Seepage flow behaviors of multi-stage fractured horizontal wells in arbitrary shaped shale gas reservoirs

The horizontal well incorporated with massive hydraulic fracturing has become a key and necessary technology to develop shale gas reservoirs efficiently, and transient pressure analysis is a practical method to evaluate the effectiveness of the fracturing. Until now, however, the related studies on the pressure of such wells have mainly focused on regular outer-boundaries, such as infinite, circular and rectangular boundary shapes, which do not always fulfill the practical conditions and, of course, could cause errors. By extending the boundary element method (BEM) into the application of multi-staged fractured horizontal wells, this paper presents a way of analyzing the transient pressure in arbitrary shaped shale gas reservoirs considering ad-/de-sorption and diffusion of the shale gas with the 'tri-porosity' mechanism model. The boundary integral equation can be obtained by coupling the fundamental solution of the Helmholtz equation with the dimensionless diffusivity equation. After discretizing the outer-boundaries and the fractures, the boundary integral equations are linearized and the coefficient matrix of the pressure on the boundaries is assembled, after which bottom-hole pressure can be calculated conveniently. Comparing the BEM solution with semi-analytical solution cases, the accuracy of the new solution can be validated. Then, the characteristic curves of the dimensionless pseudo pressure, as well as its derivative for a well in shale gas reservoirs, are drawn, based on which the parameters' sensitivity analyses are also conducted. This paper not only enriches the well testing theory and method in shale gas reservoirs, but also provides an effective method to solve problems with complex inner-and outer-boundaries.