I n d . Eng. Chem. Res. 1987, 26, 246-254
246
and the cavity wall does not change by more than 5% of the previous distance. However, an upper limit for the time step is provided. Literature Cited Arri, L. E.; Amundson, N. R. AIChE J . 1978, 24(1), 72. Bischoff, K. B. Chem. Eng. Sci. 1963, 18, 711. Campbell, J. H. Fuel 1978,57, 217. Chlew, Y. C.; Glandt, E. D. Ind. Eng. Chem. Fundam. 1983, 22(3), 276. Dutta, S.; Wen Y.; Belt, R. J. Ind. Eng. Chem. Process Des. Deu. 1977, 16(1), 20. Greenfeld, M. Presented a t the Proceedings of the 6th Underground Coal Conversion Symposium, Afton, OK, July 1980, p IV-70. Harloff, G. J.; Corlett, R. C. Analysis of Results of Laboratory Simulation of Underground Coal Gasification, Presented at the ASME/JSME Thermal Engineering Joint Conference, Honolulu, HI, March 1983. Mai, M. C.; Park, K. Y.; Edgar, T. F. I n Situ 1985, 9(2), 119.
Massaquoi, J. G. M.; Riggs, J. B. AIChE J . 1983, 29(6), 975. Mondy, L. A.; Blottner, F. G. Presented a t the Proceedings of the 8th Underground Coal Conversion Symposium. Keystone, CO, Aug 1982; p 1. Murray, W. D.; Landis, F. J . Heat Transfer 1959 ( M a y ) 106. Park, K. Y. Ph.D. Dissertation, University of Texas, Austin, 1984. Poon, S. S. M. S. Thesis, University of Texas, Austin, 1985. Shannon, M. J.; Thorsness, C. B.; Hill, R. W. Report UCRL-84584, June 1980; Lawrence Livermore Laboratories. Sundaresan, S.; Amundson, N. R. Ind. Eng. Chem. Fundam. 1980, 19(4), 351. Thorsness, C. B.; Hill, R. W. Presented at the Proceedings of the 7th Underground Coal Conversion Symposium, Fallen Leaf Lake. CA. Sept 1981; p 331. Tsang, T. H. T.; Edgar, T. F. In Situ 1983, 7(3), 237. Tseng, H. P. Ph.D. Dissertation, University of Texas, Austin, 1982. Wellborn, T. A. M.S. Thesis, University of Texas, Austin, 1982.
Received for reuieu January 14, 1985 Accepted June 24, 1986
Effect of Nonuniform Distribution of Solid Reactant on Fluid-Solid Reactions. 2. Porous Solids H o n g Yong S o h n * a n d Yong-Nian Xia Department of Metallurgy and Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112-1183
T h e grain model for fluid-solid reactions is extended t o the solids with nonuniform distribution of the solid reactant. T h e nonuniform distribution can have a substantial effect on the conversion-vs.-time relationship as well as the time for complete reaction when pore diffusion affects the overall rate. In general, a monotonically increasing distribution of the solid reactant will accelerate the overall rate, and a monotonically decreasing one will delay the process, when compared with the case of the uniform distribution. T h e law of additive reaction times previously proposed for fluid-solid reactions involving uniform distribution is shown to yield a useful approximate solution even for the reaction of a porous solid with nonuniform distributions of the solid reactant. In part 1 (Sohn and Xia, 1986), we discussed the reaction of an initially nonporous solid with a nonuniform distribution of solid reactant. Although the case of a nonporous solid covers a lot of practical situations, a porous solid with nonuniform distribution of solid reactant is also often encountered. A pellet in which particles of pure, dense solid reactant are distributed in a porous matrix of an inert solid or a pellet into which the particles are compacted with nonuniform compactness is an example of this situation. In chemical and metallurgical systems, the sinters and agglomerates, some ores, and the active absorbents deposited in an inert carrier are some of the actual examples. There has been a great deal of work treating the subject of fluid-solid reactions of porous solids with uniform distribution of solid reactant (Sohn, 1979, 1981; Sohn and Szekely, 1972; Szekely and Evans, 1970, 1971a,b; Szekely et al., 1976). However, as we have pointed out in part 1 (Sohn and Xia, 1986), only in certain circumstances can we treat the problem with the theory for uniform distribution with acceptable accuracy. In view of this, a systematic analysis of the problem is necessary in order to obtain more accurate information. In the following, a grain model with a nonuniform distribution of solid reactant is developed, which is based on the grain model mainly described in Sohn and Szekely (1972) and Szekely et al. (1976). We will emphasize the model formulation and general observations for an arbitrary form of the distribution function, as well as some numerical results for certain specific distributions. We will also present the results of applying the law of additive
