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^

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

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

An Analytical Study of Interference in Composite Reservoirs

1985 ◽  
Vol 25 (02) ◽  
pp. 281-290 ◽  
Author(s):  
Abdurrahman Satman
Keyword(s):  
Pressure Drop ◽  
Composite System ◽  
Pressure Response ◽  
Oil Field ◽  
Observation Well ◽  
Wellbore Storage ◽  
Interference Test ◽  
Interference Tests ◽  
Inner Region ◽  
Observation Wells

Satman, Abdurrahman; SPE; Technical U. of Istanbul Abstract This paper discusses the interference test in composite reservoirs. The composite model considers all important parameters of interest: the hydraulic diffusivity, the mobility ratio, the distance to the radial discontinuity, the distance between wells, the wellbore storage, and skin effect at the active well. Type curves expressed as a function of proper combinations of these parameters are presented. Introduction Interference tests are widely used to estimate the reservoir properties. An interference test is a multiwell test that requires at least one active well, either a producer or injector, and at least one observation well. During the test, pressure effects caused by the active well are measured at the shut-in observation wells. Basic techniques for analyzing interference tests in uniform systems are discussed in Ref. 1. Usually, type-curve matching is the preferred technique for analyzing the pressure data from the test. Early interference test studies assumed that the storage capacity of the active well and the skin region around the sandface have a negligible effect on the observation well response. Recently, investigators have focused on wellbore storage and skin effects. Tongpenyai and Raghavan presented a new solution for analyzing the pressure response at the presented a new solution for analyzing the pressure response at the observation well, which took into account the effects of wellbore storage and skin at both the active and the observation wells. They produced type curves expressed as a function of exp(2S) products, the ( / ) ratios, and ( / ) to correlate the pressure response at the observation well. Composite systems are encountered in a wide variety of reservoir situations. In a composite system, there is a circular inner region with fluid and rock properties different from those in the outer region. Such a system can occur in hydrocarbon reservoirs and geothermal reservoirs. The injection of fluids during EOR processes can cause the development of fluid banks around the injection wells. This would be true in the case of a in-situ combustion or a steamflood. In a geothermal reservoir, pressure reduction in the vicinity of the well may cause the phase boundaries. A producing well completed in the center of a circular hot zone surrounded by producing well completed in the center of a circular hot zone surrounded by a concentric cooler water region is also a composite system. During the early to late 1960's, there was great interest in the composite reservoir flow problem. Hurst discussed the "sands in series" problem. He presented the formulas to describe the pressure behavior of problem. He presented the formulas to describe the pressure behavior of the unsteady-state flow phenomenon for fluid movement through two sands in series in a radial configuration, with each sand of different permeability. Mortada studied the interference pressure drop for oil fields located in a nonuniform extensive aquifer comprising two regions of different properties. He presented an expression for the interference pressure drop properties. He presented an expression for the interference pressure drop in an oil field resulting from a constant rate of water influx in another oil field. Loucks and Guerrero presented a qualitative discussion of pressure drop characteristics in composite reservoirs. Ramey and Rowan and pressure drop characteristics in composite reservoirs. Ramey and Rowan and Clegg developed approximate solutions. Refs. 11 through 13 also discuss composite reservoir systems and present either analytical or numerical solutions. Composite system model solutions have been used to determine some critical parameters during the application of EOR processes. The formation of a fluid bank around the injection well makes the reservoir a composite system. Van Poollen and Kazemi discussed how to determine the mean distance to the radial discontinuity in an in-situ combustion project. Refs. 16 and 17 discuss the effect of radial discontinuity in interpretation of pressure falloff tests in reservoirs with fluid banks. Sosa et al. examined the effect of relative permeability and mobility ratio on falloff behavior in reservoirs with water banks. The presence of different temperature zones in nonisothermal reservoirs may resemble permeability boundaries during well testing. Mangold et al. presented a numerical study of a thermal discontinuity in well test analysis. Their results indicated that nonisothermal influence could be detected and accounted for by tests of sufficient duration with suitably placed observation wells. Horne et al. indicated the possibility of determining compressibility and permeability contrasts across the phase boundaries in geothermal reservoirs. The most recent study of well test analysis in composite reservoirs was by Eggenschwiler, Satman et al. Their studies presented a very general composite system model. The problem was solved analytically by using the Laplace transformation with numerical inversion. The solution concerned the transient flow of a slightly compressible fluid in a porous medium during injection or falloff for a single well confined in concentric regions of differing mobilities and hydraulic diffusivities. The system assumed both wellbore storage and a skin effect. Their results indicated that a pseudosteady-state pressure response exists in the transition region between the inner region and outer region semilog straight lines. This response is drawn on a Cartesian vs. plot, the slope of which is used to estimate the bulk volume of the inner region. SPEJ p. 281

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.).

