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Fronts in two-phase porous media flow problems: The effects of hysteresis and dynamic capillarity |
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| Authors: | K Mitra T Köppl I S Pop C J van Duijn R Helmig |
| Institution: | 1. Faculty of Mathematics, Technical University of Dortmund, Dortmund, Germany;2. Department of Mathematics, University of Technology Munich, Garching bei München, Germany;3. Faculty of Science, Hasselt University, Hasselt, Belgium
Department of Mathematics, University of Bergen, Norway;4. Department of Earth Sciences, University of Utrecht, Utrecht, The Netherlands Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;5. Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Stuttgart, Germany |
| Abstract: | In this work, we study the behavior of saturation fronts for two-phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses traveling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include nonmonotone profiles, multiple shocks, and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we discuss the implication of our findings in the context of available experimental results. |
| Keywords: | dynamic capillarity hysteresis Riemann problem traveling waves two-phase flow |