Variable-Permeability Well-Testing Models and Pressure Response in Low-Permeability Reservoirs with non-Darcy Flow

Abstract

This paper proposes the concept of variable-permeability effect and sets up the one-dimensional and two-dimensional non-Darcy well testing models. The finite difference algorithm is employed to solve the differential equations of the variable-permeability model, and the non-convergence of the numerical solutions is solved by using the geometric mean of permeability. The type curves of pressure and pressure derivative with variable-permeability effect are obtained, and sensitivity analysis is conducted. The results show that the type curves upturn in the middle and late sections, and the curves turn more upward with the severer of the variable-permeability effect. The severer the non-Darcy effect is, the less obviously the curve upturns caused by boundary effect. Furthermore, the boundary effect is increased by increasing the number of impermeable boundaries or decreasing the distance between the well and boundary.