Influence of Matrix Composition on the Solubility of Hydroxybenzoic

4686

Ind. Eng. Chem. Res. 1996, 35, 4686-4699

Influence of Matrix Composition on the Solubility of Hydroxybenzoic Acid Isomers in Supercritical Carbon Dioxide Frank P. Lucien and Neil R. Foster* School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney 2052, Australia

Solubilities of p-hydroxybenzoic acid (p-HBA) and mixtures of the para and ortho isomers have been determined in supercritical carbon dioxide at 318 and 328 K for pressures in the range 101-203 bar. The solubility of p-HBA in carbon dioxide (p-HBA/CO2 binary system) is 2 orders of magnitude lower than the binary system solubility of o-HBA. However, measurements undertaken with an equilibrium chamber of mixed para and ortho isomers demonstrate a strong enhancement in the solubility of p-HBA. Furthermore, the enhancement was found to be independent of the composition of the equilibrium chamber. The binary and ternary (p-HBA/ o-HBA/CO2) solubility data were correlated using a modified form of the Peng-Robinson equation of state. Covolume-dependent mixing rules were also used with the Peng-Robinson model in an attempt to improve the correlation of solubility data. Conventional supercritical fluid (SCF) extraction of a mixture of the isomers is capable of producing an extract which is 99% pure o-HBA in one extraction step. The potential for separation of the isomers using retrograde crystallization appears limited because of the similar crossover pressure for both isomers. Introduction The measurement of the solubilities of solids and liquids in supercritical fluids continues to be an important part of supercritical fluid (SCF) research. Despite the extensive progress that has been made, equations of state (EOS) and related models used to describe supercritical fluid phase behavior are still not capable of being completely predictive across all solute-SCF systems (Johnston et al., 1989). Solubility data not only facilitate the development of predictive models but are an important starting point in the consideration of potential process applications (Macnaughton et al., 1993). An extensive compilation of supercritical solubility data is given by Bartle et al. (1991) and Foster et al. (1991). Much of the available solubility data deals with binary systems (single solute, single SCF) whereas data for multicomponent systems are more scarce. Most of the available solubility data for solid mixtures in carbon dioxide are summarized in Table 1. Some of these solid mixtures undergo melting under conditions of high pressure, and so a few examples of the solubility of liquid-liquid and solid-liquid mixtures are presented for comparison. The focus of the work described in this paper is on ternary systems consisting of two solid solutes in equilibrium with a single SCF. The study of mixed solute systems is important because most potential applications of SCF extraction involve the removal of a desired compound from a matrix of components. Recent studies involving mixed solutes demonstrate that the solubility of individual solutes can be greater than that observed in their respective binary systems (Kurnik and Reid, 1982; Chimowitz and Pennisi, 1986; Dobbs and Johnston, 1987). A good example of solubility enhancement is provided by the naphthalene/benzoic acid/CO2 system (Kurnik and Reid, 1982), in which the solubility of benzoic acid is enhanced by up to 280% while the corresponding increase for naphthalene is 107%. This example demonstrates that binary solubility data will not always provide the worst case scenario for the required solvent-to-feed ratio for a given application, and this has immediate ramifications for the design of any process. S0888-5885(95)00649-X CCC: $12.00

Kurnik and Reid (1982) have explained the solubility enhancement in mixed solute systems in terms of the upper critical end point. Component solubilities in binary systems increase as the upper critical end point is approached, and it is thought that the upper critical endpoint for a ternary system generally occurs at a lower temperature than that for a binary system. Thus, at the same temperature higher solubilities would be expected in the ternary system since it is closer to the upper critical end point. Alternatively, Dobbs and Johnston (1987) suggest that the solubility of a solid in a ternary system will increase relative to its binary system in proportion to the solubility of the other solid in the ternary system. This simple explanation adequately describes most solubility enhancement effects. However, in some cases, solubility diminution may occur (Macnaughton and Foster, 1994). Specific interactions may also reverse the order of solubility enhancement as seen in the benzoic acid/hexamethylbenzene/CO2 system (Dobbs and Johnston, 1987). Differences in solubilities between components in a SCF can be exploited to effect separations as in conventional processes. Fractionation of mixtures using SCFs has been demonstrated for nonionic surfactants (Eckert et al., 1992) and fatty acid esters (Liang and Yeh, 1991; Ikushima et al., 1988). Another interesting application is the separation of isomers (McHugh and Krukonis, 1986), which can often be difficult to separate using conventional techniques, like distillation, because of their similar physical properties. Krukonis and Kurnik (1985) measured the solubility of two families of disubstituted aromatic isomers in supercritical CO2. For the hydroxybenzoic acid (HBA) family, the para isomer solubility was found to be 2 orders of magnitude lower than that for the ortho isomer (salicylic acid). This suggests that 99% pure salicylic acid could be obtained in one extraction step. A unique feature of supercritical separation technology has recently been developed whereby separation can be achieved by exploiting the difference in crossover pressures of the pure components (Chimowitz and Pennisi, 1986; Chimowitz et al., 1988; Kelley and Chimowitz, 1989). The crossover pressure for a single © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4687 Table 1. Published Solubility Data for Mixed Solute Systems in Supercritical CO2a system 2-aminobenzoic acid + anthracene anthracene + carbazole anthracene + fluorene anthracene + 2-naphthol anthracene + phenanthrene aspirin + salicylic acid benzoic acid + 1,10-decanediol benzoic acid + hexamethylbenzene benzoic acid + naphthalene benzoic acid + phenanthrene bibenzyl + naphthalene biphenyl + naphthalene carbazole + phenanthrene 2,4-D + DDT dibenzothiophene + naphthalene 2,3-dimethylnaphthalene + 2,6-dimethylnaphthalene 2,6-dimethylnaphthalene + 2,7-dimethylnaphthalene 2,3-dimethylnaphthalene + naphthalene 2,6-dimethylnaphthalene + naphthalene 2,3-dimethylnaphthalene + phenanthrene 2,6-dimethylnaphthalene + phenanthrene diphenylmethaneb + 2-methylnaphthaleneb 5-methoxy-1-tetralone + 7-methoxy-1-tetralone 6-methoxy-1-tetralone + 7-methoxy-1-tetralone 1-methylnaphthaleneb + 2-methylnaphthaleneb 2-methylnaphthaleneb + naphthalene methyl m-nitrobenzoate + methyl o-nitrobenzoateb methyl o-nitrobenzoateb + methyl p-nitrobenzoate naphthalene + phenanthrene naphthalene + phenol naphthalene + 2,5-xylenol 1-naphthol + 2-naphthol 2-naphthol + phenanthrene trilaurin + trimyristin trilaurin + trimyristin + tripalmitin trilaurin + tripalmitin trimyristin + tripalmitin

T (K)

P (bar)

ref

308 313 313 308 308, 318 313 318 308, 318 308 308, 318 308 308 308 308, 318 313 313 309 308, 323 308, 318 308, 318 308 303, 308, 313, 315, 317 308, 318 308 308 308 308 308 308 308 308 308, 318 308 308, 318 308 308 308, 318, 323, 328 313 313 313 313

120-350 100-200 100-200 120-350 104-242 100-200 83-245 164-307 100-350 120-280 120-280 77-272 77-280 57-278 100-200 104-208 77-277 101-144 120-280 90-247 120-280 244-314 120-280 120-280 77-257 110 110 77-246 76-262 110 110 77-280 120-280 54-277 85-262 92-162 136-344 92-249 92-250 91-247 92-304

Dobbs and Johnston, 1987 Kwiatkowski et al., 1984 Kwiatkowski et al., 1984 Dobbs and Johnston, 1987 Kosal and Holder, 1987 Kwiatkowski et al., 1984 Tavana and Randolph, 1991 Pennisi and Chimowitz, 1986 Dobbs and Johnston, 1987 Kurnik and Reid, 1982 Kurnik and Reid, 1982 Chung and Shing, 1992 Chung and Shing, 1992 Gopal et al., 1985 Kwiatkowski et al., 1984 Macnaughton and Foster, 1994 Mitra et al., 1988 Johnston et al., 1987 Kurnik and Reid, 1982 Iwai et al., 1993 Kurnik and Reid, 1982 Lemert and Johnston, 1990 Kurnik and Reid, 1982 Kurnik and Reid, 1982 Chung and Shing, 1992 Chang and Morrell, 1985 Chang and Morrell, 1985 Chung and Shing, 1992 Chung and Shing, 1992 Chang and Morrell, 1985 Chang and Morrell, 1985 Gopal et al., 1985 Kurnik and Reid, 1982 Gopal et al., 1985 Mori et al., 1992 Tan and Weng, 1987 Lemert and Johnston, 1990 Bamberger et al., 1988 Bamberger et al., 1988 Bamberger et al., 1988 Bamberger et al., 1988

a The term mixed solute refers to a mixture prepared by blending two or more pure chemical species in a specified ratio. b Exists as a liquid at the experimental temperature and 1 atm.

