Validated computing approach for high-pressure chemical and multiphase equilibrium

Abstract

For the computation of chemical and phase equilibrium at constant temperature and pressure, there have been proposed a wide variety of problem formulations and numerical solution procedures, involving both direct minimization of the Gibbs energy and the solution of equivalent nonlinear equation systems. Still, with very few exceptions, these methodologies may fail to solve the chemical and phase equilibrium problem correctly. Nevertheless, there are many existing solution methods that are extremely reliable in general and fail only occasionally. To take good advantage of this wealth of available techniques, we demonstrate here an approach in which such techniques can be combined with procedures that have the power to validate results that are correct, and to identify results that are incorrect. Furthermore, in the latter case, corrective feedback can be provided until a result that can be validated as correct is found. The validation procedure is deterministic, and provides a mathematical and computational guarantee that the global minimum in the Gibbs energy has been found. To demonstrate this validated computing approach to the chemical and phase equilibrium problem, we present several examples involving reactive and nonreactive components at high pressure, using cubic equation-of-state models.