Ind. Eng. Chem. Fundam.
368 T,
= wall shear stress
I ’ = L / L C= A / 2 = tortuosity factor
Literature Cited Bies, D. A. “Noise and Vibration Control”; Beranek. L., Ed.; McCaaw-Hill: New York, 1971; Chapter 10, p 245. Bird, R. 6.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiiey: New York, 1960; Chapter 6, p 197. Carman, P. C. Trans. Inst. Chem. Eng. 1937, 15, 150. Ciiffel, E. M., Jr.; Smith, W. E.; Schwope, A. D. Mod. Dev. Powder Metall. 1966, 3 114. Darcy, H. “Lesfontainer pubiiques de la viile de DiJon”, Dalmont, Paris, 1856. DeHoff. R. T.; Rhines, R. N., Eds. “Quantitative Microscopy”; McGraw-Hill: New York, 1968. Dudgeon, L. R. Houllle Blanche 1966, 21 785. Ergun, S . Chem. Eng. Prog. 1952, 4 8 , 89. Forchheimer, P. Z . Ver. Dtsh. Ing. 1901, 45, 1782. German, R. M. Powder Technol. 1981, 30, 81. Kozeny, J. S.-Ber Wlener Akad., Abt. I I A 1927, 136, 27 1 Kyan, C. P.; Wasan. D. T.; Kintner. R. C. Ind. Eng. Chem Fundam. 1970, 9 ,596.
1985,2 4 , 368-373 MacdonaM, I. F.; ECSayed, M. S.; Mow. K.; Duilien, F. A. L. Ind. Eng. Chem. Fundam. 1979, 18, 199. O’Brien, J. E.; Sparrow, E. M. Trans. ASME 1982, 104, 410. Pahi. M. H. Dissertation, Universitat Fridericiana Karisruhe, 1975. Pauiln, M.; Hutin, D.; Coeuret, F. J . Electrochem. Sci. Techno/. 1977, 124, 180. Robinson, A. T. Trans. ASME1964, 57, 650. Rumpf, H.; Gupte, R. Chem.-Ing.-Tech. 1971, 4 3 , 367. Schiichting, H. “Boundary-Layer Theory”; McGraw-Hill: New York, 1968; Chapter 20, p 584. Shapiro, A. H. ”Compressible FluM Flow”; Ronald Press: New York. 1953; Voi. 1, Chapter 6, p 167. Shcheichkov, A. G. Sov. Powder Metall. Met. Ceram. (Engl. Trans/.)1975, 14, 834. Smkh, D. W.; Marth, T. Mod. Dev. Powder Metall. 1980, 12, 835. Underwood, E. E. “Quantitative Stereology”; Addison-Wesley: Reading, MA, 1970.
Received for review March 6, 1984 Revised manuscript received October 10, 1984 Accepted December 3, 1984
Hydrodynamic Characteristics of an in Vitro Drug Permeation Cell Kakuji ToJo,’ Joseph A. Masl, and Yle W. Chlen Controlled Drug Delivery Research Center, College of Pharmacy, Rutgers, The State Universlty of New Jersey, Piscataway, New Jersey 08854
A correlating equation was derived for the purpose of determining the hydrodynamic conditions present in an in vitro membrane permeation system and to calibrate this apparatus for use as a standardized in vitro system in membranemoderated controlled drug permeation studies. The equation correlated the mass transfer and dissolution of benzoic acid in various volume fractions of poly(ethyleneglycol) 400, a water miscible cosdvent used to enhance the aqueous solubility of drugs, in terms of the conventional Sh-Re-Sc relationship. This mathematical expression is applicable to all compounds tested in the system and allows not only the estimate of aqueous diffusion layer thickness but also the determination of the intrinsic permeation rate of a compound under ideal hydrodynamic conditions.
