Computation of solid–fluid–fluid equilibria for binary asymmetric mixtures in wide ranges of conditions

In this work, we propose and test a numerical continuation method (NCM) for calculating solid–fluid–fluid (SFF) equilibrium loci for binary asymmetric systems. Such loci generally exist over a wide range of conditions. The method is able to track SFF lines of varying shape and degree of non-linearity. When building a curve for which, as in the case of a SFF curve, every point is defined by a non-linear system of equations, NCMs have the ability of selecting, among the variables involved, the optimum one, i.e., the variable that should be specified for calculating the next point on the curve. The initial guess for such next point is, when using NCMs, more sophisticated than simply setting it equal to the previously converged point of the curve. These features of NCMs make possible to track complete SFF lines with minimum user intervention. Among other algorithms, we propose in this work a procedure to obtain SFF lines that have been previously regarded as difficult to compute due to the very low concentration of the heavy component of the binary asymmetric system in either fluid phase. We illustrate the use of the present algorithms for a model that uses the Peng-Robinson equation of state (EOS) for the fluid phases, and an equation that relates the fugacity of the pure heavy component with pressure and temperature. We do not consider in this work the precipitation of the light component.