Slightly compressible and immiscible two-phase flow in porous media |
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| Institution: | 1. School of Civil, Environmental and Architectural Engineering, Korea University, Seoul 136-701, Republic of Korea;2. Department of Geotechnical Disaster Protection Engineering, Daejeon University, Daejeon 300-716, Republic of Korea;1. PAI + group, Department of Energetics & Mechanics, Universidad Autónoma de Occidente, Cali, Colombia;2. Multiphase Flow Systems, Faculty of Process and Systems Engineering, Otto-von-Guericke University, D-06120 Halle (Saale), Germany;1. Faculty of Transportation Sciences, Czech Technical University in Prague, Konviktska 20, Prague 1, Czech Republic;2. SEG-CEMUC — Department of Mechanical Engineering, University of Coimbra, 3030-788 Coimbra, Portugal;3. Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Prague 6, Czech Republic;4. nCATS, Engineering Sciences, University of Southampton, Highfield, Southampton, United Kingdom |
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| Abstract: | We describe the flow of two compressible phases in a porous medium. We consider the case of slightly compressible phases for which the density of each phase follows an exponential law with a small compressibility factor. A nonlinear parabolic system including quadratic velocity terms is derived to describe compressible and immiscible two-phase flow in porous media. In one-dimensional space, we establish the existence and uniqueness of a local strong solution for the regularized system. We show also that the saturation is physically admissible. We describe the asymptotic behavior of the solutions when the compressibility factor goes to zero. |
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