Improvements in Simulation of Naturally Fractured Reservoirs

1983 ◽  
Vol 23 (04) ◽  
pp. 695-707 ◽  
Author(s):  
James R. Gilman ◽  
Hossein Kazemi

Abstract Simulation of multiphase flow in heterogeneous two-porosity reservoirs such as naturally fractured systems is a difficult problem. In the last several years much progress has been made in this area. This paper focuses on progress has been made in this area. This paper focuses on the practical aspects of that technology. It describes a stable, flexible, fully implicit, finite-difference simulator in heterogeneous, two-porosity reservoirs. Flow rates and wellbore pressures are solved simultaneously along with fracture and matrix fluid saturations and pressures at all grid points. Hydrodynamic pressure gradient is maintained at formation perforations in the wellbore. The simulator is accurate enough to match analytical solutions to single-phase problems. The equations have been extended to include polymer flooding and tracer transport with nine-point connection for determining severe local channeling and directional tendencies. It is shown that the two-porosity model presented in this paper will produce essentially the same answers as the paper will produce essentially the same answers as the common single-porosity model of a highly heterogeneous system but with a substantial reduction of computing time. In addition, this paper describes in detail several two-porosity parameters not fully discussed in previous publications. previous publications. Introduction Naturally fractured reservoir simulators are developed to simulate fluid flow in systems in which fractures are interconnected and provide the main flow path to injection and production wells. The fractures have high permeability and low storage volume, the reservoir rock permeability and low storage volume, the reservoir rock (matrix blocks) has low permeability and high storage volume. The idealization of assuming one porosity as the continuum can apply to many heterogeneous systems where one porosity provides the main path for fluid flow and the other porosity acts as a source. Throughout this paper, the fracture should be thought of as the continuum paper, the fracture should be thought of as the continuum and the matrix perceived as the adjacent sources or sinks. For single-phase flow of a gas or liquid, fluid compression and viscous forces control fluid movement. Gravity and capillary forces are not pertinent. Several single-phase idealizations that produce essentially the same practical engineering answers are discussed in the literature. Fig. 1 shows a model with both vertical and horizontal fractures. Separate nodes are used for fracture and matrix. For this case, 77 nodes are used to model the system. Fig. 2 also shows a model that allows vertical and horizontal fractures. However, this model requires far fewer nodes because areas in which the matrix blocks behave similarly are grouped in a single node. Each gridblock may contain many matrix blocks. The matrix blocks act as sources that feed into the fractures in a gridblock. The fractures can be thought of as a system of connected pipes. This model was proposed by Warren and Root. The boundary conditions used can make a dramatic difference in simulation results. Generally, we assume that only the fractures produce into the wellbore and are the path of fluid flow from one gridblock to the next. For multiphase flow, three forces must be properly accounted for--viscous, gravity, and capillary. In this case, we might require that the matrix blocks be further divided into grid blocks to obtain better definition of saturation distribution (Fig. 3). However, this will lead to additional work and may not be required. Kazemi et al. extended the Warren-Root model to multiphase systems to account for capillary and gravity forces. SPEJ P. 695

SPE Journal ◽  
2013 ◽  
Vol 18 (04) ◽  
pp. 670-684 ◽  
Author(s):  
S.. Geiger ◽  
M.. Dentz ◽  
I.. Neuweiler

Summary A major part of the world's remaining oil reserves is in fractured carbonate reservoirs, which are dual-porosity (fracture-matrix) or multiporosity (fracture/vug/matrix) in nature. Fractured reservoirs suffer from poor recovery, high water cut, and generally low performance. They are modeled commonly by use of a dual-porosity approach, which assumes that the high-permeability fractures are mobile and low-permeability matrix is immobile. A single transfer function models the rate at which hydrocarbons migrate from the matrix into the fractures. As shown in many numerical, laboratory, and field experiments, a wide range of transfer rates occurs between the immobile matrix and mobile fractures. These arise, for example, from the different sizes of matrix blocks (yielding a distribution of shape factors), different porosity types, or the inhomogeneous distribution of saturations in the matrix blocks. Thus, accurate models are needed that capture all the transfer rates between immobile matrix and mobile fracture domains, particularly to predict late-time recovery more reliably when the water cut is already high. In this work, we propose a novel multi-rate mass-transfer (MRMT) model for two-phase flow, which accounts for viscous-dominated flow in the fracture domain and capillary flow in the matrix domain. It extends the classical (i.e., single-rate) dual-porosity model to allow us to simulate the wide range of transfer rates occurring in naturally fractured multiporosity rocks. We demonstrate, by use of numerical simulations of waterflooding in naturally fractured rock masses at the gridblock scale, that our MRMT model matches the observed recovery curves more accurately compared with the classical dual-porosity model. We further discuss how our multi-rate dual-porosity model can be parameterized in a predictive manner and how the model could be used to complement traditional commercial reservoir-simulation workflows.


SPE Journal ◽  
2007 ◽  
Vol 12 (03) ◽  
pp. 367-381 ◽  
Author(s):  
Reza Naimi-Tajdar ◽  
Choongyong Han ◽  
Kamy Sepehrnoori ◽  
Todd James Arbogast ◽  
Mark A. Miller

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).