Introduction Recently, the mass transfer through various types of membranes has received increasing attention in both the pharmaceutical and allied industries. Especially in the pharmaceutical industry, novel approaches of drug delivery through both polymeric membranes and human or animal skin have become one of the most challenging research areas. Studies on drug transport through membranes are booming, and various kinds of in vitro setups for drug permeation measurement have been used by many researchers. However, no standardized permeation equipment has been proposed for investigation so far. The effects of hydrodynamics of diffusion cell design on the membrane transport properties have been extensively studied in the engineering fields, particularly in the fields of batch dialyzers or diaphragm diffusion cells (Holmes et al., 1963; Kaufmann and Leonard, 1968; Smith et al., 1968; Colton and Smith, 1972), which are much larger in size compared with the system used in this study. In the drug delivery research, the size of diffusion cells is usually small in order to minimize the necessary amount of drugs and membrane surface area as well. In spite of the fact that the subject on drug transport through membranes has become one of the rapidly growing research areas in recent years, insufficient attention has been paid to the effect of diffusion boundary layer on the rate of intrinsic permeation for membrane-moderated
controlled drug release studies. It is obvious that the rate of drug permeation through a membrane should be analyzed precisely by using a well-calibrated permeation cell. Otherwise, permeation rate data may be easily distorted by the diffusion boundary layers existing on the membrane. Generally, the in vitro membrane permeation system should be designed to assure the study of intrinsic release rate, which is independent of the flow field in the diffusion cell. However, this is sometimes difficult to achieve because a drug may be highly lipophilic (have a large partition coefficient) or a viscous cosolvent such as poly(ethy1ene glycol) 400 (PEG) is frequently used in the solution to enhance the aqueous solubility of drugs and to maintain a sink condition throughout the experiment to simulate the physiological condition. A new permeation cell design was recently developed for studying the membrane permeation of drugs (Chien and Valia, 1984). Because this design has some advantages, which will be discussed later, it is expected to be broadly utilized for in vitro membrane permeation studies. In the present paper, we have investigated the hydrodynamic characteristics of the in vitro membrane permeation cell to see the feasibility that this permeation system can be calibrated as a standardized in vitro system for studying the membrane-moderated controlled release of drugs.
0 196-4313/85/1024-0368$01.50/00 1985 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 24, No. 3, 1985
Stopper
Filling &
Sampling Port
,
DONOR (Left) HALFCELL
RECEPTOR (Right) HALF-CELL
Figure 1. In vitro drug permeatin system for membrane-moderated drug permeation studies: effective surface area of membrane, 0.64 cm2; star-head magnet, 0.8-cm diameter, 0.6-cm height (-90% of actual size).
The dissolution rate of a planar benzoic acid disk was measured in various aqueous PEG 400 solutions. The mass transfer coefficient and dissolution rate constant were determined and then correlated in terms of the conventional Sh-Re-Sc relationship. From the final correlating equation established here, the thickness of the hydrodynamic diffusion boundary layer will be calculated and then the effect of environmental flow conditions on the rate of membrane permeation can be accurately interpreted. Membrane Permeation System The details of the membrane permeation system used in the present study are illustrated in Figure 1. This system has been developed for studying the long-term permeation kinetics of drugs through both polymeric membranes and human or animal skins under both finite and infinite dose conditions. Both donor and receptor compartments (half cell length, 3.8 cm) are maintained at the same hydrodynamic conditions by a matched set of "star-head" magnets (diameter, 0.8 cm; height, 0.6 cm) which are caused to rotate by a synchronous drive motor (rated at 3 W, 600 rpm). The solutions in the donor and receptor Compartments (3.5 mL) are maintained in a completely enclosed environment to minimize any loss in solution volume due to solvent evaporation. This consideration in design is particularly