Heterogeneous Materials Porous Media Two-Phase Flow

Dimensional analysis and upscaling of two-phase flow in porous media with piecewise constant heterogeneities

R. Hilfer, R. Helmig

Advances in Water Resources 27, 1033 (2004)

submitted on
Monday, March 15, 2004

Dimensional analysis of the traditional equations of motion for two-phase flow in porous media allows to quantify the influence of heterogeneities. The heterogeneities are represented by position dependent capillary entry pressures and position dependent permeabilities. Dimensionless groups quantifying the influence of random heterogeneities are identified. For the case of heterogeneities with piecewise constant constitutive parameters (e.g. permeabilities, capillary pressures) we find that the upscaling ratio defined as the ratio of system size and the scale at which the constitutive parameters are known has to be smaller than the fluctuation strength of the heterogeneities defined e.g. as the ratio of the standard deviation to the mean value of a fluctuating quantity.

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