63. integrated fractured reservoir modeling using both discrete and continuum approaches

Copyright 2000, Society of Petroleum Engineers Inc.

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AbstractA new approach that combines the use of continuum anddiscrete fracture modeling methods has been developed. Theapproach provides the unique opportunity to constrain thefractured models to all existing geologic, geophysical, andengineering data, and hence derive conditioned discretefracture models. Such models exhibit greater reality, since thespatial distribution of fractures reflects the underlying driversthat control fracture creation and growth.

The modeling process is initiated by constructing continuousfracture models that are able to capture the underlyingcomplex relationships that may exist between fractureintensity (defined by static measures, such as fracture count, ordynamic measures, such as hydrocarbon production), andmany possible geologic drivers (e.g. structure, thickness,lithology, faults, porosity). Artificial intelligence tools areused to correlate the multitude of geologic drivers with thechosen measure of fracture intensity. The resulting continuousfracture intensity models are then passed to a discrete fracturenetwork (DFN) method.

The current practice in DFN modeling is to assume fracturesare spatially distributed according to a stationary Poissonprocess, simple clustering rules, or controlled by a singlegeologic driver. All these approaches will in general be overlysimplistic and lead to unreliable predictions of fracturedistribution away from well locations. In contrast, the newapproach determines the number of fractures in each grid-block, based on the value of the fracture intensity provided bythe continuous model. As a result, the discrete fracture models

honor all the geologic conditions reflected in the continuousmodels and exhibit all the observed fracture features.

The conditioned DFN models are used to build a realistic anddetailed model of flow in discrete conduits. There are twomain areas where detailed discrete fracture models can beused: (1) Upscaling of fracture properties (permeability,porosity and s factor) for input into reservoir simulators; and(2) Optimization of well-design, completion and operationbased on an understanding of the inter-well scale flows.

For accurate results, the full permeability tensor is calculatedfor each grid-block based on flow calculations usinggeneralized linear boundary conditions. Inter-well flows areanalyzed in terms of the variability in flow paths,characterized by distance and time traveled, through thefracture network connecting injectors and producers.

IntroductionMany large oil and gas fields in the most productive regionssuch as the Middle East, South America, and Southeast Asiahappen to be fractured. The exploration and development ofsuch reservoirs is a true challenge for many operators who donot possess the tools and technology to completely understandand predict the effects of fractures on the overall reservoirbehavior. Although many fractured reservoirs could bedeveloped economically, it is very common to see operatorsabandoning these fields because of their inability to drill wellsthat intercept fractures, and/or inability to estimate correctlyreservoir pressure during a pressure transient test. After manyyears, if not decades, of missed opportunities, the petroleumindustry is realizing the need for better fractured reservoirmodeling tools.

The rock properties in a conventional reservoir dependprimarily on the deposition process that is typically a smooth,and "linear" process. As a result of this continuous depositionprocess, spatial correlations of key rock properties, such asfacies proportion and porosity, appear at different scales. Thisgeologic characteristic can be exploited mathematically usinggeostatistical tools that lead to reliable reservoir models inalmost any depositional environment. For a conventionalreservoir deposition is the key process in the reservoir’s

SPE 62939

Integrated Fractured Reservoir Modeling Using Both Discrete and ContinuumApproachesAhmed Ouenes, (RC)2, Lee J. Hartley, AEA Technology

2 AHMED OUENES, LEE J. HARTLEY SPE 62939

formation. For fractured reservoirs it is only the first. Afterdeposition, many events can perturb the geologic layers givingrise to a far more complex and heterogeneous situation. In thispaper we are primarily interested in structural deformation dueto folding and faulting. Although there are other circumstancesthat create fractures, we shall focus only on fractures related totectonics.

A schematic story of a fractured reservoir begins withgeologic beds with different ranges of thickness, and arecharacterized by a heterogeneous lithology/facies distributionalong and across the layers. Subject to different tectonicregimes, these heterogeneous layers experience differentmagnitudes and directions of stress. Depending on the bedthickness and the lithology/facies that exist at each point, aswell as the prevailing stress magnitudes and directions, therock will either fracture or resist by rearranging itself. Theactual process of fracturing is complex. However, by notingthe following important facts, progress in modeling fracturedreservoirs becomes possible:1. Tectonic events act on geologic layers whose structure

(i.e. geologic drivers such as thickness and distribution oflithology/facies) is spatially heterogeneous which can leadto very heterogeneous distributions of 3D mechanicalproperties.

