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 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.

introduced the log-log type curves to find out when AB:TllAcT wellbore stor~ge effects are negligible f~r a test. Later McKinley iind Earlougher and Kersch presented A general method of analysis for pressure transient type curves for the interpretation of bo?.h pressu~= tests 1s presented. This i.echnique is based on the drawdown and build up tests under the influence of pressure response of an instantaneous source and it wellbore storage and skin damage. rovides a mean to compute the first and second derivatives of the influence function (unit flow rate Gringarten et al.4 improved Ramey's type curves to response) of the well-reservoir system. This reduce the uniqueness problem in analysls. During the information is basic in identifying the flow regimes Lime wellbore storage and skin type curves were occurring during the test. This method eliminates developed, similar studies were conducted for the the effect of producing time on pressure buildup analysis of pressure data in hydraulically fractured data. wells; for this cg:f5the use cf type curve matching was also proposed . These type curves (log PD vs An explicit and stable procedure is discussed to log T ) were presented ! for both reservoir and compute both the derivatives of the influence frd~tll e Darameter

The aim of this work is to examine the well bore pressure behavior in reservoirs with single phase non-Darcy flow conditions produced at a constant sandface rate. The transient flow period is analyzed by means of results generated with a finite difference model. Analytical expressions of pressure drop and its semilog-arithmic slope are presented for the first time. These equations contain the laminar flow solution as a particular case and they provide means to evaluate the total skin factor. Another use of the analytical solution to the non-Darcy flow problem is to be able of identifying the presence of inertial effects by using a diagnostic plot which consists of graphing the derivative of the pressure data. versus the inverse of the square root of time on a cartesian paper. In this way, an analyst can easily predict the magnitude of the skin due to non-laminar flow under any condition of mechanical skin and rate. Furthermore, better stimulation jobs can be designed if non-Darcy flow conditions during a transient test are properly identified through the methodology presented in this study. The use of the methodology obtained in this work is illustrated with synthetic examples for homogeneous and naturally fractured reservoirs. Also, a field example of an undersaturated reservoir and a dry gas case (taken from the literature) show the application of this technique. For the case of naturally fractured reservoirs new insights are provided.