Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs

Abstract

Abstract Shale gas resources have received great attention in the last decade due to the decline of the conventional gas resources. Unlike conventional gas reservoirs, the gas flow in shale formations involves complex processes with many mechanisms such as Knudsen diffusion, slip flow (Klinkenberg effect), gas adsorption and desorption, strong rock-fluid interaction, etc. Shale formations are characterized by the tiny porosity and extremely low-permeability such that the Darcy equation may no longer be valid. Therefore, the Darcy equation needs to be revised through the permeability factor by introducing the apparent permeability. With respect to the rock formations, several studies have shown the existence of anisotropy in shale reservoirs, which is an essential feature that has been established as a consequence of the different geological processes over long period of time. Anisotropy of hydraulic properties of subsurface rock formations plays a significant role in dictating the direction of fluid flow. The direction of fluid flow is not only dependent on the direction of pressure gradient, but it also depends on the principal directions of anisotropy. Therefore, it is very important to take into consideration anisotropy when modeling gas flow in shale reservoirs. In this work, the gas flow mechanisms as mentioned earlier together with anisotropy are incorporated into the dual-porosity dual-permeability model through the full-tensor apparent permeability. We employ the multipoint flux approximation (MPFA) method to handle the full-tensor apparent permeability. We combine MPFA method with the experimenting pressure field approach, i.e., a newly developed technique that enables us to solve the global problem by breaking it into a multitude of local problems. This approach generates a set of predefined pressure fields in the solution domain in such a way that the undetermined coefficients are calculated from these pressure fields. In other words, the matrix of coefficients is constructed automatically within the solver. We ran a numerical model with different scenarios of anisotropy orientations and compared the results with the isotropic model in order to show the differences between them. We investigated the effect of anisotropy in both the matrix and fracture systems. The numerical results show anisotropy plays a crucial role in dictating the pressure fields as well as the gas flow streamlines. Furthermore, the numerical results clearly show the effects of anisotropy on the production rate and cumulative production. Incorporating anisotropy together with gas flow mechanisms in shale formations into the reservoir model is essential particularly for predicting maximum gas production from shale reservoirs.