Discrete fracture model with unsteady-state adsorption and water–gas flow for shale-gas reservoirs

A shale-gas reservoir possesses many complex characteristics, including coexisting free and adsorbed gases, a complex distribution of fractures, and the existence of movable water in these fractures. In this study, we improved the conventional discrete fracture model by considering viscous flow, diffusion flow, and slip flow to describe the transport of free gas in the matrix, the unsteady-state adsorption to describe the mass exchange between the free gas and adsorbed gas, and the gas–water two-phase flow to describe the fluid transport in fractures. We compared the proposed model with a previous discrete fracture model and found it to be credible. In addition, we discussed different influence factors on the results and found the following: (1) The net desorption rate was most dependent on fracture and development time, which had different influences on the net desorption rate; the existence of a fracture improved the net desorption rate, but this effect could be reduced along with the development time. (2) The adsorption and free-gas distribution were more related to surface diffusion and fracture, which showed different sensitivity to the influence of those two gases. The effect of surface diffusion on the distribution of adsorbed gas was more sensitive than that of free gas, whereas the influence of fractures was more sensitive to the distribution of free gas than adsorbed gas. Moreover, we used the proposed model to simulate a shale-gas reservoir developed by a horizontal well in the Ordos Basin in China. The study findings showed that if we used the model considering only single-gas transport in the fracture to simulate this reservoir, the average relative error could reach up to 135%, whereas if we used our model, the average relative error was only 1%, which indicated that our model was accurate for actual shale-gas reservoir.