Fractured Reservoir Model Research Articles

ABSTRACT: Integrated fractured reservoir modelling using geomechanics and flow simulation

ABSTRACT: Integrated fractured reservoir modelling using geomechanics and flow simulation

Modelling the Performance of an Iranian Naturally Fractured Reservoir

Introduction An Iranian Asmari reservoir with an initial oil-in-place of about 381 million m3 (2.4 billion bbls) and a history of 18 years of oil production is studied in this: work. The field is a typical Iranian fractured carbonate oil reservoir which has a matrix rock of poor quality and a highly permeable fracture network. The subject of the study was to simulate the reservoir flow performance with an elaborate two-dimensional vertical model capable of simulating non-conventional producing mechanisms such as gravity drainage and block to block interaction. After successful proving of the model capability by reservoir production history, the model was used to predict the reservoir behaviour under natural depletion, and to evaluate two cases of pressure maintenance by gas injection. Results showed that in both cases of pressure maintenance, an ultimate additional oil production of about 150 million bbls will be achieved over natural depletion. This additional oil production corresponds to approximately 6% of original oil-in-place. Introduction The oil reservoir under study is an elongated NW-SE anticline symmetrical along its minor axis located in southwest of Iran. The structure plunge to the southeast is more gentle than to the northwest. The productive area is 19.5 kilometres long and 7.75 kilometres wide at the original WOC located at 1,890 metres subsea. Heavy mud losses during drilling, production tests, and good pressure communication between the wells indicate the existence of an active fracture system. The original reservoir pressure at a depth of 1,600 mss, was measured to be 210.7 bars, about 57 bars above saturation pressure. Commercial oil production commenced in 1973 at a rate of 3,100 m3/day. The rate was then successively increased as more wells were drilled in the field. During the early time of the field production, a relatively fast pressure drop as shown in Figure 1 was encountered which is characteristic of an undersaturated reservoir. In 1978, the pressure at the crest had dropped below the bubble point pressure causing the liberation of solution gas and the formation of a secondary gas cap. The field was shut-in from 1979 to 1984 during which 0.2 billion m3 of gas was injected intermittently. During this period the average reservoir pressure increased by approximately 20 bars. Then production resumed at a rate of 6,000-6,500 m3/D with a gas injection rate of 1.4 million m3/D continuously. From 1986 the amount of injected gas was insufficient to maintain the reservoir pressure, resulting in a gradual decline of the reservoir pressure. Figure 2 depicts the reservoir production history. The producing mechanisms in the fractured reservoirs of Iranian type are substantially different from those in conventional homogeneous reservoirs. Therefore, to study their performance a special mathematical model should be used. In this study it will be shown that the two-dimensional fractured reservoir model, a "stacked block model," which describes the reservoir as a series of stacked interacting blocks surrounded by fracture space, can be successfully applied to simulate the performance of the reservoir.

THE DEVELOPMENT OF A FRACTURED RESERVOIR MODEL FOR THE PALM VALLEY GAS FIELD

A fractured reservoir model has been developed for the Palm Valley gas field, located WSW of Alice Springs, in the Amadeus Basin, NT. Definition of this complex, naturally fractured, Ordovician gas reservoir has required an integrated approach involving multiple studies to develop the geological model that has formed the basis for reservoir simulation and the rationale for the location of new wells. In addition, new seismic data provided fundamental input to the structure/fracture model of the field. Results suggest a primary, northsouth compression for the origin of structures in the basin and that Palm Valley resulted from a single, balanced folding phase. The seismic data show that Palm Valley is not an arcuate anticline as previously mapped, but is an elongate WSW to ENE trending, doubly plunging anticline with an offset crest and minor reverse faults at reservoir level. Investigations have shown that the majority of fractures in the reservoir outcrop are extremely ordered and there is definite structural control of the fracture spacing in the brittle reservoir rocks. Fracture trajectory and fracture intensity maps have been constructed, the latter providing the mechanism for distribution of fracture parameters around the field. The orientation of fractures measured at depth in the reservoir match exactly the fractures predicted from the structure/fracture model. This is the first time a fractured reservoir model that has been developed for Palm Valley, and it will form the basis for the further study and future development of the field.

