Abstract
This paper presents a critical analysis of some recently published papers on naturally fractured reservoirs. These published papers on naturally fractured reservoirs. These publications have pointed out that for a publications have pointed out that for a matrix-to-fracture-gradient flow regime, the transition portion of pressure test data on the semilog plot develops a portion of pressure test data on the semilog plot develops a slope one half that of the late-time data. We show that systems under pseudosteady state also may develop a 1:2 slope ratio. Examples from published case studies are included to show the significant errors associated with the characterization of a naturally fractured system by using the 1:2 slope concept for semicomplete well tests.
Introduction
Idealistic models of the dual-porosity type often have been recommended for interpretation of a well test in naturally fractured reservoirs. The evolutionary aspects of these models have been reviewed by several authors. Gradual availability of actual field tests and recent developments in analytical and numerical solution techniques have helped to create a better understanding of application and limitation of various proposed models. Two important observations should be made here. First, just as it is now recognized that classical work published by Warren and Root in 1963 was not the end of the line for interpretation of the behavior of naturally fractured systems, the present state of knowledge later may be considered the beginning of the technology. Second, parallel with the ongoing work by various investigators who progressively include more realistic assumptions in their progressively include more realistic assumptions in their analytical modeling, one needs to ponder the implication of these findings and point out the inappropriate impressions that such publications may precipitate in the mind of practicing engineers. practicing engineers. This paper is intended to scrutinize statements published in recent years about certain aspects of the anticipated transition period developed on the semilog plot of pressure-drawdown or pressure-buildup test data. pressure-drawdown or pressure-buildup test data. The Transition Period
In the dual-porosity models published to date, a naturally fractured reservoir is assumed to follow the behavior of low-permeability and high-storage matrix blocks in communication with a network of high-permeability and low-storage fractures. The difference among the models has been the assumed geometry of the matrix blocks or the nature of flow between the matrix and the fracture. However, in all cases, it is agreed that a transition period develops that is strictly a function of the matrix period develops that is strictly a function of the matrix properties and matrix-fracture relationship. Fig. 1 shows properties and matrix-fracture relationship. Fig. 1 shows a typical semilog plot depicting the transition period and the parallel lines. Estimation of Warren and Root's proposed and to characterize a naturally fractured proposed and to characterize a naturally fractured system requires the development of the transition period.
The Warren and Root model assumes a set of uniformly distributed matrix blocks. Furthermore, the flow from matrix to fracture is assumed to follow a pseudosteady-state regime. Under such conditions, in theory, this period is an S-shaped curve with a point of inflection. Uldrich and Ershaghi developed a technique to use the coordinates of this point of inflection for estimating and under conditions where either the early- or the late-time straight lines were not available.
Kazemi and de Swann presented alternative approaches to represent naturally fractured reservoirs. They assumed a geometrical configuration consisting of layered matrix blocks separated by horizontal fractures. Their observation was that for such a system the transition period develops as a straight line with no inflection point. Bourdet and Gringarten identified a semilog straight line during the transition period for unsteady-state matrix-fracture flow. Recent work by Streltsova and Serra et al emphasized the transient nature of flow from matrix to fracture and pointed out the development of a unique slope ratio. These authors, later joined by Cinco-L. and Samaniego-V., stated that under a transient flow condition, the straight-line shape of the transition period develops a slope that is numerically one-half the slope of the parallel straight lines corresponding to the early- or late-time data.
It was further pointed out that the transient flow model is a more realistic method of describing the matrix-fracture flow. As such, they implied that in the absence of wellbore-storage-free early-time data, or late-time data in the case of limited-duration tests, one may use the slope of the transition straight line and proceed with the estimation of the reservoir properties.
Statement of the Problem
The major questions that need to be addressed at this time are as follows.
SPEJ
P. 445
Interference test interpretation in naturally fractured reservoirs