Multi-scale Asymptotic Analysis of Gas Transport in Shale Matrix

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Organic-rich resource shales play an important role in global natural gas production. However, many uncertainties exist in an engineering analysis of gas transport and production such as the reservoir-scale flow simulation, history-matching, and optimization. In this work, we introduce a new set of governing equations to describe the characteristic features of porous structures of the organic-rich resource shale. We apply multi-scale analysis to mass balance equations, the equation of state (for free gas), and an adsorption isotherm. Using the macroscopic model, we study gas transport in shales, consisting of nanoporous organic material (kerogen) and the inorganic material. We conclude that both gas in-place and gas production rate depend on the amount of kerogen in the shale matrix. Adsorbed-phase transport by the organic pore walls is responsible for the increase in production rate. We investigate both Henry and Langmuir adsorption as well as different values of length scale ratio and diffusion coefficients.


Gas transport; Adsorption; Shale; Kerogen; Nanopore; Multi-scale; Homogenization


Applied Mathematics | Oil, Gas, and Energy

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