SPE 62939 Integrated Fractured Reservoir Modeling Using Both Discrete and Continuum Approaches 2
Ahmed Ouenes, (RC) , Lee J. Hartley, AEA Technology
Copyright 2000, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1–4 October 2000. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract A new approach that combines the use of continuum and discrete fracture modeling methods has been developed. The approach provides the unique opportunity to constrain the fractured models to all existing geologic, geophysical, and engineering data, and hence derive conditioned discrete fracture models. Such models exhibit greater reality, since the spatial distribution of fractures reflects the underlying drivers that control fracture creation and growth.
honor all the geologic conditions reflected in the continuous models and exhibit all the observed fracture features. The conditioned DFN models are used to build a realistic and detailed model of flow in discrete conduits. There are two main areas where detailed discrete fracture models can be used: (1) Upscaling of fracture properties (permeability, porosity and σ factor) for input into reservoir simulators; and (2) Optimization of well-design, completion and operation based on an understanding of the inter-well scale flows. For accurate results, the full permeability tensor is calculated for each grid-block based on flow calculations using generalized linear boundary conditions. Inter-well flows are analyzed in terms of the variability in flow paths, characterized by distance and time traveled, through the fracture network connecting injectors and producers.
The modeling process is initiated by constructing continuous fracture models that are able to capture the underlying complex relationships that may exist between fracture intensity (defined by static measures, such as fracture count, or dynamic measures, such as hydrocarbon production), and many possible geologic drivers (e.g. structure, thickness, lithology, faults, porosity). Artificial intelligence tools are used to correlate the multitude of geologic drivers with the chosen measure of fracture intensity. The resulting continuous fracture intensity models are then passed to a discrete fracture network (DFN) method.
Introduction Many large oil and gas fields in the most productive regions such as the Middle East, South America, and Southeast Asia happen to be fractured. The exploration and development of such reservoirs is a true challenge for many operators who do not possess the tools and technology to completely understand and predict the effects of fractures on the overall reservoir behavior. Although many fractured reservoirs could be developed economically, it is very common to see operators abandoning these fields because of their inability to drill wells that intercept fractures, and/or inability to estimate correctly reservoir pressure during a pressure transient test. After many years, if not decades, of missed opportunities, the petroleum industry is realizing the need for better fractured reservoir modeling tools.
The current practice in DFN modeling is to assume fractures are spatially distributed according to a stationary Poisson process, simple clustering rules, or controlled by a single geologic driver. All these approaches will in general be overly simplistic and lead to unreliable predictions of fracture distribution away from well locations. In contrast, the new approach determines the number of fractures in each gridblock, based on the value of the fracture intensity provided by the continuous model. As a result, the discrete fracture models
The rock properties in a conventional reservoir depend primarily on the deposition process that is typically a smooth, and "linear" process. As a result of this continuous deposition process, spatial correlations of key rock properties, such as facies proportion and porosity, appear at different scales. This geologic characteristic can be exploited mathematically using geostatistical tools that lead to reliable reservoir models in almost any depositional environment. For a conventional reservoir deposition is the key process in the reservoir’s
2
AHMED OUENES, LEE J. HARTLEY
SPE 62939
formation. For fractured reservoirs it is only the first. After deposition, many events can perturb the geologic layers giving rise to a far more complex and heterogeneous situation. In this paper we are primarily interested in structural deformation due to folding and faulting. Although there are other circumstances that create fractures, we shall focus only on fractures related to tectonics.
by utilizing one source of static or dynamic data. The methods fall under three categories: 1) models for reservoir engineers who are interested in the bottom line which is the ability to reproduce well performances, 2) models for geologists who are interested in geometrically complex patterns of 3D fracture planes, and finally 3) models derived from geomechanics. Examples of these three categories are given below.
A schematic story of a fractured reservoir begins with geologic beds with different ranges of thickness, and are characterized by a heterogeneous lithology/facies distribution along and across the layers. Subject to different tectonic regimes, these heterogeneous layers experience different magnitudes and directions of stress. Depending on the bed thickness and the lithology/facies that exist at each point, as well as the prevailing stress magnitudes and directions, the rock will either fracture or resist by rearranging itself. The actual process of fracturing is complex. However, by noting the following important facts, progress in modeling fractured reservoirs becomes possible: 1. Tectonic events act on geologic layers whose structure (i.e. geologic drivers such as thickness and distribution of lithology/facies) is spatially heterogeneous which can lead to very heterogeneous distributions of 3D mechanical properties. 2. The non-linear process of rock failure, and hence the resulting fracture intensity, depends considerably on this 3D heterogeneous distribution of mechanical properties. 3. The geologic drivers are the result of the deposition process and hence can be characterized by their spatial structure.
