Transient Pressure Analysis for Fractured Wells

Abstract

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) >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

Two-dimensional numerical investigations on the termination of bilinear flow in fractures

“…E. Ortiz R. et al: Two-dimensional numerical investigations with previous theoretical and numerical analyses (Cinco-Ley and Samaniego-V., 1981;Weir, 1999), the derivatives follow a straight line with a slope of 1/4 over over a certain period of dimensionless time. For sufficiently high dimensionless fracture conductivities (i.e., T D 1), the derivative first turns counterclockwise into a straight line with slope ½cor-responding to formation linear flow, fully developed only for T D > 50 (Fig.…”

“…A1 in Cinco-Ley and Samaniego-V., 1981), the transient term on the left side appears multiplied by the diffusivity ratio κ = D m /D F . When this ratio is small, the effect of the intrinsic transient term on wellbore pressure becomes important only for extremely small values of time, and thus can be neglected for bilinear flow (see Cinco-Ley and Samaniego-V., 1981;Riley, 1991).…”

“…The theoretical background of bilinear flow was first presented by Cinco-Ley et al (1978) and Cinco-Ley and Samaniego-V. (1981), who studied the solution of (1) and (2) using a two-dimensional numerical model and Laplace transform, respectively. They demonstrated that the pressure in a vertically fractured well producing at constant flow rate is proportional to the fourth root of time in the bilinear flow regime.…”

“…The time window, during which this fourth-root relation can be observed, is however finite, and thus long-term predictions -of great practical importance for exploitation of liquid or gaseous resources -are erroneous when using this relationship. Therefore, constraining estimates of the end time of bilinear flow received attention in previous research (Cinco-Ley and Samaniego-V., 1981;Weir, 1999). Since radial flow dominated by the matrix properties develops when this time is exceeded, it specifically marks the end of the gain due to a stimulation operation involving hydraulic fracturing.…”

Three-dimensional and two-phase numerical simulation of fractured dry gas reservoirs

“…The efficiency of the first step depends on fracture dimension length "x f " and height "h f, " and the efficiency of the second step depends on fracture permeability "k f. " The importance of each of the steps can be analyzed using the concept of parameter fracture conductivity "F CD " defined as (Agarwal et al 1979;Cinco-Ley 1981): (w f is fracture width)…”