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Flow of fluids in porous media with reference to Athabasca tar sands Wood, Norman Mouat 1949

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PLOW OP FLUIDS IN POROUS MEDIA w i t h r e f e r e n c e t o the ATHABASCA TAR SANDS 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 S c ience i n the Department of Chemical E n g i n e e r i n g by Norman Mouat Wood U n i v e r s i t y of B r i t i s h Columbia October, 1949. ABSTRACT A study of the flow of f luids in porous media has been made. The porosity and permeability of a sample of Athabasca Tar Sand have been measured. The screen analyses of a representative series of samples have been interpreted on the basis of the Internal erosion of the sand mass. ACKNOWLEDGEMENT author wishes t o thank Dr. W. P. Seyer f o r h i s h e l p and suggestions i n t h i s work. CONTENTS Page Introduction 1 Permeability of Unconsolidated Porous Media Experimental 3 Apparatus 5 Procedure 7 Results 8 Porosity of Unconsolidated Porous Media Experimental 8 Apparatus 9 Procedure 9 Results 11 Application of Screen Analyses Introduction 12 Screen Analyses 12 Contour Map 28 Conclusion 28 FIGURES Page 1 . Permeability Apparatus 6 2 . Porosity Apparatus 1 0 3 . Screen Analyses of Sea Sand and River Sand 1 ^ *K Screen Analysis of Tar Sand 18 5-10.Screen Analyses of Tar Sand 19-24-1 1 . Location of Screen Analyses 25 1 2 . Contour Map 26 1 3 . Cross-section of Tar Sand Area 27 TABLES 1 . Abridged Analyses of S. C. E l l s 1 6 2 . Most Probable Sizes L i s t e d 17 1. THE PLOW OP FLUIDS IN POROUS MEDIA with part icular reference to the ATHABASCA TAR SANDS. Introduction The Athabasca Tar Sands which underly an area of a thousand square miles i n a f a i r l y continuous bed of approxi-mately 100 feet in thickness, are considered one of the larg-est reserves of petroleum hydrocarbons i n the world. Numerous attempts have been made and are being made to extract the bitumen from the sand i n a commercially feasible operation. I t i s the purpose of this thesis to deal with the flow of the or iginal o i l , which now forms the bitumen content of the sands, into the clean sands. These clean sands were thought to have been l a i d down during the period of submersion i n the great sea way that engulfed the centre of this continent. Dr, Seyer has suggested that the or ig inal o i l might have flowed up through the clean sands from the underlying stratum after 2. a rupture had occurred i n the rock. The o i l apparently flowed out from the central or igin horizontally and r ad i a l ly , and i n so doing, scoured fine part icles from the sand near the or igin and deposited these fines at the extremities of the o i l flow. A size gradient could thus have been formed which should give an Indication of the direct ion of flow. The evaporation of the l i g h t fractions from the o i l caused the bitumen to become increasingly viscous u n t i l a l l flow became impossible. I t i s the bel ief of the writer that a study of the internal erosion of the sand mass can provide valuable information i n determining the location of the or iginal o i l pool. The f i r s t two sections of this thesis w i l l deal with the permeability and the porosity of porous media. No study w i l l be made of consolidated media since we are concerned only with loose sands of the unconsolidated type. The d i s -cussion of these properties i s largely academic. There is a description of the actual measurements and the values that were determined for a specific sample of Sand. The sample of Sand that was used for the measurements was completely ex-tracted with carbon disulphide. The f i n a l section w i l l deal with the application of screen analyses to the determination of the size gradients and the estimation of the direction of the o i l flow i n the sand bed. 3. PERMEABILITY OF UNCONSOLIDATED POROUS MEDIA  Experimental. The b a s i c p r i n c i p l e of p e r m e a b i l i t y measurements con-s i s t s of the measurement of the volume r a t e of flow of a f l u i d through d e f i n i t e c r o s s - s e c t i o n a l area, over a d e f i n i t e l e n g t h , and under a d e f i n i t e p r e s s u r e g r a d i