Hybrid finite volume-finite element methods for hydro-mechanical analysis in highly heterogeneous porous media

Abstract

In this study, two classes of advanced finite volume schemes, including Multi-Point Flux Approximation (MPFA) and Dual Discrete Finite Volume (DDFV) method, have been employed in conjunction with the finite element (FE) geomechanics simulator to model the coupled fluid-solid system. Fully saturated porous media with poroelastic behavior, random field permeability and elastic modulus are considered as parameters. The performance of the proposed hydro-mechanical models, including MPFA O-FEM and DDFV-FEM, is examined through different test cases. First, the models are validated and compared with the closed-form solutions in the homogeneous domain. Second, the methods' stability and convergence properties are analyzed in highly heterogeneous porous media with different permeability and elastic modulus realizations. Finally, implementing the models in a large-size realistic problem of a synthetic reservoir accomplishes this comprehensive study. Although both methods agree well with the analytical solutions in homogeneous porous media, the DDFV-FEM yields higher accuracy. In the cases where the random field of permeability varies over several orders of magnitude (4th and more), the MPFA O-FEM suffers from significant oscillations and even instability. The analysis illustrates that MPFA O-FEM exhibits oscillation in the cases with high anisotropy ratio, while the DDFV-FEM demonstrates superior performance for handling anisotropy and heterogeneity.