reaction times previously proposed for solids with uniform distribution of the solid reactant (Sohn, 1978, 1981). This law gives an approximate closed-form solution for the conversion-vs.-time relationship. It will be shown in this paper that the relatively simple approximate solution gives a satisfactory representation of the reaction of solids with nonuniform distribution of the solid reactants. During the preparation of this paper, Ramachandran and Dudukovic (1984) published a paper on a similar problem. There is, however, a substantial difference in the model formulation between the two studies. We will discuss this difference in the following section. Model Formulation The physical model under consideration is sketched in Figure 1. The essential feature of the physical structure is that the pellet consists of two parts: one is the small, dense grains of the solid reactant, and the other is either the void which is actually the interstices among the grains or the inert solid with porosity in which the grains are nonuniformly dispersed. The grains are assumed to have identical shapes and sizes. Both the pellet and the grains can have one of the three basic shapes: flat plates, long cylinders, and spheres. The fluid-solid reaction under consideration is
A,, + W
S ,
=
c,,,+ dD,,,
with intrinsic kinetics
0SSS-SSS5/S~/2626-0246$O1.50/0 0 1987 American Chemical Society
(1)
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 247 ,Reactant
where f ( R )is the dimensional distribution function of the solid reactant B along R , based on the molar density pB. We further define a dimensionless parameter 6 as
Solid
which is the ratio of the average concentration of the solid reactant to the molar density of pure B. The dimensionless distribution function h(q)is subject to the constraints 1 O 0) or a decreasing ( a < 0) function, respectively, and that the larger the absolute value of a , the stronger the effect. This result implies that, so far as a monotonic distribution function is concerned, the increasing function will cause the process of conversion to be faster than that of the uniform distribution with the solid reactant concentration identical with the average value of the nonuniform distribution, whereas the decreasing function will cause the opposite effect. It is of interest to examine the error caused by using the reaction time for a uniform distribution to approximate
f
FP
Equation 45 can be used to predict the error for any allowable value of a for the three basic geometries. Figure 3 is the plot of Exz1against a. Thus, if an error of &lo% is acceptable for practical purposes, the corresponding values of a are 0.55, -0.67; 0.4, -0.5; and 0.36, -0.44 for slabs, cylinders, and spheres, respectively. Here the positive error corresponds to the positive a , whereas the negative error is the opposite. Although the above results are valid only in the case of a linear distribution function and it is difficult to obtain a corresponding explicit expression for E for a more complex distribution function, we still can, based on the trend observed from Figure 3, draw some general conclusions for any monotonic distribution function. They are as follows: (i) the error is to overestimate or underestimate reaction time for a monotonically increasing or decreasing distribution function, respectively; (ii) the error will not be symmetrical with respect to the distribution parameter, i.e., the absolute value of the error will be larger for the increasing function than for the decreasing one when the absolute value of the slopes for both distributions are the same; and (iii) for the same parameters of the distribution,
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 251
I
I
00
I O
l
l
I
2 0
a
Figure 4. Reaction time for complete conversion vs. fusional control.
