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Liquid diffusion in porous media, referring in particular to the Athabasca tar sands Hopper, David Allan 1945

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LIQ.UID DIFFUSION IN POROUS MEDIA, REFERRING I N PARTICULAR TO THE ATHABASCA TAR SANDS A T h e s i s s u b m i t t e d i n P a r t i a l F u l f i l m e n t o f The R e q u i r e m e n t s f o r t h e Degree o f MASTER OF APPLIED SCIENCE i n t h e Department o f CHEMISTRY D a v i d A l a n Hopper The U n i v e r s i t y o f B r i t i s h C o l u m b i a O c t o b e r , 1945 TABLE OF CONTENTS I . I n t r o d u c t i o n 1 I I . D i f f u s i o n a l T h e o r y A» G e n e r a l C o n s i d e r a t i o n s 1 T a b l e 1 2 B. A n a l y s i s L e a d i n g t o E q u a t i o n s 3 T a b l e 2 6 F i g u r e 1 f a c i n g 6 F i g u r e 2 f a c i n g 6 T a b l e 3 7 I I I . P r e v i o u s Work by O t h e r I n v e s t i g a t o r s 7 I T . I n v e s t i g a t i o n on A t h a b a s c a T a r - S a n d A* G e n e r a l 9 B» Sample Employed and Equipment D e v i s e d 10 F i g u r e 3 f a c i n g 3.0 F i g u r e 4 " 11 C. D e n s i t y - C o m p o s i t i o n R e l a t i o n s h i p 11 F i g u r e 5 f a c i n g l i D. E x p e r i m e n t a l P r o c e d u r e 11 £• R e s u l t s f • 13 T a b l e 4 13 F i g u r e 6 f a c i n g 15 F i g u r e 7 f a c i n g 15 V. C o n c l u s i o n s 15 N o m e n c l a t u r e 16 L i t e r a t u r e C i t e d 17 LIQ.UID DIFFUSION IN POROUS MEDIA REFERRING: IN PARTICULAR TO THE ATHABASCA TAR SANDS I - INTRODUCTION A g r e a t many c h e m i c a l e n g i n e e r i n g o p e r a t i o n s p r o -ceed by t h e mechanism o f d i f f u s i o n -- t h e t r a n s f e r o f ma-t e r i a l f r o m one phase t o a n o t h e r , a c t u a t e d by a c o n c e n t r a t i o n g r a d i e n t . Among s u c h o p e r a t i o n s may be l i s t e d d i s t i l l a t i o n , a b s o r p t i o n , a d s o r p t i o n , e x t r a c t i o n , h u m i d i f i c a t i o n , d r y i n g , s t r i p p i n g , c o n d e n s a t i o n , c o m b u s t i o n , and c r y s t a l l i z a t i o n * I t i s t h e o b j e c t o f t h i s t h e s i s t o o u t l i n e t h e t h e o r e t i c a l b a s i s o f d i f f u s i o n i n g e n e r a l , and i n p a r t i c u l a r , t h a t o f d i f f u s i o n t h r o u g h p o r o u s m e d i a ; t o r e v i e w t h e a t t e m p t s o f v a r i o u s w o r k e r s t o c o r r e l a t e e x p e r i m e n t a l e x t r a c t i o n d a t a on t h e b a s i s o f t h i s t h e o r y ; and t o p r e s e n t t h e i n t e r i m r e s u l t s o f an i n v e s t i g a t i o n , made by t h e a u t h o r d u r i n g t h e 1944-45 t e r m a t t h e U n i v e r s i t y o f B.C., on t h e s o l v e n t e x t r a c t i o n o f a sample o f t a r - s a n d f r o m t h e A t h a b a s c a r e g i o n . I I - DIFFUSIONAL THEORY A - G e n e r a l C o n s i d e r a t i o n s I n any o p e r a t i o n i n v o l v i n g d i f f u s i o n , a t l e a s t two p h a s e s a r e i n v o l v e d ; one w h i c h i s b e i n g c o n t a c t e d , and the o t h e r t h e c o n t a c t i n g a g e n t * Each o f t h e two p h a s e s may be a s o l i d , a l i q u i d o r a g a s . Thus, n i n e p o s s i b l e c a s e s p r e -' 1) • • • ' ' s e n t t h e m s e l v e s , as l i s t e d i n t h e f o l l o w i n g t a b l e , w i t h examples, Case Ho, 1 2 3 4 5 8 9 P h a s e C o n t a c t e d Gas Gas Gas L i q u i d L i q u i d L i q u i d S o l i d S o l i d S o l i d TABLE 1. C o n t a c t i n g P h a s e Gas L i q u i d S o l i d Gas L i q u i d S o l i d Gas L i q u i d S o l i d Example None ( g a s e s eomp. m i s c i b l e ) A b s o r p t i o n ( b u t a n e by p e t r o l e u m s o l v e n t s ) A d s o r p t i o n (gas mask) Steam s t r i p p i n g E x t r a c t i o n ( p e t r o l e u m w i t h H 2 S 0 4 ) P e r c o l a t i o n d e c o l o r i z i n g o f s u g a r s o l u t i o n s D r y i n g o f wood o r b r i c k by .hot a i r L e a c h i n g o f s u g a r b e e t s None ( t r a n s f e r r a t e s s l o w ) As m i g h t be e x p e c t e d , c