r a t i o n , and y i s l e s s than C w s i n c e stream R comes from a r e g i o n of comparatively low c o n c e n t r a t i o n . That the value of x cannot exceed C w i s seen from the above mater-c i a l balance equation since f o r x g r e a t e r than C , R w i l l have a w c negative, and, t h e r e f o r e , impossible value. E v i d e n t l y G w i s some s o r t of average between x and y. This average must be l e s s than cw c-A c a l c u l a t i o n f o r Run 68 i s shown i n the f o l l o w i n g i n order to give a very rough id e a as to the magnitude of R. A value of C w equal to 0.0280 l b . m o l e s / f t . 3 was taken from the experimental water phase p r o f i l e shown i n Figure 9, The corresponding C w was c O.O323 l b . moles/ft.-^ x was assumed to be 0.030 l b . m o l e s / f t . 3 , and y to be 0.027 l b . m o l e s / f t . 3 . Then u s i n g the previous equation (18.2 4 R) 0.030 - R(0.027) - 18.2 (0.0323) •*• R = f t ' 3 / h r . f t . 2 which would seem to be a reasonable value ( f o r Run 68, = 73 f t . 3 / f t . 2 n r . ) . Furthermore, i f i t i s assumed that the present sampling tech-nique does not give a r e p r e s e n t a t i v e sample of the water phase, perhaps because of not sampling c l o s e enough to the drops, l e t C be the concentration of a r e p r e s e n t a t i v e sample.^ Then C w„ w R r WR would be l e s s than C , which was a value measured away from drops (assumed), s i n c e e x t r a c t i o n of a c i d was from the water to the ketone phase i n normal runs. Hence, *a bulk, or mixed value. 63 C S G WR ^ w Therefore, making the samples more representative from the point of view of approach of the sampling probe to the drops would move the measured profile further away from the calculated profile rather than nearer to i t . From the point of view of sampling the streams L^ . + t-R, and R, i t has already been shown that any average of x and y, for example C w, must be less than C w . The calculated profile certainly does not represent any true average concentrations in the column. Somewhat similar arguments to these are presented by Gier and Hougen (16). Although, Cw, as measured in the present investigation may not be a perfectly representative sample (a point which requires further investigation), i t probably i s almost correct. Appearance of Drops and Stability of Jets. Visual observations were made of the formation of drops by keeping the continuous phase flow rate constant and slowly i n -creasing the ketone flow through the nozzle. At very low flow, drops formed at the nozzle tips and grew in size u n t i l the buoyant force overcame interfacial tension, and the drops were released. Drops were large, uniform, and oblong. On increasing the flow slightly, liquid jets of length roughly equal to the diameter of one drop appeared at the nozzle tips. The drops detached as a result of constrictions which formed at the tops of the jets. On further increase of flow the constrictions became less pro-nounced so that the jet length increased, and eventually, a short 64 " continuous neck of liquid of height equal to approximately two drop diameters existed between the nozdle tip and the point of drop detachment. The linear velocity of the ketone in the nozzle tips at this stage* i s called the "jetting velocity", and the nozzle i s said to be at the "jetting point" (31a). Drops were s t i l l uniform but less ellipsoidal, and a very few small drops became v i s i b l e . As the flow was increased slowly, the jets rapidly lengthened to about 1.5 i n . and consisted of smooth col-umns of liquid with occasional transient lumps; also the diam-eter of the jets tapered from the nozzle tips to the point of drop detachment. Corresponding to this behaviour the linear vel-ocity through the nozzle i s termed the " c r i t i c a l velocity" ( 3 1 a ) . Drops were s t i l l f a i r l y uniform except that a few small drops were present. On further increase of flow the jets started to shorten in length u n t i l a point was reached when jet breakup re-treated to the nozzle tips, and a non-uniform spray of small drops resulted; the corresponding velocity through the nozzle tips i s called the "disruptive velocity" (31a). Uniformity of drop size i s a f a i r l y strong function of the velocity used at the nozzle tips. From the observations of Johnson and Bliss ( 9 ) , i t can be concluded that scattered re-sults with spray towers for high velocities through the nozzles might be due to excessive non-uniformity of the drop sizes. Hence in the present investigation an attempt was made to keep this velocity at a value which would produce as uniform drops as sort of possible. According to the^observations just described, of drop formation as the ketone flow rate is increased, reasonably 6'5 uniform drops are obtained up to a certain linear velocity i n the nozzle tips, 0.398 ft/sec-, for a 0.100 ins. I.D. nozzle according to Johnson and Bliss ( 9 ) . Ewanchyna (14) used a velocity of 0.279 ft/sec. for 0.0989-in. I.D. nozzle tips. In the present research, a velocity through the nozzle approximately equal to that used by Ewanchyna was maintained from Run47 to Run 60 inclusive. In these runs the ketone jets through the nozzle were 1.25 to 1 .5-in. in length and somewhat tapered from the nozzle tips to the point of drop detachment. The jet length reported by Ewanchyna (14) was about 0.75-in. Since i t was desired to compare the present re-sults with those of Ewanchyna, attempts were made to obtain a jet length of about 0.75-in. As mentioned previously, jets were quite unstable at the beginning of this work. On the other hand, stable jets are essential throughout the study so that drop size may be as uniform as possible and therefore reproducibility as high as possible, i n a l l the work. Hence various changes were made in the apparatus as described previously, and in the linear velocity through the nozzle tips to obtain stable jets of the proper length. The following i s a l i s t of changes made throughout the course of this work; See page following:-In Runs 47 to 53, inclusive an attempt was made to keep the linear velocity through the nozzle tips the same as that of Ewanchyna, but st a b i l i t y of the jets could not always be obtained. As a result, i t was often necessary in these runs to momentarily LIST OF CHANGES MADE IN THE APPARATUS THROUGHOUT THE COURSE OF THE PRESENT WORK I n c l u s i v e Run No's. From To Mode o f Attachment o f N o z z l e t o Bottom P l a t e . A rea o f col u m n 1 Area of, Annulus' Average I n s i d e Diameter T i p s , i n . Average L i n e a r V e l o c i t y o f N o z z l e T i p s , f t / s e c . 47 54 61 53 60 70 As i n F i g u r e 4. As i n F i g u r e 5^  As i n F i g u r e 5> 0.48 0.64 0.64 0.1024 0.1024 0.1029 0.266 0.274 0.357 1 C r o s s s e c t i o n a l a r e a o f column p r o p e r . 2 ' A r e a o f t h e a n n u l u r space around maximum n o z z l e diameter. 