Summary
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.
Introduction
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.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
13 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
22 August 2007
- Manuscript approved:
22 September 2007
- Version of record:
25 April 2008
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