Ind. Eng. Chem. Res. 1987,26, 56-65
56
When the cost of exergy is the same in all sections, the ratio P/C, should be equipartitioned. In other words "...in the optimal process, the changes in apparatus price are balanced by the changes of thermodynamic irreversibility ... for expensive apparata, only very intensive processes can be optimal...". The latter statements are quoted from Sieniutycz (1984) who substantiates them by extensive studies of drying processes. Similar considerations are put forward implicitly or explicitly by Bejan (1982): "...the heat transfer area should be concentrated in that region where the heat transfer is most intense...". The idea of an optimum distribution of investment, related to the distribution of irreversibility, is in fact more or less explicit in much of the literature on exergy analysis (Szargut, 1980). We have attempted to formalize this idea and to give it a somewhat general and fundamental basis. We believe the interest of the equipartition concept is primarily qualitative, in that it helps finding new routes for process improvement and avoiding misconception in the design of new processes. The extension of some of the arguments presented to multicomponent transfer and the generalization of the equipartition concept to nonlinear flux-force relations is left for further research. Acknowledgment We thank Maurice Roger, ENSIC-Nancy, discussions and constructive criticism.
for fruitful
Nomenclature a , b, c = cost constants in eq 40 A = cost factor for size-dependent investment cost (eq 43) B = cost factor for exergy-dependent operating cost (eq 44) c = solute concentration in solvent phase, mo1.L-l Ci, C8 = total and fixed in. estment costs, respectively (eq 43)
C, = variable investment cost, equal to the difference Ci - Cif C,, COf total and fixed operating costs, respectively (eq 44) f , f,f l , f = driving force: scalar, vector, component of vector, and average, respectively F = flow rate of solvent H = enthalpy j , j , J , J = transfer flux: local scalar, local vector, overall scalar, overall vector, respectively K,, K2 = constants defined by eq 48
L, L, Lij = transfer coefficient, matrix of transfer coefficients, and element thereof p = local rate of entropy production, J.K-'-S-'.~-~ P,Pc = overall rate of entropy production in arbitrary and in equipartitioned configuration, respectively, J.K-'.s-' Q = flow rate of treated stream As = specific entropy change A S = total entropy change AEx = exergy consumption t = time T , TO= absolute temperature and absolute ambient temperature V = volume or size variable of process Greek Symbols
R = cost function (eq 40 and 49) A = Lagrange multiplier in eq 41 2 = variance of the driving force distribution, in eq 7 T = amortization rate of investments L i t e r a t u r e Cited Bass, J. COUMde Muthematiques; Masson: Paris, 1968; Vol. 1. Bejan, A. Entropy Generation through Heat and Fluid Flow;Wiley Interscience: New York, 1982. Benedict, M. Trans. Am. Inst. Chem. Eng. 1947, 43, 41. De Groot, S. R.; Mazur, P. Non-equilibrium Thermodynamics; North Holland: Amsterdam, 1962. Franklin. N. L.; Wilkinson, M. B. Trans. Inst. Chem. Eng. 1982,60, 276. Glansdorff, P.; Prigogine, I. Structure, StabilitQ et Fluctuations; Masson: Paris, 1971. Gouy, M. J . Phys. (Orsay, FF.) 1889, 8, 501. Keenan, J. H. Mech. Eng. 1932, 54, 195. King, C. J. Separation Processes; McGraw Hill: New York, 1971. Kvaalen, E. Ph.D. Thesis, Purdue University, West Lafayette, IN, 1981. Le Goff, P. Energetique Industrielle; Technique et Documentation: Paris, 1982a; Vol. 1. Le Goff, P. Energetique Industrielle; Technique et Documentation: Paris, 198213; Vol. 3. Lewis, W. K. Ind. Eng. Chem. 1936,28 (4), 399. Mah, R. S. H.; Nicholas, J. J.; Wodnik, R. B. AZChEJ 1977,23, 651. Onsager, L. Phys. Rev. 1931, 37, 405; 1931, 38, 2265. Rant, Z. Forsch. Zngenieurwes. 1956, 22, 36. Sieniutycz, S. Chem. Eng. Sei. 1984, 39(12), 1647-1659. Stodola, A. Steam and Gas Turbines; McGraw Hill: New York, 1910. Szargut, J. Exergy 1980, 5, 709.
Received for review April 18, 1985 Accepted March 12, 1986
Modification of Supercritical Fluid Phase Behavior Using Polar Cosolvents J. M. Dobbs, J. M. Wong, R. J. Lahiere, and K.P. J o h n s t o n * Department of Chemical Engineering, T h e University of Texas, Austin, Texas 78712
T h e solubility of certain solids was increased markedly in supercritical carbon dioxide by adding small amounts of various cosolvents. For 2-aminobenzoic acid, the addition of only 3.5 mol % methanol increased the solubility 620%. By use of a modified van der Waals equation of state, over 15 new solubility isotherms were correlated within 7% and were predicted qualitatively by calculating the attraction constants using dispersion, orientation, acidic, and basic solubility parameters. These binary supercritical solvents can be highly selective for particular solutes due t o specific types of intermolecular interactions. The density and likewise the solubility parameter of a supercritical solvent vary strongly with respect to pressure and temperature in the critical region. A number of experimental investigators have found that the solubility of a hydrocarbon solid varies exponentially with the density of a nonpolar supercritical solvent such as carbon dioxide, 0888-5885/87/ 2626-0056$01.50/0
ethane, or ethylene (Diepen and Scheffer, 1953; Johnston et al., 1982; Johnston and Eckert, 1981; Kurnik et al., 1981). Therefore, the solubility is an extremely strong function of pressure and temperature in the near critical region, e.g., a t a reduced density below 1.3 where the magnitude of the isothermal compressibility and the 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 57 partial molar volume of the solute is large (Eckert et al., 1983, 1984; Kim et al., 1985; Sengers et al., 1983). This "density effect" can be utilized in supercritical fluid extraction to separate molecules based on volatility differences (Paulaitis et al., 1983; McHugh, 1984; Johnston, 1984; Schmitt and Reid, 1984). The approach of the present paper is to exploit an additional dimension of supercritical fluid extraction in which substances may be separated based on polar forces such as electron donor-acceptor complexation as well as on volatility differences. The thermodynamic analysis is focused on the supercritical phase by choosing a pure solid for the condensed phase and examining solid-fluid equilibria. We propose to superimpose a "polarity effect" on top of the density effect by the use of small amounts of cosolvents that contain polar and in some cases acidic or basic functional groups. The polar cosolvents used in this study cannot be used as pure supercritical solvents since their critical temperatures are prohibitively high for thermally labile substances. Carbon dioxide was chosen as the primary component of the solvent since it is nontoxic, is nonflammable, and has a critical temperature of 304 K. The polarizability of CO, is 26.5 X cm3which is less than that of all of the hydrocarbons except methane. A t 35 "C and 200 bar, the square root of the cohesive energy density or the solubility parameter of C 0 2 is 6.5 (call cm3)'I2; which is nearly comparable to that of liquid isopentane. At these conditions, the solubility in CO, of an aromatic solid such as benzoic acid is several orders of magnitude below the ideal solubility of a solid in a liquid (Prausnitz, 1969). As a result, the addition of a small amount of a hydrogen bond acceptor cosolvent or Lewis base such as acetone promotes a large solubility enhancement, so that the solubility may become several percent by weight. Larson and King (1986) show for a solubility of only 0.1% by weight that the cost of processing a drug is only about $28/kg even with 90% C 0 2 recycle. The literature contains only a few examples of experimental solid-fluid equilibria data for solid-cosolvent-supercritical fluid systems where the volatility of the cosolvent lies between that of the other two components. Kurnik and Reid (1982) demonstrated that the solubility of a solid may be enhanced in a supercritical solvent by the presence of a second solute. A new interpretation of this phenomenon is presented below. Irani and Funk (1977) showed that the introduction of benzene induces miscibility in the carbon dioxide-decalin system. Peter and Brunner (1978) increased the concentration of glycerides in C 0 2 by adding small amounts of acetone. Brunner (1983) also studied the effect of cosolvents on the separation factor of hexadecanol and octadecane in CO, and in NzO. The composition of the liquid phase was not measured, and consequently it was difficult to determine how much of the cosolvent affected the supercritical phase relative to the liquid phase. Cosolvents are useful in supercritical fluid chromatography (SFC), as they often promote large modifications in the retention times of compounds such as purines (Randall, 1983; Gere, 1983). These data represent the combined effects of the cosolvent in the supercritical as well as in the stationary phase. Unfortunately, it is difficult if not impossible to use these data to determine the effects of the cosolvent in the supercritical phase alone. Joshi and Prausnitz (1984) calculated the effects of cosolvents on the solubility of benzoic acid by using the Redlich-Kwong equation of state.
