We present a simple treatment of supercritical fluid extraction for binary (solvent-solute) and ternary (solvent-solute-cosolvent) systems. Solubility predictions are made using the virial equation of state. The solute chemical potential is calculated up to fourth order in the fluid density. There are no adjustable parameters: the pressure mixture virial coefficients B_(α β), C_(α β γ) and D_(α β γ δ) are computed directly from the potentials representing the interactions of solvent, solute and cosolvent molecules. For the purposes of illustration we assume these are of Lennard-Jones form; however, the method is considerably more general, and may be applied even when the potentials are anisotropic. Computer simulations have also been performed, and confirm the accuracy of this approach at densities up to twice the critical density. Our analysis of ternary systems helps to identify the nature of the interactions primarily responsible for entrainer effects.
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