2006 ◽  
Vol 16 (10) ◽  
pp. 1627-1651 ◽  
Author(s):  
LI-MING YEH

In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let ε denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order ε2, microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε2, the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε2, then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.


1965 ◽  
Vol 5 (01) ◽  
pp. 60-66 ◽  
Author(s):  
A.S. Odeh

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


1983 ◽  
Vol 23 (01) ◽  
pp. 42-54 ◽  
Author(s):  
L. Kent Thomas ◽  
Thomas N. Dixon ◽  
Ray G. Pierson

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


1985 ◽  
Vol 25 (03) ◽  
pp. 445-450 ◽  
Author(s):  
I. Ershaghi ◽  
R. Aflaki

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


Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3699 ◽  
Author(s):  
Faisal Awad Aljuboori ◽  
Jang Hyun Lee ◽  
Khaled A. Elraies ◽  
Karl D. Stephen

Gravity drainage is one of the essential recovery mechanisms in naturally fractured reservoirs. Several mathematical formulas have been proposed to simulate the drainage process using the dual-porosity model. Nevertheless, they were varied in their abilities to capture the real saturation profiles and recovery speed in the reservoir. Therefore, understanding each mathematical model can help in deciding the best gravity model that suits each reservoir case. Real field data from a naturally fractured carbonate reservoir from the Middle East have used to examine the performance of various gravity equations. The reservoir represents a gas–oil system and has four decades of production history, which provided the required mean to evaluate the performance of each gravity model. The simulation outcomes demonstrated remarkable differences in the oil and gas saturation profile and in the oil recovery speed from the matrix blocks, which attributed to a different definition of the flow potential in the vertical direction. Moreover, a sensitivity study showed that some matrix parameters such as block height and vertical permeability exhibited a different behavior and effectiveness in each gravity model, which highlighted the associated uncertainty to the possible range that often used in the simulation. These parameters should be modelled accurately to avoid overestimation of the oil recovery from the matrix blocks, recovery speed, and to capture the advanced gas front in the oil zone.


Solid Earth ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 35-58
Author(s):  
Martin Balcewicz ◽  
Benedikt Ahrens ◽  
Kevin Lippert ◽  
Erik H. Saenger

Abstract. The importance of research into clean and renewable energy solutions has increased over the last decade. Geothermal energy provision is proven to meet both conditions. Therefore, conceptual models for deep geothermal applications were developed for different field sites regarding different local conditions. In Bavaria, Germany, geothermal applications were successfully carried out in carbonate horizons at depths of 4000 to 6000 m. Matrix permeability and thermal conductivity was mainly studied in karstified carbonates from the Late Jurassic reef facies. Similar to Bavaria, carbonates are located in the east of the Rhenohercynian Massif, in North Rhine-Westphalia (NRW), for which quantification of the geothermal potential is still lacking. Compared to Bavaria, a supraregional carbonate mountain belt is exposed at the Remscheid-Altena anticline (in NRW) from the Upper Devonian and Lower Carboniferous times. The aim of our study was to examine the potential geothermal reservoir by field and laboratory investigations. Therefore, three representative outcrops in Wuppertal, Hagen-Hohenlimburg, and Hönnetal were studied. During field surveys, 1068 discontinuities (139 open fractures without any filling, 213 joints, 413 veins filled with calcite, and 303 fractures filled with debris deposits) at various spatial scales were observed by scanline surveys. These discontinuities were characterized by trace length, true spacing, roughness, aperture, and filling materials. Discontinuity orientation analysis indicated three dominant strike orientations in NNW–SSE, NW–SE, and NE–SW directions within the target horizon of interest. This compacted limestone layer (Massenkalk) is approximately 150 m thick and located at 4000 to 6000 m depth, dipping northwards at a dip angle of about 30 to 40∘. An extrapolation of the measured layer orientation and dip suggests that the carbonate reservoir could hypothetically extend below Essen, Bochum, and Dortmund. Our combined analysis of the field and laboratory results has shown that it could be a naturally fractured carbonate reservoir. We evaluated the potential discontinuity network in the reservoir and its orientation with respect to the prevailing maximum horizontal stress before concluding with implications for fluid flow: we proposed focusing on prominent discontinuities striking NNW–SSE for upcoming geothermal applications, as these (1) are the most common, (2) strike in the direction of the main horizontal stress, (3) have a discontinuity permeability that significantly exceeds that of the reservoir rock matrix, and (4) only about 38 % of these discontinuities were observed with a calcite filling. The remaining discontinuities either showed no filling material or showed debris deposits, which we interpret as open at reservoir depth. Our results indicate that even higher permeability can be expected for karstified formations related to the reef facies and hydrothermal processes. Our compiled data set, consisting of laboratory and field measurements, may provide a good basis for 3D subsurface modelling and numerical prediction of fluid flow in the naturally fractured carbonate reservoir.


Sign in / Sign up

Export Citation Format

Share Document