67 increase the flow through the nozzle i n order to obtain uniform jets through a l l the tips. Subsequently the flow could be returned to i t s previous value with the jets remaining stable, at least for a time. However, care was taken not to withdraw any samples from the column u n t i l steady state was re-established after any such dis-turbance. The ketone jets were s t i l l tapered and between 1.25- and 1.5-in. long in spite of using a vertical nozzle as in Figure 4, and a column area to annulus ratio of 0.48(2). As mentioned pre-viously a l l runs of this series except 47 and 48 were discarded be-cause of unsatisfactory jet behaviour and for other reasons. In Runs 54 to 60 inclusive, the ratio of the area of the column proper to that of the annulus was 0.64. The increase from the previous value of 0.48 did not seem to have any effect either on jet length, or on jet s t a b i l i t y . However no runs in this series had to be discarded. When the jets became unstable the pro-cedure already described of momentarily increasing the flow was resorted to. At this point in the research i t was decided to check on the uniformity of the nozzle tips. Consequently measurements were made of the nozzle tip diameters by means of a travelling microscope. These averaged 0.1024-in. but tips were not uniform. To improve uniformity of nozzle tips, they were d r i l l e d to an average size of 0.1029-in. I.D. In Runs 61 to 70 inclusive an average velocity of 0.357 ft/sec. through the nozzle tips was used. With the d r i l l e d out tips and this velocity, s t a b i lity of jets was achieved. Any lower 68 velocity resulted in i n s t a b i l i t y . The range of suitable operating velocities for 0.1029-in. I.D. nozzle tips was found to be from 0.302 ft/sec. to 0.452 ft/sec. by Keith and Hinson (31a). The upper limit represents the point where drop non-uniformity begins. The average velocity of 0.357 ft/sec. used in Runs 61 to 70 i n -clusive i s well within this recommended range and conforms also to the recommendation of Johnson and Bliss (9) . Figure 17 shows a photograph of the jets taken under conditions of Run 65. However the jets were s t i l l tapered from the nozzle tip to the point of drop detachment. Keith and Hinson (31a). , also observed this phenomenon with systems such as methyl isobutyl ketone, ethyl acetate, isopropyl ether, and cyclohexane; the tapering of jets with these systems wajs observed only in the region of 0.10~in. I.D. nozzle. The exact cause of this tapering of the jets in this nozzle range i s not known. Although an average velocity of 0.271 ft/sec. was used through the nozzle tips in Runs 47 to 60 inclusive, and an average velocity of 0.357 ft/sec. in Runs 61 to 70 inclusive, the effect of this change on the concentration profiles i s negligible from the point of view of the present work. This statement i s borne out by Figure 13, where Runs 55 and 61 are plotted. In Run 55 a linear velocity of 0.277 ft/sec. was used in the nozzle tips, and in Run 61 a velocity of 0.357 ft/sec. The differences i n the concentration profiles from these two runs are similar to those obtained when two runs were made under identical conditions. From the results shown in Figure 13, i t i s concluded that the change to a higher velocity did not affect the drop size distribution to a FIGURE 17. KETONE JETS FROM NOZZLE DURING RUN 65 « 70 ' measurable extent. In runs where the acetic acid was transferred from the continuous water phase to the dispersed ketone phase (normal runs) drops appeared to be f a i r l y uniform i n size as shown in Figure 18, for Run 68. L i t t l e or no coalescence occurred during their r i s e . Unfortunately, due to lack of time, i t was not pos-sible to perform any measurements on drop size. During drop detachment, a number of very small, spheri-cal droplets were formed, most of which seemed to rise with the larger drops but with a much slower velocity. A few of the smaller ones did seem to f a l l towards the nozzle on occasion. This formation of a few small drops in the column could not be avoided in the present work, at reasonable velocities through the nozzle. It i s f e l t that much i s yet to be learned about jet behaviour and i t s relationship to drop uniformity, especially in the region of 0.10-in. nozzle. In runs where acetic acid was transferred from the dis-persed ketone phase to the continuous water phase (reverse runs) the drops were i n i t i a l l y quite uniform, but in a short distance up the column they coalesced to form large liquid masses of various and changing irregular shapes. Although considerable coalescence of drops was observed before they reached the inter-face, there were a few spherical drops that did not coalesce u n t i l that plane was reached. In the reverse runs drops coalesced immediately on reaching the interface, and hence no extraction of acetic acid was observed due to drop agitation and coalescence FIGURE 18. KETONE DROPS COLUMN DURING RUN 68. 72 there. However, in normal runs the drops did not coalesce immediately on reaching the interface. One layer of drops was always maintained there, and, as more drops arrived, a spouting effect was observed in the centre, and the drops moved out to-wards the wall of the 6-in. I.D. section. This spouting effect was mainly a function of the ketone flow rate and was found to increase with increasing ketone flow rate. At the middle of the 6-in. I.D. section considerable turbulent agitation of the drops was observed. Also, by following the movement of fine sus-pensions ? (dust), considerable turbulence was evident in the con-tinuous, phase. The drops that moved towards the wall usually coalesced before reaching i t . Figure 19 shows a photograph of the interface under conditions of Run 70. It can be seen from this figure that some of the drops coalesced to form large l i -quid masses before f i n a l coalescence took place. The general mode of drop behaviour in both normal and reverse runs, and both in the column and at the interface i s similar to that described by Ewanchyna (14). Simplified Model . Before discussing the operating variables in detail i t i s convenient to review the simplified model mentioned earlier, on which the present calculations were based. Simplifications inherent in the model were: 1. It was assumed that the water phase f i r s t entered the column at the interface where i t encountered the bed of agitat-74' i n g and c o a l e s c i n g drops a t t h e t o p o f t h e column and underwent a f a l l i n c o n c e n t r a t i o n from C t o D i n F i g u r e 9 . A c t u a l l y t h i s i s not c o m p l e t e l y t r u e . The w a t e r phase e n t e r e d t h r o u g h 1 / 8 - i n . p i p e s n e a r the bottom o f t h e 6 - i n . I.D. s e c t i o n and t h e n f l o w e d upward and o v e r the t i p of t h e 1 . 