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Liquid diffusion in porous media, with specific reference to the Athabasca tar sands Haliburton, James 1947

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LIQUID DIFFUSION IN POROUS MEDIA, WITH SPECIFIC REFERENCE TO THE ATHABASCA TAR SANDS by James H a l i b u r t o n , B.Sc. A Thesis submitted i n P a r t i a l F u l f i l l m e n t o f The Requirements f o r the Degree of MASTER OF APPLIED SCIENCE i n the 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 May, 1947. The research h e r e i n described was c a r r i e d out under the d i r e c t i o n of Dr. W. F . Seyer, P r o f e s s o r o f Chemical Engineering, at the U n i v e r s i t y of B r i t i s h Columbia dur i n g the p e r i o d September 1946 to May 1947. James H a l i b u r t o n , B.Sc. May, 1947. CONTENTS I I n t r o d u c t i o n 1 I I Theory of D i f f u s i o n 1 General 1 T a b l e l . . . . . . 2 Mathematical A n a l y s i s 3 Table 2 < 6 F i g u r e 1 f a c i n g 5 Figure 2 f a c i n g 6 I I I Previous Work by other I n v e s t i g a t o r s 6 IV The Athabasca Tar Sands 8 Composition« 8 Products , 8 E x t r a c t i o n of Bitumen . . 9 V Experimental Procedure 10 General 10 F i g u r e 3 f a e i n g 10 "Diffusion C e l l 10 . Figure 4 f a c i n g 10 P r e p a r a t i o n of C e l l 10 D i f f u s i o n Bath 11 D i f f u s i o n and E x t r a c t i o n Procedure 11 ABSTRACT The v e l o o i t y of d i f f u s i o n of the bitumin from s e c t i o n s of 'Tar Sands' has been measured i n a s p e o i a l l y designed d i f f u s i o n c e l l . The solvent used i n t h i s oase was benzene* The d i f f u s i o n constant was found to be D - 2.39 x 10-^/ f t 2 / h r . Page O r i g i n a l Method of A n a l y s i s f o r Tar C o n t e n t . . 12 Figure 5 fa.cj.ng 12 F i n a l Method of A n a l y s i s f o r Tar Content 13 VI Experimental Data and Treatment 13 Table 3 14 Figure 6 f a c i n g 15 Figure 7 m f a c i n g 15 VII Conclusions 15 Nomenclature 16 B i b l i o g r a p h y 17 LIQUID DIFFUSION Ig POROUS MEDIA  WITH SPECIFIC REFERENCE TO THE  ATHABASCA TAB SANDS \ N I - INTRODUCTION In chemical engineering a l a r g e number of u n i t pro-cesses depend on the d i f f u s i o n of m a t e r i a l through f l u i d f i l m s . Some of these operations are d r y i n g , r e c t i f i c a t i o n , gas absorp-t i o n , e x t r a c t i o n , and c r y s t a l l i z a t i o n . This t h e s i s w i l l d i s -cuss the t h e o r e t i c a l b a s i s of d i f f u s i o n w i t h s p e c i a l reference to d i f f u s i o n through a porous body; i t w i l l mention p r e v i o t s work based on t h i s theory; and i t w i l l endeavour to f i t i n t o t h i s theory data obtained by experimental methods from the solvent e x t r a c t i o n of bitumen from the Tar Sands of the Atha-basca region o f northern A l b e r t a . I I - THEORY OF DIFFUSION General The operation of d i f f u s i o n i n v o l v e s the t r a n s f e r of m a t e r i a l t h r o u g h . f l u i d f i l m s from one phase to another. The many operations which make use of the general p r i n c i p l e s of 1 d i f f u s i o n are c l a s s i f i e d f o r study as i n the f o l l o w i n g t a b l e which c o r r e l a t e s the phase contacted and the c o n t a c t i n g phase i n the nine p o s s i b l e cases obtained from the three s t a t e s of 2 matter - gas, l i q u i d , and s o l i d . e Ho. Phase Contacted TABLE Contacting Phase 1 