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Fluid Phase Equilibria 179 (2001) 67–84

Calculation of the solid solubilities in supercritical carbon dioxide using a modified mixing model
Cheng-Chia Huang, Muoi Tang1 , Wei-Han Tao1 , Yan-Ping Chen∗
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, ROC Received 25 September 2000; accepted 2 October 2000

Abstract The Peng–Robinson equation of state and amodified Huron–Vidal type mixing model with a volume correction term are applied in this study to calculate the solid solubilities of aromatic, fatty acid and heavy alcohol compounds in supercritical carbon dioxide. The UNIFAC activity coefficient model with its optimally fitted binary interaction parameters is used in this study. A volume correction term is employed, and its parameters are correlated asfunctions of the solid molar volume for both non-polar and polar systems. The effect of the sublimation vapor pressure on the calculation of solid solubilities in supercritical carbon dioxide is examined. The sublimation vapor pressures for heavy compounds are fitted in this study to yield the optimally calculated results of the solid solubility. Reasonable sublimation vapor pressures are obtainedand their values are well correlated by the Antoine equation. A generalized calculation model is proposed in this study which gives satisfactory results of the solid solubility in supercritical carbon dioxide for both the binary and ternary systems. © 2001 Elsevier Science B.V. All rights reserved.
Keywords: Equation of state; Group contribution method; Mixing rules; Solid solubilities;Supercritical carbon dioxide

1. Introduction Supercritical fluids (SCF) are widely applied in extraction, reaction, separation and crystal growth processes. The key point for the design of process equipment and selection of operating condition is the equilibrium solubility data. Only a few solid solubility data were reported in literature [1]. The accurate measurement of the solid solubility insupercritical fluid is also difficult and time consuming. For the purpose of a wider range of application, a suitable thermodynamic model should be used to correlate and predict the equilibrium solubility data required in those related fields [2]. Thermodynamic models that employ equations of state (EOS) and mixing rules for the calculation of solubilities of solids in supercritical fluids have been presentedby many investigators [3–7]. The traditional van der Waals (VDW) mixing rules
Corresponding author. Tel.: +886-2363-5230; fax: +886-2362-3040. E-mail address: ypchen@ccms.ntu.edu.tw (Y.-P. Chen). 1 Present address: Department of Chemical Engineering, Chinese Culture University, Taipei, Taiwan, ROC. 0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 0) 0 0 4 8 3 - 0
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C.-C. Huang et al. / Fluid Phase Equilibria 179 (2001) 67–84

are usually employed with optimally fitted binary interaction parameters. Unfortunately, those parameters cannot be well correlated as functions of temperature or pressure, especially for systems involving heavy or complex compounds [8]. On the other hand, empirical models can be used for the calculationsof solid solubilities. Since the parameters in the empirical models are usually not generalized, it is difficult to apply them for predictive or multi-component computations. A modified Huron–Vidal [9] type mixing model with a volume correction term has been proposed for calculating the solid solubilities in supercritical carbon dioxide [10]. Solubilities of five aromatic compounds in supercriticalcarbon dioxide were calculated by that modified model using the Patel–Teja EOS [11]. The mixture energy parameter of the EOS was determined by using a UNIFAC group contribution method. The volume correction term has been well correlated as a function of the solid molar volume. Further investigations [12–14] also applied this modified model to calculate the solubilities of steroids, polar and...