solute represents the point at which there is a change in the temperature dependence of solubility. For multicomponent systems, a crossover region is identified in which the solubility of one component increases with temperature while the other decreases and thus precipitates out of solution in a theoretically pure form. Such a separation method, also referred to as retrograde crystallization (Johnston et al., 1987), may prove useful in the separation of isomers. In this work the solubilities of p-HBA and o-HBA, in pure and mixed form, were determined in supercritical CO2 and the possibility of separating the two isomers was considered. The principle synthesis route for salicylic acid is the Kolbe-Schmitt reaction (Lindsey and Jeskey, 1957), which typically produces smaller amounts of the para isomer. Both isomers are industrially relevant: salicylic acid is used in the manufacture of aspirin, and p-HBA is the common starting material for the manufacture of the “paraben” series of preservatives, which are used in cosmetics and pharmaceuticals (Erickson, 1982). Experimental Section Equipment. Solubility measurements were made using a continuous flow apparatus similar to that used by Gurdial and Foster (1991). A schematic representation of the apparatus is shown in Figure 1. The system

pressure was maintained with an ISCO model 260D HPLC syringe pump. The pump can be operated in either constant flow or constant pressure mode for flow rates and pressures up to 90 mL/min and 500 bar, respectively. The equilibrium cell consisted of a Whitey 300 cm3 sample cylinder which was packed with alternate layers of glass wool and the solute of interest. Glass wool was plugged at the end of the equilibrium cell as a precaution against the physical entrainment of undissolved solute into the saturated SCF stream. A Nupro 2 µm in-line filter was also installed after the equilibrium cell to prevent physical entrainment. The saturated SCF stream was depressurized through a Whitey 31RS4 metering valve where the dissolved solute precipitated and was trapped by a Nupro 0.5 µm in-line filter. The volume of CO2 associated with the precipitated solute was measured with a wet gas meter (Alexander Wright & Co., type DM3A) or a Brooks mass flow sensor (5860E series). Both types of volume measurement devices were calibrated to determine the CO2 volume to within (1%. Pressure at the inlet and outlet of the equilibrium cell was monitored with Druck pressure transducers (PDCR 911) while the system temperature was measured with a platinum resistance thermometer. The pressure drop across the equilibrium cell, as indicated by the two pressure transducers, was negligible for the range of flow rates used in these

4688 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996

Figure 1. Continuous flow apparatus for solubility measurements in supercritical CO2. Table 2. Source and Purity of Materials material

source

purity

carbon dioxide naphthalene o-hydroxybenzoic acid p-hydroxybenzoic acid methanol glacial acetic acid

CIG/Liquid Air Ajax Chemicals Sigma Sigma BDH Jaegar Chemicals

99.8% min 99% min 99+% 99% min 99.8% min 99% min

experiments. The equilibrium cell was placed in a water bath, and the temperature was maintained to within (0.2 K with a bath heater (Grant control unit, type ZD). Procedure. Liquid CO2 was directed from a cylinder into the syringe pump, where it was compressed to the desired operating pressure. After leaving the pump, the pressurized CO2 entered a preheating coil within the water bath, which enabled the CO2 to reach the extraction temperature. Prior to commencing experiments, the system was purged with low-pressure CO2 and then pressurized to the desired operating conditions. At the commencement of each run, the system was maintained under static conditions for a period of approximately 30 min. This allowed the system to attain equilibrium once all of the valves were opened to pressurize the various sections of the apparatus. The metering valve was then opened, which commenced the flow of saturated CO2 and the precipitation of the dissolved solute. At this point the syringe pump was in constant pressure mode and the pressure was maintained to within (0.5% of the set point. The solubility of the solute was determined from the mass of solute collected in the metering valve and filter and the volume of CO2. Solubility is expressed here as the mole fraction of the solute in the SCF mixture. Individual solubility data points are the average of at least three experimental runs with a relative standard deviation (RSD) of 5% or less. All of the materials used in this work were used as received. The sources and purities of the materials are shown in Table 2. Calibration. The suitability of the apparatus for solubility measurement was assessed by measuring the solubility of naphthalene at 318 K and comparing the results with the data of Tsekhanskaya et al. (1964). Good agreement was obtained between this work and studies reported in the literature with an average

absolute relative deviation (AARD) of around 7%. These results also indicate that equilibrium was established between CO2 and naphthalene within the equilibrium cell at the flow rates used. The solubility of naphthalene is around 1-2 orders of magnitude greater than that for o-HBA, and the flow rates used to establish equilibrium do not necessarily apply to the HBA binary systems. Separate experiments were therefore required to confirm operating flow rates for the solutes of interest. Flow-rate experiments were conducted on the o-HBA and p-HBA binary systems to establish the conditions under which equilibrium would be achieved. Variation of the flow rate in the range of 10 to 20 standard liters per hour (SLPH) was found to have no significant effect on the solubility of both isomers. The solubility data set for o-HBA provided by Gurdial and Foster (1991) was reconfirmed by checking several points at 35, 45, and 55 °C. Data generated at 35 and 45 °C agreed well with those in the literature (3% and 7% AARD, respectively), but at 55 °C the data were observed to be significantly lower at pressures above 130 bar. Consequently, a new data set was measured for the solubility of o-HBA in supercritical carbon dioxide at 55 °C. Analysis of Mixtures. The solubilities of mixtures of isomers were measured with the same apparatus and procedure used for binary systems (Figure 1). However, these experiments required the additional task of determining the composition of the solid collected in the metering valve and filter. This was carried out using a rinsing procedure to remove the precipitate from the valve and filter. A solution containing the precipitate was prepared, and the mass of solute, as well as its composition, was determined analytically using HPLC. A Waters HPLC Nova-Pak C18 column (150 mm × 3.9 mm) was used to separate the isomers, which were then detected with an ISCO V4 absorbance detector set at 254 nm. The column was operated in reversed-phase mode (Rittich and Pirochtova, 1990; Delcour et al., 1989) using a mobile phase of water, methanol, and glacial acetic acid (75:21:4 vol %). Calibration standards were injected so as to generate an area-concentration calibration curve. A new calibration curve was made each time an analysis of sample solutions was conducted.

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4689

Calibration and sample solutions were normally injected twice, and the reproducibility of peak areas was typically better than 99%. The metering valve and filter containing the solute were rinsed with the same solvent as the HPLC mobile phase. To ensure complete dissolution of the solute, the valve and filter were sonicated for a period of 10 min. All rinsings were combined into a known volume of sample solution, thus enabling the total amount of solute to be determined. A second sample solution was also prepared by repeating the rinsing procedure on the valve and filter. The second sample solution was analyzed to estimate the amount of any residual solute remaining after the first rinse. The residual solute was typically less than 2% of the total mass collected, indicating that there was no need to rinse more than twice. For mixed solute systems, the mass of solute collected was also determined gravimetrically. The analytically determined mass was found to be 2-3% less on average than the gravimetrically determined mass. This was considered to be an acceptable error given that the reported solubility points are the average of three measurements with a RSD of 5% or less. In the determination of the binary solubility of p-HBA, gravimetric determination of the mass of solute collected was not possible because of the very low solubility. The mass of solute collected in this case was determined analytically using the same procedure described for mixed solutes. Effect of Bed Composition. Three different bed compositions were used in the mixture solubility measurements: 50:50, 80:20, and 20:80 mol %. Approximately 150 g of each mixture was prepared by weighing out the required amount of each isomer into a container, which was then shaken vigorously for at least a halfhour. Analysis of top, middle, and bottom samples from the mixtures confirmed that they were homogeneous. Each mixture was then packed into an equilibrium cell (300 cm3) in the manner described previously. The same mass of solute (pure or mixed) was used for all of the other solubility experiments. The effective contact time between the solute and the SCF in a 50:50 mixed bed of two isomers is half of that observed in a pure bed of a single isomer. To ensure that this did not impose any mass transfer limitations, flow-rate experiments were conducted on the 50:50 o-HBA/p-HBA (OP) system. Variation of the flow rate in the range 5-16 SLPH was found to have no significant effect on the solubility of each isomer. As such, operating at a flow rate of 5-10 L/h was considered sufficient for saturation in the 80:20 and 20:80 OP systems. Sequential Bed Experiment. A sequential bed experiment was established for the OP system whereby two equilibrium cells, each containing a pure isomer, were placed in series in the solubility apparatus shown in Figure 1. The purpose of this experiment was to simulate a cosolvent solubility experiment. The experiment was conducted in two stages to isolate possible interactions between the isomers. The flow rate of CO2 through the apparatus was maintained at around 10 SLPH for both stages. In the first stage, supercritical CO2 was initially saturated with o-HBA, thus forming a pseudo-SCFcosolvent mixture. This stream was then passed through the p-HBA bed, and the solubilities of both isomers were determined as for the mixed solute systems. The order