Example 1 Gas Gas Hone; gases are completely m i s c i b l e 2 Gas L i q u i d Absorption, butane by petroleum solv e n t s 3 Gas S o l i d Adsorption, gas r e s p i r a t o r s 4. L i q u i d Gas Steam s t r i p p i n g 5 6 L i q u i d L i q u i d L i q u i d S o l i d E x t r a c t i o n , petroleum with H SO 2 4 P e r c o l a t i o n d e c o l o r i z i n g of sugar s o l u t i o n 7 S o l i d Gas Drying of wood or b r i c k by hot a i r 8 S o l i d L i q u i d Leaching of sugar beets 9 S o l i d S o l i d Hone; t r a n s f e r r a t e s are slow This paper i s p r i n c i p a l l y i n t e r e s t e d i n case eight i n which a s o l i d phase i s treated w i t h a l i q i i d phase. In the d i s t r i b u t i o n of a substance between two mater-i a l s a d i s t r i b u t i o n e q u i l i b r i u m i s set up. In the case o f a porous s o l i d impregnated w i t h a s o l u t i o n which i s being removed by a l e s s concentrated e x t e r n a l surrounding s o l u t i o n the i n t e r -n a l s o l u t i o n w i l l come to an e q u i l i b r i u m w i t h the e x t e r n a l s o l u t i o n . This f a c t o r s e t s the l i m i t on the qua n t i t y of e x t e r -n a l s o l u t i o n r e q u i r e d f o r the e x t r a c t i o n process. The time element i s another important f a c t o r . The ra t e of t r a n s f e r of m a t e r i a l w i l l be p r o p o r t i o n a l to the surface of contact between the phases. There are two main mechanisms of t r a n s f e r ; one i s a c t u a l hulk motion (convection) and the other i s true molecular d i f f u s i o n as a r e s u l t of c o n c e n t r a t i o n g r a d i e n t . These two mechanisms operate simultaneously; t r a n s f e r "by molecular d i f -f u s i o n goes on through the f i l m from the i n t e r f a c e while con-v e c t i o n goes on i n the main body. I t i s g e n e r a l l y assumed t h a t phases i n contact are at e q u i l i b r i u m at the i n t e r f a c e although there i s only l i m i t e d data f o r t h i s assumption i n the i n t e r a c t i o n of s o l i d s and l i q u i d s . This paper w i l l show some evidence that the p r i n c i p l e mechanism of t r a n s f e r between s o l i d and l i q u i d i s molecular d i f f u s i o n c o n t r o l l e d by the d i f f e r e n c e i n c o n c e n t r a t i o n of the s o l u t e i n the l i q u i d at the i n t e r f a c e and the s o l u t e i n the porous s o l i d . Surface f i l m r e s i s t a n c e i s assumed s m a l l and i s neglected. 3 Mathematical A n a l y s i s The general theory of d i f f u s i o n i s based upon analogy to the flow of heat through s o l i d media, as i s e x e m p l i f i e d i n the c l a s s i c a l treatments o f F o u r i e r and a l s o of Lord K e l v i n i n the Encyclopedia, There are two s t a t e s of flow by d i f f u s i o n - the s t a t i o n a r y and the n o n - s t a t i o n a r y s t a t e s . This a n a l y s i s w i l l be based on non-stationary, u n i d i r e c t i o n a l d i f f u s i o n i n a s l a b of thickness 2R. C e r t a i n d e f i n i t e p h y s i c a l c o n d i t i o n s p e r t a i n i n g to the porous s o l i d under d i s c u s s i o n w i l l be assumed. In a c t u a l p r a c t i c e these c o n d i t i o i s w i l l be maintained as f a r as p o s s i b l e 4 w i t h i n the hounds of experiment. The co n d i t i o n s are as f o l l o w s : 1. D i f f u s i o n , takes place through "both faces and along one a x i s only. 2. The thickness of the s o l i d i s uniform. 