Reliable computation of solid solubility in dense gases through homotopy continuation approach

A method to reliably compute the solid solubility in supercritical fluids is described. The method is based on computing all the possible roots of equifugacity equation at given temperature and pressure through homotopy continuation. The equifugacity equation is reformulated through global fixed-point homotopy. The global fixed-point homotopy guarantees that all the solutions of a non-linear equation can be located on a single homotopy path when it is forced to start from a single starting point. The starting point is selected from a criterion which minimizes the number of real roots of the global fixed-point homotopy function. Homotopy continuation-based formulation of equifugacity equation is also used to directly generate the solubility-pressure and solubility-temperature bifurcation diagrams by selecting either pressure or temperature as continuation parameter. These bifurcation diagrams provide a direct pathway to locate the cross-over pressures. The effect of equation of state model parameters on solid solubility through homotopy continuation based sensitivity analysis is also analyzed. Peng Robinson Stryjek Vera equation of state with conventional and Wong-Sandler mixing rules are used.