On front solutions of the saturation equation of two-phase flow in porous media |
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Affiliation: | AF-Consult Switzerland Ltd, Täfernstrasse 26, CH-5405 Baden, Switzerland |
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Abstract: | We investigate the existence of “front” solutions of the saturation equation of two-phase flow in porous media. By front solution we mean a monotonic solution connecting two different saturations. The Brooks–Corey and the van Genuchten models are used to describe the relative-permeability – and capillary pressure–saturation relationships. We show that two classes of front solutions exist: self-similar front solutions and travelling-wave front solutions. Self-similar front solutions exist only for horizontal displacements of fluids (without gravity). However, travelling-wave front solutions exist for both horizontal and vertical (including gravity) displacements. The stability of front solutions is confirmed numerically. |
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Keywords: | Two-phase flow Saturation equation Front solutions Self-similar solutions Travelling-wave solutions Numerical stability |
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