4.- integrated fractured reservoir characterisation. a case study in a north affrica field

8/12/2019 4.- Integrated Fractured Reservoir Characterisation. a Case Study in a North Affrica Field

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Integrated Fractured ReservoirCharacterization: A Case Study in a

North Africa FieldB.D.M. Gauthier, TotalFinaElf; M. Garcia,FSS Intl.; and J.-M. Daniel,IFP

SummaryIn fractured reservoirs, data directly related to fractures are scarceand 1D (e.g., core and image-log data). Other types of data aremore widespread (e.g., seismic data) but generally are related onlyindirectly to fracture distribution. In such reservoirs, it is necessaryto understand and then to model the fracture network on a field-wide scale by integrating all available data.

We propose a methodology to achieve this objective. The meth-odology establishes relationships between the fracturing and othersources of data in a systematic workflow that goes from static 1Ddata to a 3D dynamic model. The methodology is described andillustrated with a case study from north Africa. In this field, frac-ture data from image logs and cores are related to (1) 3D seismicattributes (e.g., amplitude, coherency), (2) fault patterns, and (3)other types of well data (e.g., interval thickness, lithology index,

and porosity). Production data also are used to quantify the con-tribution of each fracture set to flow, which then can be mapped ona reservoir basis with the more widely distributed log and seismicdata. The resultant set of maps then is entered into a dynamicreservoir model. The methodology has been validated with a newwell, the fracture network of which was accurately predicted in thereservoir by the model.

Introduction

Fractured reservoirs are by nature highly heterogeneous. In suchreservoirs, fracture systems control permeability and can also con-trol porosity. Fracture modeling is therefore a key developmentissue and requires an integrated approach from geology to reser-voir simulation and well planning. Because fractures are below thelimit of seismic resolution, the static models of fractures are con-

strained mainly by well data (e.g., cores or image logs) usingconventional structural geology techniques.1 These models includethe mechanical origin (shears vs. joints), the geometry (orientation,size, and frequency) and the typology (open vs. cemented) of thefracture network. The fracture permeability then can be assessedby relating the fracture aperture to the fracture excess conductivitymeasured on electrical image logs,2 critically stressed fractureswithin the present-day stress field,3,4 or both. It is the authorsopinion, however, that such approaches only give, at best, a rela-tive estimate of permeability that must be calibrated against dy-namic data. This requires the quantitative modeling of fractureflow behaviors. At the drainage-radius scale of wells, discretefracture networks (DFNs)5,6 can be constructed and used to simu-late flows and match them to well-test data.7 This allows us toderive the fracture input parameters for reservoir simulation.8 Farfrom wells, however, the lack of data makes DFN models veryuncertain. The static modeling of the spatial distribution of frac-tures at the field scale and the use of these models as input todynamic reservoir models are the purposes of this paper.

Methods have been presented to model field distributions offractures based solely on the fracture density measured alongwells.9 The scarcity of wells in which fracturing data are available

makes such a direct mapping difficult and very uncertain, how-ever. Geometrical methods based on the fractal theory predict

subseismic fractures from seismic faults.10,11 These methods can

be hazardous when used to extrapolate over several orders of mag-

nitude (i.e., from seismic faults down to core scale fractures) and

generally apply only to shear fractures, not to joint systems.12

Bourne et al.13 propose a geomechanical method to predict the

fracture distribution related to the elastic stress field perturbation

around faults. This technique does not allow the prediction of

fractures that do not result from the activation of seismic faults

(e.g., doming). Leroy and Sassi14 and Guiton15 suggest another

geomechanical method that relies on an idealization of the real

fractured rock by a continuum. They introduce opening and sliding

displacements to represent the reservoir-scale deformation and the

diffuse fracture patterns that accommodate it. This approach as-

sumes a homogeneously fractured rock and therefore does notpredict fracturing or faulting localization. Hefferet al.16 propose a

geostatistical technique to interpolate strain/tensor components

supposedly related to fracturing. The estimation is conditioned towell and structural data and is calibrated against well-test perme-abilities. All these methods assume that the fracturing process isrelated to a limited number of geological parameters that constrainthe mechanical behavior of fractured rocks. Although only oneparameter may be needed to characterize a fractured reservoir,1719

it is often the lack of a methodology to integrate the combinedeffects of structure, thickness, and lithology that leads geologists tofocus only on the most important factor. With complex reservoirs,however, more comprehensive descriptions are unavoidable whenproducing reliable fracturing models. Ericsson et al.20 build anempirical and deterministic approach to derive a fracture density

index that is a function of other indices related to reservoir vari-ables like the structural curvature, the crestal distance, or the faciestype. Similarly, Agarwalet al.21 relate the fracture intensity to bothgeological parameters and effective permeabilities to model fieldpermeability distributions. Their approach is less empirical butremains fully deterministic (and hence inappropriate) to addressthe uncertainty inherent in the spatial distribution of fractures orpermeabilities. Stochastic methods are the only way to account forsuch uncertainties. One approach22,23 consists of using a multi-variate, nonlinear regression function of secondary (geological)parameters to fit well fracturing data (i.e., related to a fractureindex). The stochastic aspect addresses the uncertainty on the re-gression model by random sampling of the data set. Repeatedly, adata subset is drawn and used to fit the regression function, whichcan be accepted or rejected according to some correlation criteria.If accepted, the multivariate regression function is applied to thewhole field to produce a realization of the fracture index. Theparticularity of this approach is the use of a neural-network archi-tecture to define the regression function. However, the approachgenerates unconditional realizations (fracturing data are partlyhonored) and does not allow the reproduction of any statisticalmodel as inferred from the data.