e n t . The v a l u e "k" i s c a l c u l a t e d by the f o l l o w i n g equation: where Jr- = the p e r m e a b i l i t y i n D'arcys V- cm. per second • A y/U — v i s c o s i t y i n c e n t i p o i s e s • P - P ^ p r r - * p r e s s u r e g r a d i e n t i n atmospheres and t h e r e f o r e ^ , , . - V CP-P*.) T h i s equation i s v a l i d i f "v" i s co n s t a n t throughout the l e n g t h of the flow column. The equation h o l d s t h e r e f o r e f o r measurements where l i q u i d s are used. When compressible f l u i d s are used "v" w i l l not be constant b ut n%$- i s uniform through-out the flow column. ("^" i s the d e n s i t y of the gas). Assum-i n g t h a t the gas expands i s o t h e r m a l l y as an I d e a l gas "p2j£" can be c o n s i d e r e d uniform and where "p" i s the a r i t h m e t i c mean p r e s s u r e " + % " and Equation (1) then takes-the form: L 4. te *- P. V where "v" r e f e r s to the v e l o c i t y a t p r e s s u r e "p". S i n c e "vp" i s p r o p o r t i o n a l to the mass v e l o c i t y of the systemjaad "vp" i s the v e l o c i t y a t "p". By d e n o t i n g the volume outflow r a t e as measured a t "p" as "Q", then "k" can be w r i t t e n a s : which i s v a l i d f o r gas f l o w measurements. The experimental d e t e r m i n a t i o n of the p e r m e a b i l i t y of the unconsolidat&d porous media i s d i f f i c u l t owing to the g r e a t v a r i a t i o n i n pac k i n g t h a t can occur i n l o o s e sands. Although the e f f e c t i v g r a i n diameter of a g i v e n sand i s f a i r l y constant, the poros-i t y i s changed c o n s i d e r a b l y by v a r i a t i o n s i n packing and henc a g r e a t l y m a g n i f i e d e f f e c t on tihe p e r m e a b i l i t y r e s u l t s . T h i s e f f e c t of the p o r o s i t y on the p e r m e a b i l i t y has been s t u d i e d by S l i c h t e r (1) and Kozeny (2). S l i c h t e r s t a t e s that the v a r i a t i o n from cubic p a c k i n g to c l o s e hexagonal produces a change i n p e r m e a b i l i t y of the order of 7.5 f o l d . Kozeny, by the use of the f u n c t i o n — ! where " f " i s the a b s o l u t e p o r o s i t y , s t a t e s t h a t the v a r i a t i o n i n p e r m e a b i l i t y between the above l i m i t s of 26 to 47 per cen t p o r o s i t y i s 11.5 f o l d * 5 . I t i s f a i r l y obvious from t h i s t h a t measurements of permeabil-i t y on u n c o n s o l i d a t e d sands are of l i t t l e s i g n i f i c a n c e u n l e s s the measurements are made on u n d i s t u r b e d samples of sand. The values t h a t were ob t a i n e d f o r the p e r m e a b i l i t y o f the Atha-basca Tar Sands f a l l i n t h i s category. The samples t h a t were t e s t e d i n t h i s work were a l l d i s t u r b e d samples. The va l u e s f o r the p e r m e a b i l i t y a r e , however, probably a f a i r average s i n c e the sand was tamped as compact as p o s s i b l e b e f o r e c l o s i n g the c e l l . Apparatus. F i g u r e I i s a diagrammatic s k e t c h of a p e r m e a b i l i t y apparatus f o r u n c o n s o l i d a t e d sands. The r e s e r v o i r c o n s i s t e d o f a 5 l i t r e f l a s k c o n t a i n i n g d i s t i l l e d water which was conn-ecte d to the c e l l by a t e n f o o t l e n g t h o f neoprene t u b i n g . The p e r m e a b i l i t y c e l l was made o f Pyrex t u b i n g of 2 i n c h i n -s i d e diameter. At the o u t l e t s f o r the p r e s s u r e manometers and a t the i n l e t Pyrex stopcocks were i n s t a l l e d . The pr e s s u r e gauges were water manometers backed by a s c a l e r e a d i n g i n inc h e s . These manometers were i n s t a l l e d a t e i t h e r s i d e of the sand h o l d e r which c o n s i s t e d of two 200 mesh screens s o l d e r e d to brass f l a n g e s . The c e l l was capable of b e i n g dismantled r e a d i l y by d i s c o n n e c t i n g the f l a n g e s . The Pyrex tubing was s e a l e d i n t o s l o t s i n the f l a n g e s w i t h Dekhotinsky cement. The flow tube was s e t i n a v e r t i c a l p o s i t i o n so t h a t the e f f e c t s of c h a n n e l i n g and s e t t l i n g were minimized. I n Reservo/r