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Batch distillation Cooke, Norman Edward 1946-12-31

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BATCH DISTILLATION. by Norman Edward Cooke A t h e s i s submitted i n p a r t i a l f u l f i l l m e n t of the requirements f o r the degree of Master of A p p l i e d Science i n Chemical E n g i n e e r i n g , THE UNIVERSITY OF BRITISH COLUMBIA. October 1946. iu+ji Table of Contents . T i t l e Page i . Table of Contents i i . Acknowledgements i i i . I n t r o d u c t i o n 1» Theory -i 4 . General 4 . B o i l i n g Po in t Curve 4 . E q u i l i b r i u m Diagram 4 , . M a t e r i a l Balance on Pe r f ec t P l a t e 4 . M a t e r i a l Balance on Head of Column 7 . C a l c u l a t i o n of Number of T h e o r e t i c a l P l a t e s 10. D e r i v a t i o n of Raylft i 'gh 's E q u a t i o n 122 Minimum R e f l u x R a t i o 12. D e r i v a t i o n of Time Curve 16. Exper imen ta l Work 2 1 . Apparatus Used 2 1 . De te rmina t ion of Vapour V e l o c i t y 2 1 . R e s u l t s 22 . Suggest ions f o r Fu r the r Work 22 . Conc lus ions and Summary 26 . B i b l i o g r a p h y 27 . ii Acknowledgements.. The w r i t e r wishes to acknowledge the . encouragement and a s s i s t a n c e g iven to him by D r . Seyer • du r ing the course of t h i s r e sea r ch . iii ABSTRACT The p rev ious l i t e r a t u r e i s c r i t i c a l l y d i s c u s s e d . A conc i se and e f f i c e n t method i s g iven f o r o p e r a t i n g a ba tch d i s t i l l a t i o n column. Exper imen ta l r e s u l t s are g i v e n to show the . v a l i d i t y o f the t heo ry . Suggest ions are made f o r f u r t h e r mechanical improvements on the column. BATCH DISTILLATION I n t r o d u c t i o n . Ba t ch d i s t i l l a t i o n , w h i l e i t i s not as important commercia l ly as continuous d i s t i l l a t i o n , i s an exceed ing ly important u n i t p rocess . A ba tch column can r e c t i f y a l a rge number of components, each to a h i g h degree of p u r i t y , whereas a con t inuous column can on ly separate two Components i n t o t h e i r pure s t a t e s . I 2 As a lways, a mathematical a n a l y s i s of the problem g ives a c l e a r e r understanding o f the p h y s i c a l - c h e m i c a l mechanism and i n d i c a t e s the most e f f i c i e n t manner o f o p e r a t i n g a column. In 1931 B o g a r t 2 developed a theory of b a t c h d i s  t i l l a t i o n i n . w h i c h he pos tu l a t ed tha t the compos i t ion of the d i s t i l l a t e would remain cons tan t . He a r r i v e d a t the f o l l o w i n g equa t ions : /\_ M ( * n - xn) where D r amount d i s t i l l e d M - amount of feed xj,r compos i t ion of d i s t i l l a t e x 0 = compos i t ion of feed x ^ compos i t ion of l i q u i d i n s t i l l - p o t , (compare t h i s equa t ion w i t h equat ions 21 and 23) , and v J X q (i-MLyv)(xD-x^ where T = time V = vapour v e l o c i t y L - r e f l u x y e l d c i t y , ' ('" compare. t h i s equat ion w i t h equat ions 27 and 3 2 ) . Both of B o g a r t 1 s equat ions i n v o l v e a l a rge amount of g r a p h i c a l work w i t h McCabe-Th ie l e 4 diagrams, and the l a t t e r equat ion can on ly be i n t e g r a t e d by p l o t t i n g i t g r a p h i c a l l y . I t should be po in ted out tha t these equa t ions , w h i l e they are i d e a l , 3 g ive no i n d i c a t i o n of how the compos i t ion of the d i s t i l l a t e i s to he kept cons tan t . Edgeworth-Johnstone 3 extended t h i s idea to take i n t o account the column hold-up and a l so presented equat ions f o r the v a r i a t i o n of the r e f l u x r a t i o w i t h the f r a c t i o n d i s t i l l e d which can be a p p l i e d i n c e r t a i n cases . H i s equat ions become r a t h e r complex and a s imple r method i s to be d e s i r e d . . Smoker and Rose** have developed a method of a n a l y s i s f o r columns operated a t a constant r e f l u x r a t i o . Th i s 5 i n v o l v e s the use o f the Rayle^gh e q u a t i o n . A constant r e f l u x r a t i o , w h i l e i t i s ve ry s imple to .operate, i s very i n e f f i c i e n t because a t low r e f l u x r a t i o s a very poor separa t ion i s ob ta ined and a t h i g h r e f l u x r a t i o s a great dea l of heat and time i s wasted. From a study of a l l these methods, i t i s seen tha t the best way to operate a b a t c h column i s to keep the compos i t ion o f the d i s t i l l a t e constant but t h i s i s exceed ing ly hard to accompl i sh . E i t h e r some automat ic c o n t r o l l e r must be made that w i l l take i n t o account a l l the v a r i a b l e s or some l i m i t i n g curve must be developed which cata be e a s i l y approximated. In what f o l l o w s , a l i m i t i n g curve i s developed, and a l s o a method i s i n d i c a t e d from which an automatic c o n t r o l l e r can be b u i l t . For the sake of completeness, the f o l l o w i n g theory i s developed from f i r s t p r i n c i p l e s . Theory. General. In the f o l l o w i n g d i s c u s s i o n , l e t us c o n s i d e r two l i q u i d s , A and B, which do not form a constant b o i l i n g mixture, A having the lower b o i l i n g p o i n t . (The same d i s c u s s i o n would apply, w i t h c e r t a i n m o d i f i c a t i o n s , to l i q u i d s which form such mixtures.) B o i l i n g Point Curve. The b o i l i n g p o i n t curve, which i s found experimen t a l l y , i s the s t a r t i n g point f o r a l l f u r t h e r work. Fig u r e 1 shows the b o i l i n g p o i n t curve f o r benzene and tolu e n e . When a l i q u i d of any composition XQ i s b o i l e d the vapour which i s given o f f i s not x 0 but i n s t e a d X]_ (see f i g u r e 1) T h i s f a c t a l l o w s d i s t i l l a t i o n to take p l a c e . E q u i l i b r i u m Diagram. A more convenient diagram to use i n d i s t i l l a t i o n c a l c u l a t i o n s i s the e q u i l i b r i u m diagram. T h i s diagram is'made from the b o i l i n g p o i n t curve by p l o t t i n g y, the composition of the vapour, a g a i n s t x, the composition of the l i q u i d . F i g u r e 2 shows t h i s diagram f o r benzene and t o l u e n e . M a t e r i a l Balance on a P e r f e c t P l a t e . Now, l e t us c o n s i d e r a p e r f e c t p l a t e i n a f r a c t i o n a t i n g column as represented i n f i g u r e 3. P R I N T E D fN U . S . A . E U G E N E D 1 E T Z 6 E N C O . N O . 3ks B X P R I N T E D I N U.S.A. • • , • ' . . ' .- • "' ' . E U G E N E O I E T Z 0 . E N C O , N O . 3 4 6 B X In f i g u r e 3, V = vapour Y = compos i t ion of vapour L = r e f l u x x - composi t ion of l i q u i d . The s u b s c r i p t s r e f e r to the p l a t e a t which the f low o r i g i n a t e s Tak ing a m a t e r i a l balance over the n ^ n p l a t e , Ln-.