A New Methodology for Fractured Reservoir Analysis and Modelling: ABSTRACT

A New Methodology for Fractured Reservoir Analysis and Modelling: ABSTRACT

Characterization of Natural Fractures in the Frontier Formation, Green River Basin, Wyoming; Application to Reservoir Simulation of Horizontal Wells: ABSTRACT

Significant gas reserves are present in the low-permeability sandstones of the Frontier Formation in the Green River Basin, Wyoming. Successful exploitation of these reservoirs through horizontal drilling requires understanding the orientations and distributions of natural fractures. Outcrop studies, core analyses, and welltest data have been integrated to characterize these reservoirs and implement a realistic simulation of horizontal well productivity. Detailed maps of fracture systems have been constructed from outcrop pavements, of the Frontier sandstones at the edge of the basin. They show relatively uniform distributions of vertical regional extension fractures and that bed thickness is the dominant geologic parameter controlling fracture behavior. Spatial frequency distribution of features has been derived from statistical analysis of fracture orientation, spacings, lengths, and interconnections and correlated to bed thickness. Fracture spacing and length decrease and fracture interconnectivity increases with decreasing bed thickness. A natural fractured reservoir model has been developed using this fracture relationship. This model incorporates fracture and matrix permeability determined in laboratory tests conducted at in-situ reservoir conditions. The model shows that the relationship between bed thickness and fracture frequency distribution and the contrast between matrix and fracture permeability determines the reservoir`s effective transmissibility. Optimum productivity of horizontal wells has been calculatedmore » as a function of wellbore orientation and length relative to bed thickness to guide field development. Wellbore and welltest data provide validations for the geologic predictions of fracture characteristics and for simulation predictions of reservoir response.« less

Pressure-Transient Analysis of a Composite Naturally Fractured Reservoir

Summary An analytical model describing the transient pressure behavior of a well completed in a composite naturally fractured reservoir is presented. This model was derived by extending the naturally fractured reservoir model with unrestricted interporosity flow to a composite reservoir. The composite reservoir has a circular inner region with fluid and rock properties different from those of the outer region. It is a concentric composite model with a finite-radius well located in the center. Two new solutions for analyzing the pressure response at the producing (or injection) well in infinitely large composite and bounded composite naturally fractured reservoirs are given. The results were obtained with the Stehfest algorithm for Laplace-transform inversion. Depending on the reservoir and fluid properties, various semilog straight lines may be observed in a particular pressure/time curve. The pseudo-steady-state approach can be used to determine the swept volume. On the basis of model results for different parameter values, guidelines are provided for conducting and interpreting a pressure test to determine the characteristics of a composite naturally fractured system, provided that wellbore-storage effects do not mask early-time data.