3. There i s a uniform c o n c e n t r a t i o n of s o l u t e i n the s o l i d at the beginning of the experiment. 4. The solvent i s maintained at constant concen-t r a t i o n throughout the experiment. 5 . The d i f f u s i o n c o e f f i c i e n t i s constant. 6. The temperature i s constant. 7. The t r a n s f e r of m a t e r i a l at the surf a c e of the s o l i d i s s u f f i c i e n t l y r a p i d not to i n t e r f e r e w i t h the i n t e r n a l d i f f u s i o n process. 8. The porous s o l i d i s r i g i d and i n e r t . The mathematical conditions f o r d i f f u s i o n w i t h i n p a r a l l e l boundaries a r e : . . ( i i ) a t t = 0 , C = f ( x ) f o r 0 ^ x ^ 2 R • ( i i i ) 0=0 a t x = 0 and. x=2R f o r a l l t . Co n d i t i o n ( i ) i s the d i f f e r e n t i a l form of F i c k ' s law of d i f f u s i o n . D i s the d i f f u s i o n c o e f f i c i e n t whose dimensions are area, and i s a constant f o r a s p e c i f i e d system f o r a constant time set o f c o n d i t i o n s . 5 The s o l u t i o n under these c o n d i t i o n s f o r the amount of s o l u t e l e f t i n a porous s o l i d a t any time t i s TT Jo ZR L +K* J Equation 1 Upon i n t e g r a t i o n t h i s g i ves -irz ( 2 m v i > * f 4»?« J Equation 2 The corresponding equation f o r the amount of s o l u t e removed • i n any time t i s L TT» r l J ] E q u a t i o n 3 The f r a c t i o n E of the e x t r a c t a b l e s o l u t e l e f t unextracted a t any time t i s ZRAGi JP I 4*?* J . Equation 4 This equation may he expanded i n t o the r a p i d l y converging s e r i e s TT^L 4^R*/ * I / 2S" 1 / J Equation 5 4 Sherwood has solved Equation 5 f o r a number of values of the dimensionless q u a n t i t y JD£ which are presented i n Table 2 and p l o t t e d on semi-log paper as Figure 1. The curve so represented i s a s t r a i g h t l i n e except f o r values of E above 0 .7. i TABLE 2 E E 0.000 1.000 0.200 0.496 0.005 0.909 0.300 0.387 0.010 0.885 0.500 0.237 0.025 0.822 0.600 0.184 0.050 0.748 0.700 0.144 0.100 0.642 1.000 0.069 0.150 0.564 Equation 5 i s r e p l o t t e d as Figure 2 according to a 5 scal e suggested by Sherwood whereby the s c a l e of E i s com-pressed so as to s t r a i g h t e n out the curved p o r t i o n . A c c o r d i n g l y any e x t r a c t i o n data f a l l i n g on a s t r a i g h t l i n e on Sherwood's s p e c i a l paper shows that the mechanism of t r a n s f e r i s molecular d i f f u s i o n f o l l o w i n g as i t does F i e k ' s law of d i f f u s i o n w i t h i n p a r a l l e l boundaries f o r s p e c i f i e d c o n d i t i o n s . I l l - PREVIOUS WORK BY OTHER INVESTIGATORS The i n v e s t i g a t i o n of d i f f u s i o n i n Athabasca Tar Sands 6 has been s t u d i e d by Hopper who found the value of ttie d i f f u s i o n c o e f f i c i e n t f o r the tar-sand i n carbon t e t r a c h l o r i d e to be -5 2 Q 4.25 x 10 f t . per hour at 25 C. A t h e o r e t i c a l study of the mechanism of d i f f u s i o n 7 has been c a r r i e d out by March and Weaver who derived an equation f o r the d i f f u s i o n of a n o n - e l e c t r o l y t e out of a porous mass based on an i n t e g r a t i o n of F i c k ' s law equation, and presented data on the 1 d i f f u s i o n of area from a g e l s t r u c t u r e i n t o a l a y e r 7 « 8 of water. Barrer has presented a monograph on d i f f u s i o n "both from a t h e o r e t i c a l and an experimental viewpoint which has a l -ready been made use of i n t h i s paper. 