Inverse models. The main source of data in these approaches1-2 is well performances (pressure or production). The fractures are represented by their flow properties on a predefined grid or lattice. The problem consists of finding the distribution of fracture flow properties that best matches the observed well performances. The initial distribution of the fracture properties could benefit from some a priori geologic knowledge, but has been rarely used in such approaches.
These observations indicate that there is a relationship between the observed fracture intensity at any location and a series of geologic and geomechanical drivers at the same location. It is tempting to say that finding this relationship is a simple exercise in continuum mechanics. In that, given some boundary and initial conditions, and a 3D distribution of mechanical properties, then the well-known stress and strain equations can be applied to compute the tectonic stresses in the reservoir. The tectonic stresses and overburden stresses are then combined and compared with failure criteria to determine the fracture distribution. Unfortunately, this relationship is neither simple nor universal and each fractured reservoir must be treated separately. This paper will describe the framework used to derive these relationships for any fractured reservoir.
Discrete fracture networks (DFN). The main source of data in this approach is image logs and what can be extracted from a borehole. In contrast to the previous approach, where well performance is a simple measurement, acquiring data from cores and image logs for DFN modeling is a real challenge. There is a large number of geologic papers describing the problems related to core and image log interpretations, and we highly recommend to the reader the Lorenz and Hill3 paper that illustrates very well some of the difficulties in obtaining basic fracture properties used as input in DFN modeling. Since explicit fracture information is only available at the well location, the data is formulated as a probabilistic characterization of fracture properties and spatial distribution away from the well. A number of unconditioned stochastic realizations of discrete fracture planes are generated in the 3D reservoir volume by a stationary Poisson process. The main ideas related to this approach are discussed in Cowie et al.4 Since the spatial distribution of fractures away from the well locations is uncertain, the resulting models lack "geologic" meaning, and the upscaled fracture permeability have been used with little success in layered sedimentary systems. For the same reason, accuracy of the generated models is only reliable in the near wellbore region, and the unconditioned random filling of the interwell region limits the use of such models beyond the near wellbore scale. This major drawback will be alleviated with the new approach described in this paper.
This paper begins with a review of current techniques used to model fractured reservoirs. Each of these techniques uses only a single type of data. We argue the need for an integrated approach that combines various forms of data, and an explanation on how this is achieved. For illustration, an application to a fractured carbonate reservoir is presented.
Geomechanical approaches. The main source of data used in these approaches is the structural surface derived from markers picked on well logs and/or from seismic reflectors. There are many geomechanical approaches for modeling fractured reservoirs varying from simple curvature analysis to more complex systems where non-linear continuum mechanics equations are solved numerically usually based on the finite-element method.
Fracture modeling techniques Many modeling approaches are documented in the literature. Most attempts to describe the fracture distribution were done
Many authors5-7 have used curvature analysis with varying degrees of success. Most of the successes have been obtained on "homogeneous" reservoirs (small variation in bed thickness
SPE 62939
INTEGRATED FRACTURED RESERVOIR MODELING USING BOTH DISCRETE AND CONTINUUM APPROACHES
and lithology) that have undergone extensional deformation. In such an idealistic situation, the curvature is proportional to the strain and the curvature analysis could be sufficient. Unfortunately, "homogeneous" reservoirs are rare and one has to deal with a large number of changing reservoir properties in most fractured reservoirs. To handle the real heterogeneity of the reservoirs, numerical geomechanical models are used to predict the strain distribution. Although strain does not automatically mean fracture intensity, it can be considered as a strong indicator. The basic idea is that the reservoir becomes deformed from an initial undeformed plane state as some lateral boundary conditions are applied. A major difficulty is that the initial and boundary conditions of this problem are not known and need to be guessed. Depending on the guess, the final deformed structure is compared to the actual present day one, and the guess is adjusted if there is a large disagreement. This trial and error process is similar to the production history matching in reservoir simulation and can be very tedious. Heffer et al.8 introduced some geostatistical concepts in the general continuum mechanics equations to derive a correlation of displacements. Although the asymptotic behavior of this correlation when r Æ 0 raises some serious questions, the explicit formulation could be very useful to derive a correlation for strain. Unfortunately, having an explicit formulation for strain did not come free and a hefty price was paid in the assumptions that were made. The most detrimental assumption was the homogeneous elastic properties (i.e. a "homogeneous" reservoir). As in the geomechanical approaches, this method relies only on reservoir structure, while very influential drivers such as lithology are ignored for the sake of obtaining an explicit form for the correlation of strain. This approach points again to the need for a true integrated approach where