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Kuchuk, Fikri, and Denis Biryukov. "Pressure-Transient Tests and Flow Regimes in Fractured Reservoirs." SPE Reservoir Evaluation & Engineering 18, no. 02 (March 31, 2015): 187–204. http://dx.doi.org/10.2118/166296-pa.
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Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.
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Kuchuk, Fikri, and Denis Biryukov. "Pressure-Transient Behavior of Continuously and Discretely Fractured Reservoirs." SPE Reservoir Evaluation & Engineering 17, no. 01 (January 30, 2014): 82–97. http://dx.doi.org/10.2118/158096-pa.
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Summary Fractures are common features of many well-known reservoirs. Naturally fractured reservoirs contain fractures in igneous, metamorphic, and sedimentary formations. Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to many fractures with varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (i.e., not a connected-network fracture system). New semianalytical solutions are used to understand the pressure behavior of naturally fractured reservoirs containing a network of discrete and/or connected (continuous) finite- and infinite-conductivity fractures. We present an extensive literature review of the pressure-transient behavior of fractured reservoirs. First, we show that the Warren and Root (1963) dual-porosity model is a fictitious homogeneous porous medium because it does not contain any fractures. Second, by use of the new solutions, we show that for most naturally fractured reservoirs, the Warren and Root (1963) dual-porosity model is inappropriate and fundamentally incomplete for the interpretation of pressure-transient well tests because it does not capture the behavior of these reservoirs. We examined many field well tests published in the literature. With few exceptions, none of them shows the behavior of the Warren and Root (1963) dual-porosity model. These examples exhibit very diverse pressure behaviors of discretely and continuously fractured reservoirs. Unlike the single derivative shape of the Warren and Root (1963) model, the derivatives of these examples exhibit many different flow regimes depending on fracture distribution and on their intensity and conductivity. We show these flow regimes with our new model for discretely and continuously fractured reservoirs. Most well tests published in the literature do not exhibit the Warren and Root (1963) dual-porosity reservoir-model behavior. If we interpret them by use of this dual-porosity model, then the estimated permeability, skin factor, interporosity flow coefficient (λ), and storativity ratio (ω) will not represent the actual reservoir parameters.
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Evans, R. D., and S. D. L. Lekia. "A Reservoir Simulation Study of Naturally Fractured Lenticular Tight Gas Sand Reservoirs." Journal of Energy Resources Technology 112, no. 4 (December 1, 1990): 231–38. http://dx.doi.org/10.1115/1.2905763.
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The results of parametric studies of two naturally fractured lenticular tight gas reservoirs, Fluvial E-1 and Puludal Zones 3 and 4, of the U.S. Department of Energy Multi-Well Experiment (MWX) site of Northwestern Colorado are presented and discussed. The three-dimensional, two-phase, black oil reservoir simulator that was developed in a previous phase of this research program is also discussed and the capabilities further explored by applying it to several example problems. The simulation studies lead to the conclusion that 1) at early times the reservoir performance does not depend on lenticularity; 2) the initial reservoir performance does not depend on natural fracture concentration, although at later times the performance predictions of systems with lower natural fracture concentrations begin to fall below the ones with higher concentrations; 3) porosity change with time and pressure leads to double performance prediction reversals when comparing gas flow rates and cumulative gas production from naturally fractured and non-naturally fractured tight gas reservoirs; 4) the assumption of zero capillary pressure in the fractures can lead to erroneous predictions in the simulation of naturally fractured tight gas reservoir performance; and 5) the simulator developed in a prior phase of this project is capable of handling a reservoir block that is blanket sand, lenticular, completely fractured, partially fractured or completely unfractured and is amenable to an anisotropic heterogeneous reservoir whether the reservoir is fractured or not.
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Ali, Mahmoud T., Ahmed A. Ezzat, and Hisham A. Nasr-El-Din. "A Model To Simulate Matrix-Acid Stimulation for Wells in Dolomite Reservoirs with Vugs and Natural Fractures." SPE Journal 25, no. 02 (October 23, 2019): 609–31. http://dx.doi.org/10.2118/199341-pa.
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Summary Designing matrix-acid stimulation treatments in vuggy and naturally fractured carbonate reservoirs is a challenging problem in the petroleum industry. It is often difficult to physically model this process, and current mathematical models do not consider vugs or fractures. There is a significant gap in the literature for models that design and evaluate matrix-acid stimulation in vuggy and naturally fractured carbonate reservoirs. The objective of this work is to develop a new model to simulate matrix acidizing under field conditions in vuggy and naturally fractured carbonates. To obtain accurate and reliable simulation parameters, acidizing coreflood experiments were modeled using a reactive-flow simulator. A 3D radial field-scale model was used to study the flow of acid in the presence of vugs (pore spaces that are significantly larger than grains) and natural fractures (breaks in the reservoir that were formed naturally by tectonic events). The vugs’ size and distribution effects on acid propagation were studied under field conditions. The fracture length, conductivity, and orientation, and the number of fractures in the formation, were studied by the radial model. The results of the numerical simulation were used to construct Gaussian-process (GP)-based surrogate models for predicting acid propagation in vuggy and naturally fractured carbonates. Finally, the acid propagation in vuggy/naturally fractured carbonates was evaluated, as well.The simulation results of vuggy carbonates show that the presence of vugs in carbonates results in faster and deeper acid propagation in the formation when compared with homogeneous reservoirs at injection velocities lower than 8×10–4 m/s. Results also revealed that the size and density of the vugs have a significant impact on acid consumption and the overall performance of the acid treatment. The output of the fracture model illustrates that under field conditions, fracture orientations do not affect the acid-propagation velocity. The acid does not touch all of the fractures around the well. The GP model predictions have an accuracy of approximately 90% for both vuggy and naturally fractured cases. The vuggy/naturally fractured model simulations reveal that fractures are the main reason behind the fast acid propagation in these highly heterogeneous reservoirs.
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Xu, Lin Jing, Shi Cheng Zhang, and Jian Ye Mou. "Acid Leakoff Mechanism in Acid Fracturing of Naturally Fractured Carbonate Gas Reservoirs." Advanced Materials Research 868 (December 2013): 682–85. http://dx.doi.org/10.4028/www.scientific.net/amr.868.682.
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In acid fracturing, excessive acid leakoff is thought to be the main reason that limits fracture propagation and live acid penetration distance, so its very important to do research about acid leak-off on naturally fractured carbonates. we developed a new model in this paper to simulate acid leakoff into a naturally fractured carbonates gas reservoir during acid fracturing. Our model incorporates the acid-rock reaction on the fractured surfaces. Given the information of the Puguang gas reservoir, the model predicts acid filtration and leakoff rate over time. In this study, we found that acid leak-off mechanism in naturally fractured carbonates is much different from that in reservoirs without natural fractures. The leakoff volume is several times of nonreactive acid. Since the acid widened natural fractures, leakoff velocity increase with time firstly , then decrease. While the leakoff velocity of the nonreactive fluid decrease sustained. We also analyze other sensitivity parameters of the acid leakoff. In this model, we explain the acid leakoff mechanism in naturally fractured carbonates, and provide a more accurate calculating of fluid loss.
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Rezk, Mohamed Gamal, and A. A. Abdelwaly. "Estimation of characteristics of naturally fractured reservoirs by pressure transient analysis." World Journal of Engineering 14, no. 5 (October 2, 2017): 368–80. http://dx.doi.org/10.1108/wje-10-2016-0110.
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Purpose This paper aims to analyze the pressure behavior in dual porosity reservoirs using different techniques in an attempt to correctly characterize reservoir properties. Pressure transient tests in naturally fractured reservoirs often exhibit non-uniform responses. Design/methodology/approach The pressure transient tests in naturally fractured reservoirs were analyzed using conventional semi-log analysis, type curve matching (using commercial software) and Tiab’s direct synthesis (TDS) technique. In addition, the TDS method was applied in case of a naturally fractured formation with a vertical hydraulic fracture. These techniques were applied to a single-layer, naturally fractured reservoir under pseudosteady state matrix flow. By studying the unique characteristics of the different flow regimes appear on the pressure and pressure derivative curves, various reservoir characteristics can be obtained such as permeability, skin factor and fracture properties. Findings For naturally fractured reservoirs, a comparison between the results semi-log analysis, software matching and TDS method is presented. In case of wellbore storage, early time flow regime can be obscured that lead to incomplete semi-log analysis. Furthermore, the type curve matching usually gives a non-uniqueness solution, as it needs all the flow regimes to be observed. However, the direct synthesis method used analytical equation to calculate reservoir and well parameters without type curve matching. For naturally fractured reservoirs with a vertical fracture, the pressure behavior of wells crossed by a uniform flux and infinite conductivity fracture is analyzed using TDS technique. The different flow regimes on the pressure derivative curve were used to calculate the fracture half-length in addition to other reservoir properties. Originality/value The results of different field cases showed that TDS technique offers several advantages compared to semi-log analysis and type curve matching. It can be used even if some flow regimes are not observed. Direct synthesis results are accurate compared to the available core data and the software matching results. It can be used to confirm the software matching results and to give reliable reservoir characteristics when there is lack of data.
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Moinfar, Ali, Abdoljalil Varavei, Kamy Sepehrnoori, and Russell T. Johns. "Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs." SPE Journal 19, no. 02 (July 24, 2013): 289–303. http://dx.doi.org/10.2118/154246-pa.
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Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.
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Al-Rubaie, Ali, and Hisham Khaled Ben Mahmud. "A numerical investigation on the performance of hydraulic fracturing in naturally fractured gas reservoirs based on stimulated rock volume." Journal of Petroleum Exploration and Production Technology 10, no. 8 (August 17, 2020): 3333–45. http://dx.doi.org/10.1007/s13202-020-00980-8.
