Correlation and Prediction of the Solubility of Solid Solutes in Chemically Diverse Supercritical Fluids Based on the Expanded Liquid Theory

Affiliation(s)

Department of Pharmaceutical Engineering, University Constantine 3, Constantine, Algeria.

Department of Pharmaceutical Engineering, University Constantine 3, Constantine, Algeria.

ABSTRACT

For the proper design of any extraction procedure based on supercritical solvents, it is essential to have a sound knowledge of the solubility data of different compounds and the accurate way to represent it. The solute’s solubility in a supercritical solvent is dependent on the solute, the solvent, and the operating conditions (temperature and pressure). Developing a comprehensive experimental data set is an onerous task and time consuming and, thus, the incentive to develop predictive tools is substantial. In this paper, a technique is presented and tested to correlate and predict solute’s solubility in different supercritical fluids with a methodology based on the expanded liquid theory, in which the solid-fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with empiric equations. The most advantages of this model include: it does not require the knowledge of critical properties and sublimation pressure of solid solutes and does take into account the binary interaction between solid solute and solvent. The evaluation of the proposed model capabilities is done by testing it on a large data base consisting of experimental solubility data taken from literature of 33 binary systems solid-SC fluid. The results obtained for both correlation and prediction show good agreement with the experimental data used. For the comparison we have considered some literature models that account for effect of the system conditions (temperature and pressure) in addition to the sublimation pressure of the solute through their introduction of the enhancement factor and a model based on a modified Peng-Robinson equation of state.

For the proper design of any extraction procedure based on supercritical solvents, it is essential to have a sound knowledge of the solubility data of different compounds and the accurate way to represent it. The solute’s solubility in a supercritical solvent is dependent on the solute, the solvent, and the operating conditions (temperature and pressure). Developing a comprehensive experimental data set is an onerous task and time consuming and, thus, the incentive to develop predictive tools is substantial. In this paper, a technique is presented and tested to correlate and predict solute’s solubility in different supercritical fluids with a methodology based on the expanded liquid theory, in which the solid-fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with empiric equations. The most advantages of this model include: it does not require the knowledge of critical properties and sublimation pressure of solid solutes and does take into account the binary interaction between solid solute and solvent. The evaluation of the proposed model capabilities is done by testing it on a large data base consisting of experimental solubility data taken from literature of 33 binary systems solid-SC fluid. The results obtained for both correlation and prediction show good agreement with the experimental data used. For the comparison we have considered some literature models that account for effect of the system conditions (temperature and pressure) in addition to the sublimation pressure of the solute through their introduction of the enhancement factor and a model based on a modified Peng-Robinson equation of state.

KEYWORDS

Solubility Modeling; Supercritical Fluids; Correlation; Prediction; Expanded Liquid; UNIQUAC

Solubility Modeling; Supercritical Fluids; Correlation; Prediction; Expanded Liquid; UNIQUAC

Cite this paper

L. Nasri, S. Bensaad and Z. Bensetiti, "Correlation and Prediction of the Solubility of Solid Solutes in Chemically Diverse Supercritical Fluids Based on the Expanded Liquid Theory,"*Advances in Chemical Engineering and Science*, Vol. 3 No. 4, 2013, pp. 255-273. doi: 10.4236/aces.2013.34033.

L. Nasri, S. Bensaad and Z. Bensetiti, "Correlation and Prediction of the Solubility of Solid Solutes in Chemically Diverse Supercritical Fluids Based on the Expanded Liquid Theory,"

References

[1] G. Madras, C. Kulkarni and J. Modak, “Modeling the Solubilities of Fatty Acids in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 209, No. 2, 2003, pp. 207-213.

http://dx.doi.org/10.1016/S0378-3812(03)00148-1

[2] N. R. Foster, G. S. Gurdial, J. S. L. Yun, K. K. Liong, K. D. Tilly, S. S. T. Ting, H. Singh and J. H. Lee, “Significance of the Crossover Pressure in Solid Supercritical Fluid Phase-Equilibria,” Industrial and Engineering Chemistry Research, Vol. 30, No. 8, 1991, pp. 1955-1964.