o m b i n a t i o n s o f t h e above c a s e s may o c c u r . The p r o c e s s o f d i s t i l l a t i o n , f o r example, combines c a s e s 2 and 4, a b s o r p t i o n p r o c e e d i n g i n t h e u p p e r s e c t i o n o f a f r a c t i o n a t i n g c o lumn, and s t r i p p i n g i n t h e low e r . T h i s p a p e r w i l l be p r i m a r i l y c o n c e r n e d w i t h c a s e 8 -- t h e ex-t r a c t i o n o f a s o l i d by a l i q u i d p h a s e * When a m a t e r i a l i s s o l u b l e i n b o t h o f two a d j a c e n t 1. W a l k e r L e w i s McAdams & G i l l i l a n d - " P r i n c i p l e s o f Chem. E n g i n e e r i n g " , p. 424. McGraw H i l l ( 1 9 3 7 ) . p h a s e s j and t h e c o n d i t i o n s o f t e m p e r a t u r e and p r e s s u r e h e l d c o n s t a n t , t h e s y s t e m w i l l t e n d t o i v a r d a d e f i n i t e e q u i l i b r i u m d i s t r i b u t i o n , i n d e p e n d e n t o f t h e d i r e c t i o n f r o m w h i c h t h e e q u i l i b r i u m i s a p p r o a c h e d . S i n c e t h i s e q u i l i b r i u m d i s t r i b u -t i o n s e t s an a b s o l u t e l o w e r l i m i t on t h e q u a n t i t y o f t r e a t i n g phase r e q u i r e d t o remove a d e f i n i t e f r a c t i o n of t h e d i s s o l v e d m a t e r i a l , i t s p r a c t i c a l i m p o r t a n c e w i l l be a p p a r e n t . E q u a l l y i m p o r t a n t i s the r a t e a t w h i c h t h e e q u i l i -b r i u m i s a p p r o a c h e d * T h i s w i l l depend (among o t h e r f a c t o r s ) upon t h e c o n t a c t s u r f a c e between t h e p h a s e s and i s , i n gen-e r a l , d i r e c t l y p r o p o r t i o n a l t o t h e m a g n i t u d e o f t h i s s u r f a c e . E x c e p t when one o f t h e p h a s e s i s s o l i d , t h e d i f f u s -i n g m a t e r i a l i s c a r r i e d t h r o u g h b o t h p h a s e s by c o n v e c t i o n ; ( b u l l s m o t i o n o f t h e phase m a t e r i a l ) o n l y i n t h e r e l a t i v e l y m o t i o n l e s s f i l m s s e p a r a t i n g t h e p h a s e s i s t h e t r a n s f e r e f f e c t -ed by t r u e ( o r m o l e c u l a r ) d i f f u s i o n . F r e q u e n t l y , t h e e f f e c t o f one f i l m may be n e g l e c t e d , i t s r e s i s t a n c e t o d i f f u s i o n b e i n g much l e s s t h a n t h a t o f t h e o t h e r . An i n s t a n c e o f t h i s i s ammonia d i s s o l v i n g i n w a t e r , where t h e gas f i l m i s c o n -s i d e r e d as c o n t r o l l i n g and t h e l i q u i d f i l m r e s i s t a n c e n e g l i g i b l e , on a c c o u n t o f t h e g r e a t s o l u b i l i t y o f t h i s g a s . O t h e r i n s t a n c e s o c c u r , h owever, when t h e e f f e c t o f each f i l m must be c o n s i d e r e d s e p a r a t e l y , ( e xample - s u l p h u r d i o x i d e d i s s o l v i n g i n w a t e r ) , B« - A n a l y s i s L e a d i n g t o E q u a t i o n s The f o l l o w i n g a n a l y s i s w i l l be made on t h e b a s i s o f h e a t f l o w 1 , as t h i s p r o c e s s i s p e r h a p s more r e a d i l y v i s u a l i z e d t h a n t h a t o f m a t e r i a l t r a n s f e r . The e q u a t i o n s d e v e l o p e d w i l l t h e n be m o d i f i e d t o a p p l y t o m a t e r i a l t r a n s f e r . C o n s i d e r an e l e m e n t dx dy dz ( r e c t a n g u l a r c o o r d i n a -t e s ) and d e a l w i t h t h e h e a t f l o w a l o n g t h e x - a x i s only<, The h e a t e n t e r i n g t h e element d u r i n g t h e t i m e d i s ( d Q ) ^ n and by t h e w e l l known F o u r i e r e q u a t i o n ( d Q ) i n = -k d t .A.d« «. -£/dt ] ( d y . d z ) d e dL U x / L=x The h e a t l e a v i n g t h e el e m e n t i n t h e same t i m e i n t e r v a l i s ( d Q ^ u t = -k^/dtj 4.{ay. dz)d<? T h e n e t h e a t r e m a i n i n g t h e n , L= x + dx i s S /v ^* ( k |1) (dx) (dy.dz)d© T h i s c a n be e q u a t e d t o t h e h e a t s t o r e d ( d x . d y . d z ) P . C . ^ J l .d© C a n c e l l i n g o u t common t e r m s and r e a r r a n g i n g , we get * . <T t _ ^ W _ ,. . J T = £ T 1 7 2 " ~ T T 3 . " " e q u a t i o n 1. 