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Abstract All reservoirs are fractured to some degree. Depending on the density, dimension, orientation and the cementation of natural fractures and the location where the hydraulic fracturing is done, preexisting natural fractures can impact hydraulic fracture propagation and the associated flow capacity. Understanding the interactions between hydraulic fracture and natural fractures is crucial in estimating fracture complexity, stimulated reservoir volume, drained reservoir volume and completion efficiency. However, because of the presence of natural fractures with diffuse penetration and different orientations, the operation is complicated in naturally fractured gas reservoirs. For this purpose, two numerical methods are proposed for simulating the hydraulic fracture in a naturally fractured gas reservoir. However, what hydraulic fracture looks like in the subsurface, especially in unconventional reservoirs, remain elusive, and many times, field observations contradict our common beliefs. In this study, the hydraulic fracture model is considered in terms of the state of tensions, on the interaction between the hydraulic fracture and the natural fracture (45°), and the effect of length and height of hydraulic fracture developed and how to distribute induced stress around the well. In order to determine the direction in which the hydraulic fracture is formed strikethrough, the finite difference method and the individual element for numerical solution are used and simulated. The results indicate that the optimum hydraulic fracture time was when the hydraulic fracture is able to connect natural fractures with large streams and connected to the well, and there is a fundamental difference between the tensile and shear opening. The analysis indicates that the growing hydraulic fracture, the tensile and shear stresses applied to the natural fracture.
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Costa, Luís Augusto Nagasaki, Célio Maschio, and Denis José Schiozer. "A new methodology to reduce uncertainty of global attributes in naturally fractured reservoirs." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 (2018): 41. http://dx.doi.org/10.2516/ogst/2018038.
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Accurately characterizing fractures is complex. Several studies have proposed reducing uncertainty by incorporating fracture characterization into simulations, using a probabilistic approach, to maintain the geological consistency, of a range of models instead of a single matched model. We propose a new methodology, based on one of the steps of a general history-matching workflow, to reduce uncertainty of reservoir attributes in naturally fractured reservoirs. This methodology maintains geological consistency and can treat many reservoir attributes. To guarantee geological consistency, the geostatistical attributes (e.g., fracture aperture, length, and orientation) are used as parameters in the history matching. This allows us to control Discrete Fracture Network attributes, and systematically modify fractures. The iterative sensitivity analysis allows the inclusion of many (30 or more) uncertain attributes that might occur in a practical case. At each uncertainty reduction step, we use a sensitivity analysis to identify the most influential attributes to treat in each step. Working from the general history-matching workflow of Avansi et al. (2016), we adapted steps for use with our methodology, integrating the history matching with geostatistical modeling of fractures and other properties in a big loop approach. We applied our methodology to a synthetic case study of a naturally fractured reservoir, based on a real semi-synthetic carbonate field, offshore Brazil, to demonstrate the applicability in practical and complex cases. From the initial 18 uncertain attributes, we worked with only 5 and reduced the overall variability of the Objective Functions. Although the focus is on naturally fractured reservoirs, the proposed methodology can be applied to any type of reservoir.
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Naimi-Tajdar, Reza, Choongyong Han, Kamy Sepehrnoori, Todd James Arbogast, and Mark A. Miller. "A Fully Implicit, Compositional, Parallel Simulator for IOR Processes in Fractured Reservoirs." SPE Journal 12, no. 03 (September 1, 2007): 367–81. http://dx.doi.org/10.2118/100079-pa.
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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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Schulte, William M., and Arnold S. de Vries. "In-Situ Combustion in Naturally Fractured Heavy Oil Reservoirs." Society of Petroleum Engineers Journal 25, no. 01 (February 1, 1985): 67–77. http://dx.doi.org/10.2118/10723-pa.
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Abstract In fractured reservoirs primary production of heavy oil is mainly from fractures (secondary porosity). Matrix oil can be produced only at a very low rate because of low oil mobility. In this paper, in-situ combustion is considered as an EOR method. Experiments are described which show that the burning process is governed by diffusion of oxygen from the fractures into the matrix. The main oil-production mechanisms were found to be thermal expansion and evaporation with subsequent condensation of the oil from the matrix. A semi-two-dimensional (2D) numerical simulator has been constructed for modeling the process. It incorporates the main physical mechanisms as found in the experiments; heat losses to cap or base rock and gravitational effects are not included. The model predicts that in-situ combustion in fractured reservoirs is feasible and will have a high recovery efficiency in the swept zone. Oxygen breakthrough was observed when the air-injection rate exceeded a critical value predominantly determined by the fracture spacing. This phenomenon and also the shape and width of the combustion zone can be explained by a simple analytical model, which is in fair agreement with the simulator results. The effect of heat losses on the velocity of the combustion front is estimated and a lower bound for the injection rate can be obtained in this way. Combining this lower bound with the upper bound for oxygen breakthrough leads to a maximum value for fracture spacing. This distance will be on the order of 1 m [3.28 ft]. The conclusion is that in-situ combustion appears to be a feasible process in a naturally fractured reservoir with a high recovery in the swept zone. However, for predictions for a particular reservoir, vertical sweep efficiency should be taken into account. Introduction For the production of oil from heavy-oil reservoirs, thermal methods are applied widely. One of these is the in-situ combustion (ISC) process. In this process, air is injected into the reservoir and the oxygen in the air burns part of the oil, thereby generating heat. In some field trials of this method the combustion process could not be sustained if there were fractures in the reservoir. Since fractures are much more permeable than the surrounding reservoir rock, the injected air will flow almost exclusively through the fractures and will contact only oil present in these fractures or in their immediate vicinity. Evidently this is not sufficient to sustain the combustion process; either the reaction rate is too low because the contact area between air flow and fracture walls is very small, or the total amount of fuel available for combustion might be insufficient. If only the low reaction rate is responsible for the dying out of the combustion process, the question arises whether ISC is feasible in densely fractured reservoirs (such as occur, for example, in the Middle East in Iran and Oman). These reservoirs are believed to contain several vertical fractures per 1 m [3.28 ft] of formation. It is easily tested that in densely fractured reservoirs the contact area between air flow and fracture walls might be sufficiently large to sustain combustion, assuming that sufficient fuel is available. Hence, to predict whether ISC is feasible in such reservoirs, it is necessary to gain predict whether ISC is feasible in such reservoirs, it is necessary to gain insight into the mechanisms by which fuel and oxygen come into contact. Experimental Setup The experimental setup is shown schematically in Fig. 1. Basically it consists of a stack of oil-saturated core plugs in a vertical pressure vessel. This vessel, designed for a working pressure of 4 MPa [580 psi] has an 1D of 27 mm [1 in.] and an internal length of 432 mm [17 in.]. To reduce heat losses from the vessel it can be heated locally by eight independently controlled elements. They maintain the vessel wall at a temperature slightly lower than that of the adjacent core material. The heating elements are separated by 5-mm [0.2-in] wide openings. Circular gas coolers are mounted around these openings. These coolers blow cold nitrogen gas directly onto the vessel wall (if required) to reduce conductive heat transport in the longitudinal direction through the thick wall of the vessel. During an experiment, air (or nitrogen) is fed continuously into the top of the pressure vessel. The flow men passes through the small gap (1 mm [0.04 in]) between the stack of plugs and the vessel wall (this gap is, of course, the simulated fracture). Finally, air and produced fluids leave the vessel at the bottom. Liquid and gas are separated, and the gas is analyzed by means of a mass spectrometer. Typical measurements include oxygen consumption and CO2 production. SPEJ p. 67
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Chipperfield, Simon T. "After-Closure Analysis To Identify Naturally Fractured Reservoirs." SPE Reservoir Evaluation & Engineering 9, no. 01 (February 1, 2006): 50–60. http://dx.doi.org/10.2118/90002-pa.
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Summary After-closure analysis (ACA) in homogeneous-matrix reservoirs provides a method for extracting critical reservoir information from pre-frac injection tests. This paper extends the theory and practice of ACA to identify the presence of productive natural fractures. Natural fractures are important to identify before conducting a stimulation treatment because their presence may require designs that differ from conventional matrix treatments. Literature shows that naturally fractured reservoirs are very susceptible to formation damage and require stimulation treatments to account for this issue. The historical problem, however, has been to confidently characterize the reservoirs pre-frac in terms of both the reservoir quality and the deliverability mechanism (fractures vs. matrix) before committing to these design specifications. This paper presents the results of a simulator used to analyze the mini-frac after-closure period to identify the presence of natural fractures. The simulation results are distilled into a field implementation methodology for determining the extent of natural fracturing and the formation reservoir quality. This methodology is also applied to a field case study to verify the practicality of the technique. Unlike previous mini-frac-analysis methods, this approach identifies natural fractures that are material to production and allows the engineer to distinguish them from "fissures" that are open only during injection and are not a production mechanism. Introduction Motivation for Identifying Natural Fractures. Identifying the presence of natural fractures is important for a broad range of reasons. On a field scale, realizing the presence of natural fractures can impact reserves estimation, initial well rates, production declines, and planned well locations. With respect to well completions, fractured reservoirs may necessitate a special stimulation approach. Because fractured reservoirs tend to produce from a relatively small reservoir volume (i.e., the fractures), these formations can be highly susceptible to damage (Cippolla et al. 1988). The literature shows that the use of foamed treatments (Cippolla et al. 1988), 100 mesh, and low gel loadings can be used to stimulate these reservoirs effectively. The literature also shows the disastrous results that can arise when damage-prevention steps are not taken (Cippolla et al. 1988). As a result, there is a definite need to identify natural fractures before a stimulation treatment so that the appropriate design decisions can be made. In the past, conventional well testing, such as pressure-buildup tests, has been used for determining the reservoir description. However, these techniques often prove costly both in terms of additional equipment requirements and delays in well on-line dates. In addition, conventional well testing may not be successful in low-permeability reservoirs because these wells may not flow at measurable rates before stimulation. These cost and reservoir limitations have forced the engineer to seek other low-cost methods for determining reservoir properties. One such option for acquiring these data is the use of a mini-frac injection test conducted before a stimulation treatment. The mini-frac analysis techniques available to provide estimates of the formation capacity (kh) and indications of the presence of natural fractures include preclosure and post-closure methods.
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Sarma, Pallav, and Khalid Aziz. "New Transfer Functions for Simulation of Naturally Fractured Reservoirs with Dual Porosity Models." SPE Journal 11, no. 03 (September 1, 2006): 328–40. http://dx.doi.org/10.2118/90231-pa.