2. The non-linear process of rock failure, and hence theresulting fracture intensity, depends considerably on this3D heterogeneous distribution of mechanical properties.

3. The geologic drivers are the result of the depositionprocess and hence can be characterized by their spatialstructure.

These observations indicate that there is a relationshipbetween the observed fracture intensity at any location and aseries of geologic and geomechanical drivers at the samelocation. It is tempting to say that finding this relationship is asimple exercise in continuum mechanics. In that, given someboundary and initial conditions, and a 3D distribution ofmechanical properties, then the well-known stress and strainequations can be applied to compute the tectonic stresses inthe reservoir. The tectonic stresses and overburden stresses arethen combined and compared with failure criteria to determinethe fracture distribution. Unfortunately, this relationship isneither simple nor universal and each fractured reservoir mustbe treated separately. This paper will describe the frameworkused to derive these relationships for any fractured reservoir.

This paper begins with a review of current techniques used tomodel fractured reservoirs. Each of these techniques uses onlya single type of data. We argue the need for an integratedapproach that combines various forms of data, and anexplanation on how this is achieved. For illustration, anapplication to a fractured carbonate reservoir is presented.

Fracture modeling techniquesMany modeling approaches are documented in the literature.Most attempts to describe the fracture distribution were done

by utilizing one source of static or dynamic data. The methodsfall under three categories: 1) models for reservoir engineerswho are interested in the bottom line which is the ability toreproduce well performances, 2) models for geologists whoare interested in geometrically complex patterns of 3D fractureplanes, and finally 3) models derived from geomechanics.Examples of these three categories are given below.

Inverse models. The main source of data in theseapproaches1-2 is well performances (pressure or production).The fractures are represented by their flow properties on a pre-defined grid or lattice. The problem consists of finding thedistribution of fracture flow properties that best matches theobserved well performances. The initial distribution of thefracture properties could benefit from some a priori geologicknowledge, but has been rarely used in such approaches.

Discrete fracture networks (DFN). The main source of datain this approach is image logs and what can be extracted froma borehole. In contrast to the previous approach, where wellperformance is a simple measurement, acquiring data fromcores and image logs for DFN modeling is a real challenge.There is a large number of geologic papers describing theproblems related to core and image log interpretations, and wehighly recommend to the reader the Lorenz and Hill3 paperthat illustrates very well some of the difficulties in obtainingbasic fracture properties used as input in DFN modeling. Sinceexplicit fracture information is only available at the welllocation, the data is formulated as a probabilisticcharacterization of fracture properties and spatial distributionaway from the well. A number of unconditioned stochasticrealizations of discrete fracture planes are generated in the 3Dreservoir volume by a stationary Poisson process. The mainideas related to this approach are discussed in Cowie et al.4

Since the spatial distribution of fractures away from the welllocations is uncertain, the resulting models lack "geologic"meaning, and the upscaled fracture permeability have beenused with little success in layered sedimentary systems. Forthe same reason, accuracy of the generated models is onlyreliable in the near wellbore region, and the unconditionedrandom filling of the interwell region limits the use of suchmodels beyond the near wellbore scale. This major drawbackwill be alleviated with the new approach described in thispaper.

Geomechanical approaches. The main source of data usedin these approaches is the structural surface derived frommarkers picked on well logs and/or from seismic reflectors.There are many geomechanical approaches for modelingfractured reservoirs varying from simple curvature analysis tomore complex systems where non-linear continuummechanics equations are solved numerically usually based onthe finite-element method.

Many authors5-7 have used curvature analysis with varyingdegrees of success. Most of the successes have been obtainedon "homogeneous" reservoirs (small variation in bed thickness

SPE 62939 INTEGRATED FRACTURED RESERVOIR MODELING USING BOTH DISCRETE AND CONTINUUM APPROACHES 3

and lithology) that have undergone extensional deformation.In such an idealistic situation, the curvature is proportional tothe strain and the curvature analysis could be sufficient.Unfortunately, "homogeneous" reservoirs are rare and one hasto deal with a large number of changing reservoir properties inmost fractured reservoirs. To handle the real heterogeneity ofthe reservoirs, numerical geomechanical models are used topredict the strain distribution. Although strain does notautomatically mean fracture intensity, it can be considered as astrong indicator. The basic idea is that the reservoir becomesdeformed from an initial undeformed plane state as somelateral boundary conditions are applied. A major difficulty isthat the initial and boundary conditions of this problem are notknown and need to be guessed. Depending on the guess, thefinal deformed structure is compared to the actual present dayone, and the guess is adjusted if there is a large disagreement.This trial and error process is similar to the production historymatching in reservoir simulation and can be very tedious.