5-in. I.D. g l a s s p i p e , and so down t h e column. The e n t e r i n g w a t e r t h e r e f o r e e n c o u n t e r e d d r o p s r i s i n g t o t h e i n t e r f a c e , as w e l l as drops a t t h e i n t e r f a c e . More-o v e r , the w a t e r phase underwent a 360° change i n d i r e c t i o n i n f l o w i n g t h r o u g h the l / 8 - i n . c o n t i n u o u s phase i n l e t p i p e s , and up-ward t o e n t e r the 1 . 5 - i n . column p r o p e r . T h i s change i n d i r e c t i o n p r o b a b l y produced some m i x i n g , w h i c h p r o b a b l y gave f a i r l y good c o n t a c t o f t h e i n l e t w a t e r phase w i t h t h e a g i t a t i n g and c o a l e s c i n g d r o p s . 2. I t was assumed t h a t t h e f a l l i n t h e measured c o n c e n t r a -t i o n of t h e c o n t i n u o u s phase from D t o E i n F i g u r e 9 o c c u r r e d i n f i n i t e s i m a l l y below t h e i n t e r f a c e . The f a l l i n c o n c e n t r a t i o n f r o m D t o E i s a t t r i b u t e d t o b a c k - m i x i n g , whereas t h a t from C t o D i s a t t r i b u t e d t o a g i t a t i o n and c o a l e s c e n c e and c o r r e s p o n d s t o t h e r i s e B t o A o f t h e c o n c e n t r a t i o n of t h e ketone drops as p r e v i o u s l y e x p l a i n e d . T h e r e f o r e , on t h e b a s i s o f t h e s e a s s u m p t i o n s , t h e l o g a r i t h m i c mean d r i v i n g f o r c e f o r g e t t i n g F m was c a l c u l a t e d u s i n g p o i n t s D, B, L, and M(e.g. i n F i g u r e 9) because D and B would have been the p o i n t s a t t h e t o p o f t h e column i f t h e r e had been no a g i -t a t i o n and c o a l e s c e n c e e f f e c t . Thus the H.T.U. h e r e was c a l c u l a t e d t o a p l a n e i n f i n i t e s i m a l l y below t h e i n t e r f a c e , i . e . p o i n t D. 3. The a s s u m p t i o n was made t h a t t h e i n l e t w a t e r phase had 75 a concentration equal to Gw^c> corresponding to points C in the experimental profiles and referring in the model to the water phase entering the top of the bed of agitating and coalescing drops at the interface. However, in practice, the inlet water phase samples ordinarily were taken at Valve I in Figure 1, i.e., from the line feeding the water phase to the rotameter, and the water entered not through the bed of drops, but rather below that level. In one of the runs, to show that the concentration at valve I applies at least in the bottom of the 6-in. I.D. section at the top of the column, a sample was taken through valve 0 in Figure 1, and was found to be of the same concentration as that of another inlet water phase sample taken at Valve I. These three assumptions are involved in the interpreta-tion of the data. Effect of Concentration. The effect of in l e t acid concentration on the capacity coefficient was found to be quite small by other investigators (14,9). However, while studying the effect of other variables, i t i s probably best to keep the inlet acid concentrations constant to be on the safe side. In the present investigation the i n l e t concentrations were kept approximately constant except in Runs 57, 58, and 60. There was a pipette error in only the water phase concentration measurements in these runs. However, the error was carefully corrected, with the result that i t was found that these runs had about 9% lower inlet water phase concentration than had 76 the other runs described in this thesis. The capacity coeffic-' ients would probably have been decreased but by not more than 2.5% (14). The effect of increasing ketone flow rate on the con-centration profile i s shown in Figures 20, 21, and 11; the effect of increasing water flow rate i s shown in Figures 11, 22, and 23. It can be seen from Figures 11, 22, and 23 that as the water phase flow rate increases at constant ketone flow rate the direction of curvature of the concentration profiles i s reversed. In Run 65 the phases approach equilibrium near the top end of the column, but in Run 67 they approach equilibrium near the bottom end of the column. With increase of ketone flow rate at constant water flow, the water phase concentration profiles tend to become more con-cave upward. At the same time the concentration gradients in the profiles decrease near the bottom of the column and increase near the top. The area of contact increases with increasing ketone flow and more acid i s extracted from the water phase. Hence, the concentration of the water phase f a l l s very rapidly near the top of the column and eventually approaches equilibrium with the ketone phase near the bottom. Increase of the number of drops with i n -creasing ketone flow means more total drop volume (and transfer surface) in the column, and hence less change in concentration per drop. (This result of the presence of increased amounts of ketone predominates over the increased mass transfer rate due to increased interfacial area). Therefore the gradients in the ketone phase profiles change more slowly than the corresponding 77 60 L w 6 3 6 . 5 F T . 3 / ( H R . ) ( F T . 2 ) 16.5 F T . 3 / ( H R . ) ( F T . 2 ) VALUES ^ o 5 0 | r O in 4 0 ui - i o 2 Z o < C A L C U L A T E D WATER PHASE PROFILE WATER PHASE PROFILE INTERFACE K E T O N E PHASE PROFILE BTM 4.0 5.0 6.0 HEIGHT , FT. 7.0 FIGURE 20. CONCENTRATION PROFILES FOR RUN 67 78 C L HE IGHT , F T . FIGURE 21. CONCENTRATION PROFILES FOR RUN 69 79 BTM. 1 2 3 4 5 HEIGHT , FT. FIGURE 22. CONCENTRATION .PROFILES FOR.RUN 66 80 L K '• 7 2 . 9 FT. //(HR.)( F T . 2 ) L w » 5 4 . 7 FT. ' / (HR .M F T . 2 ) O = C K * V A L U E S HEIGHT , FT . FIGURE 23 CONCENTRATION PROFILES FOR RUN 65 81 1 gradients in the water profiles as the ketone flow i s increased, at constant water flow. When the water flow i s increased at constant ketone flow, drops rise more slowly relative to the laboratory resulting in a greater contact time, and hence more extraction i.e. more lb. moles per hour is transferred. Because of the greater con-tact time at increasing water flow the ketone drops extract more and more acid out of the descending water phase, and therefore approach equilibrium with the water phase near the top of the column. For high water rates the concentration gradients in both profiles are greatest near the bottom of the column and least near the top. For low water rates the reverse i s true. More-over, there is an intermediate stage where the gradients of both phases are approximately constant throughout the column as shown in Figure 22. (Figure 20 shows a similar stage for the case of changing the ketone flow at constant water flow). Overall Capacity Coefficients and Height of the Transfer Units. In Figure 24 the overall capacity coefficient, K ka, obtained by the graphical integration method after eliminating the agitation end effect, i s plotted against the ratio of the flow rates, L^/I^. The capacity coefficient data are given in Table X, and the flow rates in Table VI. K ka i s found to increase with increasing ketone flow rate at a constant water flow. Due to increase in ketone flow rate the interfacial area, a, i s increased and hence Kk& should increase. These results are consistent with those of other workers (9,11,32,33). It can be seen from Figure 83,! 