Mathematical Modeling of Gas Transport in Porous Geological Media with Contrast of Properties and Irregular Distribution of Pores

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In this work, we perform multiscale modeling of gas transport through the geological media having irregular pore structure and contrast of properties on different spatial scales. We assume that the medium consists of inorganic matrix with organic inclusions imbedded into it. There exist a contrast of properties and spatial scales between the matrix and organic inclusions. The pore sizes vary from micro to nanometers, permeability and diffusivity can differ by several orders of magnitude. We consider filtration and molecular diffusion as mechanisms for free gas transport in both inorganic and organic materials, and surface diffusion as the main mechanism for sorbed gas transport through nanoporous organic inclusions. The irregularities of porous structure we characterize by their deviations from the periodic distribution. We implement multiscale homogenization together with an averaging with respect to random deviations of distribution of pores to derive the macroscopic equation for evaluating the free gas amount in‐place. It turns out that macroscale parameters characterizing gas transport depend on diffusivity, permeability, and porosity of the components of the system, the amount of inclusions and their spatial distribution. We determine the distribution of gas concentration through the production time and investigate its sensitivity to irregularities of pores distribution. We are also interested in the effect of bottom‐hole pressure and study how depletion can be affected by the interchange of gas between kerogen inclusions and inorganic material.


Adsorption; Diffusion; Filtration; Gas phase transport; Irregular distribution of pores; Multi-scale homogenization; Organic-rich shales; Porous media


Earth Sciences | Mathematics



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