Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng-Robinson equation of state

TL;DR

This paper develops a thermodynamically consistent diffuse-interface model for nonisothermal two-phase flow using the Peng-Robinson equation of state, with a focus on hydrocarbons, and proposes a stable numerical scheme validated by tests.

Contribution

It introduces a new thermodynamically consistent model with the Peng-Robinson EOS and temperature-dependent parameters, along with a stable numerical scheme for realistic gas-liquid flows.

Findings

Model accurately characterizes hydrocarbon behaviors

Proposed numerical scheme satisfies thermodynamic laws

Numerical tests confirm effectiveness of the simulation method

Abstract

In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas-liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, and thereby derive a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex-concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method.