Thermodynamic modeling

An equation of state (EOS) is widely used to represent the relationship of temperature, pressure and composition of compounds in supercritical fluids. Solubility may be predicted as a function of the temperature and pressure along with solute and solvent properties. Some of the most commonly used EOS models are the Peng-Robinson and Soave-Redlich-Kwong equations. Both produce similar results; however, the Peng-Robinson equation of state (PR-EOS) will be discussed here as it is more widely used. The PR-EOS equation is p = RL =___[io.i]

where v is the molar volume, a accounts for intermolecular interactions between species of the mixture and b accounts for size differences between the species of the mixture (Peng and Robinson, 1976; McHugh and Krukonis, 1994).

An exact thermodynamic relationship exists for compounds in all phases at equilibrium. This relationship states that the fugacity, which is directly related to the chemical potential of a component, in one phase is equal to the fugacity of the same species in any other phase at equilibrium. The fugacity can be thought of in terms of 'corrected pressure' of a pure com ponent or 'corrected partial pressure' of a component in a mixture. The equilibrium relationship is a function of system temperature, T, and pressure, P, for the component having the concentration, y, in the supercritical CO2 phase and a concentration, c, in the condensed phase. The relation is

where the fugacity follows the relation (Prausnitz et al., 1999), rP V°dP

where Oisat is the fugacity coefficient of component i at p,sat, vic is the molar volume of solute in the condensed phase and R is the gas constant. Assuming the condensed phase is incompressible and the fugacity coefficient for the component at the saturation pressure is approximately unity (because the vapor pressures are typically low enough to assume an ideal gas), the solubility may be defined as

Pisat 1

Thermodynamic and phase equilibrium properties dictate the feasibility of the SFE process and conditions for maximum possible separations, whereas knowledge of transport properties of supercritical fluids and resistances to the transport processes are required for calculating time required for the extraction and the sizes of the critical components of the plant (Espinosa et al., 2002; Mukhopadhyaya, 2000). Because of the rapid changes in the properties such as viscosity, m, and diffusivity, D, etc., with small changes in the conditions of the supercritical solvent around the critical point, predictions of these properties are difficult and require sound theoretical considerations and understanding of the process.

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