Effect of Knudsen diffusion and Langmuir adsorption on pressure transient response in tight- and shale-gas reservoirs

Klinkenberg number is not constant in tight- and shale-gas reservoir. We first derived an expression of b/p in Klinkenberg apparent permeability correlation based on Knudsen number, which is a function of µ/p in an isothermal shale-reservoir system. For pressure in [15MPa, 30MPa], µ/p changes slowly and is very small, and the permeability correction factor is 1.15 for 17MPa, 1.14 for 20MPa, 1.12 for 28MPa for the case in this paper. To characterize the physics of multi-transport mechanisms, and gas adsorption and desorption, a mathematical model for flow in tight- and shale-gas reservoirs with wellbore storage effect is used to understand transient pressure response. A full implicit numerical simulation based on PEBI gridding is developed to quantify the transient pressure behaviors for flow in tight- and shale-gas reservoirs. Based on numerical results, we firstly find that the adsorption makes the curves of the bottom-hole pressure (BHP) have a seeming singular point. The intrinsic permeability determines the position of the seeming singular point, and the ultimate adsorption capacity (UAC) determines the size of the angle around the seeming singular point. Because the turning points appear at early time flow, the position and angle of the seeming singular point may give us an economic and quick methodology to approximately estimate the UAC and intrinsic permeability for the tight- and shale-gas reservoir. This phenomenon can help us to understand the behavior of the flow in tight- and shale-gas reservoir better. [Display omitted] •Adsorption produces a singular point on the curves of the HBP.•The intrinsic permeability determines the position of the singular point.•The ultimate adsorption capacity determines the angle around the singular point.•The turning point appears at early time flow.•The finding may give us a quick method to estimate adsorption and permeability.