all data could be used to reach a better model. Integrated Reservoir Modeling An integrated reservoir modeling approach consists of a collection of computational tools and methods that utilize simultaneously, or sequentially different static and/or dynamic data representing different reservoir responses at different scales. The objective and prospect of an integrated reservoir modeling approach is to reduce the uncertainties. To better understand this concept, some examples are given below. One of the first original integrated approaches was proposed by de Marsily et al.9 using the concept of pilot points. Their objective was to find a permeability model by using two types of data: well performances and spatial correlations. To handle the two types of data, two computational tools were used: an optimization method to match well performances and estimate the permeability at a limited number of locations, and a geostatistical method to derive a full model, utilizing the spatial correlation and the known well permeability values. In this case, the integration process was made possible by the combination of an optimization method and geostatistics. Another good example is the use of a geostatistical framework
3
that has an abundant number of methods able to handle different types of data. The most common example is the use of seismic information as “soft” data when building geologic models. This integration process can be achieved with different methods ranging from simple co-kriging to more sophisticated ones such as cloud transform techniques.10 This example illustrates the ability to integrate seismic information directly in the geologic modeling using the geostatistical framework. When the need came to integrate more data, many authors used global optimization methods such as simulated annealing as a framework. Here, a model is derived by minimizing an objective function that can contain a variety of static and dynamic data. A large number of applications are discussed in Ouenes et al.11 and show the flexibility of such an approach. Reviewing these three examples shows that integration of data in reservoir modeling requires a framework with appropriate computational tools that are able to handle simultaneously, or sequentially different types of data. The drawback of all three modeling approaches discussed in the previous section is their inability to provide an integration framework where various data could be used to reduce the model uncertainties. Integrated Fractured Reservoir Modeling Starting from the simple observation that fracture intensity depends on many geologic drivers (the most commonly known being, structural setting, proximity to a fault, lithology and thickness), it is imperative to find a framework where these drivers could be easily incorporated in the fracture modeling process. Furthermore, it is important to recognize the complexity of the non-linear process of fracturing, which means that any attempt to find a simple and explicit relationship between drivers and fracture intensity may require some limiting assumptions that are not acceptable. Given these constraints, Ouenes et al.12 introduced a collection of artificial intelligence tools to model fractured reservoirs. The approach was successfully used on various fields and basins12-16. The methodology is described in Ouenes,17 in this paper we limit ourselves to a short summary. Since there is a complex but undetermined relationship between a large number of geologic drivers and fracture intensity, the use of artificial intelligence (AI) tools such as neural networks has great merit. Utilizing the available data at well locations, one can let a neural network find the underlying relationship, then use the derived model to predict fracture intensity everywhere in the 3D reservoir volume. Since this is a data driven approach, one must pay attention to common pitfalls and take some precautions. In other words, the successful use of AI tools is not simply a matter of downloading a neural network from the World Wide Web. To ensure that AI tools are applied efficiently and with integrity to fractured reservoirs, the following issues must be addressed: ranking the geologic drivers; optimizing the neural network
4
AHMED OUENES, LEE J. HARTLEY
architecture; a robust training algorithm; selecting efficiently data for training; and creating a stochastic framework. The neural network is an "equation maker" or a "complex regression analysis tool" that takes several reservoir properties (the inputs), and tries to correlate them with a fracture intensity indicator (the output). The neural network is trained using a set of wells where both the inputs and the output are known to find the relation, or the "equation," between the inputs and the output. Once this relation is found, the neural network uses only the inputs available throughout the entire reservoir volume, to predict the fracture intensity. In this application, the neural network is used to find the undetermined relationship that exists between the geologic drivers and the fracture intensity. Hence, no a priori knowledge about this relationship is required. Rather we let the actual data direct us to the key drivers. This relationship is then utilized for the key objective of estimating the fracture intensity in the interwell regions. As indicated earlier, it is important to notice that most of the geologic drivers that control fracture intensity are related to deposition, and are easily mapped in the entire 3D volume using geostatistics. For example, by combining the use of markers picked on well logs with a seismic reflector, one can use the integration abilities of geostatistics to derive a very accurate reservoir structure. This can be used to compute first (slopes) and second (curvatures) structural derivatives in different directions that can be used as geologic drivers, and are potential indicators of fracture intensity. Among all the geologic drivers, lithology/facies and porosity play a major role in any fractured reservoir modeling (Assuming a “homogeneous” reservoir will likely lead to a completely misleading model). These two key drivers control the mechanical rock properties that in their turn control the rock failure and fracture intensity. For a given lithology, the increase of porosity makes a rock more ductile. Conversely, a reduction of a few percent in porosity can lead to many orders of magnitude increase in fracture intensity. On the other hand, a rock with just a few more percent of shale can become very ductile and exhibit no fractures, or just a few more percent of dolomite can lead to a completely fractured rock. These simple well-known examples illustrate the importance of porosity and lithology or facies proportions in fractured reservoir modeling and any modeling effort must include these reservoir properties as input. In addition to structural derivatives, facies proportions, bed thickness and proximity to a fault can play a major role in determining the fracture intensity. Besides these well-known drivers, most fractured reservoirs have some particular feature that needs to be incorporated in the modeling in order to be complete. The key concept in fractured reservoir modeling is that different geologic drivers are dominant in different areas of the reservoir. For example, if we consider two simple drivers such as structural curvature and the percent of shale in the
SPE 62939
rock, and also assume that the fractures were created as a result of some extensional deformation, we expect a location with high curvature to contain a large number of fractures. This “linear” thinking is wrong in a fractured reservoir because many other factors have an influence on how many fractures will be present. In this example, the percent of shale contained in the rock will play a major role and beyond a certain threshold value, (for example 45% shale), the rock will be without fractures however high the curvature. When realizing that there is a multitude of geologic drivers that could affect fracturing, it is easy to imagine how complex the non-linear relationship between drivers and fracture intensity could be, and how illusive is the search for an explicit analytical form. On the other hand, one has to remember the reasons behind the development of AI tools such as neural networks that were specifically designed for such complex non-linear problems. In addition to geologic drivers that played a role during fracturing, one can use present day information such as seismic amplitude, seismic impedance (a good indicator of lithology), strain or stress 3D models, or even permeability estimated by automatic history matching as illustrated in Barman et al.18 Given all the potential geologic drivers and present day fracture indicators, one has to choose the framework where the integration of these data could be achieved. Integrated Continuous Models The framework required to correlate all of the geologic drivers and present day fracture indicators is a continuous one. Because most of the drivers are related to deposition we assume that the reservoir acts as an equivalent continuum on some scale, which is known as the representative elementary volume (REV). The entire reservoir is discretized into gridblocks whose size is dictated by the size of the REV. This assumption is appropriate for geologic drivers related to deposition, but could seem to neglect smaller fractures that range from microfractures to joints. At this stage, one has to remember the purpose of the fractured reservoir modeling effort that is to understand the flow behavior and the overall fracture network controlling it. There are two ways of looking at this problem and achieving the objective stated above. First the reservoir engineer point of view, and second the geologist perspective. There is a major conceptual difference between the two views. On one hand, reservoir engineers recognize the fact that fractured reservoir provide very little data that can be used for modeling purposes. Hence, they settle for some average property assigned to a certain volume. This is the same approach used for more than a century with the use of Darcy equation to describe flow in porous media. Although the actual flow in a rock could be described by using the NavierStokes equations, the lack of information on the detailed pore structure required for the boundary conditions, have lead to
SPE 62939
INTEGRATED FRACTURED RESERVOIR MODELING USING BOTH DISCRETE AND CONTINUUM APPROACHES
the use of a REV over which average properties such as permeability are defined. On the other hand, geologists believe that a correct fracture model must contain the actual discrete objects (fracture planes), although the amount of available information could be completely inadequate due the difficulty of intercepting fractures with the commonly used vertical wells. There is no doubt that fractures exist at different scales ranging from microfractures to joints, but what is often neglected is the fact that getting reliable information about the fracture characteristics at any scale is an art rather than a science. Therefore, one cannot expect to achieve an understanding of reservoir flow at the level of micro-fractures if there are no means of measuring adequately all the characteristics of these small features. Hence, we need to rise at a higher scale where reliable measurements are possible and meaningful. This discussion leads to the conclusion that the definition of the REV is simply related to what we will consider as fracture intensity for our modeling purposes. When using image logs interpretations we can consider a fracture intensity defined by the fracture count which represents the number of fractures encountered in a REV that is in the range of a few feet. There are many problems associated with the use of fracture count as a fracture intensity indicator. The main one being the lateral extent of this information which is valid only in the near wellbore region sometimes no more than few inches away. It is also common to find fracture swarms dominated by a large number of microfractures