Abstract
This paper presents the pressure transient response for reservoirs with an internal circular subregion. The solution is a generalization of that previously presented in the literature, which assumed that the subregion was either an impermeable barrier or a constant pressure circle. Two cases were considered, with the well located either inside or outside the circular discontinuity. When the well is located inside the circular subregion, the solution developed in the study is also a generalization of the well-known pressure response for a composite two-region system.
The solution was obtained by using the concept of Green's function and by applying the Laplace transformation technique. The Laplace space response, although very complex, was inverted to real space with the Stehfest1 algorithm.
When the well is located inside the circular subregion, the wellbore pressure response shows a behavior typical of radial composite systems, except for the effect of the well eccentricity, which acts as a skin factor. For the case where the active well is external to the subregion, three flow regimes are observed. The initial infinite-acting behavior and the late-time pseudoradial flow produce semilog straight lines which are parallel and reflect the transmissivity of the external region. The long-time effect of the discontinuity can be regarded as an apparent skin effect.
The dependence of the solution on the diffusivity ratio, the mobility ratio, the geometric configuration and the size of the system was also investigated in the study.
The solution can be used to simulate the pressure behavior for reservoirs which contain circular or approximately circular discontinuities, such as those caused by variations in rock and/or fluid properties due to the presence of shale lenses or fluid injection, for instance. The pressure solution can also be used to interpret single-well or interference tests in systems with these configurations.