In this paper, a geostatistical approach is presented to simulatefracture frequencies with the integration of primary fracturing dataand any variety of secondary geological, geomechanical, or seis-mic information reflecting the understanding of the fracturing pro-cess. In the following, the method is presented and applied to anorth Africa field. The results are validated against new drillingdata, and their use as input to a reservoir model is discussed.

Copyright 2002 Society of Petroleum Engineers

This paper (SPE 79105) was revised for publication from paper SPE 65118, first presentedat the 2000 SPE European Petroleum Conference, Paris, 2425 October. Original manu-script received for review 14 November 2000. Revised manuscript received 12 April 2002.Paper peer approved 24 June 2002.

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Methodology

Full-field static fracture modeling requires that we first character-

ize the geometry of the entire fracture network: orientation, fre-

quency, and size. Orientations are often direct measurements (e.g.,

in image log data). Gauthier et al.1 describe a method to quantify

fracture dimensions from well data using the proportion of frac-

tures that terminate within the wellbore. We focus here on the

spatial distribution of fracture frequencies for directional sets of

fractures observed in wells. The fracture frequency (FF) is defined

as the number of fractures per unit length measured perpendicu-

larly to the fracturing plane. It can be seen as a fracture density

geometrically corrected to be independent of well directions.1

A geostatistical approach that is based on both multivariatestatistical analysis and sequential simulation is our proposed so-

lution to the data integration problem.

Primary and Secondary Variables.Two types of variables are

considered for each oriented fracture set.

The primary variable, the one to be modeled, is the FF. FF

data are calculated at wells in which image-log or core interpre-

tations are available. Secondary variables (SV) are variables derived from field

data or simulation and potentially correlated with fracturing. Sec-ondary variables can be of a different nature: lithological (porositydistribution), mechanical (geomechanical simulation results), orstructural (seismic attributes like coherency or curvature). They areknown over the entire field (exhaustive information).

Modeling Steps.The two-step geostatistical approach tackles theproblem of modeling the spatial distribution of a fracturing vari-able (the FF) and quantifying the uncertainty about it. In the firststep, discriminant analysis is used to derive a single geologicalcomponent that best capitalizes the indirect information about theFF from all secondary variables. In the second step, the objectiveis to generate FF realizations that honor well fracturing data andreproduce different statistical models inferred from the data. Thesestatistical models include the global distribution of the FF (histo-gram); variogram models that specify the spatial correlation of theFF and its cross-correlation with the geological component; and abivariate distribution model of the FF and the geological compo-nent. The bivariate distribution model provides the conditionaldistribution of the FF for any geological component value. The

geological component being known everywhere over the field, thismodel determines the a priori FF distribution (before simulating)at any location according to the local geological component value.In that sense, the geological component carries information aboutspatial fracturing trends. The roles of the two steps of multivariatestatistical analysis and sequential simulation are as follows.

Multivariate Statistical Analysis. As discussed earlier, it isseveral secondary (explanatory) variables, taken together, that al-low us to identify spatial fracturing trends. To integrate them intothe geostatistical approach, discriminant analysis is used to deter-mine the linear combination of SVs that best distinguishes selectedFF classes (e.g., low, medium, and high fracturing classes). Byconsidering classes, discriminant analysis can recognize nonlinearrelationships with the SVs. Because the SVs are not necessarilyindependent or linearly correlated, improved (i.e., linear) correla-tion can be obtained by transforming them into distribution prob-abilities (cumulative distribution function values). From the dis-criminant analysis, only the first component (the so-called geo-logical component) is retained, provided that it indeed shows amonotonic relationship with the FF. At this stage, the geologicalcomponent remains the unique secondary variable that capitalizesat best all indirect information about FF.

Sequential Simulation.To better represent the rather complexnonlinear relationship between the FF and the geological compo-nent, sequential indicator simulation is used to simulate the FF.The integration of the geological component (secondary informa-tion) is done by cokriging through a Bayesian formalism in whichthe geological information is converted into soft (probability-like)data.24,25 A Markov model is adopted, which leads to a collocated

cokriging simulation approach, with the cross-variogram (betweenFF indicators and soft probabilities) being written as a function ofone of the two autovariograms.26

Application to a North Africa Field

Geology of the Field.The case study is an oil-bearing field. Theporosity ranges from 10 to 35% (average is 20%). The matrixpermeability measured from core plugs ranges from 0 to as high as1,000 md (several tens of md, on average), whereas the well-testpermeability is within the interval of 10 to 110 md. The ratiobetween test and plug permeability, which is generally interpretedas an indicator of fracturing effects, varies from 1 to 10. This ratiobarely reaches 10, which is the minimum ratio admitted to classify

a reservoir as fractured.19 Therefore, this field cannot be consid-ered strictly as a fractured reservoir. It also can be noted that singleporosity/permeability reservoir simulations give, on average, goodwell history matches. Bad matches observed in some locationswould be caused by high-permeability streaks related to small-scale faults, fracture swarms, or both. In other locations, fracturingis believed to improve the matrix performance homogeneously.

In this field, a carbonate sequence of Late Paleocene age sub-divides into an oil-producing upper reservoir unit and a mostlywater-bearing lower interval. These two units are separated bynonreservoir shale/carbonate alternations. The upper reservoir unitis subdivided into four layers that are 5 to 40 ft thick. They consistof tight limestones (variably argillaceous), good-porosity lime-stones (locally interbedded with dolomitic streaks), and calcareousshales. This study focuses on the good-porosity limestone layers.