http://dx.doi.org/10.1021/ie00056a044

[3] J. Chrastil, “Solubility of Solids and Liquids in Supercritical Gases,” Journal of Physical Chemistry, Vol. 86, No. 15, 1982, pp. 3016-3021.

http://dx.doi.org/10.1021/j100212a041

[4] D. L. Sparks, R. Hernandez and L. A. Estévez, “Evaluation of Density-Based Models for the Solubility of Solids in Supercritical Carbon Dioxide and Formulation of a New Model,” Chemical Engineering Science, Vol. 63, No. 17, 2008, pp. 4292-4301.

http://dx.doi.org/10.1016/j.ces.2008.05.031

[5] L. Nasri, Z. Bensetiti and S. Bensaad, “Correlation of the Solubility of Some Organic Aromatic Pollutants in Supercritical Carbon Dioxide Based on the UNIQUAC Equation,” Energy Procedia, Vol. 18, 2012, pp. 1261-1270.

http://dx.doi.org/10.1016/j.egypro.2012.05.142

[6] J. W. Lee, J. M. Min and H. K. Bae, “Solubility Measurement of Disperse Dyes in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 44, No. 4, 1999, pp. 684-687.

http://dx.doi.org/10.1021/je9802930

[7] J. W. Lee, M. W. Park and H. K. Bae, “Measurement and Correlation of Dye Solubility in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 173, No. 2, 2000, pp. 277-284.

http://dx.doi.org/10.1016/S0378-3812(00)00404-0

[8] J. M. Prausnitz, R. N. Lichtenthaler and G. de Azevedo, “Molecular Thermodynamics of Fluid-Phase Equilibria,” 3rd Edition, Prentice Hall Inc., Engelwood Cliffs, 1999.

[9] M. Vázquez da Silva and D. Barbosa, “Prediction of the Solubility of Aromatic Components of Wine in Carbon Dioxide,” Journal of Supercritical Fluids, Vol. 31, No. 1, 2004, pp. 9-25.

http://dx.doi.org/10.1016/j.supflu.2003.09.018

[10] R. Span and W. Wagner, “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” Journal of Physical and Chemical Reference Data, Vol. 25, No. 6, 1996, pp. 1509-1596.

http://dx.doi.org/10.1063/1.555991

[11] S. E. Guigard and W. H. Stiver, “A Density-Dependant Solute Parameter for Correlating Solubilities in Supercritical Fluids,” Industrial and Engineering Chemistry Research, Vol. 37, No. 9, 1998, pp. 3786-3792.

http://dx.doi.org/10.1021/ie9702946

[12] NIST database.

http://webbook.nist.gov/chemistry/name-ser.html

[13] K.-W. Cheng, M. Tang and Y.-P. Chen, “Calculations of Solid Solubility in Supercritical Fluids Using a Simplified Cluster Solvation Model,” Fluid Phase Equilibria, Vol. 214, No. 2, 2003, pp. 169-186.

http://dx.doi.org/10.1016/S0378-3812(03)00350-9

[14] C. L. Laws, “Thermophysical Properties of Chemicals and Hydrocarbons,” Wiliam Andrew Inc., 2008.

[15] D. R. Lide, “CRC Handbook of Chemistry and Physics,” 84th Edition, 2003-2004.

[16] L. Li, Z.-C. Tan, S.-H. Meng and Y.-J. Song, “A Ther-mochemical Study of 1,10-Decanediol,” Thermochim Acta, Vol. 342, No. 1-2, 1999, pp. 53-57.

http://dx.doi.org/10.1016/S0040-6031(99)00305-6

[17] M. Mukhopaday and G. V. Raghuram Rao, “Thermodynamique Modeling for Supercritical Fluid Process Design,” Industrial & Engineering Chemistry Research, Vol. 32, No. 5, 1993, pp. 922-930.

http://dx.doi.org/10.1021/ie00017a021

[18] W. H. Stiver, S. E. Guigard and Beausoleil, “Predicting Ternary Solubilities Using a Solubility Parameter Approach,” Proceedings of the 5th International Symposium on Supercritical Fluids, Atlanta, April 8-12, 2000.