Heffer et al.8 introduced some geostatistical concepts in thegeneral continuum mechanics equations to derive a correlationof displacements. Although the asymptotic behavior of thiscorrelation when r à 0 raises some serious questions, theexplicit formulation could be very useful to derive acorrelation for strain. Unfortunately, having an explicitformulation for strain did not come free and a hefty price waspaid in the assumptions that were made. The most detrimentalassumption was the homogeneous elastic properties (i.e. a"homogeneous" reservoir). As in the geomechanicalapproaches, this method relies only on reservoir structure,while very influential drivers such as lithology are ignored forthe sake of obtaining an explicit form for the correlation ofstrain. This approach points again to the need for a trueintegrated approach where all data could be used to reach abetter model.

Integrated Reservoir ModelingAn integrated reservoir modeling approach consists of acollection of computational tools and methods that utilizesimultaneously, or sequentially different static and/or dynamicdata representing different reservoir responses at differentscales. The objective and prospect of an integrated reservoirmodeling approach is to reduce the uncertainties. To betterunderstand this concept, some examples are given below.

One of the first original integrated approaches was proposedby de Marsily et al.9 using the concept of pilot points. Theirobjective was to find a permeability model by using two typesof data: well performances and spatial correlations. To handlethe two types of data, two computational tools were used: anoptimization method to match well performances and estimatethe permeability at a limited number of locations, and ageostatistical method to derive a full model, utilizing thespatial correlation and the known well permeability values. Inthis case, the integration process was made possible by thecombination of an optimization method and geostatistics.Another good example is the use of a geostatistical framework

that has an abundant number of methods able to handledifferent types of data. The most common example is the useof seismic information as “soft” data when building geologicmodels. This integration process can be achieved withdifferent methods ranging from simple co-kriging to moresophisticated ones such as cloud transform techniques.10

This example illustrates the ability to integrate seismicinformation directly in the geologic modeling using thegeostatistical framework.

When the need came to integrate more data, many authorsused global optimization methods such as simulated annealingas a framework. Here, a model is derived by minimizing anobjective function that can contain a variety of static anddynamic data. A large number of applications are discussed inOuenes et al.11 and show the flexibility of such an approach.

Reviewing these three examples shows that integration of datain reservoir modeling requires a framework with appropriatecomputational tools that are able to handle simultaneously, orsequentially different types of data. The drawback of all threemodeling approaches discussed in the previous section is theirinability to provide an integration framework where variousdata could be used to reduce the model uncertainties.

Integrated Fractured Reservoir ModelingStarting from the simple observation that fracture intensitydepends on many geologic drivers (the most commonlyknown being, structural setting, proximity to a fault, lithologyand thickness), it is imperative to find a framework wherethese drivers could be easily incorporated in the fracturemodeling process. Furthermore, it is important to recognizethe complexity of the non-linear process of fracturing, whichmeans that any attempt to find a simple and explicitrelationship between drivers and fracture intensity may requiresome limiting assumptions that are not acceptable. Given theseconstraints, Ouenes et al.12 introduced a collection of artificialintelligence tools to model fractured reservoirs. The approachwas successfully used on various fields and basins12-16. Themethodology is described in Ouenes,17 in this paper we limitourselves to a short summary.

Since there is a complex but undetermined relationshipbetween a large number of geologic drivers and fractureintensity, the use of artificial intelligence (AI) tools such asneural networks has great merit. Utilizing the available data atwell locations, one can let a neural network find theunderlying relationship, then use the derived model to predictfracture intensity everywhere in the 3D reservoir volume.Since this is a data driven approach, one must pay attention tocommon pitfalls and take some precautions. In other words,the successful use of AI tools is not simply a matter ofdownloading a neural network from the World Wide Web. Toensure that AI tools are applied efficiently and with integrityto fractured reservoirs, the following issues must be addressed:ranking the geologic drivers; optimizing the neural network


architecture; a robust training algorithm; selecting efficientlydata for training; and creating a stochastic framework.

