Abstract
Constant producing pressure solutions that define declining production rates with time for a naturally fractured reservoir are presented. The solutions for the dimensionless flow rate are based on a model presented by Warren and Root. The model was extended to include constant producing pressure in both infinite and finite systems. The results obtained for a finite no-flow outer boundary are new and surprising. It was found that the flow rate shows a rapid decline initially, becomes nearly constant for a period, and then a final decline in rat,- takes place.A striking result of the present study is that ignoring the presence of a constant flow rate period in a type-curve match can lead to erroneous estimates of the dimensionless outer radius of a reservoir. An example is presented to illustrate the method of type-curve matching for a naturally fractured system.
Introduction
Naturally fractured reservoirs consist of heterogeneous porous media where the openings (fissures and fractures) vary considerably in size. Fractures and openings of large size form vugs and interconnected channel, whereas the tine cracks form block systems which are the main body of the reservoir (Fig. 1). The porous blocks store most of the fluid in the reservoir and are often of low permeability, whereas the fractures have a low storage capacity and high permeability. Most of the fluid flow will occur through the fissures with the blocks acting as fluid sources. Even though the volumetric average permeability in a naturally fractured system is low, such systems often exhibit an effective permeability that is higher than the block matrix permeability, and behave differently from ordinary homogeneous media.
These systems have been studied extensively in the petroleum literature. One of the first such studies was published by Pirson in 1953. In 1959, Pollard presented one of the first pressure transient models available for interpretation of well test data from two-porosity systems. The most complete analysis of transient flow in two-porosity systems was presented in 1960 by Barenblatt and Zheltov. The Warren and Root study in 1963 is considered the forerunner of modern interpretation of two-porosity systems. Their paper has been the subject of study by many authors. The behavior of fractured systems has long been a topic of controversy Many authors have indicated that the graphical technique proposed by Pollard in 1959 is susceptible to error caused by approximations in the mathematical model. Nevertheless, the Pollard method still is used. The most complete study of two-porosity systems appears to be the Mavor and Cinco-Ley study in 1979. This study considers wellbore storage and skin effect, and also considers production, both at constant rate and at constant pressure. However, little information is presented concerning the effect of the size of the system on pressure buildup behavior.Although decline curve analysis is widely used, methods specific to two-porosity fractured systems do not appear to be available. It is the objective of this paper to produce and study decline curve analysis for a naturally fractured reservoir. The Warren and Root model was chosen as the basis for this work.
Partial Differential Equations
The basic partial differential equations for fluid flow in a two-porosity system were presented by Warren and Root in 1963. The model was extended by Mavor and Cinco-Ley to include wellbore storage and skin effect.
SPEJ
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Decline curve analysis using a pseudo-pressure-based interporosity flow equation for naturally fractured gas reservoirs