9 Uewman has app l i e d the theory of d i f f u s i o n to the 10 11 drying of s.olids. T u t t l e and Sherwood a p p l i e d the d i f f u s i o n theory to the drying of wood. A s p e c i a l f e a t u r e of Sherwood's d i s c u s s i o n i s the i n t r o d u c t i o n of a p l o t t i n g paper used to compare experimental data with t h e o r e t i c a l curves. IE 13,14 Friedman and Kraemer and Friedman i n v e s t i g a t e d the s t r u c t u r e of gels by measuring the r a t e of d i f f u s i o n of s o l u -t i o n s of n o n - e l e c t r o l y t e s i n t o and out of the g e l s , and showed that the movement of the n o n - e l e c t r o l y t e s was a proeess of pure d i f f u s i o n governed by the laws of molecular d i f f u s i o n . 15,16 Cady and W i l l i a m s extended the theory of molecular d i f f u s i o n i n t o a g e l to d i f f u s i o n i n t o a porous s o l i d such as wood. In the f i e l d of e x t r a c t i o n Boucher, B r i e r , and 17 Oshurn c a r r i e d out experimental work on semi-batch and continu-ous counter-current e x t r a c t i o n of porous p l a t e s s aturated w i t h soybean o i l . The e x t r a c t i o n , u s i n g as solv e n t s p e r c h l o r e t h y -lene and a carbon t e t r a c h l o r i d e - e t h y l e n e d i c h l o r i d e mixture was found to be one o f pure molecular d i f f u s i o n . Osburn and 18 Katz expanded the d i f f u s i o n theory of sol v e n t e x t r a c t i o n from i a porous s o l i d to include the s t r u c t u r e of the s o l i d , and proved that the comparison of e x t r a c t i o n data f o r d i f f e r e n t m a t e r i a l s can be made only when d e t a i l s of the s t r u c t u r e of 19 the s o l i d s are compared. King, Katz, and B r i e r confirmed the a p p l i c a t i o n of the theory of molecular d i f f u s i o n to the e x t r a c t i o n of o i l from a uniform, porous, inorganic s o l i d , but found that the theory d i d not conform f o r the e x t r a c t i o n of o i l from soybean f l a k e s . The s t r u c t u r e of the soybean f l a k e s was considered as the cause of .the divergence from theory. IV - THE ATHABASCA TAR SAJSTDB Composition One of the world's l a r g e s t reserves of bituminous m a t e r i a l s i s the Athabasca Tar Sands of northern A l b e r t a . Tar-£0 sands are c o l l o i d a l systems of bitumen (which i t s e l f i s a c o l l o i d a l s o l u t i o n of asphalt i n hydrocarbon o i l s ) , water, and 21 mineral matter. A breakdown of the sands r e v e a l s that the sandstone texture ranges from coarse to f i n e s i l t 80$ of which w i l l pass through a 150 mesh screen. The bitumen content ranges from 8 t o 20$, averaging 15 to 18%. An average sample i s as f o l l o w s : bitumen s o l u b l e i n CS g - 18.5%, sand - 80.2%, water -1.3%, S.G. - 1.75 at 25°C/25°C. The bitumen i s a heavy, dark brown, vis c o u s o i l , S.G. - 1.010 to 1.035 at 25°C/25°C, with a sulphur content of 4.5 to 5%. A f u r t h e r d e s c r i p t i o n of the b i -22 tumen by K r i e b l e and Seyer represents the bitumen as of a type between the T r i n i d a d and Bermudez asphalts w i t h respect to i t s resinous and o i l y c o n s t i t u e n t s , and completely soluble i n car-bon d i s u l p h i d e and carbon 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. Produe ts 23 The work