Summary
Field studies have shown that, if an inclined fracture has a significant inclination angle from the vertical direction or the fracture has a poor growth along the inclined direction, this fracture probably cannot fully penetrate the formation, resulting in a partially penetrating inclined fracture (PPIF) in these formations. It is necessary for the petroleum industry to conduct a pressure-transient analysis on such fractures to properly understand the major mechanisms governing the oil production from them. In this work, we develop a semianalytical model to characterize the pressure-transient behavior of a finite-conductivity PPIF. We discretize the fracture into small panels, and each of these panels is treated as a plane source. The fluid flow in the fracture system is numerically characterized with a finite-difference method, whereas the fluid flow in the matrix system is analytically characterized on the basis of the Green's-function method. As such, a semianalytical model for characterizing the transient-flow behavior of a PPIF can be readily constructed by coupling the transient flow in the fracture and that in the matrix. With the aid of the proposed model, we conduct a detailed study on the transient-flow behavior of the PPIFs. Our calculation results show that a PPIF with a finite conductivity in a bounded reservoir can exhibit the following flow regimes: wellbore afterflow, fracture radial flow, bilinear flow, inclined-formation linear flow, vertical elliptical flow, vertical pseudoradial flow, inclined pseudoradial flow, horizontal-formation linear flow, horizontal elliptical flow, horizontal pseudoradial flow, and boundary-dominated flow. A negative-slope period can appear on the pressure-derivative curve, which is attributed to a converging flow near the wellbore. Even with a small dimensionless fracture conductivity, a PPIF can exhibit a horizontal-formation linear flow. In addition to PPIFs, the proposed model also can be used to simulate the pressure-transient behavior of fully penetrating vertical fractures (FPVFs), partially penetrating vertical fractures (PPVFs), fully penetrating inclined fractures (FPIFs), and horizontal fractures (HFs).