The structural history of the field is quite complex but is gen-erally interpreted as a transtensional basin, initialized in the Cre-taceous and reactivated during the Tertiary. However, the tectonicphase(s) post-dating reservoir deposition is (are) poorly docu-mented. Fig. 1 shows the structural map of the top reservoir, withthe fault pattern at a deep level overlaid. One can note the changewith depth in the main strike of the seismically defined faults. Atthe top, the faults are mainly oriented N120-130. This fault net-work developed just above the deep main trends, which strikepreferentially N170. Subsequently, the field structure can be ex-plained by the reactivation of deep basement faults within an ob-lique extension regime. This structural style results in the dominantoblique northwest/southeast normal faults and in N170 secondaryfaults and flexures at the top of the reservoir. From the faultpattern, the deformation seems to be concentrated on the flanks of

the structure just above the deep faults. Indeed, the top fault den-sity and continuity increase in the southern part of the field wherethe two main deep faults join.

The determination of the present-day stress field suggests amaximum compressive horizontal stress, oriented east-northeast/west-southwest, and a normal stress regime. This stress field istherefore not compatible with the northeast/southwest-faulting ex-tension direction. One could then argue that faults and fractureswere formed under of paleo-stress state and associated to dolo-mitization before hydrocarbon fill, which protected them fromcementation. The present-day stress field therefore cannot activatenew fractures or close the old ones.

Fracture Network Characterization.In faulted and fracturedreservoir characterization, both 3D seismic and horizontal wellsprovide key data.27 On one hand, a seismic fault map can be usedto define fault control on small-scale fracturing; on the other hand,horizontal wells help to characterize the geometry of the frac-ture network.

3D Seismic. In addition to clear seismic faults, interactive shad-ings of the horizon also support the picking of tiny features thatprove laterally coherent. The simultaneous analysis of several seis-mic attribute maps shows that these subseismic features also cor-respond to low amplitude and low coherence lineaments (i.e., astandard fault signature).28 Image logs from horizontal wells alsovalidate this interpretation of faults (see the next section). The finalstructural map is shown in Fig. 1. This map includes faults with avertical throw less than 10 m. Using this map and the image-loginterpretations, one also can demonstrate that fractures tend to be

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more numerous near subseismic scale faults. The fault map istypically used to control the reservoir structural map and some-times to modify interblock transmissibilities in the flow simulationgrid. Less conventionally, attributes related to the fault networkcan be computed to map the faultsareas of influence on reservoirproperties. This should be done when faults are suspected of in-ducing significant strain accommodated by fractures or pressuresolutions. Maps can be constructed that integrate the throw (i.e.,vertical displacement) along fault traces within a moving window.

S= i=1

i=N

Vti dliWS, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)where N number of fault segments; dli length of segment i;

Vti average vertical throw along dli; and Ws surface of the

moving window.

This measure weights the faults according to their throw and

has the same dimension as strain. An accurate measure of strain

would have required more information than just the throw of

mapped faults. To avoid any misinterpretation, this map will be

called S-map in the following examples. Without evidence of

strike-slip movement in this field, the S-map can be seen as a goodapproximation of the actual fault-related-strain field (Fig. 2).

Horizontal Wells.Although some 70 wells were drilled in thisfield, the only available fracturing data come from image logsalong two vertical wells and five horizontal wells. Two of them arelocated in the northern part, four are in the central part, and one isin the southern part of the field. The five horizontal wells (Fig. 1),drilled in the main reservoir unit, have various orientations, withsome of them turning 90 along the hole (multidrains). This dataset is therefore a representative sampling of the field fracture net-work. The quality of the image logs is good to relatively poor.Fig. 3 shows the overall fracture interpretation. One can note thatthe dominant fracture trend strikes parallel to subparallel to theseismic fault trend. Fig. 4a shows the orientation distribution offractures in each well. The size of the rose diagrams is proportional

to the apparent average fracture density. A secondary east/westtrend can also be noticed locally. Fig. 4b illustrates the distributionof fractures along one particular horizontal well. This interpreta-tion shows that (1) the FF is much higher in the southern drain thanin the other horizontal wells and (2) the fractures are generallydistributed in background fracturing (0 to 2 fractures/m) and infracture swarms (3 to 9 fractures/m).

To better understand the parameters that control the observedfracture distributions, other valuable information can be obtainedfrom the horizontal wells. Indeed, these wells provide high-resolution data about facies and fracture density. Their 3D analysisin ageomodeler,also depicting the reservoir layers and the faultnetwork, offers a powerful integrated picture of the reservoir. It isalso a good practice to highlight the correlation along wells torefine the picking of intrareservoir layers from logs, especially

when horizontal drains repeatedly cross the same reservoir marker.In addition, the interactive editing of markers and layer surfaces,with the visualization of faults, allows us to verify the reliability ofthe fault map. Such a visualization also can be used to understandthe occurrence of fracture clusters.

The highly fractured intervals along wells can be explainedeither by fracture swarms located near faults or by dolomitic layersknown to be fractured (Fig. 5). These two configurations havedifferent impacts on the hydraulic behavior and the fracture mod-eling strategy. It is therefore essential to understand and be able torecognize which configuration prevails at any location. In thisfield, the 3D model helped to establish that the apparent correlationbetween fracture cluster and dolomite is mainly caused by thindolomitic layers intersected repeatedly by wells, especially in thesouthern part of the field.

Relation Between Fracturing and Production Data. The rela-tion between fracture and production data reflects the role of frac-turing in the dynamic behavior of the field. Fig. 6 shows thedistribution of the productivity index (PI) over the entire field andfor both horizontal and vertical wells. The following commentscan be made: (1) the PI distribution is log-normal, which is in-dicative of wells drilled in a heterogeneous reservoir; (2) althoughthe best two producers are horizontal wells, the performance of thistype of well is not systematically better than vertical wells; (3)wells located in the southern part of the field (where dolomitiza-tion occurred) show better production performances than thoselocated in the central and northern parts; and (4) the three regionsshow the same type of PI distribution. It could be argued that this

Fig. 1Structural map at the top of the reservoir with deepfaults overlaid, and the well layout.



