A pseudospectral approach to the McWhorter and Sunada equation for two-phase flow in porous media with capillary pressure

Bjørnarå, T.I.; Mathias, S.A.

Abstract

Two well-known mathematical solutions for two-phase flow in porous media are the Buckley–Leverett equation and the McWhorter and Sunada equation (MSE). The former ignores capillary pressure and can be solved analytically. The latter has traditionally been formulated as an iterative integral solution, which suffers from convergence problems as the injection saturation approaches unity. Here, an alternative approach is presented that solves the MSE using a pseudospectral Chebyshev differentiation matrix. The resulting pseudospectral solution is compared to results obtained from the original integral implementation and the Buckley–Leverett limit, when the capillary pressure becomes negligible. A self-contained MATLAB code to implement the new solution is provided within the manuscript. The new approach offers a robust and accurate method for verification of numerical codes solving two-phase flow with capillary pressure.

Citation

Bjørnarå, T., & Mathias, S. (2013). A pseudospectral approach to the McWhorter and Sunada equation for two-phase flow in porous media with capillary pressure. Computational Geosciences, 17(6), 889-897. https://doi.org/10.1007/s10596-013-9360-4

• Journal Article Type: Article
• Publication Date: Dec 1, 2013
• Deposit Date: Jul 29, 2013
• Publicly Available Date: Jun 18, 2014
• Journal: Computational Geosciences
• Print ISSN: 1420-0597
• Electronic ISSN: 1573-1499
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 6
• Pages: 889-897
• DOI: https://doi.org/10.1007/s10596-013-9360-4
• Keywords: Analytical solutions, Two-phase flow, Porous media, Pseudospectral, Differentiation matrix, Chebyshev, Capillary pressure.
• Public URL: https://durham-repository.worktribe.com/output/1480291