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

Several methods have been proposed in the literature for analyzing drawdown data for the determination of fracture conductivity of vertically fractured wells. These techniques have paved accurate, but in some cases the fracture conductivity calculated is much smaller than anticipated. This study shows that producing fractured wells at high flow rates will cause nondarcy effects in the fracture, resulting in a pessimistic fracture conductivity.Numerical and semianalytical models were developed to analyze the unsteady flow behavior of finite conductivity fractures producing at high flow rates. Two methods are presented for determining the true fracture conductivity when drawdown data are available at two different flow rates. The amount of turbulent effects also is quantified by the techniques. Examples are presented to illustrate the solution methods. Introduction The increasing use of hydraulic fracturing as a means of improving the productivity of oil and gas wells in low-permeability formations has resulted in many research efforts aimed at increasing fracturing capabilities as well as evaluating the characteristics of the fracture in the postfracturing period. With the advent of the massive postfracturing period. With the advent of the massive hydraulic fracturing (MHF) treatment in recent years, the need for new solutions for evaluating these systems has increased. The problem with the older solutions was the need for many assumptions to arrive at a simple solution. One of the more common assumptions made in these systems was the use of linear flow to describe the flow within the fracture. In gas wells with finite-conductivity fractures producing at high flow rates, the non-Darcy effect is created within the fracture. Hence, new solutions must be developed for these systems. The objective of this paper is to present a new semianalytical solution to this problem that can be applied both to the linear and to the nondarcy flow regimes within the fracture.Over the years. several methods have been developed to analyze postfracture data. Gringarien et al. first solved the fracture system analytically for three special cases: infinite-conductivity vertical fracture, uniform flux vertical fracture, and horizontal fracture. At that time, its application became quite useful. But since not all systems behaved in this manner, the need for further solutions was warranted. Cinco-L. et al. investigated the general case of finite-conductivity vertical fractures, which included the above solution. as well as fracture conductivities as low as 0.1. This research also led to the need to analyze short-time data to obtain unique solutions. Similar results were obtained by Agarwat et al., who presented a finite-difference solution to this problem, considering both the constant rate as well as the problem, considering both the constant rate as well as the constant pressure cases.One of the first papers written on the effects of non-Darcy flow in fractured systems was by Wattenbarger and Ramey. They investigated the effects of non-Darcy flow in the formation and concluded that these effects cannot be felt if the fracture is long or intermediate in size. They further concluded that the effects of turbulent flow within the fracture were more significant.Holditch and Morse investigated the effect of turbulent flow in a fracture and analyzed the transient behavior of specific conductivities (low, medium, and high), giving a qualitative approach to the solution. They stressed the need for greater detail on these solutions and showed that there was indeed a large reduction in the fracture conductivity when non-Darcy flow was included. Although Holditch and Morse gave a detailed descriptive insight into the flow regime problem, they did not develop any general methods for determining the actual conductivity of the fracture. SPEJ P. 681

This paper presents the results obtained in the study of the transient behavior of a well intersected by a finite conductivity vertical fracture in a double porosity reservoir. Two models are considered to take into account the fluid transfer between matrix blocks and fractures: the pseudo-steady-state matrix flow mode and the transient matrix flow model. A general semianalytical model and simplified fully analytical models are presented. It is demonstrated that these systems exhibit the basic behavior of a well with a finite conductivity fracture: that is bilinear flow, pseudolinear flow and pseudoradial flow in addition to the transition flow periods. Each of these flow periods is under the influence of the different states of the fluid transfer between matrix and fractures; that is fracture dominated period, transition period and total system dominated period. It is shown that correlating parameters are the dimensionless fracture conductivity (), the fracture storativity coefficient and the interporosity flow parameter (or the dimensionless matrix hydraulic diffusivity). It was found, for the transient matrix flow model, that the pressure behavior exhibits 1/8 slope in a log-log graph during the bilinear flow dominated by the transition period of the fluid transfer. Hence a graph of pressure versus yields a straight line passing through the origin. During the pseudolinear flow, and if the fluid transfer is in the transition period, a log-log graph of the pressure versus time exhibits 1/4 slope straight line. This means that a graph of p versus yields a straight line. Hence it is concluded that bilinear flow is not the only type of flow that exhibits the one quarter slope type of behavior. Type curves are presented to analyze data falling in the bilinear pseudolinear flow regions. The effect of wellbore storage are also included. The general semianalytical models yields simultaneous the constant flow rate and the constant pressure solutions as well as the pressure derivative function for the constant rate case. Introduction In recent years interest has been growing for the evaluation of hydraulically fractured wells producing in double porosity reservoirs. Although considerable efforts have been dedicated to study either fractured wells in homogeneous reservoirs or wells producing in double porosity reservoirs, there is not a complete study that includes fractures in double porosity reservoirs. It has been shown in the past that well intersected by finite conductivity vertical fracture in a homogeneous reservoir can exhibit several flow periods: bilinear, pseudolinear and pseudo-radial in addition to the transition between them. For each of these flow periods there is a specific graph of interpretation that produces a straight line portion for the pressure data. The pressure data within the bilinear flow, the pseudolinear flow and the pseudoradial flow exhibit a straight line in a graph of pressure versus, and log t, respectively. The complete behavior of the system can be correlated by a parameter called dimensionless fracture conductivity (). In order to identify the different flow regimes type curves have been presented in terms of pressure or pressure derivative. On the other hand, the studies on the behavior of wells in double porosity reservoirs have considered two kinds of models for the matrix-fracture fluid transfer: the pseudo-steady-state flow model (Warren and Root) and the transient matrix flow model (de Swaan and Kazemi). P. 645^

Constant producing pressure solutions that define declining production rates with time for a naturally fractured reservoir are presented. The solutions for the dimensionless flow rate are based on a model presented by Warren and Root. I The model was extended to include constant producing pressure in both infinite and finite systems. The results obtained for a finite no-flow outer boundary are new and surprising. It was found that the flow rate shows a rapid decline initially, becomes nearly constant for a period, and then a final decline in rate takes place.A striking result of the present study is that ignoring the presence of a constant flow rate period in a type-curve match can lead to erroneous estimates of the dimensionless outer radius of a reservoir. An example is presented to illustrate the method of typecurve matching for a naturally fractured system.

This work presents the basic pressure behavior differences between a finite conduc tivity fracture and different types of damaged fractures. Two kinds of fracture damage conditions are studied: a) a damaged zone around the fracture, and b) a damaged zone within the fracture in the vicinity of the wellbore. The first case is caused by the fracturing fluid loss in the formation and the last case 1S originated by crushing, embedding or loss of propant within the fracture in the vicin ity of the wellbore. This paper emphasizes that although nite fracture conductivity and fracture damage condition are both flow restrictions, their effectson transient pressure behavior are quite different at early time. Type curves and both linear flow and bilinear flow graphs can be used to identify different cases when applied properly.