CY
under dif-
the spheres and the slabs will result in the largest and smallest error, respectively. All of the results concerning the error mentioned above are related to the variation of the time of complete conversion with the parameter a. By setting vC = 0 in eq 42, the reaction time for complete conversion for each geometry is
Corresponding results for quadratic distribution functions are given as eq T12 in Table I. Equation 46 is plotted in Figure 4. It is shown that, depending on whether h(q)is an increasing or a decreasing function, the time for complete conversion will be, respectively, smaller or larger than that of the uniform distribution the concentration of which is identical with the average value of the distribution. The larger the absolute value of a , the larger the difference of the complete conversion time between the nonuniform distribution case and the corresponding uniform case. It is expected that this result is also qualitatively valid for any monotonic distribution function. Simultaneous Chemical Reaction and Diffusional Control. Numerical Solution. In this general case, eq 18-22 must be solved numerically. These equations are similar to those solved previously (Sohn and Szekely, 1972; Szekely et al., 1976). Some of the computed results are shown in Figure 5. In this figure, the parameter u in eq 18-22 has been replaced by b defined by eq 35. The form of eq 33 actually determines the definition of b. This particular choice of b is based on the previous analysis of fluid-solid reaction systems (Sohn, 1978; Sohn and Braun, 1980, 1984). The generalized modulus defined by this method gives, for various geometries, the same numerical criteria for asymptotic regimes of rate control by chemical kinetics or diffusion. It can be expected that the relationship between the conversion and the reaction time, in this general case, will depend on both a and 8. Parts a and b of Figure 5 show the plots of conversion X against reaction time t* for flat slabs (F, = Fg = 1)with b = 1 and spheres (FP= Fg = 3) with b = 1 and 2, respectively. The curves in the figures show that the rate of conversion decreases with the change in the value of a from positive to negative. Among the curves, the one with a = 0 is identical with that obtained from the uniformly distributed grain model reported in Sohn and Szekely (1972) and Szekely et al. (1976). Al-
though these curves have been obtained based on the linear distribution function, they are expected to also represent the qualitative features and trends for the case of any monotonic distribution function of the solid reactant. Thus, according to whether the distribution function is monotonically increasing or decreasing, the effect of the nonuniform distribution of the solid reactant on the rate of conversion, when compared with the uniform distribution, is to accelerate or delay the process, respectively. This conclusion is true for all three basic geometries. When the family of curves for b = 1are compared with those for b = 2 in Figure 5b, it is seen that the effect of nonuniform distribution is greater for a larger value of b, These effects can be seen more clearly in Figure 6, in which the ratio of the time for complete conversion in the case of a nonuniform distribution to that in the case of the uniform distribution for Fg = 3 and Fp = 3 is plotted against a with b as a parameter. In the figure, lines for b = and 5 = 0.0 correspond to the limiting cases of diffusional control and chemical reaction control, respectively. It is noted that the line for b = 0.0 is a horizontal one with the ratio of 1. This means that the time of complete conversion as well as the whole reaction process is independent of the a value, namely the distribution function, as we have pointed out earlier in the section of chemical reaction control. Between the two limiting cases, the figure shows that for a fixed value of a,a larger value of ?i will cause the reaction to take a shorter or longer time to complete depending on whether the distribution is an increasing one (a> 0) or decreasing one (a < 0), respectively. Approximate Solution. Although the numerical solution of the model equations is rather straightforward, it would be useful to have a closed-form solution, especially in the design and analysis of multiparticle systems involving wide particle-size distributions and/or the temporal/spatial variations of temperature and bulk-fluid concentrations (Sohn, 1978; Sohn and Braun, 1980,1984). Therefore, the numerical solution has been compared with an approximate solution obtained by applying the law of additive reaction times for an isothermal fluid-solid reaction (Soh, 1978; Sohn and Braun, 1980, 1984). This law states that the time required to attain a certain overall conversion is equal to the sum of the time required to attain the same conversion in the absence of the resistance due to the intrapellet diffusion of fluid reactant and the time required to attain the same conversion under the control of intrapellet diffusion. For the reaction system under consideration, this law can be stated in the mathematical form
t*
= gF,(x) + %,(X)
(47)
where p F p ( X is ) the conversion function in terms of X for diffusional control and can be obtained by simultaneously solving eq 33, 42, and 43. The results obtained from eq 47 are compared with those of the numerical solution in Figures 7 and 8 for a spherical pellet composed of spherical grains with an increasing and a decreasing linear distribution function, respectively. The value of b for the curves of the two figures is either 1.0 or 2.0, which represents the case in which chemical reaction and pore diffusion are of comparable importance. It is seen that eq 47 gives a very satisfactory representation of the numerical solution. For small and larger values of 2, the agreement will be better than shown in these figures. In fact, eq 47 is asymptotically exact as b 0 or b m. Furthermore, eq 47 is exact at X = 0 and, more importantly, at X = 1. The latter was originally established for
-
-
252 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
cussed in the literature (Sohn, 1978,1981; Sohn and Braun, 1980, 1984).
x
2 ’
~
33
5 3
43
sa
80
73
9u
t’ Figure 5. Conversion vs. reaction time under mixed control: (a, top) slabs; (b. bottom) spheres. 2 0\
-
1
-.
3-
’“c
3’2
-do
-‘c
. 33
0
ic
a
Figure 6. Time ratio for complete conversion vs. control (spheres).