important for long-term membrane permeation studies. The donor and receptor compartments are both jacketed and thermostated by an external circulatory bath to maintain an isothermal condition, or if desired, the temperature in either the donor or receptor compartment can be programmed to simulate environmental variations. Experimental Section In order to obtain the aqueous solubilities of benzoic acid in various PEG 400 solutions, the saturated solutions of benzoic acid in water containing 0-4070 v/v of PEG 400 were prepared at 20 or 37 "C by placing an excess amount of benzoic acid in the test tubes containing the various PEG 400 solutions. These tubes were then placed in a shaking water bath (Fisher Scientific Model 127) at 20 or 37 OC with oscillation at 75 cpm. After 24 h the solutions were removed, filtered through Millipore (0.45pm) filters,
369
and quickly diluted with the same solution medium as was used in the test tubes. The concentrations were then analyzed by using a UV/vis spectrophotometer (PerkinElmer Model 559A). The viscosity of each PEG 400 solution was measured in an Ostwald capillary viscometer. The diffusion coefficients of benzoic acid in various solutions were calculated from a literature value on the diffusivity in pure water at 25 "C fpund to be 1.082 X lov5 cmz/s (Braun and Parrott, 1972) and by using the Wilke equation (Wilke, 1949). A thin benzoic acid disk of a suitable size (diameter, 2 cm; thickness, 0.3-0.4 cm; effective diameter for benzoic acid dissolution, 0.9 cm) was made by pouring fused benzoic acid into a metal mold positioned on a pill tile. The disk was then mounted to the permeation cell between the donor and receptor compartments. With the benzoic acid disk in place, 3.5 mL of each solution, previously maintained at 20 or 37 "C, was pipetted into the receptor compartment while the donor compartment remained empty. At predetermined time intervals, samples of 20 p L were withdrawn from the receptor solution and diluted to 10 mL with the same solution medium (containing no benzoic acid) and then analyzed by the UV techniques mentioned previously. The rotation speed of the stirring magnet was measured by using a phototachometer (Cole-Parmer) and was found to be constant (600 rpm) under the present experimental conditions. Data Treatment The mass transfer coefficient, le,, is obtained by analyzing a concentration-time curve, under perfect mixing conditions in the receptor solution. The mass balance equation for the solute diffusion in the receptor solution is given by dC V- = k,A(C, - C ) (1) dt where C is the time-dependent concentration, C, is the saturated concentration, A is the surface area for mass transfer (0.64 c d ) , V is the volume of the fluid in the compartment, and t is the time. Integration of eq 1with the initial concentration (C,) yields
or C,-Co K,At log -= C, - C 2.303V
(3)
The mass transfer coefficient, k,, is obtained from the slope of the log [(C, - C,)/(C, - C)] vs. AtIVplot. If this plot does not result in a straight line, eq 1is not applicable and a more general flow pattern in the receptor compartment should be taken into account. Physical properties of the present system are listed in Table I. Correlation of the Mass Transfer Coefficient In general, the mass transfer coefficient can be correlated in terms of three dimensionless numbers, namely the Sherwood (Sh = k,d/Df), Reynolds (Re = d u p / p ) , and Schmidt (Sc = p / p D f ) numbers, in which Dfis the diffusivity in bulk fluid, u is a characteristic velocity of the fluid such as the mean fluid flow velocity, p is density, p is viscosity, and d is a characteristic dimension of the system. In the permeation system used in the present study, the mass transfer from the surface of the benzoic acid disk is mainly controlled by the turbulence of the fluid motion
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Table I. Physical Properties of Benzoic Acid and Poly(ethy1ene glycol) 400 Solutions fraction of PEG 400 in water at 37 "C, v/v fraction physical properties 0% 10% 20% 40 % 0% densitv. e / m L 0.9934 1.007 1.020 1.047 0.9982 viscosity, lo2 g/ (cm s) 0.6915 1.016 1.826 4.646 1.002 4.39 f 0.12 7.85 f 0.26 15.36 f 0.29 54.2 f 2.3 2.64 f 0.06 saturated concn of benzoic acid," mg/mL 0.984 X diffusivity of benzoic acid, 1.45 X 0.986 X 0.549 X 0.216 X cmz/s
-
(I
of PEG 400 in water at 20 " C , v/v 20 %
40 %
1.65 4.23 f 0.09
1.024 2.70 7.53 f 0.05
1.050 7.0 22.6 f 0.71
0.597 X
0.370 X
0.14
10%
1.001
Y ,
x 10-5
Mean k standard deviation. _ _
1
.
