Study on the steady and transient pressure characteristics of shale gas reservoirs

•A new non-linear seepage model considering diffusion, slippage and desorption effect was established.•The steady and transient governing equation was constructed.•The pressure characteristic analytical solution was obtained.•The microscale effect was found in nano/micropore reservoirs.

The flow law was obtained by combining the mechanics of continuous media and molecular kinematics method for shale gas reservoirs with nano/micropores. The new non-linear seepage model considering the diffusion, slippage and desorption effects was established and simplified. The steady and transient governing equations were constructed on the basis of the non-linear model. The pressure characteristic analytical solution was then obtained. The permeability adjustment factor changes largely when the pore throat radius is less than 100 nm. Therefore, the flow law in nano/micropore departs significantly from Darcy's law. Numerical simulation results show that the flux of gas changes significantly with the permeability of the pore throat radius, and the flow in nano/micropore reservoir shows the microscale effect. Compared with the pressure distribution calculated by Darcy's law, the pressure distribution calculated by the new model decreases slowly because of the diffusion and desorption effect. The results provide a theoretical foundation for developing shale gas reservoirs.