Transient Pressure Behavior Of Naturally Fractured Reservoirs
Authors: Mavor M.J. , Cinco-Ley H. 
Published: December 2007

Abstract
The naturally fractured reservoir model presented by Warren and Root was extended to improve analysis of field data and to account for practical wellbore and reservoir conditions. These conditions include wellbore storage and damage, and constant producing pressure in infinite define pseudo-steady state and pressure in infinite define pseudo-steady state and long time reservoir behavior.

Introduction
In recent years, numerous models have been proposed to explain transient pressure behavior of naturally fractured reservoirs. The term "naturally fractured" can be misleading. In reality, these models consider a reservoir composed of two porous media regions, primary and secondary porosity. Primary porosity is primary and secondary porosity. Primary porosity is synonymous with the matrix rock whose properties are controlled by sedimentation, cementation, and lithification of the original deposits. Secondary porosity, i.e., the fracture network, is considered to porosity, i.e., the frac ture network, is considered to have been developed subsequent to the primary system as a result of mechanical deformation, solution, or dolimitization of the original matrix.
Streltsova presented a thorough discussion of fluid flow in fractured reservoirs and included the classification system illustrated in Figure 1. Four media categories are utilized as follows. The first, a fractured medium, consists of a formation whose primary porosity contains the majority of the fluid primary porosity contains the majority of the fluid storage volume while the secondary porosity contributes the transmissivity of the zone. This is the situation most frequently modeled to describe naturally fractured reservoir pressure. A purely fractured medium was envisioned as a system whose matrix permeability and porosity were negligible. In this case, the storativity and transmissivity of the reservoir would be due entirely to the fracture network. This classification is one limiting form of the first category behavior. The third group is a double porosity medium in which the storage volumes of the primary and secondary regions are of the same order of magnitude while the transmissivity is a result of the fracture system. The final classification is a heterogeneous medium. In this case, the fracture system is filled with a material of lower permeability than the matrix.
This study concentrates on the first two categories, fractured and purely fractured media. Both treat the reservoir as a continuum. The smallest incremental volume which is visualized mathematically is of an extent large enough to include both primary and secondary porosity. The degree of fracturing is such that the fractures appear to be homogeneously distributed throughout the matrix.
Warren and Root's version of a naturally fractured reservoir model was chosen as the basis for this work for several reasons. The primary reason for this work many publications have been presented which support the analytic results of Warren and Root even with varying idealizations. The model has been applied to interpretation of field data with apparent success, indicating the model's practicality. From an engineering standpoint, these conditions are a necessity.
The study is discussed in four section; Mathematical Development and Idealizations, Limiting Forms of Reservoir Behavior, Infinite Reservoirs, and Closed Reservoirs, Conclusions from these sections are presented at the end of the paper. presented at the end of the paper.

Mathematical Development and Idealizations
In order to develop equations which describe fluid flow in naturally fractured reservoirs, idealizations are necessary to obtain a model in a mathematically tractable form. This section discusses these idealizations and the method of solution of the governing equations.
This study considers a horizontal radial reservoir initially at uniform pressure with impermeable upper and lower boundaries. The system was treated as a continuum with the fracture network superimposed on the primary porosity. This idealization resulted in two pressures, matrix and fracture, at each location in space.