Frac Res Modelling

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© 2005 EAGE 33 technical article first break volume 23, September 2005 Although the specific flow behaviour of fractured reservoirs was identified and modelled a relatively long time ago (Barenblatt et al., 1960; Warren and Root, 1963), until recently no consistent methodology and software really enabled the integration of field information about natural fracturing in reservoir engineering studies. The availability of direct information about fractures, in particular borehole images, was an incentive for such integration. The unexpect- ed production behaviour of many fields arising from an insufficient consideration of fracture effects on flow also emphasized the need for better characterizing the distribu- tion of fractures at various scales and transferring the mean- ingful part of this information to field simulation models. A recent example concerns a giant Middle East Carbonate field where sub-seismic fracture swarms and stratiform super-K intervals were found to establish preferential flow paths between injection and production wells (Cosentino et al., 2001). Therefore, the present trend in fractured field studies is toward the use of methodologies and software platforms to integrate all information about fractures into flow simula- tion models. The main features of those methodologies are described here, on the basis of fracture modelling examples set up using our own workflow (Bourbiaux et al., 2002). The latter involves the following steps: constrained modelling of the geological fracture network based on the analysis, interpolation, and extrapolation of fracture information acquired in wells and derived from seismic data, sometime completed by outcrop analogue data; characterizing the hydrodynamic properties of this natural network from flow-related data; choosing a flow simulation model suited to the role played by fractures and faults at various scales and assigning to this model upscaled parameters derived from the flow-calibrat- ed geological fracture model; simulating the reservoir flow behaviour on the basis of a physical assessment of multiphase flow mechanisms acting in transfers between matrix and fractures. In the following, those four steps are reviewed and illustrat- ed from a representative synthetic field case. Emerging tech- niques to further capture the complexity and flow behaviour of fractured reservoirs are also identified. Building a geological model of faults and fractures The proposed modelling methodology, described by Cacas et al., (2001) and summarized hereafter, starts with a careful geological analysis of natural fracturing information avail- able from wellbores, surface seismic, and outcrops. The over- all data integration workflow is shown in Figure 1. Although geologists can provide a detailed classification of fractures with various sets associated with tectonic events and tensile or shear mechanisms, the reservoir engineer is led to discard and/or lump the sets expected to have negligible or similar impact on flows. That is, in practice, we generally end up with two main categories, the large-scale fractures or faults at seismic and sub-seismic scale, and the small-scale or diffuse fractures observed in wellbores. Based on the previous analysis results, a multi-scale frac- ture model is then built using stochastic methods constrained by deterministic observations of fractures and by fracture genesis rules. Figures 2 and 3 show a typical distribution of a multi- scale fracture network generated with our own fracture mod- elling software and including both large-scale and small-scale fractures. Figure 2 shows the large-scale, i.e. reservoir-scale, seismic and sub-seismic fault network model and Figure 3 the small-scale fracture network model that can be recon- structed at any location of this reservoir. Large-scale fractures (faults). In practice, 3D seismic data provide the most reliable information to set up such a model. 3D seismic is firstly used to locate faults, identified Fractured reservoirs modelling: a review of the challenges and some recent solutions B. Bourbiaux * , R. Basquet, J.M. Daniel, L.Y. Hu, S. Jenni, A. Lange, and P. Rasolofosaon. Figure 1 Geological modelling of multi-scale fractures (faults and joints): overall approach. * Institut Français du Pétrole, 1 & 4 Avenue Bois-Preau, 92852 Rueil Malmaison CEDEX. E-mail: [email protected]

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Transcript of Frac Res Modelling

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Although the specific flow behaviour of fractured reservoirswas identified and modelled a relatively long time ago(Barenblatt et al., 1960; Warren and Root, 1963), untilrecently no consistent methodology and software reallyenabled the integration of field information about naturalfracturing in reservoir engineering studies. The availability ofdirect information about fractures, in particular boreholeimages, was an incentive for such integration. The unexpect-ed production behaviour of many fields arising from aninsufficient consideration of fracture effects on flow alsoemphasized the need for better characterizing the distribu-tion of fractures at various scales and transferring the mean-ingful part of this information to field simulation models. Arecent example concerns a giant Middle East Carbonate fieldwhere sub-seismic fracture swarms and stratiform super-Kintervals were found to establish preferential flow pathsbetween injection and production wells (Cosentino et al.,2001).

