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On the upstream mobility scheme for two-phase flow in porous media

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Abstract

When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretising in one dimension with a finite volume method, we investigate two numerical fluxes, an extension of the Godunov flux and the upstream mobility flux, the latter being widely used in hydrogeology and petroleum engineering. Then, in the case of a changing rock type, one can give examples when the upstream mobility flux does not give the right answer.

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Authors and Affiliations

  1. Center of Mathematics for Applications, University of Oslo, Oslo, 0316, Norway

    Siddhartha Mishra

  2. INRIA, BP 105, 78153, Le Chesnay Cedex, France

    Jérôme Jaffré

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  1. Siddhartha Mishra
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  2. Jérôme Jaffré
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Correspondence to Jérôme Jaffré.

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Mishra, S., Jaffré, J. On the upstream mobility scheme for two-phase flow in porous media. Comput Geosci 14, 105–124 (2010). https://doi.org/10.1007/s10596-009-9135-0

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