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is related to the fractured nature of the field. However, the combinedeffect of fractures and matrix heterogeneities is more likely here.

To assess the role of fractures qualitatively, well-parameterratios were calculated between the four central and northern drains,and the most fractured well (S-H1) was taken as a reference. Thewell parameters are PI, overall average fracture density, averageFF for the dominant northwest/southeast set only, and wellborelength.Fig. 7shows the results of this exercise. Though the south-ern reference well is two to seven times shorter than the four otherwells, it produces 3 to 15 times more. Two factors can explain thisbehavior: (1) the matrix property with more dolomite in Well SH-1and (2) the greater abundance of open fractures, especially thosestriking northwest/southeast (the latter strongly influence the PIratio). Knowing that dolomite streaks tend to be more fractured, itcan be concluded that both factors play a role.

Regarding seismic faults and fracture corridors, their capacityto conduct flows is still difficult to assess at this stage. Indeed, apilot waterflood strongly suggests a high-flow-capacity channel inthe northwest/southeast direction that can be interpreted as theeffect of a fault, of fracture swarms, or both. This qualitativeanalysis demonstrates that if fracture systems do play a role, theyare not the only factor contributing to permeability. Their model-ing therefore should be part of a more integrated reservoir model(see the next section).

Fig. 2S map. This map is one of the secondary informationsources about fracturing.

Fig. 3Stereoplot (Schmidt projection, lower hemisphere) andstrike histogram of raw open fracture orientation interpreted inimage log data.

Fig. 4(a) Fracture orientation in each studied well. The rosediagrams are normalized according to the relative fracture den-sity in each well. The well orientation is given in brackets.(b) Example of along-hole FF distribution.



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Secondary Variables Affecting Fracturing in This SpecificField. Fractures are interpreted here as conjugate shear fracturesrelated to faults. Their distribution over the field is related to thepresence of faults but also to the lithological control of dolomiticstreaks. Using the approach given by Bartonet al.,4 it is found thatwith the present-day stress field, only a few fractures of the east/west family are critically stressed. This suggests that the present-day stress field cannot be solely responsible for the fracture per-meability. Consequently, only parameters related to the paleostruc-tural history and lithology of the field are likely to explain thefracture sets. Four types of such parameters can be distinguished aspossible explanatory (secondary) information about fracturing:

Seismic-derived structural attributes: amplitude, coherence,deep faults (distance from the projected faults, interpreted at adeeper horizon).

Calculated structural variables: S-map and distance to thetop faults.

Log-derived lithological variables: porosity and gross thickness. Core-related lithological variables: dolomite, calcite, and il-

lite contents.All these secondary variables are available as maps with values

known at the center of 100100 m2 cells (total number of cells16,534). It should be noted that lithological variables are interpo-lated from a large number of well data, whereas structuralvariables are fully defined by the seismic. This paper focusesmainly on the modeling of the dominant northwest/southeast frac-ture set interpreted in four out of the five horizontal wells (datafrom vertical wells and northwest/southeast-oriented C-H3 are

deemed unreliable).

Results.Fracture-frequency data are calculated every 25 m alongall wells, within a moving window of 25 m. The number of data socalculated is 55. Among the 10 available secondary variables, onlysix are retained here; the four others (calcite and illite contents,porosity, and seismic coherency) are strongly correlated to themand hence are redundant. The discriminant analysis and sequentialsimulation results can be summarized as follows.

Discriminant Analysis.The number and ranges of fracture-frequency classes influence the results. Different class definitionsmay lead indeed to different discriminant functions (i.e., geologi-cal components), which may be correlated differently with the

secondary variables. Two extreme cases are evaluated. One in-volves a few (three) classes representing low-, medium-, and high-FF values. The other relies on many (approximately 20) classes,with most classes containing no more than three or four data. Thissecond class definition allows us to distinguish the few highest-fracture-frequency data, the latter belonging to the same class(with other data) in the three-class definition. Fig. 8 shows thediscriminant analysis correlation plots, with the first two discrimi-

nant components represented by the x

and y

axes. With threeclasses, the geological component is dominated by the seismicamplitude and the deep faults, with a positive correlation, and bythe gross thickness and the distance to faults, with a negativecorrelation. With 20 classes, the dominating explanatory variablesbecome the deep faults, the S-map, and the dolomite content witha positive correlation and the distance to faults with a negativecorrelation. The scatterplots of the FF vs. the first geological com-ponent is given in Fig. 9 for the two class definitions. Though thetwo clouds of points look very similar, the three-class componentbetter separates at least some of the very small, high-fracture fre-quencies (i.e., cases from the two extreme classes). The reason canbe found in the number of classes; it is simply easier to distinguisha few classes than many of them.

Sequential Simulation. The two previous geological compo-nents (with 3 and 20 classes) can be calculated at grid-nodes where

the secondary variables are known. Each geological component isused independently as secondary (soft) information to simulate thenorthwest/southeast FF with the sequential indicator simulationapproach presented previously. For each geological component,100 realizations are generated from which probability maps can bederived. The probability maps in Fig. 10 show that the northwest/southeast FF be greater than or equal to 0.5 frac/m.

These probability maps call for some comments. First of all, themaps look very similar in terms of trends and show similar high-

Fig. 5Possible interpretations of fracture-density peaks inhorizontal wells.

Fig. 6Relative PI distributionin thestudied field forall testedwells.

Fig. 7Comparison of various parameters between Well SH-1taken as reference and the other horizontal wells.