2 where ex. i s t h e i f e r m a l d i f f u s i v ' i t y , and has t h e d i m e n s i o n s — T h i s i s t h e g e n e r a l e q u a t i o n f o r u n s t e a d y , u n i - d i r e c t i o n a l 6 h e a t f l o x v . Now c o n s i d e r a s l a b o f t h i c k n e s s 2R, a t a u n i f o r m t e m p e r a t u r e o f t ^ , p l a c e d i n an i n f i n i t e medium o f t e m p e r a t u r e T a t a t i m e 6 = 0. S o l v i n g t h e above d i f f e r e n t i a l e q u a t i o n , a s s u m i n g t h e d i f f u s i o n c o e f f i c i e n t t o r e m a i n c o n s t a n t , and s u b s t i t u t i n g i n t h e b o u n d a r y c o n d i t i o n s t = T a t x = 0 and a t x = 2R; t = t , a t 0 = 0 ; and t = T a t 0 = 00 we have t h e r a p i d -l y c o n v e r g i n g s e r i e s : ( E q u a t i o n 2.) 1. Sherwood, T.K., I n d . Eng. Chem. 21, 12-16 (1929) 5. The - t o t a l h e a t a b s o r b e d up t o t i m e 0- i s o b t a i n e d by i n t e g r a t -i n g ( t - t-|_)Cp P A between t h e l i m i t s 0 and 2R. Thus, t h e f r a c t i o n (E) of t h e t o t a l h e a t t r a n s f e r s t i l l u n -e f f e c t e d a f t e r t i m e & i s g i v e n by U E - 7 ^ , . 1 2 Sherwood and Newman showed t h a t E q u a t i o n 3 may be m o d i f i e d t o a p p l y t o t h e a i r d r y i n g o f wood and s o a p , and i n g e n e r a l , t o t h e e x t r a c t i o n o f a s o l u t e f r o m b o t h s i d e s o f a p o r o u s s l a b o f t h i c k n e s s 2R where i n t e r n a l d i f f u s i o n i s c o n -t r o l l i n g , ( s u r f a c e f i l m r e s i s t a n c e b e i n g n e g l i g i b l e . ) -7> 2 where "D" i s t h e m a t e r i a l d i f f u s i v i t y d e f i n e d by t h e e q u a t i o n ^c.. - O. i) c _ _ ~ E q u a t i o n 5. and c o r r e s p o n d s t o " i n E q u a t i o n 1. E q u a t i o n 5 i s t h e 1. Sherwood, T.K., I n d . & Eng. Chem. 21, 12-16 (1929) 2. Newman, A.B., T.A.I.O.H.E., 27, 310-33 (1931) w e l l - k n o w n F i c k ' s E q u a t i o n f o r non s t a t i o n a i y , u n i d i r e c t i o n a l mass t r a n s f e r . A number o f s o l u t i o n s t o E q u a t i o n 4 a r e p r e s e n t e d i n T a b l e 2, and t h e p o i n t s p l o t t e d on semi l o g p a p e r as F i g u r e 1. The c u r v e can be seen t o be a s t r a i g h t l i n e , ex-ce p t a t v a l u e s o f E above 0.7. • TABLE 2. E E 0.000 1.000 0.200 0.49 6 0.005 0.909 0.300 0.387 0.010 0.885 0.500 0.237 0 .02 5 0.822 0. 600 0.184 0.0 50 0.748 0.700 0.144 0.100 0.642 1.000 0.0 69 0.150 0.564 E q u a t i o n 4 i s t h e n r e p l o t t e d i n F i g . 2, a c c o r d i n g t o a s u g g e s t i o n by S h e r w o o d 1 , w h e r e i n t h e s c a l e o f E has been compressed so as t o s t r a i g h t e n o ut t h e c u r v e d p o r t i o n . Any e x t r a c t i o n d a t a f a l l i n g on a s t r a i g h t l i n e on- t h i s s p e c i a l p a p e r t h e n , i n d i c a t e t h a t t h e mechanism o f e x t r a c t i o n c o r r e s -ponds t o t h e a s s u m p t i o n s on w h i c h t h e t h e o r e t i c a l e q u a t i o n was d e r i v e d ; v i z . e x t r a c t i o n f r o m b o t h s i d e s o f a s l a b o f t h i c k -n e s s 2R by p u r e m o l e c u l a r d i f f u s i o n , w i t h s o l v e n t t e m p e r a t u r e and c o n c e n t r a t i o n c o n s t a n t , and w i t h n e g l i g i b l e s u r f a c e f i l m r e s i s t a n c e . To f a c i l i t a t e t h e c o n s t r u c t i o n o f t h i s s p e c i a l g r a p h 1. Sherwood, T.K., I n d . & Eng. Chem., 21, 12-16 (1929) p a p e r , T a b l e 3 i s on t h e E s c a l e . I n t e r v a l s on E S c a l e R a t i o s on a L i n e a r S c a l e 0.1 t o 0.15 19.4 0.1 t o 0.2 33.2 0.1 to 0.3 52.5 0.1 t o 0.4 66.3 0.1 t o 0.5 77.0 0.1 t o 0.6 85.4 0.1 t o 0.7 91» 8 0.1 to 0.8 9 S « 5 0.1 to 0.9 99.0 0.1 t o 1.0 . 