Frequency-dependent effective hydraulic conductivity in randomly layered porous medium - strong contrast approximation
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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.
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Caspari, Eva; Gurevich, Boris; Muller, T. (2013)The determination of the transport properties of heterogeneous porous rocks, such as an effective hydraulic conductivity, arises in a range of geoscience problems, from groundwater flow analysis to hydrocarbon reservoir ...
Caspari, Eva; Mϋller, Tobias; Rubino, G.; Gurevich, Boris (2013)We study Biot’s slow wave propagation in the presence of strong hydraulic conductivity fluctuations in the low-frequency range. The latter condition implies that the slow wave is a diffusion process. To elucidate the ...
Müller, T.; Gurevich, Boris (2018)© 1996-2018 Society of Exploration Geophysicists. All rights reserved. Modern reservoir monitoring technologies often make use of diffusion waves in order to estimate the hydraulic conductivity and diffusivity of reservoir ...