Analysis of Pressure Buildup Tests in a Naturally Fractured Reservoir
Authors: Crawford G.E. , Hagedorn A.R. , Pierce A.E. 
Published: December 2007

A previously published model describing pressure-buildup behavior of naturally fractured reservoirs was combined with a nonlinear, least-squares regression technique to analyze buildup data. The model adequately described the buildup response and was useful for obtaining effective formation permeability in the cases studied.

Introduction
The pressure drawdown and buildup behavior of naturally fractured reservoirs has been investigated theoretically by several authors. Warren and Root depicted the fractured reservoir as a system of identical, rectangular parallelopipeds separated by a regular network of parallelopipeds separated by a regular network of fractures and derived a pressure-response function for this system. Two additional parameters were required to describe the interflow between the granular matrix porosity and that of the interconnecting fracture network. porosity and that of the interconnecting fracture network. The standard semilog plot of the buildup-pressure response vs shut-in time, neglecting wellbore storage effects, is characterized by parallel straight lines at "early" and "late" times, as shown in Fig. 1. The displacement and end points of these straight lines are functions of the two new parameters introduced into the model. Odeh's model for a naturally fractured reservoir and his predicted pressure response are essentially the same as those of Warren and Root. However, Odeh concluded that the effects of fractures would be negligible and the pressure response for a uniformly fractured reservoir pressure response for a uniformly fractured reservoir would be the same as that for a homogeneous reservoir. Unfortunately, Odeh based this conclusion on calculations using properties of a particular naturally fractured reservoir for which these effects were negligible. (The results of these calculations are consistent with those based on the Warren and Root model.) In addition, the expression for wellbore-pressure response contained two terms of opposite sign that were a result of the fracture-matrix interflow. Odeh concluded that these terms tended to cancel; thus, the fractures could be neglected in cases of homogeneous fracturing. These results, however, depend on the properties of the fracture-matrix system investigated and cannot be generalized to cover all homogeneously fractured reservoirs. In a discussion of Odeh's paper, Warren and Root published limited data that showed the effects of the fracture-matrix interflow can be prevalent in the buildup-pressure response. Kazemi approximated a naturally fractured reservoir with a layered system composed of a thin, highly conductive layer, representing the fracture, adjacent to a thicker layer with low conductivity and high storage capacity, representing the matrix. Pressure responses were obtained using numerical integration and were compared with those given by the Warren and Root model. The results agreed quite well, with some minor differences attributed to the removal of the Warren and Root approximation of pseudosteady-state flow between matrix and fractures. Kazemi concluded that the Warren and Root model was valid in reservoirs with uniform fracture distribution and with large contrast between matrix and fracture flow capacities. Although there is general agreement among these theories, only limited data have been published that can be used for their verification. Since most buildup tests are run with surface shut-in, the characteristic response of a naturally fractured system (if it is present) is probably often masked by wellbore-storage effects.
JPT
P. 1295