Devonian Shale Gas Production: Mechanisms and Simple Models

Summary We show that, even without consideration of their special storage and flowproperties, Devonian shales are special cases of dual porosity. We also showthat, while neglecting these properties in the short term is appropriate, suchneglect in the long term will result in an under-estimation of production. Introduction Tremendous accumulations of gas occur in the Devonian shale formations ofthe eastern U.S. Because the formations are so tight, gas can be produced onlywhen extensive networks of natural fractures exist. In areas where fracturingis sufficient to promote production, the gas basically will flow theproduction, the gas basically will flow the short distance from storage in thetight rock matrix to the fracture network and then through the fracture networkto the producing well. Only minute quantities of gas flow directly from therock to the well. These production characteristics make shale gas productioncharacteristics make shale gas reservoirs examples of so-called dual-porositybehavior. The problem with the term "dual-porosity" in shales, however, is that shales have very little open porosity. Unlike conventional gasreservoirs, where gas is stored in the open pore space of the rock, shalesstore an enormous amount of gas in a sorbed (adsorbed or absorbed) state. Thebehavior of fluid flow in the shale matrix also deviates from that of aconventional gas-reservoir/rock matrix. The permeability of conventionalreservoir rock is permeability of conventional reservoir rock is really amacroscopic average of viscous open-channel flow occurring on a pore level. Inshales, the conduits are generally so small that only a few molecules can slipthrough the openings at any given time. Open-channel flow cannot exist for themost part; thus, flow through the shale matrix results predominantly frommolecular diffusion. predominantly from molecular diffusion. The objectives ofthis paper are to clarify the roles that these unusual storage and flowproperties have in the general dual-porosity properties have in the generaldual-porosity system; to estimate their effects on the production behavior ofcommon Devonian shale production behavior of common Devonian shale wellsheuristically; and to show that even without the unusual storage and flowbehaviors, Devonian shale gas reservoirs are special cases of dual porositybecause of the tight nature of the rock matrix. This paper does not present newpredictive models for the behavior of shale reservoirs, nor does it usesophisticated numerical models normally required for predictions of theperformances of these nonlinear systems. The objectives of this paper areachieved through the application and intuitive comparison of the most simplemodels available for shale reservoirs. Theory Dual-Porosity Equation Formulation. Devonian shale gas reservoirs areexamples of the classic dual-porosity, fractured-reservoir model. In thisdual-porosity model, the reservoir is composed of matrix elements andfractures. Fig. 1 shows two examples of very idealized fractured reservoirs. The matrix, represented by individual blocks in Fig. 1, is a portion of thereservoir that can store large quantities of gas, but it does not have theconductivity to transport gas for long distances. The fractures, whichpartition the matrix elements, can transport the partition the matrix elements, can transport the gas but have limited storage capability Production fromdual-porosity reservoirs differs from the production of conventionalsingle-porosity systems, where gas flows directly from the formation to thewell. In fractured reservoirs, gas flows through the fracture network to thewell. The fracture network, in turn, is being constantly recharged by flow fromthe matrix elements. Given a sample control volume in a fractured reservoir(Fig. 1a or 1b), a control volume mass balance can be performed. − = 0, Ac t ..................(1) where v f = average flow velocity through the fractures with respect to anentire cross section, A c = external surface area of the control volume, qt =total mass flow rate from the matrix to the fractures within the controlvolume, and delta x delta y delta z = magnitude of the control volume. The plussign in Eq. 1 results from the assumption that flow from the matrix to thefracture is a positive quantity. For conceptual simplification, it is assumedthat density and pressure are approximately constant in the control volume. Because the total matrix recharge includes flow from all the individual matrixelements, the total matrix flow rate can be rewritten as qt = N (q ma), where qma is the average volumetric flow rate per element, and N is the total numberof elements in the control volume.

Fracture Swarms in Low-Permeability-Sandstone Gas Reservoir Rocks in New Mexico, Colorado, and Wyoming: Implications for Exploration and Development

Fracture permeability is of primary importance to producibility of gas from many low-permeability sandstone gas reservoirs in the western US; but the location, orientation, spacing, and connectedness of fractures in the subsurface are difficult to measure directly. Maps of fractures provide the most accurate representation of fracture spatial distribution, trace length, connectivity, and size and shape of fracture-bounded blocks. In this study, fracture patterns were characterized by mapping five large exposures of Pictured Cliffs and Frontier sandstone along the margins of the San Juan and Green River basins. A set of fractures, interpreted as having formed in flat rocks prior to local Tertiary folding and uplift, is recognized in both formations. In contrast to the conventional model of regional fractures in which fractures are arranged in regularly spaced, orthogonal arrays, these fractures occur in discrete swarms separated laterally by domains that either lack fractures or have only rare fractures. These less fractured domains may be as much as several hundred meters wide. Within swarms, fractures are well interconnected along the length of the swarm but poorly interconnected across the width of the swarm. Fractures between swarms are commonly isolated. For the Pictured Cliffs and Frontier outcrops that were studied, themore » fracture pattern is self-similar over scales ranging from outcrop to interwell scale with fractal dimension D {approximately}1.2. In low-permeability sandstones of the Rocky Mountain region, irregularly spaced fracture swarms are potential targets for gas exploration and should be incorporated into fractured-reservoir models.« less