making fracture count difficult to quantify. Finally, the issue of dynamic effects, often ignored during image and core analysis, could lead to overestimated fracture count because not all observed fractures contribute to production. Despite all these problems, many geologists view fracture count as the best indicator of fracture intensity, and hence tend to underestimate the value of information contained in production indicators. When seeking fractured reservoir models that could help understand the interwell region, it is imperative to find a fracture intensity that could “see” farther than the few inches around the wellbore. The production based indicators such as productivity index (PI), transmissiblity (kh) estimated from well test, and Estimated Ultimate Recovery (EUR), are some of the examples that provide an average fracture intensity that encompasses an area as big as the drainage radius. These production based fracture intensity indicators that only seem appropriate for 2D models, have been successfully used in 3D modeling simply by allocating the single measurement along the wellbore. Different means could be used to transform a single kh or PI value into a vertical log, the most common being the production logs or the φh allocation. Once the fracture intensity is chosen it will represent the output of the neural network. The inputs that could be related to the fracture intensity are the geologic drivers (porosity, permeability, lithology, facies proportion, bed thickness,
5
proximity to faults, etc.) and present day indicators (seismic, stress, strain, etc), all of which can be obtained over the entire reservoir volume by using appropriate geostatistical methods. The search for the possible relationship that exist between the important drivers and the chosen fracture intensity is a three stage process described below: Ranking the drivers. Prior to any modeling, appropriate ranking methods must be used to analyze the effect of each driver on the chosen fracture intensity. The engineer, or geologist must check at this stage for the validity of the ranking over the entire area of the study, and on specific zones. For example, if the reservoir was under extensional deformation, it is expected to see the curvatures rank high. There are many benefits that can be derived from the ranking exercise, the most notable one is to achieve a better understanding of what the primary drivers are. There are also computational benefits, whereas, low ranked drivers could indicate that they have no effect on the fracture intensity and therefore, they do not need to be included in the inputs. Training and testing the models. Once the user has decided on which drivers he would use in the modeling process, the set of available data is divided into two subsets: a training set and a testing set. Since this approach is done in a stochastic framework, many realizations are needed. Each realization can be derived by selecting randomly or according to some rule the training set. The neural network modeling process consists of adjusting some weights until the actual fracture intensity matches the estimated ones. Once the matching process is done, we can assume that a model was available, and could be used for testing and cross-validation on the testing data set that was not used during the training process. Depending on the ability of the model to predict fracture intensity at testing locations, the model could be kept for further use or discarded. Fracture analysis and probability volumes. Since all the drivers are available in the entire 3D reservoir volume, and a relationship has been established between the drivers and the fracture intensity, the application of the neural network to all the gridblocks in the reservoir will lead to a 3D distribution of fracture intensity. These models could be used to estimate fracture directions, analyze fracture connectivity, serve as input for dual porosity model parameters, and derive probability maps. Given a large number of realizations, all of which provide a good testing correlation coefficient, one could construct a 3D probability volume that can be used for further modeling using a discrete approach. The role of DFN models The Dual-Porosity Continuum (DPC) concept19, 20 is commonly applied to fractured reservoirs. This idealizes the reservoir in terms of an orthogonally connected fracture system that penetrates a set of identical rectangular gridblocks representing the matrix blocks and deliver fluid to the wells. Each of the rectangular blocks may contain several matrix
6
AHMED OUENES, LEE J. HARTLEY
blocks allowing the problem to be scaled up if required. DPC models are well suited to multiphase flow, and to models with a large number of blocks. However, the simplified geometry makes the choice of parameters that describe the heterogeneous permeability and connectivity characteristics of fractured reservoirs difficult. DFN models provide a more natural framework in which models of fracture geometry and the stochastic methods used to characterize sub-seismic fractures can be applied. Equivalent continuum properties that accurately capture the heterogeneity, anisotropy and connectivity of the fracture system can be derived using appropriate upscaling techniques on the DFN models. Hence, the approach is to populate the reservoir volume with discrete fractures, and then upscale the properties of the fracture system for each grid block of an equivalent DPC model. Constrained DFN models Since the introduction of DFN models, there was a need for constraining the realization to some geologic input. Attempts have been made to control the fracture generation with some indicator. However, these past attempts used a single geologic driver and ignored the others, and most importantly did not account for the complex interplay of the drivers as described in the previous sections. This problem was solved by the use of the continuous modeling approach described in the previous section, which passes to the DFN the entire 3D reservoir volume map of fracture intensity, or probability that can be used as a spatial constraint. Therefore, all the geological realism of a detailed geometrical representation of discrete fractures at the near-well scale can be coupled with realistic constraints on fracture distribution over the larger interwelland reservoir-scales. Generating a DFN model. DFN modeling is based on the stochastic approach, and hence the specific details of individual fractures change between realizations. However, in this approach each realization is constrained such that amount of fracturing, fracture area per unit volume, in any given gridblock is the same for each realization and is derived from the continuous model. Additional parameters that describe the properties of discrete fractures are required to generate a model: 1) Fracture orientation derived from image logs or inferred as an additional output of the neural network approach. 