Summary
Decline-curve-analysis models are used frequently but still have many
limitations. Approaches of decline-curve analysis used for naturally fractured
reservoirs developed by waterflooding have been few. To this end, a
decline-analysis model derived on the basis of fluid-flow mechanisms was
proposed and used to analyze the oil-production data from naturally fractured
reservoirs developed by waterflooding. Relative permeability and capillary
pressure were included in this model. The model reveals a linear relationship
between the oil-production rate and the reciprocal of the oil recovery or the
accumulated oil production. We applied the model to the oil-production data
from different types of reservoirs and found a linear relationship between the
production rate and the reciprocal of the oil recovery as foreseen by the
model, especially at the late period of production. The values of maximum oil
recovery for the example reservoirs were evaluated with the parameters
determined from the linear relationship. An analytical oil-recovery model was
also proposed. The results showed that the analytical model could match the
oil-production data satisfactorily. We also demonstrated that the frequently
used nonlinear type curves could be transformed to linear relationships in a
log-log plot. This may facilitate the production-decline analysis. Finally, the
analytical model was compared with conventional models.
Introduction
Estimating reserves and predicting production in reservoirs has been a
challenge for many years. Many methods have been developed in the last several
decades. One frequently used technique is the decline-curve-analysis approach.
There have been a great number of papers on this subject.
Most of the existing decline-curve-analysis techniques are based on the
empirical Arps equations: exponential, hyperbolic, and harmonic. It is
difficult to foresee which equation the reservoir will follow. On the other
hand, each approach has some disadvantages. For example, the exponential
decline curve tends to underestimate reserves and production rates; the
harmonic decline curve has a tendency to overpredict the reservoir performance.
In some cases, production-decline data do not follow any model but cross over
the entire set of curves.
Fetkovich combined the transient rate and the pseudosteady-state decline
curves in a single graph. He also related the empirical equations of Arps to
the single-phase-flow solutions and attempted to provide a theoretical basis
for the Arps equations. This was realized by developing the connection between
the material balance and the flow-rate equations on the basis of his previous
papers.
Many derivations were based on the assumption of single-phase oil flow in
closed-boundary systems. These solutions were suitable only for undersaturated
(single-phase) oil flow. However, many oil fields are developed by
waterflooding. Therefore, two-phase fluid flow (rather than single-phase flow)
occurs. In this case, Lefkovits and Matthews derived the exponential decline
form for gravity-drainage reservoirs with a free surface by neglecting
capillary pressure. Fetkovich et al. included gas/oil relative permeability
effects on oil production for solution-gas drive through the pressure-ratio
term. This assumes that the oil relative permeability is a function of
pressure. It is known that gas/oil relative permeability is a function of fluid
saturation, which depends on fluid/rock properties.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
5 November 2003
- Revised manuscript received:
23 March 2005
- Manuscript approved:
30 March 2005
- Version of record:
15 June 2005
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