+ V . - L n + Vn ( l ) . a l s o , L x - l -V y = L x + Y y n-i n-i n+i 'nt i n n n 'n ( 2 ) . I t can he shown, "by t a k i n g an o v e r a l l heat balance and u s i n g Trou ton ' s r u l e 1 , tha t L n - . U , a n d Vn - V„ t , • • ( 3) • • * 4 V W - L x n - . = W n ^ L x n ( 4 ) . M a t e r i a l Ba'lance on Head of Column. Now-, l e t us cons ide r a m a t e r i a l balance, over the head of the column, as: shown i n f i g u r e 4v V - L + - D ( 5 ) . ^ 4 - , - - L x n + - D x p  ( 6 ) . e l i m i n a t i n g V, y = L xn _ i _ D x L+ D L+ D By d e f i n i t i o n , n . Tt- — p (7) a -n- i x n-i PLAT E n n-f-i n+1 n FI.GURE 3 9 S u b s t i t u t i n g R i n equa t ion ( 7 ) , x o ' : ' • ' (9).,. Rf I E q u a t i o n 9 i s a s t r a i g h t l i n e and i s known as the ope ra t i ng l i n e ; . I t can be p l o t t e d on the e q u i l i b r i u m diagram .from the- fac t : tha t i t c rosses the d i agona l a t x D and crosses x = 0 "at y - x p . T h i s l i n e g ives the compo- RtI s i t i o n of the l i q u i d on the p l a t e s when a p a r t i c u l a r r e f l u x r a t i o i s b e i n g used. When columns w i t h a l a rge number of p l a t e s are' used, such diagrams become very cramped and i t i s o f ten found advantageous to skew the coord ina te system to an angle o f 4 5 ° . C a l c u l a t i o n of Number of T h e o r e t i c a l P l a t e s . The number of t h e o r e t i c a l p l a t e s i n a ba tch column may be determined by c o n s i d e r i n g the c o n d i t i o n s tha t e x i s t when the maximum sepa ra t ion has been o b t a i n e d . A skewed diagram has been used i n f i g u r e 5 to c a l c u l a t e the number o f t h e o r e t i c a l p l a t e s i n a column which i s capable of s epa ra t i ng CgHg and C7H3 to the extent tha t there i s on ly 0,2% to luene i n the overhead product and on ly 0 .5$ benzene i n the l i q u i d i n the s t i l l - p o t when the r e f l u x r a t i o i s 198. I t may be seen tha t t h i s column has 14 t h e o r e t i c a l p l a t e s . R+-I 12 D e r i v a t i o n of R a y l e i g h ' s 5 E q u a t i o n . Let us cons ider f i g u r e 6 which i s e s s e n t i a l l y an e q u i l i b r i u m curve where w •= t o t a l amount of l i q u i d and u = t o t a l amount of A i n l i q u i d . By d e f i n i t i o n , x _ u „ — d o ) . . As soon as any vapour leaves the s t i l l - p o t , u changes by-du and w changes by-dw . y= ( I D . dw y= f(x) but (12) . y= du _ d(xw) _ xdw + wdx , ( 1 3 ) . d w dw dw _dw r jjx ( 1 4 ) . .w tW- x r x -x X ' I j i t t s l d x jdx_ _|dx . ( 1 5 ) . wo JyKx)-x "Jy-x JiW-x *o *0 % Minimum R e f l u x R a t i o . I f the ho ldrup i s n e g l i g i b l e and the column i s operated to g i v e „ a n - o v e r h e a d product which i s very pure. ( say between 99.8 and 100$) x D may be cons ide red a constant equa l to 1. 14 lnW n = | die (16) jdx t *n-i and W n ^ l=JbL* ( 1 7 ) . x n At any time the f r a c t i o n i n the s t i l l - s p o t i s the product of a l l the in te rmedia te f r a c t i o n s up to tha t p o i n t . W T n = V ^ x W x W^x xWn ( 1 8 ) . Each in te rmedia te f r a c t i o n i n t u r n s a t i s f i e s equa t ion (17).. w =- JJJJiD- 1 - »fe 1 - x 2 . 