Sand F/G. 1 PERMEABILIT 3 t h i s c e l l the con s t a n t s of D'arcys e q u a t i o n were: L ~ 0? cm. Procedure. A sample of completely e x t r a c t e d t a r sand was p l a c e d i n the sand h o l d e r and tamped to maximum compactness. The top of ttie c e l l was then assembled and the f l a n g e s b o l t e d s e c u r e l y together. The c e l l was then t e s t e d to see i f there were any l e a k s by p a s s i n g some water through the system. A f t e r the c e l l was found to be t i g h t the d e t e r m i n a t i o n of the permea-b i l i t y was begun. The stopcobk a t the top of the c e l l was opened, thus a l l o w i n g water to pass through the sand and c o l l e c t i n g i n the graduate. When 15 seconds had ela p s e d the stopcocks l e a d i n g to the manometers were c l o s e d i n order to get a f a i r l y average v a l u e f o r the p r e s s u r e d i f f e r e n t i a l . A t 30 seconds the flow was cut o f f . The p r e s s u r e d i f f e r e n t i a l was Jthen r e a d o f f and the amount of water i n the graduate was recorded. The temperature o f the water a t both ends of the system was recorded. S i n c e the water and the contents of the c e l l were allowed to come to thermal e q u i l i b r i u m b e f o r e the experiment, the temperatures a t e i t h e r end were v e r y c l o s e . The v a r i a b l e s i n D'arcys e q u a t i o n f o r p e r m e a b i l i t y , v i s c o s i t y , r a t e o f flow, and p r e s s u r e d i f f e r e n t i a l , were determined. 8. Experimental Results, Temp. A ( C . P . ) ft g-Pg-(atm) K (D'arcy's) Run #1 20.5 1 1 .0555 4.37 Run #2 20.5 1 1.1 .0611 4.41 Run #3 20.5 1 1.1 .611 4.41 POROSITY OF UNCONSOLIDATED POROUS M5DIA. Experimental. The percentage of a i r space i n a porous medium i s called the absolute .porosity of the medium. Variations i n packing of the grains obviously change the amount of a i r space and thus affect the porosity. Cubic packing has an a i r space of 47.64 per cent and close hexagonal packing has an a i r space of 25.95 per cent. Apart from the property of absolute porosity, there i s another property known as the "effective porosity" which for the purposes of this study i s more Important. There may be pores i n a porous medium which are not accessible to the flow of f luids owing to the complete shut off of the pores by assembled grains. The term "effect-ive porosity" Is then applied to the percentage of a i r space that i s accessible to the flow of f l u id s . I t i s quite obvious that this property i s the only one that has a direct bearing on the flow of f lu ids i n porous media. The principle of Boyfes Law was applied to measure the "effective porosity" of an ex-tracted sample of Tar Sand. 9. Apparatus. The apparatus t h a t was used i n the de t e r m i n a t i o n of p o r o s i t y was much the same as t h a t used by Torstennson and E r i k s o n (3). A few minor s i m p l i f i c a t i o n s were a p p l i e d , how-ever. F i g u r e 2 i s a diagrammatic sketch of the apparatus. E s s e n t i a l l y , i t c o n s i s t s of an arrangement to i n c r e a s e the pr e s s u r e on an enclosed volume of a i r and from the r e s u l t i n g p r e s s u r e change to c a l c u l a t e tiie new volume of the a i r . The sand c o n t a i n e r was a pyrex f l a s k which was detachable from the t u b i n g by a ground g l a s s j o i n t which p r o v i d e d a constant volume c o n n e c t i o n . An a i r o u t l e t near the sand c o n t a i n e r was pr o v i d e d to enable the p r e s s u r e to be e q u a l i z e d . The tube from the sand c o n t a i n e r was connected to a v o l u m e t r i c tube which i n t u r n was connected to a l e v e l l i n g b u lb c o n t a i n i n g mercury and a p r e s s u r e tube. A s c a l e marked i n inches was p l a c e d behind the v o l u m e t r i c tube and the p r e s s u r e tube so that the p r e s s u r e d i f f e r e n t i a l c o u l d be measured. F l e x i b l e c o u p l i n g s of p r e s s u r e t u b i n g were used f o connect the l e v e l l i n g bulb and the p r e s s u r e tube to the v o l u m e t r i c tube. Procedure. The f i r s t d e t e r m i n a t i o n that was made