Co-solvent
t
L - - - - - - J
Qj
co2
Figure 1. Flow apparatus for solid-fluid equilibria.
The ratio of the solubility in the C02-cosolvent mixture over that in pure carbon dioxide follows qualitative trends based on dispersion, orientation, and acid-base solubility parameters for the solute and cosolvent, as discussed below in the Cosolvent-Induced Solubility Enhancement section. The relevant solute (2)-C02 (1)and solute (2)-cosolvent (3) attractive interaction constants, uI2 and ~ 2 3 respec, tively, are obtained from the data by using each of several equations of state in the next section. These attraction energies are calculated in the final section in terms of the physical properties of the pure components. The objective is to understand fundamentally and to predict cosolvent-induced solubility enhancement as a function of the physical properties of the pure components. It is an important step in our long-term objective which is to predict the solution properties of nonpolar and polar multicomponent supercritical mixtures based on the strength of dispersion, dipolar, and acid-base forces. This will provide a basis for future attempts to demonstrate that a multicomponent supercritical solvent mixture can be highly selective for particular solutes due to polar forces, hydrogen bonding, or other specific chemical forces (Dobbs et al., 1985). Rational utilization of these cosolvents could improve the economics of existing or proposed processes because of a reduction in the pressure and/or the recycle ratio or an increase in the yield. It could lead to more selective extractions for components which have similar volatility but different types of chemical forces and for compounds which have extremely limited solubilities in pure fluids, e.g., biomolecules.
Experimental Section The solubility vs. pressure isotherms were obtained for the solids benzoic acid (Fisher A-65), 2-aminobenzoic acid (A2,360-9), phthalic anhydride (Aldrich A-24,123-7), 2naphthol (Aldrich 135-19-3), and acridine (Aldrich A2,360,9),used as received, in pure C02 (Linde, Bone Dry Grade 99.8%) and C0,-cosolvent mixtures. The flow apparatus in Figure 1includes several major modifications compared to previous ones that were not designed for cosolvents (see references in introduction). The cosolvent solution was prepared by mixing a known weight of cosolvent in reservoir R3 (55 cm3) with a calibrated volume (906 f 5 cm3) of C 0 2 in reservoirs R1 and R2 using a reciprocating compressor. The digital pressure gauge, Heise 710A, was factory calibrated to 10.1% as traced to a NBS standard. During a run, the pressure fluctuations were on the order of *O.l MPa. The temperature of the solvent was controlled to *O.l "C in a thermostated water bath. The density of the solvent g/cm3 by using a mixture was measured to f1.0 X Mettler Paar DMA-512 vibrating tube densitometer, which was placed immediately in front of the first saturator S1. Each 316 stainless steel saturator, S1 and S2 (0.79-cm i.d. by 15-cm length), was packed with equal volumes of
58
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
I-
z w
Yw
05 -
a w
$ 01 80
160
240
320
I
I
I
J
16
18
20
22
DENSITY (MOL/L)
PRESSURE (BAR)
Figure 2. Solubility of benzoic acid in carbon dioxide with sulfur 4.35 mol dioxide cosolvent: (0)pure COz, (A)1.86 mol % SOz, (0) % SOz, (0)5.85 mol % SOz, (-) calculated by using uZ3from 4.35 mol '70 SO2 curve and HSVDW equation of state.
reagent grade sand, MCB-SX76, and solid solute in order to disperse the solvent flow. The equilibrated solution was separated by expansion to ambient pressure through a modified Autoclave 39VRM-4812 micrometering valve which also served as a flow controller, FC. The internal volume of the 1.4-mm-i.d. X 30-mm-long tube between S2 and the micrometering valve was 0.045 cm3, and the dead volume in the valve was reduced to less than 0.12 cm3. In order to minimize this volume, the densitometer was not positioned between the saturator and valve. Previous results indicate that the presence of less than 0.2 mol % solute changes the density less than 1% for reduced pressures above 1.2 (Ziger, 1983). The mass flow of the mixed gas, which was always above the dew point, was determined by using a Tylan Model 360 flow meter. In order to collect 50-200 mg of solute, the typical run time was 10-30 min for flow rates on the order of 0.5-1.0 std L/min. The measured pressure drop across the saturators was less than 1bar. The typical experimental reproducibility and uncertainty in y 2 were each 5%. A 6-mm-0.d. by 2-mm-i.d. quartz view cell, sealed with a standard Teflon ferrule, was used in a separate experiment to determine the phase boundaries of the solidC0,-cosolvent systems. A magnetically driven steel rod provided agitation. All of the data in Table I represent solid-fluid equilibria with no liquid phase present. One particular system, C0,-methanol-resorcinol (melting point 111 "C), was eliminated as 3.5% methanol and led to the formation of a liquid phase at 35 "C and at pressures of 100-350 bar.