1OO«0 The p r e c e d i n g d e r i v a t i o n has been, b a s e d on d i f f u s i o n t h r o u g h a u n i f o r m , p o r o u s medium, whose s t r u c t u r e r e m a i n s unchanged as t h e e x t r a c t i o n p r o c e e d s . The e f f e c t o f t h e i n e r t medium i s t o l e n g t h e n t h e p a t h o f d i f f u s i o n , d i r e c t i n g t h e f l o w by t o r t u o u s c h a n n e l s t h r o u g h t h e mass• T h i s r e s u l t s i n a much l o w e r v a l u e o f t h e d i f f u s i o n c o e f f i c i e n t t h a n f o r t h e c a s e where d i f f u s i o n p r o c e e d s w i t h o u t t h e i n t e r v e n t i o n o f any p o r o u s m a t e r i a l . I l l - P r e v i o u s Work by O t h e r I n v e s t i g a t o r s The g e n e r a l mechanism o f d i f f u s i o n i n p o r o u s s o l i d s p r e s e n t e d , s h o w i n g t h e r e l a t i v e i n t e r v a l s TABLE 3 has been s t u d i e d by B a r r e r , M a r c h & Weaver , and Newman • The t h e o r y d e v e l o p e d has been a p p l i e d t o a number o f s p e c i f i c 4 c a s e s -- t o t h e d r y i n g o f wood and soap by T u t t l e and by 5 fi Sherwood ; t o d i f f u s i o n i n t o wood by Cady & W i l l i a m s ; and t o 7 8 g e l s t r u c t u r e s by F r i e d m a n and F r i e d m a n & Kramer • I n each o f t h e s e c a s e s , t h e mechanism was f o u n d t o be p u r e m o l e c u l a r d i f f u s i o n , w i t h a c o n s t a n t d i f f u s i o n c o e f f i c i e n t * B o u c h e r , 9 10 B r i e r & Osborn , and K i n g , K a t z & B r i e r a p p l i e d i t t o t h e e x t r a c t i o n o f p o r o u s c l a y p l a t e s s a t u r a t e d w i t h soy bean o i l , 10 and K i n g , K a t z & B r i e r t o soy bean f l a k e s * F o r t h e p o r o u s p l a t e s , t h e e x t r a c t i o n d a t a f i t t e d t h e t h e o r y w e l l , t h e d i f f u s i o n c o e f f i c i e n t ( s o y bean o i l - t r i c h l o r e t h y l e n e s y s t e m @ 80°F.) r e m a i n i n g s u b s t a n t i a l l y c o n s t a n t a t 4*07 x 1Q~ 6 sq.. f t . p e r h o u r . The d a t a f o r soy bean f l a k e s , however, c o u l d n o t be c o r r e l a t e d t o t h e t h e o r y , p r e s u m a b l y due t o v a r i a t i o n s i n t h e s t r u c t u r e o f t h e f l a k e s and d i s t r i b u t i o n o f t h e o i l , 11 Osborn & K a t z made a m a t h e m a t i c a l a n a l y s i s o f t h e e f f e c t o f s t r u c t u r e o f t h e a p p l i c a t i o n o f d i f f u s i o n a l t h e o r y t o e x t r a c t i o n . They c o n c l u d e t h a t i n t h e c a s e o f t h e soy bean f l a k e d a t a , 70 - 90% o f t h e o i l i s e x t r a c t e d w i t h a 1* B a r r e r , R.M., " D i f f u s i o n I n & Th r o u g h S o l i d s " - Cambridge M a c M i l l a n - 1941 3* M a r c h , H., & Weaver, W,, P h y s . R e v i e w ; 31,1072-1081 (1928) 3. Newman, A.B., T.A.I.Ch.E., 27, 310-33 (1931) 4. T u t t l e , F . J . , J . F r a n k l i n I n s t , , 200, 609-614 (1925) 5. Sherwood, T.K., I n d . Eng. Chem., 2 1 , 12-16 (1929) . 6. Cady, L.C., W i l l i a m s , J.W., J . P h y s . Chem., 39, 87-102(1935) 7. F r i e d m a n , L., J.A.C.S., 52, 1305-10 (1930) 8. F r i e d m a n , L. , K r a m e r , E.O., I b i d . , 52, 1295-1304 (1930) (1942) 9. B o u c h e r , D.F., B r i e r , J.C. & O s b o r n , J.D.,TAICE,38,967-9 91/ 10. K i n g , C O . , K a t z , D.L. ,& B r i e r , J.C. , TAICE, 40,533-556 (1944) 1 1 . Osborn,J.D.,& K a t z , D . L , , T.A.I.C.E., 40, 511-531 (1944) d i f f u s i o n c o e f f i c i e n t o f 4 x 10"" s q . f t . p e r h o u r , w h i l e t h e -7 r e m a i n d e r i s e x t r a c t e d a t t h e much l o w e r c o e f f i c i e n t o f 5 x 10 f t / h o u r . I f t h e s t r u c t u r e o f a medium i s known t h e n , i t s d i f f u s i o n c o e f f i c i e n t s h o u l d be c o m p u t a b l e f r o m a k n o w l e d g e o f t h e c o e f f i c i e n t s o f i t s c o n s t i t u e n t p a r t s . S i n c e t h i s k n o w l e d g e i s g e n e r a l l y n o t a v a i l a b l e , however, d i r e c t e x p e r i -ment r e m a i n s t h e o n l y r e l i a b l e method a t p r e s e n t f o r e s t i m a t -i n g e x t r a c t i o n r a t e s * A. - G e n e r a l What i s p r o b a b l y t h e w o r l d ' s g r e a t e s t d e p o s i t o f b i t u m i n o u s m a t e r i a l i s l o c a t e d i n t h e A t h a b a