_
I
~
t---
-
1
I
1
10
20 Time
J 30
(minl
Figure 3. Concentration profiles of benzoic acid in the receptor solution as a function of time. The value on the lines is the volume fraction of PEG 400. The solid lines are calculated from eq 2. 0.8
0.6.
-
3
ci'
q LY
,
0.4
"0
10
20
30
Time lminl
Figure 4. Replot of the concentration data in Figure 3 according to eq 3. Mass transfer coefficient k, is determined from the relation k , = (slope)V/A.
the aqueous solutions is shown in Figure 3. Because the solubility of benzoic acid in 40% PEG 400 solution is much higher than that in water (as shown in Figure 2), perfect sink conditions can be easily achieved and maintained, C, - C E C,, throughout the experiment. The benzoic acid concentration in the 40% PEG 400 solution was observed to increase proportionally with time during the present experimental period (Figure 3). Such a perfect sink condition as a rmult of increased solubility by cosolvency can significantly ease the treatment of experimental data in controlled release studies. The benzoic acid concentration
Ind. Eng. Chem. Fundam., Vol. 24, No. 3, 1985
10'
371
Table 11. Thickness (a,) of Diffusion Boundary Layer on the Benzoic Acid Disk at 37 OCn volume fraction of PEG 400 in water,
c
VJV
5 L
d,, wm
c
0% 50.0
10% 57.2
20 %
40 %
70.4
98.0
aAverage value of six data points.
1 lo"
//K-c
Ce//
€9. 8
t lo2
5
10"
Re
lo4
Figure 5. Dimensionless correlationof the mass transfer coefficients in the membrane permeation system used in the present study (Figure 1). The slope of the line yields the exponent m while the y intercept denotes the equation constant. Each point represents the mean of six data points at (0)37 and ( 0 )20 "C. The dark solid line represents eq 8, the light solid line represents the K-C cell, and the dashed line represents the corrected K-C cell.
profiles in Figure 3 were replotted in the relationship of log [C,/(C,- C)]vs. time in Figure 4 according to eq 3. The good straight lines indicate that perfect mixing conditions were well maintained in the receptor compartment. The mass transfer coefficients can be determined from the slope of the linearity for each of the receptor solutions. Correlation of Mass Transfer Coefficient. The mass transfer coefficients, k,, can be correlated in terms of the conventional dimensionless equation given by eq 6. Figure 5 shows the plot of the present data by the relation of log ( S ~ / S C ' vs. / ~ log ) Re (eq 6 ) . All the data points fall on the straight line defined by the following correlation equation:
Sh/Sc113= 0.0157Re1.03
(8)
It is interesting to compare the present correlation equation (8) with the results obtained previously. Smith et al. (1968) studied the diffusion boundary layer in a batch dialyzer agitated by a four-blade impeller rotating parallelly to the membrane. They found that the exponent value m on Reynolds number varied from 0.634 to 0.752, dependent on the system geometry. Kaufmann and Leonard (1968) obtained the exponent on Reynolds number of 0.68 for the similar diffusion cell to that used by Smith et al. Colton and Smith (1972) also studied the mass transfer from the base of a flat-bottom tank agitated by a four-blade paddle impeller, and the exponent value m was found to be 0.567 and 0.746 under low and high Reynolds number operations, respectjvely. Holmes et al. (1963) investigated the diffusion boundary layer characteristics of the diaphragm diffusion cell, and they correlated the mass transfer coefficients by Sh = 0.050Re0~79Sc0~38. Because of the difference in cell design, the correlation obtained in this study (eq 8) may not be compared directly with the results reported previously. However, it can be concluded that the exponent value on Re is varied from 0.5 to 1.0, dependent on the design of in vitro membrane permeation systems. For a small-volume diffusion cell like the present in vitro system, the solution can be agitated effectively by a stirring magnet and the resulting highly turbulent flow can be wholly developed throughout the cell compartments.