Cosolvent-Induced Solubility Enhancement Since the effects of cosolvents have not been investigated systematically in the literature, we begin by describing a qualitative method that relates the ratio of solubility in the mixed solvent over that in pure COz to the physical properties of the pure components. The solubility isotherms for benzoic acid and 2-aminobenzoic acid in COS and in COz-cosolvent mixtures are shown in Figure 2-4. The solubility data for all the systems studied are shown in Table I. As noted previously (Johnston and Eckert, 1981), the solubility behavior is simplified when plotted against density instead of pressure, as this eliminates the effect of pressure on density. Figure 2 shows solubility isotherms a t 35 "C for benzoic acid for various mole percent concentrations of SO2 in C02. At 45 "C, the binary benzoic acid-C0, data (not shown) agree with the results
Figure 3. Solubility of benzoic acid in carbon dioxide with 3.5 mol % cosolvent at 35 O C : (0) pure cOz, (A)acetone + COz, (0) methn-octane + COz, (-) correlated by using HSVDW anol + COP,(0) equation of state.
t
,
1031 16
18
I 20
I 22
DENSITY (MOL/L)
Figure 4. Solubility of 2-aminobenzoic acid in carbon dioxide with 3.5 mol 70cosolvent a t 35 "c: (0) pure cop,(A)acetone + co2,(0) methanol + COz, (-1 correlated by using HSVDW equation of state.
of Kurnik and Reid (1981) to within 2%. The solubility at 120 bar with 5.8 mol % SOz is comparable to the solubility in pure C02 at 280 bar. This example demonstrates that the yield may be maintained at a greatly reduced pressure by adding only a small amount of cosolvent. The shape of each ternary isotherm is similar to the binary ones in Figures 2-4 such that the ratio of y , in the ternary system (COz + cosolvent) to y2 in the binary system (pure COz) is relatively invariant with respect to pressure. This serendipitous discovery simplifies the development of the models for the phase equilibria. The density effect is about the same in the mixed solvent as in pure CO,, but in the mixed solvent the polarity effect shifts the isotherm upward by a relatively constant factor. In Table 11, the solubility enhancements are listed for a variety of cosolvents and solutes at 35 "C and at a constant density of 20.5 g-mol/L (25 MPa for pure COJ. These solubility enhancements may be discussed qualitatively based on the pure component data in Tables I11 and IV, although it is necessary to consider repulsive as well as attractive forces. For example, even though octane has the largest polarizability of the cosolvents listed in Table 111, it also has the largest molecular volume, which would give the greatest repulsive forces. Therefore, it is more useful to relate the solubility enhancement to an energy divided by the volume, i.e., a cohesive energy density or a solubility parameter. A variety of types of
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 59 Table I. Solubility of Solids in C 0 2 and in C 0 2 Doped with 3.5 mol 70 Acetone or Methanol at 35 OC benzoic acid-C02 benzoic acid-acetone-C02 benzoic acid-methanol-C02
P, bar
P,
120 160 200 240 280
mol/L 17.46 18.81 19.67 20.34 20.92
103y 1.25 2.19 2.53 2.81 3.03
P, bar
1 0 3 ~
P, bar
benzoic acid-octane-C02
P, bar
P,
100 150 250 300 300
mol/L 16.29 17.60 18.99 19.45 19.45
2-aminobenzoic acid-methanol-COz P, bar R . mol/L 90 16.53 120 18.11 150 19.01 200 20.04 250 20.77 300 21.36 acridine-C02 P. bar o. mol/L 120 17.46 150 18.54 150 18.54 200 19.67 280 20.92 350 21.62
hexamethylbenzeneacetone-C02
P, bar 100 100 100 100 120 150 200 250 350 350
p,
mol/L 17.23 17.23 17.23 17.23 18.04 18.81 19.79 20.49 21.49 21.49
103y 1.58 1.51 1.55 1.66 1.83 2.17 2.24 2.30 2.24 2.21
Pt
100 120 120 150 200 250 330
mow 17.23 18.04 18.04 18.81 19.79 20.49 21.33
1 0 3 ~
2.90 4.31 5.55 6.07 5.82
1 0 3 ~
120 150 200 250 300 350
103y 0.080 0.099 0.113 0.127 0.135 0.161
P, bar
1.42 1.53 2.27 3.14 3.45
acridine-acetone-C02 o. mol/L 18.04 18.04 19.79 19.79 20.49 21.06 21.49
103v 1.25 1.25 1.80 1.92 1.97 2.05 2.21
120 150 200 300 350
103v 0.585 0.743 0.751 0.775 1.09 1.26
P. bar 120 120 200 200 250 300 350
hexamethylbenzenemethanol-C02 103y p , mol/L P, bar 100 17.21 1.50 120 18.11 1.63 2.11 200 20.04 200 20.04 2.32 350 21.84 2.21
solubility parameters are listed in Table IV. The total solubility parameter, 6T, is the standard Hildebrand value calculated from the heat of vaporization and subcooled liquid volume (Barton, 1983). The component solubility parameters describe dispersion, 6D, orientation or permanent dipole forces, 6O, induction forces, 6', acidity, 6A, and basicity, 6B. Although the calculation of 6D is straightforward (Barton, 1983), the calculated values of 6A and aB are approximate and depend upon the basis, e.g., spectroscopic data (Karger et al., 1976) or excess properties (Tijssen and Billiet, 1976; Thomas and Eckert, 1984). The 6A of benzoic acid was obtained from spectroscopic data for the dimethyl sulfoxide-benzoic acid adduct (Taniewska and Goralski, 1981) by using an expression that was developed by Karger et al. (1976), eq 1. The (1)
P, bar 100 120 150 200 250 250 300 350 350
mol/L 16.53 17.21 18.11 18.11 19.01 20.04 20.77 20.77 21.84 21.84
104 5.33 6.01 7.43 7.18 8.77 10.1 10.6 10.9 11.2 11.9
2-aminobenzoic acid-acetone-COz
phthalic anhydride-COz o. mol/L 17.46 18.54 19.67 21.17 21.62
P, bar
0.48 0.60 0.69 0.82 0.91 0.96
AH = 1.86A6Bu
moW 17.46 18.54 19.67 20.47 21.11 21.62
P,
90 100 120 120 150 200 250 250 350 350
2-aminobenzoic acid-C02 P,
P, bar
3.34 3.83 3.98 4.49 5.37 5.92 6.40
1 0 3 ~
2-naphthol-C02 p , mol/L 16.24 17.46 18.54 19.67 20.47 20.47 21.11 21.62 21.62
P,
90 120 150 180 250 300
mol/L 16.83 18.04 18.81 19.51 20.49 21.06
103~
0.16 0.25 0.27 0.29 0.39 0.45
phthalic anhydride-acetone-C02 o. mol/L 103v 200 19.79 4.29 200 19.79 4.31 300 21.06 5.46 300 21.06 5.21
P, bar
acridine-methanol-C02 o. mol/L 18.11 19.01 20.77 20.77 21.36 21.36 21.84 21.84
P. bar 120 150 250 250 300 300 350 350
103y 0.277 0.372 0.437 0.557 0.661 0.635 0.678 0.754 0.726
103v 2.40 2.77 3.11 2.90 3.24 3.05 3.04 3.10
2-naphthol-methanol-C02 p , mol/L 103y 1.85 120 18.11 150 19.01 2.15 200 20.04 2.64 250 20.77 2.86 300 21.36 2.84 350 21.84 3.08
P, bar
other acid and base solubility parameters were obtained based on Table I in Karger (1976) and group contribution concepts in Chapter 6 of Barton (1983). The concept of a pure component JA is oversimplified as aA depends to a certain degree on the nature of the basicity of the other component. Most of the examples of the cosolvent-induced solubility enhancement in Table I1 can be explained qualitatively by using the dispersion and acid-base solubility parameters of the solute and cosolvent. For example, the solubility enhancement for benzoic acid, 6* = 9.3 (cam/cm3)ll2,is = 8.3 (cal/cm3)'/', significantly greater for methanol, than for the weaker base, acetone, for which hB = 3.0 (cal/cm3)'1'. Octane gives an enhancement which is comparable to that of acetone due to the large degree of dis/ ~ .these conditions (35 "C persion, 6D = 7.6 ( c a l / ~ m ~ ) ' At and 25 MPa), aD is only 6.5 ( c a l / ~ m ~ )for ' / ~COz.