(Y
under mixed
the case of a uniform distribution of solid reactant by Sohn and Szekely (1972). Recently, Sohn et al. (1984) presented a mathematical proof for this relationship. In this work, we established this for a linear distribution of solid reactant from numerical computation. It is likely that a mathematical proof for this can be found by following a similar procedure to that by Sohn et al. (1984). When eq 25,33, 46, and 47 for X = 1 and qc = 0 are combined,
I.)’(
t*ayY=l =1
+ i?2[
1-
Fp+l 3
(48)
The application of an approximate equation such as eq 47 to systems of other geometries and to multiparticle reactor systems, in which the fluid concentration and temperature vary with position and time, has been dis-
Discussion In the paper the grain model has been extended to a situation in which the pellet has a nonuniform distribution of the solid reactant. The model is stated in quite general terms, so that allowances can be made for arbitrary distribution functions and geometries of the grains and the pellet. By use of a linear distribution of the solid reactant as an example, the results have been discussed separately for different rate-controlling steps. General features and trends of the results for an arbitrary linear distribution function have been obtained. It is shown that under the condition of pure chemical reaction control, the relationship between the overall conversion and reaction time for a pellet with nonuniform distribution of the solid reactant is independent of the distribution and is identical with that of a uniform distributed pellet. But for the cases in which pore diffusion affects the overall rate, the distribution of the solid reactant can have considerable effects on the relation between conversion and time. The extent of the effect depends on the values of the parameters of the distribution function and the value of the parameter 5. In general, a monotonically increasing distribution of the solid reactant will accelerate the overall rate and a decreasing one will delay the process, compared with the reaction of the corresponding uniformly distributed case mentioned above. For the same distribution, a larger value of b will enhance the effects of the distribution on the process. The approximate solution based on the law of additive reaction times proposed by Sohn (1978) and given by eq 47 yields a satisfactory representation of the conversionvs.-time relationship for reaction of a porous solid with a nonuniform distribution of the solid reactant. The model in its present form is restrictive because of the assumption of a constant porosity of the pellet. This means some effects of the structural changes on the rate have not been included in the model. However, the model is thought to represent a wide range of practical systems, as discussed above. It should also provide a useful starting point for further work in this area. As noted earlier, let us examine the differences between the formulations by Ramachandran and Dudukovic (1984) and by us. The physical picture on which our formulation is based was given in Figure 1. A t the end of the Mathematical Formulation section, we mentioned that, although the two formulations might appear equivalent, there are important differences. This can best be illustrated by using the example of a case corresponding to n = 0. In our grain model this corresponds to the case of flat grains. According to the formulation of Ramachandran and Dudukovic, the rate per unit volume is independent of the initial solid concentration as well as the conversion. This is equivalent to the situation in which the number of particles per unit volume is uniform but the thickness of the particle varies with position. This is why, in their model, in the chemical-reaction-controlled regime the complete conversion can first take place in the interior of the pellet. In our formulation, since the grain sizes are uniform, the complete conversion takes place at the same time everywhere in the chemical-reaction-controlled regime. The rate per unit pellet volume is independent only of fractional conversion but not of the initial solid concentration. This clearly illustrates the fact that “reaction order” must be established with much greater care in heteroge-
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 253
x
o.6
t
0 4 1
,i/
Fp * 3, Fg = 3
a 11.0
- E X O EC II S o l uuttiioonn
___
I
00
10
I
Approximate Solullon AP
I
I
2 0
3 0
4 0
t’
Figure 7. Comparison of approximate solution with exact solution for b = 1and 2 and for spheres with an increasing linear distribution function of LY = 1.0.
08
x Fp:3, F g = 3
a=-io noct Solution _ _ _ EApproximote Solution
00
I I O
I
20
1 3 0
1 4 0
I
50
6 0
t’ Figure 8. Comparison of approximate solution with exact solution for b = 1 and 2 and for spheres with a decreasing linear distribution function of LY = 1.0.
