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, an approximate analytical solution has been published to analyze pressure-transient tests in stress-sensitive reservoirs using the concept of "permeability modulus". However, because of the non-linear character of the partial differential equation for stress-sensitive reservoirs, application of superposition to model buildup tests is not straightfoward.
Using the concept of "permeability modulus", this study presents numerical solutions for stress-sensitive reservoirs. Pressure transient solutions with wellbore storage, skin, permeability modulus, and outer boundary effects have been studied in detaiL Both drawdown and buildup solutions have been investigated. Solutions presented in this study also include multiple permeability modulus values for a given situation, where permeability modulus changes with respect to stress level in the reservoir in a stepwise mode.
This study has pointed out inaccuracies involved in previous analytical solutions, especially for wellbore storage and skin effects, and buildup tests. Previously, it has been stated that stress-sensitive permeability effects can cause wellbore storage early-time unit slope line to be masked. This investigation shows that, irrespective of the severity of stress sensitivity, wellbore-storage-dominated unit-slope line always appears at early time. We also show that the use of multiple permeability modulus values to study pressure-transient analysis for stress-sensitive reservoirs is consistent with available laboratory measurements of permeability as a function of stress.
Porous media are not always rigid and nondeformable. To a certain extent, the properties of rock and fluid are pressure dependent or stress sensitive. The laboratory studies and the mathematical modelling research for stress-sensitive reservoirs have been reported by several investigators. The pseudopressure method has been applied to investigate drawdown, buildup, injection and falloff testing by several investigators. The main disadvantage of this method is that the tabulated properties of rock and fluids versus pressure should be known a priori at each pressure level. In addition, a nonlinear diffusivity term still exists at the right-hand side of the diffusivity equation. This nonlinearity is usually evaluated at the initial pressure value to linearize the nonlinear diffusivity equation.
Another approach to solving the nonlinear diffusivity equation arising due to a consideration of the pressure-dependent permeability is to define a permeability modulus analogous to the definition of compressibilities. In other words, permeability, porosity, and fluid density are exponential functions of pressure. Using the concept of permeability modulus and regular perturbation method, Pedrosa presented the first-order approximate analytical solution for a line-source well producing at a constant rate from an infinite radial flow system. Kikani and Pedrosa presented the second-order approximate analytical solution for the same problem using the same solution methodology.