Thermodynamic Equilibria Modeling of Ternary Systems of Solid Organics in Compressed Carbon Dioxide

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1 Thermodynamc Equlbra Modelng of Ternary Systems of Sold Organcs n Compressed Carbon Doxde Yousef Bakhbakh Department of Chemcal Engneerng, Kng Saud Unversty, P.O. Box 800, Ryadh, 11421, Saud Araba. ybakhbak@ksu.edu.sa Carbon doxde as a compressed gas s a non-polar molecule, thus t s not a partcularly good solvent for polar organc compounds. Therefore, a polar cosolvent s usually recommended for enhancng the solublty power of compressed gas for polar organc compounds. Moreover, accurate predcton of compressed gas behavor n mxtures s hghly requred, besdes the expermental assessments of the nfluence of key operatng parameters. Many authors have used equatons of state combned wth mxng rules to develop mathematcal models for the determnaton of solubltes of systems composed of a solute, a solvent, and a cosolvent. In ths work, the Stryjek and Vera modfed Peng-Robnson equaton of state (PRSV EoS) wth the van der Waals mxng rules were used to formulate a mathematcal model for the solublty of solds n supercrtcal fluds wth cosolvents,.e., n ternary systems. All three bnary nteracton parameters nvolved were determned for dfferent ternary systems for whch expermental data were avalable; these parameters were used to calculate the solubltes for those systems. Results obtaned showed that the model ftted very well the expermental data for all the systems studed. 1. Introducton The recent ncrease n the use of supercrtcal fluds for separaton processes requres the knowledge of theoretcal nterpretatons and predctons of phase behavor of supercrtcal fluds n multcomponent systems. Moreover, n order to desgn and to scale a supercrtcal flud based process up to the ndustral level, t s of paramount mportance to get a detaled understandng of all the phenomena nvolved. Good understandng of the phase behavor of supercrtcal fluds wth varous compounds become necessary for effcent desgn of such producton systems. The nvestgated nfluence of polar cosolvents on the solublty of polar solds n supercrtcal carbon doxde showed that the addton of a small amount of a polar cosolvent could sgnfcantly ncrease the solvatng power of supercrtcal CO 2. Nonetheless, n an effort to develop a model that can predct the solublty of solds n mxtures of supercrtcal fluds wth cosolvents, several methods have been used by dfferent nvestgators. These models nclude the use of equaton of state (EoS) ( Cháfer et al., 2004), solutons theores (L et al., 2004), expanded lqud model (Brogle, 1982), cluster solvaton model (Cheng et al., 2003), and densty-based model (Jn et al., 2004). Models usng EoS are based on relatng the solublty to the pressure and the temperature through the fugacty coeffcent evaluated from an EoS. Guha and Madras (2001), proposed a model that combnes the cubc Patel-Teja (PT) EoS wth the Wong-

2 Sandler (WS) mxng rule. The model was appled to correlate the solubltes of dfferent ternary systems and the correspondng bnares. Cháfer et al., used two types of thermodynamc models to calculate the solublty of quertecn n supercrtcal CO 2 and ethanol. One of the models used the group contrbuton (GC) EoS whle the other used the Soave-Redlch-Kwong (SRK) EoS. The frst model combnes the Carnahan Starlng repulsve-type equaton for hard spheres, wth a group contrbuton verson of a densty-dependent NRTL-type expresson to evaluate attractve nteractons between molecules. The second model s a well known, and wdely used representatve of the cubc equatons from van der Waals EoS famly. Moreover, Huang et al., (2004) used the Peng-Robnson (PR) EoS and the emprcal densty-based models of Chrastl and Kumar and Johnston to correlate the solublty data of cholesterol and cholesteryl benzoate n supercrtcal CO 2 n the presence of the polar cosolvents methanol and acetone. Ther results concluded that although the densty-based models provded a better correlaton of the expermental data wth a far lower value of average absolute relatve devaton (AARD) than the PR EoS, the latter has the advantage that t provdes reasonable estmates of the complex solublty behavor of solds n supercrtcal CO 2 as a functon of temperature and pressure once the requred physcal propertes are known. Furthermore, cubc equatons of state are proved to be hghly successful for phase equlbrum calculatons of multcomponent systems. In ths nvestgaton, the PRSV approach was employed for modelng the solublty of anthracene n supercrtcal carbon doxde wth and wthout cosolvents. 2. Mathematcal Framework As stated above, the lmtaton of expermental data dealng wth supercrtcal fluds mxtures and snce these mxtures deal wth hgh-pressure phase equlbra, there s consderable nterest n mathematcal models that can accurately predct the phase behavor of such systems. The equaton of state (EoS) method s consdered to be the most sutable approach for modelng such knd of systems. Although many nvestgatons have been carred out for modelng the solublty of solds n supercrtcal flud mxtures, the modelng of the solublty of solds n supercrtcal fluds wth cosolvents are much less, and cubc EoSs are commonly used. The Stryjek and Vera modfed Peng-Robnson equaton of state, the so-called PRSV has receved great attenton snce ts publcaton. In ths work, the PRSV approach s further appled to model the solublty of solute sold n supercrtcal flud wth cosolvent mxture. The volumetrc expanson of the lqud phase s smulated usng the Stryjek and Vera modfed Peng-Robnson equaton of state (PRSV) EoS. The Peng-Robnson equaton of state s gven by: RT a P (1) 2 2 v b v 2v b b The solublty of the sold n a supercrtcal flud and cosolvent s determned by the followng equaton:

3 sat P y sol V P exp P (2) RT (16) where P, V, and are the sublmaton pressure, sold molar volume, and the sat sol n ether the lqud or vapor phase. The optmzaton procedure s based on the mnmzaton of the error between the calculated and expermental values. The expresson for the objectve functon s: fugacty coeffcent of component mn 1 n OF p dst y p m ; n R n 1 3. Results and Dscusson p (3) The values for the expermental solubltes of anthracene n supercrtcal carbon doxde wth cosolvents, acetone, ethanol and cyclohexane were taken from lterature (Bae et al., 2004, Cháfer et al., 2004). Fgs. 1 and 2 show the solublty behavor at temperatures, K and K, of the system anthracene- CO 2 wth three dfferent cosolvents and wth no cosolvent; therefore, the effect of the cosolvent s shown. The cosolvents used are ethanol and cyclohexane, all at 4 mole %. It s obvous that the calculated nteracton parameters yeld good agreement between the calculated and expermental solublty data. The best agreement was obtaned wth the expermental solublty data of acetone as a cosolvent. However, errors can occur n the solublty measurements and also n the thermal analyss usng DSC. An error of ±10% n measurng the heat of fuson, and thus heat capacty and meltng pont, can result n a devaton up to 80% n the solublty predcton. Fgs. 3 and 4 show the effect of temperature on the solublty for the systems anthracene- CO 2 - acetone, anthracene- CO 2 - ethanol, and anthracene- CO 2 - cyclohexane usng the calculated solublty data wth the PRSV EoS and the calculated nteracton parameters. It s clear that the addton of a cosolvent can have a dramatc effect on the supercrtcal fluds phase behavor and on the solublty of the solute. It should be ponted out that one of the uses of knowng the effect of the cosolvent concentraton on the solublty s that t provdes nformaton or nsght on the amount of cosolvent needed to obtan a partcular solublty result. Fgs. 3 and 4 show the effect of temperature on the solublty for the systems anthracene- CO 2 - acetone, anthracene- CO 2 - ethanol, and anthracene- CO 2 - cyclohexane usng the calculated solublty data wth the PRSV EoS and the calculated nteracton parameters. It s clear that the addton of a cosolvent can have a dramatc effect on the supercrtcal fluds phase behavor and on the solublty of the solute. It should be ponted out that one of the uses of knowng the effect of the cosolvent concentraton on the solublty s that t provdes nformaton or nsght on the amount of cosolvent needed to obtan a partcular solublty result. For each sotherm studed the solublty ncreases as the pressure ncreases. The sotherms show that the solublty of the solute n CO 2 was mproved when the cosolvent was added.

4 Fgure 1. Behavor of the system anthracene-co 2 and the cosolvents, acetone, ethanol, and cyclohexane at K. The data ponts {,,,, }are expermental values whereas the lnes are EoS predcted data. The sotherms also showed that the type of cosolvent used has an mpact on the solute solublty. For the case of anthracene, the cosolvent strength ncreases as follow: cyclohexane > ethanol > acetone. The solublty of anthracene, whch s a non-polar solute, was hgher wth the non-polar cosolvent cyclohexane than wth the polar cosolvents ethanol and acetone. Tng et al. (1993), ndcated that the use of a polar cosolvent for polar solutes, may cause the largest ncrease n solublty as a result of some specfc chemcal nteractons lke hydrogen bondng or charge transfer complex formaton. The temperature has an effect on the solublty of the solute n CO 2. Fgure 2. Behavor of the system anthracene-co 2 and the cosolvents, acetone, ethanol, and cyclohexane at K. The data ponts {,,,, }are expermental values whereas the lnes are EoS predcted data.