24a that K ka also increases linearity with increasing water phase flow rate at constant ketone flow, but the increase i s relatively slow. With increase of water flow, drops rise more slowly, re-lative to the laboratory, and hence more crowding of drops in the column takes place, i.e., 'a' i s increased. Increase of 'a' with increasing water flow at constant ketone flow is much slower than when the ketone flow i s increased at constant water flow, i.e., a is a much stronger function of L k than of L^. Hence, Kka should depend only slightly on 1^. Figure 25 shows that the overall ( H . T . U . i n c r e a s e s as the ratio of ketone to water flow increases. The data for (H.T.U.){, are given in Table X. Figure 25 includes (H.T.U.)/ OK O K data for 3 heights of column: 1.36 f t , 7.36 f t , and 3.83 f t from the present investigation, and also data from Ewanchyna's (14) work on a 3.8 f t high column. A straight line was f i t t e d by the method of least squares, using the data from the 7.36 f t column only, with the following result: log (H.T.U. ) / k = 0.1238 log ( i ) + 0.1261 Lw The regression coefficient was 0.1238 with a standard error (34) of 0.0762. Use of this method on Ewanchyna's data yielded the following equation: log ( H . T . U . ) / k = 0.1461 l o g f e ) * 0.1767 1^ The regression coefficient was 0.1461, with a standard error of A-85 O COLUMN HEIGHT = 7 . 4 FT. O COLUMN HEIGHT = 1.4 FT. A.O COLUMN HEIGHT = 3 .8 FT . A DATA FROM EWANCHYNA (14) A L L POINTS i I I 1 I I 0.3 0.6 1.0 2 .0 4.0 6.0 L w FIGURE 25. VARIATION OF (H.T.U. ){ ) k WITH \ / \ 86 '0.0062. The q u e s t i o n t h e n a r i s e s as t o whether t h e r e i s any s i g -n i f i c a n t d i f f e r e n c e between t h e s e two e q u a t i o n s o r n o t . The answer t o t h i s q u e s t i o n was o b t a i n e d by p e r f o r m i n g t h e " t -d i s t r i b u t i o n " t e s t (35). B r i e f l y t h e t e s t was c a r r i e d out as f o l l o w s : Two hypotheses were s e t up. One was t h a t t h e r e g r e s s i o n c o e f f i c i e n t s f o r t h e p r e c e d i n g e q u a t i o n s were e q u a l ; and t h e o t h e r was t h a t t h e two i n t e r c e p t s were e q u a l . Thus, assuming a p r e a s s i g n e d p r o b a b i l i t y of Type 1 e r r o r 1 (36) e q u a l t o 0 .05, a v a l u e o f t was c a l c u l a t e d f o r t h e r e g r e s s i o n c o e f f i c i e n t s and a l s o one f o r t h e i n t e r c e p t s of t h e two l i n e s by s t a n d a r d methods (35,37). F o r a b s o l u t e v a l u e s of t h e s e s t a t i s t i c s e q u a l t o o r g r e a t e r t h a n t h e c o r r e s p o n d i n g v a l u e s o f t 2 t h e n t h e 0 . 0 5 ( n i +n 2 - 4 ) , h y p o t h e s e s would be r e j e c t e d ; f o r t h e a b s o l u t e v a l u e s o f t l e s s t h a n t h e c o r r e s p o n d i n g v a l u e s o f t Q5(n-]_+n -^ 4) t n e n t n e hy-p o t h e s i s would be a c c e p t e d . The r e s u l t o f t h i s t e s t showed t h a t f o r the r e g r e s s i o n c o e f f i c i e n t s 1 I f we r e j e c t our h y p o t h e s i s when i t i s a c t u a l l y t r u e , we have committed an " e r r o r o f t h e f i r s t k i n d " , o r a Type I e r r o r . 2 S u b s c r i p t 0.05 i s t h e assumed p r o b a b i l i t y o f c o m m i t t i n g a Type I e r r o r , n i and n 2 a r e r e s p e c t i v e l y t h e number o f p o i n t s on which each r e g r e s s i o n l i n e i s based. n^+n2-4 i s t h e degrees o f freedom ( 3 5 ) . T h i s i s t h e v a l u e o f »t' o b t a i n e d from a s t a n d a r d t - d i s t r i b u t i o n t a b l e ( 3 5 ) . • f .. .. : . 87 t = .718, and f o r t h e i n t e r c e p t s t = 1.601. The v a l u e o f t .., , , « . 0 5 ( n i + n 2 - 4) i s 2.101. S i n c e the v a l u e s o f t f o r b o t h t h e i n t e r c e p t s and f o r t h e r e g r e s s i o n c o e f f i c i e n t s a r e fo u n d t o be l o w e r t h a n t h a t o f t.05(n + n - 4) t i i e t w o h y p o t h e s e s a r e a c c e p t e d . T h e r e f o r e , t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between t h e two l i n e s i n F i g u r e 25, and i t can be co n c l u d e d t h a t t h e column h e i g h t has no s i g -n i f i c a n t e f f e c t on t h e (H.T.U.)/ v a l u e s i n t h e p r e s e n t i n v e s t i -ok g a t i o n . Hence, one l i n e , shown d o t t e d i n F i g u r e 25, was drawn th r o u g h a l l t h e p o i n t s r e g a r d l e s s o f t h e h e i g h t s o f t h e column i n w hich t h e ru n s were p e r f o r m e d . By t h e method o f l e a s t s q u a r e s t h e eo^uation o f t h i s d o t t e d l i n e i s ' l o g ( H . T . U . ) / = 0.1498 l o g (^c) +0.1375 L w The r e g r e s s i o n c o e f f i c i e n t was 0.1498, w i t h a s t a n d a r d e r r o r 0.0551. The t r u e r e g r e s s i o n l i e s between -0.3899 and -r 0.6895, and t h e t r u e i n t e r c e p t l i e s between -0.2959 and + 0.5709, b o t h w i t h 95% c o n f i d e n c e (37). The H.T.U. v a l u e s were c a l c u l a t e d by t h e g r a p h i c a l i n t e g r a t i o n method as averages o v e r each f o o t , s t a r t i n g f r om t h e bottom of t h e column, f o r Runs 57, 65 and 68. I n F i g u r e 2 6 t h e s e H.T.U. v a l u e s a r e p l o t t e d a g a i n s t t h e c o r r e s p o n d i n g mean h e i g h t above t h e n o z z l e t i p s . Table X I I I shows t h e c o r r e s p o n d i n g d a t a . A t a h i g h r a t i o o f ketone t o w a t e r r a t e the H.T.U. appears t o 88 0 1 2 3 4 5 6 7 HEIGHT ABOVE NOZZLE TIPS , FT. FIGURE 2 6 . VARIATION OF AVERAGE H.T.U. OVER EACH FOOT WITH MEAN HEIGHT ABOVE NOZZLE TIPS TABLE XIII AVERAGE H.T.U. VALUES OVER EACH FOOT Mean distance H.T.U. for • from nozzle t i p s , f t Run 5 7 , f t . Run 65,ft. Run 6 8 , f t . 0.5 1.744 1.107 2.526 1.5 1.614 1.149 2.381 2.5 1.615 1.063 1.581 3.5 1.522 1.245 1.652 4.5 1.536 1.443 1.634 5.5 1.502 1.663 1.569 6.5 1.516 1.322 1.412 90 f a l l comparatively rapidly particularly close to the bottom of the column. Near an I ^ / l ^ ratio equal to 2, the H.T.U.. appears to be independent of the column height; Run 57 i s a close approach to this situation. It can be shown mathematically that the H.T.U. calcul-ated by the method of graphical integration is independent of the distance from the nozzle tips with the present system i f 1. the water and the ketone phase profiles are straight lines (as they are in Run 57 - Figure 20), and 2. the slope of the ketone phase profile i s half the slope of the water phase profile (as is approximately true in Run 57). Let the equations of the water and the ketone phase profiles be ew = m/h + b/ and C k = r J I h + b/ . respectively, where m i s the slope, b-' the intercept, and h is any height from the nozzle ti p s . L e t the equation of the equi-librium distribution curve be ck = m Gw where m is equal to 0.5, which i s very nearly the case with the present system. Now from