Summary
We consider the behavior of incompressible two-phase flow in heterogeneous reservoirs with randomly placed heterogeneities; that is, a porous medium with permeability A and porosity Ф which are statistically homogeneous random fields oscillating at the dimensionless scale ε. Using the tools of stochastic homogenization we get the nonlinear effective equations which govern the flow behavior in a homogeneous medium being equivalent, in the sense of homogenization theory, to the original one. The computation of the effective permeability tensor A hom is done by solving auxiliary stochastic problems, similar to the ones for the linear one-phase flow case. Under ergodicity assumption, and using the primal and dual formulation of these auxiliary problems, we design a numerical algorithm computing both the effective parameters and the minimal volume on which these effective properties are valid. The validity of our algorithm is tested on a two-phase groundwater flow with injection of one-phase from a well.
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© 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Badea, A., Bourgeat, A. (1997). Numerical Simulations by Homogenization of Two-Phase Flow Through Randomly Heterogeneous Porous Media. In: Helmig, R., Jäger, W., Kinzelbach, W., Knabner, P., Wittum, G. (eds) Modeling and Computation in Environmental Sciences. Notes on Numerical Fluid Mechanics (NNFM), vol 59. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89565-3_2
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DOI: https://doi.org/10.1007/978-3-322-89565-3_2
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-89567-7
Online ISBN: 978-3-322-89565-3
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