Therefore, the present trend in fractured field studies istoward the use of methodologies and software platforms tointegrate all information about fractures into flow simula-tion models. The main features of those methodologies aredescribed here, on the basis of fracture modelling examplesset up using our own workflow (Bourbiaux et al., 2002). Thelatter involves the following steps:■ constrained modelling of the geological fracture network

based on the analysis, interpolation, and extrapolation offracture information acquired in wells and derived fromseismic data, sometime completed by outcrop analoguedata;

■ characterizing the hydrodynamic properties of this naturalnetwork from flow-related data;

■ choosing a flow simulation model suited to the role playedby fractures and faults at various scales and assigning to thismodel upscaled parameters derived from the flow-calibrat-ed geological fracture model;

■ simulating the reservoir flow behaviour on the basis of aphysical assessment of multiphase flow mechanisms actingin transfers between matrix and fractures.

In the following, those four steps are reviewed and illustrat-ed from a representative synthetic field case. Emerging tech-niques to further capture the complexity and flow behaviourof fractured reservoirs are also identified.

Building a geological model of faults andfracturesThe proposed modelling methodology, described by Cacas etal., (2001) and summarized hereafter, starts with a carefulgeological analysis of natural fracturing information avail-able from wellbores, surface seismic, and outcrops. The over-all data integration workflow is shown in Figure 1.

Although geologists can provide a detailed classificationof fractures with various sets associated with tectonic eventsand tensile or shear mechanisms, the reservoir engineer is ledto discard and/or lump the sets expected to have negligible orsimilar impact on flows. That is, in practice, we generally endup with two main categories, the large-scale fractures orfaults at seismic and sub-seismic scale, and the small-scale ordiffuse fractures observed in wellbores.

Based on the previous analysis results, a multi-scale frac-ture model is then built using stochastic methods constrainedby deterministic observations of fractures and by fracturegenesis rules.

Figures 2 and 3 show a typical distribution of a multi-scale fracture network generated with our own fracture mod-elling software and including both large-scale and small-scalefractures. Figure 2 shows the large-scale, i.e. reservoir-scale,seismic and sub-seismic fault network model and Figure 3the small-scale fracture network model that can be recon-structed at any location of this reservoir.■ Large-scale fractures (faults). In practice, 3D seismic data

provide the most reliable information to set up such amodel. 3D seismic is firstly used to locate faults, identified

Fractured reservoirs modelling: a review of thechallenges and some recent solutions

B. Bourbiaux*, R. Basquet, J.M. Daniel, L.Y. Hu, S. Jenni, A. Lange, and P. Rasolofosaon.

Figure 1 Geological modelling of multi-scale fractures (faultsand joints): overall approach.

* Institut Français du Pétrole, 1 & 4 Avenue Bois-Preau, 92852 Rueil Malmaison CEDEX.E-mail: [email protected]

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as ‘deterministic’ objects. In addition, various 3D seismicamplitude attributes like coherency are analysed and turnedinto probability maps of sub-seismic fault presence. Such prob-ability maps are used as constraints to ‘extrapolate’, througha stochastic modelling technique, the fault network to sub-seis-mic scales. Other modelling constraints for sub-seismic faultnetwork generation are derived from the ‘deterministic’ faultmap and include statistics of orientation and a fractal param-eter for distribution in space.

■ Small-scale fractures. The important initial step consists inanalysing and identifying the various fracture sets from well-bore image logs and cores. Different sets are defined accord-ing to given average orientations, which are related to struc-tural features and/or tectonic events. The nature of rock faciesconstitutes another classification parameter as the expressionof a fracturing event in a given facies or group of facies is close-ly related to its own mechanical properties. Once fracture setsand relevant facies in terms of fracturing properties have beenidentified, a fracture geomodel describing the distribution offracture parameters – namely orientation and density – for eachset in each facies, is built using the matrix geomodel as under-lying information. In our example, the small-scale diffuse frac-ture network is made up of two sets of systematic joints andtwo facies have been defined in terms of fracture properties.The fracture density of one set is controlled both by the faciesand by the reservoir curvature, whereas for the second set, thefacies nature and the proximity to faults are the controlling fac-tors. Finally, a stochastic model of the small-scale (diffuse) frac-ture network can be generated at any location of the reservoiron the basis of fracture geomodel parameters.

