The calculation of critical points

Abstract

AbstractGibb's classical theory of critical points leads to two simultaneous, nonlinear equations in the intensive variables of the critical phase. In this paper is presented a new procedure for evaluating the functions which appear in these nonlinear equations. The new procedure simplifies and permits the speeding up of the computation of critical points in multicomponent mixtures.Computations have been performed for critical points in binary and multicomponent mixtures described by the SRK equation. The methods developed will be equally applicable to other two‐constant equations of state. The equations to be solved are organized as two equations in the unknown critical temperature and specific volume for a mixture of known composition. One of the two equations, the determinant which establishes the stability limit for the mixture, is shown to be satisfied by more than one volume at a given temperature and by several temperatures at a given volume. A technique is proposed to assure that the correct temperature, volume solution can be found for this equation. For critical points in ordinary gas‐liquid systems, an overall computational procedure is suggested in which it proves to be unnecessary to provide initial guesses for either the temperature or the volume.Application has also been made to several systems with high density (liquid‐liquid) critical points.