Permeability and thermal conductivity models of shale matrix with a bundle of tortuous fractal tree-like branching micropore networks

The complex pore structures are of great significance to gas transport and heat transfer in shale gas reservoirs, but an accurate prediction of permeability and thermal conductivity is a challenge to a porous medium with the complex geometry and distribution of pore networks. This study investigates the permeability and thermal conductivity of shale matrix with a bundle of tortuous fractal tree-like micropore networks. First, a new permeability model and a new dimensionless effective thermal conductivity model of shale matrix are developed to include the branching and tortuous characteristics of the fractal tree-like network. Then, the permeability model is validated by experimental data, and the dimensionless effective thermal conductivity model is compared with simulation results in literature. Last, sensitivity analysis is conducted to identify key parameters in these two new models. It is found that the two new models can well describe the gas transport and heat transfer in shale matrix with a bundle of tortuous fractal tree-like pore networks. The permeability model has much higher accuracy than traditional models. Tortuosity fractal dimension and radius fractal dimension of shale matrix with the bundle of tortuous fractal tree-like networks have negative influences on both permeability and thermal conductivity. Length ratio and radius ratio significantly alter the gas flow resistance and thermal resistance, and thus lead to the change of permeability and thermal conductivity. Branching angle has insignificant effect on the permeability and thermal conductivity and thus is ignorable.