[19] S. Garnier, E. Neau, P. Alessi, A. Cortesi and I. Kikic, “Modelling Solubility of Solids in Supercritical Fluids Using Fusion Properties,” Fluid Phase Equilibria, Vol. 158-160, 1999, pp. 491-500.

http://dx.doi.org/10.1016/S0378-3812(99)00151-X

[20] C.-C. Huang, M. Tang, W.-H. Tao and Y.-P. Chen, “Calculation of the Solid Solubilities in Supercritical Carbon Dioxide Using a Modified Mixing Model,” Fluid Phase Equilibria, Vol. 179, No. 1-2, 2001, pp. 67-84.

http://dx.doi.org/10.1016/S0378-3812(00)00483-0

[21] P. Coutsikos, K. Magoulas and D. Tassios, “Solubilities of Phenols in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 40, No. 4, 1995, pp. 953-958. http://dx.doi.org/10.1021/je00020a049

[22] X. Wang and L. Tavlarides, “Solubility of Solutes in Compressed Gases: Dilute Solution Theory,” Industrial and Engineering Chemistry Research, Vol. 33, No. 3, 1994, pp. 724-729. http://dx.doi.org/10.1021/ie00027a035

[23] J. Mendez-Santiago and A. Teja, “The Solubility of Solids in Supercritical Fluids,” Fluid Phase Equilibria, Vol. 158-160, 1999, pp. 501-510.

http://dx.doi.org/10.1016/S0378-3812(99)00154-5

[24] W. J. Schmitt and R. C. Reid, “Solubitity of Monofunctional Organic Solids in Chemically Diverse Supercritical Fluids,” Journal of Chemical and Engineering Data, Vol. 31, No. 2, 1986, pp. 204-212.

http://dx.doi.org/10.1021/je00044a021

[25] A. Laitinen and M. Jaentti, “Solubility of 6-Caprolactam in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996, pp. 1418-1420. http://dx.doi.org/10.1021/je9600313

[26] K. J. Pennisi and E. H. Chimowitz, “Solubilities of Solid 1,10-Decanediol and a Solid Mixture of 1,10-Decanediol and Benzoic Acid in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 31, No. 3, 1986, pp. 285-288.

http://dx.doi.org/10.1021/je00045a008

[27] Z. Eckert, “Correlation and Prediction of Solid-Supercritical Fluid Phase Equilibria,” Industrial & Engineering Chemistry Process Design and Development, Vol. 22, No. 4, 1983, pp. 582-588.

http://dx.doi.org/10.1021/i200023a005

[28] Z. Huang, S. Kawi and Y. C. Chiew, “Application of the Perturbed Lennard-Jones Chain Equation of State to Solute Solubility in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 216, No. 1, 2004, pp. 111-122.

http://dx.doi.org/10.1016/j.fluid.2003.10.004

[29] A. Delle Site, “The Vapor Pressure of Environmentally Significant Organic Chemicals: A Review of Methods and Data at Ambient Temperature,” Journal of Physical and Chemical Reference Data, Vol. 26, No. 1, 1997, p. 157. http://dx.doi.org/10.1063/1.556006

[30] V. Oja and E. M. Suuberg, “Vapor Pressures and Enthalpies of Sublimation of Polycyclic Aromatic Hydrocarbons and Their Derivatives,” Journal of Chemical and Engineering Data, Vol. 43, No. 3, 1998, pp. 486-492.

