On the computation of complex equilibria

A method is described for solving the problem: given fixed pressure, temperature, the amounts of the chemical elements, and the chemical potentials of possible chemical species at the pressure and temperature specified, determine the equilibrium composition. The method requires a minimum of judgment on the part of the user. A modification of Naphtali's method for direct minimization of Gibbs' function provides an estimate of the composition of sufficient accuracy to insure convergence of solution, by the Newton-Raphson method, of the nonlinear equations describing the equilibrium. Problems in treating multiple phaes of unknown stability and chemical species present in small amouts are handled by ignoring unstable phases and small quantitites in the direct minimization until the amounts of the major consitituents have been at least approximately determined. To accomplish this, species temporarily ignored are assigned a ficitious mol fraction so that their re-entry into the calculation can be established. Truncation errors in the direct minimziation can be tolerated because of the two-step method. Examples of some of the problems solved are given.