Two-Phase Flow in Heterogeneous Porous Media with Non-Wetting Phase Trapping |
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Authors: | Adam Szymkiewicz Rainer Helmig Hartmut Kuhnke |
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Institution: | (1) Department of the Civil Engineering, National Chiao Tung University, Hsin Chu, Taiwan;(2) Department of the Civil Engineering, Min Hsin University Science Technology, Hsin Chu, Taiwan |
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Abstract: | This article presents a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium
contains disconnected inclusions embedded in the background material. The background material is characterized by higher value
of the non-wetting-phase entry pressure than the inclusions, which causes non-standard behavior of the medium at the macroscopic
scale. During the displacement of the non-wetting fluid by the wetting one, some portions of the non-wetting fluid become
trapped in the inclusions. On the other hand, if the medium is initially saturated with the wetting phase, it starts to drain
only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be represented
by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. We propose a relevant
modification of the upscaled model obtained by asymptotic homogenization. The modification concerns the form of flow equations
and the calculation of the effective hydraulic functions. This approach is illustrated with two numerical examples concerning
oil–water and CO2–brine flow, respectively. |
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Keywords: | |
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