Solubility of solids in supercritical fluid using the hard-body expanded virial equation of state

• A hard body expanded virial equation of state (HBE-VEOS).
• Solubility of organic solids in carbon dioxide.
• Shape factor of hard convex body related to the distance of closest approach.
• NpT Monte Carlo simulation for supercritical carbon dioxide.
• Widom insertion method for the infinite dilute system different shapes.

The solubility of solids in supercritical fluids was examined using the hard-body expanded virial equation of state (HBE-VEOS). Due to the semi-soft core potential function, the developed EOS is analytic and has a closed form, which makes it appropriate for the engineering level. Molecular shape was considered in that the molecules were standardized as hard convex bodies (HCB) such as ellipsoids or spherocylinders. Distance-angle decoupling approximation was used in the integration of the cluster integrals to derive a simple equation for the second virial coefficient. Using the semi-soft core potential function, isothermal-isobaric Monte Carlo simulations were performed to generate a pVT diagram of pure carbon dioxide and canonical Monte Carlo simulations using the Widom insertion method were performed to calculate the residual chemical potentials for infinite dilute systems. Experimental solubility data of naphthalene, benzoic acid and phenanthrene in carbon dioxide were compared with the calculation of the developed EOS mapping of the molecules into ellipsoids. We confirmed from the results that second order expansion in the HBE-VEOS is the optimal combination in terms of both simplicity and accuracy for industrial supercritical extraction of solids.