2) Fracture length distribution from image logs, seismic or outcrop mappings. These data supply fracture length data on very different scales leaving gaps in the length distribution. A natural solution to this problem is to use a power law distribution that provides a continuous model between the various length-scales of fractures, and many geologists21, 22 have demonstrated the validity of such a model. 3) Fracture transmissivity (to calculate permeability) derived from high-density production logs and calibrated against interference and/or tracer tests. 4) Fracture aperture (to calculate porosity) calibrated against tracer tests
SPE 62939
Different fracture sets can be constrained against different fracture intensity maps related to different groups of geologic drivers. For example, two-conjugate sets characterized by geologic drivers associated with folding (e.g. curvature, lithology, and porosity) can be combined with other sets characterized by geologic drivers associated with deformation zones around faults (e.g. proximity to fault). Directional fracture permeability. It is desired to calculate an effective permeability tensor that best represents the behavior, in the environment of the surrounding network, of a block within a DFN model. An effective permeability that represents the block, not just at a point, is required, because permeability is to be used for the corresponding block in a discretized DPC model. It is important to determine directional permeabilities, a tensor, not just the axial components. This is more robust in cases with anisotropy, which is common in fracture systems, where the dominant flow connections are between adjacent sides of a block rather than between opposite sides. To calculate the permeability of a block, uniform pressure gradients are imposed in three orthogonal directions across the boundaries of the block. The pressure distribution and flows in the block are calculated by discretizing each fracture into finite-elements. The total flow through each face of the block is evaluated, and an effective permeability tensor is fitted that gives the best overall match through each face for the different gradient directions. The self-consistency between DFN models and equivalent continuum models has been demonstrated by Jackson et al.23.
Application To illustrate this new approach, we will consider a 3D example of a fractured carbonate reservoir. Like many fractured reservoirs, the one considered had seen many tectonic events, each leaving behind a complex fracture network. Because of a lack of image logs and core data, most of the continuum modeling effort relied on the use of the productivity index (PI) which was available at all the wells. Hence, a large gridblock size of 200 m by 200 m was considered for the continuous model. At each well location, the single PI value was allocated along the borehole to create a PI log. Within the considered 3D grid, a large number of geologic drivers, and present-day indicators were available for the modeling effort. Four major types of drivers were available: 1) Geological drivers such as porosity, and the facies proportion of three different facies. 2) Geomechanical drivers that include structural derivatives and fault related information. 3) Geophysical drivers such as seismic impedance. 4) Stress related information such as effective permeability estimated by automatic history matching as described in Barman et al.18 Out of all the drivers, the ranking pointed to 4 major ones:
SPE 62939
INTEGRATED FRACTURED RESERVOIR MODELING USING BOTH DISCRETE AND CONTINUUM APPROACHES
percentage of a certain rock type, porosity, proximity to a fault and structural derivatives along the present day horizontal maximum stress direction. Using all the drivers as inputs, and the PI as a fracture intensity indicator, a large number of realizations (e.g. Fig. 1) were derived using the procedure described earlier. Using a threshold value for the PI, a probability volume was calculated from the 10 best realizations that had the most accurate testing prediction. Both a PI realization as well as the probability could be used as a constraint for the DFN models. For this application we will illustrate the use of both stochastic, and deterministic continuum models. There are two major types of fractures present in this field: 1) fractures related to faults, and 2) fractures related to structural deformation. To model the structural related fractures we will use the continuous model (Fig. 1) derived by integrating all the available geologic drivers pertaining to these fractures. This continuous model is used as a constraint to produce different DFN realizations (Fig. 2). Notice that the fracture intensity in the DFN model Fig. 2 follows the information provided by the integrated continuous model Fig. 1. Since the fracture related to faults are mostly present in the vicinity of the fault, we created a deterministic model (Fig. 3) of proximity to fault that utilizes mostly the seismic interpretation of the faults. This deterministic model will serve as a constraint to derive a DFN representing the fault related fractures (Fig. 4).
2.
3.
4.
5.
