Thermodynamically Consistent Modeling of Compressible Two‐Phase Flow in Porous Media

ABSTRACT In this paper, we develop a thermodynamically consistent model for compressible two‐phase flow in porous media according to the Reynolds transport theorem and the second law of thermodynamics. The Helmholtz free energy and saturation free energy are introduced to characterize fluid compressibility and capillary pressure effects, respectively. Especially, we use molar density instead of pressure as one of the primary variables and derive a Darcy‐type momentum equation with chemical potential gradient as the main driving force. Furthermore, the discrete total free energy dissipation and prior error estimates of the proposed numerical scheme are derived. Numerical results are presented to validate the accuracy, stability, and effectiveness of our proposed method.