Well Pressure Behavior of a Naturally Fractured Reservoir

1983 ◽  
Vol 23 (05) ◽  
pp. 769-780 ◽  
Author(s):  
Tatiana D. Streltsova
Keyword(s):  
Pressure Response ◽  
Transitional Period ◽  
Late Time ◽  
Fractured Reservoir ◽  
Fracture Pressure ◽  
Matrix Fracture ◽  
Naturally Fractured ◽  
The Matrix ◽  
Uniform Medium ◽  
Fluid Transfer

Abstract The pressure response pattern of a naturally fractured reservoir is considered under the assumption allowing matrix-to-fracture crossflow to result from a diffusion mechanism of fluid transfer through the matrix. The transitional pressure during time-variant crossflow is shown to develop on a semilog plot a linear segment with a slope equal to one-half that of the early- and late-time pressure segments. For a single well, this allows use of a conventional Homer-type analysis. Introduction A naturally fractured formation is generally represented by a tight matrix rock broken up by fractures of secondary origin. The fractures are assumed continuous throughout the formation and to represent the paths of principal permeability. The high diffusivity of a fracture results in a rapid permeability. The high diffusivity of a fracture results in a rapid response along the fracture to any pressure change such as that caused by well production. The rock matrix, having a lower permeability but a relatively higher primary porosity, has a "delayed" response to pressure changes that occur in the surrounding fractures. Such nonconcurrent responses cause pressure depletion of the fracture relative to the matrix, which in turn induces matrix-to-fracture crossflow. This period of transient crossflow takes place immediately after the fracture pressure response and before the matrix and the fracture pressures equilibrate, after which the formation acts as a uniform medium with composite properties. The effect of assumptions made on the nature of matrix and properties. The effect of assumptions made on the nature of matrix and fracture interaction is manifested during this transitional period of matrix-to-fracture fluid transfer. The flux of fluid released by the matrix depends on the matrix size, porosity, permeability, and the matrix/fracture pressure difference. At the matrix/fracture interface, the matrix flux contribution to fracture flow may be assumed proportional to either the pressure difference between matrix and fracture or to the averaged pressure gradient throughout the matrix block. The former assumption, introduced in fractured reservoir description by Barenblatt and Zheltov and Barenblatt et al. and employed by Warren and Root, has an advantage of simplifying the mathematical analysis of the flow problem and a disadvantage of not correctly representing either the mechanism of pressure readjustment between matrix and fracture by time-variant crossflow pressure readjustment between matrix and fracture by time-variant crossflow or the formation pressure response during the transitional time. According to this assumption, the matrix flux is independent of spatial position, which can be true only when pressure is linearly distributed in space-i.e., at a state of pressure equilibrium or at a pseudosteady-state time. This assumption, therefore, is often referred to as a "pseudosteady-state" or "lumped-parameter" flux assumption. It neglects the matrix storage capacitance by allowing an instantaneous pressure drop throughout the matrix as soon as fracture depletion occurs. The pressure response of a medium subject to this assumption has a characteristic S-shape transitional curve with an inflection point. The curve connects the initial pressure segment (the early-time fracture response) to the final pressure segment, representative of the late-time pseudosteady-state flow of an equivalent uniform medium that has fracture permeability and composite (the sum of fracture and matrix) storage. By contrast, the averaged gradient assumption on matrix-to-fracture crossflow, while somewhat complicating a mathematical analysis of the problem, has an advantage of more correctly describing the pressure problem, has an advantage of more correctly describing the pressure equilibration process that occurs during the transitional period. Matrix fluxes arising from fluid expansion forces are subject to Darcy flow and, thus, to diffusivity-type flow constraints. SPEJ p. 769

Fractured Reservoir Simulation

1983 ◽  
Vol 23 (01) ◽  
pp. 42-54 ◽  
Author(s):  
L. Kent Thomas ◽  
Thomas N. Dixon ◽  
Ray G. Pierson
Keyword(s):  
Fractured Reservoirs ◽  
Fracture Flow ◽  
Fracture System ◽  
Fractured Reservoir ◽  
Three Phase ◽  
Matrix Fracture ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix ◽  
Saturation History