the preceding 3 equations, 91' C k - C k = mCw - r J h - t / - m(n/ h \ b/) - J h - b^ m(0.5 m/ - n/) h * (0.5 b / - b^) When 0.5 n/= m^ then ck " ck* (0*5 b/- b//) . constant, 1 (say) *1 Hence, x c k a t h dC ^ i L . = % (C - C ) K x ( n / h 4 b ^ - n/ (0) - b^) K x m// h And H.T.U. h h d o k 2 °k - C k K x m' h = constant With reference again to Figure 26, as the ketone to water flow is decreased below about 2 the H.T.U. values increase from the bottom to the top of the column. From Figure 26 i t can be concluded that as the ratio, ^ / L ^ . J i s increased, the most 92 efficient region in the tower i s shifted from the bottom to the top. It can be seen from the concentration profiles, that a region of high efficiency is also accompanied by a region of high concentration gradient. For a l l the runs in the present investigation and for a l l the runs of Ewanchyna's work average H.T.U. values were cal-culated over the f i r s t foot from the bottom of the column using the graphical integration method. The data are given in Table XIV. Holdup and Interfacial Area of Contact. The fractional holdup of ketone drops, H^ , was cal-culated by Equation 12, and the percentage holdup values pre-sented as a function of L^/L^, in Figure 27. The corresponding data are in Table VII. As expected, the holdup increases close to linearly with ketone flow rate at a constant water rate at relatively low holdups, and i s almost independent of water rate, (Figure 27a). Ewanchyna (14) plotted holdup versus ketone rate and drew one straight line for a l l water rates although a small dependence on the water flow was noted. Also for constant drop;, size and uniform distribution of drops in the column, the specif-i c surface area 'a* i s directly proportional to H^ , and therefore i s a linear function of L k at constant L^ .. Also, from Figure 24, K ka i s a linear function of L k at constant L^. From these facts i t follows that the mass transfer coefficient, Kk, i s a constant independent of ketone flow rate at constant water flow. This res-ult would be expected for constant sized drops for free settling conditions. With increase of water flow at constant ketone flow TABLE XIV AVERAGE H.T.U. VALUES OVER FIRST FOOT FROM THE BOTTOM OF THE COLUMN Run H.T.U. No.1 Lw f t . 43 5.31 2.249 33 4.43 1.480 39 0.43 1.274 24 1.42 1.504 30 0.71 1.428 41 1.05 1.046 23 0.84 1.280 27 2.10 1.309 31 2.85 1.542 48 0.83 0.990 55 0.88 0.919 56 1.06 1.111 57 2.21 1.744 58 0.70 1.426 60 1.05 1.006 61 0.87 1.037 62 3.00 1.320 63 1.50 1.085 65 1.33 1.107 66 2.00 1.131 67 4.00 1.418 68 4.00 2.526 69 3.00 1.640 70 0.86 1.122 1 23 to 43 inclusive are taken from Ewanchyna' work (14). 96 rate the holdup increases linearly , although very slowly, (Figure 27a), i.e. a i s also a linear function of L^. Also, K ka increases linearly, but relatively slowly, with increase of L w at constant L k (Figure 24a). Hence, the mass transfer coefficient, Kk, i s independent of both ketone and water flow rates, which i s in accordance with the general theory. Back Mixing and End Effects. It can be seen from many of the experimental profiles obtained that considerable back mixing of the continuous phase often exists in spray tower operation. The phenomenon of back-mixing is complicated because of the number of variables involved in spray tower operation and the lack of knowledge of exactly which affect back mixing. The d i f f i c u l t y immediately arises when the question of keeping some of the variables constant appears. As a result, i t was not possible i n this investigation to make a thorough study of this phenomenon. A dimensionless factor, F m, was defined as (H.T.U.)/ Fm = 2* , (H.T.U.)ok and the calculation procedure for F m described in detail earlier in this thesis under Treatment of Data. - Figure 28 represents the variation of F m with the ratio L^/L^. The data appear in Tables VI and X. The value of F m i s independent of column height, or, at any rate, any variation of F m with column height i s small enough to be hidden by the uncertainties in the data. This re-sult i s in agreement with the previous conclusion that the overall 1.0 0.8 0.6 0.2 0 o o Or a o f y Or cD-O •o cD COLUMN HEIGHT = 3.8 FT. O DATA OF EWANCHYNA (14) — O COLUMN HEIGHT - 7.4 FT. ! 1 1 6 1 COLUMN l HEIGHT = 1.4 I FT. 1 0.1 0.2 0.3 0.5 1.0 2 3 6 10 FIGURE 28. VARIATION OF Fm WITH L /L, m w k 98 ( H . T . U . v a l u e s a r e i n d e p e n d e n t c f column h e i g h t . F m seems t o approach u n i t y as L^/^k i n c r e a s e s . I t s h o u l d be n o t e d h e r e , t h a t t h e d e v i a t i o n o f t h e e x p e r i m e n t a l p r o f i l e from the c a l c u l a t e d p r o -f i l e ( e . g . , the d o t t e d l i n e i n F i g u r e 9 ) , f o r v a r i o u s f l o w r a t e s i s t a k e n as a measure o f back m i x i n g . As mentioned p r e v i o u s l y , t h e s c a t t e r o f t h e F^ d a t a may be due p a r t l y t o p o s s i b l e e r r o r s i n the g r a p h i c a l i n t e g r a t i o n method a r i s i n g when the phases approach e q u i l i b r i u m . The v a r i a -t i o n o f F m w i t h L w / L k i s shown i n F i g u r e 29, o n l y f o r r u n s where the v e l o c i t y t h r o u g h t h e n o z z l e t i p s was k e p t c o n s t a n t a t 0.357 f t / s e c . The l i n e s drawn i n F i g u r e s 28 and 29 check q u i t e w e l l i n s p i t e o f t h e s c a t t e r i n t h e d a t a i n F i g u r e 28. However, i t does seem t h a t v a r y i n g t h e v e l o c i t y i n t h e n o z z l e t i p s may i n c r e a s e t h e s c a t t e r o f t h e F m d a t a . F i g u r e 30 r e p r e s e n t s the v a r i a t i o n o f F m w i t h w a t e r phase f l o w r a t e a t c o n s t a n t k e t o n e f l o w . The g e n e r a l t r e n d i s t h a t F m i n c r e a s e s w i t h i n c r e a s i n g w a t e r f l o w r a t e . I n g o i n g f rom Run 63 t o Run 60 t h e t r e n d i s r e v e r s e d . The group o f Runs 62, 69, 63,and 60 was performed a t c o n s t a n t k e tone r a t e ; the o n l y known d i f f e r e n c e o t h e r t h a n t h e d i f f e r i n g w a t e r r a t e s , was t h a t Run 60 had a l o w e r v e l o c i t y t h r o u g h t h e n o z z l e t i p s . A l s o , i n t h e group o f Runs 57, 56, 55, 61 and 58, o n l y Run 61 had a h i g h e r v e l o c i t y t h r o ugh t h e n o z z l e t i p s . An i n c r e a s e i n t h e v e l o c i t y t h r o u g h t h e n o z z l e t i p s may d e c r e a s e the drop s i z e w i t h r e d u c t i o n i n c i r c u l a -t i o n as a consequence. F i g u r e 31 shows t h e v a r i a t i o n o f F m w i t h k e t o n e f l o w r a t e a t c o n s t a n t w a t e r f l o w . The g e n e r a l t r e n d i s t h a t F 1.0 o.e — 0.6 -2 U_ / — ^ / 0.4 / / o COLUMN HEIGHT = 7.4 FT. / / / - o COLUMN HEIGHT = 3.8 FT. 0.2 0 I 1 1 • 1 1 1 0.1 0.2 0.5 1.0 2 3 6 10 L w / L FIGURE 29. VARIATION OF F m w i t h \ / \ , BASED ON RUNS, WHERE THE LINEAR VELOCITY THROUGH THE NOZZLE TIPS WAS KEPT CONSTANT 1.0 0.9 0.8 0.T O.G 0.5 0.4 0.3 L K • 37 FT./(HR.)