Modeling transient flow behavior of a multiscale triple porosity model for shale gas reservoirs

Gas flow in shales is a complex process from nanoscale to macroscale which includes diffusion of dissolved gas molecules in kerogen bulk, desorption from the pore walls, Knudsen diffusion and slip flow in nanopores, and conventional flow in natural fracture network according to recent studies. However, little work has been done in literature to simultaneously incorporate all these complex storage and flow mechanisms in well testing models for shale gas reservoirs. This paper presents a new tri-porosity model for shale gas reservoirs to describe that gas flows from formation to wellbore with consideration of all the mechanisms mentioned above. Compared with current well testing models for shale gas reservoirs, this model will be more close to the actual reservoir situation by simulating the physics behind the actual process. Partial differential equations of this tri-porosity model are derived and Laplace transform is employed to solve these equations analytically. The analytical solution of the transient pressure is obtained in real space with Stehfest numerical inversion method, and standard bi-logarithmic type curves are plotted. The characteristics of transient pressure behavior are analyzed thoroughly and different flow regimes are observed in type curves for shale gas reservoirs. Effects of relevant parameters are analyzed as well, which has important significance to understand the transient flow behavior for shale gas reservoirs.