60 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 Table 11. Cosolvent-Induced Solubility Enhancements of Solids in Carbon Dioxide at 35 "C and at a Density of 20.5 g-mol/L yZ (ternary)/ y 2 (binary) solid cosolvent benzoic acid methanol 3.7 2.1 acetone 2.3 n-octane 7.2 2-aminobenzoic acid methanol 3.1 acetone 1.7 phthalic anhydride acetone 1.1 hexamethylbenzene methanol 1.2 acetone 2.1 n-octane" 1.8 n-pentane" 2.3 acridine methanol 1.7 acetone 4.5 2-naphthol methanol
" Dobbs et al.,
1986.
The solubility of hexamethylbenzene, which is only slightly basic (aB = 2 ( ~ a l / c m ~ ) ' /is~ affected ), equally by acetone and methanol. They have the same 6D, although the latter is significantly acidic (BA = 8.3 (cal/cm3)'I2). The solubility enhancement is a factor of 2 greater for octane compared with methanol because of the larger FD. The 6D of hexamethylbenzene is so much larger than FB that the acidity of the cosolvent appears to be immaterial. This argument may be somewhat oversimplified as COz,a Lewis acid, is an unusually good solvent for strong bases such as acridine, as discussed below. The solubility of 2-aminobenzoic acid was enhanced an order of magnitude by methanol addition, as both compounds have significant acidity as well as basicity. A comparison of the benzoic acid-methanol and 2-aminobenzoic acid-methanol systems suggests that multiple acid-base interactions occurred in the latter despite steric limitations. The enhancement was four for acetone which is less basic than methanol and is not acidic.
The solubility of acridine was increased less than that of benzoic acid by adding methanol. Methanol is equally basic and acidic according to Karger et al. (1976). This may be explained by the values of 6* = 9.3 (cal/cm3)ll2for benzoic acid relative to FB = 3.8 ( ~ a l / c m ~ for ) l / acridine. ~ A comparison of F0 with FD for acridine suggests that the enhancement for acridine is affected more by dispersion than orientation forces. In order to emphasize the polarity effect, most of the experiments were performed at a pressure above 12 MPa, where the reduced density is greater than 1.3 and the fluid is relatively incompressible. In addition, it is necessary to maintain the pressure at a sufficiently high level such that the cosolvent and C02 are miscible. The molar density of the cosolvent-C0, mixture is greater than that of pure COPa t the same pressure and temperature for all of the cosolvents with the exception of octane. The molar density of pure octane is only 6.15 g-mol/L at 20 "C compared to 20.5 g-mol/L for C 0 2 at 35 "C and 250 bar. A t this temperature and pressure, the molar density is 19.09 g-mol/L for a 3.5 mol % octane in C02 solution and 20.77 g-mol/L for a 3.5 mol % methanol in COz solution. In pure C 0 2at 35 OC, the solubility of benzoic acid would increase by a factor of 1.02 for a change in the density from 20.5 to 20.77 g-mol/L. This increase is much less than the enhancement of 3.7 which is obtained by adding 3.5 mol % methanol (see Table 11). Therefore, in the dense supercritical region, the modification in the solvent's density due to addition of the cosolvent contributes only slightly to the solubility enhancement. Solid-fluid equilibria of nonpolar systems can be calculated only to within an order of magnitude by using the original version of regular solution theory (Prausnitz, 1977; Wong et al., 1985). At 35 "C and 25 MPa, the solubility parameter of C 0 2 is 2-7 ( c a . / ~ m ~ )below ' / ~ that of each of the solids listed in Table IV; thus, regular solution theory predicts large positive deviations or activity coefficients on the order of 102-103. The accuracy of the theory is
Table 111. Physical Properties of Solids and Cosolvents fi? D a , cm3 x IOz5 Solutes 1.7 133b benzoic acid 2-aminobenzoic acid 1.5 145b phthalic anhydride 5.2 15Zb hexamethylbenzene 0 208' 1.95 255d acridine 1.5 173' 2-naphthol
Patat. 35 "C, Pa x 10'-
u ~ cm3/g-mol , ~ 104 106 112 175 149 119
b,k cm3/g-moi 65 66.7 75 96 101 81.9
35' 1.29 18 h
50' 2.11 6.8
Cosolvents 63.3b
2.9 1.7 0
acetone methanol n-octane
73.5 41.7 163.5
32.3b
154b
36 21 89
McClellan, 1974. *Calculated from Miller (1979). Sanyal, 1973. Schuyler, 1953. eEstimated from Prausnitz (1969, Chapter 9), Bondi (1968), Al-Mahdi (1953), and Chertkoff (1960). fColomina, 1982. gde Kruif, 1979. hDas, 1979. 'Ambrose, 1976. jMcEachern, 1975. Wong et al., 1985; Bondi, 1968.
Table IV. Solubility Parameters ((cal/cmg)'/*)of Solids and Cosolvents benzoic acid 2-aminobenzoic acid phthalic anhydride hexamethylbenzene 2-naphthol acridine acetone methanol n-octane
6T"
6D
60 e
6'
6A e
6B
13.0 12.7 11.0 8.3 12.2 10.5 9.6 14.5 7.6
8.9 8.9 8.9 8.0 10.1 9.5 7.2 6.8 7.6
2.5 2.5 4.5
0.3
9.3d
0.0
1.8 3.0 5.1 4.9 0.0
0.2 0.3 1.5 0.8 0.0
0.0 8.6 0.0 0.0 8.3 0.0
2.0 2.0 3.8O 3.0 8.3
2.9
0.0
"Barton, 1983. "gD for solids from Small's group contribution method and by comparison with homomorphs (Barton, 1983, Chapters 3 and 4). 'Karger, 1976. dEstimated from spectroscopic data of Taniewska (1981) by using Karger's method. "Based on pyridine and quinoline (Karger, 1976).
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 61 Table V. ComDarison of Predicted and ExDerimentally Regressed Values of the Solute-Cosolvent Attraction Energy
aI2, solute benzoic acid
cosolvent acetone methanol n-octane 2-aminobenzoic acid acetone methanol phthalic anhydride acetone hexamethylbenzene acetone methanol acridine acetone methanol 2-naphthol methanol
bar.cm6 1.51 1.53 1.63 1.66 1.86 1.64
AUZgTdd
azdaiz
2.86 2.92 4.61 3.27 3.73 2.62 2.33 1.66 2.71 2.42 3.09
AUZ3T,exPtl c
e
49.1 66.7 52.7 59.5 82.9 47.2 34.3 32.2 48.1 57.1 72.0
47.4 58.6 37.1 40.6 30.5 29.0 41.3 44.8 65.4
% U R D in y z using the regressed aZ3shown in the table (correlated). kJ/g-mol.
limited since the supercritical fluid solution is far removed from an ideal reference. In engineering applications, it may be possible to choose the appropriate “cosolvent” for a particular solute by matching the component solubility parameters, b”, 6O, iIA, and bB, of the cosolvent with those of the solute (Barton, 1983). However, a modified regular solution theory approach that uses ljD,So, bA, and 6B is not recommended for the quantitative calculation of activity coefficients since large errors result for the dispersion term if 62D > blD.