( FT. ) 55 FT./'CHS.H FT. 2 ) L * o O" t.K * 73 FT.?/CHR.)(FT.2 ) NUMBERS SHOWN BESIDE POINTS ARE RUN NUMBERS. 10 20 30 40 50 6 0 70 L w , FT.'V'.hR.) (FT FIGURE 30. VARIATION OF F WITH T TM n m WITH L w IN 7.4ft COLUMN, 58 6 0.9h 6 0 6 66 62 0.6h 0.5k 56 57 O-69 68 6 ? 0 O- L w = 18 F T . 3 / ( H R.)(FT 2) Q L w = 36 F T . ^ H R . K F T 2 ) ^ L w = 53 F T . f / l h R . M F T . 2 ) NUMBERS SHOWN BESIDE POINTS ARE RUN NUMBERS. 10 20 30 40 50 60 70 80 L K , FT.V(HR.)(FT. 2) FIGURE 31. VARIATION OF F m WITH L k i n 7.4 f t . COLUMN 102 ' i n c r e a s e s as t h e ketone f l o w i s r e d u c e d a t c o n s t a n t w a t e r r a t e . I n t h e group o f r u n s 57, 62, 69, 67, and 68, Run 57 was performed w i t h a l o w e r v e l o c i t y o f k e t o n e t h r o u g h t h e n o z z l e t i p s t h a n a p p l i e d i n t h e o t h e r runs o f the group. A s i m i l a r s t a t e m e n t a p p l -i e s t o Ru© 56 i n the group 56, 63, and 66, and t o 58 and 60 i n t h e group 58, 60, and 65. Both i n F i g u r e s 31 and i n F i g u r e 30 t h e v a l u e s o f F m a r e r e l a t i v e l y l o w i n t h e runs where l o w e r v e l o c i t y t h r o u g h t h e n o z z l e was u s e d . The i n f e r e n c e i s , o f c o u r s e , t h a t , a l t h o u g h such changes i n v e l o c i t y do not a f f e c t t h e c o n c e n t r a t i o n p r o f i l e s t o any marked e x t e n t , as n o t e d e a r l i e r , t h e r e i s s u f -f i c i e n t i n f l u e n c e on t h e s e p r o f i l e s t h a t the r e s u l t o f v a r i a t i o n o f v e l o c i t y i n t h e n o z z l e t i p s shows up, perhaps i n m a g n i f i e d form> i n t h e v a l u e o f F m . The s c a t t e r o f t h e F m d a t a i n F i g u r e 28 n o t e d p r e v i o u s l y may w e l l be a n o t h e r m a n i f e s t a t i o n o f t h i s p r o b a b l e e f f e c t o f changes i n t h e v e l o c i t y i n t h e n o z z l e t i p s oh F m . F i g u r e 32 r e p r e s e n t s the v a r i a t i o n o f F m w i t h L w H f / L k x (1 - Uf). The c o r r e s p o n d i n g d a t a f o r F m a r e p r e s e n t e d i n Table X. and the holdup d a t e i n Table V I I . The q u a n t i t y 1^/(1 - H f ) , i s t h e n e t t r u e average v e l o c i t y o f t h e c o n t i n u o u s phase, and t h e q u a n t i t y , L k / H f , i s t h e t r u e average v e l o c i t y o f t h e d i s p e r s e d phase, b o t h r e l a t i v e t o the l a b o r a t o r y . The r a t i o o f t h e s e two average v e l o c i t i e s was chosen i n o r d e r t o compare th e p r e s e n t d a t a w i t h t h a t G a y l e r and P r a t t (30) f o r a packed column. One would e x p e c t t h e c u r v e f o r t h e p r e s e n t s p r a y column and t h e c u r v e o f G a y l e r and P r a t t t o have s i m i l a r t r e n d s , and t h i s e x p e c t a t i o n i s f u l f i l l e d . However, the v a l u e s F m a r e o f d i f f e r e n t magnitude be-cause t h e method of c o n t a c t i n g the phases d i f f e r s i n t h e two c a s e s . 0 . 8 0 . 6 0 . 4 0 . 2 1 0 2 0 COLUMN HEIGHT = 3 . 8 FT. COLUMN HEIGHT » 7 . 4 FT . COLUMN HEIGHT - 1 . 4 FT. DATA OF EWANCHYNA ( 1 4 ) , COLUMN HEIGHT - 3.8 FT. DATA OF GAYLER AND PRATT ( 3 0 ) ON PACKED COLUMN 5 0 1 0 0 2 0 0 ( L w H f ) X I 0 3 4 0 0 1 0 0 0 L K ( i - H f ) FIGURE 32. VARIATION OF F m WITH V f A * < l - H f ) o The quantities used in Figures 2& and 32 as correlating variables for F m must be considered as a tentative suggestions only since, there may well be variables affecting F m other than those shown in these plots. For example, the correction factor, F m, may also depend on the ratio of concentration changes of the two phases, and on their approach to equilibrium (30). However, more experimental data are required, with conveniently chosen flow rates, in order to test such other parameters as correlating variables. The quantity L^H^/L^d - H f)is the ratio of water to ketone velocity; an increase in this ratio . results in a since closer approach to true countercurrent flow, A with increase of wa-ter to ketone rate i t i s found that the calculated water phase profile eventually coincides with the experimental water phase profile. This result implies a close approach to true counter-current flow,since the calculated profile i s based on such an as-sumption. True countercurrent flow results in improved performance shown in the present case by increased lb.moles per hour trans-ferred, and in general, by decreased overall H.T.U. values. As already noted, such are actually obtained by increase of the ratio of water to ketone flow. Another important effect was observed in the present investigation. This was described by Ewanchyna as an end effect of the concentration profiles due to the agitating and coalescing drops at the interface. The symbol,^ , used by Ewanchyna to designate this effect, represents the number of l b . moles trans-ferred per hour due to the agitation and coalescence. As ex-105 p l a i n e d e a r l i e r , t h e jump B t o A i n t h e ketone c o n c e n t r a t i o n p r o -f i l e c o r r e s p o n d s t o t h e jump ttCDn i n t h e w a t e r phase p r o f i l e , so t h a t t h e use o f a s i m p l e mass b a l a n c e a t t h e i n t e r f a c e g i v e s 1$ - L k A ( c o n c e n t r a t i o n d i f f e r e n c e A t o B) ss L^A ( c o n c e n t r a t i o n d i f f e r e n c e C t o D) 13. The o t h e r p o r t i o n , DE, o f t h e c o n t i n u o u s phase end e f f e c t was a t t r i b u t e d by Ewanchyna t o the m i x i n g o f the c o n t i n u o u s phase. F m i s used h e r e t o a c c o u n t f o r t h e back m i x i n g i n t h e c o n t i n u o u s phase i n s t e a d o f an end e f f e c t term., s i m p l y because the f o r m e r uses t h e e n t i r e p r o f i l e f o r i t s e v a l u a t i o n , whereas the l a t t e r uses o n l y t h e jump a t t h e i n t e r f a c e . Hence, F m i s a b e t t e r mea-s u r e o f back m i x i n g t h a n t h i s end e f f e c t term u s e d by Ewanchyna. From E q u a t i o n 13, ^ i s p r o p o r t i o n a l t o t h e f l o w r a t e s o f the phases. As p r e v i o u s l y seen, t h e s p e c i f i c s u r f a c e a r e a f a c -t o r , a, i s a l i n e a r f u n c t i o n o f b o t h ketone and w a t e r phase f l o w r a t e s . Hence ^ i s a l s o a l i n e a r f u n c t i o n o f ' a T . T h i s i s q u i t e c o n c e i v a b l e , s i n c e more l b . moles p e r hour w i l l be t r a n s f e r r e d a t t h e i n t e r f a c e i f more t r a n s f e r a r e a i s a v a i l a b l e . A l t h o u g h , by d e f i n i t i o n , the s p e c i f i c s u r f a c e a r e a f a c t o r , a, i s i n t h e column and n o t a t the i n t e r f a c e , f o r normal r u n s i t i s o b s e r v e d t h a t when the k e tone f l o w i s i n c r e a s e d , 'a* i s i n c r e a s e d , and t h e p i l e up o f drops a t t h e i n t e r f a c e i s a l s o i n c r e a s e d . F u r t h e r m o r e , s i n c e t h e mass t r a n s f e r c o e f f i c i e n t , K k, i s independent o f f l o w r a t e s , i t can alBO be s a i d t h a t ^ i s a l i n e a r f u n c t i o n o f K k a . F i g u r e 33 shows 1^ p l o t t e d v e r s u s K k a . K k a i s u sed i n s t e a d o f f a T a l o n e s i n c e v a l u e s o f t h e l a t t e r a r e n o t a v a i l a b l e . The v a l u e s o f K k a DATA OF EWANCHYNA (14) 9 L W » 42 F T . ^ t H R . X F T . 