by tfao dotormiaa-t i o n of the volume e n c l o s e d i n the tu b i n g and f l a s k A from the p o i n t B. With the c o n t a i n e r A empty and the stopcock a t the a i r o u t l e t open the l e v e l l i n g b u lb was lowered u n t i l the Sco/e 11. mercury i n the volumetric tube reached C. The stopcock wa3 then closed and the l eve l l ing bulb raised u n t i l the mercury reached B. The pressure di f ferent ia l was then measured. By denoting the volume from H to A as Vb, and B to C as Vc, Vb can be found by the following equation: Vb x P , = Vc x P - j . and Vc =Vb plus # Vbc In this apparatus Vb equals 71.7 cc. By a similar method the volume Vb- Vs can be determined where Vs is the effective volume of sand grains. The bulk volume of the sand was measured by the use of a volumetric scale on the side of A. The effective porosity then i s the difference of the bulk volume of the sand and the apparent volume of the sand grains divided by the bulk volume of the sand and mult ipl ied by 100 per cent. Results. Bulk Volume P i PJL . Vj Vj . V 3 2 cc. 29.3 i n . 34.15 71.9- Vs 71.7-Vs-10 1.237 Effective porosity^ 2-1.257 x 100 «. 38.15$ 12. APPLICATIONS OF SCREEN ANALYSES  I n t r o d u c t i o n . I t has been suggested by Dr. Seyer t h a t sands which have been l a i d down by a s e t t l i n g motion should possess a f a i r l y even d i s t r i b u t i o n of p a r t i c l e s i z e s . In e f f e c t , t h i s would mean th a t the p r o b a b i l i t y curve of p a r t i c l e s i z e s Is uniform. As i n the case of the Athabasca Tar Sands, however, the i n t r u s i o n of o i l and the l a t e r a l f low through the sands should skew the p r o b a b i l i t y curve i n the d i r e c t i o n of l a r g e r p a r t i c l e s i z e s . T h i s e f f e c t can be accounted f o r by the s c o u r i n g of the f i n e p a r t i c l e s from the sand mass. A t the e x t r e m i t i e s of the flow, thei p r o b a b i l i t y curve would be skewed i n the d i r e c t i o n of the s m a l l e r p a r t i c l e s i z e s . I t i s w i t h t h i s r e a s o n i n g i n mind t h a t t h i s p a r t of the t h e s i s w i l l be presented. S i n c e p r o b a b i l i t y curves are not r e a d i l y drawn from screen analyses data, cumulative curves are p r e s e n t e d and the p o i n t of g r e a t e s t s l o p e on these curves Is taken as the most probable g r a i n s i z e . Screen a n a l y s e s . F i g u r e 3 i s a p l o t i n cumulative form of the s c r e e n a n a l y s i s of a sample of sea sand which was l a i d down by wave a c t i o n , and the s c r e e n analyses of r i v e r sand l a i d down a t the shore. I t should be noted here t h a t the sea sand curve i s v e r y c l o s e to a true p r o b a b i l i t y curve i n the cumulative form. The Screen a n a l y s i s of the sample of sea sand gave the 13. following resul ts : Per Gent Retained Mesh Per Cent Cumulative. 20 4 4 30 25 29 42 54 83 60 16 99 80 1 100 100 The most probable size of this.:sand can be chosen from the sea sand graph oh Figure 3 as 35 mesh. The Screen Analysis of the sample of r ive r sand gave the following resul ts : Per Cent Retained Mesh Per Cent Cumulative. 40 7.5 7.5 60 8.5 16.0 80 9.0 25.0 100 22.5 47.5 200 45.0 92.5 Passing 200 7.5 100.0 The graph of r iver sand shows also a s imi la r i ty to a true probabili ty cufive in cumulative form but the part icles are generally f iner . The most probable mesh size can be taken 15. as about 105 mesh. On a completely extracted sample of Atha-basca Tar Sand, a screen analyses revealed the following: Per Cent Retained Mesh ____ Per Cent Cumulative. 