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A semi-implicit method for incompressible three-phase flow in porous media

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Abstract

In this paper, we present a semi-implicit method for the incompressible three-phase flow equations in two dimensions. In particular, a high-order discontinuous Galerkin spatial discretization is coupled with a backward Euler discretization in time. We consider a pressure-saturation formulation, decouple the pressure and saturation equations, and solve them sequentially while still keeping each equation implicit in its respective unknown. We present several numerical examples on both homogeneous and heterogeneous media, with varying permeability and porosity. Our results demonstrate the robustness of the scheme. In particular, no slope limiters are required and a relatively large time step may be taken.

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Authors and Affiliations

  1. Computational and Applied Mathematics Department, Rice University, Houston, TX, USA

    Justin Dong & Béatrice Rivière

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  1. Justin Dong
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  2. Béatrice Rivière
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Correspondence to Béatrice Rivière.

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Both authors acknowledge the support of the National Science Foundation grant NSF-DMS 1318348.

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Dong, J., Rivière, B. A semi-implicit method for incompressible three-phase flow in porous media. Comput Geosci 20, 1169–1184 (2016). https://doi.org/10.1007/s10596-016-9583-2

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