of the equilibrium cells was reversed in the second stage with the solubility of each isomer determined as before. Material balances showed that the maximum contamination of the second bed in each case never exceeded 0.1%. Melting Point Depression. Organic solids under the influence of high-pressure carbon dioxide may undergo melting point depression (Bamberger et al., 1988; Chang and Morrell, 1985; McHugh and Yogan, 1984). The phase behavior under supercritical conditions for all hydroxybenzoic acid systems was checked using a Jerguson sight gauge. Several grams of the solute were placed in the sight gauge, which was then fitted in place of the sample cylinder shown in Figure 1. The system was pressurized slowly at 55 °C over a period of several hours to the maximum pressure used in this work and was then held under static conditions for an additional 1 h. In all of the systems investigated (pure and mixed solutes), no melting point depression was observed. Data Correlation Details of the thermodynamic relations involved in the modeling of the solubility of a solid in a SCF phase are given by Prausnitz et al. (1986) and Reid et al. (1987). The standard equations involved have also been reproduced extensively in solubility publications, and so only a brief description of the modeling procedure is given here. Strictly speaking, the fluid mixture of solvent and solute is not a supercritical fluid unless the mixture critical temperature and pressure are exceeded. The term SCF phase more aptly refers to a fluid phase which contains a component above its critical temperature and pressure. The SCF phase can be considered as a compressed gas or an expanded liquid phase, although the former has been adopted predominantly in the literature. If the compressed gas model is used, the defining equation for the mole fraction of solid i in the SCF phase is

yi )

[

]

νis Pisat 1 (P - Pisat) exp P φi RT

(1)

where Pisat, φi, and νis are the vapor pressure, fluid phase fugacity coefficient, and molar volume of the solid, respectively. The main assumption involved in deriving eq 1 is that the solid phase remains pure under pressure, i.e., the SCF does not dissolve in the solid. In mixed solute systems where the solids form a simple mechanical mixture, i.e., no solid solutions, eq 1 applies for each solid component in the system. The fugacity coefficient is evaluated with an equation of state that describes the volumetric behavior of the SCF phase. The PengRobinson (1976) equation of state (PREOS) is one of the most commonly used EOS for the modeling of solidSCF solubility data and was also implemented in this study. The attractive and repulsive parameters required by the PREOS for a fluid mixture are calculated from the pure component values using mixing rules. The conventional van der Waals mixing rules incorporate a binary interaction parameter, kij , which characterizes the interactions between unlike molecular species. By convention, kij ) 0 for identical molecules. The geometric mean term in the equation for the mixture

4690 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 3. Solubilities of HBA Isomers in Supercritical CO2 isotherm (°C)

pressure (bar)

o-HBAa (mole fraction)

p-HBA (mole fraction)

45

101.3 121.6 131.7 152.0 172.2 202.6 101.3 121.6 131.7 152.0 172.2 202.6

8.30E-5 1.72E-4 2.27E-4 3.05E-4 3.59E-4 4.32E-4 3.17E-5 1.32E-4 2.06E-4 3.24E-4 4.35E-4 5.62E-4

4.52E-7 1.14E-6 1.37E-6 1.84E-6 2.24E-6 2.80E-6 1.42E-7 7.30E-7 1.13E-6 1.89E-6 2.78E-6 3.72E-6

55

a Data at 45 °C is taken from Gurdial and Foster (1991). Data at 55 °C is new data measured by the present authors.

attractive parameter usually causes an overprediction, in which case kij assumes a small positive value between 0 and 1. This value is adjusted to make the EOS fit the experimental data. The larger the kij, the lesser the physical attraction between unlike molecules. Negative values for the interaction parameter are less frequently reported and indicate stronger than normal interactions between the molecular species (Macnaughton and Foster, 1994; Ting et al., 1993). For binary systems (SCF-1, solute-2), only one adjustable parameter, k12, is needed in the modeling of solubility data. In ternary systems (SCF-1, solute-2, solute-3), the evaluation of the fugacity coefficient requires an additional interaction parameter, k23, to account for solute-solute interactions in the fluid phase. The interaction parameters for solute-solvent interactions, k12 and k13, are determined from binary solubility data as described previously. Many types of mixing rules have been developed to improve the estimation of the fluid mixture parameters (Chen et al., 1995; Pongsiri and Viswanath, 1989; Mansoori, 1986). In this study, an additional mixing rule was used in which the expression for the attractive parameter becomes covolume-dependent (CVD). Such a modification has been shown to significantly improve the correlation of binary solubility data (Rao and Mukhopadhyay, 1989, 1990). More recently, Mukhopadhyay and Rao (1993) have modified the CVD mixing rule and extended it to include the solubility of mixed solids in supercritical carbon dioxide containing cosolvents. The CVD mixing rule is defined as N N

amix )

( )

∑i ∑i yiyiaij

bmix bij

mij

(2)

where a is the attractive (or energy) parameter, b is the repulsive (or size) parameter, aij ) (aiiajj)1/2, bij ) (biibjj)1/2, and bmix is identical to the van der Waals definition. The pure component parameters are indicated by the subscripts ii and jj. The binary interaction parameter from the van der Waals mixing rule has now been eliminated and replaced with the adjustable parameter mij , where mii ) mjj ) 1. As in the previous case, only one adjustable parameter, m12, is required for binary systems. The use of the CVD mixing rules with the PREOS results in a different expression for the fugacity coefficient of the solute in the SCF phase. Equation 3 is identical to the fugacity coefficient expression obtained using conventional mixing rules (Reid et al., 1987)

Figure 2. Solubility of o-HBA in supercritical CO2 and modeling results using the PREOS with conventional mixing rules.

except that the term A1 + A2 now replaces the term δi

ln φk ) (Z - 1)B1 - ln(Z - B) amix Z + 2.414B (A1 + A2 - B1) ln (3) Z - 0.414B 2x2RTbmix

(

)

where

B)

bmixP RT

(4)

B1 ) bk/bmix A1 )

A2 )

1 amix

2 amix

(5)

∑i yiaik(bmix/bik)m

(6)

ik

∑i ∑j yiyjaijmij(bmix/bij)m

(B1 - 1)

ij

(7)

Alternative thermodynamic models which have demonstrated advantages over the PREOS were not considered in this study. The current approach to modeling was adopted in view of the lack of fundamental property information available on the HBA isomers that other models require. Such properties include critical data, vapor pressure, normal boiling point, and the enthalpy of vaporization. Methods are available for estimating many of these properties, but they are generally recognized as being unreliable for polar solids. A fundamental investigation of the more conventional cubic equation of state was therefore considered as a necessary step for establishing a basis for future modeling of the HBA systems. Results and Discussion Binary Solubility. The measured solubilities of each isomer in supercritical CO2 are listed in Table 3 and shown graphically as a function of pressure in Figures 2 and 3. The solubility data for p-HBA gener-

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4691

Figure 3. Solubility of p-HBA in supercritical CO2 and modeling results using the PREOS with conventional mixing rules.

Figure 5. Binary solubility of o-HBA as a function of carbon dioxide density.

Figure 4. Binary solubilities of HBA isomers at 318 and 373 K.

