An extension of Darcy’s law incorporating dynamic length scales

Wang, Yuhang; Aryana, Saman A.; Allen, Myron B.

doi:10.1016/j.advwatres.2019.05.010

Title: An extension of Darcy’s law incorporating dynamic length scales

Journal Article · 17 May 2019 · Advances in Water Resources

DOI: https://doi.org/10.1016/j.advwatres.2019.05.010 · OSTI ID:1757997

Wang, Yuhang ^[1];

^[1]; Allen, Myron B. ^[1]

Univ. of Wyoming, Laramie, WY (United States)

We propose a physics-based, macroscale formulation of multiphase porous-media flows that both honors the validity of Darcy’s law in steady or near-steady flows and accommodates the effects of heterogeneities and nonlinearities in unsteady flows. The new formulation recognizes that parameters characterizing the system operate at different length-scales. In particular, the use of Darcy’s law, predicated on the assumption of near-steady flows, requires dynamic length scales, owing to the possibility of rapid fluctuations in rock properties and fluid saturations attributable to heterogeneity and nonlinearity. We accommodate these dynamic length-scales through dynamic spatial averaging. The length and position of the averaging window are characterized by the length of the mixing zone and the direction of propagation of information in the transport process. Here, we validate the proposed formulation by comparing highly accurate,two dimensional numerical solutions against core-scale displacement experiments. The proposed paradigm is consistent with the classical multiphase Darcy formulation, in the sense that the latter also represents the results of an averaging approach.

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Research Organization:: Univ. of Wyoming, Laramie, WY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE

Grant/Contract Number:: SC0019165

OSTI ID:: 1757997

Alternate ID(s):: OSTI ID: 1564484

Journal Information:: Advances in Water Resources, Vol. 129; ISSN 0309-1708

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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Title: An extension of Darcy’s law incorporating dynamic length scales

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