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.