Pressure Transient Behavior In Reservoirs With An Internal Circular Discontinuity
- Adalberto J. Rosa (Petrobras - CEN-NOR) | Av. Antonio Carlos Magalhaes (Stanford University) | Roland N. Horne (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 1996
- Document Type
- Journal Paper
- 83 - 92
- 1996. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 4.6 Natural Gas, 5.3.1 Flow in Porous Media, 5.4.2 Gas Injection Methods, 5.6.4 Drillstem/Well Testing
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This paper presents the pressure transient response for reservoirs with aninternal circular subregion. The solution is a generalization of thatpreviously presented in the literature, which assumed that the subregion, waseither an impermeable barrier or a constant pressure circle. Two cases wereconsidered, with the well located either inside or outside the circulardiscontinuity. When the well is located inside the circular subregion, thesolution developed in the study is also a generalization of the well-knownpressure response for a composite two-region system.
The solution was obtained by using the concept of Green's function and byapplying the Laplace transformation technique. The Laplace space response,although very complex, was inverted to real space with the Stehfestalgorithm.
When the well is located inside the circular, subregion, the wellborepressure response shows a behavior typical of radial composite systems, exceptfor the effect of the well eccentricity, which acts as a skin factor. For thecase where the active well is external to the subregion, three flow regimes areobserved. The initial infinite-acting behavior and the late-time pseudoradialflow produce semilog straight lines which are parallel and reflect thetransmissivity of the external region. The long-time effect of thediscontinuity 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 inthe study.
The solution can be used to simulate the pressure behavior for reservoirswhich contain circular or approximately circular discontinuities, such as thosecaused by variations in rock and/or fluid properties due to the presence ofshale lenses or fluid injection, for instance. The pressure solution can alsobe used to interpret single-well or interference tests in systems with theseconfigurations.
Circular discontinuities may be present in reservoir systems due tovariations either in rock or in fluid properties. In the former case, thediscontinuity may be due to shale lenses and may not be exactly circular, butthe model presented in this study can serve as a reasonable approximation.Changes in fluid properties may be caused by fluid injection and are likely tobe approximately circular.
The objective of this work was to develop a general analytical solution forthe pressure transient response in reservoirs which contain an internalcircular discontinuity caused by any of the factors mentioned.
It is assumed in the model considered in this study that only one activewell is present within the area of influence of the pressure disturbance. Twodistinct situations may occur in a real case: the well may be located eitherinside or outside the discontinuity region. The pressure transient solutionsfor these two cases will be developed in the following sections. A discussionof the effects of various parameters on the pressure response will beprovided.
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