Large Scale Mixing for Immiscible Displacement in Heterogeneous Porous Media |
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Authors: | Neuweiler I. Attinger S. Kinzelbach W. King P. |
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Affiliation: | (1) Department of Earth Sciences and Engineering, Imperial College of Science, Technology and Medicine, Prince Consort Road, SW7 2BP London, U.K.;(2) Institute for Hydromechanics and Water Resources Management, ETH Hoenggerberg, 8093 Zurich, Switzerland |
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Abstract: | We derive a large scale mixing parameter for a displacement process of one fluid by another immiscible one in a two-dimensional heterogeneous porous medium. The mixing of the displacing fluid saturation due to the heterogeneities of the permeabilities is captured by a dispersive flux term in the large scale homogeneous flow equation. By making use of the stochastic approach we develop a definition of the dispersion coefficient and apply a Eulerian perturbation theory to determine explicit results to second order in the fluctuations of the total velocity. We apply this method to a uniform flow configuration as well as to a radial one. The dispersion coefficient is found to depend on the mean total velocity and can therefore be time varying. The results are compared to numerical multi-realization calculations. We found that the use of single phase flow stochastics cannot capture all phenomena observed in the numerical simulations. |
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Keywords: | upscaling two-phase flow Buckley-Leverett flow stochastic method heterogeneous porous media macrodispersion |
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