Similarity solution for capillary redistribution of two phases in a porous medium with a single discontinuity |
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| Institution: | 1. Grupo Aragosaurus-IUCA, http://www.aragosaurus.com, Universidad de Zaragoza, E-50009 Zaragoza, Spain;2. CONICET-Museo Provincial de Ciencias Naturales “Profesor Dr. Juan A. Olsacher”, Zapala, 8340, Neuquén, Argentina;3. Departamento de Ciências da Terra, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, 2829-526 Caparica, Portugal;4. Estratigrafía, Departamento de Ciencias de la Tierra, Universidad de Zaragoza, 50009 Zaragoza, Spain;5. CONICET-Instituto de Investigación en Paleobiología y Geología, Universidad Nacional de Río Negro, General Roca, Río Negro, Argentina;6. Bayerische Staatssammlung für Paläontologie und Geologie and GeoBioCenter, Ludwig-Maximilians-Universität, Richard-Wagner-Str. 10, 80333 Munich, Germany |
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| Abstract: | In this paper we consider one-dimensional capillary redistribution of two immiscible and incompressible fluids in a porous medium with a single discontinuity. We study a special time-dependent solution, a similarity solution, which is found when the initial saturation is discontinuous at the same point as the permeability and porosity, and is constant elsewhere. The similarity solution can be used to validate numerical algorithms describing two-phase flow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we pay special attention to the interface conditions at the discontinuity, both for media with positive and zero entry pressure. Moreover, we discuss some qualitative properties of the solution, and outline a numerical procedure to determine its graph. Examples are given for the Brooks-Corey and Van Genuchten model. We also consider similarity solutions for unsaturated water flow, which is a limit case of two-phase flow for negligible nonwetting phase viscosity. |
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