The low permeability and submicron throats in most shale or tight sandstone reservoirs have a significant impact on microscale flow. The flow characteristics can be described with difficultly by the conventional Darcy flow in low-permeability reservoirs. In particular, the thickness of the boundary layer is an important factor affecting the formation permeability, and the relative permeability curve obtained under conventional conditions cannot accurately express the seepage characteristics of porous media. In this work, the apparent permeability and relative permeability were calculated by using non-Darcy-flow mathematical modeling. The results revealed that the newly calculated oil–water relative permeability was slightly higher than that calculated by the Darcy seepage model. The results of the non-Darcy flow based on the conceptual model showed that the area swept by water in non-Darcy was smaller than that in Darcy seepage. The fingering phenomenon and the high bottom hole pressure in the non-Darcy seepage model resulted from the larger amount of injected water. There was a large pressure difference between the injection and production wells where the permeability changed greatly. A small pressure difference between wells resulted in lower variation of permeability. Consequently, the non-Darcy simulation results were consistent with actual production data.

This paper presents a combined experimental–analytical investigation of coal strain development under fluctuating applied hydrostatic stress. The laboratory setup mimics the isotropic volumetric compaction of coal under burial–uplift cycles in the absence of tectonic stress. Special emphasis is placed on the corresponding permeability evolution of the coal strata. Our results show that the stress–strain path is exponential, approaching a linear relation in the logarithmic stress–strain space with the monotonic increase in stress. A similar behavior is found for the strain–permeability path in the logarithmic strain–permeability space. The permeability recovery undergoes hysteresis with respect to the stress in a stress loading–unloading cycle, but the hysteresis is not manifest with respect to the strain. A theoretical geomechanical consolidation analysis was performed using an elastoplastic modelling framework. The analysis suggests that plastic strain is the cause of the hysteresis of the strain recovery in a stress loading–unloading cycle. The closed hysteresis loops manifested in stress loading–unloading–reloading cycles are promoted by the plastic strain during stress unloading and the difference in evolution rates of the elastic core between loading and unloading. The results of this study are helpful for understanding the mechanism of permeability evolution and optimizing water and coal seam gas production.