42 60 80 100 150 200 Passing 200 100.00 Figure 4 is a plot of this analysis in cumulative form. The most probable size i s 104 Mesh. In Table I , the results of S. C. E l l s (4) analyses of 57 samples of tar sands are set down. Figures 5-10 are cumu-la t ive plots of these analyses.. To f a c i l i t a t e plot t ing of the analyses, each cumulative curve has been assigned a special graph number. In Table 2, a co-relation of this data and a l i s t of the most probable sizes are compiled. The most prob-able sizes were as before computed from the cumulative curves of Figures 5-9. I t w i l l be noted from Table 2 that on a basis of the whole tar sand f i e l d , the most probable sand sizes vary from 18 Mesh to 132 Mesh. This fact seems to give further .151 .376 6.490 31.82 48.533 9.57 3.06 .151 .527 7.017 38.837 87.37 96.94 100.00 support to our reasoning that the o i l flowed throughout the sand and thus displaced the probabil i ty curve. TABLE I . E l l 1 s Test No. Test No. 200 100 80 50 40 30 20 10 1 11 Athabaska River 2 11 54 16 10 5 2 2 12 » rt 6 54 25 13 3 12 M it 7 77 14 2 4 15 it ti 24 64 9 3 5 15 rt it 3 38 19 40 6 16 it tt 9 33 11 47 7 21 tt it 3 5 1 8 7 15 33 27 8 21 it tt 4 26 11 48 3 2 3 3 9 22 it tt 11 70 14 5 10 47 Christ ina River 3 6 8 12 14 45 ; 12 11 49 ti it 3 15 11 70 1 12 52 it II 2 35 12 51 13 52 tt tt 4 34 16 46 14 39 Clearwater River 4 14 14 48 9 7 4 15 43 Hangingstone n 3 22 9 51 9 4 2 16 31 Horse River 5 38 8 47 2 17 32 II tt 5 47 16 32 18 33 tt tt 5 36 14 45 19 34 it n 10 33 19 37 1 20 35 tt it 4 27 11 56 2 21 35 n it 7 77 5 11 22 36 « ti , 4 40 5 51 23 36 n tt 5 39 27 29 24 37 tt n 3 35 15 57 25 38 tt tt 5 42 18 35 26 38 tt it 4 30 18 47 1 27 73 McKay River 2 49 26 22 28 74 it tt 6 25 16 40 4 9 29 64 ELl«s River 6 75 18 1 30 67 n tt 6 53 19 20 31 63 Muskeg River 7 10 1 27 20 16 10 6 32 54 Steepbank River 3 8 2 25 16 20 15 9 33 55 it it 7 4 1 12 10 17 27 22 34 56 tt tt 2 4 1 42 22 13 9 4 35 58 ti II 5 33 2 43 7 4 2 3 36 59 it tt 3 14 2 72 5 5 1 37 61 tt rt 7 10 1 27 20 16 10 6 17. TABLE 2.  DATA FOR GRAPHS Cumulative Curves. Most Probable ih No. Size Mesh. Test No. 1 18 7 2 37 10 3 50 34 4 20 33 5 30 32 6 86 1 7 61 36 8 74 11 9 58 14 10 42 31 11 42 37 12 58 15 13 70 24 14 72 8 15 74 20 16 68 28 17 75 26 18 73 19 19 66 13 20 66 35 21 74 15 22 66 18 23 58 6 24 57 16 25 63 12 26 57 22 27 80 23 28 72 25 29 64 17 30 66 27 31 88 2 32 100 29 33 120 9 34 116 3 35 132 21 36 130 4 Test #: Refer to the abridged analyses of S.C. E l l s numbered numerically from the beginning. Reference: Bituminous Sands of N.Alberta p.50-51 Department of Mines (Canada) Graph#: Refers to the number assigned to each Cumulative Curve. Fig. I. Fig. 8. Fig. 1. Diagrammatic section E. and W. near McMurray (A) Cretaceous Shales. Sandstones, etc. (B) Bituminous Sands. (C) Devonian Limestone. The presence of small areas of bottom lands along Horse creek, coupled with the fact that former erosion has not cut down to the Devonian Limestone, make it probable that occasional small deposits of Bituminous Sands with moderate overburden will be found in this valley. 28. In Figure 11, the most probable par t ic le sizes are plotted against the test numbers, and consequently present a picture of the variat ion i n certain l o c a l i t i e s . Contour Map. Figure 12 Is a map of the Tar Sand area with the contour l ines representing regions of equal size d is t r ibut ion. The black dotted l i n e joins regions averaging 120 mesh as the most probable s ize . The green l ine joins regions averaging 70 mesh. The yellow l ine joins regions averaging 40 mesh. The red l ine joins regions averaging 20 mesh and should i n d i -cate the or igin of the o i l stream. Profiles of the Tar Sand f i e l d are shown in Figure 13. These show how the r ivers have cut through the overburden to expose the outcrops of bitumin-ous sand. Underlying the tar sand i s the Devonian limestone which i s considered the source of the o i l i n the area. CONCLUSIONS. In studying the properties of the Alberta Tar Sands during the course of the work for this thesis, three conclus-ions have been arrived at. 1. The permeability of the sand i n question has an average value of 4.4 D'arcys. 2. The average effective porosity i s approxi-mately 40 per cent. 3. The contour map indicates that the or igin of the o i l stream should l i e In the region shown by the red l i n e . r BIBLIOGRAPHY 1. S l i c h t e r , C. S., U. S. Geol. Survey, 1897-1898,pt.II, P .295 2. Kozeny, J . , Waseerkraft und Wasserwirtechaft, 22, 67, 86, 1927 3. Toretennson and Erikson, S o i l Science, 1936, Vol.kZ t p.405-^07 k. S. C. E l l e , Dept. of Mines(Canada), Bituminous Sands of Northern Alberta, Occurences and Poss-i b i l i t i e s , 192*1<, p.50 

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