5 Fgure 3. Behavor of the system anthracene-co 2 -ethanol at K, K, and K. The data ponts {,,, }are expermental values whereas the lnes are EoS predcted data. For the system studed n ths work, t was observed that at low pressures, an ncrease of temperature adversely affects the solublty snce t s reduced. However, there s a crossover pont beyond whch an ncrease of temperature mproves the solute solublty. Ths effect s shown n Fgs. 1 and 2 for the system anthracene- CO 2 -acetone at temperatures of K and K where the hghest solubltes were obtaned at the hghest temperature and pressures above approxmately 15 MPa. Chmowtz and Penns (1986), explaned that the solublty enhancement at hgh pressures and temperatures may be caused by the fact that at pressures below the crossover pressure, the densty of the gas s more senstve to temperature changes than at hgher pressures. At hgher pressures, above the crossover pont, the vapor-pressure effect s more mportant than the densty effect. Fgure 4. Behavor of the system anthracene-co 2 -cyclohexane at K, K, and K. The data ponts {,,, }are expermental values whereas the lnes are EoS predcted data.

6 4. Conclusons In ths nvestgated thermodynamc equlbra, the Stryjek and Vera modfed Peng- Robnson equaton of state (PRSV) EoS and the VDW mxng rules model were used to determne solubltes of systems that nvolved sold, supercrtcal flud, and cosolvent. The solublty of the systems anthracene- CO 2 - acetone, anthracene- CO 2 - ethanol, and anthracene- CO 2 - cyclohexane was nfluenced by the pressure and temperature. The best agreement was obtaned wth the expermental solublty data of acetone as a cosolvent although the solublty of anthracene, was hgher wth the non-polar cosolvent cyclohexane than wth the polar cosolvents ethanol and acetone. Acknowledgments The author wsh to acknowledge the fnancal support by Deanshp of Scentfc Research at the Kng Saud Unversty. References Bae H., Jeon J., and Lee. H., 2004, Influence of Co-solvent on Dye Solublty n Supercrtcal Carbon Doxde. Flud Phase Equlbra, , Brogle H., 1982, CO 2 as a solvent: ts propertes and applcatons. Chemstry and Industry, Chafer A., Fornar T., Berna A., and Stateva R.P., 2004, Solublty of Quercetn n Supercrtcal CO2 + Ethanol as a Modfer: Measurements and Thermodynamc Modellng. The Journal of Supercrtcal Fluds, 32, Cheng K., Tang M., and Chen Y., 2003, Calculatons of Sold Solublty n Supercrtcal Fluds usng a Smplfed Cluster Solvaton Model. Flud Phase Equlbra, 214, Chmowtz E.H. and Penns. K.J., 1986, Process Synthess Concepts for Supercrtcal Gas Extracton n the Crossover Regon. AIChE Journal, 32, Guha S. and Madras G., 2001, Modelng of Ternary Solubltes of Organcs n Supercrtcal Carbon Doxde. Flud Phase Equlbra, 4736, Huang Z., Kaw S., and Chew Y.C., 2004, Solublty of Asprn n Supercrtcal Carbon Doxde wth and wthout Acetone. J. Chem. Eng. Data, 49, , Jn J., Zhong C., Zhang Z., and L Y., 2004, Solubltes of Benzoc Acd n Supercrtcal CO2 wth Mxed Co-Solvent. Flud Phase Equlbra, 226, L Q., Zhong C., Zhang Z., and Zhou Q., 2004, Modelng of the Solublty of Sold Solutes n Supercrtcal CO2 wth and wthout Cosolvent usng Soluton Theory. Korean J. Chem. Eng., 21, Peng D. and Robnson D.B., 1976, A New Two-Constant Equaton of State. Ind. Eng. Chem. Fundam., 15, Stryjek R., Vera J. H., 1986, PRSV: an mproved Peng Robnson equaton of state for pure compounds and mxtures, Can. J. Chem. Eng. 64,323. Tng S.S.T., Macnaughton S.J., Tomasko D.L., and Foster N.R., 1993, Solublty of Naproxen n Supercrtcal Carbon Doxde wth and wthout Cosolvents. Ind. Eng. Chem. Res., 32,