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Summary This paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual-porosity models. Most of the existing dual-porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady state flow. More importantly, a direct generalization of single-phase flow equations is used to model multiphase flow, which can lead to significant inaccuracies in multiphase flow-behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs. Firstly, combining the differential form of the single-phase transfer function with analytical solutions of the pressure-diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudosteady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Finally, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e., nonorthogonal fractures) is proposed. This technique also accounts for both transient and pseudosteady-state pressure behavior. The results were verified against fine-grid single-porosity models and were found to be in excellent agreement. Secondly, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting-phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine-grid single-porosity models are used to verify the validity of the new transfer function. The results from single-block dual-porosity models and the corresponding single-porosity fine-grid models were in good agreement. Introduction A naturally fractured reservoir (NFR) can be defined as a reservoir that contains a connected network of fractures (planar discontinuities) created by natural processes such as diastrophism and volume shrinkage (Ordonez et al. 2001). Fractured petroleum reservoirs represent over 20% of the world's oil and gas reserves (Saidi 1983), but are, however, among the most complicated class of reservoirs. A typical example is the Circle Ridge fractured reservoir located on the Wind River Reservation in Wyoming, U.S.. This reservoir has been in production for more than 50 years but the total oil recovery until now has been less than 15% (www.fracturedreservoirs.com 2000). It is undeniable that reservoir characterization, modeling, and simulation of naturally fractured reservoirs present unique challenges that differentiate them from conventional, single-porosity reservoirs. Not only do the intrinsic characteristics of the fractures, as well as the matrix, have to be characterized, but the interaction between matrix blocks and surrounding fractures must also be modeled accurately. Further, most of the major NFRs have active aquifers associated with them, or would eventually be subjected to some kind of secondary recovery process such as waterflooding (German 2002), implying that it is essential to have a good understanding of the physics of multiphase flow for such reservoirs. This complexity of naturally fractured reservoirs necessitates the need for their accurate representation from a modeling and simulation perspective, such that production and recovery from such reservoirs be predicted and optimized.
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Kuchuk, Fikri, Denis Biryukov, and Tony Fitzpatrick. "Fractured-Reservoir Modeling and Interpretation." SPE Journal 20, no. 05 (October 20, 2015): 983–1004. http://dx.doi.org/10.2118/176030-pa.
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Summary Fractures are common features of many well-known reservoirs. Naturally fractured reservoirs (NFRs) consist of fractures in igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones and are connected to numerous fractures with varying conductivities. In many NFRs, faults and fractures frequently have discrete distributions rather than connected-fracture networks. Because faulting often creates fractures, faults and fractures should be modeled together. Accurately modeling NFR pressure-transient behavior is important in hydrogeology, the earth sciences, and petroleum engineering, including groundwater contamination to shale gas and oil reservoirs. For more than 50 years, conventional dual-porosity-type models, which do not include any fractures, have been used for modeling fluid flow in NFRs and aquifers. They have been continuously modified to add unphysical matrix-block properties such as matrix skin factor. In general, fractured reservoirs are heterogeneous at different length scales. It is clear that even with millions of gridblocks, numerical models may not be capable of accurately simulating the pressure-transient behavior of continuously and discretely NFRs containing variable-conductivity fractures. The conventional dual-porosity-type models are obviously an oversimplification; their serious limitations for interpreting well-test data from NFRs are discussed in detail. These models do not include wellbore-intersecting fractures, even though they dominate the pressure behavior of NFRs for a considerable length of testing time. Fracture conductivities of unity to infinity dominate transient behavior of both continuously and discretely fractured reservoirs, but again, dual-porosity models do not contain any fractures. Our fractured-reservoir model is capable of treating thousands of fractures that are periodically or arbitrarily distributed with finite- and/or infinite conductivities, different lengths, densities, and orientations. Appropriate inner-boundary conditions are used to account for wellbore-intersecting fractures and direct wellbore contributions to production. Wellbore-storage and skin effects in bounded and unbounded systems are included in the model. Three types of damaged-skin factors that may exist in wellbore-intersecting fracture(s) are specified. With this highly accurate model, the pressure-transient behavior of conventional dual-porosity-type models are investigated, and their limitations and range of applicability are identified. The behavior of the triple-porosity models is also investigated. It is very unlikely that triple-porosity behavior is caused by the local variability of matrix properties at the microscopic level. Rather, it is caused by the spatial variability of conductivity, length, density, and orientation of the fracture distributions. Finally, we have presented an interpretation of a field-buildup-test example from an NFR by use of both conventional dual-porosity models and our fractured-reservoir model. A substantial part of this paper is a review and discussion of the earlier work on NFRs, including the authors’ work.
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Chen, Zhiming, Xinwei Liao, Xiaoliang Zhao, Sanbo Lv, and Langtao Zhu. "A Semianalytical Approach for Obtaining Type Curves of Multiple-Fractured Horizontal Wells With Secondary-Fracture Networks." SPE Journal 21, no. 02 (April 14, 2016): 538–49. http://dx.doi.org/10.2118/178913-pa.
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Summary In naturally fractured reservoirs, complex fracture systems can easily develop along a horizontal wellbore during hydraulic fracturing. In the fracture systems, multiple, discrete secondary fractures are connected to the multiple-fractured horizontal well (MFHW). Because of the fracture complexity, most studies about performance forecast of such MFHWs highly depend on numerical simulators. In this paper, a new semianalytical approach is proposed to overcome the challenge to analyze the pressure behavior of MFHWs in complex-fracture systems. First, a mathematical model for MFHWs with secondary-fracture networks is established. Then, with Gauss elimination and the Stehfest numerical algorithm (Stehfest 1970), the transient-pressure solution of the mathematical model is solved, and type curves of MFHWs with secondary-fracture networks are obtained. After that, model validation and sensitivity analysis are conducted. It is found that the presented approach can rapidly and accurately generate type curves of MFHWs with secondary-fracture networks. This work provides very meaningful references for reservoir engineers in fracturing evaluations as well as performance estimations of MFHWs in naturally fractured reservoirs.
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Zhang, Kai, Jinding Zhang, Xiaopeng Ma, Chuanjin Yao, Liming Zhang, Yongfei Yang, Jian Wang, Jun Yao, and Hui Zhao. "History Matching of Naturally Fractured Reservoirs Using a Deep Sparse Autoencoder." SPE Journal 26, no. 04 (February 22, 2021): 1700–1721. http://dx.doi.org/10.2118/205340-pa.
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Summary Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.
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Posadas-Mondragón and Camacho-Velázquez. "Partially Penetrated Well Solution of Fractal Single-Porosity Naturally Fractured Reservoirs." Fractal and Fractional 3, no. 2 (April 24, 2019): 23. http://dx.doi.org/10.3390/fractalfract3020023.
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In the oil industry, many reservoirs produce from partially penetrated wells, either to postpone the arrival of undesirable fluids or to avoid problems during drilling operations. The majority of these reservoirs are heterogeneous and anisotropic, such as naturally fractured reservoirs. The analysis of pressure-transient tests is a very useful method to dynamically characterize both the heterogeneity and anisotropy existing in the reservoir. In this paper, a new analytical solution for a partially penetrated well based on a fractal approach to capture the distribution and connectivity of the fracture network is presented. This solution represents the complexity of the flow lines better than the traditional Euclidean flow models for single-porosity fractured reservoirs, i.e., for a tight matrix. The proposed solution takes into consideration the variations in fracture density throughout the reservoir, which have a direct influence on the porosity, permeability, and the size distribution of the matrix blocks as a result of the fracturing process. This solution generalizes previous solutions to model the pressure-transient behavior of partially penetrated wells as proposed in the technical literature for the classical Euclidean formulation, which considers a uniform distribution of fractures that are fully connected. Several synthetic cases obtained with the proposed solution are shown to illustrate the influence of different variables, including fractal parameters.
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Escobar, Freddy Humberto, Carlos Andrés Torregrosa Marlés, and Guiber Olaya Marín. "Interference test interpretation in naturally fractured reservoirs." DYNA 87, no. 214 (July 1, 2020): 121–28. http://dx.doi.org/10.15446/dyna.v87n214.82733.
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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.
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Chen, Chih-Cheng, Kelsen Serra, Albert C. Reynolds, and Rajagopal Raghavan. "Pressure Transient Analysis Methods for Bounded Naturally Fractured Reservoirs." Society of Petroleum Engineers Journal 25, no. 03 (June 1, 1985): 451–64. http://dx.doi.org/10.2118/11243-pa.
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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
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Zhao, Xueping, and R. Paul Young. "Numerical modeling of seismicity induced by fluid injection in naturally fractured reservoirs." GEOPHYSICS 76, no. 6 (November 2011): WC167—WC180. http://dx.doi.org/10.1190/geo2011-0025.1.
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The interaction between hydraulic and natural fractures is of great interest for the energy resource industry because natural fractures can significantly influence the overall geometry and effectiveness of hydraulic fractures. Microseismic monitoring provides a unique tool to monitor the evolution of fracturing around the treated rock reservoir, and seismic source mechanisms can yield information about the nature of deformation. We performed a numerical modeling study using a 2D distinct-element particle flow code ([Formula: see text]) to simulate realistic conditions and increase understanding of fracturing mechanisms in naturally fractured reservoirs, through comparisons with results of the geometry of hydraulic fractures and seismic source information (locations, magnitudes, and mechanisms) from both laboratory experiments and field observations. A suite of numerical models with fully dynamic and hydromechanical coupling was used to examine the interaction between natural and induced fractures, the effect of orientation of a preexisting fracture, the influence of differential stress, and the relationship between the fluid front, fracture tip, and induced seismicity. The numerical results qualitatively agree with the laboratory and field observations, and suggest possible mechanics for new fracture development and their interaction with a natural fracture (e.g., a tectonic fault). Therefore, the tested model could help in investigating the potential extent of induced fracturing in naturally fractured reservoirs, and in interpreting microseismic monitoring results to assess the effectiveness of a hydraulic fracturing project.
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Pereira, Carlos A., Hossein Kazemi, and Erdal Ozkan. "Combined Effect of Non-Darcy Flow and Formation Damage on Gas Well Performance of Dual-Porosity and Dual-Permeability Reservoirs." SPE Reservoir Evaluation & Engineering 9, no. 05 (October 1, 2006): 543–52. http://dx.doi.org/10.2118/90623-pa.
