Thermodynamically consistent modeling of immiscible gas–liquid flow in porous media

Abstract

Modeling of immiscible gas–liquid two-phase flow with gas compressibility in porous media plays an important role in shale gas production, geological sequestration of carbon dioxide, and underground gas storage. The second law of thermodynamics is universally recognized as an essential principle any promising model should obey. The existing models have no proper concept of free energies for such a problem, thereby failing to obey this law. In this paper, we first introduce free energies to account for the liquid–gas capillarity effect and gas compressibility, and then using the second law of thermodynamics, we rigorously derive a thermodynamically consistent model for immiscible gas–liquid two-phase flow in porous media. The proposed free energy that describes the capillarity effect is verified by the laboratory data. For gas flow, we use molar density rather than pressure as the primary variable and take the Helmholtz free energy density determined by a realistic equation of state to characterize the gas compressibility. Numerical simulation results are also presented to demonstrate the thermodynamical consistency of the model and the applicability to simulate the liquid and gas displacement processes.