Attraction Parameters Obtained from the Data The flow diagram in Figure 5 depicts a useful thermodynamic approach for analyzing cosolvent-induced polarity effects on the solubility. The binary solute ( 2 ) - C 0 2 (1) attraction constant, aI2,is obtained from cosolvent (3)-free binary data. The solute-cosolvent attraction parameter, ~ 2 3 is , the key property that influences the cosolvent-induced solubility enhancement. Path A in the figure indicates a method for correlating ternary data in terms of the interaction parameter, ~ 2 3 . The solubility of a solid (2) in a supercritical fluid (1) (Prausnitz, 1969), is Pzsat
Y2
u,(P - P p ) RT
ex.(
)
=
42p where the key variable, 42, is given by
RT In 42 = jm[(dP/dn2)T,v,nl,nr - R T / u ] du
A
u
23.6 16.8 37.1 20.8 14.2 24.3 27.3 19.5 30.4 21.6 18.8
y 2 ~ r e d .6 YzCorr~ a A~ u~ AuzJ ~~ ~~ A ~ u ~ ~% AARD ~ ~ %~AARD 4.7 3.2 15.9 5.0 7.0 32.0 3.4 2.5 35.9 12.0 0.0 0.0 0.0 51.0 2.5 5.5 21.0 8.7 7.6 28.2 3.8 26.4 4.4 0.0 3.2 0.0 29.9 0.0 1.4 8.1 6.7 23.8 5.3 6.8 4.1 0.0 50.0 4.9 1.9 16.4 8.3 2.6 1.7 42.3 19.6 5.1 32.5 av 7.3%
* %AARD in y z using A
~ to ~obtain ~ aZ3 * (predicted). ~ ~ ~ In ~
u
Ternary y2 versus P d a t a CO2 ( I ) - S o l u t e ( 2 ) - C o s o l v e n t ( 3 )
I
C 0 2 (I)-Solute ( 2 )
Equation
of state
z7 Equation of slate
Physical Properties o f Pure Components D
S., I
O
A
B
I . ,S i , 6 . 1
Figure 5. Thermodynamic modeling strategy for the correlation and prediction of the effects on cosolvents of solid-fluid equilibria.
(2)
- RT In z
U
(3) The Peng-Robinson (PR) (Peng and Robinson, 1976) and hard sphere van der Waals (HSVDW) equations of state are used during this study in eq 3. The HSVDW equation of state consists of an accurate expression for the hard sphere mixture (Mansoori et al., 1971) plus the standard van der Waals attractive term. Substitution of the HSVDW equation of state, including the van der Waals onefluid theory (VDW1) mixing rule, a =EEyyjaij (4) i l
into eq 3 yields In ( 4 2 2 ) =
The key parameters in this expression are the binary interaction constants, aI2and ~ 2 3 shown , in Table V.
Eckert et al. (1984) and Johnston and Kim (1984) analyzed the property, n(dP/dn2);,v,nl, which is the most fundamental macroscopic thermodynamic property that describes solution behavior. It is a normalized partial molar volume as indicated by the relationship n(dP/dn2)?,~,nl = V/(UI~T)
(6)
where kT is the isothermal compressibility and D2- is the partial molar volume at infinite dilution. In the dense supercritical region where pr > 1.3, it was assumed that the radial distribution function gI2(r) does not vary with density. This gives the result n(dP/dn2Ettractive= -p12(constant)
(7)
which does not depend upon any assumptions regarding mixing rules. However, the combination of the van der Waals attractive term with the VDWl mixing rule (eq 4) gives the same result as eq 7. The experimental D2- data (Ziger, 1983; Eckert et al., 1984) were correlated accurately by using eq 7 in the dense supercritical region for nonpolar binary systems. We choose to approximate the behavior of polar systems by using the VDWl mixing rule for reasons explained below. Supercritical solution behavior is difficult to model because the mixtures are often highly compressible and
62 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
as shown in eq 2 and 5. Although a Z 3 / a l 2is 4.6 for the system benzoic acid-octane-C02, the solubility enhancement is only 2.3 since the ratio of molecular volumes b2/bl is 6. Therefore, an exponential increase in the solubility which is due to the attraction parameter, ~ 2 3 ,can be partially offset by the repulsive forces due to b2. The solubility isotherms of the benzoic acid-S02-C02 system are predicted with an AARD of 8% for the cosolvent concentrations shown in Figure 2. The a23 value was regressed from the isotherm where 3t3 = 4.35 mol 9'0 and was used to calculate the isotherms at x3 = 1.86% and 5.85%. This demonstrates that the model can predict the cosolvent-induced solubility enhancement as a function of the concentration of cosolvent. For a mixture of two solids in a pure supercritical solvent, the solubility isotherms may be interpreted by using eq 5. Kurnik and Reid (1982) measured the solubility of naphthalene (20%)-phenanthrene (75% 1, benzoic acid (280%)-naphthalene (107%), 2,3-dimethylnaphthalene (144%)-naphthalene (46%), and phenanthrene (-10%)2,3-dimethylnaphthalene (-10%) mixtures in COB. The number in parentheses represents the maximum increase in the solubility of a component of the ternary system compared to that in the binary system. The solid components in each pair are designated at 2 and 3, respectively. In this first-order analysis of the solubility increases, we consider the effects of the term ~ 2 ~ in2 eq 3 5 and neglect those of the term y2azz. The constant a 2 3 is much larger than a I 2since the polarizability of component 3 is much larger than that of component 1, COP. The solubility, y2, will increase for every molecule of component 3 that replaces a COP molecule in the fluid phase. Therefore, we propose the rule that the solubility of a given solid in the ternary system will increase relative to that in the binary system in proportion to the solubility of the other solid in CO,. For example, in COz, naphthalene is much more soluble than phenanthrene. Consequently, in the ternary system naphthalene raises phenanthrene's solubility 75 % , while its solubility increases only 20%. Naphthalene and benzoic acid are both highly soluble in COS,and therefore both solubilities are increased over 100%. The solubilities of phenanthrene and 2,3-dimethylnaphthalene, which are low in the binary case, actually decrease in the ternary case.
