6533b860fe1ef96bd12c2dc2

RESEARCH PRODUCT

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

Rainer HelmigRudolf HilferRudolf Hilfer

subject

Capillary pressureMaterials scienceCapillary actionMultiphase flowPiecewiseEquations of motionThermodynamicsTwo-phase flowMechanicsPorous mediumWater Science and TechnologyDimensionless quantity

description

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.

yearjournalcountryeditionlanguage
2004-10-01Advances in Water Resources
https://doi.org/10.1016/j.advwatres.2004.07.003