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and low-probability areas. The significant differences from onemap to another are in regions in which the model is in extrapola-tion situations (i.e., where the geological component is outside thedata intervals of Fig. 9). The northern part of the field is the mostillustrative. The 20-class geological component gives, in someregions, a high probability of finding northwest/southeast fracturefrequencies greater than 0.5 frac/m; this is not apparent with thethree-class geological component. The latter relies on a class defi-

nition that gathers all fracture frequencies greater than 0.5 frac/minto the same class without any distinction between them. Thenorthern high-probability regions therefore can be seen as influ-enced (in extrapolation conditions) by the high-fracture-frequencydata that the 20-class discriminant analysis function tries to fit.Because these data are located in the southern part of the field,their influence in the north can be questioned. Otherwise, bothprobability maps show uncertain regions of medium probabilities(e.g., from 40 to 60% chance). In these regions, the availableinformation is not enough to predict with confidence whether theFF is above or below 0.5 frac/m. A comparison of this method withthe method of Ouenes et al.23 can be found in Gauthier et al.29

Incorporation of the Results Into a Full-FieldReservoir Model

Reservoir (flow) simulations require that the fracture frequenciesrelated to small-scale fracture distributions be transformed intoequivalent dynamic properties. Because of the strongly coupledinfluence of matrix, small-scale fractures, and faults on the averagewell performances, a direct calibration to well-test permeabilitiesis not suitable. Instead, the FF realizations are used to control thegeneration of DFNs. The latter can be used in turn to upscalefracture dynamic properties (see Bourbiaux et al.8 for details), topredict fracture-network attributes for well planning, or to validatethe model against new well data, as discussed later.

Discrete Fracture Models.The FF and lithology are available on2D and 3D grids, respectively, with the same horizontal resolution(100100 m2 cells). The lithology is limited to three facies types:dolomite, reservoir limestones, and tight limestones. Because thesefacies types are not fractured equally, the FF must be simulatedagain within each of these facies types (facies-dependent FF real-izations). The methodology of Cacas et al.6 is used to model thesmall-scale fractures (DFNs) as regional joint sets.

Given a particular vertical column of the 3D lithologic model,the two fracture sets (northwest/southeast and east/west) are simu-lated with a Poisson process, honoring the following constraints.

Mean strike value, assumed constant at the reservoir scale. The Fischer coefficient (measure of the standard deviation of

azimuth data) describing the strike distribution. Lithology profile along the column.

Fig. 8Correlation plots corresponding to the first two discriminant components for different class definitions.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 1 0 1 2 3

Geological Component (dimensionless)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 1 0 1 2 3 4

Geological Component (dimensionless)

NW/SEFF,

fractures/m

3-Class Component

20-Class Component

NW/SEFF,

fractu

res/m

Fig. 9Scatterplots of the northwest/southeast FF vs. the geo-logical component for different class definitions.



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Average fracture density within each facies type. This con-straint is controlled by a set of FF simulations in each facies type.The same FF value applies to all cells within the same facies typein the column.

The distribution of fracture lengths is also required to charac-terize fully the geometry of the DFN. Without information toconstrain this parameter, as proposed by Gauthier et al.,1 a log-normal distribution is considered. Sensitivity analysis shows that,unless unrealistic, the fracture length has a limited impact on up-scaling results.

Equivalent Flow Parameters of the Fracture System.It is be-yond the scope of this paper to discuss in detail the match of the6-year history of the field. Instead, a procedure is presented toderive, from simulated FF maps, equivalent dynamic properties(e.g.,kx, ky, kz) assigned to the blocks of a reservoir simulation grid.

30

The simulation of flows in DFNs requires conductivities to beassigned to fractures. Without evidence in this field of in-situ stresscontrols of the fracture conductivity or of geographical aperturevariations caused by diagenesis, a constant aperture is assumed forthe entire reservoir. Consequently, lateral and vertical permeability

Fig. 10Probability maps showing that the northwest/southeast FF will be greater than or equal to 0.5 frac/m for (a) the 20-class

geological component and (b) the 3-class component.



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changes depend only on simulated facies types and FF. The con-stant aperture is calibrated by matching fluid-flow simulations inDFNs to well tests or to some production data.

For computing reasons, DFNs cannot be generated in all cellsof the (full-field) 3D lithological grid to derive equivalent proper-ties. Instead, the following procedure is proposed.

DFNs are generated in 1,000 cells drawn randomly in the 3Dlithological grid.

Equivalent dynamic properties are computed for each ofthese DFNs.8

Principal component analysis is run to derive, for each dy-namic property, a unique FF component that it is best correlated to it.

The relationships between FF components and dynamic

properties are then applied to all cells of the 3D lithological grid toassign them equivalent properties from the simulated FF maps.

The fine 3D permeability grid is finally upscaled on the res-ervoir simulation grid with standard upscaling tools.

At this stage, the faults have not yet been introduced in thereservoir simulation grid. In particular, the subseismic faults,which are reservoir scale objects crossing several simulation grid-blocks, are to be taken into account. Faults are treated separatelyand modeled explicitly inside the reservoir grid. From historymatch, some are known to be transversal fluid barriers and aretranslated into interblock transmissibility multipliers according tothe throw. Others, for which nearby well behaviors could not bematched, are interpreted as longitudinal drains (i.e., fault parallel

1 frac / 5m1 frac / 5m

1 frac / 0.75 m1 frac / 0.75 m

0 4 km

Dolomitic zones

Poor FMI data quality zones

FF threshold

Prob(NW/SEFF

>=1frac/Xm)

Along-HoleMeasured

NW/SEFF

Prob(NW/SEFF>=1

frac/Xm)

Along-HoleMeasured

NW/SEFF

3,350

3,400

3,450

3,500

TVD (ft)1 frac / 2m1 frac / 2m

Fig. 11Comparison between interpreted and predicted northwest/southeast FFs in the dolomite facies along Well S-H2.