Under such a turbulent flow condition, the exponent m on Re was reported to be 0.9-1.0 (Davies, 1972). Tojo et al. (1984) studied the diffusion boundary layer characteristics of a vertical-type diffusion cell (effective volume, 12 mL; effective surface area for mass transfer, 3.14 cm2;developed by Keshary and Chien, 1984) equipped with the same driving unit (600 rpm) and the same stirring magnet as used in the present in vitro system (Figure 1). The correlation equation of the mass transfer coefficient for the K-C cell is also plotted in Figure 5 for comparison. As can be seen from this figure, the mass transfer coefficient for the present diffusion cell is greater by approximately 50% than that for the K-C diffusion cell. This deviation can be attributed to the difference in the effective volume of the diffusion cell used. Because the same driving unit and the same agitator were used in each membrane permeation system, the Reynolds number Re can be adjusted in terms of (volume)-'/3 based on the Kolmogoroff theory (Tojo and Miyanami, 1982). The Reynolds number for K-C cell (volume, 12 mL) was corrected for the meaningful comparison with the present system (3.5 mL), and the results are plotted in Figure 5 as a dashed line. It is found that the corrected correlation for the K-C cell agrees excellently with that obtained in the present study in spite of the difference in the cell design. This finding suggests that the characteristics of the diffusion boundary layer in the membrane permeation system may be described by a universal equation in spite of the difference in the details of cell design if the same driving unit and the same agitator are used. The correlating equation (eq 8) established here can be used to evaluate the mass transfer coefficient and the thickness of the diffusion boundary layer, d , (= d/Sh),for the in vitro drug permeation studies using the present permeation cell (Figure 1). The thickness of the diffusion boundary layer calculated for benzoic acid/various PEG 400 solutions is listed in Table 11. By using the correlating equation established, we can analyze the effect of the hydrodynamic diffusion layer on the rate of controlled drug release in the present in vitro membrane permeation system. This is achieved by solving the governing equation (mass transfer equation), subjected to the appropriate boundary conditions (which are dependent on the hydrodynamic characteristics of the system) and initial conditions (Tojo and Fan, 1981). The intrinsic permeation rate, which is useful in the establishment of a reliable in vitro/in vivo correlation, can then be determined for any drug-solvent system (Tojo et al., 1985; Tojo, 1984). Use of the Correlation Equation in Determining Intrinsic Permeation Rate. The majority of the experiments conducted in the present in vitro drug permeation system use a saturated drug solution, C,, in the donor compartment and monitor the permeation of the drug through a membrane by sampling from the receptor compartment at various time intervals. The permeation rate will be a function of the partition coefficient of the drug toward the membrane and the thickness of the diffusion bounary layer present on both sides of the membrane. A typical concentration profile is shown in Figure
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Donor
Membrane
Receptor
Figure 6. Schematic illustration of the drug concentration profile in the membrane permeation system based on the film theory. 6. The permeation rate through a unit area of the membrane can be represented by
where D = diffusivity of drug through the membrane, K = partition Coefficient, 1 = membrane thickness, k, = mass transfer coefficient, C1 = concentration of drug in the donor-phase boundary, C2 = concentration of drug in the receptor-phase boundary, C = concentration of drug in the bulk solution, and Q = cumulative amount of drug permeated. Rearranging eq 9 yields
If the mixing is so vigorous that the diffusion boundary layer can be eliminated, eq 10 can be reduced to
The effect of the diffusion boundary layer on the rate of drug permeation can be characterized in terms of the ratio of eq 10 to eq 11: Y=
y(z) Sh-m
-
1 2K/ShL +
Shl is the Sherwood number in terms of membrane thickness. However, the correlating equation is based on Sh, the Sherwood number in terms of d. It is therefore necessary to represent Shl by Sh; S h = Shl(D/Df)(d/l). Substituting for Shl in eq 12c gives y in the following relationship: = [1+ 2(D/D,)(K/Sh)(d/l)l-'
(13)
From eq 13, we can evaluate the effect of the diffusion boundary layer on the rate of drug permeation. It can be seen that a large partition coefficient and a small Sherwood number will cause a significant effect on the intrinsic permeation rate. For example, when water is used as the elution media and a polymeric membrane, two drugs of similar molecular weight have the following parameters: drug I : D = 4.5 x 10.- c m z / s D f= 7' x 10 cm'is K = 50.2 I - 0.05 cm c l = 0.9 cm
drug 11: D = 4.5 x 10 c m 2 / s D f= 7 x I O - * c m 2 / s K = 0.05 l = 0.05 cm d = 0.9 cm
-
The Sherwood number calculated by eq 8 for both drugs is 229. The y values for drugs I and I1 are 0.663 and 0.995, respectively. Assuming, for the purposes of illustration,
Figure 7. Effect of Sherwood number Sh on the apparent rate of drug permeation in reference to the intrinsic release rate. The value on curves denotes the magnitude of partition coefficient K.