Figure 6. Binary solubility of p-HBA as a function of carbon dioxide density.

ally fall in the range 10-7-10-5 mole fraction. Such extremely low values for solubility are not frequently reported in the literature. The data for p-HBA also exhibited the same trends as those for o-HBA, which reinforces the validity of the experimental method. The relative difference in solubility between the two isomers is illustrated in Figure 4, and it can be seen that the solubility of o-HBA is typically 2 orders of magnitude higher than that for the p-HBA. This is consistent with the findings of Krukonis and Kurnik (1985), who measured the solubilities at 373 K and for pressures greater than 207 bar. Stahl et al. (1978) also measured the solubility of p-HBA but at 40 °C, and data in the range 101.3-202.6 bar are shown in Figure 3. The relative solubility between the three isotherms is consistent with that for o-HBA (Gurdial and Foster, 1991). At high pressures,

solubility increases with temperature because of the vapor pressure effect, while at low pressures, solubility decreases with temperature because of the more dominant density effect. It should be noted that a distinct crossover pressure for all three isotherms is not evident. Solubility data are also commonly related to the density of the pure solvent (Kumar and Johnston, 1988; Lee and Ellington, 1987; Adachi and Lu, 1983; Chrastil, 1982). A linear relationship often exists between the logarithm of solubility and solvent density as shown in Figures 5 and 6. The data measured at 55 °C appear to deviate from linearity for densities below about 0.5 g/cm3, as indicated also by the higher AARD. An improved correlation at 55 °C is obtained between the logarithm of solubility and the logarithm of solvent density. The AARDs at 55 °C in this case are 3.6% and 5.4% for o-HBA and p-HBA, respectively. In summary,

4692 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 4. Solubility of a 50:50 mol % Mixture of o-HBA and p-HBA in Supercritical CO2 pressure (bar) 101.3 121.6 131.7 152.0 172.2 202.6

o-HBA (mole fraction) 8.01E-05 1.89E-04 2.36E-04 3.13E-04 3.66E-04 4.47E-04

Temperature 45 °C -3 10 4 3 2 3

3.11E-05 1.38E-04 2.01E-04 3.16E-04 4.34E-04 5.54E-04

Temperature 55 °C -2 5 -2 -2 0 -1

average 101.3 121.6 131.7 152.0 172.2 202.6 average

solubility enhancementa (%)

p-HBA (mole fraction)

solubility enhancementa (%)

8.03E-07 2.41E-06 3.14E-06 4.65E-06 5.99E-06 7.53E-06

78 111 129 153 167 169

3

-1

135 2.05E-07 1.55E-06 2.55E-06 4.72E-06 7.00E-06 9.93E-06

44 112 126 150 152 167 125

a

Solubility enhancement is defined as the percent relative deviation of the ternary solubility from the binary solubility of a component at the same temperature and pressure.

the log-linear and log-log relationships provide an accurate representation of the data with all AARDs within 5%. Ternary Solubility. The solubility data obtained by passing supercritical CO2 through a 50:50 mol % mixture of o-HBA and p-HBA are presented in Table 4. The tabulated results also show the corresponding solubility enhancements relative to the binary solubility data. The ternary solubility data were measured at the same pressures used for the binary solubility data so that direct comparisons between the data sets could be made, thus eliminating the need to interpolate. The binary and ternary solubility data sets in this study were compared statistically. For example, at each temperature, the binary and ternary solubilities of a component were determined at six different pressures. An average value for the solubility enhancement was calculated from the six individual values. The average solubility enhancement was then tested statistically to determine whether it differed significantly from 0. The solubility of p-HBA, in the presence of o-HBA, was found to be enhanced by up to 170% while no change appears to have occurred in the solubility of o-HBA. This result is more clearly demonstrated in Figure 7 and supports the postulate of Dobbs and Johnston (1987) that a more soluble solid causes a more significant increase in the solubility of a less soluble component than vice versa. In this case the solubility of p-HBA is so low that it has virtually no effect on o-HBA. A corollary of the statistical test on o-HBA is that it also reconfirms the accuracy of the binary solubility data set. However, in the OP system, the solubility enhancement for o-HBA at 121.6 bar and 45 °C is substantially higher than the other data points and lies outside the range of experimental precision ((5%). This suggests that the binary value of solubility at these conditions may have been underestimated. The log-linear relationship between solubility and solvent density for o-HBA (Figure 5) also shows that this data point deviates below the line of best fit. An interesting feature of the solubility enhancement for p-HBA in the OP system is that it increases with respect to the fluid phase concentration of o-HBA as shown in Figure 8. This suggests that the o-HBA behaves like a cosolvent in the OP system. Solubility enhancement in cosolvent systems is considered in

Figure 7. Binary (B) and ternary (T) solubilities of o-HBA and p-HBA at 318K.

terms of the cosolvent effect, which is defined as the ratio of the solubility obtained with a cosolvent to that obtained without a cosolvent. Cosolvent effects can vary linearly with cosolvent composition (Ekart et al., 1993) or nonlinearly (Ting et al., 1993). In this work the solubility enhancement varies nonlinearly but in a logarithmic way, leveling out at higher mole fractions of o-HBA, and appears independent of temperature. Ting et al. (1993) were able to isolate the effects of both the cosolvent concentration and pressure on the observed cosolvent effect. At constant pressure, an approximately exponential relationship was observed between the cosolvent effect and the cosolvent concentration. At constant cosolvent concentration, the cosolvent effect decreased with increasing pressure. Pressure and cosolvent concentration therefore appear to be competing factors on the cosolvent effect. In the OP system, the concentration of o-HBA in the fluid phase increases simultaneously as pressure increases. The negative effect of pressure on cosolvent effects may therefore partly explain why the solubility enhancement levels out at the higher concentrations of o-HBA.

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4693 Table 6. Sequential Bed Experiment at 45 °C pressure (bar) 101.3 152.0 202.6 average 101.3 202.6 average

Figure 8. Variation of the solubility enhancement of p-HBA with the mole fraction of o-HBA in the fluid phase. Table 5. Effect of Bed Composition on Ternary Solubility at 45 °C pressure (bar) 101.3 152.0 202.6 average 101.3 152.0 202.6 average

rel deviation from 50:50 mol % bed (%) o-HBA p-HBA (mole fraction) (mole fraction) ortho para Ortho-Para Mixture: 80:20 mol % 7.69E-05 8.25E-07 -4.0 2.94E-04 4.51E-06 -6.1 4.30E-04 7.49E-06 -3.8

2.7 -3.0 -0.5

-4.6

-0.3

Ortho-Para Mixture: 20:80 mol % 7.84E-05 8.17E-07 -2.1 3.04E-04 4.60E-06 -2.9 4.38E-04 7.54E-06 -2.0

1.7 -1.1 0.1

-2.3

0.2

Effect of Bed Composition. For a mixed solute system in which the solids remain pure under pressure, eq 1 predicts that the solubility of each solid in the SCF phase is independent of the solid mixture composition. The effect of changing the bed composition in this work was found to be consistent with this prediction as shown in Table 5. In other experiments where solid-fluid (SF) equilibria have been investigated, the composition of the condensed phase was also found to have no effect on the solubility of individual components (Bamberger et al., 1988; Kurnik and Reid, 1982). In contrast, fluid phase solubilities become dependent on the composition of the condensed phase when it undergoes melting point depression (Chung and Shing, 1992; Chang and Morrell, 1985). This highlights the need to accurately determine the phase equilibria in mixed solute systems when interpreting solubility enhancement effects. Sequential Bed Experiment. The parallel between solubility enhancements in mixed solute systems and cosolvent effects in cosolvent systems was examined further by setting up a sequential bed experiment. Details of the procedure were described previously, and the results are shown in Table 6. In the first stage of the experiment, with o-HBA as the “cosolvent”, the p-HBA solubility was enhanced to the same levels observed for the 50:50 ortho/para bed (the three data points are also shown in Figure 8). The concentration

o-HBA (mole fraction)

p-HBA (mole fraction)

