Frequency-dependent effective hydraulic conductivity in randomly layered porous medium - strong contrast approximation

Abstract

Upscaling of transport properties of heterogeneous porous rocks, such as hydraulic conductivity, is controlled not only by the spatial heterogeneity, but also by the temporal variations of the flow field. Thus effective hydraulic conductivity and permeability of a heterogeneous porous medium is frequency dependent. Existing upscaling methods for this property are often limited to small spatial variations of permeability, which is a significant limitation. In this study we apply a strong contrast expansion method, originally suggested in the context of the dynamic dielectric constant, to the problem of upscaling hydraulic conductivity in a 1D random medium. A closed-form expression for the effective hydraulic conductivity, which depends on the second order statistics, is derived. Unlike the small contrast approximations, in the low- and high-frequency limits this new expression yields harmonic and arithmetic averages of permeability, respectively, which are known to be exact low- and high-frequency limits in 1D.