The neural network is an "equation maker" or a "complexregression analysis tool" that takes several reservoir properties(the inputs), and tries to correlate them with a fractureintensity indicator (the output). The neural network is trainedusing a set of wells where both the inputs and the output areknown to find the relation, or the "equation," between theinputs and the output. Once this relation is found, the neuralnetwork uses only the inputs available throughout the entirereservoir volume, to predict the fracture intensity. In thisapplication, the neural network is used to find theundetermined relationship that exists between the geologicdrivers and the fracture intensity. Hence, no a prioriknowledge about this relationship is required. Rather we letthe actual data direct us to the key drivers. This relationship isthen utilized for the key objective of estimating the fractureintensity in the interwell regions.

As indicated earlier, it is important to notice that most of thegeologic drivers that control fracture intensity are related todeposition, and are easily mapped in the entire 3D volumeusing geostatistics. For example, by combining the use ofmarkers picked on well logs with a seismic reflector, one canuse the integration abilities of geostatistics to derive a veryaccurate reservoir structure. This can be used to compute first(slopes) and second (curvatures) structural derivatives indifferent directions that can be used as geologic drivers, andare potential indicators of fracture intensity.

Among all the geologic drivers, lithology/facies and porosityplay a major role in any fractured reservoir modeling(Assuming a “homogeneous” reservoir will likely lead to acompletely misleading model). These two key drivers controlthe mechanical rock properties that in their turn control therock failure and fracture intensity. For a given lithology, theincrease of porosity makes a rock more ductile. Conversely, areduction of a few percent in porosity can lead to many ordersof magnitude increase in fracture intensity. On the other hand,a rock with just a few more percent of shale can become veryductile and exhibit no fractures, or just a few more percent ofdolomite can lead to a completely fractured rock. Thesesimple well-known examples illustrate the importance ofporosity and lithology or facies proportions in fracturedreservoir modeling and any modeling effort must include thesereservoir properties as input. In addition to structuralderivatives, facies proportions, bed thickness and proximity toa fault can play a major role in determining the fractureintensity. Besides these well-known drivers, most fracturedreservoirs have some particular feature that needs to beincorporated in the modeling in order to be complete.

The key concept in fractured reservoir modeling is thatdifferent geologic drivers are dominant in different areas ofthe reservoir. For example, if we consider two simple driverssuch as structural curvature and the percent of shale in the

rock, and also assume that the fractures were created as aresult of some extensional deformation, we expect a locationwith high curvature to contain a large number of fractures.This “linear” thinking is wrong in a fractured reservoirbecause many other factors have an influence on how manyfractures will be present. In this example, the percent of shalecontained in the rock will play a major role and beyond acertain threshold value, (for example 45% shale), the rock willbe without fractures however high the curvature. Whenrealizing that there is a multitude of geologic drivers thatcould affect fracturing, it is easy to imagine how complex thenon-linear relationship between drivers and fracture intensitycould be, and how illusive is the search for an explicitanalytical form. On the other hand, one has to remember thereasons behind the development of AI tools such as neuralnetworks that were specifically designed for such complexnon-linear problems.

In addition to geologic drivers that played a role duringfracturing, one can use present day information such asseismic amplitude, seismic impedance (a good indicator oflithology), strain or stress 3D models, or even permeabilityestimated by automatic history matching as illustrated inBarman et al.18

Given all the potential geologic drivers and present dayfracture indicators, one has to choose the framework where theintegration of these data could be achieved.

Integrated Continuous ModelsThe framework required to correlate all of the geologic driversand present day fracture indicators is a continuous one.Because most of the drivers are related to deposition weassume that the reservoir acts as an equivalent continuum onsome scale, which is known as the representative elementaryvolume (REV). The entire reservoir is discretized intogridblocks whose size is dictated by the size of the REV. Thisassumption is appropriate for geologic drivers related todeposition, but could seem to neglect smaller fractures thatrange from microfractures to joints. At this stage, one has toremember the purpose of the fractured reservoir modelingeffort that is to understand the flow behavior and the overallfracture network controlling it. There are two ways of lookingat this problem and achieving the objective stated above. Firstthe reservoir engineer point of view, and second the geologistperspective.