1 ' xn-l ( 1 9 ) - I - x,,- l - x 2 | - x 3 1 x7 ^ x y ' W r 1 ~~ x 0 n ( 2 0 ) . By d e f i n i t i o n , D - I — Wy _ I — ' - ^ p r ( 2 1 ) . - I — x n | — x n where D i s the t o t a l f r a c t i o n d i s t i l l e d and i s the compo s i t i o n of the l i q u i d i n the s t i l l - p o t a t any stage of the d i s t i l l a t i o n and i s a f u n c t i o n of the r e f l u x r a t i o o n l y , f o r any p a r t i c u l a r l i q u i d p a i r . For any g iven , r e f l u x r a t i o , the cor responding Xn may be found by u s i n g a McCabe-Thiele diagram as i n f i g u r e 7, W i t h l i q u i d s such as benzene and to luene , i t i s 15 16 found that t h i s f u n c t i o n may be represented by the equa t ion x n R° = b n ( 2 2 ) . where a and b are constants and can be found by p l o t t i n g l o g aga ins t l o g R on a graph as i n f i g u r e 0.. For a 14 p l a t e column sepa ra t i ng benzene and to luene , a .836 and b •= .795 . Now, combining equat ions (21) and (22) to e l i m i n a t e D "= X ° ^ _ _ D - " ( 2 3 ) . Equa t ion (23) i s p l o t t e d i n f i g u r e 9 and represents the minimum r e f l u x r a t i o which g ives 100$ overhead where a f r a c t i o n D has been d i s t i l l e d . " • I t i s e a s i l y seen tha t the most e f f i c i e n t method of ope ra t i ng a column i s to d u p l i c a t e t h i s curve e x a c t l y . T h i s , however, i s not e a s i l y done. One method which might be used to accompl i sh t h i s would be by t u r n i n g a va lve or d i v i d e d w i e r i n a prearranged way. D e r i v a t i o n of the Time Curve . In order to do t h i s i t i s necessary to know the r e l a t i o n s h i p between the time and the minimum r e f l u x r a t i o . Now, s ince P =• ( 2 4 ) . where P =• ra te of product V vapour v e l o c i t y , . EUGENE DIETZfjENCQ. NO. 3 4 6 BX 19 and a l s o D D D (25) where T = the time per u n i t charge. Combining (24) and (25) V d T - ( l+R)dD J,D-D ~R=R RdD = D + R-D— I DdR DtO R^RQ (26) . (27) . The i n t e g r a l i n equa t ion (27) can be e v a l u a t e d , g r a p h i c a l l y by u s i n g f i g u r e 9 or i n the f o l i a w i n g manner. Cons ider the i n t e g r a l by i t s e l f * R=R ;egrax oy l L s e x i * c t— b ( 2 8 ) . r*«o R"-Ro R=*o now, dR < o f V d R . ' = XQ R -f- Xjb £ — J R a_b •: J R VT= D(l+Rf—rfoR+lKxj + ll J °-b (29) > RrR b R 0 - Expanding ( R a — I f*'by the b i n o m i a l theorem^- ( 3 0 ) . fdR _ -FdR . b fdR b4 dR _v_ . . ^35 ^ ^ ( 3 1 ) . .-.VT= ibR^b d + R ) + *oR+-blx0+ O U - . ^ . ^ ; <M>< R b b (l-2a)R 2<H 21 By d i v i d i n g equa t ion (32) by V and p l o t t i n g i t on a graph, f i g u r e 10 i s ob t a ined . Expe r imen ta l Work. Apparatus Used. The apparatus used was the j a c k - c h a i n packed column b u i l t i n 1935 by W i l l i a m s o n and McGinn 7 which they have f u l l y desc r ibed i n t h e i r t h e s i s . I t was t h i s column tha t was r e f e r r e d to before and, as was shown, i t con ta ins 14 t h e o r e t i c a l p l a t e s . De te rmina t ion of .Vapour V e l o c i t y . The column was operated as a d i a b a t i c a l l y as p o s s i b l e and the vapour v e l o c i t y was determined by a heat b a l  ance on the head of the column. The f o l l o w i n g equa t ion was used: V - ( T 2 - T ! ) W ( 3 3 ) . where W weight of water through the condenser per minute, T-^  - temperature of the water e n t e r i n g , Tg = temperature of water l eav ing , , and L v = l a t e n t heat of v a p o u r i z a t i o n . In the i n i t i a l runs the water was c o l l e c t e d and measured f o r one minute . In l a t e r runs, however, a rotameter was used and the f low of water was ad jus ted to 1000 grams per minute . By do ing t h i s , the vapour v e l o c i t y became a l i n e a r f u n c t i o n of the temperature d i f f e r ence and cou ld be very e a s i l y