Ortho f Para (First Stage) 8.24E-05 8.51E-07 3.06E-04 4.68E-06 4.31E-04 7.49E-06

solubility enhancement (%) ortho para -0.7 +0.3 -0.2

88 154 168

-0.2

137

Para f Ortho (Second Stage) 8.48E-05 ∼0 +2.2 4.33E-04 ∼0 -0.2 +1.2

of o-HBA in the SCF phase was unchanged from its binary solubility even though the o-HBA had passed through the p-HBA bed. The results were not as conclusive when the order of the equilibrium cells was reversed. The p-HBA solubility was found to be 1-2 orders of magnitude below its binary solubility at both of the pressures investigated. The o-HBA solubility was again identical to its binary solubility. The negligible level of p-HBA at the outlet of the second equilibrium cell was evident after 204 standard liters (SL) of CO2 had passed through the apparatus at 101.3 bar. An additional 65 SL of CO2 were metered at 202.6 bar. In comparison, the steady state concentration for o-HBA, at 101.3 bar in the first stage of the experiment, was attained after 242 SL had passed through the apparatus, and only 137 SL were required to reach 50% of this value. The most likely explanation for the results from the second stage of the experiment is that the p-HBA precipitated or adsorbed onto the o-HBA in the second equilibrium cell. It is difficult to draw any further conclusions from this part of the experiment in view of the absence of relevant data. The first stage of the experiment, however, clearly demonstrates that the solubility enhancement of p-HBA, in the presence of o-HBA, is very similar to a cosolvent effect. The use of cosolvents to enhance the solubility of a component takes advantage of the specific interactions which occur between the solute and the cosolvent (Ekart et al., 1993). Similarly, the solubility enhancements observed in the OP system are probably the result of specific interactions between the two isomers. The nature of the interaction between the isomers, whether physical or chemical, can be deduced from the characteristics of the solutes and the magnitude of the solubility enhancement. The HBA isomers are relatively polar solutes (µ ∼ 2.7 D, McClellan, 1963) and are capable of hydrogen bonding at three sites: the two OH groups can donate or accept hydrogen bonds while the carbonyl group can accept hydrogen bonds. The maximum solubility enhancement for p-HBA seen in the OP system corresponds to a cosolvent effect of around 2.7. Cosolvent effects in excess of 10 are usually reported at similar temperatures and pressures in cosolvent systems where hydrogen bonding is thought to be prevalent (Gurdial et al., 1993; Ting et al., 1993). The concentration of cosolvent used in these systems is typically 1-4 mol %, which is around 100 times the concentration of o-HBA in the OP system. The cosolvent effect in the OP system is comparable to that in hydrogen-bonding cosolvent systems when the concentration of o-HBA is taken into account. This suggests that there is the possibility of hydrogen bonding occurring between the HBA isomers in the SCF phase.

4694 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 7. Critical Properties of CO2 and the HBA Isomers compd

MW

Pc (bar)

Tc (K)

ω

CO2a o-HBA p-HBA

44.01 138.12 138.12

73.8 51.8 51.8

304.2 739 739

0.225 0.832 0.832

a

Data for CO2 taken from Smith and van Ness (1987).

Table 8. Physical Properties of the HBA Isomers physical property mp (°C)a vapor pressure (bar) 45 °C 55 °C molar vol (cm3/mol)a a

o-HBA

p-HBA

159

214.5-215.5

2.25E-06 6.65E-06 95.7

1.37E-08b 3.76E-08b 92.4

Data from Erickson (1982). b Estimated.

Modeling Results The previously measured solubility data were modeled using the PREOS. Apart from providing an accurate description of the solubility data, the purpose of this modeling was to determine if the PREOS could account for the solubility enhancements observed in the OP system. Two different sets of mixing rules were used in the modeling of the binary solubility data. A modified form of the PREOS was also used in an attempt to improve the correlation of the binary solubility data. The modified PREOS was subsequently used for the modeling of the ternary solubility data. Physical Properties of Pure Components. The properties of the HBA isomers and carbon dioxide required for the modeling of solid solubility are listed in Tables 7 and 8. Estimated values for the critical properties and acentric factor of o-HBA are reported by Daubert and Danner (1989). The critical properties were estimated by the method of Lydersen (1955), while the acentric factor was derived from extrapolated vapor pressure data. Vapor pressure data for o-HBA in the temperature range 39-59 °C have been measured by de Kruif and van Ginkel (1977) using a combined torsion-weighing effusion apparatus. The vapor pressures reported here are the averages of the values obtained by the two experimental techniques. Solid densities for the two isomers are given by Erickson (1982), and it is assumed that solid density is essentially independent of temperature within the range of interest in this work. Critical properties for p-HBA were not available. Since estimation methods for critical properties are usually based on group contribution methods which do not differentiate between isomers, as in the case of the method of Lydersen, the critical properties for this isomer were taken to be the same as those for o-HBA. Likewise, the same value for the acentric factor was also used, and this assumes that the two isomers have similar vapor pressures at a reduced temperature of 0.7 (under these conditions the two isomers are liquids). No experimental vapor pressure data were available for p-HBA. However, a close examination of the melting points of the HBA isomers in Table 8 reveals that the solid vapor pressure for the para isomer is expected to be much lower than that for o-HBA. Methods for the estimation of solid vapor pressure are given by Lyman et al. (1990). Central to these methods is the need to know the normal boiling point of the solid, which in this case is unavailable for p-HBA. Estimation methods, for the normal boiling point (Lyman et al., 1990) are based on group contribution methods which once again do not differentiate between isomers. The use of these estima-

Table 9. Optimized Interaction Parameters for the Modeling of Binary Solubility Data with the PREOS and Conventional Mixing Rules solute

temp (°C)

k12a

AARD (%)

o-HBA

45 55 45 55

0.0460 0.0368 0.0442 0.0212

21.9 22.4 19.5 13.0

p-HBA

a k 12 refers to the interaction parameter between CO2 (component 1) and a solute (component 2).

tion techniques would therefore lead to identical vapor pressures for the two isomers, a result which is not consistent with the trend in their melting points. An alternative method for estimating solid vapor pressure can be derived from binary solubility data. Dobbs and Johnston (1987) have shown that the difference in binary solubility between pure solids is related primarily to vapor pressure. This implies that the vapor pressure of p-HBA, to a first approximation, is 2 orders of magnitude below that for o-HBA. Vapor pressure data for p-HBA were thus estimated from the average solubility ratio of the two isomers. For example, at 45 °C, the average ratio of the solubilities for the two isomers is 164:1. The vapor pressure for p-HBA was scaled in the same way relative to the experimental vapor pressure for o-HBA. Binary Systems: Conventional Mixing Rules. The modeling of binary systems using conventional mixing rules involved the determination of an optimum solute-solvent binary interaction parameter. The solute-solvent interaction parameter in each binary system is k12, where the subscript 1 refers to CO2 and the subscript 2 refers to the solute. The interaction parameter in each binary system was allowed to vary with temperature, resulting in one adjustable parameter per isotherm of solubility data for a given solute. The optimum values were calculated by minimizing the AARD for each isotherm of data. The AARD is defined as follows:

AARD )

|ycorr - yexp| yexp

∑

1 N

(8)

where ycorr and yexp are the correlated and experimental solubility values, respectively, and N is the number of data points. The modeling results for the two isomers are shown in Table 9. Overall, the correlation of the data in both systems is generally poor, with no single value of the AARD below 10%. It was seen previously that the density-based correlations were able to produce AARDs generally less than 5%. The poor correlation results may be partly attributed to the estimated physical properties of the solutes, particularly the critical properties and the acentric factor. The consistent trend in both systems is that the PREOS underestimates binary solubility at low pressures while at high pressures the solubility is overestimated as shown in Figures 2 and 3. The results for p-HBA are slightly better than those for o-HBA, more obviously at 55 °C, which is a surprising result given the greater uncertainty in the pure component properties for this isomer. The small positive values obtained for the interaction parameter (0.02-0.05) were similar to those observed in other binary systems (Lee et al., 1994; Kosal and Holder, 1987; Kurnik et al., 1981). Binary Systems: Covolume-Dependent Mixing Rules. Covolume-dependent mixing rules (Mukho-