The 3D fracture network shown in Fig. 2 is generated in a reser-voir sector of about 2 km wide and incorporates both the seis-mic/sub-seismic faults and the small-scale fractures. As can beobserved, such images can now be reconstructed in reservoirswith complex structures, involving high dips and/or throws.

With such software tools, provided that sufficient facies andstructural data are available, the geologist can now provide thereservoir engineer with a realistic model of the multi-scale frac-ture/fault network. However, such a Discrete Fracture Network(DFN) model will not be used as it is in the field flow model, butwill be simplified through homogenization procedures asdescribed later on. Then, one may wonder about their useful-ness. Actually, as shown in the next section, DFN models arefirst used to assess fracture hydraulic properties from availablefield flow data, such as well tests. Interpreting flow data usinggeologically-representative DFN models provide additionalinformation about reservoir flow properties compared to con-ventional analysis methods, regarding flow anisotropy forinstance. And also, they keep the link with the geologicalassumptions underlying the fracture model. Such a link is essen-tial to interpret the impact of fracture sets on flow and drive fur-ther acquisition of geological data that are mostly relevant forfluid transport.

Challenges. Despite the recent progress, there still remains roomfor improvement of these geological fracture models, which areoften poorly-defined for several reasons, among which:■ a limited amount of information provided by the few wells

intersecting the fracture network;■ missing information about large-scale fractures below seismic

resolution scale ; ■ poorly-defined fracture properties, especially fracture length,

connectivity, and conductivity.

Seismic anisotropy analysis is probably one of the most promis-ing solution for mapping fracture orientation and intensitybetween wells (Rasolofosaon, 2005). Indeed, assuming that pre-stack seismic data of good quality are available, the azimuthalanisotropy of seismic responses can be determined at variouslocations within the reservoir using a well-suited method andadvanced processing tools. The principal direction of seismic

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Figure 2 Reservoir-scale fault network.Figure 3 Discrete element model of the whole fracture network at a given reservoir location: - small-scale (diffuse) fracturesets in yellow and blue - faults in green.

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anisotropy can be related to the presence of rock discontinuitieswith mechanical compliance, a situation encountered in thepresence of a single set or an anisotropic network of unsealedfractures. The results of seismic anisotropy analysis necessarilyhave to be corroborated with wellbore information about frac-ture presence and orientation in regions where both informationare available, in order to check their consistency in wear-well-bore regions and allow a reliable use of seismic anisotropyresults at a distance from the wells. Furthermore, the intensity ofseismic anisotropy can also give information about the spatialvariations of fracture density if the latter can be calibrated fromwellbore data. Yet, although seismic anisotropy analysis isbecoming a contributing part to fracture studies, the interpreta-tion of results remain field-specific and mostly qualitativebecause:■ the vertical resolution scale of seismic response is some two

orders of magnitude above that of wellbore core and log data,which leads to several possible interpretations of seismicanisotropy in terms of fracture presence;

■ the theoretical models capable of relating wave propagationvelocity and amplitude to fracture network geometrical and/ormechanical properties cannot yet be formulated and/or para-meterized.

Thus, quantifying the uncertainty on the fracture informationinferred from seismic anisotropy analysis is a key challenge forextended use of seismic data in fracture characterization studies.

Additional genetic and geo-mechanical rules can also furtherconstrain the stochastic fracture models. Analogue experimentalmodels (Daniel, 2004) are being used to mimic faulting process-es, with real-time recording of transient deformation states byCT-scanning. Through the geo-mechanical simulation of exper-iments on finely-discretized models, the chronology and spatialorganisation of rupture lineaments can be reproduced and inter-preted. Such experiments are particularly useful to better con-strain the generation of sub-seismic faults in relation with majorlineaments.

To conclude, one has to recall that the reservoir engineeringrequirements drive fracture modelling studies and thus encour-age the early integration of dynamic information in the geolog-ical fracture modelling process. Ongoing progress made in thatdirection will conclude this paper as it will actually lump thepresently-reviewed modelling steps into a unique process.