There is a major conceptual difference between the two views.On one hand, reservoir engineers recognize the fact thatfractured reservoir provide very little data that can be used formodeling purposes. Hence, they settle for some averageproperty assigned to a certain volume. This is the sameapproach used for more than a century with the use of Darcyequation to describe flow in porous media. Although theactual flow in a rock could be described by using the Navier-Stokes equations, the lack of information on the detailed porestructure required for the boundary conditions, have lead to


the use of a REV over which average properties such aspermeability are defined. On the other hand, geologists believethat a correct fracture model must contain the actual discreteobjects (fracture planes), although the amount of availableinformation could be completely inadequate due the difficultyof intercepting fractures with the commonly used verticalwells. There is no doubt that fractures exist at different scalesranging from microfractures to joints, but what is oftenneglected is the fact that getting reliable information about thefracture characteristics at any scale is an art rather than ascience. Therefore, one cannot expect to achieve anunderstanding of reservoir flow at the level of micro-fracturesif there are no means of measuring adequately all thecharacteristics of these small features. Hence, we need to riseat a higher scale where reliable measurements are possible andmeaningful. This discussion leads to the conclusion that thedefinition of the REV is simply related to what we willconsider as fracture intensity for our modeling purposes.

When using image logs interpretations we can consider afracture intensity defined by the fracture count whichrepresents the number of fractures encountered in a REV thatis in the range of a few feet. There are many problemsassociated with the use of fracture count as a fracture intensityindicator. The main one being the lateral extent of thisinformation which is valid only in the near wellbore regionsometimes no more than few inches away. It is also commonto find fracture swarms dominated by a large number ofmicrofractures making fracture count difficult to quantify.Finally, the issue of dynamic effects, often ignored duringimage and core analysis, could lead to overestimated fracturecount because not all observed fractures contribute toproduction. Despite all these problems, many geologists viewfracture count as the best indicator of fracture intensity, andhence tend to underestimate the value of informationcontained in production indicators.

When seeking fractured reservoir models that could helpunderstand the interwell region, it is imperative to find afracture intensity that could “see” farther than the few inchesaround the wellbore. The production based indicators such asproductivity index (PI), transmissiblity (kh) estimated fromwell test, and Estimated Ultimate Recovery (EUR), are someof the examples that provide an average fracture intensity thatencompasses an area as big as the drainage radius. Theseproduction based fracture intensity indicators that only seemappropriate for 2D models, have been successfully used in 3Dmodeling simply by allocating the single measurement alongthe wellbore. Different means could be used to transform asingle kh or PI value into a vertical log, the most commonbeing the production logs or the φh allocation.

Once the fracture intensity is chosen it will represent theoutput of the neural network. The inputs that could be relatedto the fracture intensity are the geologic drivers (porosity,permeability, lithology, facies proportion, bed thickness,

proximity to faults, etc.) and present day indicators (seismic,stress, strain, etc), all of which can be obtained over the entirereservoir volume by using appropriate geostatistical methods.

The search for the possible relationship that exist between theimportant drivers and the chosen fracture intensity is a threestage process described below:

Ranking the drivers. Prior to any modeling, appropriateranking methods must be used to analyze the effect of eachdriver on the chosen fracture intensity. The engineer, orgeologist must check at this stage for the validity of theranking over the entire area of the study, and on specificzones. For example, if the reservoir was under extensionaldeformation, it is expected to see the curvatures rank high.There are many benefits that can be derived from the rankingexercise, the most notable one is to achieve a betterunderstanding of what the primary drivers are. There are alsocomputational benefits, whereas, low ranked drivers couldindicate that they have no effect on the fracture intensity andtherefore, they do not need to be included in the inputs.

Training and testing the models. Once the user has decidedon which drivers he would use in the modeling process, the setof available data is divided into two subsets: a training set anda testing set. Since this approach is done in a stochasticframework, many realizations are needed. Each realization canbe derived by selecting randomly or according to some rulethe training set. The neural network modeling process consistsof adjusting some weights until the actual fracture intensitymatches the estimated ones. Once the matching process isdone, we can assume that a model was available, and could beused for testing and cross-validation on the testing data set thatwas not used during the training process. Depending on theability of the model to predict fracture intensity at testinglocations, the model could be kept for further use or discarded.

Fracture analysis and probability volumes. Since all thedrivers are available in the entire 3D reservoir volume, and arelationship has been established between the drivers and thefracture intensity, the application of the neural network to allthe gridblocks in the reservoir will lead to a 3D distribution offracture intensity. These models could be used to estimatefracture directions, analyze fracture connectivity, serve asinput for dual porosity model parameters, and deriveprobability maps. Given a large number of realizations, all ofwhich provide a good testing correlation coefficient, one couldconstruct a 3D probability volume that can be used for furthermodeling using a discrete approach.