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4695 Table 10. Optimized Adjustable Parameters for the Modeling of Binary Solubility Data with the PREOS and CVD Mixing Rules solute

temp (°C)

m12

AARD (%)

o-HBA

45 55 45 55

0.628 0.604 0.625 0.570

21.6 22.1 19.5 13.0

p-HBA

padhyay and Rao, 1993) were used in an attempt to improve the correlation of the binary solubility data. The CVD mixing rules were chosen because they retain the original simplicity of the conventional mixing rules in that one adjustable parameter, m12, is required per isotherm of data. The attractive and repulsive parameters for the solute were calculated using the conventional Peng-Robinson expressions. Optimized adjustable parameters (m12) for each binary system were calculated using the same procedure for the determination of k12. The modeling results using CVD mixing rules are shown in Table 10. The CVD mixing rules produced only slightly better correlation results for o-HBA while the results for p-HBA were identical to those obtained with the conventional mixing rules. The values of m12 were within the expected range 0.5-1.0 observed for both polar and nonpolar solutes (Mukhopadhyay and Rao, 1993). The identical results for both mixing rules can be attributed to the very low values for the solubilities of the HBA isomers. In both sets of mixing rules the value for amix approaches the value of the attractive parameter for pure CO2. The values of δi and A1 + A2 are also very nearly the same for low values of mole fraction, which in effect means that the same value for the fugacity coefficient is obtained. In fact, a closer examination of the correlation results with the CVD mixing rules applied to other solute systems shows that most of the improvements over the conventional mixing rules occur when the mole fractions are higher than about 10-3. Binary Systems: Modified Peng-Robinson Equation of State. The previous two attempts to model binary solubility data highlighted two areas of difficulty which hindered the accurate correlation of the data. Firstly, the critical properties of the solutes were not known accurately, which led to poor estimates of the energy and size parameters. In addition, both sets of mixing rules were relatively insensitive to the fluid phase composition, which caused the values of amix and bmix to approach the values of the energy and size parameters for pure CO2. This made the estimation of the fugacity coefficient less sensitive to k12 and m12 because both parameters now only influenced the terms δ2 and A1 + A2, respectively. In effect, the ability to fit the model to the experimental data was reduced. To overcome these problems, the correlation of the data was performed using a modified form of the PREOS. The modification involved fitting the energy and size parameters for the solute to the experimental data with the adjustable interaction parameter set to 0. This technique removes the reliance on the critical properties of the solute, which is particularly significant for o-HBA since it is reported to decompose well below its estimated critical temperature (Daubert and Danner, 1989). The fugacity coefficient is also much more sensitive to changes in the two adjustable solute parameters than to changes in a single adjustable interaction parameter, which improves the ability of the model to fit the experimental data.

Table 11. Optimized Pure Component Parameters Based on the Modified PREOS AARD (%) solute

a2 (Pa(m3/mol)2)

b2 (m3/mol)

o-HBA

9.699

Optimized 1.594E-04

p-HBA

9.462

1.522E-04

45 °C 55 °C

7.556 7.406

Estimateda 9.228E-05 9.228E-05

45 °C 5.8 (average: 5.2 (average:

55 °C 2.4 4.1) 6.6 5.9)

a The estimated values of a and b are identical for both isomers 2 2 since the critical properties for the isomers were taken to be the same (Table 7).

Schmitt and Reid (1986) used this approach to model solid solubility whereby the solute parameters were both made independent of temperature. More recently, Macnaughton and Foster (1994) modeled the solubility of DDT and (2,4-dichlorophenoxy)acetic acid (2,4-D) in CO2 using the modified PREOS approach. In their study, the energy parameter was made a linear function of temperature. For the temperature range of interest in the present study (45-55 °C), the energy parameter for the HBA isomers decreased by around 2% with an increase in temperature. This was considered to be an insignificant change, and so the energy parameter of the solute was made independent of temperature in the fitting procedure. The energy and size parameters for CO2 were estimated in the conventional manner. Optimized values of the pure component parameters for each HBA isomer were calculated by minimizing the AARD over two isotherms of data with k12 set to 0. The modified form of the PREOS, in this case, represents the fitting of two adjustable parameters over two isotherms of data, which is equivalent to the original form of the PREOS. The modeling results are presented in Table 11. Overall, a substantial improvement was made in the correlation of solubility data for both isomers. The improvement is also shown graphically in Figures 9 and 10. The AARDs were all within 7%, which is only marginally higher than the AARDs obtained from density-based correlations (within 5%). The modified PREOS produced substantially different values for the solute parameters compared with the estimated values, which are also given in Table 11. The energy parameter increased by around 30% for each isomer while the size parameter nearly doubled in value. The optimized solute parameters do not necessarily represent the true energy and size parameters of the solute because they inherently depend on the value set for the binary interaction parameter, which was 0 in this case. The optimized parameters are probably not useful for estimating other properties of the solute, but they may be used in the correlation of ternary solubility data as described in the next section. Ternary Systems. The modeling of the OP system involved the determination of an optimal solute-solute interaction parameter. The solute-solute interaction parameter is k23, where the subscript 2 now refers to the more soluble solute and component 3 is the less soluble solute. The solute-solute interaction parameter was made a function of temperature, which meant that the ternary modeling involved the same number of adjustable parameters as the binary modeling, i.e., one adjustable parameter per isotherm of solubility data for a given solute. The optimized value of k23 at a given temperature was based on the minimum AARD for two

4696 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 12. Optimized Solute-Solute Interaction Parameters for the Modeling of Ternary Solubility Data AARD (%) temp (°C) 45 55

45 55

k23a

ortho

para

Modified PREOS -28.5 6.1 20.2 (overall: 13.2) -24.1 4.4 23.6 (overall: 14.0) Original PREOS -17.0 22.9 41.6 (overall: 32.3) -10.8 23.7 36.1 (overall: 29.9)

a Component 2 refers to the more soluble solute in the ternary system while component 3 refers to the less soluble solute.

Figure 9. Modeling results using the modified PREOS for the binary solubility data of o-HBA.

Figure 11. Modeling results using the modified PREOS for ternary solubility data at 318 K.

Figure 10. Modeling results using the modified PREOS for the binary solubility data of p-HBA.

sets of solubility data, one set for each solute present in the ternary system. The application of conventional mixing rules to ternary systems also requires two solute-solvent interaction parameters: k12 and k13. These interaction parameters are identical to the solute-solvent interaction parameters calculated for each solute in their respective binary systems. In this section of the modeling study, however, these interaction parameters were all set to 0. The optimized size and energy parameters for each solute, as determined with the modified PREOS, were used in place of the estimated values from the conventional Peng-Robinson expressions. The ternary solubility data for o-HBA were well correlated as shown in Table 12. The overall fit of the data was comparable with the correlation of the binary

data with the modified PREOS (Table 11). In contrast, the model significantly underestimated most of the ternary solubility data for p-HBA, as shown in Figure 11. Although the p-HBA solubility was significantly enhanced, the mixing rules for the ternary system were still relatively insensitive to the fluid phase composition because of the low values of mole fraction. Consequently, a large negative value for k23 was needed in an attempt to account for the solubility enhancements, as shown in Table 12. The individual AARD for the para isomer was around 20%, with data points in the low-pressure region underestimated by as much as 40%. The values of k23 obtained in the OP system were particularly unusual in that they were much lower than -1, although values of around -4 have been reported in another ternary system where solubility enhancement was observed (Macnaughton and Foster, 1994). The original PREOS with conventional mixing rules also produced large and negative values for k23, but the correlation results were inferior (Table 12). This demonstrates that the negative values of k23 obtained with the modified PREOS are not simply the result of using fitted size and energy parameters. The negative solute-solute interaction parameters therefore suggest that there are strong interactions occurring between the isomers in the fluid phase. The

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4697 Table 13. Optimized Adjustable Parameters for the Modeling of Ternary Solubility Data with the PREOS and CVD Mixing Rules AARD (%) temp (°C)

m23

45

-2.32

55

-2.28

ortho

para

22.6 41.5 (overall: 32.1) 22.3 39.3 (overall: 30.8)

possibility of hydrogen bonding occurring between the isomers was proposed earlier, and the present results further support this notion. It should be pointed out, however, that the solute-solute interaction parameter is really a fitting parameter which only gives a qualitative indication of the interactions which occur between unlike molecular species (Abbott, 1979). It is probably not useful for further evaluation of the degree of hydrogen bonding which may be occurring in the SCF phase. Since higher mole fractions were observed for p-HBA in the OP ternary system, the CVD mixing rules were again used to assess whether the observed solubility enhancements could be more accurately predicted than with the modified PREOS. The situation for ternary systems can be treated in two ways. The adjustable parameter describing unlike solute interactions, m23, can be set to 1.0, as in the case of like solute interactions, or it can be left as an adjustable parameter and regressed from ternary solubility data. The latter approach was taken in this part of the modeling. The solute-solvent adjustable parameters, m12 and m13, were taken from the modeling of binary solubility data (Table 10). The values of m23 for the OP system are presented in Table 13. At both temperatures, m23 was large and negative like k23 in an attempt to predict the solubility enhancements. The CVD mixing rules were not able to accurately predict the solubility enhancements for p-HBA. In fact, the correlation results were inferior to those obtained with the modified PREOS. Separation of Para and Ortho Isomers Since the para isomer is a byproduct in the industrial synthesis of salicylic acid, it is useful to consider the possibility of separating the two isomers using supercritical CO2. Separation can be achieved by conventional extraction of a mixture of the two isomers. This process exploits the difference in the solubility of the isomers in supercritical CO2. Alternatively, if the two isomers exhibit significantly different crossover pressures, retrograde crystallization can be used to effect the separation. The selectivity of CO2 for salicylic acid can be defined as the ratio of the respective mole fractions of the isomers in the fluid phase (yo-HBA/yp-HBA). The selectivities based on binary and ternary solubility data are shown in Figure 12 as a function of pressure. At lower pressures, the selectivity in both cases increases markedly at the expense of lower solute concentrations in the fluid phase. The occurrence of solubility enhancement in the ternary system has the effect of reducing the selectivity by a factor of around 2. However, since the selectivity in the ternary system is still quite large, solubility enhancement has had only a minimal effect on the composition of the extract. For example, at 55 °C the average selectivity based on binary solubility data is around 178, and in the absence

