Abstract
The large amount of nanoscale pores in shale results in the inability to apply Darcy’s law. Moreover, the gas adsorption of shale increases the complexity of pore size characterization and thus decreases the accuracy of flow regime estimation. In this study, an apparent permeability model, which describes the adsorptive gas flow behavior in shale by considering the effects of gas adsorption, stress dependence, and non-Darcy flow, is proposed. The pore size distribution, methane adsorption capacity, pore compressibility, and matrix permeability of the Barnett and Eagle Ford shales are measured in the laboratory to determine the critical parameters of gas transport phenomena. The slip coefficients, tortuosity, and surface diffusivity are predicted via the regression analysis of the permeability data. The results indicate that the apparent permeability model, which considers second-order gas slippage, Knudsen diffusion, and surface diffusion, could describe the gas flow behavior in the transition flow regime for nanoporous shale. Second-order gas slippage and surface diffusion play key roles in the gas flow in nanopores for Knudsen numbers ranging from 0.18 to 0.5. Therefore, the gas adsorption and non-Darcy flow effects, which involve gas slippage, Knudsen diffusion, and surface diffusion, are indispensable parameters of the permeability model for shale.
Highlights
A model that incorporates the suite of continuum, slip, transition, and free-molecular flow regimes in one equation and considers the gas adsorption/desorption effect
To properly evaluate the application of the apparent permeability model to shale gas reservoirs, the apparent permeability model, which includes the effects of gas adsorption, stress dependence, and non-Darcy flow, is used to perform the regression analysis of the measured matrix permeabilities of the Barnett and Eagle Ford shale core samples
The effect of gas adsorption leads to the reduction of the effective pore width and additional gas mobility due to surface diffusion
Summary
A model that incorporates the suite of continuum, slip, transition, and free-molecular flow regimes in one equation and considers the gas adsorption/desorption effect. Modified version of Javadpour’s model, with consideration of the impact of surface roughness on Knudsen diffusion. An expansion of the Klinkenberg slip theory expressed in quadratic format Nonlinear assembly of viscous flow and Knudsen diffusion associated with the surface diffusion effect. Combination of second-order slip flow and surface diffusion using the Langmuir slip model, with consideration of the density profile provided by the SLD-PR model. Slip flow expressed in terms of the superposition of the Klinkenberg and pore-elastic effects nanopores[19]. All of the abovementioned subjects are important for characterizing the properties of shale gas reservoirs. The purpose of this study is to develop a model that includes multiple parameters to represent the unique features of shale rocks
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