The role of DFN modelsThe Dual-Porosity Continuum (DPC) concept19, 20 iscommonly applied to fractured reservoirs. This idealizes thereservoir in terms of an orthogonally connected fracturesystem that penetrates a set of identical rectangular gridblocksrepresenting the matrix blocks and deliver fluid to the wells.Each of the rectangular blocks may contain several matrix


blocks allowing the problem to be scaled up if required. DPCmodels are well suited to multiphase flow, and to models witha large number of blocks. However, the simplified geometrymakes the choice of parameters that describe theheterogeneous permeability and connectivity characteristics offractured reservoirs difficult. DFN models provide a morenatural framework in which models of fracture geometry andthe stochastic methods used to characterize sub-seismicfractures can be applied. Equivalent continuum properties thataccurately capture the heterogeneity, anisotropy andconnectivity of the fracture system can be derived usingappropriate upscaling techniques on the DFN models. Hence,the approach is to populate the reservoir volume with discretefractures, and then upscale the properties of the fracturesystem for each grid block of an equivalent DPC model.

Constrained DFN modelsSince the introduction of DFN models, there was a need forconstraining the realization to some geologic input. Attemptshave been made to control the fracture generation with someindicator. However, these past attempts used a single geologicdriver and ignored the others, and most importantly did notaccount for the complex interplay of the drivers as describedin the previous sections. This problem was solved by the useof the continuous modeling approach described in the previoussection, which passes to the DFN the entire 3D reservoirvolume map of fracture intensity, or probability that can beused as a spatial constraint. Therefore, all the geologicalrealism of a detailed geometrical representation of discretefractures at the near-well scale can be coupled with realisticconstraints on fracture distribution over the larger interwell-and reservoir-scales.

Generating a DFN model. DFN modeling is based on thestochastic approach, and hence the specific details ofindividual fractures change between realizations. However, inthis approach each realization is constrained such that amountof fracturing, fracture area per unit volume, in any givengridblock is the same for each realization and is derived fromthe continuous model. Additional parameters that describe theproperties of discrete fractures are required to generate amodel: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 dataon very different scales leaving gaps in the lengthdistribution. A natural solution to this problem is to use apower law distribution that provides a continuous modelbetween the various length-scales of fractures, and manygeologists21, 22 have demonstrated the validity of such amodel.

3) Fracture transmissivity (to calculate permeability) derivedfrom high-density production logs and calibrated againstinterference and/or tracer tests.

4) Fracture aperture (to calculate porosity) calibrated againsttracer tests

Different fracture sets can be constrained against differentfracture intensity maps related to different groups of geologicdrivers. For example, two-conjugate sets characterized bygeologic drivers associated with folding (e.g. curvature,lithology, and porosity) can be combined with other setscharacterized by geologic drivers associated with deformationzones around faults (e.g. proximity to fault).

Directional fracture permeability. It is desired to calculatean effective permeability tensor that best represents thebehavior, in the environment of the surrounding network, of ablock within a DFN model. An effective permeability thatrepresents the block, not just at a point, is required, becausepermeability is to be used for the corresponding block in adiscretized DPC model. It is important to determinedirectional permeabilities, a tensor, not just the axialcomponents. This is more robust in cases with anisotropy,which is common in fracture systems, where the dominantflow connections are between adjacent sides of a block ratherthan between opposite sides. To calculate the permeability of ablock, uniform pressure gradients are imposed in threeorthogonal directions across the boundaries of the block. Thepressure distribution and flows in the block are calculated bydiscretizing each fracture into finite-elements. The total flowthrough each face of the block is evaluated, and an effectivepermeability tensor is fitted that gives the best overall matchthrough each face for the different gradient directions. Theself-consistency between DFN models and equivalentcontinuum models has been demonstrated by Jackson et al.23.

ApplicationTo illustrate this new approach, we will consider a 3Dexample of a fractured carbonate reservoir. Like manyfractured reservoirs, the one considered had seen manytectonic events, each leaving behind a complex fracturenetwork.