Figure 12. Selectivity of carbon dioxide for salicylic acid based on binary (B) and ternary (T) solubility data.

of solubility enhancement, this would correspond to an extract which is 99.4% pure salicylic acid. The corresponding average selectivity in the ternary system is 84, which reduces the purity of salicylic acid in the extract to 98.8%. This is still an excellent result for just one extraction step. Further purification of the extract under saturation conditions is not possible since fluid phase compositions are independent of the bed composition (see Effect of Bed Composition). The crossover pressures for both isomers in their respective binary systems were found to be almost identical (∼150 bar), and negligible change in the crossover pressures was observed in the ternary systems. Similar results were obtained in the 2,6- and 2,7dimethylnaphthalene isomer system (Iwai et al., 1993). Separation of isomers using retrograde crystallization therefore seems unlikely, although Johnston et al. (1987) have identified one candidate system (2,3- and 2,6-dimethylnaphthalene). The technical feasibility of retrograde crystallization has been demonstrated in other nonisomeric systems with varying degrees of success (Kelley and Chimowitz, 1989; Schaeffer et al., 1988). In practice, crossover regions tend to be quite narrow, perhaps less than 20 bar, and are difficult to define because a distinct crossover pressure does not necessarily exist for all temperatures between two isotherms (see Figure 3). Conclusion Solubility data have been measured for the HBA isomers and their mixtures in supercritical carbon dioxide. The solubility of p-HBA in the presence of o-HBA was found to be enhanced by up to 170% when compared with its binary solubility data. Negligible solubility enhancement was observed for o-HBA in the ternary system. On the basis of the observed solubility behavior in the ternary system, it is possible to generalize that the solubility of a solid in a ternary system will increase relative to its binary system in proportion to the solubility of the other solid in the ternary system. Three bed compositions (50:50, 80:20, and 20:80 mol %) were used in the measurement of ternary solubility

4698 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996

data. The solubility of each isomer was found to be independent of the bed composition, and this is consistent with thermodynamic modeling of the system. The results from the sequential bed experiment suggest that the enhancement of the p-HBA solubility in the ternary system is similar to the solubility enhancements observed in cosolvent systems. In this case, the solubility enhancement increases with the concentration of o-HBA in the fluid phase. The use of conventional mixing rules to model binary solubility data produced poor correlation results with all AARDs greater than 10%. No real improvements to the correlation results were made with the CVD mixing rules. In both cases, the poor results were mainly attributed to errors in the estimation of the pure component parameters for the solute. On the other hand, the modified PREOS produced much better results for the modeling of binary solubility data. The AARDs in all cases were within 7%, which is comparable to the AARDs achieved with density-based correlations (within 5%). The modified PREOS, however, was not able to quantitatively predict the solubility enhancements observed in the ternary system. The model significantly underestimated the ternary solubility data for p-HBA. Very large and negative solute-solute interaction parameters were obtained in an attempt to predict the solubility enhancements. Such values for these parameters are indicative of strong interactions between the isomers. This suggests that hydrogen bonding between the isomers in the SCF phase is a likely possibility. Separation of the ortho and para isomers can be carried out by exploiting the difference in the solubility of the isomers in supercritical CO2. While the solubility of p-HBA is considerably enhanced when a mixture of the two isomers is extracted with CO2, it is still possible to produce an extract which is 99% pure salicylic acid in one extraction step. The similar crossover pressure for both isomers (∼150 bar), however, signifies that separation of the isomers using retrograde crystallization is an unlikely possibility. Acknowledgment F.P.L. wishes to acknowledge the Australian Government for the provision of a Postgraduate Research Award. The mixed bed experiments were carried out by R. Chandler. Literature Cited Abbott, M. M. Cubic Equations of State: An Interpretive Review. In Equations of State in Engineering and Research; Chao, K. C., Robinson, R. L., Eds.; American Chemical Society: Washington, DC, 1979; Chapter 3. Adachi, Y.; Lu, B. C.-Y. Supercritical fluid extraction with carbon dioxide and ethylene. Fluid Phase Equilib. 1983, 14, 147. Bamberger, T.; Erickson, J. C.; Cooney, C. L.; Kumar, S. K. Measurement and Model Prediction of Solubilities of Pure Fatty Acids, Pure Triglycerides, and Mixtures of Triglycerides in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1988, 33, 327. Bartle, K. D.; Clifford, A. A.; Jafar, S. A.; Shilstone, G. F. Solubilities of solids and liquids of low volatility in supercritical carbon dioxide. J. Phys. Chem. Ref. Data 1991, 20 (4), 713. Chang, H.; Morrell, D. G. Solubilities of Methoxy-1-Tetralone and Methyl Nitrobenzoate Isomers and Their Mixtures in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1985, 30, 74-78. Chen, P.-C.; Tang, M.; Chen, Y.-P. Calculations of the Solubilities of Solids in Supercritical Fluids Using the Peng-Robinson Equation of State and a Modified Mixing Model. Ind. Eng. Chem. Res. 1995, 34, 332.

Chimowitz, E. H.; Pennisi, K. J. Process synthesis concepts for supercritical gas extraction in the crossover region. AIChE J. 1986, 32 (10), 1665. Chimowitz, E. H.; Kelley, F. D.; Munoz, F. M. Analysis of retrograde behaviour and the cross-over effect in supercritical fluids. Fluid Phase Equilib. 1988, 44, 23. Chrastil, J. Solubility of Solids and Liquids in Supercritical Gases. J. Phys. Chem. 1982, 86, 3016. Chung, S. T.; Shing, K. S. Multiphase behaviour of binary and ternary systems of heavy aromatic hydrocarbons with supercritical carbon dioxide. Fluid Phase Equilib. 1992, 81, 321341. Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere Publishing Corporation: New York, 1989. de Kruif, C. G.; van Ginkel, C. H. D. Torsion-weighing effusion vapour-pressure measurements on organic compounds. J. Chem. Thermodyn. 1977, 9, 725-730. Delcour, J. A.; Vinkx, C. J. A.; Vanhamel, S.; Block, G. G. A. G. Combined monitoring of UV absorbance and fluorescence intensity as a diagnostic criterion in reversed-phase highperformance liquid chromatographic separations of natural phenolic acids. J. Chromatogr. 1989, 467, 149. Dobbs, J. M.; Johnston, K. P. Selectivities in Pure and Mixed Supercritical Fluid Solvents. Ind. Eng. Chem. Res. 1987, 26, 1476. Eckert, C. A; Ekart, M. P.; Knutson, B. L.; Payne, K. P.; Tomasko, D. L.; Liotta, C. L.; Foster, N. R. Supercritical Fluid Fractionation of a Nonionic Surfactant. Ind. Eng. Chem. Res. 1992, 31, 1105. Ekart, M. P.; Bennett, K. L.; Ekart, S. M.; Gurdial, G. S.; Liotta, C. L.; Eckert, C.A. Cosolvent interactions in supercritical fluid solutions. AIChE J. 1993, 39 (2), 235. Erickson, S. H. Salicylic acid and related compounds. In KirkOthmer Encyclopedia of Chemical Technology, 3rd ed.; Grayson, M., Eckroth, D., Eds.; John Wiley & Sons: New York, 1982; Vol. 20. Foster, N. R.; Gurdial, G. S.; Yun, J. S. L.; Liong, K. K.; Tilly, K. D.; Ting, S. S. T.; Singh, H.; Lee, J. H. Significance of the Crossover Pressure in Solid-Supercritical Fluid Equilibria. Ind. Eng. Chem. Res. 1991, 30, 1955. Gopal, J. S.; Holder, G. D.; Kosal, E. Solubility of solid and liquid mixtures in supercritical carbon dioxide. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 697. Gurdial, G. S.; Foster, N. R. Solubility of o-Hydroxybenzoic Acid in Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1991, 30, 575. Gurdial, G. S.; Macnaughton, S. J.; Tomasko, D. L.; Foster, N. R. Influence of Chemical Modifiers on the Solubility of o- and m-Hydroxybenzoic Acid in Supercritical CO2. Ind. Eng. Chem. Res. 1993, 32, 1488. Ikushima, Y.; Hatakeda, K.; Ito, S.; Saito, N.; Asano, T.; Goto, T. A Supercritical Carbon Dioxide Extraction from Mixtures of Triglycerides and Higher Fatty Acid Methyl Esters Using a GasEffusion-Type System. Ind. Eng. Chem. Res. 1988, 27, 818. Iwai, Y.; Mori, Y.; Hosotani, N.; Higashi, H.; Furuya, T.; Arai, Y.; Yamamoto, K.; Mito, Y. Solubilities of 2,6- and 2,7-Dimethylnaphthalenes in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1993, 38, 509. Johnston, K. P.; Barry, S. E.; Read, N. K.; Holcomb, T. R. Separation of Isomers Using Retrograde Crystallization from Supercritical Fluids. Ind. Eng. Chem. Res. 1987, 26, 2372. Johnston, K. P.; Peck, D. G.; Kim, S. Modeling Supercritical Mixtures: How Predictive Is It? Ind. Eng. Chem. Res. 1989, 28, 1115. Kelley, F. D.; Chimowitz, E. H. Experimental data for the crossover process in a model supercritical system. AIChE J. 1989, 35 (6), 981. Kosal, E.; Holder, G. D. Solubility of Anthracene and Phenanthrene Mixtures in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1987, 32, 148. Krukonis, V. J.; Kurnik, R. T. Solubility of Solid Aromatic Isomers in Carbon Dioxide. J. Chem. Eng. Data 1985, 30, 247. Kumar, S. K.; Johnston, K. P. Modelling the solubility of solids in supercritical fluids with density as the independent variable. J. Supercrit. Fluids 1988, 1, 15. Kurnik, R. T.; Reid, R. C. Solubility of solid mixtures in supercritical fluids. Fluid Phase Equilib. 1982, 8, 93.