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Summary This paper addresses the combined effect of formation damage and non-Darcy flow in naturally fractured reservoirs using simplified analytical solutions and a 2D numerical simulator. Pressure drawdown, buildup, and isochronal tests simulated in this work indicate that, despite high fracture permeability, skin damage may accentuate the non-Darcy flow effect and drastically influence pressure-transient characteristics of low-pressure, naturally fractured reservoirs. In high-pressure reservoirs, this effect is significant only at high rates. Non-Darcy flow does not usually mask the typical pressure-transient characteristics of dual-porosity and dual-permeability reservoirs, but the conventional interpretation of the early-time data may lead to erroneous results. If the exponent, n, of the isochronal tests approaches 0.5 while the matrix permeability is low and flow rate is rather high, this would indicate the predominance of fracture flow. Under these conditions, small contributions from skin damage may greatly reduce gas-well performance in naturally fractured reservoirs. Introduction High velocity flow through porous media and fractures causes a higher pressure drop than predicted by the Darcy equation. This phenomenon, generally referred to as non-Darcy flow, was first described by Forchheimer (1901). Since then, it has been well established that the main variables that affect non-Darcy flow are the velocity, density, and saturation of the fluid and the permeability and porosity of the reservoir. Reservoir properties may be correlated to a single parameter, known as the non-Darcy flow coefficient, beta. Very little is known about the effect of other parameters, such as physical skin damage, on non-Darcy flow and their consequences in well performance. In fact, a recent literature review on non-Darcy flow by Li and Engler (2001a) indicates that most of the work has been focused on finding an accurate correlation for the non-Darcy flow coefficient, beta. There is also the issue of non-Darcy flow in dual-porosity and dual-permeability reservoirs, where high local velocities are prominent in the fractures. This paper pertains specifically to this issue. In general, the lower the formation permeability, the greater the non-Darcy pressure gradient. Formation damage in the near-wellbore region causes a drastic reduction in formation permeability, which potentially could be even more prominent in naturally fractured reservoirs. Thus, a greater non-Darcy flow effect could result in the wellbore region of a dual-porosity reservoir. The literature explaining the combined effect of physical damage and non-Darcy flow in single-porosity reservoirs is abundant (Berumen-C. et al. 1989; Camacho-V. et al. 1993; Fligelman et al. 1981); however, there is little information about such effects in dual-porosity and dual-permeability reservoirs. A finite-difference, 2D simulator in cylindrical coordinates was constructed to simulate pressure-drawdown and -buildup tests. By analyzing the simulated pressure drawdown and buildup tests, it was possible to decipher the combined effect of the skin damage and non-Darcy flow in fractured reservoirs. Both dual-porosity and dual-permeability idealizations of fractured reservoirs were considered.
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Zareidarmiyan, Ahmad, Hossein Salarirad, Victor Vilarrasa, Silvia De Simone, and Sebastia Olivella. "Geomechanical Response of Fractured Reservoirs." Fluids 3, no. 4 (September 29, 2018): 70. http://dx.doi.org/10.3390/fluids3040070.
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Geologic carbon storage will most likely be feasible only if carbon dioxide (CO2) is utilized for improved oil recovery (IOR). The majority of carbonate reservoirs that bear hydrocarbons are fractured. Thus, the geomechanical response of the reservoir and caprock to IOR operations is controlled by pre-existing fractures. However, given the complexity of including fractures in numerical models, they are usually neglected and incorporated into an equivalent porous media. In this paper, we perform fully coupled thermo-hydro-mechanical numerical simulations of fluid injection and production into a naturally fractured carbonate reservoir. Simulation results show that fluid pressure propagates through the fractures much faster than the reservoir matrix as a result of their permeability contrast. Nevertheless, pressure diffusion propagates through the matrix blocks within days, reaching equilibrium with the fluid pressure in the fractures. In contrast, the cooling front remains within the fractures because it advances much faster by advection through the fractures than by conduction towards the matrix blocks. Moreover, the total stresses change proportionally to pressure changes and inversely proportional to temperature changes, with the maximum change occurring in the longitudinal direction of the fracture and the minimum in the direction normal to it. We find that shear failure is more likely to occur in the fractures and reservoir matrix that undergo cooling than in the region that is only affected by pressure changes. We also find that stability changes in the caprock are small and its integrity is maintained. We conclude that explicitly including fractures into numerical models permits identifying fracture instability that may be otherwise neglected.
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Abbaszadeh, Maghsood, Chip Corbett, Rolf Broetz, James Wang, Fangjian Xue, Tom Nitka, Yong Zhang, and Zhen Yu Liu. "Development of an Integrated Reservoir Model for a Naturally Fractured Volcanic Reservoir in China." SPE Reservoir Evaluation & Engineering 4, no. 05 (October 1, 2001): 406–14. http://dx.doi.org/10.2118/74336-pa.
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Summary This paper presents the development of an integrated, multidiscipline reservoir model for dynamic flow simulation and performance prediction of a geologically complex, naturally fractured volcanic reservoir in the Shang 741 Block of the Shengli field in China. A static geological model integrates lithological information, petrophysics, fracture analysis, and stochastic fracture network modeling with Formation MicroImage (FMI) log data and advanced 3D seismic interpretations. Effective fracture permeability, fracture-matrix interaction, reservoir compartmentalization, and flow transmissibility of conductive faults are obtained by matching various dynamic data. As a result of synergy and multiple iterations among various disciplines, a history-matched dynamic reservoir-simulation model capable of future performance prediction for optimum asset management is constructed. Introduction The multidisciplinary approach of closely related teamwork across the disciplines of geology, geophysics, petrophysics, and reservoir engineering is now the accepted approach in the industry for reservoir management and field development.1–6Fig. 1 shows components of integrated reservoir characterization and the contribution of each discipline to the process. The strength of integrated reservoir modeling, however, can be particularly dramatized with some reservoirs that contain extreme forms of heterogeneity and unusual structural features. The Shang 741 Block of the Shengli fractured volcanic reservoirs is one such example. The Shang 741 Block contains a series of vertically separated fractured volcanic reservoirs with different characteristics. Matrix porosity and permeability are both low in most horizons; thus, natural fractures are the main flow pathways for fluids. FMI logs delineate the orientation and density of the fracture distribution. Lithology variations, extensive compartmentalization, and looping of reservoir body units are recognized from the geologic depositional model and seismic data. Tying acoustic well data to 3D seismic data through synthetic seismograms combined with FMI information controls time and depth structure maps for a reliable geological model. Reservoir modeling (RM) software provides a platform to integrate lithology correlations with seismically based structural features and petrophysical properties to yield a framework for a dual-porosity Eclipse** reservoir flow-simulation model. Fractures delineated and characterized from well data are stochastically distributed in the reservoir for each horizon with a fractal-based, fracture-mapping algorithm.7 Simulation of effective gridblock fracture permeability and matrix-fracture transfer function parameters are upscaled into coarse-scale simulation gridblocks. These upscaled values are verified and calibrated by available pressure-transient effective permeabilities for consistency. In this paper, a dual-porosity reservoir-simulation model is constructed from a static geological and geophysical (G&G) model in a stepwise fashion through successive incorporation of dynamic information from pressure-transient tests, static reservoir pressure, water breakthrough behavior, and well-production performance data. Compartmentalization incorporates effects of multiple oil/ water contacts (OWC) for proper modeling of regional pressure-trend behavior. Fault conductivity or thin channel transmissibility, verified by seismic and well tests, is augmented for better modeling of water movement in the reservoir. As a result of synergy among various G&G disciplines and incorporation of dynamic reservoir engineering data, a representative and production-data calibrated model is constructed for this reservoir. The paper shows that this is possible only through multiple iterations across the disciplines and through integrated project teams. The model also serves as a reservoir-management tool in production monitoring, in evaluating the effects of implementing pressure-maintenance injection programs, and in better understanding the impact of various uncertainties on the ultimate recovery of the field. Database The data sources available for this study include:Geological interpretations and geological framework model, including geological markers.Three-dimensional seismic survey data with 529 lines by 583 common depth points (CDPs) at 25-m bin size that covers a 200-km2 area.Three vertical seismic profile (VSP) surveys and their detailed interpretations.Petrophysical analysis on 13 nearly vertical wells that penetrate the reservoir horizons.FMI logs and analysis for fracture delineation.Pressure/volume/temperature (PVT) samples and analyses.Conventional and special core analysis for matrix and fracture relative permeability, matrix capillary-pressure characteristics, and rock compaction.Two single-well, pressure-buildup tests.Three interference tests.Spot static-pressure measurements.Production data, including flowing bottomhole and tubing pressure, oil, water, and gas flow rates.Extensive information from 13 drilled wells in the field. Reservoir Characterization Geology. Shang 741 fractured reservoirs are located within the large Shengli field in the Bohai basin, China (Fig. 2). These volcanic reservoirs, primarily of the Oligocene Shahejie and Dongying formations, are composed of fractured basalt, extrusive tuff, and fractured diabase of intrusive origin (Fig. 3). The Shang 741 consists of a stack of separated fractured reservoirs, which communicate with each other only through drilled wellbores. These are divided into the H1, H2, H3, Lower H3, H3 1, and H4 fractured reservoir units. Fig. 4 shows the stacking order of these reservoirs along with geological markers, lithology type, and facies relationships.
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Wang, Kongjie, Lian Wang, Caspar Daniel Adenutsi, Zhiping Li, Sen Yang, Liang Zhang, and Lan Wang. "Analysis of Gas Flow Behavior for Highly Deviated Wells in Naturally Fractured-Vuggy Carbonate Gas Reservoirs." Mathematical Problems in Engineering 2019 (July 29, 2019): 1–13. http://dx.doi.org/10.1155/2019/6919176.
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To improve the carbonate gas reservoir development and production, highly deviated wells (HDW) are widely used in the field. Production decline analysis of HDW is crucial for long-term gas reservoir development. However, it is a new challenge to incorporate the complex pore structure of naturally fractured-vuggy carbonate gas reservoirs and evaluate the production performance of HDW. This paper presents a semianalytical model to analyze the pressure and production behavior of HDW in naturally fractured-vuggy carbonate gas reservoirs, which consist of fractures, vugs, and matrix. The primary flow occurs only through the fracture and the outer boundary is closed. Introducing pseudopressure and pseudotime, the Laplace transformation, Fourier transformation, and its inverse and Stehfest numerical inversion were employed to establish a point source and line source solutions. Furthermore, the validity of the proposed model was verified by comparing a field data from the Arum River Basin in Turkmenistan. Finally, the effects of major parameters on the production decline curves were analyzed by using the proposed model and it was found that they had influences at different stages of gas production history and the sensitivity intensity of each parameter was different. With its high efficiency and simplicity, this semianalytical model will serve as a useful tool to evaluate the well production behavior for the naturally fractured-vuggy carbonate gas reservoirs.