s c a r e g i o n o f n o r t h e r n A l b e r t a , e x t e n d i n g r o u g h l y 50 m i l e s i n e v e r y d i r e c -t i o n f r o m F o r t M c M u r r a y . The a s p h a l t c o n t e n t r a n g e s f r o m 7 - 20$ and i s o f t h e s e m i - l i q u i d v a r i e t y . A c c o r d i n g t o S e y e r and K r i e b l e " * " , i t i s c o m p l e t e l y s o l u b l e i n c a r b o n d i -s u l p h i d e and c a r b o n t e t r a c h l o r i d e , and 98$ s o l u b l e i n benzene, and i s o f a t y p e b e t w e e n t h e T r i n i d a d and Bermudez a s p h a l t s w i t h r e s p e c t t o i t s r e s i n o u s and o i l y c o n s t i t u e n t s . A t p r e s e n t , t h e d e p o s i t s a r e b e i n g worked a t F o r t M c M u r r a y , on a s e m i - p l a n t s c a l e . F o l l o w i n g o p e n - p i t m i n i n g of t h e t a r - s a n d t h e a s p h a l t i s s e p a r a t e d f r o m t h e sand by a g i t a t i o n w i t h h o t w a t e r , and t h e n c r a c k e d f o r t h e p r o d u c t i o n o f g a s o l i n e and l o w e r e d v i s c o s i t y r e s i d u a l f u e l o r a s p h a l t • One o f t h e p r i m e economic d r a w b a c k s o f t h e method i s t h e 1. K r i e b l e , V.K., & S e y e r , W.F., J.A.C.S. X L I I I (1921) f/Guzt 5 CELL USED CELL ELEVATION 0N6 /?£QU/e£0 Dr/// & /op for£*£ F.H. screw. S/x screws (3 on e•//'ner s/de) cw a /g c/rc/e SECTION A-. E/A/6 • Dri// & cocro/-erstnk /or EM. screw (s Ipo/es on on 11 arc/e, et?aa-//y spaced. roue WW/^ft) TWO onl y to e£ F/rrea W/rtf SC#££A/S. <so mesA cop-per screen, i>raz~ed oyer SceEEN TtVO je£GU/t!EO tremendous sand h a n d l i n g problem© An a l t e r n a t i v e r e c o v e r y method m i g h t be t h e s o l v e n t e x t r a c t i o n o f t h e sands i n s i t u , l i f t i n g t h e a s p h a l t s o l u t i o n t o t h e s u r f a c e by a c o n v e n t i o n a l o i l - f i e l d w a t e r d r i v e * Such a scheme m i g h t f i n d a p p l i c a t i o n i n s e l e c t e d r e g i o n s o f t h e f i e l d where t h e u n d e r l y i n g f o r m a t i o n s a r e s u c h as t o m i n i m i z e s o l v e n t l o s s e s 9 F o r t h e d u a l p u r p o s e t h e n , o f f u r t h e r t e s t i n g t h e d i f f u s i o n t h e o r y p r e v i o u s l y o u t l i n e d and o f g a t h e r i n g d a t a w h i c h would be e s s e n t i a l t o t h e d e v e l o p m e n t o f s u c h an ex-t r a c t i o n method, a s e r i e s o f e x t r a c t i o n t e s t s were made on a sample o f t a r - s a n d f r o m t h e A t h a b a s c a d e p o s i t * B. - Sam-pie Employed and Equipment D e v i s e d The t a r - s a n d employed i n t h e i n v e s t i g a t i o n was t a k e n f r o m an o u t c r o p a t t h e s c e n e o f o p e r a t i o n s a t F o r t McMurray* As p r e l i m i n a r y t e s t s showed t h e d i f f i c u l t y o f w o r k i n g w i t h p i e c e s r e t a i n i n g t h e o r i g i n a l s t r u c t u r e (due t o c h a n n e l i n g o f t h e s o l v e n t ) the samples f r o m t h e v a r i o u s b o x e s were b r o k e n up and t h o r o u g h l y m i x e d . Carbon t e t r a c h l o r i d e was c h o s e n as the s o l v e n t by r e a s o n o f t h e c o m p l e t e s o l u b i l i t y o f t h e a s p h a l t i n i t , as w e l l as f o r i t s c h e a p n e s s and n o n - f l a m m a b i l i t y . A s i m p l e c e l l was d e v i s e d ( F i g u r e 3) t o h o l d ' t h e t a r -sand r i g i d l y and m i n i m i z e any movement o f t h e s a n d - g r a i n s as t h e t a r was removed. A f i n e - m e s h , r e m o v a b l e s c r e e n on e i t h e r s i d e o f t h e c e l l p e r m i t t e d c o n t a c t w i t h t h e s o l v e n t , and was f o u n d t o h o l d t h e s a n d w e l l i n p l a c e , even t h o u g h t h e o p e n i n g s were somewhat l a r g e r t h a n most o f t h e sand g r a i n s . As may be EXTRACT/ON CELL SETUP seen f r o m F i g u r e 3, t h e sample e x t r a c t e d was i n t h e f o r m o f a s h o r t c y l i n d e r , w i t h e x t r a c t i o n p r o c e e d i n g o v e r t h e e n t i r e f a c e a t e i t h e r end, t h u s f u l f i l l i n g t h e c o n d i t i o n s f o r t h e d i f f u s i o n t h e o r y p r e v i o u s l y p r e s e n t e d * The c e l l r e s t e d on t h e b o t t o m o f a 1000 oc b e a k e r o f s o l v e n t w h i c h i n t u r n was immersed t o t h e r i m i n a t h e r m o s t a t -c o n t r o l l e d w a t e r b a t h s e t a t 25°0. i e05° (See F i g u r e 4 ) . 