strongly asymmetric in terms of the size and energy differences of the components. For polar supercritical systems, the model must recognize (1)nonidealities that are usually described in the liquid state using an excess Gibbs free energy model and (2) equation of state or density effects. The development of a model for the polar supercritical solution is challenging as the actual conditions are far removed from either the ideal gas or the ideal solution reference states. Consider the distribution of methanol and carbon dioxide molecules about a benzoic acid molecule a t a solubility, y z , that is so low that solute-solute interactions are improbable. The local mole fractions of methanol in the first solvent shell will exceed the bulk mole fraction because methanol interacts more strongly with benzoic acid than does COz. The combination of an equation of state with local-composition, density-dependent mixing rules (Mollerup, 1981; Whiting and Prausnitz, 1982) is a powerful technique for describing this clustering phenomena. Unfortunately, neither spectroscopic nor computer simulation data are available currently for the testing and development of this approach for supercritical solutions. This type of mixing rule may require additional interaction parameters, which are presently being defined using computer simulation data for the liquid phase. Given the complex nature of the cosolvent-induced chemical effect, which involves a number of types of intermolecular forces, we have decided to begin with the well-defined VDWl attractive mixing rule. In the dense supercritical region, where the local compositions and therefore the radial distribution functions are relatively insensitive to density, this mixing rule can be used to correlate the data. The regressed value of the solute-cosolvent attraction parameter, aZ3,will be artificially large to compensate for the use of the bulk instead of the local value of y3. This basis will be useful for future models that include local-composition mixing rules. The size parameter which is used in the repulsive contribution of eq 5 was regressed for C02 by using PVT data (Oellrich et al., 1978). For the solute and cosolvent, the actual van der Waals volume, calculated rigorously (Wong et al., 1985), was used for b. Since the equations of state do not predict the density accurately, experimental densities were used for the pure and the mixed solvents. The value of aZ2was obtained using critical properties (oellrich et al., 1978), although a similar value can be calculated from the molecular volume (Wong et al., 1985). The a12 value was found in the binary case by minimizing the average absolute deviation (AARD) for the y 2 vs. P data (see Figures 2-4 and Table IV) where
Given a12,aZ3was obtained independently by minimizing the AARD in y 2 for the ternary isotherms (see Table V). Examples of these correlations of the data are shown in Figures 2-4 for the HSVDW equation of state. The average value of the AARD in y z for the ternary systems at 35 "C was 7.3% for the HSVDW and 10.6% for the Peng-Robinson equations of state. The mechanism of cosolvent-induced solubility enhancement can be explained based on the a12 and a23 values in Table V in conjunction with eq 2 and 5. For example, a solution of 3.5 mol % methanol in C 0 2 significantly enhances the solubility of benzoic acid (see Table 11) since the ratio of attraction constants a23/a12 is nearly 3 while the ratio of molecular volumes b2/bl is only 1.5. The solubility is related exponentially to the factor ~ 3 ~
Prediction of the S o l u t d o s o l v e n t Attraction Energy
2 3
Once the experimental solubility data have been correlated, the next objective is to estimate the solubilities by calculating the solute-cosolvent attraction parameter, aZ3, from the pure-component properties. The effects of dispersion, orientation, and hydrogen bonding or acid-base forces will be included in this calculation, as shown by path B in Figure 5. The contribution of the repulsive forces is obtained in a straightforward manner by using pure-component molecular volumes in eq 5. The prediction of phase equilibria is challenging for polar liquid mixtures even at low pressures. Currently, the excess Gibbs free energy models can be used to correlate (but not to predict) infinite dilution activity coefficients of systems that include hydrogen bonding (Karger et al., 1976; Tijssen and Billiet, 1976; Thomas, 1984). Equation of state approaches that use corresponding states theory based on critical properties are only correlative for solidfluid equilibria, even for nonpolar systems (Johnston and Eckert, 1981). Since the critical temperatures are far apart in these highly asymmetric mixtures, the values of the binary interaction parameter, h,,, that are obtained from the data are unpredictable. Wong et al. (1985) predicted the solubility isotherms of hydrocarbons in C 0 2 and C2H4
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 63 quantitatively by calculating u12from molecular volumes instead of from critical properties. Jonah et al. (1983) calculated solubility isotherms for octane and methanol in various solvents a t supercritical conditions using a Pade' equation of state. Although this approach treats mixtures more rigorously than those which use the VDWl mixing rules, it has not been applied to large molecules such as hexamethylbenzene with complex potentials. The theory would become extremely complex for the systems that include hydrogen bonding; thus, we choose to make several simplifying assumptions. The attractive part of the potential energy is assumed to equal a sum of pair potentials. The unperturbed or reference system consists of hard spheres. The pair potential is assumed to include dispersion, orientation (diple-dipole), and hydrogen bonding or acid-base forces where
+
+
uij(r)= uijD(r) uijO(r) uij'(r)
+ uijAB(r)
(9)
The van der Waals constant may then be expressed as
u i t B ( r ) ] g i j ( rr2 ) dr (10)
where it is assumed that the attractive forces do not affect the structure of the fluid. The form of eq 10 indicates that the van der Waals attraction constant may be written as a sum of components that correspond to the various types of intermolecular forces. The dispersion and orientation pair potentials are functions of physical properties of the pure components, e.g., the polarizability and dipole moment. These properties can also be used to calculate dispersion and orientation solubility parameters (Prausnitz, 1969, Chapter 4; Cammarata and Yau, 1972). Since tabulations of JD and 6O are abundant in the literature, it is convenient to express aij in terms of solubility parameters. This method provides a further advantage in that experimental solubility parameters include physical information that is not included in simple expressions for the pair potential, as in the London expression for dispersion. The approach shown by path B in Figure 5 is a novel combination of physical property information for the liquid phase with an equation of state. In the new approach, the component solubility parameters which represent dispersion, orientation, and acid-base forces are used to predict the attraction constant, aij,that is used in the equation of state. This method does not use an excess Gibbs free energy model. The pair configurational internal energy may be expressed in terms of the cohesive energy density Auij = c1./ .1 ~1 = . . 6.6.(u.u.)1/2 1 1 1 1 (11) The pair cohesive energy density may be written as (Prausnitz, 1969, Appendix VI)
and compared with eq 10 to give a 5,1 . = c..u.u. 11 1 I = AuijT(uiuj)1/2
(13)
The total pair configurational energy may be separated into its components AuijT = A U11 . . ~ Au..O $1 + Au.1 41 + A u11 . . ~ ~ (14)
+
according to eq 9, 12, and 13. The solute-cosolvent attraction parameter, ~ 2 3 is , calculated from eq 13 and 14. The component energies, AuBD and A u ~ ~ O are , calculated by using eq 11 along with the
solubility parameters and volumes listed in Tables I1 and 111. The hydrogen bond energy is given by A ~ 2 =3 l.8(62A63B ~ 62B63A)(~2~3)'/2 RT (15)
+
where the constant 1.8 was optimized by Karger et al. (1976) based on energies that were obtained spectroscopically. The induction energy is calculated by Au,,' = 0.6(6,'63D 62D63')(u2u3)112 (16)
+