http://dx.doi.org/10.1021/je970222l

[31] K. Tochigi, T. Iizumi and K. Kojima, “High Pressure Vapor-Liquid and Solid-Gas Equilibria,” Industrial and Engineering Chemistry Research, Vol. 37, No. 9, 1998, pp. 3731-3740. http://dx.doi.org/10.1021/ie970060m

[32] E. Kosal and G. D. Holder, “Solubility of Anthracene and Phenanthrene Mixtures in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 32, No. 2, 1987, pp. 148-150.

http://dx.doi.org/10.1021/je00048a005

[33] Y. Iwai, Y. Mori, N. Hosotani, H. Higashi, T. Furuya, Y. Arai, K. Yamamoto and Y. A Mito, “Solubilities of 2,6-and 2,7-Dimethylnaphthalenes in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 38, No. 4, 1993, pp. 509-511.

http://dx.doi.org/10.1021/je00012a006

[34] J. F. Brenneck and C. A. Eckert, “Phase Equilibria for Supercritical Fluid Process Design,” AIChE Journal, Vol. 35, No. 9, 1989, pp.1409-1427.

http://dx.doi.org/10.1002/aic.690350902

[35] R. T. Kurnik and R. C. Reid, “Solubility of Solid Mixtures in Supercritical Fluids,” Fluid Phase Equilibria, Vol. 8, No. 1, 1982, pp. 93-105.

http://dx.doi.org/10.1016/0378-3812(82)80008-3

[36] J. Kwiatkowski, Z. Lisicki and W. Majewski, “An Experimental Method for Measuring Solubilities of Solids in Supercritical Fluids,” Berichte der Bunsengesellschaft fur physikalische Chemie, Vol. 88, No. 9, 1984, pp. 865-869.

http://dx.doi.org/10.1002/bbpc.19840880919

[1] G. Madras, C. Kulkarni and J. Modak, “Modeling the Solubilities of Fatty Acids in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 209, No. 2, 2003, pp. 207-213.

http://dx.doi.org/10.1016/S0378-3812(03)00148-1

[2] N. R. Foster, G. S. Gurdial, J. S. L. Yun, K. K. Liong, K. D. Tilly, S. S. T. Ting, H. Singh and J. H. Lee, “Significance of the Crossover Pressure in Solid Supercritical Fluid Phase-Equilibria,” Industrial and Engineering Chemistry Research, Vol. 30, No. 8, 1991, pp. 1955-1964.

http://dx.doi.org/10.1021/ie00056a044

[3] J. Chrastil, “Solubility of Solids and Liquids in Supercritical Gases,” Journal of Physical Chemistry, Vol. 86, No. 15, 1982, pp. 3016-3021.

http://dx.doi.org/10.1021/j100212a041

[4] D. L. Sparks, R. Hernandez and L. A. Estévez, “Evaluation of Density-Based Models for the Solubility of Solids in Supercritical Carbon Dioxide and Formulation of a New Model,” Chemical Engineering Science, Vol. 63, No. 17, 2008, pp. 4292-4301.

http://dx.doi.org/10.1016/j.ces.2008.05.031

[5] L. Nasri, Z. Bensetiti and S. Bensaad, “Correlation of the Solubility of Some Organic Aromatic Pollutants in Supercritical Carbon Dioxide Based on the UNIQUAC Equation,” Energy Procedia, Vol. 18, 2012, pp. 1261-1270.

http://dx.doi.org/10.1016/j.egypro.2012.05.142

[6] J. W. Lee, J. M. Min and H. K. Bae, “Solubility Measurement of Disperse Dyes in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 44, No. 4, 1999, pp. 684-687.

http://dx.doi.org/10.1021/je9802930

[7] J. W. Lee, M. W. Park and H. K. Bae, “Measurement and Correlation of Dye Solubility in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 173, No. 2, 2000, pp. 277-284.

http://dx.doi.org/10.1016/S0378-3812(00)00404-0

[8] J. M. Prausnitz, R. N. Lichtenthaler and G. de Azevedo, “Molecular Thermodynamics of Fluid-Phase Equilibria,” 3rd Edition, Prentice Hall Inc., Engelwood Cliffs, 1999.