Abstract This paper describes the development of a three-dimensional (3D), three-phase model for simulating the flow of water, oil, and gas in a naturally fractured reservoir. A dual porosity system is used to describe the fluids present in the fractures and matrix blocks. Primary flow present in the fractures and matrix blocks. Primary flow in the reservoir occurs within the fractures with local exchange of fluids between the fracture system and matrix blocks. The matrix/fracture transfer function is based on an extension of the equation developed by Warren and Root and accounts for capillary pressure, gravity, and viscous forces. Both the fracture flow equations and matrix/fracture flow are solved implicitly for pressure, water saturation, gas saturation, and saturation pressure. We present example problems to demonstrate the utility of the model. These include a comparison of our results with previous results: comparisons of individual block matrix/fracture transfers obtained using a detailed 3D grid with results using the fracture model's matrix/fracture transfer function; and 3D field-scale simulations of two- and three-phase flow. The three-phase example illustrates the effect of free gas saturation on oil recovery by waterflooding. Introduction Simulation of naturally fractured reservoirs is a challenging task from both a reservoir description and a numerical standpoint. Flow of fluids through the reservoir primarily is through the high-permeability, low-effective-porosity fractures surrounding individual matrix blocks. The matrix blocks contain the majority of the reservoir PV and act as source or sink terms to the fractures. The rate of recovery of oil and gas from a fractured reservoir is a function of several variables, included size and properties of matrix blocks and pressure and saturation history of the fracture system. Ultimate recovery is influenced by block size, wettability, and pressure and saturation history. Specific mechanisms pressure and saturation history. Specific mechanisms controlling matrix/fracture flow include water/oil imbibition, oil imbibition, gas/oil drainage, and fluid expansion. The study of naturally fractured reservoirs has been the subject of numerous papers over the last four decades. These include laboratory investigations of oil recovery from individual matrix blocks and simulation of single- and multiphase flow in fractured reservoirs. Warren and Root presented an analytical solution for single-phase, unsteady-state flow in a naturally fractured reservoir and introduced the concept of dual porosity. Their work assumed a continuous uniform porosity. Their work assumed a continuous uniform fracture system parallel to each of the principal axes of permeability. Superimposed on this system was a set of permeability. Superimposed on this system was a set of identical rectangular parallelopipeds representing the matrix blocks. Mattax and Kyte presented experimental results on water/oil imbibition in laboratory core samples and defined a dimensionless group that relates recovery to time. This work showed that recovery time is proportional to the square root of matrix permeability divided by porosity and is inversely proportional to the square of porosity and is inversely proportional to the square of the characteristic matrix length. Yamamoto et al. developed a compositional model of a single matrix block. Recovery mechanisms for various-size blocks surrounded by oil or gas were studied. SPEJ P. 42

Pressure Response at Observation Wells in Fractured Reservoirs

1984 ◽  
Vol 24 (06) ◽  
pp. 628-638 ◽  
Author(s):  
C.C. Chen ◽  
N. Yeh ◽  
R. Raghavan ◽  
A.C. Reynolds
Keyword(s):  
Fractured Reservoirs ◽  
Pressure Response ◽  
Fracture System ◽  
Unsteady State ◽  
Fractured Reservoir ◽  
Observation Well ◽  
Naturally Fractured ◽  
The Matrix ◽  
Interference Test ◽  
Observation Wells

