Adaptive fully implicit and thermodynamically consistent modeling of multiphase flow in porous media on three dimensional grids

The development of innovative mathematical models and state-of-the-art simulators for multiphase flow in porous media is a key focus in hydrogeology. However, many traditional models for multiphase flow in porous media lack complete thermodynamic consistency, as the energy reconstructed from the capillary pressure fails to yield a time-dependent system with a dissipated free energy. In this paper, we utilize a thermodynamically consistent model for multiphase flow in porous media, which satisfies the second law of thermodynamics. For large-scale numerical simulation of the resultant flow model, we introduce and investigate a robust and scalable fully implicit simulator with a suitable time adaptivity strategy designed for distributed memory parallel computers. In particular, our approach enhances the numerical formulation by proposing a family of inexact Newton–Krylov methods for efficient computation and several types of field-split algorithms for large-scale preconditioning. The numerical experiments indicate that the proposed fully implicit simulator accurately predicts the highly complex physical processes of thermodynamically consistent problems, particularly those characterized by high heterogeneity with complex reservoir topography on 3D structured or unstructured grids.