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flow). Depending on the type of reservoir model considered (i.e.,single- or double-medium), different techniques are available torepresent these drains.31,32 This procedure finally leads to matrixand fracture porosities and permeabilities, as well as block-sizetransmissibilities for cells crossed by faults or fracture swarms.

In this study, the upscaling results were used in a single per-meability simulator with pseudokr/Pcfunctions that accounted forthe movement of water in fractures. A history match of pressure,water cut, and breakthrough time was achieved in 70 wells withoutany fine tuning on a well-by-well basis. This success was attrib-uted to the proposed methodology that allowed proper reproduc-tion, in the reservoir simulation grid, of the spatial distribution ofthe two types of highly conductive heterogeneities: fractured do-

lomitic streaks and fault/fracture swarm networks.

Static Calibration of the GeostatisticalFracture Model

In addition to fluid-flow simulations, the fracture models weretested against fracturing data from a new horizontal well, S-H2,which was not included in the previous geostatistical work. WellS-H2 is a 400-m-long west-northwest/east-southeast drain drilledin the southern part of the field, north of S-H1. Approximatelytwo-thirds of the well crosses dolomitic lithologies. The interpre-tation of electric image log data revealed a poorly fractured wellwith east/west to northwest/southeast fractures. Fig. 11 shows aqualitative comparison between interpreted and predicted fracturefrequencies for the northwest/southeast fracture set in the dolo-mitic facies set. The diagrams above map views depict the along-

borehole FF calculated with different moving-window sizes (5, 2,and 0.75 m, respectively). Changing the moving-window size al-lows the smoothing, more or less, of the fracture-frequency logs orthe exhibiting of some highly fractured zones. The dashed line ineach diagram indicates the FF threshold used in the correspondingprobability map and related to the moving-window size (i.e.,threshold 1 frac/window size). The areas in black, below thefrequency curves, represent the borehole sections in which the FFis above the reference frequency threshold. These zones of higherfracturing appear in all diagrams, for all three moving-windowsizes, and tend to follow the same trend. In accordance with theprobabilities, however, their proportion decreases as the referencethreshold increases. The dolomitic zones for which this compari-son applies are also indicated along the well path. The map viewsare from probability maps calculated for the dolomitic facies set.

They show the probability that the FF will be greater than thethreshold. As expected, the probabilities tend to decrease with thethreshold increasing from 1 frac/5 m to 1 frac/0.75 m. There is a60 to 80% chance that the FF will be greater than the lowestthreshold (1 frac/5 m) in dolomitic zones along the well and a 0 to20% chance it will be greater than the highest threshold (1 frac/0.75 m). Regarding the intermediate threshold (1 frac/2 m), theprobability of being higher is approximately 50%. These probabili-ties can be interpreted as follows: in dolomitic facies around WellS-H2, the northwest/southeast FF is more likely to be greater than1 frac/5 m, but without exceeding 1 frac/0.75 m. In between thesetwo thresholds, however, the available direct and indirect (second-ary) information does not allow us to know with confidencewhether the FF is above or below 1 frac/2 m. It can be noted thatthe rather small fracture frequencies predicted around S-H2 are notinfluenced or are poorly influenced (in extrapolation conditions)by the high-fracture-frequency data in the nearby Well S-H1. Thismedium-scale variability is correctly reproduced by the geostatis-tical model through the primary (fracturing) and secondary (geo-logical component) data and the input statistical models. This re-sult tends to confirm the pertinence of the geological component ascapitalizing structural and geological information that governs, atleast partly, the northwest/southeast fracture set. The geologicalcomponent is different at the two well locations and is taken intoaccount in a satisfactory manner by the model (hence the fractur-ing conditions).

Another comparison was between randomly chosen fracturesimulations and the actual fracture frequencies calculated alongWell S-H2. This comparison is illustrated in Fig. 12.The two maps

come from the randomly drawn simulations of the northwest/southeast and east/west fracture frequencies in the dolomitic faciesset. Average (predicted) fracture frequencies were calculated onthese maps within a zone around the well path (circled areas).These average values are pointed out by arrows below the legendbars. They then can be compared to the actual fracture frequenciescalculated in S-H2 (interpreted values given at the bottom of Fig.12). One can note the good agreement between the predicted andcalculated values for the two fracture sets in dolomitic facies.

A last comparison was to construct an equivalent (predicted)fracture-frequency log from the two maps in Fig. 12. Using thesemaps in the 3D geological model, a DFN model was generated (asdescribed earlier) around S-H2 and a fracture log was constructedalong the well trajectory.Fig. 13shows a surprisingly good matchbetween predicted and interpreted logs. Although this comparisonrelies only on one particular simulation of each fracture set, it tendsto corroborate the already good probability results discussed pre-

viously. Note that the peak between 12001800 is related to botha dolomitic zone and a subseismic fault. In this case, it is probablythe former parameter that influences the prediction.

From a production standpoint, Well S-H2 displays a PI threetimes lower than S-H1 (i.e., similar to C-H1 and C-H2 in Fig. 6).Because the northwest/southeast FF in S-H2 is also approximatelythree times lower than in S-H1, the role of this fracture set on flowsseems to be as important as, if not more than, the role of the(dolomitic) matrix. This well therefore suggests that dolomite isnot the only parameter that controls fracturing in this field. The PI

Fig. 12Comparison of predicted and interpreted (actual) FFsin the dolomite facies type.

0.0

0.2

0.6

1.0

1.4

1.8

0 2000 4000

Predicted

Interpreted

Fig. 13Along-hole predicted and interpreted fracture densitylogs for all fracture sets together.



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also corroborates the minor conducting effect of the other east/west fracture set, though it is dominant (i.e., more inclined to becritically stressed).

Discussion and Conclusions

Beyond the geostatistical approach, the use of geological param-eters as secondary information for full-field modeling of fracture-sets relies on two critical points or decisions.