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Bossie-Codreanu, Dimitrie, Paul R. Bia, and Jean-Claude Sabathier. "The "Checker Model," An Improvement in Modeling Naturally Fractured Reservoirs With a Tridimensional, Triphasic, Black-Oil Numerical Model." Society of Petroleum Engineers Journal 25, no. 05 (October 1, 1985): 743–56. http://dx.doi.org/10.2118/10977-pa.
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Abstract This paper describes an approach to simulating the flow of water, oil, and gas in fully or partially fractured reservoirs with conventional black-oil models. This approach is based on the dual porosity concept and uses a conventional tridimensional, triphasic, black-oil model with minor modifications. The basic feature is an elementary volume of the fractured reservoir that is simulated by several model cells; the matrix is concentrated into one matrix cell and tee fractures into the adjacent fracture cells. Fracture cells offer a continuous path for fluid flows, while matrix cello are discontinuous ("checker board" display). The matrix-fracture flows are calculated directly by the model. Limitations and applications of this approximate approach are discussed and examples given. Introduction Fractured reservoir models were developed to simulate fluid flows in a system of continuous fractures of high permeability and low porosity that surround discontinuous, porous, oil-saturated matrix blocks of much lower permeability but higher porosity. The use of conventional models that permeability but higher porosity. The use of conventional models that actually simulate the fractures and matrix blocks is restricted to small systems composed of a limited number of matrix blocks. The common approach to simulating a full-field fractured reservoir is to consider a general flow within the fracture network and a local flow (exchange of fluids) between matrix blocks and fractures. This local flow is accounted for by the introduction of source or sink terms (transfer functions). In this formulation, the model is not directly predictive because the source term (transfer function) is, in fact, entered data and is derived from outside the model by one of the following approaches:analytical computation,empirical determination (laboratory experiments), ornumerical simulation of one or several matrix blocks on a conventional model. To derive these transfer functions, imposing some boundary conditions is necessary. Unfortunately, it is generally impossible to foresee all the conditions that will arise in a, matrix block and its surrounding fractures during its field life. It would be helpful, therefore, to have a model that is able to compute directly the local flows according to changing conditions. However, to have low computing times, it is necessary to use an approximate formulation and, thus, to adjust some parameters to match results that are externally (and more accurately) derived in a few basis, well-defined conditions. By current investigative techniques, only a very general description of the matrix blocks and fissures can be obtained, so our knowledge of local flows is very approximate. This paper presents a modeling procedure that is an approximate but helpful approach to the simulation of fractured reservoirs and requires a few, simple modifications of conventional black-oil mathematical models. Review of the Literature Numerous papers related to single- and multiphase flow in fractured porous media have been published over the last three decades. On the basis of data from fractured limestone and sand-stone reservoirs, fractured reservoirs are pictured as stacks of matrix blocks separated by fractures (Figs. 1 and 2). The fractured reservoirs with oil-saturated matrices usually are referred to as "double porosity" systems. Primary porosity is associated with matrix blocks, while secondary porosity is associated with fractures. The porosity of the matrices is generally much greater than that of the fractures, but permeability within fractures may be 100 and even over 10,000 times higher permeability within fractures may be 100 and even over 10,000 times higher than within the matrices. The main difference between flow in a fractured medium and flow in a conventional porous system is that, in a fractured medium, the interconnected fracture network provides the main path for fluid flow through the reservoir, while local flows (exchanges of fluids) occur between the discontinuous matrix blocks and the surrounding fractures. Matrix oil flows into the fractures, and the fractures carry the oil to the wellbore. For single-phase flow, Barenblatt et al constructed a formula based on the dual porosity approach. They consider the reservoir as two overlying continua, the matrices and the fractures. SPEJ p. 743
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Li, Jianxiong, Shiming Dong, Wen Hua, Xiaolong Li, and Xin Pan. "Numerical Investigation of Hydraulic Fracture Propagation Based on Cohesive Zone Model in Naturally Fractured Formations." Processes 7, no. 1 (January 8, 2019): 28. http://dx.doi.org/10.3390/pr7010028.
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Complex propagation patterns of hydraulic fractures often play important roles in naturally fractured formations due to complex mechanisms. Therefore, understanding propagation patterns and the geometry of fractures is essential for hydraulic fracturing design. In this work, a seepage–stress–damage coupled model based on the finite pore pressure cohesive zone (PPCZ) method was developed to investigate hydraulic fracture propagation behavior in a naturally fractured reservoir. Compared with the traditional finite element method, the coupled model with global insertion cohesive elements realizes arbitrary propagation of fluid-driven fractures. Numerical simulations of multiple-cluster hydraulic fracturing were carried out to investigate the sensitivities of a multitude of parameters. The results reveal that stress interference from multiple-clusters is responsible for serious suppression and diversion of the fracture network. A lower stress difference benefits the fracture network and helps open natural fractures. By comparing the mechanism of fluid injection, the maximal fracture network can be achieved with various injection rates and viscosities at different fracturing stages. Cluster parameters, including the number of clusters and their spacing, were optimal, satisfying the requirement of creating a large fracture network. These results offer new insights into the propagation pattern of fluid driven fractures and should act as a guide for multiple-cluster hydraulic fracturing, which can help increase the hydraulic fracture volume in naturally fractured reservoirs.
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Hien, Ha Ngoc, Nguyen Van Diep, and Duong Ngoc Hai. "A numerical model for water-oil flow in naturally fractured reservoirs." Vietnam Journal of Mechanics 26, no. 1 (April 1, 2004): 31–38. http://dx.doi.org/10.15625/0866-7136/26/1/5687.
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This paper describes the development of a three-dimensional, two-phase model for simulating the flow of water and oil in naturally fractured reservoirs. The model is based on the dual porosity approach. Main flow in the reservoir occurs within the fractures with local exchange of fluids between the fracture system and matrix blocks. A new formula for matrix/fracture fluid exchange rate is proposed based on an extension of the equation developed by Kazemi to account the gravity effects. This formula allows to eliminate the matrix pressure in the pressure equation for fractures and makes the solution algorithm easier.Some example calculations are presented to validate the model. These include a comparison of the results of this paper with previous results, showing the gravity effects and applicability of the model for field-scale problems.
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Sarkheil, Hamid, Hossein Hassani, and Firuz Alinia. "Fractured reservoir distribution characterization using folding mechanism analysis and patterns recognition in the Tabnak hydrocarbon reservoir anticline." Journal of Petroleum Exploration and Production Technology 11, no. 6 (June 2021): 2425–33. http://dx.doi.org/10.1007/s13202-021-01225-y.
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AbstractNaturally, fractured reservoirs play a considerable part in the study, production, and development of hydrocarbon fields because most hydrocarbon reservoirs in the Zagros Basin are naturally fractured. Production from those reservoirs is usually affected by the presence of a system of connected fractures. In this study, the Tabnak hydrocarbon field on the fold–thrust belt at the Zagros zone in the Persian plate has been analyzed by the facies models, folding mechanism analysis to identify fracture reservoir patterns. The results show a flexural fold with similarity in the folding mechanism and some open fracture potential made by limestone, shale, clay, and anhydrite in the study area's facies models. Consequently, the stress pattern and type of fracture issue on the fold's upper and lower layers will be similar. On the Tabnak anticline reservoir using image processing techniques in MATLAB R2019 software and kriging geostatistical methods, fracture surface patterns as a block model extended to the depth. Using the model results, fractures’ orientation distribution in adjacent wells 11, 14, and 15 is appropriate. The results also have similarities with the facies models, folding mechanism assessment, well test, and mud loss data analysis. These results can affect the development plans’ primary approach by drilling horizontal and sleep wells and hydrocarbon reservoir management strategies.
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Alvarez, Leidy Laura, Leonardo José do Nascimento Guimarães, Igor Fernandes Gomes, Leila Beserra, Leonardo Cabral Pereira, Tiago Siqueira de Miranda, Bruno Maciel, and José Antônio Barbosa. "Impact of Fracture Topology on the Fluid Flow Behavior of Naturally Fractured Reservoirs." Energies 14, no. 17 (September 2, 2021): 5488. http://dx.doi.org/10.3390/en14175488.
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Fluid flow modeling of naturally fractured reservoirs remains a challenge because of the complex nature of fracture systems controlled by various chemical and physical phenomena. A discrete fracture network (DFN) model represents an approach to capturing the relationship of fractures in a fracture system. Topology represents the connectivity aspect of the fracture planes, which have a fundamental role in flow simulation in geomaterials involving fractures and the rock matrix. Therefore, one of the most-used methods to treat fractured reservoirs is the double porosity-double permeability model. This approach requires the shape factor calculation, a key parameter used to determine the effects of coupled fracture-matrix fluid flow on the mass transfer between different domains. This paper presents a numerical investigation that aimed to evaluate the impact of fracture topology on the shape factor and equivalent permeability through hydraulic connectivity (f). This study was based on numerical simulations of flow performed in discrete fracture network (DFN) models embedded in finite element meshes (FEM). Modeled cases represent four hypothetical examples of fractured media and three real scenarios extracted from a Brazilian pre-salt carbonate reservoir model. We have compared the results of the numerical simulations with data obtained using Oda’s analytical model and Oda’s correction approach, considering the hydraulic connectivity f. The simulations showed that the equivalent permeability and the shape factor are strongly influenced by the hydraulic connectivity (f) in synthetic scenarios for X and Y-node topological patterns, which showed the higher value for f (0.81) and more expressive values for upscaled permeability (kx-node = 0.1151 and ky-node = 0.1153) and shape factor (25.6 and 14.5), respectively. We have shown that the analytical methods are not efficient for estimating the equivalent permeability of the fractured medium, including when these methods were corrected using topological aspects.
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Yeh, N. S., M. J. Davison, and R. Raghavan. "Fractured Well Responses in Heterogeneous Systems—Application to Devonian Shale and Austin Chalk Reservoirs." Journal of Energy Resources Technology 108, no. 2 (June 1, 1986): 120–30. http://dx.doi.org/10.1115/1.3231251.
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This paper presents new methods to analyze fractured well responses in heterogeneous reservoirs. We consider wells producing formations that are naturally fractured and use the idealizations proposed by Warren and Root (pseudosteady-state flow in the matrix-system) and by deSwaan-O (unsteady-state flow in the matrix-system) to model the naturally fractured reservoir. Pressure responses are correlated in a manner suitable for direct application of field data. Methods to determine fracture half-length are presented. Two field applications are discussed. The consequences of neglecting the heterogeneous character of the porous medium are also discussed.
