A Note on Pressure Buildup Curves

Abstract

In 1954 Matthews, Brons and Hazebroek presented a method for correcting extrapolated buildup pressures on a Theis or Horner-type plot to static pressure. Matthews, Brons and Hazebroek considered buildup in a large number of geometric reservoir shapes with wells at various locations within a particular shape. In 1961 Brons and Miller pointed out that the presence of pseudo-steady state was indicated for the various shapes at long producing times, and that simple flow equations involving a producing times, and that simple flow equations involving a shape factor could be written for this condition. In 1965 Dietz extended this idea to show that static pressure could be found on the extension of the buildup straight line at a dimensionless time of where A = drainage shape area, CA = shape factor and other symbols are SPE standard. Dietz work generalized the older Miller-Dyes-Hutchinson buildup method to geometric shapes other than circular. As stressed by Dietz, the method assumed that the well had been produced to pseudo-steady state prior to shut in. Neither pseudo-steady state prior to shut in. Neither Matthews-Brons-Hazebroek nor Dietz cataloged the actual buildup curves involved in the various shapes, although a few cases were shown as examples. The purpose of this article is to present the Miller-Dyes-Hutchinson type of pressure buildup curves for most of the Matthews-Brons-Hazebroek shapes. As would be expected, assymetric location of a well in a particular drainage shape may lead to unusual bends in the pressure buildup curves. Because it is currently becoming practice to infer reservoir heterogeneities from the shape of the buildup curve, it appears useful to be aware of anomalies which may be a result of well location and drainage shape. Figs. 1 through 4 present Miller-Dyes-Hutchinson pressure buildup curves for the rectangular shapes considered. pressure buildup curves for the rectangular shapes considered. Symbols used are SPE standard; It refers to elapsed time after shut-in. Fig. 1 shows buildup curves for a square reservoir shape with three different well locations. The heavy lines are the buildup curves. Curves 1 and 2 are similar; it would be impossible to detect the effect of movement of the well from an actual buildup curve. Curve 3, however, has a peculiar bend at a dimensionless buildup time of about 0.02. This bend could be misinterpreted as the result of a general fracturing in the reservoir as studied by Warren and Root. Another interesting result is indicated by the dashed lines on Fig. 1. These lines represent the extrapolation of the initial straight line, and have the usual slope of 1.151. The intersection of the dashed lines with the ordinate at zero occurs at a dimensionless buildup time equal to the reciprocal of the shape factor Ca, for each shape. Note that the shape factors shown are the modified ones reported by Earlougher et al. P. 119