A model recently presented by Cinco et al. for the transient pressure behavior of wells with finite conductivity vertical fractures was modified to include the effects of wellbore storage and fracture damage. An infinitesimal skin was considered around the fracture, and it was handled as a dimensionless factor defined as (pi/2)(wd/xf)[(k/kd) - 1]. It was found that the well behavior is importantly affected by the fracture damage. When plotted as a function of log pwD vs lot tD for short plotted as a function of log pwD vs lot tD for short times, results show flat, almost horizontal lines that later become concave upward curves asymptotically approaching the curve for undamaged fractures. This behavior is shown even by slightly damaged fractures. It also was found that important information about the fracture characteristics may not be determined when wellbore storage effects are present. present Introduction It has been shown that the increase in the productivity of a well created by hydraulic productivity of a well created by hydraulic fracturing depends on fracture characteristics, such as fracture conductivity, length, penetration, and also on a possible damage to the penetration, and also on a possible damage to the formation immediately surrounding the fracture. During the last few years, there has been a continuously increasing interest in the determination of the characteristics and orientation of fractures by means of transient pressure analysis. Most of these methods consider the fracture to be of infinite conductivity or of uniform flux; others consider finite conductivity fractures. Generally, these methods assume that there is no skin damage around the fracture. Evans proposed a pressure analysis technique considering fracture skin damage. He assumed the flow from the formation to the fracture to be linear, passing through two porous media in series, one being the damaged zone around the fracture and the other the undamaged formation. Ramey and Gringarten discussed the transient well behavior of vertically fractured wells with large wellbore storage, and suggested a matching technique for analyzing pressure data. Recently, Raghavan discussed pressure analysis techniques for vertically fractured wells, including the effects of wellbore storage and skin. He assumed the fracture to be of uniform flux, and presented general characteristics of the pressure transient behavior for these systems. The purpose of this study is to present solutions for the transient wellbore pressure behavior of a well crossed by a finite conductivity vertical fracture, considering the effect of a damaged zone around the fracture and wellbore storage. It is also intended to show the general flow characteristics of these fractured systems. MATHEMATICAL MODELS AND METHODS OF SOLUTION The transient flow toward a well with a finite conductivity vertical fracture surrounded by a damaged zone was studied by using a modified version of the model presented by Cinco et al. The following assumptions were considered.An infinite, homogeneous, isotropic reservoir of permeability k, porosity phi, and thickness h.The formation is produced through a vertically fractured well. The wellbore is intersected by a fully penetrating vertical fracture of permeability kf, porosity cf, width w, and permeability kf, porosity cf, width w, and half-length xf. All production of fluid is via the fracture.There is a zone of reduced permeability caused by fracturing fluid loss around the fracture. This region has a permeability ks and width ws.The porous medium contains a slightly compressible fluid of viscosity mu and compressibility c.All formation, fracture and fluid properties are independent of pressure.Gravity effects are negligible and pressure gradients are small everywhere.

This paper investigates the influence of pressure-dependent fluid and rock properties on well production decline in con-stant wellbore pressure tests. The rock properties considered variable are permeability, porosity, pore compressibility and formation thickness, and thefluid properties are density, com-pressibility and viscosity. Singlephase flow through the porous medium is considered. Various geometries, ratios of in-itial to wellbore pressure, and data sets of rock and fluid pro-perties are studied. For allpractical ratios of initial to wellbore pressure and for transient flow conditions, production rate decline expressed in terms of a dimensionless rate qdis essen-tially the same as the production rate decline qo] for constant property liquid flow. The only exceptions occur for bounded reservoirs after the flow is affected by the outer boundary. These deviations are such that in pressure-sensitive systems production rate declines faster than in constant-property systems. It is shown that variable property decline solutions, when compared to constant property decline solutions, do not follow any of the three common types of production decline curves-exponential, hyperbolic or harmonic. Type curve matching of variable property production rate decline to con-stant property flow solutions gives the correct size of the reser-voir, but other reservoir parameters can be in error. When variable property type curves are used for matching, all reser-voir parameters are correctly estimated. The method of Jacob and Lohman(19) and of van Poolien(21) areproperly modified to accountfor the pressure-dependency of rock andfluid proper-ties. Introduction It is well accepted that porous media are not always rigid and non-deformable. This should influence the transient well behaviour. A frequent assumption is to use average values for both pressure-dependent rock and fluid properties. This helps to reduce the errors involved, but does not totally eliminate them. When rock and fluid property changes are important over *Now with Petroleos Mexicanos, Mexico City. pressure range of interest, then these changes cannot be neglected and a variable property solution should be obtained. A flow equation considering the pressure dependency of all rock and fluid properties has been presented in the literature(l). This equation, when expressed as a function of a pseudo-pressure m(p), resembles the diffusivity equation. Samaniego et al.(2.3) studied this variable property problem for a greater variety of flow conditions. These authors only investigated constant rate cases.There are two basic radial flow cases in the flow of fluids through porous media: (a) constant well rate; and (b) constant well pressure. It is the purpose of this study to investigate the influence of pressure-dependent rock and fluid properties on the constant pressure case. One of the objectives is to find out how production rate decline would vary in these pressure-dependent systems, and if methods of analysis for constant pressure flow testing can be properly modified...

