A Novel Apparent Permeability Model for Shale Matrix Derived under the Framework of the Energy Conservation Law

Abstract

With the rapid development of fracturing technology, unconventional oil and gas resources, such as shale oil and gas, are gradually becoming mainstream energy consumption. However, owing to the complex microstructure in shale reservoirs, it is still a challenge to accurately describe the gas transport characteristics in shale and predict the changes in its permeability. Gas transport in the shale matrix does not always fall into the continuum hypothesis of the Navier–Stokes equation; namely, when the Knudsen number increases, the proportion of the continuum flow is smaller. The gas extraction process is a nonlinear process under the alternate influence of different transport mechanisms and different microscale effects. In this work, the capillary tube space is divided into three different flow zones, and under the law of energy conservation, this study first establishes a bulk gas transport model of shale, which couples continuum flow and Knudsen diffusion. Also, based on the bulk gas transport model, an apparent permeability model of shale is developed by further considering the influence of surface diffusion, gas adsorption, and effective stress. In the apparent permeability model, this paper develops a slip velocity model, which is composed of gas coverage degree as a weight coefficient coupling both Knudsen diffusion velocity and surface diffusion velocity. It is found that the results calculated by the model fit well with the real observation. Moreover, compared with other apparent permeability models, the accuracy of the proposed model improves.