Abstract This work examines interference test data in a naturally fractured reservoir. The reservoir model examined here assumes that the reservoir can be represented by a system of horizontal fractures that are separated by the matrix. This model is identical to the deSwaan-Kazemi model. The main contribution of our work is that we combine the parameters of interest in a simple way and present solutions that can be used directly for field application. These solutions can be used to design or analyze interference tests. We also compare the solution for unsteady-state flow in the matrix with the Warren-Root model, which assumes pseudosteady-state fluid flow in the matrix. Introduction This work examines the pressure response at an observation well in a fractured reservoir. Previous works by Kazemi et al. and Streltsova-Adams have examined the pressure response based on the Warren and Root model. In this work, however, we assume unsteady-state fluid transfer from the matrix to the fracture system. We consider the model proposed by deSwaan and Kazemi. This model assumes that the fractured reservoir can be replaced by an equivalent set of horizontal fractures separated by matrix elements (Fig. 1). The results of this study, however, can be applied to other unsteady-state models proposed in the literature. The main contribution of this work is that type curves convenient for analyzing data are presented. We have combined the parameters of interest and correlated results in terms of dimensionless groups that are commonly used in well test analysis. A comprehensive discussion of the pressure behavior at an observation well in a fractured reservoir is presented. Procedures to analyze data by conventional semilog methods also are discussed. New observations on the pressure response at an observation well are presented. For purposes of comparison, we also examined the pressure response in a reservoir that obeys the Warren and Root idealization. Assumptions and Mathematical Model The mathematical model considered here assumes the flow of a slightly compressible (of constant viscosity) fluid in a naturally fractured reservoir. We assume that the matrix-fracture geometry is as shown in Fig. 1. Individually, the fractures and the matrix are assumed to be homogeneous, uniform, and isotropic porous media with distinct properties. Gravitational forces are assumed negligible. The reservoir is assumed to be infinitely large-i.e., the outer boundaries have no effect on the pressure response. The initial condition assumes that the pressure is constant at all points in the reservoir. We assume that the flowing well produces at a constant rate and that the two wells both penetrate the fracture system. In addition, we impose four fundamental assumptions:all production is from the fracture system,flow in the matrix system is one-dimensional-i.e., in the z direction (see Fig. 1),flow in the fracture system is radial, andboth the producing and observation wells are line source wells and wellbore storage and skin effects are neglected. Assumptions 1, 2, and 3 have been used extensively in previous studies of naturally fractured reservoirs. Recent results of Reynolds et al. indicate that these assumptions are valid for the model considered in Fig. 1 if the flow capacity of the matrix system is small relative to the flow capacity of the fracture system (see Ref. 9 for specific details). Assumption 4 is used in virtually all studies of interference testing. (A comprehensive discussion of the influence of wellbore storage and skin effects on interference test data is given in Refs. 10 and 11.) It is important to realize that flee preceding four assumptions (see 2 in particular) imply that the pressure response at the observation well will be equal to the pressure response in the fracture system at the point where the observation well intersects the fractured system. All results given in this study are based on dimensionless variables for purposes of convenience. The dimensionless variables are defined as follows. The dimensionless pressure drop in the reservoir is ...............(1) Here, is the permeability of the fracture system and is the total thickness of the fracture system. If the model of Fig. 1 contains horizontal fractures, then = where is the thickness of each horizontal fracture. The term represents the surface flow rate, is the formation volume factor, is the viscosity of the fluid, and ( ) is the pressure at point at time . The subscript f refers to the fracture. All quantities are expressed in SPE-preferred SI metric units. SPEJ P. 628^

A Fully Implicit, Compositional, Parallel Simulator for IOR Processes in Fractured Reservoirs

SPE Journal ◽  
2007 ◽  
Vol 12 (03) ◽  
pp. 367-381 ◽  
Author(s):  
Reza Naimi-Tajdar ◽  
Choongyong Han ◽  
Kamy Sepehrnoori ◽  
Todd James Arbogast ◽  
Mark A. Miller
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fractured Reservoir ◽  
Matrix Fracture ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
Dual Porosity Model ◽  
The Matrix ◽  
Porosity Model

