A two-scale model of two-phase ow in porous media ranging from porespace to the macro scale
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Date
2012-06-15
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Abstract
We will derive two-scale models for two-phase flow in porous media, with the microscale
given by the porescale. The resulting system will account for balance of mass, momentum
and energy. To this aim, we will combine a generalization of Rajagopal’s and Srinivasa’s assumption
of maximum rate of entropy production [39, 20, 21] with formal asymptotic expansion. The
microscopic model will be based on phase fields, in particular to the full Cahn-Hilliard-Navier-
Stokes-Fourier model derived in [23] with the boundary conditions from [20]. Using a generalized
notion of characteristic functions, we will show that the solutions to the two-scale model macroscopically
behave like classical solutions to a system of porous media flow equations. Relative
permeabilities and capillary pressure relations are outcomes of the theory and exist only for special
cases. Therefore, the two-scale model can be considered as a true generalization of classical
models providing more information on the microscale thereby making the introduction of hysteresis
superfluous.