The resulting DFN model could be used for future reservoir modeling and management. A direct benefit from such a model is to study the fracture cluster (Fig. 7) around existing wells, especially those injecting fluids in the reservoir. Another benefit is the derivation of a fracture permeability 3D model (Fig. 8) that can be used in dual-porosity reservoir simulators. The resulting fracture permeability model shown in (Fig. 8) was derived using the final DFN model shown in Figs. 5 and 6. The dark red cells represent high fracture permeability while the white cells represent low permeability. Notice the resulting distribution of low fracture permeability (the very specific shape) that is the result of the whole integration process. It is unlikely that an unconstrained DFN model will be able to delimit exactly such an area, which is the main point that we have tried to convey throughout this paper.
References 1.
3.
4.
5.
6.
7.
8. Conclusions 1. The combination of continuous and discrete approaches in fractured reservoir modeling provides many benefits among them true data integration that reduces
uncertainties. The new proposed integrated framework goes beyond data integration and constitutes a platform for integrating different disciplines (geologists, geophysicists and engineers). The use of artificial intelligence tools in continuous models allows a rapid and efficient integration of geophysical, geologic, and engineering data into fractured reservoir models. The use of continuous models as a constraint in building DFN provides more realistic fractured reservoir models that can then be used to estimate fracture permeabilities. The proposed approach and the seamless data integration process, including passing data from continuous to discrete models, is readily available in ResFrac24 and NAPSAC 25 .
Acknowledgments The authors would like to thank: David Holton of AEA Technology for useful discussions, and Arnfinn Morvik of BSSI A/S, Bergen, Norway, for assistance on visualization.
2. Given the two DFN models representing the different types of fractures, we can build an integrated DFN model that merges the two DFN models. The final DFN model (Figs. 5 and 6) contains features from the fault related fractures as well as fractures related to the structural deformation.
7
9.
Smith, R., Tan, T.: "Reservoir Characterization of a Fractured Reservoir Using Automatic History Matching," paper SPE 25251 presented at the 1993 SPE Syposium on Reservoir Simulation, Feb. 28- March 3. Long, J., et al.:" Modeling Heterogeneous and Fractured Reservoirs with Inverse Methods Based on Iterated Function Systems," paper presented at the Third International Reservoir Characterization Technical Conference, Tulsa, OK, Nov. 3-5, 1991. Lorenz, J. and Hill, R.: "Measurement and Analysis of Fractures in Core," in Geological Studies Relevant to Horizontal Drilling: Examples from Western North America, Schmoker J., Coalson, E., Brown, C. (Eds.) Rocky Mountain Association of Geologists, 1992. Cowie, P., Knipe, R., and Main, I.:"Introduction to the special issue," J. Structural Geology, Vol 18, Nos 2&3, 1996. Harris, J., Taylor, G., Walper, J.: "Relation of deformational structures in sedimentary rocks to regional and local structure,” AAPG Bulletin, (1960) v. 44 p. 1853-1873. Murray, G.: "Quantitative fracture study- Sanish Pool, McKenzie County, North Dakota," AAPG Bulletin, (1968) v. 52, no. 1, p.57-65. Lisle J. L. :"Detection of zones of abnormal strains in structures using Gaussian curvature analysis," AAPG Bulletin, (1994) v. 78, no. 12, p. 1811-1819. Heffer, K., King, P., and Jones, A.:"Fracture Modeling as Part of Integrated Reservoir Characterization," paper SPE 53347 presented at the 1999 SPE Middle East Oil Show, Feb. 20-23. Marsily, G. (de), Lavedan, G., Boucher, M., and
8
10.
11.
12.
13.
14.
15.
16.
17.
18.
19. 20.