Fractured Gas Reservoirs in the Devonian Shale of the Illinois and Appalachian Basins

The Devonian and Lower Mississippian black shale sequence of Kentucky includes the New Albany Shale of Illinois basin and the Ohio Shale of the Appalachian basin. Fractured reservoirs in the Ohio Shale contain a major gas resource, but have not been so prolific in the New Albany Shale. The authors propose two models of fractured shale reservoirs in both the Illinois and the Appalachian basins, to be tested with gas production data. (1) Where reactivated basement faults have propagated to the surface, the lack of an effective seal has prevented the development of overpressure. The resulting fracture system is entirely tectonic is origin, and served mainly as a conduit for gas migration from the basin to the surface. Gas accumulations in such reservoirs typically are small and underpressured. (2) Where basement faults have been reactivated but have not reached the surface, a seal on the fractured reservoir is preserved. In areas where thermal maturity has been adequate, overpressuring due to gas generation resulted in a major extension of the fracture system, as well as enhanced gas compression and adsorption. Such gas accumulations are relatively large. Original overpressuring has been largely lost, due both to natural depletion and to uncontrolled production. more » The relative thermal immaturity of the Illinois basin accounts for the scarcity of the second type of fractured reservoir and the small magnitude of the New Albany Shale gas resource. « less

Sixth SPE comparative solution project: dual-porosity simulators : Firoozabadi, A; Thomas, L K J Pet TechnolV42, N6, June 1990, P710–715, 762–763

Two problems are used to compare fractured reservoir models: 1) a simple single-block example, and 2) a more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. In selection of the problems for this Comparative Solution Project, some aspects of the physics of multiphase flow in fractured porous media were considered. The influence of fracture capillary pressure on reservoir performance has been addressed by cases with zero and nonzero gas/oil capillary pressure in the fractures

