Abstract
SummaryControl volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.
Highlights
The classical approach for simulating multiphase flow in porous media discretises space using fixed grids and solves the governing equations using finite-volume methods and the 2-point flux approximation.[1,2] widely used, complex geometries are often poorly represented in this approach because of the limitations of the 2-point flux approximation
In Model 2, the efficiency to solve the pressure matrix of the double control volume finite element method (DCVFEM) is tested against the classical control volume finite element methods (CVFEMs) in a 3D homogeneous domain with single phase flow
In the first numerical experiment, the DCVFEM is tested against the 1D Buckley-Leverett (BL) solution,[41] in which a nonwetting phase is displaced by a wetting phase
Summary
Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. Producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. KEYWORDS CVFEM mixed formulation, discontinuous galerkin, darcy flow, multiphase flow, porous media, unstructured mesh
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