Hybrid-mixed mimetic method for reservoir simulation with full tensor permeability

Abstract

Summary In this work, we present a fully implicit hybrid mimetic finite difference formulation for general-purpose compositional reservoir simulation. The formulation is locally conservative, and the momentum and mass balance equations are solved simultaneously; including Lagrange multipliers on element interfaces. The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems and the mixed finite element (MFE) finite-element method assures the coupling of the mass and momentum balance equations. The method utilizes automatic differentiation for the Jacobian construction. This hybrid approach accommodates unstructured grids, and we apply compositional test cases with permeability tensors. We also discuss the accuracy for the new formulation. For all tests, we compare the performance and accuracy of the proposed approach with the trivial TPFA method.