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Linear stability analysis of the explicit treatment of mobilities in non-Newtonian and non-Darcy porous media flow simulation

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Abstract

A von Neumann stability analysis of the discretized conservation equation for single-phase porous media flows is performed, where non-Newtonian and non-Darcy effects are accounted for using a velocity (or mass flux)-dependent mobility factor. Comprehensive results in three dimensions for two low-order finite-volume discretizations typically encountered in reservoir simulation are provided, based on edge-centered and upstream cell-centered mobility calculations. It is found that common semi-implicit schemes, where the pressure gradient driving the flow is taken implicitly while the velocity-dependent mobility is evaluated explicitly, are subject to restrictions on the logarithmic derivative of mobility with respect to velocity. A remarkable new result is nevertheless obtained: for any physically acceptable strength of non-Newtonian and non-Darcy effects, there exists a stable and explicit method to evaluate the mobility, rendering the need to implement costly fully implicit schemes more difficult to justify.

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  1. Total S.A., Pau, France

    Leonardo Patacchini & Romain de Loubens

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  1. Leonardo Patacchini
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  2. Romain de Loubens
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Correspondence to Leonardo Patacchini.

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Patacchini, L., de Loubens, R. Linear stability analysis of the explicit treatment of mobilities in non-Newtonian and non-Darcy porous media flow simulation. Comput Geosci 18, 185–209 (2014). https://doi.org/10.1007/s10596-013-9395-6

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  • DOI: https://doi.org/10.1007/s10596-013-9395-6

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