The first point concerns the choice of a fracture index; the latterneeds to be related directly to the fracturing intensity and notinfluenced by the well orientation or length. Fracture frequenciesproved adequate. However, they depend strongly on the recoveryof cores (poorly recovered cores being possibly related to highly

fractured zones) or on the quality of image logs. In addition,they also can be biased by the subjective interpretation of coresor images.

The second point is about the choice of explanatory variables.Although any type of attribute could be used and could show somecorrelation with the FF, it is the geologists responsibility to vali-date correlated attributes. The secondary information is not limitedto geological or structural parameters and can include other typesof data. In particular, a geomechanical model (if available) couldprovide additional variables (e.g., sliding or opening variables).Although the resolution of geomechanical models is poorer thanthat of seismic or log data, geomechanical variables can be inte-grated into the geostatistical approach as another type of secondaryinformation.

The application of this approach to a north Africa field shows

that, although the field cannot be considered strictly as a fracturedreservoir, the northwest/southeast fracture set plays a determinantrole on flows in the southern and, to a lesser degree, northern partsof the field. It is demonstrated that lithology (dolomitic streaks)and faulting are the main factors controlling this fracture set. Do-lomitic facies and faults are more frequent in the south, and bothcontribute to the better productivity of the southern wells. Thefracture-frequency model cannot be used directly for flow simu-lation, but it needs to be incorporated into a more integrated res-ervoir model. Fracture-frequency maps in particular are used tocontrol the local density of fractures for the stochastic simulationof DFNs. DFNs are then calibrated in terms of equivalent flowproperties to match well-test data and to derive dual porosity/permeability parameters for reservoir simulation (upscaling step).The probability maps are useful for risk analysis regarding newdrilling targets of horizontal wells. The good fracturing predictionsalong a well drilled more recently validate (at least partly) this model.

Nomenclature

dli length of segment i

kr relative permeability

kx, ky, kz permeability tensor components

N number of fault segments

Pc capillary pressure

S strain estimate

Vti average vertical throw along dliWs surface of the moving window

Acknowledgments

We wish to thank TotalFinaElf and its subsidiaries for authorizing

the publication of this paper. Olivier Lerat is sincerely thanked forproviding this study with key facies interpretations in horizontalwells. Abdel Zellou, Andr Toublanc, and Claude Pernin contrib-uted to the work presented here. Three anonymous reviewershelped to improve the SPE paper version of this manuscript.

References

1. Gauthier, B.D.M. et al.: Fracture networks in Rotliegend gas reser-

voirs of the Dutch offshore: implications for reservoir behaviour,Ge-

ologie en Mijnbow (2000) 79, No. 1, 45.

2. Sibbit, A.M.:Quantifying Porosity and Estimating Permeability From

Well Logs in Fractured Basement Reservoirs, paper SPE 30157 pre-

sented at the 1995 SPE PetroVietnam, Ho Chi Minh City, Vietnam, 13

March.

3. Heffer, K.J. et al.:The influence of natural fractures, faults and earth

stresses on reservoir performance-geomechanical analysis by numeri-

cal modeling,North sea oil and gas reservoirs III, Norwegian Inst. of

Technology, Kluwer Academic Publishers (1994) 201.

4. Barton, C.A. et al.: Utilizing wellbore image data to determine the

complete stress tensor: application to permeability anisotropy and well-

bore stability, The Log Analyst(NovemberDecember 1997) 21.

5. Swaby, P.A. and Rawnsley, K.D.: An Interactive 3D Fracture Mod-

eling Environment, paper SPE 36004 presented at the 1996 SPE Pe-

troleum Computer Conference, Dallas, 25 June.

6. Cacas, M.C.et al.:Nested geological modelling of naturally fractured

reservoirs, Petroleum Geoscience (2001) 7, S43.

7. Wei, L. et al.: Discriminating Fracture Patterns in Fractured Reser-

voirs by Pressure Transient Tests, paper SPE 49233 prepared for

presentation at the 1998 SPE Annual Technical Conference and Exhi-

bition, New Orleans, 2730 September.

8. Bourbiaux, B. et al.: A Fast and Efficient Methodology to Convert

Fractured Reservoir Images Into a Dual-Porosity Model, paper SPE

38907 presented at the 1997 SPE Annual Technical Conference and

Exhibition, San Antonio, Texas, 58 October.

9. Guerreiro, L. et al.: Integrated Reservoir Characterization of a Frac-

tured Carbonate Reservoir, paper SPE 58995 presented at the 2000

SPE International Petroleum Conference and Exhibition in Mexico,

Villahermosa, Mexico, 13 February.

10. Gauthier, B.D.M. and Lake, S.D.: Probabilistic modeling of faults

below the limit of seismic resolution in Pelican field, North Sea, Off-

shore United Kingdom, AAPG Bull. (1993) 77, No. 5, 761.

11. Cowie, P.A. et al.: Introduction to the special issue: Scaling law for

faults and fractures populationanalysis and applications,J. of Struc-tural Geology (1996) 18, vxi.

12. Loosveld, R.J.H. and Franssen, R.C.M.W.: Extensional vs. Shear

Fractures: Implications for Reservoir Characterisation, paper SPE

25017 presented at the 1992 SPE European Petroleum Conference,

Cannes, France, 1618 November.

13. Bourne, S.J. et al.: Predictive modelling of naturally fractured reser-

voirs using geomechanics and flow simulation, GeoArabia (2001) 6,

No. 1, 27.

14. Leroy, Y.M. and Sassi, W.: A plasticity model for discontinua, As-

pects of tectonic faulting, F. Lehner and J. Urai (eds.), Springer-Verlag

(2000).

