Abstract

A new model for the analysis of constant rate well test data from naturally fractured reservoirs is presented. The model considers three sets of presented. The model considers three sets of orthogonal fractures with fluid flow from the fractures to the well and from the rock matrix to the fractures. In comparison to other models for naturally fractured reservoirs the present model allows fully transient fluid flow from the rock matrix to the fractures and a cubic geometry of the matrix blocks.

The model has been used to develop type curves for the analysis of drawdown and build-up tests as well as pressure transient data from observation wells. The reservoir systems considered include an infinite and a finite (no-flow outer boundary) system and a system with a constant pressure outer boundary. The effects of wellbore storage and skin are illustrated. The model is applied to field data to illustrate the method of analysis and the applicability of the model.

Introduction

In the last two decades considerable work has been devoted to the analysis of well test data from naturally fractured reservoirs. The need for new analysis methods arose because of the distinct differences in the pressure response at wells completed in homogeneous porous media reservoirs to that of wells penetrating naturally fractured reservoirs. The approach used in developing analysis methods for well test data of naturally fractured reservoirs is to treat the fractures and the rock matrix separately, but couple their response by means of interaction terms. Thus, the fractures represent high permeability for fluid transport into the well, whereas the permeability for fluid transport into the well, whereas the rock matrix has a much lower permeability, and provides gradual fluid drainage to the fractures. On the provides gradual fluid drainage to the fractures. On the other hand, the fraction of the total volume occupied by the fractures (fracture porosity) is very small, and consequently the bulk of the fluids is stored in the rock matrix. This approach is currently referred to as the double porosity approach, and was developed by Barenblatt et al., and Warren and Root. They considered the model shown in Figure 1, in which each point in the system is assigned two pressures, one point in the system is assigned two pressures, one for the fractures, p2, and the other for the rock matrix p1. Thus, for a rigorous solution to the problem, one must solve diffusion equations for both media. problem, one must solve diffusion equations for both media. However, Barenblatt et al., and Warren and Root assumed a quasi-steady flow between the rock matrix and the fractures. This approximation simplifies the problem considerably so that solutions for the problem considerably so that solutions for the pressures in the fractures and rock matrix can easily be pressures in the fractures and rock matrix can easily be obtained in the Laplace domain.

Warren and Root found that the pressure solution could be characterized by two parameters lambda and omega. The parameter lambda represents the ratio of the rock matrix parameter lambda represents the ratio of the rock matrix permeability to that of the fractures; whereas omega permeability to that of the fractures; whereas omega represents the ratio of the fracture compressibility to the compressibility of the total system (see nomenclature for definitions of lambda and omega). For naturally fractured reservoirs typical values of lambda and omega fall within the ranges of 10(-3) to 10(-9) and 0.1 to 0.001, respectively.

Subsequent to the studies of Barenblatt et al. and Warren and Root, various studies have been published on the applicability and extension of their published on the applicability and extension of their models. Odeh used a model similar to that of Warren and Root, and concluded that the pressure behavior in a naturally fractured reservoir is identical to that of homogeneous porous media reservoirs. However, in his study Odeh only considered cases where the interporosity flow factor lambda was relatively large (greater than 10(-3)), in which case the differences in the transient pressure behavior are only apparent at very early times. pressure behavior are only apparent at very early times. Later, Mavor and Cinco-Ley extended the solution by Warren and Root to include the effects of wellbore storage and skin.

Many workers have developed models that do not require the approximation of quasi-steady fluid flow between the rock matrix and the fractures. However, due to the three-dimensional nature of the model considered by Barenblatt et al. and Warren and Root (Fig. 1) the treatment of transient interporosity flow is mathematically very difficult, and has been accomplished only by more or less drastic simplification of matrix block geometry. Deruyck, Kazemi, Streltsova and Serra et al., considered a slab model, whereas de Swaan, Najurieta, and Cinco-Ley et al., consider models based on spherically shaped matrix blocks.

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