A trust-region-based phase envelope construction algorithm

Abstract

Pressure-temperature (PT) and pressure-composition (Px) phase diagrams play an important role in various chemical and petroleum engineering applications. Lots of algorithms based on the Newton-Raphson method have been proposed to numerically construct PT/Px phase envelopes. No attempt is made to improve the computational efficiency of such Newton-Raphson solution method. This work develops a new trust-region-based algorithm to replace the Newton-Raphson method to provide more robust and efficient phase envelope construction calculations. We first convert the phase envelope construction problem into a minimization problem by defining a least-squares objective function. We then apply the trust-region optimization method with an exact subproblem solver to minimize the objective function. We follow the general strategy proposed by Michelsen (1980) to develop the revised phase envelope construction algorithm. We demonstrate the good performance of the trust-region-based algorithm by comparing it with the conventional Newton's method. The computational results indicate that the new trust-region-based algorithm is more robust and cost-effective than the Newton-based algorithm.