of the F u e l Testing D i v i s i o n o f the Canadian 9 Department of Mines has shown that the crude bitumen can be t r e a t e d by e i t h e r the Dubbs or Cross process - the l a t t e r y i e l d i n g as h i g h as 40% by volume of gasoline w i t h 2Q% f u e l o i l and 32% coke. Hydrogenation t e s t s show an extremely high y i e l d of g a s o l i n e . The r e f i n e d asphalt i s s a t i s f a c t o r y and t e s t s show that the o x i d i z e d p i t c h can serve as a b r i q u e t binder. E x t r a c t i o n o f Bitumen The s e p a r a t i o n of the bitumen from the sand i s a problem i n c o l l o i d a l chemistry-. U n t i l the summer of 1945 when i t was destroyed by f i r e , a p l a n t operated at Fort McMurray followed the procedure of open-pit mining o f the tar-sand, separation of the bitumen from the sand by a g i t a t i o n w i t h hot water, and subsequent c r a c k i n g f o r gasoline and r e s i d u a l pro-24 ducts. This type of separation has been described by Knight, 25 26,27,28,29 Clar k and Pasternack, and C l a r k . The p r i n c i p a l problem to the open-pit mining of tar-sand i s one of sand han d l i n g and d i s p o s a l . Another p o s s i b l e method of s e p a r a t i o n i s e x t r a c t i o n in. s i t u as i n the o i l - f i e l d water d r i v e , the Frasch process f o r sulphur, and i n the p r o d u c t i o n of common s a l t from brine 30 w e l l s . E l l s has i n v e s t i g a t e d a method of e x t r a c t i o n i n s i t u u s ing steam although a patent on t h i s process had been f i l e d 31 as e a r l y as September, 1927, by J. J.Rimmer. With the use of more v o l a t i l e s o l v e n t s , i n order to prevent e x c e s s i v e l o s s , the greatest c o n s i d e r a t i o n would be the g e o l o g i c a l formations to be tapped. A comprehensive treatment of the f l o w of C££-C 32 homogeneous f l u i d s through porous media by Muskat pays con-s i d e r a b l e a t t e n t i o n to t h i s p o i n t . ¥ - EXPERIMENTAL PROCEDURE General In c a r r y i n g out the experimental work on t h i s pro-j e c t frequent reference was made to the previous work of 33 Hopper. The experimental setup as diagrammatically shown i n Figure 4 f o l l o w s his p a t t e r n , and at h i s s u g g e s t i o n benzene was used as the solvent i n the e x t r a c t i o n of the tar-sands. D i f f u s i o n C e l l The c e l l ( F i g u r e 3)^was a simple p a r a l l e l p i p e d of cast aluminium constructed to g i v e a c y l i n d e r of tar-sand w i t h the ends exposed f o r d i f f u s i o n , as r e q u i r e d to f o l l o w the preceding d i f f u s i o n theory. The end exposure was e f f e c t e d by u s i n g a fine-mesh, removeable screen over the ends which h e l d the sand i n place while p e r m i t t i n g contact w i t h the s o l -vent. The bare r i n g s and the screened r i n g s used were machined from duraluminum. P r e p a r a t i o n of foe C e l l The c e l l was l a i d f l a t on a sm a l l piece of s t e e l p l a t e w i t h a set of bare r i n g s i n place, and a one i n c h l e n g t h of l£ inch pipe placed on top. Warm tar-sand was tamped i n t o the c e l l u n t i l the l e v e l was up i n the pipe when a one inch l e n g t h of l o o s e l y f i t t i n g round stock was pl a c e d on top of the i tar-sand. The whole was placed i n a v i s e , tightened up, and 11 l e f t f o r 5 or 6 hours. A f t e r removing the c e l l from the v i s