A dynamic apparent permeability model for shale microfractures: Coupling poromechanics, fluid dynamics, and sorption-induced strain

The widely distributed microfractures play an important role in shale gas production. However, limited studies focus on gas flow behavior in microfractures, and ignore the complex transport mechanisms, leading to a large error for gas permeability evaluation. In this work, a newly dynamic apparent permeability (AP) model, coupling poromechanics, sorption-induced strain, and gas slippage, has been proposed to effectively reveal the gas flow mechanisms through microfractures of shale. Specifically, a dynamic aperture is innovatively incorporated into the Navier-Stokes (N-S) equation using the second-order slip boundary condition to calculate the gas velocity and volume flux in single microfracture. Based on that, the gas transport model for microfracture networks considering the distributions of aperture and tortuosity is derived using the fractal theory. The newly developed model is verified well with experimental data and network simulation. Results indicate that the gas conductance highly depends on the structure of microfracture networks (i.e., the maximum aperture and fractal dimensions). There are three different AP evolutions under various boundary conditions (i.e., constant confining pressure (P-c), constant pore pressure (P-p), and constant effective stress (sigma(eff))) resulting from the coupling transport mechanisms. The AP presents a similar shape of V at reservoir conditions (i.e., constant P-c), indicating the negative contribution of poromechanics at an early stage, and the positive contribution for both gas slippage and sorption-induced strain at the late stage should be underlined during gas production. Moreover, the negative factor of poromechanics is positively correlated with fracture compressibility coefficient but negatively associated with Biot's coefficient at high pressures (>15 [MPa]). Increasing gas desorption capacity, fracture spacing, and internal swelling coefficient can enhance the positive factor of sorption-induced strain at low pressures (<15 [MPa]). This work provides a theoretical guidance to develop shale gas effectively.