neous reactions than in homogeneous reactions. Furthermore, the dependence of the rate on solid “concentration” must be separated into that on fractional conversion and on initial content. This points to the need for careful incorporation of the realistic picture of the solid into the mathematical formulation. Acknowledgment We thank the Institute of Chemical Metallurgy, Academia Sinica, for granting a leave of absence to Y .-N. Xia. This work was supported in part by a Camille and Henry Dreyfus Foundation Teacher-Scholar Award grant to H. Y. Sohn. Nomenclature A = fluid reactant species A,, A , = external surface area of the grain and the pellet, respectively B, b = solid reactant species and its stoichiometry coefficient, respectively C, c = fluid product species and ita stoichiometry coefficient, respectively CA, CAO = concentration and bulk concentration of fluid reactant A, respectively CC, Cc0 = concentration and bulk concentration of fluid product C, respectively D, d = solid-product species and its stoichiometry coefficient, respectively De = effective diffusivity of fluid A in the pellet E = relative error, defined by eq 44
F,, F, = shape factors for the grain and pellet, respectively (=l,2, and 3 for infinite slabs, long cylinders, and spheres, respectively) f(R) = distribution function of solid reactant B, based on -pB and used in eq 4 gF (x) = conversion function defined by eq 25 h(7) = dimensionless distribution function of solid reactant B k = rate constant of the fluid-solid reaction K E = equilibrium constant of the fluid-solid reaction pF,(X) = dimensionless conversion function in terms of X for diffusional control r, R = distance coordinates from the center of symmetry in the grain and the pellet, respectively rg,R, = distances from the center of symmetry to the outer surface in the grain and the pellet, respectively RA = intrinsic reaction rate of A t = reaction time t* = dimensionless reaction time, defined by eq 16 t d + = dimensionless reaction time for diffusional control, defined by eq 33 V A = local consumption rate of fluid species A per unit volume of pellet V,, V, 7 volumes of the individual grain and the pellet, respectively W F (7). = dimensionless conversion function in terms of 7, aefined by eq 36 X = conversion of solid reactant B Greek Symbols a , /3, y = parameters for the distribution function of solid
reactant B S = ratio of the volumetric average concentration of solid reactant B to its molar density 6 = porosity of the pellet 7 = dimensionless distance from the center of symmetry in the pellet [=(A$)/(FpVp)] 0, = parameter for the distribution function of solid reactant
b
X = parameter for the distribution function of solid reactant
B = dimensionless distance from the center of symmetry in
the grain = molar density of pure solid B p~ = volumetric average concentration of solid reactant B in ‘the pellet, defined by eq 4 p ~ ( 7= ) number of moles of solid reactant B per unit volume of the pellet u = fluid-solid reaction modulus defined by eq 17 2 = generalized fluid-solid reaction modulus defined by eq 35 w = parameter for the distribution function of solid reactant B = dimensionless concentration of fluid species defined by eq 14
-p~
+
Subscripts av = uniform distribution case with an average density pB
d = nonuniform distribution case f = fluid phase s = solid phase Literature Cited Ramachandran, P. A.; Dudukovic, M. P. Chem. Eng. Sci. 1984,39, 669. Sohn, H. Y. Metall. Trans. B 1978, 9B, 89. Sohn, H. Y. In Rate Processes of Extractiue Metallurgy; Sohn, H. Y., Wadsworth, M. E., Eds., Plenum: New York, 1979; pp 1-51. Sohn, H. Y. In Metallurgical Treatises; Tien, J. K., Elliott, J. F., Eds.; The Metallurgical Society of AIME: Warrendale, PA, 1981; pp 23-39. Sohn, H. Y.; Braun, R. L. Chem. Eng. Sci. 1980, 35, 1625. Sohn, H. Y.; Braun, R. L. Chem. Eng. Sci. 1984, 39, 21. Sohn, H. Y.; Johnson, S. H.; Hindmarsh, A. C. Chem. Eng. Sci. 1984, 40, 2185 (also Lawrence Livermore National Laboratory Report UCRL-90705, 1984).
Ind. Eng. Chem. Res. 1987, 26, 254-261
254
Sohn, H. Y.; Szekely, J. Chem. Eng. Sei. 1972, 27, 763. Sohn, H. Y.; Xia, Y.-N. Znd. Eng. Chem. Process Des. Dev. 1986,25, 386. Szekely, J.; Evans, J. W. Chem. Eng. Sci. 1970, 25, 1091. Szekely, J.; Evans, J. W. Chem. Eng. Sci. 1971a, 26, 1901. Szekely, J.; Evans, J. W. Metall. Trans. 1971b, 2, 1691.
Szekely, J.; Evans, J. W.; Sohn, H.Y. Gas-Solid Reactions; Academic: New York, 1976.
