Summary
Homogenization techniques have been applied successfully to pore scale models of porous media, at least in the description of single-phase fluids. In the case that two phases are present (e.g. water and oil) one expects upscaled equations in the form of the Leverett two-phase flow system. Unfortunately, due to the appearance of many interfaces inside the porous medium and a lack of control of the geometric properties of the domains, no rigorous derivation of the Leverett system can be expected in the near future. In this contribution we report on rigorous derivations for geometries that allow a uniform description of the interfaces.
This work has been supported by the German Research Foundation (DFG) through SFB 359 (Project D1) at the University of Heidelberg.
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Jäger, W., Schweizer, B. (2007). Microscopic Interfaces in Porous Media. In: Jäger, W., Rannacher, R., Warnatz, J. (eds) Reactive Flows, Diffusion and Transport. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28396-6_20
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DOI: https://doi.org/10.1007/978-3-540-28396-6_20
Publisher Name: Springer, Berlin, Heidelberg
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