Abstract
We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.
Highlights
Many geologic porous media are highly heterogeneous: they contain domains of contrasting material properties such as porosity, permeability and capillary pressure
The first key aim of this paper is to develop and implement a new CVFE method in 3D that does not require the use of control volumes (CVs) that span domain boundaries in heterogeneous porous media
Unlike conventional CVFE formulations, it does not require the use of control volumes that span domain boundaries
Summary
Many geologic porous media are highly heterogeneous: they contain domains of contrasting material properties such as porosity, permeability and capillary pressure. Fluid saturation and component concentration are smeared across neighbouring elements ([2]) This issue has led some authors to argue that, despite the advantages outlined above, CVFE methods are not suitable for modelling multiphase flow in highly heterogeneous porous media [44] separated the CVs at FE interfaces that correspond to domain boundaries, and employed the average flux between elements at the interface This approach does not guarantee local mass conservation. The first key aim of this paper is to develop and implement a new CVFE method in 3D that does not require the use of control volumes (CVs) that span domain boundaries in heterogeneous porous media. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with significant permeability contrasts across high aspect ratio geologic features such as fractures and thin mudstones, allowing efficient simulation of flow in highly heterogeneous models
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