Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture

Abstract

Introduction During the last few years, there has been an explostion of information in the field of well-test analysis. Because of increased physical understanding of transient fluid flow, it is possible to analyze the entire pressure history of a well test, not just long-time data as in conventional analysis.1 It is now often possible to specify the time of beginning of the correct semilog straight line and determine whether the correct straight lie has been properly identified. It is also possible to identify wellbore storage effects, and the nature of wellbore stimulation as to permeability improvement, or fracturing, and to quantitatively analyze those effects. Such accomplishments have been augmented by attempts to understand the short-time pressure data from well testing - data that were often classified as too complex for analysis. One recent study of short-time pressure behavior2 showed that it was important to specify the physical nature of the stimulation in considering the behavior of a stimulated well. That is, stating that the van Everdingen-Hurst infinitesimal skin effect was negative was not sufficient to define short-time well behavior. For instance, acidized (but not acid-fractured) and hydraulically fractured wells might not necessarily exhibit the same behavior at early times, even though they could possess the same value of negative skin effect. In the same manner, hydraulic fracturing leading to horizontal or vertical fractures could produce the same skin effect, but with possibly different short-time pressure data. This could then provide a way to determine the orientation of fractures created by this type of well stimulation. In fact, it is generally agreed that hydraulic fracturing usually results in one vertical fracture, the plane of which includes the wellbore. Most studies of the flow behavior for a fractured well consider vertical fractures only.3–11 Yet it is also agreed that horizontal fractures could occur in shallow formations. Furthermore, it would appear that notch-fracturing would lead to horizontal fractures. Surprisingly, no detailed study of the horizontal fracture case had been performed until recently.12 A solution to this problem was presented by Gringarten and Ramey.13 In the course of their study, it was found that a large variety of new transient pressure behavior solutions useful in well and reservoir analysis could be constructed from instantaneous Green's functions.14 Possibilities included a well with a single vertical fracture in an infinite reservoir, or at any location in a rectangle.