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4699 Kurnik, R. T.; Holla, S. J.; Reid, R. C. Solubility of Solids in Supercritical Carbon Dioxide and Ethylene. J. Chem. Eng. Data 1981, 26, 47. Kwiatkowski, J.; Zygmunt, L.; Majewski, W. An experimental method for measuring solubilities of solids in supercritical fluids. Ber. Bunsen-ges. Phys. Chem. 1984, 88, 865. Lee, C.; Ellington, R. T. Density-based correlation for solid solubility in supercritical solvents. Sep. Sci. Technol. 1987, 22 (6), 1557. Lee, H.-K.; Kim, C.-H.; Kim, S.; Choi, C.-S. Solid Solubilities of Methoxyphenylacetic Acid Isomer Compounds in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1994, 39, 163. Lemert, R. M.; Johnston, K. P. Solubilities and selectivities in supercritical fluid mixtures near critical end points. Fluid Phase Equilib. 1990, 59, 31. Liang, J. H.; Yeh, A.-I. Process conditions for separating fatty acid esters by supercritical CO2. J. Am. Oil Chem. Soc. 1991, 68 (9), 687. Lindsey, A. S.; Jeskey, H. The Kolbe-Schmitt Reaction. Chem. Rev. 1957, 57, 583-620. Lydersen, A. L. Estimation of Critical Properties of Organic Compounds; Eng. Exp. Stn. Report 3; Univ. Wisconsin Coll. Eng.: Madison, WI, 1955. Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H. Handbook of Chemical Property Estimation Methods; American Chemical Society: Washington, DC, 1990. Macnaughton, S. J.; Foster, N. R. The solubility of DDT and 2,4-D in Supercritical Carbon Dioxide and Supercritical Carbon Dioxide Saturated with Water. Ind. Eng. Chem. Res. 1994, 33, 2757. Macnaughton, S. J.; Tomasko, D. L.; Foster, N. R.; Eckert, C. A. Design considerations for soil remediation using supercritical fluid extraction. Process Saf. Environ. Prot. 1993, 71, 124. Mansoori, G. A. Mixing rules for cubic equations of state. In Equations of State: Theories and Applications; Chao, K. C., Robinson, R. L., Eds.; American Chemical Society: Washington, DC, 1986; Chapter 15. McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, 1963. McHugh, M. A.; Yogan, T. J. Three-Phase Solid-Liquid-Gas Equilibria for Three Carbon Dioxide-Hydrocarbon Solid Systems, Two Ethane-Hydrocarbon Solid Systems, and Two Ethylene-Hydrocarbon Solid Systems. J. Chem. Eng. Data 1984, 29, 112. McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworths: Boston, 1986. Mitra, S.; Chen, J. W.; Viswanath, D. S. Solubility and Partial Molar Volumes of Heavy Aromatic Hydrocarbons in Supercritical CO2. J. Chem. Eng. Data 1988, 33, 35. Mori, Y.; Shimizu, T.; Iwai, Y.; Arai, Y. Solubilities of 3,4-Xylenol and Naphthalene + 2,5-Xylenol in Supercritical Carbon Dioxide at 35 °C. J. Chem. Eng. Data 1992, 37, 317-319. Mukhopadhyay, M.; Rao, G. V. R. Thermodynamic Modeling for Supercritical Fluid Process Design. Ind. Eng. Chem. Res. 1993, 32, 922. Peng, D.-Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15 (1), 59. Pennisi, K. J.; Chimowitz, E. H. Solubilities of Solid 1,10Decanediol and a Solid Mixture of 1,10-Decanediol and Benzoic Acid in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1986, 31, 285.

Pongsiri, N.; Viswanath, D. S. A Comparative Study of Mixing Rules in the Prediction of Solid-Vapour Equilibria. Ind. Eng. Chem. Res. 1989, 28, 1918. Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice-Hall Inc.: Englewood Cliffs, NJ, 1986. Rao, V. S. G.; Mukhopadhyay, M. Effect of covolume dependency of the energy parameter on the predictability of SCFE data using the Peng-Robinson equation of state. J. Supercrit. Fluids 1989, 2, 22. Rao, V. S. G.; Mukhopadhyay, M. Solid solubilities in supercritical fluids from group contributions. J. Supercrit. Fluids 1990, 3, 66. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw Hill Inc.: New York, NY, 1987. Rittich, B.; Pirochtova, M. Chromatographic behaviour of aromatic acids in reversed-phase high-performance liquid chromatography. J. Chromatogr. 1990, 523, 227. Schaeffer, S. T.; Zalkow, L. H.; Teja, A. S. Supercritical extraction of crotalaria spectabilis in the cross-over region. AIChE J. 1988, 34 (10), 1740. Schmitt, W. J.; Reid, R. C. Solubility of Monofunctional Organic Solids in Chemically Diverse Supercritical Fluids. J. Chem. Eng. Data 1986, 31, 204. Smith, J. M.; van Ness, H. C. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill Book Co.: Singapore, 1987; pp 571-572. Stahl, E.; Schilz, W.; Schutz, E.; Willing, E. A quick method for the microanalytical evaluation of the dissolving power of supercritical gases. Angew. Chem., Int. Ed. Engl. 1978, 17, 731. Tan, C.-S.; Weng, J.-W. Solubility measurements of naphthol isomers in supercritical CO2 by a recycle technique. Fluid Phase Equilib. 1987, 34, 37. Tavana, A.; Randolph, A. D. Isobaric-isothermal fractional crystallization of organic solids from supercritical fluid mixtures. In AIChE Symposium Series, Number 284; Ramanarayanan, R., Kern, W., Larson, M., Sikdar, S., Eds.; AIChE: New York, 1991, p 5. Ting, S. S. T.; Macnaughton, S. J.; Tomasko, D. L.; Foster, N. R. Solubility of Naproxen in Supercritical Carbon Dioxide with and without Cosolvents. Ind. Eng. Chem. Res. 1993, 32, 1471. Tsekhanskaya, Y. V.; Iomtev, M. B.; Mushkina, E. V. Solubility of naphthalene in ethylene and carbon dioxide under pressure. Russ. J. Phys. Chem. 1964, 38 (9), 1173.

Received for review October 23, 1995 Revised manuscript received July 3, 1996 Accepted July 3, 1996X IE950649Q

X Abstract published in Advance ACS Abstracts, October 15, 1996.