The Influence of Vertical Fractures Intercepting Active and Observation Wells on Interference Tests

1982 ◽  
Vol 22 (06) ◽  
pp. 933-944 ◽  
Author(s):  
Naelah A. Mousli ◽  
Rajagopal Raghavan ◽  
Heber Cinco-Ley ◽  
Fernando Samaniego-V.
Keyword(s):  
Test Data ◽  
A Priori ◽  
Pressure Response ◽  
Fracture Plane ◽  
Observation Well ◽  
Compass Orientation ◽  
Vertical Fracture ◽  
Wellbore Storage ◽  
Interference Test ◽  
Observation Wells

Abstract This paper reviews pressure behavior at an observation well intercepted by a vertical fracture. The active well was assumed either unfractured or intercepted by a fracture parallel to the fracture at the observation well. We show that a vertical fracture at the observation well has a significant influence on the pressure response at that well, and therefore wellbore conditions at the observation well must be considered. New type curves presented can be used to determine the compass orientation of the fracture plane at the observation well. Conditions are delineated under which the fracture at the observation well may influence an interference test. This information should be useful in designing and analyzing tests. The pressure response curve at the observation well has no characteristic features that will reveal the existence of a fracture. The existence of the fracture would have to be known a priori or from independent measurements such as single-well tests. Introduction In this work, we examine interference test data for the influence of a vertical fracture located at the observation well. All studies on the subject of interference testing have been directed toward understanding the effects of reservoir heterogeneity or wellbore conditions at the active (flowing) well. Several correspondents suggested our study because many field tests are conducted when the observation well is fractured. They also indicated that it is not uncommon for both wells (active and observation) to be fractured. To the best of our knowledge, this is the first study to examine the influence of a vertical fracture at the observation well on interference test data. Two conditions at the active well are examined: an active well that is unfractured (plane radial flow) and an active well that intercepts a vertical fracture parallel to the fracture at the observation well. The parameters of interest include effects of the distance between the two wells, compass orientation of the fracture plane with respect to the line joining the two wellbores, and the ratio of the fracture lengths at the active and observation wells if both wells are fractured. The results given here should enable the analystto interpret the pressure response at the fractured observation well.to interpret the pressure response when both the active and the observation wells are fracturedto design tests to account for the existence of a fracture at one or both wells, andto determine quantitatively the orientation and/or length of the fracture at an observation well. We also show that one should not assume a priori that the effect of a fracture on the observation well response will be similar to that of a concentric skin region around the wellbore-i.e., idealizations to incorporate the existence of the fracture, such as the effective wellbore radius concept, may not be applicable. Mathematical Model and Assumptions In this study, we consider the flow of a slightly compressible fluid of constant viscosity in a uniform and homogeneous porous medium of infinite extent. Fluid is produced at a constant surface rate at the active well. Wellbore storage effects are assumed negligible because the main objective of our work is to demonstrate the influence of the fractures. However, note that wellbore storage effects may mask the early-time response at the observation well. Refs. 1 and 2 discuss the influence of wellbore storage on interference test data. We obtained the solutions to the problems considered here by the method of sources and sinks. The fracture at the observation well was assumed to be a plane source of infinite conductivity. SPEJ P. 933^

Calibration of naturally fractured reservoir models using integrated well-test analysis – an illustration with field data from the Barents Sea

2021 ◽  
pp. petgeo2020-042
Author(s):  
D. Egya ◽  
P. W. M. Corbett ◽  
S. Geiger ◽  
J. P. Norgard ◽  
S. Hegndal-Andersen
Keyword(s):  
Field Data ◽  
Barents Sea ◽  
Fractured Reservoirs ◽  
Pressure Response ◽  
Fractured Reservoir ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
The Barents Sea ◽  
Naturally Fractured

This paper successfully applied the geoengineering workflow for integrated well-test analysis to characterise fluid flow in a newly discovered fractured reservoir in the Barents Sea. A reservoir model containing fractures and matrix was built and calibrated using this workflow to match complex pressure transients measured in the field. We outline different geological scenarios that could potentially reproduce the pressure response observed in the field, highlighting the challenge of non-uniqueness when analysing well-test data. However, integrating other field data into the analysis allowed us to narrow the range of uncertainty, enabling the most plausible geological scenario to be taken forward for more detailed reservoir characterisation and history matching. The results provide new insights into the reservoir geology and the key flow processes that generate the pressure response observed in the field. This paper demonstrates that the geoengineering workflow used here can be applied to better characterise naturally fractured reservoirs. We also provide reference solutions for interpreting well-tests in fractured reservoirs where troughs in the pressure derivative are recognisable in the data.

Pressure Transient Analysis Methods for Bounded Naturally Fractured Reservoirs

1985 ◽  
Vol 25 (03) ◽  
pp. 451-464 ◽  
Author(s):  
Chih-Cheng Chen ◽  
Kelsen Serra ◽  
Albert C. Reynolds ◽  
Rajagopal Raghavan
Keyword(s):  
Flow Regime ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Fractured Reservoir ◽  
Pressure Data ◽  
Naturally Fractured Reservoir ◽  
State Flow ◽  
Wellbore Pressure ◽  
Naturally Fractured ◽  
The Matrix

