Interference Analysis In Bounded Systems

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Abstract
Dimensionless pressure behaviour is tabulated at various points in several closed rectangular drainage shapes. For each shape? Po data aregiven for a single constant-rate well and several "observation" wells.Additional well-observation point locations are obtained by applying the principle of reciprocity to the tables. The tables presented may be used foranalyzing interference test data in bounded systems as discussed in this paper.Such analysis allows estimation of permeability, k. storage, ?c and systemextent, A. The tables may also be used to calculate transient pressure behaviour in closed multiple-well systems by using the principle of superposition. Introduction: IN 1954, Matthews, Brons and Hazebroek(1) discussed the determination of static pressure buildup tests for a well in a variety ofclosed drainage shapes. Later, Brons and Miller(2) and Dietz(3) demonstrated other pressure buildup interpretive methodsfor these closed shapes. Ramey(-!l showed that a dimensionless pressure introduced by :Matthews, Brons and Hazebroek could be used to obtain the conventional dimensionless pressure based on the pressure difference(Pr − pwf). It is dear that the authors of Ref. 1 also understood this relationship. The Matthews-Brons-Hazebroek function may be usedto obtain the dimensionless pressure only at the well, however. For thisreason, Earlougher et al.(5) presented dimensionless pressures atthe well and at other locations within a closed square (infinite-square array).These authors also demonstrated that the infinite-square array may be used togenerate a large variety of other rectangular shapes by superposition. In theinterest of space saving, they presented only the detailed behaviour of a wellin the center of a square. Although it is reasonably simple to produce the pressure behaviour at any location within a closed rectangular shape bysuperposition with modern digital computers, the authors have found itincreasingly useful to have tables of dimensionless pressures for the: Matthews-Brons-Hazebroek shapes. Thus, the main purpose of this paper is topresent tables of the dimensionless pressure at the well and at several otherlocations within a variety of closed rectangles with a well producing atconstant rate. Because a well in a closed rectangle presents such an important flow problem inconventional reservoir engineering, the results of this study have widefundamental application. The most important application of the information isin setting closed outer boundary effects. Fluid injection problems and constant-pressure outer boundary conditions may also be solved by means of thesubject data and superposition. An example indicates applications tointerference testing. Theory: Matthews, Brons and Hazebroek(1), and Earlougher, etal.(5) have indicated how the principle of superposition may beapplied to the line source solution(6) to generate pressure behaviour in closed rectangular shapes. The technique applies both at the welland at distant points. By using the super position principle, it is possible to add such Po data together, either in space or in time, to obtain additional results.

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