Well-Test Interpretation Model of Water-Injection Well in a Low-Permeability Reservoir and Its Application

For low-permeability reservoirs, water-flooding development is usually adopted, which leads to induced fractures near the wellbore, increasing reservoir heterogeneity, and making water-flooding development more complex. This paper focuses on low-permeability reservoirs, considering the characteristics of induced fractures and elliptic-flow composite, and the well-test model for injection wells is established. The mathematical model in Laplace space is obtained through dimensionless transformation and Laplace transformation. Subsequently, the Mathieu function is introduced to obtain the bottom hole pressure, and the pressure response curve is drawn. The six flow stages of the curve are defined, and the sensitivity of parameters such as half-length of induced fractures, range of lateral-swept area, permeability in unswept area, and outer boundary distance at constant pressure are analyzed. The results show that the half-length of the fracture mainly affects the linear flow of the fracture, the range of the lateral wave-affected area mainly affects the radial flow of the swept area, the permeability of the unswept area mainly affects the radial flow of the unswept area, and the outer boundary distance at constant pressure mainly affects the boundary flow. Based on the production performance of a certain injection well in J Oilfield, a series of key parameters are obtained through analytical solution model inversion, including the induced-fracture half-length of 10.32 m, the lateral-swept range of elliptic partition flow of 128.95 m, the permeability of the swept area of 6.87 mD, and the mobility ratio of 119.92, which show the superiority of the analytical solution model.