Transient Pressure Analysis for Fractured Wells
Authors: Cinco-Ley Heber , Samaniego-V. Fernando 
Published: December 2007

Summary
A new technique is presented for analyzing pressuretransient data for wells intercepted by afinite-conductivity vertical fracture. This method is basedon the bilinear flow theory, which considers transientlinear flow in both fracture and formation. It isdemonstrated that a graph of p vs. t 1/4 produces astraight line whose slope is inversely proportional toh (k b) 1/2 . New type curves are presented thatovercome the uniqueness problem exhibited by othertype curves.

Introduction
A large amount of information concerning well testanalysis has appeared in the literature over the lastthree decades. As a result of developments in thisarea, three monographs and one book havebeen published covering different aspects of pressuretransient analysis. Ramey also has presented areview on the state of the art.The analysis of pressure data for fractured wellshas deserved special attention because of the numberof wells that have been stimulated by hydraulicfracturing techniques. A summary of the work doneon flow toward fractured wells' was presented byRaghavan' in 1977.It was recognized early that intercepting fracturescan strongly affect the transient flow behavior of awell and that, consequently, the application ofclassical methods to the analysis of transientpressure data in this situation may produce erroneous pressure data in this situation may produce erroneous results. Several methods were proposed to solvethis problem.These analysis techniques consider a wellintersected by either an infinite-conductivity verticalfracture or a uniform-flux vertical fracture.Cinco-Ley et al. demonstrated that the assumption ofinfinite fracture conductivity is valid wheneverthe dimensionless fracture conductivity(k b /kx) &gt;300; all other cases, such as thoserepresented by long or poorly conductive fractures, must be analyzed by considering a finite-conductivityfracture model.Exploitation of low-permeability gas reserves hasrequired stimulation of wells by massive hydraulicfracturing (MHF) techniques. Vertical fractures oflarge horizontal extension are created as a result ofthis operation; consequently, pressure drop along thefracture cannot be neglected.Several papers have been published on thebehavior of finite-conductivity vertical fractures.Type-curve matching has been proposed as ananalysis method under these conditions; however, some regions of the curves present a uniquenessproblem in the analysis. Barker and Ramey problem in the analysis. Barker and Ramey indicated that the use of published type curves becomespractical when a large span of pressure data is practical when a large span of pressure data is available.The purpose of this work is to present a newinterpretation technique for early-time pressure datafor a well intercepted by a finite-conductivity verticalfracture, including the criteria to determine the endof wellbore storage effects. In addition, new typecurves are discussed to overcome the uniquenessproblem exhibited by previous curves at intermediate problem exhibited by previous curves at intermediate and large time values.

Transient Pressure Behaviorfor Fractured Wells
Consider a vertically fractured well producing at aconstant flow rate, q, in an infinite, isotropic, homogeneous, horizontal reservoir that contains aslightly compressible fluid of constantcompressibility c, and viscosity mu. The porous mediumhas a permeability k, porosity phi, thickness h, andinitial pressure p .
JPT
P. 1749