Reliable computation of high-pressure solid-fluid equilibrium

The calculation of solid-fluid equilibrium at high pressure is important in the modeling and design of processes that use supercritical fluids to sele ctively extract solid solutes. We describe here a new method for reliably c omputing solid-fluid equilibrium at constant temperature and pressure or fo r verifying the nonexistence of a solid-fluid equilibrium state at the give n conditions. Difficulties that must be considered include the possibility of multiple roots to the equifugacity conditions and multiple stationary po ints in the tangent plane distance analysis done for purposes of determinin g global phase stability. Somewhat surprisingly, these issues are often not dealt with by those who measure, model, and compute high-pressure solid-fl uid equilibria, leading in some cases to incorrect or misinterpreted result s. It is shown here how these difficulties can be addressed by using a meth odology based on interval analysis, which can provide a mathematical and co mputational guarantee that the solid-fluid equilibrium problem is correctly solved. The technique is illustrated with several example problems in whic h the Peng-Robinson equation of state model is used. However, the methodolo gy is of general purpose and can be applied in connection with any model of the fluid phase.