Received for review July 8, 1985 Revised manuscript received July 28, 1986 Accepted August 12, 1986
Supercritical Fluid Extraction of Alcohols from Water Esteban A. Brignole,+Poul M. Andersen,t and Aage Fredenslund* Instituttet for Kemiteknik, T h e Technical University of Denmark, DK-2800 Lyngby, Denmark
Carbon dioxide is the most studied solvent for high-pressure recovery of alcohols. The present analysis shows, however, that using carbon dioxide does not lead to significant energy savings or to completely dehydrate alcohols. Light hydrocarbons such as propane and butanes exhibit two important properties which may be exploited in alcohol-water separation: high-pressure extracting capability and water extrainment effect. Such solvents are termed dual-effect solvents. Cyclic processes, where both of the above properties are exploited, have been synthesized for the recovery of pure alcohols from even dilute aqueous mixtures. The main elements of the cyclic processes are a high-pressure extractor, which also acts as a water entrainer, and a solvent recovery column. For ethanol recovery, propane is suggested as a solvent, for 2-propanol and isobutane. In both cases, an energy savings of a factor of 3 is achieved compared with conventional azeotropic distillation using, e.g., benzene as an entrainer. The application of near critical fluid (NCF) extraction to the recovery of alcohols from aqueous solutions has several attractive features: very high selectivity, low solubility of the nonpolar NCF in the aqueous phase, ease of separation of the NCF from the extract, low heat of vaporization of the NCF solvent. The main difficulty of the separation is the relatively great affinity between alcohols and water. The equilibrium distribution of an alcohol between the water phase and the NCF phase is defined by the distribution coefficient m, ml = Y l / X l (1) where y1 and x1 are the mole fractions of the alcohol in the NCF and the aqueous phase, respectively. The value of the distribution coefficient greatly influences the economic feasibility of the extraction process. The best studied solvent for the recovery of alcohols from water is COz. However, in the case of ethanol recovery, the results of Kuk and Montagna (1983) and Kreim (1983), using COz at supercritical conditions, and of Moses et al. (19821, with liquid COz, indicate that even though there is a high ethanol-water selectivity in this process, it is not possible to break the azeotropic composition by means of a simple CO, extraction cycle. The maximum ethanol concentrations obtained in the pilot plant studies of Moses et al. were between 84 and 91 wt %. Another problem is the rather low distribution coefficient of ethanol in compressed or liquid CO,. When liquid COz is used to extract ethanol from a 10 wt % ethanol-water mixture, 100 mol of CO, is circulated in the process for each mole of ethanol recovered. Moses et al. (1982) reported a consumption of energy of 3167 kJ/kg of ethanol. This energy requirement is based on the use of a NCF extraction cycle (Figure 1)with vapor recompression.
* To whom correspondence should be
addressed. Permanent address: Plapiqui, Universidad Nacional del Sur, Bahia Blanca, Argentina. *Permanent address: Energistyrelsen, 1119 Kbhvn K, Denmark.
In comparison it is possible to obtain by ordinary distillation 85 wt % ethanol in water using 3400 kJ/kg of ethanol (Maiorella, 1982) or 91 wt % ethanol with 3900 kJ/kg.
Phase Equilibria and NCF Extraction As demonstrated in detail by Brignole et al. (1985), it is possible to quantitatively predict phase equilibria in mixtures of alcohols (primary, secondary, and tertiary), water, and alkanes or COz by using the Group-Contribution Equation of State, GC-EOS (Skjold-Jerrgensen,1984). The predictions, which as far as possible are compared with experimental data, verify that it is not possible to break the ethanol-water azeotrope by extraction with CO, except at subambient temperatures. One of the limitations of C02 as a NCF solvent is, thus, its relatively low critical temperature, which confines the extraction temperature to values close to or below ambient temperatures. The same limitation holds for ethane and ethylene. The use of solvents of higher critical temperature, like propane or butanes, will allow operation at higher temperatures with fluids of liquid-like densities. Predicted distribution coefficients for ethanol in propane are shown at 43 and 75 bar in Figure 2. The distribution coefficients of ethanol between propane and water, m,, increase monotonically with temperature when the pressure is above the critical pressure of propane. This illustrates the favorable effect of using a NCF solvent of greater critical temperature than those of CO, or ethane. Solvent Properties and NCF Extraction: Dual-Effect Solvents An important factor in any extraction process is the product concentration in the extract (solvent free basis). This concentration is shown in Figure 3 for the extraction of ethanol with propane and with n-butane. The operation at greater temperature decreases the selectivity of the solvent. Therefore, a product less rich in ethanol is obtained. However, this loss can be regained if the NCF solvent exhibits a water entrainment effect, under the
0888-588518712626-0254$01.50/0 0 1987 American Chemical Society