Sixth SPE Comparative Solution Project: Dual-Porosity Simulators

Summary. Two problems are used to compare fractured reservoir models:a simple single-block example, anda more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. In selection of the problems for this Comparative Solution Project, some aspects of the physics of multiphase flow in fractured porous media were considered. The influence of fracture capillary pressure on reservoir performance has been addressed by cases with zero and nonzero gas/oil performance has been addressed by cases with zero and nonzero gas/oil capillary pressure in the fractures. Introduction In recent years, interest in the simulation of naturally fractured petroleum reservoirs has increased. For this SPE Comparative Solution Project, reservoir test problems were designed to illustrate some aspects of the physics of multiphase flow in fractured physics of multiphase flow in fractured reservoirs and modeling techniques to account for capillary and gravity forces. The approach to the solution of the problems has been limited to dual-porosity models. An important element in simulating a fractured reservoir with a dual-porosity technique is the proper calculation of the fluids exchange between the matrix blocks and the fractures. In the conventional approach, the transfer term for a particular phase is directly related to the shape factor, fluid mobility, and potential difference between the matrix and fracture. Shape factors have been developed based on first-order finite-difference approximations and by matching fine-grid multiphase simulations of matrix/fracture flow. In most dual-porosity models, the matrix block heights are assumed to be at the same depth as the corresponding fracture blocks, and therefore, gravity has no explicit effect on the fluid exchange between the matrix and the fracture. Pseudo capillary pressures have been used to account for the effect of gravity. The gravity-segregation concept has also been used to compute the fluid levels in the matrix and fractures to account for the gravity contribution. An alternative approach has been presented in Ref. 6 (see the second option) to account for gravity effects. Dual-porosity models also must account for the saturation distribution in a matrix block. Because the saturation is evaluated at the center of a grid cell, it represents an average value for that cell. The pseudo-capillary-pressure concept has been used pseudo-capillary-pressure concept has been used to account for both gravity effects and nonuniform saturations within a matrix block. The method of subdomain discretization has also been applied to this problem. In that approach, the matrix is problem. In that approach, the matrix is divided into a number of grid cells and pressures and saturations are calculated for each pressures and saturations are calculated for each grid cell. The subdomain approach can also take care of transient effects. These effects, however, may not be important in field-scale problems. problems. Although fracture capillary pressure is assumed to be zero in most dual-porosity models, a recent paper questions the validity of this concept. In selection of the problems for this Comparative Solution problems for this Comparative Solution Project, the influence of fracture capillary Project, the influence of fracture capillary pressure on reservoir performance was pressure on reservoir performance was addressed by including cases with zero and nonzero gas/oil capillary pressure in the fractures. The nonzero fracture capillary pressures are not based on any actual pressures are not based on any actual measurements, but are intended as a parameter for sensitivity studies. The variation of gas/oil interfacial tension (IFT) with pressure has also been incorporated in the pressure has also been incorporated in the problems. Gas/oil capillary pressure is directly problems. Gas/oil capillary pressure is directly related to IFT, and therefore, the gas/oil capillary pressure should be adjusted according to the ratio of IFT at reservoir pressure divided by IFT at the pressure at which capillary pressures are specified. Problem Statement Problem Statement We selected two problems to compare fractured reservoir models: a single-block example and a more complicated cross-sectional example developed to simulate depletion, gas-injection, and water-injection cases. Basic PVT data for the above cases were taken from Ref. 3. The rock/fluid data, with the exception of the matrix water/oil capillary pressure, were also taken from Ref. 3. Table 1 gives the matrix water/oil capillary pressure data. Matrix-block shape factors pressure data. Matrix-block shape factors have been specified for use in simulators that directly enter this variable (see Table 2). Single-Block Studies. The single-block simulation is a study of gas/oil gravity drainage at 4,500 psig [31.0 MPa] for a cubic matrix block with dimensions of 10 × 10 × 10 ft [3.05 × 3.05 × 3.05 m]. One-cell, dual-porosity runs were made for this case. Two runs were reported: the first with a zero fracture capillary pressure and the second with a constant fracture capillary pressure of 0.1 psi [0.69 kPa]. These runs pressure of 0.1 psi [0.69 kPa]. These runs were terminated at 5 years. JPT P. 710

Solutions of Heat- and Fluid-Flow Problems in Naturally Fractured Reservoirs: Part 1 – Heat-Flow Problems

SummaryThis is the first of two papers concerning the solution of heat- and fluid-flow problems in naturally fractured reservoirs. It deals with the temperature behavior of a naturally fractured reservoir. The naturally fractured reservoir model used assumes unsteady-state heat transfer between the matrix and fracture systems. The model consists of a production (or injection) well fully penetrating a reservoir containing equally spaced horizontal fractures.The problem of hot- or cold-water injection into a naturally fractured reservoir is considered, and a solution describing the temperature distribution in such a reservoir is given that can be used to locate the thermal front and to estimate the reservoir volume affected by the injection process. It also has application in estimating the amount of heat that can be extracted from a geothermal reservoir as the result of a reinjection process. The results of a field test support the validity of the model.

Numerical Simulation of Naturally Fractured Reservoirs

Summary The most important and difficult aspect of modeling a naturally fractured reservoir is the correct calculation of the exchange of fluids between the matrix rock and the surrounding fractures. Several authors have published alternative techniques for handling this problem over the past few years. However, because each of these alternatives has some limitations, a new and more general technique has been developed. This new technique is used to simulate matrix/fracture exchange with special emphasis on the gravity forces included in the exchange terms. The exchange terms and the gravity forces within the exchange terms simulate the behavior of a single matrix block surrounded by fractures that may contain several different fluids. The gravity forces are internally calculated as functions of saturation. This technique has been incorporated into a new three-dimensional (3D), three-phase, fully implicit model for simulating fluid flow in a naturally fractured reservoir. The description of the porous medium might include highly fractured, microfractured, and nonfractured regions. Several examples explain the use of a new naturally fractured reservoir model and the essential differences between the new approach and those used in earlier naturally fractured reservoir models.