e the pipe was taken o f f , and the excess tar-sand cut o f f f l u s h w i t h the outside face of the c e l l . The hare r i n g s were removed, the screened r i n g s put i n place, and the c e l l and tar-sand weighed. From the known weight of the empty c e l l the weight of the t a r -sand contained was obtained by s u b t r a c t i o n . d i f f u s i o n Bath • This bath was simply a one l i t r e beaker suspended i n the constant temperature water-bath so that the l e v e l of the l i q u i d i n the two baths was • the same. The solvent i n the bath was kept b a r e l y i n motion by a slow-moving p r o p e l l o r so that there was no impact of the solvent a g a i n s t the face of the tar-sand yet the t r a n s f e r of m a t e r i a l away from the s u r -face was s u f f i c i e n t l y r a p i d not to i n t e r f e r e w i t h the i n t e r n a l d i f f u s i o n process. The temperature o f the d i f f u s i o n bath was o • o maintained at 25 CT0.10 D i f f u s i o n and E x t r a c t i o n Procedure The. loaded c a l l was placed c e n t r a l l y i n the d i f f u s i o n bath and held there by a wire brace so that no motion o f the c e l l was permitted. A c t i v e d i f f u s i o n was timed from the moment of i n s e r t i o n of the c e l l u n t i l the removal of the c e l l at the end of the run. A f t e r removing the c e l l from the bath the p a r t i a l l y e x t r a c t e d tar-sand was put i n a tared paper Soxh-let thimble and extracted completely w i t h clean s o l v e n t . The s o l u t i o n 12 r e s u l t i n g from the Soxhlet e x t r a c t i o n was weighed i n a tared container and analysed f o r t a r content. S i m i l a r l y the s o l u t i o n from the c o n t r o l l e d d i f f u s i o n was analysed to get the weight of t a r extracted from the sample. The Soxhlet thimble c o n t a i n i n g the extracted sand o was oven-dried at 110 C f o r at l e a s t two hours, cooled i n a d e s s i c a t o r , and weighed q u i c k l y to avoid moisture pickup. Since the s o l v e n t used does not d i s s o l v e a l l the 34 t a r a f u r t h e r Soxhlet e x t r a c t i o n u s i n g carbon t e t r a c h l o r i d e was c a r r i e d out, the thimble again d r i e d and weighed to give the amount o f sand i n the o r i g i n a l sample. O r i g i n a l Method of A n a l y s i s f o r Tar Content In l o o k i n g f o r a method of a n a l y s i s the method of 35 Hopper was discarded because of the closeness o f the s p e c i f i c g r a v i t i e s of the t a r and the o benzene. I t was decided that an electrophotometer would be used to measure the amount of l i g h t t ransmitted by s o l u t i o n s of various compositions. Stan-dard s o l u t i o n s of known composition o f tar and benzene were made up, and the amount o f l i g h t p e n e t r a t i n g each noted as a reading on the electrophotometer. The readings were p l o t t e d against percent t a r as i n Figure 5. The curve i n Figure 5 was used to analyse a number of samples obtained on t e s t runs but f a i l e d to give the c o r r e c t composition. The flaw i n the a n a l y s i s was traced to the f a c t that the t a r used to make up the o r i g i n a l standard s o l u t i o n s was obtained by complete e x t r a c t i o n of a sample of tar-sand. 13 However, benzene, when e x t r a c t i n g t a r by d i f f u s i o n on a time b a s i s , f i r s t e x t r a c t s the o i l y components, then the r e s i n s , and f i n