Pressure Transient Response in Stress-Sensitive Formations

ABSTRACT Pressure transient response in stress-sensitive formations is obtained by solving analytically the radial flow equation with pressure-dependent rock properties. In cracked rock systems and tight formations, hydraulic permeability is very sensitive to pore pressure change. The mathematical model presented in this paper takes into account the reduction in permeability caused by an increase in effective stress. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. A perturbation technique is applied to determine approximate analytical solutions for transient flow in an infinite radial system with constant rate inner boundary. The model includes a new parameter, the permeability modulus, which measures the permeability dependency on pressure. The solution of the model leads to the construction of type curves that can be applied to drawdown and buildup analysis of well test data from stress-sensitive reservoirs. Type curve matching provides a way to estimate initial permeability and permeability modulus. From buildup data, initial permeability may be obtained from the slope of the semi-log straight line on Horner plot, as shown in an example using field data from a low permeability gas reservoir.