Compositional Reservoir Simulation Using Enriched Galerkin and Phase Field Formulation

Abstract This study presents a novel framework for simulating compositional two-component, two-phase CO2 sequestration models by integrating the Enriched Galerkin (EG) discretization scheme with a phase-field formulation. Traditional equation of state (EoS) compositional models often face challenges such as computational inefficiency and decoupled treatment of fluid flow and composition exchange, limiting their accuracy and scalability. The proposed approach leverages the Allen-Cahn/Cahn-Hilliard phase-field model to seamlessly couple hydrodynamics and thermodynamics, enabling precise modeling of phase transitions, gas-liquid interactions, and complex interfacial dynamics. The framework reduces computational complexity by consolidating eight governing variables into three through auxiliary relationships for mole fractions, saturations, and capillary pressures. The EG discretization ensures mass conservation and robust handling of advection and diffusion in CO2 transport. Validation is performed using Pruess’ CO2 injection problem and the "FluidFlower" SPE11A benchmark. These tests demonstrate the model's ability to capture gas saturation dynamics, compositional evolution, and pressure variations in complex porous systems with high accuracy. This integrated phase-field and EG framework significantly enhances computational efficiency and simulation fidelity, providing a transformative tool for understanding and optimizing CO2 sequestration in geological formations.