a l l y the asphaltenes. Consequently the curve obtained f o r a mixture of a l l the components of the t a r was not c o r r e c t when a p p l i e d to a s o l u t i o n obtained by s e l e c t i v e e x t r a c t i o n . Because of the d i f f i c u l t y of making up a composite curve the electrophotometric method of a n a l y s i s was discarded i n favour of a simpler one. F i n a l Method of A n a l y s i s f o r Tar Content An a l i q u o t of the s o l u t i o n to be analysed was weighed i n a tared f l a s k , and the solvent removed by d i s t i l l a t i o n over a water bath under a water pump vacuum. When a l l the solvent had been evaporated the f l a s k was again weighed to get the weight of t a r i n the a l i q u o t . From t h i s the a c t u a l weight of t t a r i n the s o l u t i o n was c a l c u l a t e d . 71 - EXPERIMENTAL DATA AMD TREATMENT The f o l l o w i n g t a b l e gives a summary of the data ob-tained i n the e x t r a c t i o n of a number of samples from the Athabasca Tar Sands. 14 TABLE 4 E x t r a c t a b l e 1'ar "E" Run Wt. of Wt. of Wt. of % Tar ex- Tar not F r a c t i o n No. Sample Sand Tar Tar t r a c t e d ex$. not e x t . Time 1 30.933g 25.647g 5.286g 17.1 1.020g 4.161g 0.603 60 i 2 29.951 25.354 4.597 15.7 1.221 3.223 0.726 120 3 31.751 26.001 5.750 18.1 1.712 . 3.698 0.684 180 4 30.183 25.127 5.056 16.7 1.812 2.941 0.619 240 5 30.526 25.335 5.191 17.0 1.823 2.649 0.593 300 6 30.651 25.537 5.114 16.7 1.970 2.746 0.583 360 7 30.074 25.494 4.580 15.2 2.143 2.442 0.532 420 8 30.119 25.386 4.733 15.7 2.334 2.460 0.513 480 9 30.229 25.409 4.820 16.0 2.390 2.150 0.473 540 10 31^276 25.837 5.439 17.4 3.110 2.408 0.437 600 11 30.558 25.576 4.982 16.3 2.784 1.703 0.380 660 12 30.169 25.423 4.746 15*8 3.201 1.535 0.325 720 13 30.342 25.462 4.880 16.1 3.472 1.265 0.267 780 14 30.061 25.176 4.885 16.3 3.478 1.241 0.263 840 16.4$ Average The f r a c t i o n of e x t r a c t a b l e tar not extracted was c a l c u l a t e d as n e a r l y as pos s i b l e on the basi s of the amount of t a r which a s u i t a b l y l a r g e amount of the sol v e n t benzene could remove over an i n f i n i t e l y l o n g period of time, and without regard f o r the e q u i l i b r i u m value o f e x t r a c t a b l e t a r which would be of n e g l i g i b l e dimensions i n any case. 15 The f r a c t i o n of e x t r a c t a b l e t a r unextracted was 36 p l o t t e d against time i n Figure 6. Following Sherwood the f r a c t i o n E was again p l o t t e d against time on semilog paper using the compressed s c a l e f o r E as i n Figure 7. • The r e s u l t i n g curve c l o s e l y approaches a s t r a i g h t l i n e d e v i a t i n g only at the upper l i m i t of time. The d e v i a t i o n might be explained as a consequence of the departure from the o r i g i n a l p h y s i c a l conditions f o r tru e d i f f u s i o n which would occur as the t a r con c e n t r a t i o n of the so l v e n t increases w i t h elapsed time. According to the d i f f u s i o n theory which has been pre-sented the data obtained i n d i c a t e s t h a t the mechanism in v o l v e d i n the e x t r a c t i o n of tar-sand by benzene i s one of true mole-c u l a r d i f f u s i o n . From Figure 7 choose E •• 0.5 f o r which t » 477 mih. From Figure 2 E =0.5 gives - 0.195 R = 3/8 inch 2 ( 2 x U " -5 2 D = 0.195 x(8 12) x 60 r 2.39 x 10 f t per hour. 177 This i s the value of the d i f f u s i o n c o e f f i c i e n t at 25°C far the e x t r a c t i o n of bitumen from Athabasca Tar Sands u s i n g benzene as a s o l v e n t . 