The paper was presented at the 59th Annual Technical Conference and Exhibition held in Houston, Texas, September 16–19, 1984. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write SPE, 6200 North Central Expressway, Drawer 64706, Dallas, Texas 75206 USA. Telex 730989 SPEDAL.
This paper examines applicability and limitations on the use of rectangular hyperbolas to analyze pressure buildup data, with emphasis on the pressure buildup data, with emphasis on the determination of average pressure and flow capacity. It is shown that the method can be used with confidence only if it is applied to data that can also be analyzed by conventional semilog methods, and that it for such data is essentially equivalent to the conventional methods in terms of information needed and information obtained. If we use semilog data, then we can determine the flow capacity from the slope of the hyperbola, and we can determine the average pressure indirectly from the asymptote, provided we pressure indirectly from the asymptote, provided we know the drainage area and the MBH function of the reservoir. Following stabilized flow we only need the shape factor in addition to the area. If we use the direct approach, and assume that the asymptote is equal to the average pressure, then we need the same type of information to make a proper choice of interval where the hyperbola should match the buildup curve. For the direct approach we will normally get an estimate of average pressure that is less than m/1.151 psi (kPa) above the last wellbore pressure being used in the analysis, where m is the conventional semilog slope. Moreover, if we use only semilog buildup data following pseudosteady-state flow, then we can only get an accurate estimate of average pressure by this approach if the shape factor is close to 21, or higher.
If nothing is known about the reservoir, then the hyperbola method can be used to get a rough estimate of the average pressure, but with a high degree of uncertainty if we only have data from a short buildup period. This claim follows from the many examples period. This claim follows from the many examples included in this paper of asymptotes determined from hyperbolas matched to dimensionless synthetic buildup data plotted vs. interval midpoints.
The Miller-Dyes-Hutchinson (MDH), Matthews-Brons-Hazebroek (MBH), and Dietz methods can be used to determine the average, or static, reservoir pressure for closed reservoirs, and the method of Kumar and Ramey can be used for constsant-pressure squares. These methods are based on an indirect use of exact pressure solutions, and hence require knowledge of the size and shape of the drainage area, and of the outer boundary condition. For a given test, all or part of this information might be missing, in which part of this information might be missing, in which case approximation must be used to carry out the analysis. This leads to uncertainties in estimates of average pressure and other parameters that depend on this information.
A different approach to pressure buildup analysis was suggested by Mead. He observed that pressure buildup curves closely resemble rectangular hyperbolas, and therefore asserted that the average reservoir pressure should be equal to the horizontal a sympotote of a hyperbola matched to a buildup curve. Mead supported his assertion by examples.
Hasan and Kabir explored Mead's empirical results further, and presented a theoretical justification for the hyperbola approach to buildup analysis when both the drawdown and buildup transients are in the inifinte-acting period. Their work was based on a truncated series expansion of the logarithmic solution. Hasan and Kabir successfully and flow conditions, and concluded that the rectangular hyperbola approach can generally be used to determine the average, or static, reservoir pressure directly from field data, and also that good pressure directly from field data, and also that good estimates can be obtained for flow capacity and skin. This without prior knowledge of the size, shape, and type of the reservoir being tested. An analysis of the inherent limitations on the method was not included in Ref. 6.
The general conclusions in Ref. 6 attracted criticism from Humphreys and Bowles and White. In their replies, Hasan and Kabir acknowledged the superiority of Horner analysis of infinite acting reservoirs, but reaffirmed the validity of the method for other cases, again supported by examples.