A Simple Method for Determining Well Pressure in Closed Rectangular Reservoirs

Abstract

In 1968, Earlougher et al., introduced a "buildingblock" concept, using a constart-rate well producing from the center of a closed square, to generate solutions for pressure behavior in several rectangular systems. Tables of the dimensionless pressure drop function for the square system are presented in Ref. 1, along with illustrations of the technique. Their procedure, while a step toward reducing laborious procedure, while a step toward reducing laborious computations, can sometimes be quite tedious. This note describes a further simplification for obtaining dimensionless pressures for these other rectangular systems at the producing well; other points within these systems are not considered. Conveniently, Earlougher et al. have tabulated the Matthews-Brons-Hazebroek pressure correction function, PDMBH, for 16 closed rectangular systems. These correction functions provide the basis from which the dimensionless wellbore pressure drop functions can easily be obtained. In a recent comprehensive review of pressure buildup analysis, it was shown thatwhereSolving Eq. 1 for pD yieldsIt is clear from Eq. 5 that pD is a function of pDMBH, tDA, and A/rw2. Thus, given pDMBH and A/rw2 for a particular system, pD as a function of tDA can be particular system, pD as a function of tDA can be calculated directly. Columns 2 and 3 of Table 1 present the pD and pDMBH data of Ref. 1 for the case of a well in the pDMBH data of Ref. 1 for the case of a well in the center of a square with it value for A/rw of 2,000. The pD data tabulated in Column 4 are obtained by direct substitution of tDA and pDMBH of Columns 1 and 3, respectively, into Eq. 5. As can be seen, the solutions in Columns 2 and 4 are identical. For dimensionless times less than those given in Table 1, pD can be obtained from pD can be obtained fromFor times greater than those given in Table 1, pD can be obtained bywhere CA is the reservoir shape factor, and is be Euler constant - approximately 1.7811. P. 1305