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Wang, Shuhua, Mingxu Ma, Wei Ding, Menglu Lin, and Shengnan Chen. "Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability." SPE Reservoir Evaluation & Engineering 18, no. 04 (November 25, 2015): 523–33. http://dx.doi.org/10.2118/174299-pa.
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Summary Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account. In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs. Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.
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Will, Robert, Rosalind A. Archer, and William S. Dershowitz. "Integration of Seismic Anisotropy and Reservoir Performance Data for Characterization of Naturally Fractured Reservoirs Using Discrete Feature Network Models." SPE Reservoir Evaluation & Engineering 8, no. 02 (April 1, 2005): 132–42. http://dx.doi.org/10.2118/84412-pa.
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Summary This paper proposes a method for quantitative integration of seismic(elastic) anisotropy attributes with reservoir-performance data as an aid in characterizing systems of natural fractures in hydrocarbon reservoirs. This method is demonstrated through application to history matching of reservoir performance using synthetic test cases. Discrete-feature-network (DFN) modeling is a powerful tool for developing fieldwide stochastic realizations of fracture networks in petroleum reservoirs. Such models are typically well conditioned in the vicinity of the wellbore through incorporation of core data, borehole imagery, and pressure-transient data. Model uncertainty generally increases with distance from the borehole. Three-dimensional seismic data provide uncalibrated information throughout the interwell space. Some elementary seismic attributes such as horizon curvature and impedance anomalies have been used to guide estimates of fracture trend and intensity (fracture area per unit volume) in DFN modeling through geostatistical calibration with borehole and other data. However, these attributes often provide only weak statistical correlation with fracture-system characteristics. The presence of a system of natural fractures in a reservoir induces elastic anisotropy that can be observed in seismic data. Elastic attributes such as azimuthally dependent normal move out velocity (ANMO), reflection amplitude vs. azimuth (AVAZ), and shear-wave birefringence can be inverted from 3D-seismicdata. Anisotropic elastic theory provides physical relationships among these attributes and fracture-system properties such as trend and intensity. Effective-elastic-media models allow forward modeling of elastic properties for fractured media. A technique has been developed in which both reservoir-performance data and seismic anisotropic attributes are used in an objective function for gradient-based optimization of selected fracture-system parameters. The proposed integration method involves parallel workflows for effective elastic and effective permeability media modeling from an initial DFN estimate of the fracture system. The objective function is minimized through systematic updates of selected fracture-population parameters. Synthetic data cases show that3D-seismic attributes contribute significantly to the reduction of ambiguity in estimates of fracture-system characteristics in the interwell rock mass. The method will benefit enhanced-oil-recovery (EOR) program planning and management, optimization of horizontal-well trajectory and completion design, and borehole-stability studies. Introduction Anisotropy and heterogeneity in reservoir permeability present challenges during the development of hydrocarbon reserves in naturally fractured reservoirs. Predicting primary reservoir performance, planning development drilling or EOR programs, completion design, and facilities design all require accurate estimates of reservoir properties and the predictions of future reservoir behavior computed from such estimates. Over the history of naturally-fractured-reservoir development, many methods have been used to characterize fracture systems and their effect on fluid flow in the reservoir. These include the use of geologic surface-outcrop analogs; core, single-well, and multiwell pressure-transient analysis; borehole-imaging logs; and surface and borehole seismic observations. To date, efforts to integrate seismic data into the workflow for characterization of naturally fractured reservoirs have been focused on the use of post-stack data. CDP stacking of seismic data takes advantage of redundancy in seismic data sets for the attenuation of noise. Unfortunately, CDP stacking also eliminates valuable information about spatial and orientational variations in the data. Such variations are often related to fracture-system characteristics. CDP-stacked seismic data are typically used to define the main structural elements of the reservoir. Fracture density has been correlated successfully with horizon curvature determined from seismic horizons. Seismic attributes frequently can be correlated with reservoir properties such as shale fraction, which often correlates with fracture-population statistics. Acoustic impedance computed from seismic data frequently exhibits dim spots in the presence of fractures.
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Wang, Junchao, Haitao Li, Yongqing Wang, Ying Li, Beibei Jiang, and Wei Luo. "A New Model to Predict Productivity of Multiple-Fractured Horizontal Well in Naturally Fractured Reservoirs." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/892594.
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In order to predict productivity of multiple-fractured horizontal well in fractured reservoir, flow models of reservoir and hydraulic fractures based on the volumetric source idealization are developed. The models are solved by utilizing Laplace transformation and orthogonal transformation, and flow rate of the well is calculated by coupling the two models. Compared to traditional point source functions, volumetric source function has many advantages in properties of function and programming calculation. The productivity predicting model is verified via an analytical ternary-porosity model. Moreover, a practical example of fractured horizontal well is studied to analyze the productivity and its influent factors. The result shows that flow rate of each fracture is different and inner fracture contributes least to productivity. Meanwhile, there are optimizing ranges for number, length, and conductivity of hydraulic fractures. In low-permeability reservoir, increasing surface area in contact with reservoir by increasing number and length of hydraulic fractures is the most effective method to improve the productivity.
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Li, Liyong, and Seong H. Lee. "Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media." SPE Reservoir Evaluation & Engineering 11, no. 04 (August 1, 2008): 750–58. http://dx.doi.org/10.2118/103901-pa.
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Summary This paper describes a hybrid finite volume method, designed to simulate multiphase flow in a field-scale naturally fractured reservoir. Lee et al. (WRR 37:443-455, 2001) developed a hierarchical approach in which the permeability contribution from short fractures is derived in an analytical expression that from medium fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. Reservoirs with well-developed natural fractures include many complex fracture networks that cannot be easily modeled by simple long fracture formulation and/or homogenized single continuity model. We thus propose a numerically efficient hybrid method in which small and medium fractures are modeled by effective permeability, and large fractures are modeled by discrete fracture networks. A simple, systematic way is devised to calculate transport parameters between fracture networks and discretized, homogenized media. An efficient numerical algorithm is also devised to solve the dual system of fracture network and finite volume grid. Black oil formulation is implemented in the simulator to demonstrate practical applications of this hybrid finite volume method. Introduction Many reservoirs are highly fractured due to the complex tectonic movement and sedimentation process the formation has experienced. The permeability of a fracture is usually much larger than that of the rock matrix; as a result, the fluid will flow mostly through the fracture network, if the fractures are connected. This implies that the fracture connectivities and their distribution will determine fluid transport in a naturally fractured reservoir (Long and Witherspoon 1985). Because of statistically complex distribution of geological heterogeneity and multiple length and time scales in natural porous media, three approaches (Smith and Schwartz 1993) are commonly used in describing fluid flow and solute transport in naturally fractured formations:discrete fracture models;continuum models using effective properties for discrete grids; andhybrid models that combine discrete, large features and equivalent continuum. Currently, most reservoir simulators use dual continuum formulations (i.e., dual porosity/permeability) for naturally fractured reservoirs in which matrix blocks are divided by very regular fracture patterns (Kazemi et al. 1976, Van Golf-Racht 1982). Part of the primary input into these simulation models is the permeability of the fracture system assigned to the individual grid-blocks. This value can only be reasonably calculated if the fracture systems are regular and well connected. Field characterization studies have shown, however, that fracture systems are very irregular, often disconnected, and occur in swarms (Laubach 1991, Lorenz and Hill 1991, Narr et al. 2003). Most naturally fractured reservoirs include fractures of multiple- length scales. The effective grid-block permeability calculated by the boundary element method becomes expensive as the number of fractures increases. The calculated effective properties for grid-blocks also underestimates the properties for long fractures whose length scale is much larger than the grid-block size. Lee et al. (2001) proposed a hierarchical method to model fluid flow in a reservoir with multiple-length scaled fractures. They assumed that short fractures are randomly distributed and contribute to increasing the effective matrix permeability. An asymptotic solution representing the permeability contribution from short fractures was derived. With the short fracture contribution to permeability, the effective matrix permeability can be expressed in a general tensor form. Thus, they also developed a boundary element method for Darcy's equation with tensor permeability. For medium-length fractures in a grid-block, a coupled system of Poisson equations with tensor permeability was solved numerically using a boundary element method. The grid-block effective permeabilities were used with a finite difference simulator to compute flow through the fracture system. The simulator was enhanced to use a control-volume finite difference formulation (Lee et al. 1998, 2002) for general tensor permeability input (i.e., 9-point stencil for 2-D and 27-point stencil for 3-D). In addition, long fractures were explicitly modeled by using the transport index between fracture and matrix in a gridblock. In this paper we adopt their transport index concept and extend the hierarchical method:to include networks of long fractures;to model fracture as a two-dimensional plane; andto allow fractures to intersect with well bore. This generalization allows us to model a more realistic and complex fracture network that can be found in naturally fractured reservoirs. To demonstrate this new method for practical reservoir applications, we furthermore implement a black oil formulation in the simulator. We explicitly model long fractures as a two-dimensional plane that can penetrate several layers. The method, presented in this paper, allows a general description of fracture orientation in space. For simplicity of computational implementation however, both the medium-length and long fractures considered in this paper are assumed to be perpendicular to bedding boundaries. In addition, we derive a source/sink term to model the flux between matrix and long fracture networks. This source/sink allows for coupling multiphase flow equations in long fractures and matrix. The paper is organized as follows. In Section 2 black oil formulation is briefly summarized and the transport equations for three phase flow are presented. The fracture characterization and hierarchical modeling approach, based on fracture length, are discussed in Section 3. In Section 4 we review homogenization of short and medium fractures, which is part of our hierarchical approach to modeling flow in porous media with multiple length-scale fractures. In Section 5 we discuss a discrete network model of long fractures. We also derive transfer indices between fracture and effective matrix blocks. In Section 6 we present numerical examples for tracer transport in a model with simple fracture network, interactions of fractures and wells, and black oil production in a reservoir with a complex fracture network system. Finally, the summary of our main results and conclusion follows.
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Ershaghi, I., and R. Aflaki. "Problems in Characterization of Naturally Fractured Reservoirs From Well Test Data." Society of Petroleum Engineers Journal 25, no. 03 (June 1, 1985): 445–50. http://dx.doi.org/10.2118/12014-pa.