that the experimental permeation rate for either drug was found to be 1.0 pg/(cm2 h), the intrinsic permeation rate, the rate which is devoid of any diffusion boundary layer effects, would be 1.5 and 1.0 Fg/(cm2 h) for drugs I and 11,respectively. In this case, the experimental permeation rate for drugs I and I1 is approximately 33% and 0% less than the intrinsic rate, respectively. Again, these examples illustrate the importance of the partition coefficient in the determination of permeation rate. Typical examples of the y vs. Sh relationship are illustrated in Figure 7. Conclusion The mass transfer characteristics of benzoic acid from a disk surface were investigated for the purpose of calibrating an in vitro membrane permeation cell used in the drug permeation studies. The solution solubility and the dissolution rate of benzoic acid were measured in aqueous solutions containing various volume fractions of poly(ethylene glycol) 400. The correlating equation for mass transfer coefficients was established by using the dimensionless Sh-Re-Sc equation. The effect of diffusion boundary layer on the rate of controlled drug release can now be evaluated accurately by using the correlation equation obtained in the present study. Nomenclature A = area of the permeation cell orifice, cm2 C = concentration in the bulk solution, mg/mL C, = concentration in the donor-phase boundary, mg/mL Cz = concentration in the receptor-phase boundary, mg/mL Co = initial concentration, mg/mL C, = saturation concentration, mg/mL d = characteristic length of the system, cm d, = hydrodynamic diffusion layer thickness, cm D = diffusivity in the membrane, cm2/s Df = diffusivity in the bulk fluid, cm2/s k , = mass transfer coefficient, cm/s K = partition coefficient E = thickness of the membrane, cm m = exponent on the modified Reynolds number n = rotation speed of stirring magnet Q = cumulative amount of drug permeated Re = Reynolds number Sc = Schmidt number Sh = Sherwood number Shl = Sherwood number based on the thickness of the membrane .t = time, s u = characteristic velocity of the fluid in the system V = volume of the fluid in the cell compartments, mL X = volume fraction of PEG 400 y = ratio of experimental to intrinsic permeation rates p = density of fluid in the system, g/mL p = viscosity of fluid in the system, g/(cm s)
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Ind. Eng. Chem. Fundam. 1005, 2 4 , 373-379
Registry No. PEG 400, 25322-68-3; benzoic acid, 65-85-0.
Literature Cited Braun, R.; Parrott, E. J . Pharm. Sci. 1972, 67, 592. Chien, Y. W. “Novel Drug Dellvery Systems”; Marcel Dekker: New York. !MJ . 1972, 78, 958.
Holmes, J. T.; Wllke, C. R.; Olander, D. R. J . h y s . Chem. 1903, 6 7 , 1469. Kaufmann, T. 0.;Leonard, E. F. A I C E J . 1988, 74, 110. Keshary, P. R.; Chlen, Y. W. Bug Dev. Ind. Pharm. 1984, 70, 883. Smith, K. A.; Colton, C. K.; Menill, E. W.; Evans, L. B. Chem. €ng. hog., Symp. Ser. 1908, 64, 45. ToJo, K. J . Soc. Powder Technd., Jpn. 1984, 27, 490. Tojo, K.; Fan, L. T. Math. Blosci. 1981, 57, 279. Tojo, K.; Miyanaml, K. Chem. €ng. Commun. 1982, 76, 159. ToJo, K.; Ghannam, M.; Sun, Y.; Chlen, Y. W. J . ContrdledReleese 1985. 7 , 197. Wllke, C. R. Chem. Eng. Rog. 1949, 45, 218.
