Construction of a minimum energy path for the VT flash model by an exponential time differencing scheme with the string method

TL;DR

This paper introduces a novel numerical approach combining an exponential time differencing scheme with the string method to efficiently and accurately compute minimum energy paths and saddle points in a stiff VT flash model using the Peng-Robinson equation of state.

Contribution

It develops a new computational method that effectively handles stiffness in phase equilibrium calculations, enabling the determination of transition paths and saddle points.

Findings

The proposed algorithm accurately computes phase equilibrium states.

It successfully finds minimum energy paths and saddle points in stiff VT flash models.

The method outperforms traditional solvers in efficiency and stability.

Abstract

Phase equilibrium calculation, also known as flash calculation, plays significant roles in various aspects of petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development, the current research interest on flash calculation has been shifted from accuracy to efficiency, but the ultimate goal remains the same focusing on estimation of the equilibrium phase amounts and phase compositions under the given variable specification. However, finding the transition route and its related saddle points are very often helpful to study the evolution of phase change and partition. Motivated by this, in this study we apply the string method to find the minimum energy paths and saddle points information of a single-component VT flash model with the Peng-Robinson equation of state. As the system has strong stiffness, common ordinary differential equation solvers have their limitations. To overcome these issues, a Rosenbrock-type exponential time differencing scheme is employed to reduce the computational difficulty caused by the high stiffness of the investigated system. In comparison with the published results and experimental data, the proposed numerical algorithm not only shows good feasibility and accuracy on phase equilibrium calculation, but also successfully calculates the minimum energy path and and saddle point of the single-component VT flash model with strong stiffness.