| Deep-seated low-permeability petroleum or geothermal reservoirs usually exhibit stress-sensitive permeability. For such reservoirs, pressure-transient analysis based on constant rock properties, especially permeability, can lead to significant errors in parameter estimation. Recently, some approximate analytical solutions have been published to analyze pressure transient tests in stress-sensitive reservoirs using the concept of "permeability modulus". Because of the non-linear character of the partial differential equation for stress-sensitive reservoirs, Laplace's transformation can not be applied directly to solve the non-linear diffusivity equation, and application of superposition to model build up tests is not straightforward.;Previously, it has been stated that stress-sensitive permeability effects can cause the wellbore storage early-time unit slope line on a log-log plot to be masked. From the numerical results, this investigation shows that, irrespective of the severity of the stress sensitivity, a wellbore-storage-dominated unit slope line always appears at early time. For buildup tests, the numerical solution is more reliable than the analytical solution because the 'superposition in time' method can not be used directly for the analytical solution of a non-linear equation. Both analytical and numerical solutions are not applicable at late times when the permeability modulus is greater than zero, because the assumption of a constant production fate at the wellbore and the exponential reduction of permeability with dimensionless pressure are not consistent at late times. To overcome this problem, based on the stress-dependent permeability data presented in the literature, a step-wise permeability modulus and a new type of permeability modulus with two parameters are developed for both the analytical and the numerical solutions. (Abstract shortened by UMI.). |