0. D e n s i t y - C o m p o s i t i o n R e l a t i o n s h i p As a c o n v e n i e n t t o o l f o r c o m p u t i n g t h e w e i g h t o f t a r e x t r a c t e d f r o m t h e s a m p l e , t h e d e n s i t y - c o m p o s i t i o n r e l a t i o n -s h i p f o r a t a r - o a r b o n t e t r a c h l o r i d e s o l u t i o n was d e t e r m i n e d , i n t h e f o l l o w i n g manner. A w e i g h t e d sample o f t a r ( n o t t a r -sand) was d i s s o l v e d i n a few h u n d r e d e s s . o f c a r b o n t e t r a -c h l o r i d e and t h e s o l u t i o n w e i g h e d , t h e w e i g h t o f s o l v e n t b e i n g o b t a i n e d by s u b t r a c t i o n . From t h e known d e n s i t y o f t h e s o l -v e n t ( a t 25°C. r e l a t i v e t o w a t e r a t 25°C., d e n o t e d h e r e a f t e r i n t h i s p a p e r by. ^ ° / 2 5 ° ) and t h e d e n s i t y o f t h e s o l u t i o n as measured by a 25 ml p y e n o m e t e r , t h e d e n s i t y o f t h e t a r (25 0/2g>) was computed. A s s u m i n g t h e volumes o f t a r and s o l v e n t t o be a d d i t i v e t h e n , t h e d e n s i t i e s o f o t h e r s o l u t i o n s o f v a r y -i n g t a r - c o n t e n t were computed and t h e r e s u l t s p l o t t e d as F i g u r e 5. Do E x p e r i m e n t a l P r o c e d u r e The c e l l was l a i d on a s m a l l p i e c e o f s t e e l p l a t e w i t h t h e r i n g s ( n o t t h e s c r e e n s ) i n p l a c e , and a 1 - i n c h l e n g t h o f 1-1/4 i n c h s t a n d a r d p i p e p l a c e d on t o p . Warm t a r -sand was t h e n tamped i n t o t h e c e l l u n t i l t h e l e v e l was up i n t h e p i p e n i p p l e , and a 1 i n c h l e n g t h o f 1-1/4 i n c h r o u n d s t o c k ( g r o u n d t o a l o o s e f i t ) s l i p p e d i n t o t h e . p i p e n i p p l e t i l l i t came t o r e s t on t h e t a r - s a n d . The w h o l e was t h e n p l a c e d i n a v i s e w h i c h was t h e n t i g h t e n e d up and l e f t f o r f i v e o r s i x hours. A f t e r r e m o v i n g t h e c e l l f r o m t h e v i s e t h e n i p p l e was t a k e n o f f , and any e x c e s s t a r - s a n d p a r e d away w i t h a h o t k n i f e -b l a d e , f l u s h w i t h t h e o u t s i d e f a c e o f t h e c e l l . The r i n g s were t h e n removed, t h e s c r e e n s s c r e w e d i n t o p l a c e , and t h e c e l l a n d . t a r - s a n d w e i g h e d t o t h e n e a r e s t m i l l i g r a m . From t h e known w e i g h t o f t h e empty c e l l t h e n , t h e w e i g h t o f t a r - s a n d was o b t a i n e d by s u b t r a c t i o n . The c e l l was t h e n immersed i n a 1000 cc b e a k e r o f c a r b o n t e t r a c h l o r i d e i n t h e c o n s t a n t t e m p e r a t u r e b a t h , (25°C ±0.05°) and t h e t i m e n o t e d . The s t i r r e r was a d j u s t e d t o keep t h e s o l v e n t b a r e l y i n m o t i o n t h u s k e e p i n g t h e c o n c e n -t r a t i o n u n i f o r m t h r o u g h o u t t h e b e a k e r , y e t a v o i d i n g any i m p a c t o f s o l u t i o n a g a i n s t t h e f a c e o f t h e t a r - s a n d . A t t h e e x p i r y o f t h e t i m e d e s i r e d , t h e c e l l was r e -moved f r o m t h e s o l v e n t , and t h e p a r t i a l l y e x t r a c t e d t a r - s a n d p l a c e d i n a t a r e d p a p e r e x t r a c t i o n t h i m b l e and e x t r a c t e d w i t h c l e a n c a r b o n t e t r a c h l o r i d e i n a S o x h l e t e x t r a c t o r . The s o l u -t i o n r e s u l t i n g f r o m t h i s (Soxhlet) e x t r a c t i o n was t h e n w e i g h e d i n a t a r e d b e a k e r , and t h e t a r c o n c e n t r a t i o n d e t e r m i n e d by m e a s u r i n g i t s d e n s i t y