A novel Monte Carlo simulation on gas flow in fractal shale reservoir

The apparent gas permeability (AGP) is one of the key parameters in shale gas exploitation, which is difficult to determine due to the mutliscale structure of shale formation. In this paper, a fractal probability law and Monte Carlo technique are used to predict the rarefied gas flow through shale reservoir, since from the adsorption-desorption experiments it is known that the distribution of pore size follows the fractal scaling law. The results indicate that the AGP increases with the increment of Knudsen number, and it grows linearly with Knudsen number when Knudsen number is larger than 0.1. When the porosity is fixed, increased pore fractal dimension reduces the AGP and the intrinsic permeability, but enhances the permeability ratio (ratio of AGP to intrinsic permeability). However, when the pore size limit is fixed, the permeability ratio can be reduced by increasing pore fractal dimension. While the increment of tortuosity fractal dimension can lower both AGP and intrinsic permeability, it has marginal effect on the permeability ratio. The proposed fractal Monte Carlo model is an efficient and economic method to predict the AGP, which bridges the microscale structures and macroscale gas flow properties of shale reservoir. •Fractal dimension of shale is measured by adsorption-desorption experiment.•Fractal Monte Carlo model is developed to predict apparent gas permeability.•Relationship between micro structure and macro gas flow properties is presented.•Gas flow mechanisms in multiscale shale are explored.