Because of a lack of image logs and core data, most of thecontinuum modeling effort relied on the use of theproductivity index (PI) which was available at all the wells.Hence, a large gridblock size of 200 m by 200 m wasconsidered for the continuous model. At each well location,the single PI value was allocated along the borehole to create aPI log. Within the considered 3D grid, a large number ofgeologic drivers, and present-day indicators were available forthe modeling effort. Four major types of drivers wereavailable: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 inBarman et al.18

Out of all the drivers, the ranking pointed to 4 major ones:


percentage of a certain rock type, porosity, proximity to a faultand structural derivatives along the present day horizontalmaximum stress direction. Using all the drivers as inputs, andthe PI as a fracture intensity indicator, a large number ofrealizations (e.g. Fig. 1) were derived using the proceduredescribed earlier. Using a threshold value for the PI, aprobability volume was calculated from the 10 bestrealizations that had the most accurate testing prediction. Botha PI realization as well as the probability could be used as aconstraint for the DFN models.

For this application we will illustrate the use of bothstochastic, and deterministic continuum models. There are twomajor types of fractures present in this field: 1) fracturesrelated to faults, and 2) fractures related to structuraldeformation. To model the structural related fractures we willuse the continuous model (Fig. 1) derived by integrating allthe available geologic drivers pertaining to these fractures.This continuous model is used as a constraint to producedifferent DFN realizations (Fig. 2). Notice that the fractureintensity in the DFN model Fig. 2 follows the informationprovided by the integrated continuous model Fig. 1.

Since the fracture related to faults are mostly present in thevicinity of the fault, we created a deterministic model (Fig. 3)of proximity to fault that utilizes mostly the seismicinterpretation of the faults. This deterministic model will serveas a constraint to derive a DFN representing the fault relatedfractures (Fig. 4).

Given the two DFN models representing the different types offractures, we can build an integrated DFN model that mergesthe two DFN models. The final DFN model (Figs. 5 and 6)contains features from the fault related fractures as well asfractures related to the structural deformation.

The resulting DFN model could be used for future reservoirmodeling and management. A direct benefit from such amodel is to study the fracture cluster (Fig. 7) around existingwells, especially those injecting fluids in the reservoir.Another benefit is the derivation of a fracture permeability 3Dmodel (Fig. 8) that can be used in dual-porosity reservoirsimulators. The resulting fracture permeability model shownin (Fig. 8) was derived using the final DFN model shown inFigs. 5 and 6. The dark red cells represent high fracturepermeability 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 wholeintegration process. It is unlikely that an unconstrained DFNmodel will be able to delimit exactly such an area, which is themain point that we have tried to convey throughout this paper.

Conclusions1. The combination of continuous and discrete approaches in

fractured reservoir modeling provides many benefitsamong them true data integration that reduces

uncertainties.2. The new proposed integrated framework goes beyond

data integration and constitutes a platform for integratingdifferent disciplines (geologists, geophysicists andengineers).

3. The use of artificial intelligence tools in continuousmodels allows a rapid and efficient integration ofgeophysical, geologic, and engineering data into fracturedreservoir models.

4. The use of continuous models as a constraint in buildingDFN provides more realistic fractured reservoir modelsthat can then be used to estimate fracture permeabilities.

5. The proposed approach and the seamless data integrationprocess, including passing data from continuous todiscrete models, is readily available in ResFrac24 andNAPSAC 25 .

AcknowledgmentsThe authors would like to thank: David Holton of AEATechnology for useful discussions, and Arnfinn Morvik ofBSSI A/S, Bergen, Norway, for assistance on visualization.

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Fig. 1: A 3D PI continuous model derived byintegrating all drivers pertaining to fracturesrelated to structural deformation.

Fig.2: Top view of 3D DFN model constrained to theabove continuous model. Two fracture sets (red andgreen) are used to represent the fractures related tostructural deformation.


Fig.3: a 3D Deterministic continuous model torepresent proximity to a fault.

Fig.4: Top view of the DFN model representing thefault related fractures and constrained to thecontinuous model shown above.

Fig. 5: Top view of the combined DFN model thatincludes both fault related fractures as well asstructural deformation fractures.

Fig. 6: Another view of the combined DFN model


Fig. 7: Cluster analysis around a particular well. Noticethe complexity of the cluster that will create acomplex flow network as a result of the interactionbetween the different fractures related to differenttectonic events.

Fig. 8: Estimated fracture permeability resulting fromthe combined DFN model. Dark red represents highfracture permeabilities while white areas representa low permeability. Notice the specific shape andlocation of the low fracture permeability that couldbe easily interpreted by utilizing the ranking andmodeling results of the continuous models. In thiscase, the low fracture permeability is a result of theabsence of fractures related to a change in facies inthese areas.

63. integrated fractured reservoir modeling using both discrete and continuum approaches

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