w i t h a 25 m l p y c n o m e t e r . From t h i s , t h e w e i g h t o f t a r u n e x t r a o t e d was c a l c u l a t e d * The S o x h l e t t h i m b l e , c o n t a i n i n g t h e s a n d , was t h e n o ven d r i e d a t 100°G. f o r 30 m i n u t e s , c o o l e d i n a d e s i c c a t o r , and w e i g h e d q u i c k l y t o t h e n e a r e s t m i l l i g r a m . (The p a p e r t h i m b l e p i c k s up m o i s t u r e r a p i d l y f rom t h e a t m o s p h e r e ) • T h i s y i e l d e d t h e w e i g h t o f sand i n t h e t a r - s a n d sample and by sub-t r a c t i o n , t h e w e i g h t o f t a r . F o r r u n s o f s h o r t d u r a t i c n , where t h e f r a c t i o n o f t a r • e x t r a c t e d was l e s s t h a n 30$, t h e w e i g h t o f t a r e x t r a c t e d was o b t a i n e d by c o n c e n t r a t i n g t h e s o l u t i o n i n t h e 1000 m l b e a k e r t o 300 - 400 m l ; w e i g h i n g i t , and m e a s u r i n g i t s t a r c o n c e n t r a -t i o n by t h e d e n s i t y method. The w e i g h t (and hence t h e f r a c -t i o n ) o f t a r u n e x t r a c t e d was t h e n o b t a i n e d by s u b t r a c t i o n . By t h u s m e a s u r i n g d i r e c t l y e i t h e r t h e " t a r e x t r a c t e d " o r t h e " t a r n o t e x t r a c t e d " , w h i c h e v e r was t h e s m a l l e r , t h e e f f e c t o f any e r r o r i n measurement was m i n i m i z e d . E. R e s u l t s The e x p e r i m e n t a l d a t a a r e summarized i n T a b l e 4. TABLE 4. F r a c t i o n Run No o Wt. o f S amp1e Wt. o f Sand Wt. Of Tar T a r T a r ex-t r a c t e d T a r n o t n o t e x t . (E) Time (mins.) ; i 29.468 24*104 5. 364 18 © S 01894 4.470 0,833 60 2 28.418 23.141 5.277 18.5 2.080 3 ® X 9 7 0. 606 150 3 28.482 23.296 5.186 18.2 2.963 2.223 •0.429 300 : 4 28.746 23.484 5.862 18.3 2.084 3.178 0 . 603 15© 5 30 $ 533 25.169 5.384 17.7 2. 668 2.726 0 . 50 5 300 6 29.928 24.678 5.250 17.6 0.637 4.613 0.879 50 7 30.012 24.573 5.439 18.1 3.124 2.315 0.425 418 ! 8 30.514 24.954 5.560 18.2 4.086 1.474 0.265 600 I 9 • 30.356 24.927 5.429 17.9 2.403 3.026 0.517 240 14 TABLE 4 c o n t i n u e d F r a c t i o n . Run No. Wt, o f Sample Wt. o f Sand Wt. o f £ Tar T a r T a r ex-t r a c t e d Tar n o t e x t . n o t e x t . ( E ) Time (mine) 10 29.969 24.583 5. 386 18,0 1.736 3,650 0.678 120 11 29,403 24.007 5.396 18,3 H e 3 2 9 3,167 0.588 200 12 .29,584 24,206 5.378 18.2 3.046 2.332 0.433 350 13 29,501 24,177 5,324 18.0 2,028 3.296 0.381 480 14 29,805 24,336 5,469 18.3 4.000 1.469 0.268 540 15 29.353 24,043 5.310 18.1 4.377 0.933 0.176 780 16 29,829 24.507 17.8 3 © 9 3 7 1,385 0.260 650 17 29,474 24.233 5.241 17.8 4.011 1.230 0.235 720 18.1$ , . J a v e r a g e The f r a c t i o n o f t a r r e m a i n i n g u n e x t r a c t e d was p l o t t e d a g a i n s t t i m e i n F i g u r e 6. S t r i c t l y s p e a k i n g , i t i s t h e " e x t r a c t a b l e " t a r o n l y w h i c h s h o u l d be c o n s i d e r e d , the e q u i l -i b r i u m t a r c o n t e n t r e m a i n i n g a f t e r an i n f i n i t e e x t r a c t i o n t i m e b e i n g t a k e n i n t o a c c o u n t . As f r e s h s o l v e n t was employed f o r each e x t r a c t i o n , however, and t h e c o n c e n t r a t i o n o f t a r a t t h e end o f t h e p e r i o d n e v e r exceeded 0,5$, t h i s e f f e c t was c o n -s i d e r e d w i t h i n t h e o v e r a l l l i m i t o f a c c u r a c y o f t h e e x p e r i m e n t , and was a c c o r d i n g l y n e g l e c t e d . O t h e r e x p e r i m e n t e r s have c e n t r i f u g e d t h e e x t r a c t e d m a t e r i a l f o l l o w i n g r e m o v a l f r o m t h e s o l v e n t , i n o r d e r t o t h r o w o u t s o l u t i o n h e l d m e c h a n i c a l l y i n t h e p o r e s o f t h e m a t e r i a l . I n v i e w o f t h e r e l a t i v e l y h i g h v o l a t i l i t y o f t h e s o l v e n t h e r e employed (and c o n s e q u e n t r a p i d d r y i n g ) t h i s was n o t f e a s i b l e . 