A multi-flow regimes model for simulating gas transport in shale matrix

The gas transport in shale matrix is of great research interest for optimised shale gas recovery. Pores and pore-throats in the gas-bearing shale are nano-scale, and hence transport of gas is governed by the slippage effect and Knudsen diffusion rather than viscous flow. Hence a proper mathematical model is needed for full understanding of shale gas transport. In this paper, a mathematical model that considers multi-flow regimes is proposed based on gas molecular kinetics theory. The flow regimes transition from slip flow to Knudsen diffusion, and can be adequately described by introducing a corrected intermolecular collision frequency. The proposed mathematical model predictions are compared with experimental data and found to match very well. Furthermore, the gas mass flux contributed by different flow regimes with the variation of Knudsen number is analysed. The numerical simulation results indicate that with the increase in Knudsen number, viscous flow becomes weakened, and the slippage flow reaches a peak and then decreases gradually. The contribution to the gas mass flux due to Knudsen diffusion starts at the early stage of transition flow, and becomes dominant at the later stage of transition flow.