[9] M. Vázquez da Silva and D. Barbosa, “Prediction of the Solubility of Aromatic Components of Wine in Carbon Dioxide,” Journal of Supercritical Fluids, Vol. 31, No. 1, 2004, pp. 9-25.

http://dx.doi.org/10.1016/j.supflu.2003.09.018

[10] R. Span and W. Wagner, “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” Journal of Physical and Chemical Reference Data, Vol. 25, No. 6, 1996, pp. 1509-1596.

http://dx.doi.org/10.1063/1.555991

[11] S. E. Guigard and W. H. Stiver, “A Density-Dependant Solute Parameter for Correlating Solubilities in Supercritical Fluids,” Industrial and Engineering Chemistry Research, Vol. 37, No. 9, 1998, pp. 3786-3792.

http://dx.doi.org/10.1021/ie9702946

[12] NIST database.

http://webbook.nist.gov/chemistry/name-ser.html

[13] K.-W. Cheng, M. Tang and Y.-P. Chen, “Calculations of Solid Solubility in Supercritical Fluids Using a Simplified Cluster Solvation Model,” Fluid Phase Equilibria, Vol. 214, No. 2, 2003, pp. 169-186.

http://dx.doi.org/10.1016/S0378-3812(03)00350-9

[14] C. L. Laws, “Thermophysical Properties of Chemicals and Hydrocarbons,” Wiliam Andrew Inc., 2008.

[15] D. R. Lide, “CRC Handbook of Chemistry and Physics,” 84th Edition, 2003-2004.

[16] L. Li, Z.-C. Tan, S.-H. Meng and Y.-J. Song, “A Ther-mochemical Study of 1,10-Decanediol,” Thermochim Acta, Vol. 342, No. 1-2, 1999, pp. 53-57.

http://dx.doi.org/10.1016/S0040-6031(99)00305-6

[17] M. Mukhopaday and G. V. Raghuram Rao, “Thermodynamique Modeling for Supercritical Fluid Process Design,” Industrial & Engineering Chemistry Research, Vol. 32, No. 5, 1993, pp. 922-930.

http://dx.doi.org/10.1021/ie00017a021

[18] W. H. Stiver, S. E. Guigard and Beausoleil, “Predicting Ternary Solubilities Using a Solubility Parameter Approach,” Proceedings of the 5th International Symposium on Supercritical Fluids, Atlanta, April 8-12, 2000.

[19] S. Garnier, E. Neau, P. Alessi, A. Cortesi and I. Kikic, “Modelling Solubility of Solids in Supercritical Fluids Using Fusion Properties,” Fluid Phase Equilibria, Vol. 158-160, 1999, pp. 491-500.

http://dx.doi.org/10.1016/S0378-3812(99)00151-X

[20] C.-C. Huang, M. Tang, W.-H. Tao and Y.-P. Chen, “Calculation of the Solid Solubilities in Supercritical Carbon Dioxide Using a Modified Mixing Model,” Fluid Phase Equilibria, Vol. 179, No. 1-2, 2001, pp. 67-84.

http://dx.doi.org/10.1016/S0378-3812(00)00483-0

[21] P. Coutsikos, K. Magoulas and D. Tassios, “Solubilities of Phenols in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 40, No. 4, 1995, pp. 953-958. http://dx.doi.org/10.1021/je00020a049

[22] X. Wang and L. Tavlarides, “Solubility of Solutes in Compressed Gases: Dilute Solution Theory,” Industrial and Engineering Chemistry Research, Vol. 33, No. 3, 1994, pp. 724-729. http://dx.doi.org/10.1021/ie00027a035

[23] J. Mendez-Santiago and A. Teja, “The Solubility of Solids in Supercritical Fluids,” Fluid Phase Equilibria, Vol. 158-160, 1999, pp. 501-510.