15. Guiton, M.: Contribution of pervasive fractures to the deformation

during folding of sedimentary rocks, PhD dissertation, Ecole Poly-

technique, France (2001).

16. Heffer, K.J., King, P.R., and Jones, A.D.W.: Fracture Modeling asPart of Integrated Reservoir Characterization, paper SPE 53347 presented

at the 1999 SPE Middle East Oil Show, Bahrain, 2023 February.

17. McQuillan, H.: Small scale fracture density in Asmari formation

southwest Iran and its relation to bed thickness and structural setting,

AAPG Bull.(1973) 57, No. 12, 2367.

18. Murray, G.: Quantitative fracture studySanish Pool, McKenzie

County, North Dakota, AAPG Bull. (1968) 52, No. 1, 57.

19. Nelson, R.: Geologic Analysis of Naturally Fractured Reservoirs, Gulf

Publishing Co., Houston (1985).

20. Ericsson, J.B., McKean, H.C., and Hooper, R.J.: Facies and Curvature

Controlled 3D Fracture Models,Geological Society of London Special

Publication (1998) 147, 299.

21. Agarwal, B. and Allen, L.R.: Ekofisk Field Reservoir Characterisa-

tion: Mapping Permeability Through Facies and Fracture Intensity,

paper SPE 35527 presented at the 1996 SPE European 3-D Reservoir

Modelling Conference, Stavanger, 1617 April.

22. Zellou, A.M, Ouenes, A., and Banik, A.K: Improved Fractured Res-

ervoir Characterization Using Neural Networks, Geomechanics, and

3-D Seismic, paper SPE 30722 presented at the 1995 SPE Annual

Technical Conference and Exhibition, Dallas, 2225 October.

23. Ouenes, A.: Practical application of fuzzy logic and neural networks

to fractured reservoir characterization, Computer and Geosciences,

Shahab Mohaghegh (ed.) (2000) 26, No. 7.

24. Gooverts P.:Geostatistics for natural resources evaluation,Oxford U.

Press (1997).

25. Zhu, H. and Journel, A.G. Formatting and Integrating Soft Data: Sto-

chastic Imaging via the Markov-Bayes Algorithm, Geostat Troia,

Soares (ed.), Kluwer Publishing (1992) 112.



11/11

26. Schmaryan, L.E. and Journel, A.G.: Two Markov models and their

applications, Math Geology (1999) 31, No. 8, 965.

27. Auzias, V. et al.: Fracture orientation modelling in the vicinity of a

horizontal well, Bull., Centre Rech. Elf Explor. Prod. (1997) 21, 381.

28. Townsend, C.et al.:Small seismic-scale fault identification and map-

ping, Faulting, Fault sealing and Fluid flow in Hydrocarbon Reser-

voirs,G. Jones, Q.J. Fisher, and R.J. Knipe (eds.), Geological Society,

Special Publications (1998) 125.

29. Gauthier, B.D.M. et al.:Integrated Fractured Reservoir Characterisa-

tion: A Case Study in a North Africa Field, paper SPE 65118 pre-

sented at the 2000 European Petroleum Conference, Paris, 2425

October.

30. Daniel, J.M. et al.: The use of discrete fracture models to constrain

full field flow simulations, paper XX presented at the 2001 EAGE

Conference & Technical Exhibition, Amsterdam.

31. Cosentino, L. et al.: Integrated Study of a Fractured Middle East

Reservoir With Stratiform Super-K IntervalsPart 2: Upscaling and

Dual Media Simulation, SPEREE(February 2002) 24.

32. Van Lingen, P. et al.: Single Medium Simulation of Reservoirs with

Conductive Faults and Fractures, paper SPE 68165 presented at the

2001 SPE Middle East Oil Show, Bahrain, 1720 March.

SI Metric Conversion Factors

ft 3.048* E 01 m

ft2 9.290 304* E 02 m2

mile 1.609 344* E + 00 km*Conversion factor is exact.

Bertrand Gauthier is Senior Geologist/Geophysicist at Total-FinaElf. e-mail: [email protected]. After sometime working in computing, he joined Shell Research in Hollandin 1988, where he worked mainly on fault modeling. In 1992, hemoved to Shell Netherlands as a production seismologist. In1996, he joined Total and was in charge of the fractured res-ervoir study team; in early 2002, he moved back to seismology.Gauthier has published papers on fault and fracture charac-terization and modeling. He holds a PhD degree in structuralgeology from the Pierre et Marie Curie U., Paris. Michel Garciais currently the manager of FSS International R&D (France). e-mail: [email protected]. His activities in-clude consulting, software design and development, andteaching in the fields of geostatistics, automatic mesh genera-

tion and optimization, and flow modeling for petroleum, envi-ronmental, and nuclear waste management applications. Hehas worked with the Stanford Center for Reservoir Forecastingon geostatistics and upscaling methods. Garcia holds an en-gineering degree and a PhD degree in mining and petroleumengineering, both from the Ecole des Mines de Paris. Jean-Marc Danielis Head of the IFP Structural Geology Dept. e-mail:

[email protected]. He is interested mainly in fracture net-work characterization and modeling, both in terms of geom-etry and fluid flow. Previously, he was a research engineer inthe IFP Geology-Geochemistry Div. and managed several re-search projects concerning the role of faults on fracturing andfluid flow. He is now in charge of analog modeling and 4Ddescription of fault networks and is involved in advanced frac-tured reservoir studies, including stochastic modeling of frac-ture networks. His main areas of interest are the geologicaldescription of fracture networks from outcrop and subsurfacedata, 4D analog modeling of fault networks, and geomodel-ing. Daniel holds a PhD degree in structural geology from thePierre et Marie Curie U., Paris.


4.- integrated fractured reservoir characterisation. a case study in a north affrica field

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