Application of Preconditioned Conjugate-Gradient-Like Methods in Reservoir Simulation

Summary Conjugate-gradient-like (CGL) methods were used to solve the matrix equations for several large-field and fine-grid models. The methods used incomplete LU (ILU) or modified incomplete LU (MILU) preconditioning coupled with orthomin acceleration. The CGL methods were applied to the original matrix or to a reduced system from red/black ordering. Test results from a black-oil model with fault throws, a fractured reservoir model, and three steamflood models are given. It was found that the CGL methods are effective for solving the matrix equations. A more powerful preconditioner improves reliability but may require more work. Guidelines for selecting the most effective method are provided.

Analysis of Interference Data in a Highly Heterogeneous Naturally Fractured Geothermal Reservoir

Summary An approach consisting of a combination of composite and naturally fractured reservoir models has been proposed to interpret pressure-transient data from an 11-well interference test in a highly heterogeneous geothermal reservoir. The approach leads to an integrated interpretation that accounts for all of the salient features of the data. An initial appraisal of the data indicates excellent agreement with theoretical results for double-porosity reservoirs. For some of the wells, however, the bulk storativity, calculated with the double-porosity model, differs significantly from the average value of this parameter. Furthermore, it increases systematically as the distance between the active and observation wells decreases. To explain this peculiar result, an alternative method of analyzing data from composite reservoirs is presented. The method demonstrates that local permeability variations can result in enormous variations in the apparent storativity without causing variations in the apparent permeability-thickness of the reservoir. A simple graphical technique, based on analyzing systematic variations in the apparent storativity, has been developed to determine the size of the region and the mobility contrast between different regions of the reservoir. By using this technique, we show that the observed variations in the storativity are the result of a small, high-permeability region that surrounds the pumped well and is penetrated by several of the observation wells.

3-D Characterization of Fractures in Mesaverde Reservoirs, or Why the Sugar Cube Reservoir Model Doesn't Always Work: ABSTRACT

Data suggest that fractures in reservoirs of the nonmarine Mesaverde rocks in the subsurface of east-central Piceance Creek basin (northwestern Colorado) are vertical, unidirectional, and subparallel. There is a continuum of fracture sizes and spacings from microscopic fractures to those extending a few tens of feet vertically and horizontally. Fractures often do not extend vertically across small-scale lithologic discontinuities within the fluvial reservoirs. The presence of orthogonal fractures in the subsurface may be less common than generally believed. Primary orthogonal fractures require special structural conditions for development in the subsurface; unidirectional fractures can develop in flat-lying rocks in areas of high pore pressures, and under relatively low differential horizontal stress conditions. Outcrop fracture characteristics must be extrapolated into the subsurface with caution because secondary orthogonal fractures can be created at the surface during erosion and stress relief simultaneously with the vertical and horizontal extension of an existing unidirectional fracture set. Mesaverde reservoir fractures are interpreted to be poorly interconnected, with connections primarily due to the intersection of subparallel adjacent fractures. Different fracture networks exist at different lithologic levels in the reservoir, and few fractures extend vertically from one level to the next. Reservoir fractures are of irregular permeability, spacing, andmore » size along their length, and no horizontal or orthogonal fractures exist. This lack of orthogonal fractures explains why sugar cube fractured reservoir models often have to be modified to match reservoir behavior. The connecting orthogonal fracture system, whereas present in outcrop, may not exist at reservoir depths.« less

Wellbore Pressure Response in Naturally Fractured Reservoirs

Wellbore Pressure Response in Naturally Fractured Reservoirs

Unsteady-State Behavior of Naturally Fractured Reservoirs

Abstract A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs from pressure build-up and/or drawdown plots. Introduction The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard, Freeman and Natanson, and Samara. The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results. Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a factured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. To understand the behavior of the pressure build-up and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions:1. The matrix blocks act like sources which feed the fractures with fluid;2. The net fluid movement toward the wellbore obtains only in the fractures; and3. The fractures' flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures' bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady-state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. SPEJ P. 60ˆ