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Summary This paper presents a solution for the inverse problem, or interpretation, to the flow of tracers in naturally fractured reservoirs. The model considers cubic block geometry. The Rosenbrock method for nonlinear regression used in this study, allowed the estimation of up to six parameters for this cubic block geometry. The nonlinear regression for the three cases was carefully tested against synthetical tracer concentration responses affected by random noise, with the objective of simulating as close as possible step injection field data. Results were obtained within 95 percent confidence lirnits. The sensitivity of the inverse problem solution on the main parameters that describe this flow problem was investigated. The main features of the nonlinear regression program used in this study are also discussed. The procedure of this study can be applied to interpret tracer tests in naturally fractured reservoirs, allowing the estimation of fracture and matrix parameters of practical interest (longitudinal fracture dispersivity a, matrix porosity, fracture half-width w, matrix block size d, matrix diffusion coefficient D2 and the adsorption constant kd). The methodology of this work offers a practical alternative for tracer flow tests interpretation to other techniques. Introduction Current hydrocarbons production comes importantly from naturally fractured formations. The behavior of these reservoirs is quite different from that of "homogeneous" - conventional - reservoirs. The complex matrix-fracture interaction of these systems makes their characterization a challenging task. Among the different tools currently available to accomplish this endeavor, tracer test interpretation is taking an ever increasing role. These interwell tracer tests have significantly contributed to the better understanding of the fluid flow in these systems. Radioactive and chemical tracers have been used for many years in groundwater hydrology to analyze the movement of water through porous formations, but their use in geothermal and petroleum reservoir engineering is more recent. It has been recognized, as already stated, that tracer test interpretation, in addition to well-to-well pressure transient tests, is a very important contribution towards accomplishing the characterization of naturally fractured reservoirs. As concluded by these authors, these two testing techniques are complementary, not competing. There are several papers that discuss the flow of tracers in naturally fractured reservoirs. For a review of the recent work the papers of Rarnirez et al. may be consulted. Most of these studies deal with the direct problem (i.e., predicting the tracer response behavior from the knowledge of pertinent reservoir and tracer parameters).

The concept of diagnosis used in this paper has a similar meaning as it used in well test analysis, and essentially refers to the identification, and its sequence as the exploitation time increases, of the production mechanisms of a gas reservoir. This paper discusses an approach for the diagnosis of the gas reservoir production mechanism, derived from a general gas material balance equation (GGMBE), that considers the possibility that the reservoir could be naturally fractured: z/p vs (z/p)Gp. This diagnosis of the production mechanisms can be especially very useful for conditions where the reservoir characterization is limited. Once this diagnosis process has been accomplished, the original gas in place (OGIP) can be more accurately estimated through the present methodology, especially when combined with the available techniques (specific graphs, such as p/z vs Gp, Havlena and Odeh, etc.). In addition, this method allows the estimation of the cumulative effective compressibility, ce(p), of the associated water volume ratio, M, and of the water influx, We(t). The new method is illustrated through its application to the most discussed gas field behavior examples published in the literature, among them the McEwen's water influx case, the volumetric Begg's case and the overpressured Duggan's Anderson L case. Introduction During recent years, it seems that it is no longer fashionable to apply the material balance equation (MBE) to oil and gas fields, the belief being that it has now been superseded by the application of the more modern technique of numerical modeling1. Acceptance of this idea has prevented engineers of using their most powerful tool for studying reservoirs and understanding their performance rather than imposing their wills upon them, as is often the case when applying numerical simulation directly in history matching. One of the best discussions on the subject of this paper, the MBE, is that presented by Dake1. This basic model includes no geometrical considerations (geological models), hence it can be used to calculate the hydrocarbons in place and define the drive mechanism. The diagnosis of the production mechanisms or drive mechanisms in a gas reservoir sometimes may not be an easy task2–5, especially when the characterization of the system (reservoir, aquifer and associated shale [non pay] volume 6,7) is limited. The diagnosis of the production mechanisms of a reservoir has a similar meaning as used in well test analysis; essentially being for the latter the identification of the various flow regimes present during a particular well test, which is ussually accomplished through log-log graphs of the pressure response and of the pressure derivative versus elapsed time8,9. A review of the literature indicates that the diagnosis of the production mechanisms of gas reservoirs has been sarcely discussed10,11. The importance of a proper diagnosis can be made clear based on the previously referenced papers2–5, regarding gas reservoirs where the production mechanism was water influx or abnormal pressure. Again following the analogy with the well testing theory, where the next stept after the diagnosis is the application of specific graphs of analysis, once the production mechanism(s) of a gas reservoir has (have) been determined, the proper MBE can be used to estimate the important parameters of the system, like the original gas in place, G, water influx, etc. The purpose of this paper is to present based on a general gas material balance equation (GGMBE), a simple method for the diagnosis of the production mechanism(s) and material balance analysis: z/p vs (z/p)Gp. This new theory is illustrated through its application to some of the most discussed gas field behavior examples published in the literature, among them the volumetric Begg's case, the McEwen's water influx case, and the overpressure Anderson L Duggan's gas condensate reservoirs.