Abstract
The deficiencies in present mathematic models of shale gas flow are outlined briefly. Based on the linear poroelasticity, the transfer of free gas in nanopores, surface diffusion of adsorbed gas, nonlinear and non-equilibrium gas adsorption-desorption kinetics as well as the rock deformation are all coupled to formulate a new mathematic model to unlock the true potential of shale-gas development. The stress-and-pressure dependent permeability and porosity models of matrix containing random fractures, together with the non-equilibrium adsorption-desorption kinetics, are also deduced in this paper. Numerical method is applied to solve the model and analyze the impacts of stress-and-pressure sensitivity, surface diffusion and non-equilibrium adsorption on shale gas flow. The results suggest: (1) The fracture density in the shale matrix plays an important role in the permeability and porosity, the stress-and-pressure sensitivity of shale rock itself can be ignored; (2) compared with the free gas flow in pores, the surface diffusion of adsorbed gas can be ignored; (3) the recovery time during non-equilibrium sorption process relies heavily on equilibrium coefficient and rock porosity, and the desorption rate significantly impacts the gas flow rate.
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