Abstract New methods for analyzing drawdown and buildup pressure data obtained at a well located in an infinite, pressure data obtained at a well located in an infinite, naturally fractured reservoir were presented recently. In this work, the analysis of both drawdown and buildup data in a bounded, naturally fractured reservoir is considered. For the bounded case, we show that five possible flow regimes may be exhibited by drawdown data. We delineate the conditions under which each of these five flow regimes exists and the information that can be obtained from each possible combination of flow regimes. Conditions under which semilog methods can be used to analyze buildup data are discussed for the bounded fractured reservoir case. New Matthews-Brons-Hazebroek (MBH) functions for computing the average reservoir pressure from buildup data are presented. pressure from buildup data are presented. Introduction This work considers the analysis of pressure data obtained at a well located at the center of a cylindrical, bounded, naturally fractured reservoir of uniform thickness. As is typical, a naturally fractured reservoir indicates a reservoir system in which the conductive properties of the rock are mainly due to the fracture system, and the rock matrix provides most of the storage capacity of the system. Several models of naturally fractured reservoirs have been presented m the literature. Warren and Root and Odeh presented m the literature. Warren and Root and Odeh assume "pseudosteady-state flow" in the matrix, whereas Kazemi, deSwaan, Najurieta, and Kucuk and Sawyers assume unsteady-state flow. The model used in this study is identical to the one considered in Refs. 4, 5, 7, and 8; however, these works considered only infinite-acting reservoirs. To our knowledge, the behavior of wells in bounded, naturally fractured reservoirs with unsteady-state flow in the matrix system has not been examined until now. This work considers the analysis of constant-rate production and buildup pressure data in a bounded, naturally production and buildup pressure data in a bounded, naturally fractured reservoir. For a bounded reservoir, we show that there are five distinct, useful flow regimes that may be exhibited by drawdown data. Flow Regimes 1, 2, and 11 are identical to the flow regimes identified in Refs. 7 and 8. During each of these three flow regimes, a semilog plot of the dimensionless wellbore pressure drop vs. plot of the dimensionless wellbore pressure drop vs. dimensionless time exhibits a straight line. The information that can be obtained from the various possible combinations of Flow Regimes 1 through 3 is discussed in Refs. 7 and 8. Flow Regime 5 corresponds to pseudo-steady-state flow. Flow Regime 4 denotes a flow pseudo-steady-state flow. Flow Regime 4 denotes a flow period during which a Cartesian graph of the dimensionless period during which a Cartesian graph of the dimensionless wellbore pressure drop vs. the square root of dimensionless time will be a straight line. In this work, we first establish the conditions under which each of the flow regimes exists. In particular, we show that Flow Regime 3 does not exist unless either the drainage radius or the dimensionless fracture transfer coefficient is large. Second, we show that useful information can be obtained from drawdown pressure data that reflect Flow Regime 4. Third, we delineate conditions that ensure that the methods of Refs. 7, and 8 can be used to analyze buildup data. Finally, we present new MBH functions for computing the average reservoir pressure in a naturally fractured reservoir. Mathematical Model We consider laminar flow of a slightly compressible, single-phase fluid of constant viscosity in an isotropic, cylindrical, naturally fractured reservoir of uniform thickness. Gravitational forces are negligible. The top, bottom, and outer reservoir boundaries are closed. A well located at the center of the cylinder is produced at a constant rate and then shut in to obtain buildup data. Initially, the pressure is uniform throughout the reservoir. We assume that all production is by way of the fracture system and that we have one-dimensional (ID), unsteady-state flow in the matrix. The matrix structure consists of "rectangular slabs"; that is, the matrix is divided by a set of parallel horizontal fractures. A schematic of the reservoir geometry is shown in Fig. 1. We consider an infinitesimally thin skin and neglect wellbore storage effects. The properties of both the matrix and fracture systems are assumed to be constant. Thus, our current model is identical to the one considered in Ref. 7 except that here the reservoir is assumed to be bounded. Because of symmetry, the mathematical problem can be formulated by considering only the repetitive element of Fig. 1. SPEJ p. 451

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

scholarly journals Interference test interpretation in naturally fractured reservoirs

DYNA ◽  
2020 ◽  
Vol 87 (214) ◽  
pp. 121-128
Author(s):  
Freddy Humberto Escobar ◽  
Carlos Andrés Torregrosa Marlés ◽  
Guiber Olaya Marín
Keyword(s):  
Reservoir Characterization ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Fractured Reservoir ◽  
Pressure Derivative ◽  
Naturally Fractured ◽  
Characteristic Points ◽  
Interference Test ◽  
Interference Tests ◽  
Analytical Expressions

The naturally fractured reservoir characterization is crucial because it can help to predict the flow pattern of fluids, and the storativity ratio of the fractures and to understand whether two or more wells have communication, among others. This paper presents a practical methodology for interpreting interference tests in naturally fractured reservoirs using characteristic points found on the pressure derivative curve. These kinds of tests describe a system that consists of a producing well and an observation well separated by a distance (r). Using characteristic points and features found on the pressure and pressure derivative log-log plot, Analytical expressions were developed from the characteristic points of the pressure and pressure derivative log-log plot to determine the interporosity flow parameter (λ) and the storativity ratio of the fractures (ω). Finally, examples are used to successfully verify the expressions developed so that the naturally-fractured parameters were reproduced with good accuracy.

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).

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