1 5 , F i g u r e 6 was r e p l o t t e d on t h e s p e c i a l p a p e r p r e -v i o u s l y m e n t i o n e d , as F i g u r e 7. Inasmuch as t h e p e r c e n t v o i d s i n t h e t a r sand i s g r e a t e r t h a n t h e minimum c a l c u l a t e d f r o m t h e s a n d s c r e e n a n a l y s i s , ( i . e , - t h e sand g r a i n s a r e n o t q u i t e i n c o n t a c t ) some s e t t l i n g and o r i e n t a t i o n o f t h e g r a i n s u n d o u b t e d l y o c c u r s as t h e e x t r a c t i o n p r o c e e d s . I t i s f e l t t h a t t h i s was p r o b a b l y t h e c h i e f f a c t o r l i m i t i n g t h e r e p r o d u c i b i l i t y o f t h e r e s u l t s . I t can be s e e n , however, t h a t the p o i n t s l i e f a i r l y w e l l on a s t r a i g h t l i n e , i n d i c a t i n g ( t h o u g h o f c o u r s e n o t p r o v i n g c o n c l u s i v e l y ) t h a t t h e mechanism i n v o l v e d i s one o f p u r e m o l e c u l a r d i f f u s i o n . S e l e c t i n g any c o n v e n i e n t p o i n t on t h e c u r v e o f F i g u r e 7 t h e n : E = 0,40 From F i g u r e 2; E » 0.40 g c .*. D - 0.886 x (|) x (J^ x = 4.25 x 1 0 ~ 5 f t 2 p e r h o u r . ' .y ' ' . T h i s t h e n , i s t h e v a l u e o f t h e d i f f u s i o n c o e f f i c i e n t f o r the t a r - s a n d i n c a r b o n t e t r a c h l o r i d e a t 25°C« when e = 3 9 5 w h e n 21 = 0.286 R V - CONCLUSIONS On t h e b a s i s o f t h e s e r u n s , i t i s h e l d p r o b a b l e t h a t t h e e x t r a c t i o n o f A t h a b a s c a t a r - s a n d i n c a r b o n t e t r a c h l o r i d e p r o c e e d s by m o l e c u l a r d i f f u s i o n and f o l l o w s t h e t h e o r e t i c a l e x t r a c t i o n c u r v e of F i g u r e 2. I t would be d e s i r a b l e t o r e p e a t t h e r u n s , u s i n g o t h e r s o l v e n t s ( s a y c a r b o n d i s u l p h i d e and 16 b e n z e n e ) . More a c c u r a t e r e s u l t s c o u l d d o u b t l e s s be o b t a i n e d o r w i t h an e x t r a c t i s a a . s i m i l a r t o t h a t o f B o u c h e r , B r i e r and 1 O s b o r n , w h e r e i n t h e s o l v e n t f l o w s c o n t i n u o u s l y p a s t t h e s u r f a c e o f t h e m a t e r i a l . 1. B o u c h e r , A.F., B r i e r , J . G . & O s b o r n , J.O, T.A.I,Oh.1. , 38, 967-991 (1942) N o m e n c l a t u r e x, y & z « r e c t a n g u l a r c o o r d i n a t e s . o = = s u r f a c e ( s q . f t • ) =» t i m e , ( h o u r s ) A f D R = d e n s i t y , ( l b s . / f t ) = s p e c i f i c h e a t fBTU/lb./deg.F.) = t h e r m a l c o n d u c t i v i t y (BTU/sq. f t/h o u r / d e g . F . ) o 1-C l = e L = d i f f u s i o n c o e f f . ( s q . f t / h o u r ) E = h a l f t h i c k n e s s o f p l a t e . c o n c e n t r a t i o n ( l b s / f t )\ " a t t i m e e w a t e q u i l -i b r i u m = i n i t i a l c o n c e n t r a t i o n = b a s e o f n a t u r a l l o g s = a d i s t a n c e , ^ f eet) = t e m p e r a t u r e , (0F,) = f r a c t i o n o f e x t r a c t -a b l e o i l l e f t un-e x t r a c t e d . LITERATURE CITED B a r r e r , R.M. , " D i f f u s i o n I n And Through S o l i d s " -Cambridge & M c M i l l a n (1941) B o u c h e r , D.F., B r i e r , J . C & O s b o r n , J.O. , T r a n s . A . I . C h . E . 38, 967 - 991 (1942) Cady, L.C. , & W i l l i a m s , J.W. , J . P h y s . Chem. , 39, 87-102(1935) F r i e d m a n , L. , J . C C S . , 52, 1305-10, (1930) F r i e d m a n , L., & Kra m e r , E.O., I b i d . , 52, 1295 - 1304 (1930) K i n g , C O . , K a t z , D.L., & B r i e r , J.C. , T.A. I.Ch.E. , 40, 533-556 (1944) K r i e b l e , V.K. , & S e y e r , W.F., I.A.O.S., V o l . X V I I I (1921) M a r c h , H., & Weaver, W., P h y s i c a l R e v i e w , 3 1 , 1072-1081, (1928) Newman, A.B., T.A.I.Ch.E., 27, 310-333, (1931) O s b o r n , J.O., & K a t z , D.L., T.A.I.Ch.E., 40, 511-531 (1944) Sherwood, T.K., I n d . Eng. Chem., 2 1 , 12-16 (1929) i T u t t l e , F . J . , J o u r n a l F r a n k l i n I n s t . , 200, 609-614 (1925) W a l k e r , L e w i s , McAdams & G i l l i l a n d - " P r i n c i p l e s o f C h e m i c a l E n g i n e e r i n g " , p. 424, McGraw H i l l Co. ( 1 9 3 7 ) . 

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