Solvent Extraction of Mined Athabasca Oil Sands Helen Leung and Colin R. Philllps’ Department of Chemical Engineerlng and Applied Chemistry, University of Toronto, Toronto, Ontario M5S 7A4, Canada
A semiempirical analysis of the solvent extraction process for Athabasca oil sands was carried out in order to arrive at process design criteria. A generalized extraction equation of the form (1 - t)”’ = 1 - T‘ where [ = extraction efficiency and T’ = dimensionless contact time is derived. The analysis is applied to experimental data on kerosene in a rotating contactor together with previously published results for several solvents in stirred vessels. The effects of the oil sand to solvent ratio and stirrer speed (or rotational speed for the rotating contactor) are examined.
Introduction Extraction schemes proposed for recovery of bitumen from oil sands include the Clark hot water process (Clark, 1944), cold water processes (Grant et al., 1980; Djinghenzian, 1951), and anhydrous solvent extraction processes (Cottrell, 1963; Kenchington et al., 1981; Cormack et al., 1977; Fu and Phillips, 1979; Funk, 1979). A solvent extraction process appears to promise both high extraction efficiency at a reasonable cost and reduction of the environmental problems that arise in the commercially adopted hot water process. A detailed technical and economic analysis has been made on a process for the production of 1900 m3/day of bitumen from 136000 kg/h of Athabasca oil sands (Kenchington and Phillips, 1981). The process design consisted of the following major steps: (i) solvent extraction, (ii) draining and washing, (iii) solvent recovery from spent sands, and (iv) solvent recovery from bitumen solution. The present work constitutes a detailed investigation of solvent extraction in rotating contactors. Preliminary work in stirred tanks at laboratory scale has already been reported (Cormack et al., 1977). In the present work, a semiempirical analysis of the extraction process is applied in order to arrive at process design criteria. The analysis is supplemented by experimental work in large laboratory scale rotating contactors. Comparison is made between the stirred tanks and the rotating contactor. Model The process of dissolution of bitumen from oil sands aggregates depends on the solvent to oil sands ratio, solvent type, and degree of agitation. The process may involve the following stages: (1)transfer of solvent from the main fluid through the fluid film to the surface of the solid particle, (2) diffusion of solvent into the aggregates, (3) breakup of the aggregate due to the “softening” effect of the solvent together with the effect of the agitation, (4) dissolution of bitumen from the aggregate surface, and (5) 0196-4313l85/1024-0373$01.50l0
transfer of bitumen from the surface of the aggregate through the fluid film into the main body of the fluid. In the case of a dilute system (that is, a high solvent to oil sands ratio) and a solvent having a high solubilizing power, stages 1-3 may not be important and the extraction becomes a simple convective diffusion process. Oil sands aggregates consist of sand particles fairly uniformly embedded in a bitumen film, the whole aggregate being roughly spherical in shape (Figure 1). A mass balance on a spherical oil sands aggregate results in the equation
in terms of k , the mass transfer coefficient. Here, CA is the mass concentration of bitumen in the main solution, CAOis the equilibrium mass concentration of bitumen in the solution at the interface between the oil sands particle and the fluid, ,C is the density of the bitumen, and el and e2 are, respectively, the fraction of the exposed aggregate surface which is bitumen and the volume fraction of bitumen in the aggregate. In the case of a large particle and a high Reynolds number (1 C Re C 450, Sc < 250) (Hughmark, 1969) and for larger particles (>1500 pm) (Nienow, 1975)
k
a
U:I2/R1l2
Ut
R112
(2) (3)
Here
k = &-‘I4 (4) where a is a dimensional proportionality constant. Substitution of eq 4 into eq 1 yields the equation
0 1985 American Chemical Society
