Modeling Flow in Porous Media with Double Porosity/Permeability: Mathematical Model, Properties, and Analytical Solutions

[+] Author and Article Information
Kalyana Babu Nakshatrala

Associate Professor, Dept. of Civil & Environmental Eng., University of Houston, Houston, Texas 77204

Seyedeh Hanie Seyed Joodat

Graduate Student, Dept. of Civil & Environmental Eng., University of Houston, Houston, Texas 77204

Roberto Ballarini

Thomas and Laura Hsu Professor and Chair, Dept. of Civil & Environmental Eng., University of Houston, Houston, Texas 77204

1Corresponding author.

ASME doi:10.1115/1.4040116 History: Received February 14, 2018; Revised April 24, 2018


Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydro-mechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flow in such porous media, they lack a strong theoretical basis. This paper aims to fill this lacuna by providing the much needed theoretical foundations of the flow in porous media that exhibit double porosity/permeability. We first obtain a mathematical model using the maximization of rate of dissipation hypothesis, and thereby providing a firm thermodynamic underpinning. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems and obtain the corresponding analytical solutions, which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations.

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