INSTABILITY OF SUCCESSIVE SUBSTITUTION

The method of successive substitution for phase equilibrium calculatio ns can only converge to a minimum of the mixture Gibbs free energy, an d it is commonly assumed that, given proper initial estimates, converg ence will always occur. Unfortunately, although the exemptions are rar e, the assumption is incorrect. Divergence, regardless of the quality of the initial estimate, can occur in mixtures that exhibit strong neg ative deviations from ideal solution behavior, such as polymer solutio ns and gas hydrates. Unless special precautions are taken, algorithms that implement successive substitution as part of the solution procedu re are likely to fail on such mixtures. In this paper we present an an alysis of the thermodynamic conditions that may lead to divergence of successive substitution and present some numerical examples. In additi on we briefly discuss some methods capable of solving the appropriate equilibrium equations under conditions where successive substitution f ails.