read from a 22 graph. De te rmina t ion o f R e f l u x R a t i o and F r a c t i o n D i s t i l l e d . The product was c o l l e c t e d and weighed f o r a g iven l e n g t h of t ime . The r e f l u x r a t i o was c a l c u l a t e d from the r e l a t i o n R — -pr — I . (34).. R e s u l t s . , The r e f l u x r a t i o s a c t u a l l y used f o r the f r a c t i o n d i s t i l l e d are p l o t t e d on f i g u r e 11 . For purposes of comparison equa t ion (23) i s a l s o p l o t t e d on f i g u r e 11 . That t h i s method does g ive a pure product i s shown "by f i g u r e 12, on which i s p l o t t e d the p u r i t y of prbduct versus the f r a c t i o n d i s t i l l e d . Suggest ions f o r Fu r the r Work. I t was at tempted to make a c o n t r o l l e r to r egu la t e the r e f l u x r a t i o a c c o r d i n g to the time (equa t ion (32) and f i g u r e 10) . Th i s attempt was made oh the b a s i s of the c h a r a c t e r i s t i c s of the va lve used . When the vapour v e l o c i t y was kept cons tant , the r e f l u x r a t i o was found to vary w i t h the p o s i t i o n of the va lve stem i n d i c a t o r as shown i n f i g u r e 13. Since f i g u r e 13 and f i g u r e 10 are of approx imate ly the same shape, i t would appear tha t by t u r n i n g the va lve a t P R I N T E D I N U . S . A . ' •- ' EUGENE DIETZ6EN CO. NO. 346 BX 26 a constant speed a good approx imat ion of equat ion (32) c o u l d "be ob t a ined . Th i s was found to be the case but i t was s t i l l very much an approximat ion and needed f u r t h e r Improvement. The va lve mechanism cou ld be improved i n e i t h e r of two ways. F i r s t , by t u r n i n g the va lve a t a v a r y i n g speed and second, by r e d e s i g n  i n g the va lve to modify the f l ow c h a r a c t e r i s t i c s . Ins tead of u s i n g a va lve i t might be b e t t e r to use a d i v i d e d w e i r and t u r n i t a t a v a r y i n g speed. A method which would probably be the s imples t of a l l would be to des ign a va lve operated by a s e n s i t i v e temperature c o n t r o l l e r which would c lose the va lve a u t o m a t i c a l l y . In any method used p r o v i s i o n must be made to keep the vapour v e l o c i t y cons tan t . Th i s would i n v o l v e u s i n g a temperature c o n t r o l l e r i n the s t i l l - p o t which would inc rease the. power as the temperature i n c r e a s e d . Conc lus ions and Summary. The preceding pages have o u t l i n e d a conc i se and e f f i c i e n t method f o r ope ra t i ng a ba tch d i s t i l l a t i o n column when the ho ld-up can be cons idered n e g l i g i b l e . Exper imen ta l r e s u l t s are g i v e n to show the v a l i d i t y of the theo ry . Suggest ions are made f o r f u r t h e r improvements i n the manner of o p e r a t i o n . 27 B i b l i o g r a p h y , (1) . Badger, W . L . and McCabe, W.L . Elements of Chemical E n g i n e e r i n g , p . 343, M c G r a w t H i l l Book C o . , I n c . , (1935) . (2) . Bogar t , M. Trans . A . I . C h . E . 33, 139, (1937) . (3) . Edgeworth-Johnstone, R. Ind . E n g . Chem. 38. 1068, (1944) . (4) . McCabe, W . L . and T h i e l e , E.W. I n d . E n g . Chem. 17, 605, (1925) . (5) . R a y l e i g h . P h i l . Mag. 534, (1904) . (6) . Smoker and Rose. Trans . A . I . C h . E . 32, 285, (1940) . (7) . W i l l i a m s o n and McGinn. B . A . S c . T h e s i s , U . B . C . , (1935) . 

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