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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
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ZHANG, LIMING, CHENYU CUI, XIAOPENG MA, ZHIXUE SUN, FAN LIU, and KAI ZHANG. "A FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR HISTORY MATCHING OF NATURALLY FRACTURED RESERVOIRS." Fractals 27, no. 01 (February 2019): 1940008. http://dx.doi.org/10.1142/s0218348x19400085.
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The distribution of fractures is highly uncertain in naturally fractured reservoirs (NFRs) and may be predicted by using the assisted-history-matching (AHM) that calibrates the reservoir model according to some high-quality static data combined with dynamic production data. A general AHM approach for NFRs is to construct a discrete fracture network (DFN) model and estimate model parameters given the observations. However, the large number of fractures prediction required in the AHM process could pose a high-dimensional optimization problem. This difficulty is particularly challenging when the fractures form a complex multi-scale fracture network. We present in this paper an integrated AHM approach of NFRs to tackle these challenges. Two essential ingredients of the method are (1) a 2D fractal-DFN model constructed as the geological simulation model to describe the complex fracture network, and (2) a mixture of multi-scale parameters, built according to the fractal-DNF model, as an inversion parameter model to alleviate the high-dimensional optimization burden caused by complex fracture networks. A reservoir with a multi-scale fracture network is set up to test the performance of the proposed method. Numerical results demonstrate that by use of the proposed method, the fractures well recognized by assimilating production data.
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Puyang, Ping, Arash Dahi Taleghani, and Bhaba Sarker. "An integrated modeling approach for natural fractures and posttreatment fracturing analysis: A case study." Interpretation 4, no. 4 (November 1, 2016): T485—T496. http://dx.doi.org/10.1190/int-2016-0016.1.
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Hydraulic fracturing has been the principal production enhancement technique in low-permeability reservoirs for the past few decades. Through core and outcrop studies, advanced logging tools, microseismic mapping and well testing analysis, the complexity of induced fracture network in the presence of natural fractures has been further elucidated. Although most natural fractures are cemented by precipitations due to diagenesis, they can be reactivated during fracturing treatments and serve as preferential paths for fracture growth and fluid flow. However, current technologies for posttreatment fracture analysis are incapable of accurately determining the induced fracture geometry or estimating the distribution of preexisting natural fractures. Despite significant advances in the numerical modeling of fractured reservoirs, those numerical models require detailed characterization of natural fractures, which is essentially impossible to obtain. Moreover, most modeling techniques could not incorporate posttreatment data to reflect actual reservoir characteristics. We have developed an integrated modeling workflow to estimate the actual characteristics of fracture populations based on formation evaluations, microseismic data, treatment data, and production history. A least-squares modeling approach is first used to define possible realizations of natural fractures from selected double-couple microseismic events. Forward modeling incorporating a discrete fracture network will subsequently be used for matching treatment data and screening generated fracture realizations. Reservoir simulation tools will also be used thereafter to match the production data to further evaluate the fitness of natural fracture realizations. Our workflow is able to integrate data from multiple aspects of the reservoir development process, and the results from this workflow will provide geologist and reservoir engineers a robust tool for modeling naturally fractured reservoirs.
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Closmann, Philip J. "Block Model for Growth of Steam-Heated Zone in Oil-Bearing Naturally Fractured Carbonate Reservoirs." SPE Journal 17, no. 03 (July 3, 2012): 671–79. http://dx.doi.org/10.2118/158236-pa.
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Summary A model for steam injection into naturally fractured carbonate reservoirs provides a method of calculating the volume of heated formation for a given amount of steam, provided that the assumptions of the model are satisfied. The model represents the fractured reservoir by a system of blocks, dependent on fracture spacing and dimensions. The amount of oil mobilized can be estimated from prior measurements of oil saturation and laboratory tests of oil-displacement efficiency. Results comparable to observations are obtained. In addition, the temperature distribution along the direction of propagation in the reservoir may also be estimated, providing a guide to variation in the local oil mobility. These results can assist in evaluating the effectiveness of steam injection in the recovery of oil from naturally fractured formations.
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Sun, Jianlei, and David Schechter. "Optimization-Based Unstructured Meshing Algorithms for Simulation of Hydraulically and Naturally Fractured Reservoirs With Variable Distribution of Fracture Aperture, Spacing, Length, and Strike." SPE Reservoir Evaluation & Engineering 18, no. 04 (November 25, 2015): 463–80. http://dx.doi.org/10.2118/170703-pa.
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Summary Multistage hydraulically fractured wells are applied widely to produce unconventional resource plays. In naturally fractured reservoirs, hydraulic-fracture treatments may induce complex-fracture geometries that one cannot model accurately and efficiently with Cartesian and corner-point grid systems or standard dual-porosity approaches. The interaction of hydraulic and naturally occurring fractures almost certainly plays a role in ultimate well and reservoir performance. Current simulation models are unable to capture the complexity of this interaction. Generally speaking, our ability to detect and characterize fracture systems is far beyond our capability of modeling complex natural-fracture systems. To evaluate production performance in these complex settings with numerical simulation, fracture networks require advanced meshing and domain-discretization techniques. This paper investigates these issues by developing natural-fracture networks with fractal-based techniques. After a fracture network is developed, we demonstrate the feasibility of gridding complex natural-fracture behavior with optimization-based unstructured meshing algorithms. Then we can demonstrate that one can simulate natural-fracture complexities such as variable aperture, spacing, length, and strike. This new approach is a significant step beyond the current method of dual-porosity simulation that essentially negates the sophisticated level of fracture characterization pursued by many operators. We use currently established code for fractal discrete-fracture-network (FDFN) models to build realizations of naturally fractured reservoirs in terms of stochastic fracture networks. From outcrop, image-log, and core analysis, it is possible to extract fracture fractal parameters pertaining to aperture, spacing, and length distribution, including center distribution as well as a fracture strike. Then these parameters are used as input variables for the FDFN code to generate multiple realizations of fracture networks mimicking fracture clustering and randomly distributed natural fractures. After incorporating hydraulic fractures, complex-fracture networks are obtained for further reservoir-domain discretization. To discretize the complex-fracture networks, a new mesh-generation approach is developed to conform to nonorthogonal and low-angle intersections of extensively clustered discrete-fracture networks with nonuniform aperture distribution. Optimization algorithms are adopted to reduce highly skewed cells, and to ensure good mesh quality around fracture tips, intersections, and regions of extensive fracture clustering. Moreover, local grid refinement is implemented with a predefined distance function to control cell sizes and shapes around and far away from fractures. Natural-fracture spacing, length, strike, and aperture distribution are explicitly gridded, thus introducing a new simulation approach that is far superior to dual-porosity simulation. Finally, initial sensitivity studies are performed to demonstrate both the capability of the optimization-based unstructured meshing algorithms, and the effect of aforementioned natural-fracture parameters on well performance. This study demonstrates how to incorporate a fractal-based characterization approach into the current work flow for simulating unconventional reservoirs, and most importantly solves several issues such as nonorthogonal intersections, extensive clustering, and nonuniform aperture distribution associated with domain discretization with unstructured grids for complex-fracture networks. The proposed meshing techniques for complex fracture networks can be easily implemented in existing preprocessing, unstructured mesh generators. The sensitivity study and the simulation runs demonstrate the importance of fracture characterization as well as uncertainties associated with naturally fractured reservoirs on well-production performance.
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Ma, Tianran, Hao Xu, Chaobin Guo, Xuehai Fu, Weiqun Liu, and Rui Yang. "A Discrete Fracture Modeling Approach for Analysis of Coalbed Methane and Water Flow in a Fractured Coal Reservoir." Geofluids 2020 (June 25, 2020): 1–15. http://dx.doi.org/10.1155/2020/8845348.
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As a complex two-phase flow in naturally fractured coal formations, the prediction and analysis of CBM production remain challenging. This study presents a discrete fracture approach to modeling coalbed methane (CBM) and water flow in fractured coal reservoirs, particularly the influence of fracture orientation, fracture density, gravity, and fracture skeleton on fluid transport. The discrete fracture model is first verified by two water-flooding cases with multi- and single-fracture configurations. The verified model is then used to simulate CBM production from a discrete fractured reservoir using four different fracture patterns. The results indicate that fluid behavior is significantly affected by orientation, density, and fracture connectivity. Finally, several cases are performed to investigate the influence of gravity and fracture skeleton. The simulation results show that gas migrates upwards to the top reservoir during fluid extraction owing to buoyancy and the connected fracture skeleton plays a dominant role in fluid transport and methane production efficiency. Overall, the developed discrete fracture model provides a powerful tool to study two-phase flow in fractured coal reservoirs.
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Geiger, S., M. Dentz, and I. Neuweiler. "A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs." SPE Journal 18, no. 04 (May 27, 2013): 670–84. http://dx.doi.org/10.2118/148130-pa.
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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.
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Al-Abri, Abdullah, and Robert Amin. "Numerical simulation of CO2 injection into fractured gas condensate reservoirs." APPEA Journal 51, no. 2 (2011): 742. http://dx.doi.org/10.1071/aj10122.
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More than sixty percent of the world’s remaining oil reserves are hosted by intensely fractured porous rocks, such as the carbonate sequences of Iran, Iraq, Oman, or offshore Mexico (Bedoun, 2002). The high contrast of capillarity between the matrix and the fractures makes a significant difference in the recovery performance of fractured and non-fractured reservoirs (Lemonnier and Bourbiaux, 2010). Simulation of naturally fractured reservoirs is a challenging task from both a reservoir description and a numerical standpoint (Selley, 1998). This paper presents the recovery performance of CO2 injection into a local fractured and faulted gas condensate reservoir in Western Australia. Tempest 6.6 compositional simulation model was used to evaluate the performance of uncertain reservoir parameters, injection design variables, and economic recovery factors associated with CO2 injection. The model incorporates experimental IFT, relative permeability data and solubility data at various thermodynamic conditions for the same field. These measurements preceded the simulation work and are now published in various places. The model uses Todd-Longstaff mixing algorithm to control the displacement front expansion. This paper will present, with aid of simulation output graph and tornado charts, the results of natural depletion, miscible and immiscible CO2 injection, waterflooding, WAG, sensitivity of fracture porosity, permeability and fracture intensity. The results also demonstrate the effect of initial reservoir composition, well completion and injection flow rate. All simulation cases were carried out at various injection pressures. The results are discussed in terms of transport mechanisms and fluid dynamics. This project was sponsored by a consortium of companies.