2 ) O L-K » 60 F T . V C H R . K F T . 2 ) i? . P - P R E S E N T WORK o L w = 18 F T . ^ / C H R . K F T 2 ) 9 L K = 73 F T . / ^ t H R . M F T . 2 ) NUMBERS SHOWN BESIDE POINTS ARE 0 10 20 3 0 4 0 50 6 0 K K a , H R . - ' FIGURE 33. /3 A S A FUNCTION OF K k a 107 used are the results of the graphical integration method, using the entire experimental profile, i.e., the area under the curve of 1 vs. C k up to point 'A' in the ketone profile. The corresponding data are mostly taken from Ewanchyna's work; a few were from the present work and, appear in Table X. The use of the entire profile for the evaluation of K ka here, was due to the fact that the end effect, fl, t i s accompanied by actual transfer of material from the water to the ketone phase, and therefore cal-culation of E ka should include the jump ttAB". Actually this re-finement does not produce much difference here. Figure 33 shows the variation of ^ with K ka. ^ i s found to increase with de-crease of K ka at constant ketone flow rate of about 60 cu.ft/ (hr)(sq.ft.) and varying water flow. As previously discussed, K ka decreases with decrease of water flow at constant ketone rate?.. When the water flow i s decreased at constant ketone rate, the con-centration profiles move away from their positions corresponding to equilibrium being reached between the phases near the top of the column. Greater driving forces result, and hence greater ex-traction at the interface, which increases ^ . This point was apparently not clear to Ewanchyna. ft i s also found to increase with increase of K ka at constant water flow rate. This increase i s produced by the increase in 'a' resulting from increasing the ketone flow. A very large scatter was observed in the measure-ments of agitation end effects. In Figure 33 average values of the parameters were used in cases where runs were repeated. Thus when two numbers appear beside a point, the point i s the average °f the t w oruns. This, method o f p l o t t i n g h i d e s t h e s c a t t e r t o a c e r t a i n e x t e n t . I t i s a l s o o b s e r v e d t h a t the v a l u e o f ^ de-c r e a s e s w i t h i n c r e a s e o f t h e h e i g h t o f t h e column; f o r example, /$ had a v a l u e o f 31.3 x 10 l b . m o l e s / h r . i n Run 70 (h = 3.83 f t . ) b u t was z e r o i n Run 61 (h = 7.36 f t . ) . W i t h l o n g e r columns 0 d e c r e a s e s because t h e phases approach e q u i l i b r i u m near t h e t o p o f t h e column f o r such r u n s , e s p e c i a l l y when t h e - p water r a t e i s h i g h as can be seen from T a b l e X. Hence many o f t h e jQ ' s f o r t h e p r e s e n t runs a r e v e r y l o w , and, i n c i d e n t a l l y , p r o b a b l y , i n v o l v e c o n s i d e r a b l e p e r c e n t a g e e r r o r because of t h e d i f f i c u l t y o f m e a s u r i n g a c c u r a t e l y t h e d i f f e r e n c e between two c o n c e n t r a t i o n s o f a p p r o x i m a t e l y t h e same v a l u e ( i . e . i n t h e nomen-c l a t u r e u s e d i n F i g u r e 9, P o i n t B f a l l s a l m o s t on P o i n t A ) . F i g u r e 34 shows t h e v a r i a t i o n o f t h e p r o d u c t ^> K^a w i t h L k r e g a r d l e s s o f u s i n g t h e d a t a r e p o r t e d by Cavers and Ewanchyna (15) f o r a 3.8 f t . column. The p r o d u c t K k a i s a l m o s t i ndependent o f w a t e r f l o w r a t e p r o b a b l y because t h e d e c r e a s e i n K^a w i t h d e c r e a s e i n L^. b a l a n c e s t h e i n c r e a s e i n ^ o r v i c e v e r s a , W i t h i n c r e a s e o f L^, i n normal r u n s , 'a' i n c r e a s e s i n t h e column, and so a l s o does t h e number o f drops p i l e d up a t t h e i n t e r f a c e . T h i s i n c r e a s e d drop b u i l d u p r e s u l t s i n more e x t r a c t i o n a t t h e i n t e r f a c e and hence i n c r e a s e s . The use o f t h e method o f l e a s t mean square y i e l d e d t h e f o l l o w i n g e q u a t i o n f o r t h e c u r v e : l o g ( ft K k a x 10 5 ) = 2.725 l o g L R - 1.222 Reader must a l s o r e f e r t o Table V I . A l l t h e v a l u e s o f /3 from t h e p r e s e n t i n v e s t i g a t i o n a r e n o t p l o t t e d i n F i g u r e 33. COLUMN HEIGHT = 3.8 FT . (14) O DATA OF EWANCHYNA ( 1 4 ) , 3 .8 FT.COLUMN OjO PRESENT WORK <b 3.8 FT. COLUMN O 7.4 FT. COLUMN. 3 d lo M COLUMN v I I HEIGHT V w ; = 3.8 FT. Jp/ 1 I / / — C O L U M N / K HEIGHT / / =7.4 FT . 10 50 100 10 50 100 L K , FT . 3 / (HR. ) (FT . 2 ) FIGURE 34. /£ K k a AS A FUNCTION OF L k n o 1 w i t h an " s t a n d a r d e r r o r o f e s t i m a t e " (35) o f 0.1493. The t r u e r e g r e s s i o n l i e s between 1.5751 and 3.8749 and t h e t r u e i n t e r c e p t l i e s between -3.3067 and 0.8627, b o t h w i t h 95% c o n f i d e n c e (37). F i g u r e 34 a l s o i n c l u d e s i n f o r m a t i o n on t h e v a r i a t i o n of K^a w i t h L k f o r two h e i g h t s o f column. F o r each h e i g h t a c o n s t a n t w a t e r r a t e a p p l i e s . Almost p a r a l l e l s t r a i g h t l i n e s a r e o b t a i n e d . These two s t r a i g h t l i n e s a r e not s t r i c t l y comparable f r o m t h e p o i n t o f v i e w of n o t h a v i n g i d e n t i c a l w a t e r f l o w r a t e s , b u t , as j u s t argued, th e e f f e c t o f water r a t e p r o b a b l y i s s m a l l . I t may be c o n c l u d e d t e n t a t i v e l y t h a t t h e s e l i n e s w i l l move up o r down, p a r a l l e l t o t h e m s e l v e s , depending on whether t h e column h e i g h t i s d e c r e a s e d or i n c r e a s e d . As an a f t e r t h o u g h t i t s h o u l d be n o t e d t h a t a more p r o f -i t a b l e approach t o t h e problem o f t h e end e f f e c t due t o a g i t a t i o n would p r o b a b l y be t o d i v i d e t h e ^ ' s by t h e a p p l i c a b l e d r i v i n g f o r c e (15). I l l CONCLUSIONS Concentration profiles of both continuous and dispersed phases were measured by internal sampling without disturbing the steady state conditions in the operation of the column. The effect of varying the relative flow rates of the phases on the curvature of the profiles was determined. Due to longitudinal mixing in the continuous phase the rate of mass transfer across the interface between the two phases was lower than that calculated on the basis of true countercurrent flow. Hence, the experimental concentration profiles were used instead of terminal concentrations, to cal-culate the true overall capacity coefficients and H.T.U.'s. A simplified model was developed to describe the pheno-mena at the interface. The agitation end effect, j$ , was separated from the back mixing effect using the simplified mod-e l . 