The Use of Interpolation to Obtain Shape Factors for Pressure Buildup Calculations

As pointed out by Brons and Miller, it is convenient to use a shape factor to calculate drainage region static pressures from pressure buildup tests. If the well is produced pressures from pressure buildup tests. If the well is produced at a constant rate long enough for pseudo steady-state conditions to be reached prior to shut-in, the drainage region average pressure may be calculated from (1) where: p = drainage region average pressure, p* = shut-in pressure linearly extrapolated toinfinite shut-in time on a plot of p vs log[ ], A = drainage area of the well, and CA = shape factor. Shape factors have another useful significance. Brons and Miller showed that (2) where the constant y is the exponential of Euler's constant and has the value 1.781. Eq. 2 is the general flow equation that describes the pseudo steady-state flow for any bounded (closed) shape. Both Brons and Miller, and Dietz have tabulated values for the shape factor C, for various drainage region shapes and well locations. Nevertheless, a value of C, often is needed for a system that is not included in the tabulations. In this case the techniques of Ramey and of Earlougher et al. can be used to calculate the needed shape factor. However a simpler method may be used in many instances. This method consists of making a plot of C, against some shape-determining quantity (such as well location or length to-width ratio of a rectangular system) and graphically interpolating. Fig 1 And 2 are examples of such plots. Fig. 1 shows the shape factor plotted against well location for three rectangular systems. To assume the accuracy of this plot, values of C4 have been calculated for a few points not given in the Dietz table. Actually, the figure could be constructed without calculating these Ca values if slightly inaccurate results were acceptable, or if only well locations for 0.25 less than x less than 0.5 were of interest. P. 449