Summary Naturally fractured reservoirs contain a significant amount of the world oil reserves. A number of these reservoirs contain several billion barrels of oil. Accurate and efficient reservoir simulation of naturally fractured reservoirs is one of the most important, challenging, and computationally intensive problems in reservoir engineering. Parallel reservoir simulators developed for naturally fractured reservoirs can effectively address the computational problem. A new accurate parallel simulator for large-scale naturally fractured reservoirs, capable of modeling fluid flow in both rock matrix and fractures, has been developed. The simulator is a parallel, 3D, fully implicit, equation-of-state compositional model that solves very large, sparse linear systems arising from discretization of the governing partial differential equations. A generalized dual-porosity model, the multiple-interacting-continua (MINC), has been implemented in this simulator. The matrix blocks are discretized into subgrids in both horizontal and vertical directions to offer a more accurate transient flow description in matrix blocks. We believe this implementation has led to a unique and powerful reservoir simulator that can be used by small and large oil producers to help them in the design and prediction of complex gas and waterflooding processes on their desktops or a cluster of computers. Some features of this simulator, such as modeling both gas and water processes and the ability of 2D matrix subgridding are not available in any commercial simulator to the best of our knowledge. The code was developed on a cluster of processors, which has proven to be a very efficient and convenient resource for developing parallel programs. The results were successfully verified against analytical solutions and commercial simulators (ECLIPSE and GEM). Excellent results were achieved for a variety of reservoir case studies. Applications of this model for several IOR processes (including gas and water injection) are demonstrated. Results from using the simulator on a cluster of processors are also presented. Excellent speedup ratios were obtained. Introduction The dual-porosity model is one of the most widely used conceptual models for simulating naturally fractured reservoirs. In the dual-porosity model, two types of porosity are present in a rock volume: fracture and matrix. Matrix blocks are surrounded by fractures and the system is visualized as a set of stacked volumes, representing matrix blocks separated by fractures (Fig. 1). There is no communication between matrix blocks in this model, and the fracture network is continuous. Matrix blocks do communicate with the fractures that surround them. A mass balance for each of the media yields two continuity equations that are connected by matrix-fracture transfer functions which characterize fluid flow between matrix blocks and fractures. The performance of dual-porosity simulators is largely determined by the accuracy of this transfer function. The dual-porosity continuum approach was first proposed by Barenblatt et al. (1960) for a single-phase system. Later, Warren and Root (1963) used this approach to develop a pressure-transient analysis method for naturally fractured reservoirs. Kazemi et al. (1976) extended the Warren and Root method to multiphase flow using a 2D, two-phase, black-oil formulation. The two equations were then linked by means of a matrix-fracture transfer function. Since the publication of Kazemi et al. (1976), the dual-porosity approach has been widely used in the industry to develop field-scale reservoir simulation models for naturally fractured reservoir performance (Thomas et al. 1983; Gilman and Kazemi 1983; Dean and Lo 1988; Beckner et al. 1988; Rossen and Shen 1989). In simulating a fractured reservoir, we are faced with the fact that matrix blocks may contain well over 90% of the total oil reserve. The primary problem of oil recovery from a fractured reservoir is essentially that of extracting oil from these matrix blocks. Therefore it is crucial to understand the mechanisms that take place in matrix blocks and to simulate these processes within their container as accurately as possible. Discretizing the matrix blocks into subgrids or subdomains is a very good solution to accurately take into account transient and spatially nonlinear flow behavior in the matrix blocks. The resulting finite-difference equations are solved along with the fracture equations to calculate matrix-fracture transfer flow. The way that matrix blocks are discretized varies in the proposed models, but the objective is to accurately model pressure and saturation gradients in the matrix blocks (Saidi 1975; Gilman and Kazemi 1983; Gilman 1986; Pruess and Narasimhan 1985; Wu and Pruess 1988; Chen et al. 1987; Douglas et al. 1989; Beckner et al. 1991; Aldejain 1999).

Development of an Embedded Discrete Fracture Model for Multi-Phase Flow in Fractured Reservoir

2014 ◽  
Vol 668-669 ◽  
pp. 1488-1492
Author(s):  
Fang Qi Zhou
Keyword(s):  
Neumann Boundary ◽  
Fracture Model ◽  
Fractured Reservoir ◽  
Discrete Fracture Model ◽  
Matrix Fracture ◽  
Discrete Fracture ◽  
The Matrix ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
Fracture Interface

Considering the discontinuities of the phase saturations and pressure gradients at the matrix-fracture interface, a modified algorithm for the embedded discrete fracture model is proposed. In this algorithm, the exchange rate between fracture and matrix on two sides of the interface are calculated separately. To avoid the problem for defining the physical variables on the matrix grid blocks overlaid by fracture, the Neumann boundary conditions are instead in the calculations of other matrix grid blocks. The numerical examples show that the simulation results of the proposed algorithm agree very well with those of the discrete fracture model. In reservoir with high matrix capillary pressure, the grids must be enough refined in the neighborhood of the matrix-fracture interface to achieve high numerical accuracy.

Unsteady-State Behavior of Naturally Fractured Reservoirs

1965 ◽  
Vol 5 (01) ◽  
pp. 60-66 ◽  
Author(s):  
A.S. Odeh
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Unsteady State ◽  
Fractured Reservoir ◽  
State Behavior ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix ◽  
Porosity And Permeability ◽  
Bulk Volume

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

Hydraulic Characterization of Fractured Reservoirs: Simulation on Discrete Fracture Models

2002 ◽  
Vol 5 (02) ◽  
pp. 154-162 ◽  
Author(s):  
S. Sarda ◽  
L. Jeannin ◽  
R. Basquet ◽  
B. Bourbiaux
Keyword(s):  
Reservoir Simulation ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Dual Porosity ◽  
Fractured Reservoir ◽  
Fracture Networks ◽  
Matrix Fracture ◽  
Discrete Fracture ◽  
The Matrix