1$ 's were correlated with overall capacity coefficients and ketone flow rates. ^ i s found to decrease as the column i s lengthened and as the water rate i s increased. It was necessary to distinguish two kinds of the over-a l l height of a transfer unit: the (H.T.U.)ok, based on ter-minal conditions using the log-mean driving force; and the (H.T.U.)/k, obtained by the graphical integration method using the experimental profiles. Both of these H.T.U.'s include the effect of back mixing, but, not of agitation and coalescence of the drops at the interface. In the presence of back mixing, the (H.T.U. )QJ£ i s always less than the (H.T.U. ) o k , and the 112 ratio of the former to the lat t e r i s defined as F m, the driving force correction factor. F m was correlated with the ratio of the flow rates, LW . The overall H.T.U.s, and the F m values Lk were independent of the height of the column in the present investigation. NOMENCLATURE 113 Except where noted otherwise, the following nomenclature was used throughout the Thesis: Symbols A Gross-sectional area of column, f t 2 , a Interfacial area per unit volume of extraction column, f t 2 / f t 3 . C Solute concentration, l b . moles/f t 3. C* Phase solute concentration which could be in equilibrium with the other phase, l b . moles/f t 3. AC 1 t n Phase logarithmic mean driving force, l b . moles/ft3. c/ I n i t i a l concentration of solute in ketone phase during K l internal sampling, l b . moles/f t 3« C^2 Concentration of solute i n ketone phase of ketone sample as measured at time of analysis, l b . moles/ft3. C ^ I n i t i a l concentration of solute in water phase during internal sampling, l b . moles/f t 3 c(f^ Concentration of solute in water phase of ketone sample as measured at time of analysis, l b . moles/f t 3. F m Driving force correction factor, dimensionless. Hf Fractional hold up of the dispersed phase in the column s volume fraction of the dispersed phase i n the column. (H.T.U. )0 Height of a transfer unit based on over-all conditions, after eliminating agitation end effect, f t . (H.T.U.)/ Height of a transfer unit obtained from graphical i n -tegration method after eliminating agitation end effect, s ft. 114 h Effective height of extraction section of column, f t . K Over-all mass transfer coefficient, l b . moles.  (hr.) ( f t 2 . ) (lb.moles/f t3.) Ka Over-all extraction capacity coefficient, hr." 1. L Phase flow rate, ftV(hr.) ( f t 2 ) 9 m Distribution or partition coefficient. N Amount of solute transferred based on inl e t and outlet con-centrations, l b . moles/j^ Amount of solute transferred after eliminating agitation end effect, l b . moles S Interfacial area, f t_2. V Volume of phase in ketone sample, ml« V Average velocity of rise of the ketone drops relative to the laboratory, *"Vhr. ^ End effect due to the agitating and coalescing drops at the interface, l b . moles/ n r. r2 l Integral between elevation 1 and elevation 2 in the column. 1 Subscripts A Point "A" in the ketone phase profile (e.g., in Figure 9 ) . B Point "BM in the ketone phase profi l e . C Point "C" in the water phase profile. D Point nDtt in the water phase profi l e . E Point nE" in the water phase profile. k Ketone phase. o Over-all. 115 w Water phase. 1 Top end o f column. 2 Bottom end o f column. 116 LIST OF REFERENCES 1. Morello, V.S. and Poffenberger, N., Ind. Eng.Chem. 42, 1021, 1950. 2. Treybal, R.E., Liquid Extraction. 292-293. McGraw H i l l Book Co., New York, 1951. 3. Appel, F.J. and Elgin, J.C., Ind. Eng. Chem. 2 2 , 451, 1937. 4. Blanding, F.H., and Elgin, J.C., Trans. Am. Inst. Chem. Engrs. 28, 305, 1942. 5. Elgin, J.C., and Browning, F.M., Trans. Am. Inst. Chem. Engrs., 21, 639, 1935. 6. Fleming, J.F. and Johnson, H.F., Chem. Eng. Prog. 49, 497, 1953. ' 7. Garwin, Leo and Smith, B.D., Chem. Eng. Prog. 4£, 591, 1953. 8. Minard, G.W., and Johnson, A.I., Chem. Eng. Prog. 48, 62, 1952. 9. Johnson, H.F. and Bliss, H., Trans. Am. Inst. Chem. Engrs. U2., 331, 1946. 10. Geankoplis, C.J. and Hixson, A.N., Ind. Eng. Chem. 42, 1141, 1950. 11. Sherwood, T.K., Evans, J.E., and Longcor,J.V.A. Ind. Eng. Chem. 21, 1144, 1939. 12. Licht, W. and Conway, J.B., Ind. Eng. Chem. 42, 1151, 1950. 13. Harmathy, T., Acta Technica Academiae Scientiarum Hungaricae 12,210, 1955. 14. Ewanchyna, J.E., M.Sc. Thesis, University of Saskatchewan, 1955. 15. Cavers, S.D., and Ewanchyna, J.E., Can. J. of Chem. Eng. 35, 113, 1957. 16. Gier, T.E., and Hougen, J.O., Ind. Eng. Chem. 45, 1362, 1953. 17. Heertjes, P.M., Holve, W.A. and Talsma, H. Chem. Eng. Sci. 2 , 122, 1954. 18. Vermijs, H.J.A., and Kramers, H.jChem. Eng. Sci. 2 , 55,1959. 117 19. M i y a u c h i , T., UCRL R e p o r t 3911 (August 1957). 20. M c M u l l e n , A.K., M i y a u c h i , T., and Vermeulen, T., UCRL Re p o r t 3911 (Supplement), J a n u a r y 1958. 21. J a c q u e s , G.L. and Vermeulen, T. UCRL Repo r t 8029 (November 1957). 22. S l e i c h e r , C.A.Jr., S h e l l Development Co. R e p o r t P-700, E m e r y v i l l e , C a l i f o r n i a , 1959. 23. B r u t v a n , D.R., Ph.D. T h e s i s . R e u s s e l a e r P o l y t e c h n i c I n s t i -t u t e , T r oy, New Y o r k , June 1958. 24. Mar, B.W., Ph.D. T h e s i s . U n i v e r s i t y o f Washington, S e a t t l e , 1958. 25. W i g i n t o n , J.C., B.A.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o lumbia, 1957. 26. Lepage, N.A.W., B.A.Sc. T h e s i s . U n i v e r s i t y o f B r i t i s h C o l umbia, 1956. 27. Dean, R.R., B.E. T h e s i s . U n i v e r s i t y o f Saskatchewan, 1954. 28. S e l t z e r , S., D i s s e r t a t i o n A b s t r a c t . 12, 464, 1952. 29. M e l l a n , I . , I n d u s t r i a l S o l v e n t s . 602, R e i n h o l d , New Yo r k , 1950. 30. G a y l e r , R., and P r a t t , H.R.C., T r a n s . I n s t . Chem. E n g r s . 35, 267, 19571 31. W i l k , M.B., The Elements o f L i q u i d - L i q u i d E x t r a c t i o n P r o -c e s s e s . Pamphlet CEI - 3 1 , 19. Atomic energy o f Canada L t d . , C h a l k R i v e r , Ont. 1950. 31a. K e i t h , F.W., and H i x s o n , A.N. I n d . Eng. Chem. 47, 258, 1955. 32. Laddha, G.S. and S m i t h , J.M., Chem. Eng. P r o g . 46, 195, 1950. 33. - Row, S.B., K o f f o l t , J.H., and Withrow, J.R., T r a n s . Am. I n s t . Chem. E n g r s . , 2Z> 559, 1941. 34. E z e k i e l , M., Methods o f C o r r e l a t i o n A n a l y s i s , 313, J . W i l e y and Sons, New York, 1941.-35. O s t l e , B., S t a t i s t i c s i n R e s e a r c h . 127, 128, 451, t h e Iowa S t a t e C o l l e g e P r e s s , Ames, 1954. 36. O s t l e , B., I b i d . 27. 37. B a g a i , O.P., P e r s o n a l Communication. Dept. o f M a t h e m a t i c s , U n i v e r s i t y of B r i t i s h C olumbia, September 1959. 

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