Abstract
In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Johannes van Duijn, C., Eichel, H., Helmig, R. et al. Effective equations for two-phase flow in porous media: the effect of trapping on the microscale. Transp Porous Med 69, 411–428 (2007). https://doi.org/10.1007/s11242-006-9089-9
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DOI: https://doi.org/10.1007/s11242-006-9089-9