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A Comparison between Simulation and Experiment for Hysteretic Phenomena During two-phase Immiscible Displacement

F. Doster{}^{{1,2}} and R. Hilfer{}^{{3,4}}
{}^{1}Department of Civil and Environmental Engineering, Princeton University, 08544 Princeton, NJ, USA
{}^{2}Department of Mathematics, Bergen University, Bergen, Norway
{}^{3}Institute for Computional Physics, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
{}^{4}Institut für Physik, Universität Mainz, 55099 Mainz, Germany

The paper compares a theory for immiscible displacement based on distinguishing percolating and non-percolating fluid parts (Physica A, 371, 209 (2006)) with experimental observations from multistep outflow experiments (Water Resources Res, 27, 2113 (1991)). The paper focusses on hysteretic phenomena resulting from repeated cycling between drainage and imbibition processes in multistep pressure experiments. Taking into account the hydraulic differences between percolating and non-percolating fluid parts provides a physical basis to predict quantitatively the hysterestic phenomena observed in the experiment. While standard hysteretic extensions of the traditional theory are nonlocal in time the theory used in this paper is local in time. Instead of storing the pressure and saturation history it requires only the current state of the system to reach the same quantitative agreement.