where the constant 0.6 was obtained empirically. In Table V, the calculated and experimental values of A~2= 3~ are compared by using units of kJ/ g-mol. The same comparison may be performed for the a23 values, but the units of bar cm6/g-mol2are less desirable. The uncertainty in A u ~is on ~ the~ order , ~ of 10% ~ ~ for systems with small cosolvent-induced solubility enhancements but is smaller for systems with large enhancements. The agreement in the calculated and experimental A ~ 2 values 3 ~ was found to be nearly within the experimental uncertainty for nonpolar pairs, including hexamethylbenzene-octane or -pentane and phenanthrene-octane or -pentane (Dobbs et al., 1986). The solubility isotherms of these nonpolar systems are predicted to within an average deviation of 14% using no adjustable parameters. For these nonpolar systems, the success of the VDWl mixing rule is not so surprising, given the results which were explained above for n(dP/dn2)" (see eq 7 ) . The prediction of the solubility isotherms is only qualitative for the polar systems due to the greater complexity of polar forces and to the limitations of the VDWl mixing rule. In eq 5 , the uncertainty in the solubility is more sensitive to uncertainties in a12than those in ~ 2 3 , which are multiplied by y 1 = 0.965 and y3 = 0.035, respectively. As a result, the ternary solubility data can be predicted within an average deviation of 32.5%, even with the crude mixing rule. In every case, the experimental value of A ~ 2 exceeds 3~ the calculated value. The solubility increases with the presence of the cosolvent in every system so that the ratio of the regressed constants, a23/a12,is greater than unity. Since the cosolvent interacts more strongly with the solute than does COP,the solvent cage is enriched in the cosolvent. In order to illustrate an important point, we neglect the effects of other interactions, e.g., 3-3 and 1-1 interactions, on the local-composition behavior. The regressed or experimental value of A ~ 2 is 3 ~artificially high to compensate for the failure to include the local-composition behavior or enrichment of the cosolvent about the solute. These systems will provide a significant challenge for future models that include density-dependent, local-composition mixing rules or that are based on perturbation theory. The large disagreement (51%) for the n-octane-benzoic acid interaction energy, A ~ 2 3may ~ , be due to dimerization of the benzoic acid. The percent dimerization is about 90% in pure carbon tetrachloride and is negligible in acetone (Dobbs, 1986). The interaction energies for the benzoic acid system should be considered to be qualitative as the theory neglected dimerization. Since the product, 6Du, for acetone and methanol is similar to that for C02,the solubility enhancements due to these cosolvents must be attributed to polar forces. For benzoic acid, a23 is significantly greater than a12for these cosolvents due to hydrogen bonding. The hydrogen bonding energy is nearly comparable to the dispersion energy for acetone-benzoic acid, while it is more than twice the dispersion energy for methanol-benzoic acid. Unfortunately, the acid and base solubility parameters could not
~
~
64
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
be calculated for 2-aminobenzoic acid due to a lack of spectroscopic data. For the methanol-2-aminobenzoic acid system, the experimental total energy is 7 times the dispersion energy and the solubility enhancement is nearly an order of magnitude. For the methanol-2-naphthol system, the hydrogen bonding energy is nearly twice the dispersion energy, so that the solubility enhancement is 4.5. The solubility is predicted to within 19.6%. The ratio of orientation to dispersion energy was less than 25% in most cases. For phthalic anhydride, which has a dipole moment of 5.2 D, the ratio of orientation to dispersion energy reached 0.4. The solubility of the relatively nonpolar solid, hexamethylbenzene, was not affected significantly by acetone or methanol where the only important force is dispersion. This is further evidence that the induction energy due to these dipolar cosolvents is insignificant. Conclusions The cosolvent-induced solubility enhancements, which are almost independent of pressure, can be understood qualitatively as a function of dispersion, orientation, and acid-base solubility parameters. In the dense supercritical region, pr > 1.3, the modification in the solvent density due to presence of the cosolvent contributes only slightly to the solubility enhancement. The enhancements can be predicted qualitatively by using component solubility parameters to calculate the solute-cosolvent attraction constant, uB, which can be used in either a HSVDW or a P R equation of state. This new approach for the dense gas state avoids corresponding states theories based on critical properties, while it includes dispersion, orientation and acid-base interactions as well as equation of state or density effects. The predictions are quantitative for nonpolar systems, for which the effects of local-composition behavior appear to be minimal. The enhancement increases exponentially as the ratio u23/u12 increases (1, CO,; 2, solute; 3, cosolvent) but decreases strongly as the molecular volume b3 increases. Large solubility enhancements greater than 300 % were observed and predicted for small cosolvents, such as methanol, that form strong hydrogen bonds with the solute. The effects of orientation forces are relatively insignificant for solutes that have a dipole moment below 5 D. The most significant conclusion is that a nonpolar supercritical solvent when doped with a small amount of certain cosolvents can become highly selective based on chemical functionality for compounds of similar volatility. Acknowledgment This material is based on work supported by the National Science Foundation under Grant CPE-8306327. Any opinions, findings, and conclusions or recommendations expressed in this publication do not necessarily reflect the views of the National Science Foundation. We also acknowledge the Separations Research Program a t The University of Texas a t Austin and the Atlantic Richfield Foundation. Nomenclature a = van der Waals attractive parameter b = van der Waals volume c = cohesive energy density kT = isothermal compressibility u(r) = pair potential Au = configurational pair energy uL 2 subcooled liquid volume u," = partial molar volume at infinite dilution z = compressibility factor
Greek Symbols 4 = fugacity coefficient = volume fraction 6 = solubility parameter, ( ~ a l / c m ~ ) ' / ~ u = hard sphere diameter a = molecular polarizability p = dipole moment Superscripts
A = acid B = base D = dispersion 0 = orientation I = induction Subscripts
co*
1= 2 = solute 3 = cosolvent Registry No. COP,124-389;methanol, 67-56-1; 2-aminobenzoic acid, 118-92-3;benzoic acid, 65-85-0; acetone, 67-64-1; octane, 111-65-9; phthalic anhydride, 85-44-9; 2-naphthol, 135-19-3; acridine, 260-94-6; hexamethylbenzene, 87-85-4.
L i t e r a t u r e Cited Al-Mahdi, A. K.; Ubbelohde, A. R. Proc. R. SOC.London, Ser. A. 1953, A220, 143-156. Ambrose, D.; Lawrenson, I. J.; Sprake, C. H. S. J . Chem. Thermodyn. 1976, 8 , 503-504. Barton, A. Handbook of Solubility Parameters and Other Cohesive Parameters; CRC: Boca Raton, FL, 1983. Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968. Brunner, G. Fluid Phase Equilib. 1983, I O , 289-298. Cammarata, A.; Yau, S. J. J . Pharm. Sci. 1972, 61, 723-727. Chertkoff, M. J.; Martin, A. N. J . Am. Pharm. Assoc. 1960, 49, 444-474. Colomina, M.; Jimenez, P.; Tarrion C. J . Chem. Thermodyn. 1982, 14, 779-784. Das, D.; Dharwadkar, S. R.; Chandrasekharaiah, M. S. Thermochimica 1979, 30, 371-376. de Kruif, C. G.; Voogd, J.; Offringa, J. C. A. J. Chem. Thermodyn. 1979, 11, 651-656. Diepen, G. A. M.; Scheffer, F. E. C. J . Phys. Chem. 1953, 57, 575-577. Dobbs, J. M. Ph.D. Dissertation, University of Texas at Austin, 1986. Dobbs, J. M.; Johnston, K. P., submitted for publication in Ind. Eng. Chem. Process Des. Dev., 1985. Dobbs, J. M.; Wong, J. M.; Johnston, K. P. J . Chem. Eng. Data 1986, 31, 303-308. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Ellison, T. K. Fluid Phase Equilib. 1983, 14, 167-175. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986, in press. Gere, D. R. Science (Washington,D.C.) 1983, 222, 253-259. Irani, C. A,; Funk, W. W. Recent Deu. Sep. Sci. 1977,3A, 171-192. Johnston, K. P. Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, 1984. Johnston, K. P.; Eckert, C. A. AIChE J . 1981, 27, 773-779. Johnston, K. P.; Ziger, D. H.; Eckert, C. A. Ind. Fng. Chem. Fundam. 1982, 21, 191-197. Jonah, D. A,; Shing, K. S.;Venkatasubramanian, V.; Gubbins, K. E. In Chemical Engineering at Supercritical Fluid Conditions; Paulaitis, M. E., et al., Ed.; Ann Arbor Science; Ann Arbor, MI,
1983. Joshi, D. K.; Prausnitz, J. M. AIChE J . 1984, 30, 522-525. Karger, B. L.; Snyder, L. R.; Eon, C. J . Chromatog. 1976,125,71-88. Kim, S.; Wong, J. M.; Johnston, K. P. In Supercritical Fluid Technology; Penninger, J. M. L., Radosz, M., McHugh, M., Krukonis, V., Eds.; Elsevier: Amsterdam, 1985. Kurnik, R. T.; Holla, S. J.; Reid, R. C. Chem. Eng. Data 1981, 26, 47-51. Kurnik, R. T.; Reid, R. C. AIChE J . 1981, 27, 861-863. Kurnik, R. T.; Reid, R. C. Fluid Phase Equilib. 1982, 8 , 93-105. Larson, K. A,; King M. L., submitted for publication in Biotechnol. Prog., 1986. Mansoori, G. A.; Carnahan, F. F.; Starling, K. E.; Leland, T. W. J . Chem. Phys. 1971, 54, 1523.