AHMED OUENES, LEE J. HARTLEY
Fasanino, G.: “Interpretation of Interference Tests in a Well Field Using Geostatistical Techniques to Fit the Permeability Distribution in a Reservoir Model,” Geostatistics for Natural Resources Characterization, Part 2, Verly G. (Eds.), Reidel D. Publishing Company, Dordrecht (1987), 831-849. Bashore, W., Araktingi, U., Levy, M., and Scheweller, W.: “Importance of a Geological Framework and Seismic Data Integration for Reservoir Modeling and Subsequent Fluid-Flow Predictions,” Stochastic Modeling and Geostatistics, Principles, Methods, and case Studies, Yarus and Chambers (Eds.), AAPG Computer Applications in Geology, No3, Tulsa, (1994) Ouenes, A. , Bhagavan, S., Bunge, P., and Travis, B.: “Application of simulated annealing and other global optimization methods to reservoir description: myths and realities,” paper SPE 28415 presented at the 1994 Annual Technical Conference and Exhibition, New Orleans, 2528 Sept. Ouenes, A., Richardson, S., Weiss, W.: “Fractured reservoir characterization and performance forecasting using geomechanics and artificial intelligence,” paper SPE 30572 presented at the 1995 SPE Annual Technical Conference and Exhibition, Oct. 22-25. Zellou, A., Ouenes, A., Banik, A.: “Improved naturally fractured reservoir characterization using neural networks, geomechanics and 3-D seismic,” paper SPE 30722 presented at the 1995 SPE Annual Technical Conference and Exhibition, Oct. 22-25 Basinski, P., Zellou, A., Ouenes, A.: “Prediction of Mesaverde estimated ultimate recovery using structural curvatures and neural network analysis, San Juan Basin, New Mexico USA,” paper presented at the 1997 AAPG Rocky Mountain Section, Denver CO, Aug. Ouenes, A., Zellou, A., Basinski, P., and Head, C.:"Use of Neural Networks in Tight Gas Fractured Reservoirs: Application to the San Juan Basin,’’ paper SPE 39965 presented at the 1998 Rocky Mountain Regional Low Permeability Reservoirs Symposium, Denver 5-8 April Gauthier, B., Zellou, A., Toublanc, A., and Garcia, M.:”Integrated Fractured Reservoir Characterization: a Case Study in a North Africa Field,” paper SPE 65118 presented at the 2000 European Petroleum Conference, Paris, Oct.24-25. Ouenes, A.,: "Practical application of fuzzy logic and neural networks to fractured reservoir characterization," Computers and Geosciences, Shahab Mohagegh (Ed.) (2000) v. 26, no 7 Barman, N., Ouenes, A., Wang, M.:”Fractured Reservoir Characterization Using Streamline Based Inverse Modeling and Artificial Intelligence Tools,” paper SPE 63067 presented at the 2000 SPE Annual Technical Conference and Exhibition, Oct. 1-4 Warren, J.E. and Root, P. J.: “The Behaviour of Naturally Fractured Reservoirs”. SPEJ pp. 245-255, (1963). Kazemi, H., Merrill, L.S., Porterfield, K.L. and Zeman, P.R.: “Numerical Simulation of Water-Oil Flow in
21.
22.
23.
24. 25.
SPE 62939
Naturally Fractured Reservoirs”. SPEJ, pp. 317-326, (1976). Barton, C.C. and Larsen, E.: “Fractal geometry of twodimensional fracture networks at Yucca Mountains”. In Proceedings of the International Symposium on Fundamentals of rock joints, pp. 77-84, (Björkliden, Sweden, 1985). Okubo, P. G. and Aki, K.: “Fractal geometry in the San Andreas fault system”. J. Geophys. Res., 92, pp. 345-355, (1987). Jackson, C.P., Hoch, A.R. and Todman, S.: “Selfconsistency of a heterogeneous continuum porous medium representation of a fractured medium”. Water Resour. Res. 36, No. 1, pp.189-202, (2000). http://www.rc2.com/products/ResFrac.html http://www.aeat-env.com/groundwater/napsac.htm
Fig. 1: A 3D PI continuous model derived by integrating all drivers pertaining to fractures related to structural deformation.
Fig.2: Top view of 3D DFN model constrained to the above continuous model. Two fracture sets (red and green) are used to represent the fractures related to structural deformation.
SPE 62939
INTEGRATED FRACTURED RESERVOIR MODELING USING BOTH DISCRETE AND CONTINUUM APPROACHES
9
Fig.3: a 3D Deterministic continuous model to represent proximity to a fault.
Fig. 5: Top view of the combined DFN model that includes both fault related fractures as well as structural deformation fractures.
Fig.4: Top view of the DFN model representing the fault related fractures and constrained to the continuous model shown above.
Fig. 6: Another view of the combined DFN model
10
AHMED OUENES, LEE J. HARTLEY
Fig. 7: Cluster analysis around a particular well. Notice the complexity of the cluster that will create a complex flow network as a result of the interaction between the different fractures related to different tectonic events.
Fig. 8: Estimated fracture permeability resulting from the combined DFN model. Dark red represents high fracture permeabilities while white areas represent a low permeability. Notice the specific shape and location of the low fracture permeability that could be easily interpreted by utilizing the ranking and modeling results of the continuous models. In this case, the low fracture permeability is a result of the absence of fractures related to a change in facies in these areas.
SPE 62939