Summary Advanced characterization methodology and software are now able to provide realistic pictures of fracture networks. However, these pictures must be validated against dynamic data like flowmeter, well-test, interference-test, or production data and calibrated in terms of hydraulic properties. This calibration and validation step is based on the simulation of those dynamic tests. What has to be overcome is the challenge of both accurately representing large and complex fracture networks and simulating matrix/ fracture exchanges with a minimum number of gridblocks. This paper presents an efficient, patented solution to tackle this problem. First, a method derived from the well-known dual-porosity concept is presented. The approach consists of developing an optimized, explicit representation of the fractured medium and specific treatments of matrix/fracture exchanges and matrix/matrix flows. In this approach, matrix blocks of different volumes and shapes are associated with each fracture cell depending on the local geometry of the surrounding fractures. The matrix-block geometry is determined with a rapid image-processing algorithm. The great advantage of this approach is that it can simulate local matrix/fracture exchanges on large fractured media in a much faster and more appropriate way. Indeed, the simulation can be carried out with a much smaller number of cells compared to a fully explicit discretization of both matrix and fracture media. The proposed approach presents other advantages owing to its great flexibility. Indeed, it accurately handles the cases in which flows are not controlled by fractures alone; either the fracture network may be not hydraulically connected from one well to another, or the matrix may have a high permeability in some places. Finally, well-test cases demonstrate the reliability of the method and its range of application. Introduction In recent years, numerous research programs have been focusing on the topic of fractured reservoirs. Major advances were made, and oil companies now benefit from efficient methodologies, tools, and software for fractured reservoir studies. Nowadays, a study of a fractured reservoir, from fracture detection to full-field simulation, includes the following main steps: geological fracture characterization, hydraulic characterization of fractures, upscaling of fracture properties, and fractured reservoir simulation. Research on fractured reservoir simulation has a long history. In the early 1960s, Barenblatt and Zheltov1 first introduced the dual-porosity concept, followed by Warren and Root,2 who proposed a simplified representation of fracture networks to be used in dual-porosity simulators. Based on this concept, reservoir simulators3 are now able to correctly reproduce the main driving mechanisms occurring in fractured reservoirs, such as water imbibition, gas/oil and water/oil gravity drainage, molecular diffusion, and convection in fractures. Even single-medium simulators can perform fractured reservoir simulation when adequate pseudocapillary pressure curves and pseudorelative permeability curves can be input. Indeed, except for particular cases such as thermal recovery processes, full-field simulation of fractured reservoirs is no longer a problem. Geological characterization of fractures progressed considerably in the 1990s. The challenge was to analyze and integrate all the available fracture data to provide a reliable description of the fracture network both at field scale and at local reservoir cell scale. Tools have been developed for merging seismic, borehole imaging, lithological, and outcrop data together with the help of geological and geomechanical rules.3 These tools benefited from the progress of seismic acquisition and borehole imaging. Indeed, accurate seismic data lead to reliable models of large-scale fracture networks, and borehole imaging gives the actual fracture description along the wells, which enables a reliable statistical determination of fracture attributes. Finally, these tools provide realistic pictures of fracture networks. They are applied successfully in numerous fractured-reservoir studies. The upscaling of fracture properties is the problem of translating the geological description of fracture networks into reservoir simulation parameters. Two approaches are possible. In the first one, the fractured reservoir is considered as a very heterogeneous matrix reservoir; therefore, one applies the classical techniques available for heterogeneous single-medium upscaling. The second approach is based on the dual-porosity concept and consists of upscaling the matrix and the fracture separately. Based on this second approach, methodologies and software were developed in the 1990s to calculate equivalent fracture parameters with respect to the dual-porosity concept (i.e., a fracture-permeability tensor with main flow directions and anisotropy and a shape factor that controls the matrix/fracture exchange kinetics3–5). For a given reservoir grid cell, the upscaling procedures consist of generating the corresponding 3D discrete fracture network and computing the equivalent parameters from this network. In particular, the permeability tensor is computed from the results of steady-state flow simulations in the discrete fracture network alone (without the matrix).