Ind. Eng. Chem. Res. 1987,26, 65-72 McCellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, CA, 1974; Vol. 11. McEachern, D. M.; Sandoval, 0.;Inigaze, J. C. J. Chem. Thermodyn. 1975, 7, 299. McHugh, M. A. In Recent Developments in Separation Science;Li, N. N., Carlo, J. M., Eds.; CRC: Boca Raton, FL, 1984; Vol. IX. Miller, K. J.; Savchik, J. A. J. Am. Chem. SOC.1979,101,7206-7213. Mollerup, T. Fluid Phase Equilib. 1981, 7 , 121-128. Oellrich, L. R.; Knapp, H.; Prausnitz, J. M. Fluid Phase Equilib. 1978,2, 163-171. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Rev. Chem. Eng. 1983, 1, 179. Peng, D.; Robinson, D. B. Znd. Eng. Chem. Fundam. 1976,15,59-62. Peter, S.; Brunner, G. Angew Chem., Znt. Ed. Engl. 1978, 17, 746-750. Prausnitz, J. M. Molecular Thermodynamics of Fluid Phase Equilibria; Prentice-Hall: Englewood, NJ, 1969. Prausnitz, J. M. Asilomar Conference Grounds, Pacific Grove, CA, 1977. Randall, L. G. Technical Paper No. 102,1985;Hewlett-Packard,San Diego.
65
Sanyal, N. K.; Ahmad, P.; Dixit, L. J . Phys. Chem. 1973, 77, 2552-2556. Schmitt, W. J.; Reid, R. C. presented at the AIChE Annual Meeting, San Francisco, 1984 Paper 103d. Schuyler, J.; Blom, L.; van Krevelen, D. W. Trans. Faraday SOC. 1953,49, 1391. Sengers, J. M. H. L.; Morrison, G.; Chang, R. F. Fluid Phase Equilib. 1983,14, 19-44. Taniewska, S. 0.;Goralski, P. J. Chem. SOC. Faraday Trans. 1 1981, 77, 969-974. Thomas, E. R.; Eckert, C. A. Znd. Eng. Chem. Process Des. Deu. 1984, 23, 194-209. Tijssen, R.; Billiet, H. A. H.; Schoenmakers, P. J. J. Chromatog. 1976, 122, 185-203. Whiting, W. B.; Prausnitz, J. M. Fluid Phase Equilib. 1982,9, 119. Wong, J. M.; Pearlman, R. S.; Johnston, K. P. J. Phys. Chem. 1985, 89, 2671. Ziger, D. H. Ph.D. Thesis, University of Illinois at Urbana, 1983.
Received for review April 19, 1985 Accepted May 1, 1986
Estimating Copolymer Compositions from On-Line Headspace Analysis in Emulsion Polymerization Miquel Alonso, Marcel Oliveres, Luis Puigjaner,* and Francesc Recasens Department of Chemical Engineering, Uniuersitat PolitBcnica de Catalunya, 08028 Barcelona, Spain
An improved methodology has been studied for the calculation of instantaneous copolymer compositions that occur during batch emulsion polymerization of monomers exhibiting partial water solubility, as in the case of styrene and acrylonitrile. T o achieve this, a newly designed chromatographic probe installed in the reactor gas space is operated periodically. T o accurately relate vapor compositions to copolymer compositions, the parameters that define the multiple phase equilibria (liquid-liquid-vapor) and the reactivity ratios must be obtained in separate experiments. Thus, liquid-liquid distribution coefficients, as well as monomer activity Coefficients and reactivities, were experimentally determined. By use of simple equilibrium and reaction models, it is thus possible t o compute conversion and copolymer compositions from observed vapor analyses.
Introduction and Purpose Emulsion polymerization is an important process by which large amounts of plastics, rubbers and fibers are made. The kinetics and mechanism of the process have been elucidated in the past and are currently interpreted by the theory of Harkins-Smith-Ewart (Gardon, 1972). However, a rigorous extension of these theories to copolymers is not straightforward, although comprehensive models are appearing (Min and Ray, 1974; Ballard et al., 1981). The main subject of interest here is the emulsion polymerization of styrene (ST)and acrylonitrile (AN), where AN exhibits a significant solubility in water. In the general case of batch copolymer production, careful attention is needed in predicting and controlling the composition drift, as this adversely affects the properties and quality of the polymer. In the particular case of ST-AN, a dramatic improvement in product performance with the use of a composition control system has been shown (Hendy, 1975). Composition control can be carried out either by using off-line, time-dependent kinetic models (Haskell and Settlage, 1970; Johnson et al., 1981), time-independent composition models (Hanna, 1957), or off-line, temperature-conversion optimum profiles (Ray and Gall, 1969; Tirrell and Gromley, 1981). Recent work on emulsion polymerization shows the convenience of developing online sensing devices for conversion monitoring in the study of system dynamics (Schork and Ray, 1981; Kiparissides, 0888-5885/87/2626-0065$01.50/0
1980) and copolymer composition control (Hendy, 1975; Guyot et al., 1981; Abbey, 1981). The use of conversion or composition sensing devices requires a considerable amount of knowledge of the chemical nature of the reacting system. In the case of ST-AN, the water solubility of AN complicates the picture. Early studies reveal that, if liquid-liquid distribution equilibrium of AN is considered, bulk and emulsion copolymer curves almost coincide (Smith, 1948). Recent authors (Kikuta et al., 1976; Guillot and Rios, 1982) show that monomer-swollen polymer particles in equilibrium with the water phase determine the copolymer composition. Therefore, if on-line analysis of the global liquid is used for calculating copolymer compositions, the distribution of the feed monomers in the organic phase should be taken into account (Haskell and Settlage, 1970; Guillot and Rios, 1982). To implement a control system practical and robust enough for industrial use, it occurred to us to investigate how to relate the composition of the reactor headspace with that prevailing in the liquid phase responsible for the copolymer composition. In practice, vapor-phase sampling and analysis are much less troublesome than sampling a polymer emulsion, where fouling by coagulum occurs in the lines. Although much information and hardware on sampling techniques for headspace analysis are available (Kolb, 1980; Comberbach et al., 1984), the relationship between the vapor- and the organic-phase compositions 0 1987 American Chemical Society
