Analytical Solutions for the Radial flow Equation with Constant-Rate and Constant-Pressure Boundary Conditions in Reservoirs with Pressure-Sensitive Permeability

Abstract

Abstract The transient pressure response in stress-sensitive formations is derived by solving analytically the radial flow equation with pressure-dependent rock properties. New solutions are obtained for slightly compressible fluids and real gas flow with constant-rate and constant-pressure wellbore boundary conditions using the Boltzmann transformation. In particular in low-permeability formations, a sensitivity exists to pore pressure changes. Permeability there normally declines with the increase of effective stress. The mathematical model presented here takes into account the reduction in permeability caused by an increase in effective stress for two common parameterized pressure-permeability functions, i.e., a linear and an exponential relationship. The analytical solutions are verified with numerical simulation. They are applicable for well test analysis and prediction of flow rates, as demonstrated in this paper.