Problems in Characterization of Naturally Fractured Reservoirs From Well Test Data

1985 ◽  
Vol 25 (03) ◽  
pp. 445-450 ◽  
Author(s):  
I. Ershaghi ◽  
R. Aflaki
Keyword(s):  
Test Data ◽  
Transition Period ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Late Time ◽  
Time Data ◽  
Straight Line ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix

Abstract This paper presents a critical analysis of some recently published papers on naturally fractured reservoirs. These published papers on naturally fractured reservoirs. These publications have pointed out that for a publications have pointed out that for a matrix-to-fracture-gradient flow regime, the transition portion of pressure test data on the semilog plot develops a portion of pressure test data on the semilog plot develops a slope one half that of the late-time data. We show that systems under pseudosteady state also may develop a 1:2 slope ratio. Examples from published case studies are included to show the significant errors associated with the characterization of a naturally fractured system by using the 1:2 slope concept for semicomplete well tests. Introduction Idealistic models of the dual-porosity type often have been recommended for interpretation of a well test in naturally fractured reservoirs. The evolutionary aspects of these models have been reviewed by several authors. Gradual availability of actual field tests and recent developments in analytical and numerical solution techniques have helped to create a better understanding of application and limitation of various proposed models. Two important observations should be made here. First, just as it is now recognized that classical work published by Warren and Root in 1963 was not the end of the line for interpretation of the behavior of naturally fractured systems, the present state of knowledge later may be considered the beginning of the technology. Second, parallel with the ongoing work by various investigators who progressively include more realistic assumptions in their progressively include more realistic assumptions in their analytical modeling, one needs to ponder the implication of these findings and point out the inappropriate impressions that such publications may precipitate in the mind of practicing engineers. practicing engineers. This paper is intended to scrutinize statements published in recent years about certain aspects of the anticipated transition period developed on the semilog plot of pressure-drawdown or pressure-buildup test data. pressure-drawdown or pressure-buildup test data. The Transition Period In the dual-porosity models published to date, a naturally fractured reservoir is assumed to follow the behavior of low-permeability and high-storage matrix blocks in communication with a network of high-permeability and low-storage fractures. The difference among the models has been the assumed geometry of the matrix blocks or the nature of flow between the matrix and the fracture. However, in all cases, it is agreed that a transition period develops that is strictly a function of the matrix period develops that is strictly a function of the matrix properties and matrix-fracture relationship. Fig. 1 shows properties and matrix-fracture relationship. Fig. 1 shows a typical semilog plot depicting the transition period and the parallel lines. Estimation of Warren and Root's proposed and to characterize a naturally fractured proposed and to characterize a naturally fractured system requires the development of the transition period. The Warren and Root model assumes a set of uniformly distributed matrix blocks. Furthermore, the flow from matrix to fracture is assumed to follow a pseudosteady-state regime. Under such conditions, in theory, this period is an S-shaped curve with a point of inflection. Uldrich and Ershaghi developed a technique to use the coordinates of this point of inflection for estimating and under conditions where either the early- or the late-time straight lines were not available. Kazemi and de Swann presented alternative approaches to represent naturally fractured reservoirs. They assumed a geometrical configuration consisting of layered matrix blocks separated by horizontal fractures. Their observation was that for such a system the transition period develops as a straight line with no inflection point. Bourdet and Gringarten identified a semilog straight line during the transition period for unsteady-state matrix-fracture flow. Recent work by Streltsova and Serra et al emphasized the transient nature of flow from matrix to fracture and pointed out the development of a unique slope ratio. These authors, later joined by Cinco-L. and Samaniego-V., stated that under a transient flow condition, the straight-line shape of the transition period develops a slope that is numerically one-half the slope of the parallel straight lines corresponding to the early- or late-time data. It was further pointed out that the transient flow model is a more realistic method of describing the matrix-fracture flow. As such, they implied that in the absence of wellbore-storage-free early-time data, or late-time data in the case of limited-duration tests, one may use the slope of the transition straight line and proceed with the estimation of the reservoir properties. Statement of the Problem The major questions that need to be addressed at this time are as follows. SPEJ P. 445

Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distribution

1969 ◽  
Vol 9 (04) ◽  
pp. 451-462 ◽  
Author(s):  
H. Kazemi
Keyword(s):  
Fractured Reservoirs ◽  
Low Flow ◽  
Fractured Reservoir ◽  
Naturally Fractured Reservoir ◽  
Pressure Transient ◽  
Flow Capacity ◽  
Naturally Fractured ◽  
The Matrix ◽  
Fracture Distribution

Abstract An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. Introduction The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.).

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