This paper describes a new method for estimating average reservoir pressure from long-pressure-buildup data on the basis of the classical Muskat plot. Current methods for estimating average reservoir pressure require a priori information about the reservoir and assume homogeneous reservoir properties or use empirical extrapolation techniques.
The new method applies to heterogeneous reservoirs and requires no information about reservoir or fluid properties. The idea of the method is to estimate from the pressure derivative the first few eigenvalues of the pressure-transient decay modes. These values are characteristic of the reservoir and fluid properties, but not of the pressure history or well location in the reservoir. The smallest eigenvalue is used to extrapolate the long-time behavior of the transient to estimate the final reservoir pressure. The second eigenvalue can be used to estimate the quality of the estimate.
Numerical tests of the method show that it estimates average reservoir pressure accurately, even when the reservoir is heterogeneous or when partial-flow barriers are present. Examples with real data show that the behavior predicted by the theory is actually observed.
We expect the method to have value in reservoir limits testing, in making consistent estimates of average reservoir pressure from permanent downhole gauges, and in characterizing complex reservoirs.
Several different methods of interpreting pressure-buildup data to obtain average reservoir pressure have been proposed (Muskat 1937; Horner 1967; Miller et al. 1950; Matthews et al. 1954; Dietz 1965) in the past, and in recent years some new techniques have appeared in the literature (Mead 1981; Hasan and Kabir 1983; Kabir and Hasan 1996; Kuchuk 1999; Chacon et al. 2004). Larson (1963) revisited the Muskat method and put it on a firm theoretical ground for a homogeneous cylindrical reservoir. Some of the existing techniques depend on knowledge of the reservoir size and shape and assume homogeneous properties (Horner 1967; Miller et al. 1950; Matthews et al. 1954; Dietz 1965). Such methods may result in uncertain predictions when reservoir data are unavailable or reservoir heterogeneity exists. The inverse time plot by Kuchuk (1999) is essentially a modification of Horner's method (1967) and works well in reservoirs that can be treated as infinite during the time of the test. The hyperbola method proposed by Mead (1981) and further developed by Hasan and Kabir (1983) is an empirical technique, not based on fundamental fluid flow principles for bounded reservoirs (Kabir and Hasan 1996). Chacon et al. (2004) develop the direct synthesis technique, in which conventional theory is used to derive an average pressure directly from standard log-log plots. Homogeneous properties and radial symmetry are assumed. Muskat's original derivation was a wellbore storage model. Larson reinterpreted Muskat's method and derived relationships showing how Muskat's plot could be used to estimate average reservoir pressure in a cylindrical, homogeneous reservoir. This paper revisits the ideas underlying Larson's paper. Similar ideas are shown to hold for heterogeneous reservoirs of any shape. A new analysis technique replacing the Muskat plot by a plot of the pressure derivative simplifies the determination of average reservoir pressure. It is shown that parameters from analysis of a long buildup on a reservoir can be used in subsequent buildup tests to shorten the required time of the subsequent buildups. Finally, estimates for time required for a buildup in homogeneous reservoirs of any shape are given.