Wellbore Pressure Response in Naturally Fractured Reservoirs
Authors: Reynolds A.C. , Chang W.L. , Yeh N. , Raghavan R. 
Published: December 2007

Summary
Recently, a new flow regime has been identified for pressure drawdown or buildup data obtained from a well pressure drawdown or buildup data obtained from a well producing a naturally fractured reservoir. The identification producing a naturally fractured reservoir. The identification of this new, intermediate-time flow regime means that pressure data may exhibit as many as three semilog pressure data may exhibit as many as three semilog straight lines. A virtually complete analysis of well-test pressure data is possible when the data exhibit two or more pressure data is possible when the data exhibit two or more of the three possible semilog straight lines. In this work, we present type curves that can be used to obtain a virtually complete analysis of pressure data when only one of the three semilog straight lines is reflected by the data.
One model that frequently has been used assumes that a naturally fractured reservoir is equivalent to a system of plane horizontal fractures. The use of this model suggests that the pressure response should be similar to the pressure response in a two-layer reservoir. In this work, pressure response in a two-layer reservoir. In this work, we establish the conditions under which the pressure response in a two-layer reservoir with crossflow between the layers will be identical to the pressure response in a naturally fractured reservoir. The two-layer analog provides information on the well response when the matrix provides information on the well response when the matrix feeds directly into the wellbore.

Introduction
From the pressure transient analysis viewpoint, the classical naturally fractured reservoir model is the one proposed by Warren and Root. Their model assumes proposed by Warren and Root. Their model assumes "pseudosteady-state" flow in the matrix and yields an analysis procedure based on the existence of two parallel semilog straight lines.
Much recent work on naturally fractured reservoirs has assumed unsteady-state flow in the matrix. Although Kazemi considered unsteady-state flow in the matrix by using a numerical simulator as early as 1969, the main impetus for recent work has been provided by deSwaan, who obtained an analytical solution for the unsteady-state model. Using the deSwaan model, Serra et al., Streltsova, and Cinco-Ley and Samaniego independently derived the equation that describes a new flow regime. During this new flow regime, a semilog plot of drawdown (or buildup) pressure vs. time exhibits a semilog straight line of pressure vs. time exhibits a semilog straight line of slope m/2, where m is the slope of both the early- and late-time semilog straight lines of Warren and Root. The results of Refs. 4 through 6 indicate that drawdown or buildup pressure data may exhibit three semilog straight lines. As discussed in Refs. 4 through 6, when two or more of these semilog straight lines are present, a virtually complete analysis of pressure data is possible.
When field data exhibit only one of the three possible semilog straight lines, a complete analysis based solely on semilog techniques is not possible. In this work, we present new type curves that can be used to analyze present new type curves that can be used to analyze pressure data that reflect only the second or third semilog pressure data that reflect only the second or third semilog straight line. For this situation, the new type curves can be used to obtain a more complete analysis of well-test data obtained from naturally fractured reservoirs. The new type curves neglect wellbore storage effects and, thus, can be used only to analyze pressure data recorded after wellbore storage effects have become negligible. Refs. 6 and 7 present type curves for analyzing wellbore-storage-dominated data. These type curves suffer from the usual limitations of all wellbore storage and skin type curves. Specifically, it is difficult to obtain a unique match because data recorded after wellbore storage effects diminish have little character. The new type curves presented here should improve our ability to analyze the portion of the data that are not affected by wellbore storage effects.
We show that under certain conditions, our naturally fractured reservoir model (Fig. 1) is equivalent to a two-layer reservoir. The two-layer analog is used to determine the consequences of the assumptions made in Refs. 3 through 6 to obtain an analytical solution to the naturally fractured reservoir problem. In particular, we consider the effect of production directly from the matrix system, whereas the results of Refs. 3 through 6 assume all production is by way of the fracture system. In addition, we production is by way of the fracture system. In addition, we delineate conditions under which the analysis procedures of Ref. 4 can be applied to analyze well-test data obtained from a two-layer reservoir with crossflow between the layers.

Mathematical Model
We consider the flow of a slightly compressible fluid of constant viscosity in an isotropic naturally fractured reservoir of uniform thickness. As in Refs. 4 through 6, we use the model of deSwaan, which assumes that a fractured reservoir may be considered to be equivalent to a system of plane horizontal fractures as shown in Fig. 1. The rock properties of the matrix system are assumed constant, as are the rock properties of the fracture system.
JPT
P. 908