Multiscale Modeling of Gas Flow Through Organic-Rich Shale Matrix

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In this work, we study gas flow through shale matrix consisting of a microporous inorganic material and nanoporous organic material (kerogen). We apply a multiscale analysis to mass balance equations taking into account such processes as desorption of gas from nanopores in kerogen, diffusion, and filtration. As a result, we get a macroscopic initial boundary-value problem with effective coefficients. The effective coefficients are determined from the solution of a problem on representative elementary volume (REV or periodicity cell). They are influenced by the structure of shale matrix. The values of the effective coefficients depend on permeability and porosity, diffusivity of adsorbed and free gas, adsorption/desorption mechanism, and the concentration of kerogen. We study the free gas amount across the shale matrix as a function of coordinates and time. We conclude that due to the adsorbed-phase transport by the organic pore walls, the amount of gas in-place and gas production rate increase with the concentration of kerogen. We investigate both the Henry and Langmuir adsorption, and also the effect of nonlinearity caused by the dependence of matrix permeability on pressure.


Applied Mathematics | Oil, Gas, and Energy