Transient Pressure Behavior in Vertically Fractured Reservoirs
Authors: Russell D.G. , Truitt N.E. 
Published: December 2007

Abstract
The transient pressure behavior of a well which produces a single compressible fluid through a single-plane vertical fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited radial extent, and to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are sometime inaccurate. As fracture penetration increases radially, kh values calculated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the calculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimension less pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells.
Introduction
Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs. During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al. first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells: however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora and Dyes, Kemp, and Caudle employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study were
to obtain synthetic pressure build-up and flow test curves to assess the effects of a vertical fracture, and to determine the modifications which need to be made to conventional pressure build-up and flow test analysis theory for the case of a vertically fractured well.
JPT
P. 1159ˆ