Applied Pressure Analysis for Fractured Wells
Authors: Gringarten A.C. , Ramey H.J. , Raghavan R. 
Published: December 2007

A number of recent studies have resulted in an increased understanding of fractured-well behavior. Two of these studies provide new information on applying log-log type-curve matching procedures to pressure data obtained from fractured wells. This paper compares the applicability of type-curve and conventional semilog methods.

Introduction
The pressure behavior of fractured wells is of considerable interest because of the large number of wells that intersect fractures. As a result of a number of studies, an increased understanding of fractured-well behavior has been obtained. Although the shape of actual fractures is undoubtedly complicated, most studies assume that real fractures may be ideally visualized as planes intersecting the wellbore. It is generally believed that hydraulic fracturing normally results in one vertical fracture, the plane of which includes the wellbore; however, it is also plane of which includes the wellbore; however, it is also agreed that, if formations are shallow, horizontal fractures can result. The specific orientation of the fracture plane with respect to the wellbore may be subject to debate if the well intersects a natural fracture.
Two recent studies provide new information whereby log-log type-curve matching procedures may be applied to pressure data obtained from fractured (vertical or horizontal) wells. These studies also showed that, under conditions that would appear normal, it is likely that horizontal and vertical fractures would affect well behavior sufficiently such that the orientation, vertical vs horizontal, could be determined. The purpose of this paper is to illustrate the applicability of the results paper is to illustrate the applicability of the results obtained in Refs. 1 and 2.

Vertically Fractured Wells
As mentioned in Ref. 1, new solutions for the transient pressure behavior of a vertically fractured well were pressure behavior of a vertically fractured well were needed because earlier studies were not blended for type-curve analysis. This study examined two boundary conditions on the fracture plane. The first solution, like earlier studies, assumed that the fracture plane is of infinite conductivity. This implies that there is no pressure drop along the fracture plane at any instant in pressure drop along the fracture plane at any instant in time. The second solution, called the uniform-flux solution, gives the appearance of a high, but not infinite, conductivity fracture. (This boundary condition implies that the pressure along the fracture plane varies.) Application of these solutions to field data indicates that the uniform-flux solution usually matches pressure behavior of wells intersecting natural fractures better than does the infinite-conductivity solution. On the other hand, the infinite-conductivity solution often matches the behavior of hydraulically fractured, propped fractured wells better than does the uniform-flux solution.
The Infinite-Conductivity Vertical Fracture in A Square Drainage Region
Gringarten et al. have presented drawdown data for an infinite-conductivity vertical fracture located at the center of a closed-square drainage region and producing a lightly compressible constant-viscosity fluid at a constant rate. The solution for the producing pressure at time t is
kh PwD (tD, Xe/Xf) = (pi - pwf),......(1) 141,2 qB
where
0.000264 kt tD = .........................(2) c Xf2
JPT
P. 887