711 - CONCLUSIONS The data which has been presented serves t o i n d i c a t e that the e x t r a c t i o n of the bitumen from, the Athabasca Tar Sands involves the mechanism of t r u e molecular d i f f u s i o n f o l l o w i n g as V 16 i t does so c l o s e l y the t h e o r e t i c a l curve of Figure 2. NOMENCLATURE x, y, z - re c t a n g u l a r coordinates A - surface area i n square f e e t t - time i n hours D - d i f f u s i o n c o e f f i c i e n t i n square f e e t per hour R - h a l f thickness of slab i n f e e t C - concentration i n pounds per cubic f o o t at any time t Co - concentration i n pounds per cubic foot at time t * 0 Ql - weight i n pounds of s o l u t e l e f t i n porous s o l i d at any time t Qg - weight i n pounds of solute removed at any time t • E - f r a c t i o n o f e x t r a c t a b l e s o l u t e l e f t unextracted at any time t BIBLIOGRAPHY 1. Walker, Lewis, McAdam, and G i l l i l a n d - " P r i n c i p l e s of Chemical Engineering", p.424 McGraw-Hill (1937) 2. Hopper, D.A. - Master's Thesis - " L i q u i d D i f f u s i o n i n Porous Media, R e f e r r i n g i n P a r t i c u l a r to the Athabasca Tar Sands", (1945) 3. Bar r e r , R.M., " D i f f u s i o n In and Through S o l i d s " , pp. i x , x i , 13, 17, Cambridge U n i v e r s i t y Press (1941) 4 . Sherwood, T.K., Ind. and Eng. Chem., 21, 12-16, (1929) 5. Sherwood, T.K., i b i d . 6. Hopper, D.A., Loc. s i t . 7. March, H., and Weaver, 1., Phys. Rev., 31, 1072-1081 (1928) 8. Ba r r e r , R.M., Loc. s i t . 9. lawman, A.B., T.A.I.Ch.l., 27, 310-333 (1933) 10. Tut t i e , F.J., J . F r a n k l i n I n s t . , 200, 609-614 (1925) 11. Sherwood, T.K., Loc. s i t . 12. Friedman, L., and Kraemer, E.O., J.A.C.S., 52, 1295-1304 (1930) 13. Friedman, L., I b i d . , 52, 1305-1310 (1930) 14. Friedman, L., I b i d . , 52, 1311-1314 (1930) 15. Cady, L . C , and W i l l i a m s , J . ! . , Chem. Rev., 14, 171-217 (1934) 16. Cady, L.C. and Wi l l i a m s , J.W., J. Phys. Chem., 39, 87-102 (1935) 17. Boucher, D.F., B r i e r , J.C., and Osbum, J.O., T.A.I.Ch.E., 38, 967-991 (1942) 18. Osburn, J.O., and Ea t z , D.L., T.A.I.Ch.E., 40, 511-531 (1944) 19. King, CO., Katz, D.L. and B r i e r , J.C., T.A.I.Ch. E., 40, 533-556 (19 44) 20. Clark, K.A., Can. Min. and Met. B u l l e t i n , 212, 1385-1395 (1930) 21. E g l o f f , C , md M o r r e l l , J . C , T.A.I.Ch.E,, 18, 347-357 (1926) 22. E r i e b l e , V.E., and Seyer, , J.A.C.S., 43, 1337-1349, (1921) 23. E l l s , S.C., Mining Mag., 54 , 329-341 (1936) 24. Knight, C.. Can. Patent O f f i c e Record, 278,861; 278,862. (1928) 25. Cl a r k , K.A., and Pasternack, I>.S. , Ind. and Eng. Chem., 24, 1410-1416 (1932) 26. Clark, E.A., Can. Min. and Met. B u l l e t i n , 212, 1385-1395 (1930) 27. Cl a r k , E.A., Nature, 127, 199 (1931) 28. Clark, K.A., Nat. Petroleum News, 27, 3032-3036 (1935) 29. Clark, K.A., T. Can. I n s t , of Min. and Met., 47, 257-274 (1940) 30. E l l s , S.C., Can. Dept. of Mines,. Report 719, 28-42 (1930) 31. Rimmer, J. J., Can. Patent O f f i c e Record, 278,618 (1928) 32. Muskat, M., "The Plow of Homogeneous F l u i d s Through Porous Media", McGraw-Hill (1937 ) 33. Hopper, D.A., I>oc. s i t . 34. E r i e b l e , V.K., and Seyer, W.P., Loc. s i t . 35. Hopper, D.A., Loc. s i t , p. 11 36. Sherwood, T.K., Loc. s i t . 

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