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JPT staff, _. "Techbits: Understanding Naturally Fractured Reservoirs." Journal of Petroleum Technology 58, no. 05 (May 1, 2006): 24–26. http://dx.doi.org/10.2118/0506-0024-jpt.
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Dean, R. H., and L. L. Lo. "Simulations of Naturally Fractured Reservoirs." SPE Reservoir Engineering 3, no. 02 (May 1, 1988): 638–48. http://dx.doi.org/10.2118/14110-pa.
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Medeiros, F., B. Kurtoglu, E. Ozkan, and H. Kazemi. "Analysis of Production Data From Hydraulically Fractured Horizontal Wells in Shale Reservoirs." SPE Reservoir Evaluation & Engineering 13, no. 03 (June 7, 2010): 559–68. http://dx.doi.org/10.2118/110848-pa.
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Summary This paper discusses the analysis of production data from hydraulically fractured horizontal wells in shale reservoirs. The stimulated volume around the well is simulated by a naturally fractured region. A semianalytical model incorporating the key features of reservoir heterogeneity and the details of hydraulic fracture and wellbore flow is used to present production-decline characteristics in terms of transient-productivity index. Production-decline analysis of fractured horizontal wells in shale-oil and shale-gas formations by transient-productivity index is explained and demonstrated by field applications.
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Zheng, Yingcai, Xinding Fang, Michael C. Fehler, and Daniel R. Burns. "Seismic characterization of fractured reservoirs by focusing Gaussian beams." GEOPHYSICS 78, no. 4 (July 1, 2013): A23—A28. http://dx.doi.org/10.1190/geo2012-0512.1.
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Naturally fractured reservoirs occur worldwide, and they account for the bulk of global oil production. The most important impact of fractures is their influence on fluid flow. To maximize oil production, the characterization of a fractured reservoir at the scale of an oil field is very important. For fluid transport, the critical parameters are connectivity and transmittivity plus orientation. These can be related to fracture spacing, compliance, and orientation, which are the critical seismic parameters of rock physics models. We discovered a new seismic technique that can invert for the spatially dependent fracture orientation, spacing, and compliance, using surface seismic data. Unlike most seismic methods that rely on using singly scattered/diffracted waves whose signal-to-noise ratios are usually very low, we found that waves multiply scattered by fractures can be energetic. The direction information of the fracture multiply scattered waves contains fracture orientation and spacing information, and the amplitude of these waves gives the compliance. Our algorithm made use of the interference of two true-amplitude Gaussian beams emitted from surface source and receiver arrays that are extrapolated downward and focused on fractured reservoir targets. The double beam interference pattern provides information about the three fracture parameters. We performed a blind test on our methodology. A 3D model with two sets of orthogonal fractures was built, and a 3D staggered finite-difference method using the Schoenberg linear-slip boundary condition for fractures was used to generate the synthetic surface seismic data set. The test results showed that we were able to not only invert for the fracture orientation and spacing, but also the compliance field.
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Liu, Hong, Lin Wang, Yu Wu Zhou, and Xi Nan Yu. "A Mathematical Model for Natural Fracture Evolution in Water-Flooding Oil Reservoir." Advanced Materials Research 868 (December 2013): 535–41. http://dx.doi.org/10.4028/www.scientific.net/amr.868.535.
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The fractured low permeability reservoirs develop complex fracture network. As the of waterflooding recovery heightens, excessive high injection pressures and excessive water injection rate will result in open, initiation, propagation and coalescence of micro-fracture, connecting injection with production form the high permeability zone, which results in a one-way onrush of waterflooding, water cut in oil well water rise quickly, causing a severe oil well flooding and channeling, thereby reducing the ultimate oil recovery efficiency. The effect of the waterflooding seepage within natural fracture on fracture initiation is studied and analyzed here, applying the theory of rock fracture mechanics to analyze the interaction of fracture system for naturally fractured reservoirs in waterflooding developing process, studying the mechanical mechanism of opening, initiation, propagation and coalescence of natural fracture under injection pressure, which is important theoretical significance for studying the distribution law of fracture and defining appreciate water injection mode and injection pressure in the process of injection development of the naturally fractured reservoir and for delaying the directivity water break-through and water flooding rate of oil well in the process of injection development.
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Civan, F., and M. L. L. Rasmussen. "Parameters of Matrix/Fracture Immiscible-Fluids Transfer Obtained by Modeling of Core Tests." SPE Journal 17, no. 02 (February 8, 2012): 540–54. http://dx.doi.org/10.2118/104028-pa.
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Summary Methodology is presented and proved for determination of the best-estimate parameter values affecting the matrix/fracture-interface fluid transfer in naturally fractured reservoirs. Fracture/surface-hindered interface transfer of immiscible fluids is considered between matrix blocks and surrounding natural fractures. Improved matrix/fracture-transfer models are applied on the basis of presumed matrix-block shapes. Analytical solutions and the limiting isotropic-matrix long-time shape factors developed for special boundary conditions are used for interpretation of typical laboratory tests conducted using rectangular- and cylindrical-shaped rock samples. Workable equations and straight-line data-plotting schemes are developed for effective analysis and interpretation of laboratory data obtained from various-shaped oil-saturated reservoir-rock samples immersed into brine. Applications concerning the water/air and water/decane systems in laboratory core tests are also presented. The present approach allows rapid determination of the characteristic parameters of the matrix/fracture-transfer models for various-shaped matrix blocks, which are essential for prediction of petroleum recovery from naturally fractured reservoirs. The methodology is verified using various experimental data, and the values of the characteristic parameters (e.g., the average diffusion-coefficient and the interface-skin-mass-transfer coefficient) are determined. The Arrhenius (1889) equation is shown to represent the temperature dependency of these parameters effectively.
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Balogun, Adetayo S., Hossein Kazemi, Erdal Ozkan, Mohammed Al-kobaisi, and Benjamin Ramirez. "Verification and Proper Use of Water-Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs." SPE Reservoir Evaluation & Engineering 12, no. 02 (April 14, 2009): 189–99. http://dx.doi.org/10.2118/104580-pa.
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Summary Accurate calculation of multiphase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture- and matrix-flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer-function equations can be used easily to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil-recovery correlations. The study was accomplished by conducting a 3-D fine-grid simulation of a typical matrix block and comparing the results with those obtained through the use of a single-node simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari 2002) we had conducted for a 1D gas-oil system. The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary-pressure curves, densities of the flowing fluids, and matrix block dimensions. Introduction Naturally fractured reservoirs contain a significant amount of the known petroleum hydrocarbons worldwide and, hence, are an important source of energy fuels. However, the oil recovery from these reservoirs has been rather low. For example, the Circle Ridge Field in Wind River Reservation, Wyoming, has been producing for 50 years, but the oil recovery is less than 15% (Golder Associates 2004). This low level of oil recovery points to the need for accurate reservoir characterization, realistic geological modeling, and accurate flow simulation of naturally fractured reservoirs to determine the locations of bypassed oil. Reservoir simulation is the most practical method of studying flow problems in porous media when dealing with heterogeneity and the simultaneous flow of different fluids. In modeling fractured systems, a dual-porosity or dual-permeability concept typically is used to idealize the reservoir on the global scale. In the dual-porosity concept, fluids transfer between the matrix and fractures in the grid-cells while flowing through the fracture network to the wellbore. Furthermore, the bulk of the fluids are stored in the matrix. On the other hand, in the dual-permeability concept, fluids flow through the fracture network and between matrix blocks. In both the dual-porosity and dual-permeability formulations, the fractures and matrices are linked by transfer functions. The transfer functions account for fluid exchanges between both media. To understand the details of this fluid exchange, an elaborate method is used in this study to model flow in a single matrix block with fractures as boundaries. Our goal is to develop a technique to produce accurate results for use in large-scale modeling work.
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Ding, Didier–Yu. "Modeling of Matrix/Fracture Transfer with Nonuniform-Block Distributions in Low-Permeability Fractured Reservoirs." SPE Journal 24, no. 06 (September 18, 2019): 2653–70. http://dx.doi.org/10.2118/191811-pa.
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Summary Unconventional shale–gas and tight oil reservoirs are commonly naturally fractured, and developing these kinds of reservoirs requires stimulation by means of hydraulic fracturing to create conductive fluid–flow paths through open–fracture networks for practical exploitation. The presence of the multiscale–fracture network, including hydraulic fractures, stimulated and nonstimulated natural fractures, and microfractures, increases the complexity of the reservoir simulation. The matrix–block sizes are not uniform and can vary in a very wide range, from several tens of centimeters to meters. In such a reservoir, the matrix provides most of the pore volume for storage but makes only a small contribution to the global flow; the fracture supplies the flow, but with negligible contributions to reservoir porosity. The hydrocarbon is mainly produced from matrix/fracture interaction. So, it is essential to accurately model the matrix/fracture transfers with a reservoir simulator. For the fluid–flow simulation in shale–gas and tight oil reservoirs, dual–porosity models are widely used. In a commonly used dual–porosity–reservoir simulator, fractures are homogenized from a discrete–fracture network, and a shape factor based on the homogenized–matrix–block size is applied to model the matrix/fracture transfer. Even for the embedded discrete–fracture model (EDFM), the matrix/fracture interaction is also commonly modeled using the dual–porosity concept with a constant shape factor (or matrix/fracture transmissibility). However, in real cases, the discrete–fracture networks are very complex and nonuniformly distributed. It is difficult to determine an equivalent shape factor to compute matrix/fracture transfer in a multiple–block system. So, a dual–porosity approach might not be accurate for the simulation of shale-gas and tight oil reservoirs because of the presence of complex multiscale–fracture networks. In this paper, we study the multiple–interacting–continua (MINC) method for flow modeling in fractured reservoirs. MINC is commonly considered as an improvement of the dual–porosity model. However, a standard MINC approach, using transmissibilities derived from the MINC proximity function, cannot always correctly handle the matrix/fracture transfers when the matrix–block sizes are not uniformly distributed. To overcome this insufficiency, some new approaches for the MINC subdivision and the transmissibility computations are presented in this paper. Several examples are presented to show that using the new approaches significantly improves the dual–porosity model and the standard MINC method for nonuniform–block–size distributions.