http://dx.doi.org/10.1016/S0378-3812(99)00154-5

[24] W. J. Schmitt and R. C. Reid, “Solubitity of Monofunctional Organic Solids in Chemically Diverse Supercritical Fluids,” Journal of Chemical and Engineering Data, Vol. 31, No. 2, 1986, pp. 204-212.

http://dx.doi.org/10.1021/je00044a021

[25] A. Laitinen and M. Jaentti, “Solubility of 6-Caprolactam in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 41, No. 6, 1996, pp. 1418-1420. http://dx.doi.org/10.1021/je9600313

[26] K. J. Pennisi and E. H. Chimowitz, “Solubilities of Solid 1,10-Decanediol and a Solid Mixture of 1,10-Decanediol and Benzoic Acid in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 31, No. 3, 1986, pp. 285-288.

http://dx.doi.org/10.1021/je00045a008

[27] Z. Eckert, “Correlation and Prediction of Solid-Supercritical Fluid Phase Equilibria,” Industrial & Engineering Chemistry Process Design and Development, Vol. 22, No. 4, 1983, pp. 582-588.

http://dx.doi.org/10.1021/i200023a005

[28] Z. Huang, S. Kawi and Y. C. Chiew, “Application of the Perturbed Lennard-Jones Chain Equation of State to Solute Solubility in Supercritical Carbon Dioxide,” Fluid Phase Equilibria, Vol. 216, No. 1, 2004, pp. 111-122.

http://dx.doi.org/10.1016/j.fluid.2003.10.004

[29] A. Delle Site, “The Vapor Pressure of Environmentally Significant Organic Chemicals: A Review of Methods and Data at Ambient Temperature,” Journal of Physical and Chemical Reference Data, Vol. 26, No. 1, 1997, p. 157. http://dx.doi.org/10.1063/1.556006

[30] V. Oja and E. M. Suuberg, “Vapor Pressures and Enthalpies of Sublimation of Polycyclic Aromatic Hydrocarbons and Their Derivatives,” Journal of Chemical and Engineering Data, Vol. 43, No. 3, 1998, pp. 486-492.

http://dx.doi.org/10.1021/je970222l

[31] K. Tochigi, T. Iizumi and K. Kojima, “High Pressure Vapor-Liquid and Solid-Gas Equilibria,” Industrial and Engineering Chemistry Research, Vol. 37, No. 9, 1998, pp. 3731-3740. http://dx.doi.org/10.1021/ie970060m

[32] E. Kosal and G. D. Holder, “Solubility of Anthracene and Phenanthrene Mixtures in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 32, No. 2, 1987, pp. 148-150.

http://dx.doi.org/10.1021/je00048a005

[33] Y. Iwai, Y. Mori, N. Hosotani, H. Higashi, T. Furuya, Y. Arai, K. Yamamoto and Y. A Mito, “Solubilities of 2,6-and 2,7-Dimethylnaphthalenes in Supercritical Carbon Dioxide,” Journal of Chemical and Engineering Data, Vol. 38, No. 4, 1993, pp. 509-511.

http://dx.doi.org/10.1021/je00012a006

[34] J. F. Brenneck and C. A. Eckert, “Phase Equilibria for Supercritical Fluid Process Design,” AIChE Journal, Vol. 35, No. 9, 1989, pp.1409-1427.

http://dx.doi.org/10.1002/aic.690350902

[35] R. T. Kurnik and R. C. Reid, “Solubility of Solid Mixtures in Supercritical Fluids,” Fluid Phase Equilibria, Vol. 8, No. 1, 1982, pp. 93-105.

http://dx.doi.org/10.1016/0378-3812(82)80008-3

[36] J. Kwiatkowski, Z. Lisicki and W. Majewski, “An Experimental Method for Measuring Solubilities of Solids in Supercritical Fluids,” Berichte der Bunsengesellschaft fur physikalische Chemie, Vol. 88, No. 9, 1984, pp. 865-869.

http://dx.doi.org/10.1002/bbpc.19840880919