Following the methodology presented in the introduction,the question of characterizing the hydraulic properties of a geo-logical fracture model of geometric and static nature is exam-ined.

Hydraulic characterization of the fracturegeological modelThe reservoir engineer needs to validate the geometry of the‘static’ fault/fracture model provided by the geologist asregards fluid flow behaviour, and to calibrate missing flowproperties such as conductivities.

To that end, a patented simulator was developed withinour fracture modelling software platform. It simulates steady-

state and transient well tests on the DFN model built by thegeologist, for comparison with the actual field measurementsof those tests (Sarda et al., 2002). Its original features consistin an optimal discretization of the DFN using a minimumnumber of cells defined by fracture intersections, and also inan accurate simulation of matrix-fracture transfers (Figure 4).The actual distribution of matrix block sizes and shapes istaken into account as each fracture node is associated withthe proper matrix volume it can drain at this precise location,such matrix volume being determined through a specific pro-cessing of geological images. The range of application of thissimulator was extended to highly-compressible fluid flowsfor application to fractured gas fields (Basquet et al., 2004).Furthermore, a ‘dual-permeability’ option of this simulator(Lange et al., 2004) enables us to simulate matrix flows inthe model regions where fractures are scarce or absent. Thus,the dynamic behaviour of any type of reservoir crossed byfractures or faults can be characterized, including poorly-connected fractured reservoirs, which actually turn out to bequite frequent in practice.

Considering the previous field-representative case, a build-up test of a well located in a fractured area and 200 m from anearby fault was simulated on the geologically-representativemodel (Figure 3) including a discrete representation of bothfaults and fractures. The derivative curve shown in Figure 5reveals successive flow regimes corresponding to the contribu-tions from fracture and matrix media, and also to the impactof the fault. The latter establishes a hydraulic connection withthe fractured medium far from wellbore and also with reser-voir limits. This example illustrates the capabilities of DFNsimulators to analyze the hydraulic behaviour of complexmulti-scale fractured reservoirs as the analytical solutionsunderlying conventional interpretation techniques cannot takeinto account such a complexity.

Challenges. An early characterization of fault and fractureflow properties is a concern for reservoir engineers as only afew fractures generally contribute to most of the well deliv-erability. That is, the ‘flow-effective’ fault/fracture networkturns out to be very different from the static geologicalimages of those networks. Therefore, as will be underlined

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Figure 4 Discretization of a Discrete Fracture Network andassignment of matrix blocks to fracture nodes.

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again at the end of this paper, integrating any available flowdata in the fracture modelling process is definitely a way ofprogress for the near future. In this view, the use of DFNflow simulators based on ‘static’ geological models shoulddevelop in the near future. However, the computation effi-ciency of such tools should still be increased to be able tosimulate within a reasonable time the flow data collected atvarious scales, in particular at the scale of reservoir regionsincluding multiple wells where flow and pressure interfer-ence tests, and sometimes tracer tests, provide essential infor-mation about fault/fracture network connectivity andanisotropy. To this end, modelling techniques combiningsimplified or homogenized fracture models far from well-bores, and discrete fracture models in the wellbore vicinity,are being developed.

Despite all the efforts made to draw as much informa-tion as possible from early flow data, the hydraulic charac-terization of the field fault/fracture network remainsincomplete and/or uncertain. The production data collectedall during field history constitute as many data to gradual-ly complete, correct or refine the ‘flow-effective’ fault/frac-ture model of the field. Taking into account flow data in thegeological fracture modelling process may be complex at thisstage as the flow history most often involves both single-phase and multiphase production steps. For this reason, inaddition to conventional reservoir engineering information,4D seismic data are a valuable source of direct informationto identify the large-scale flow heterogeneities possiblyresulting from conductive faults or fractured zones.

Setting up a flow-representative field-scale modelThe complex DFN models derived from geological informa-tion are usable for simulating flow at the well-drainage-areascale but, for obvious computational limitations, cannot beused straightforwardly to simulate multiphase fluid flow at

field scale. The field-scale simulation model is necessarily asimplified representation of the actual geology of the frac-tured medium. The simplification procedure depends on (i)the fracture scale compared to that of model grid cells, (ii)the continuity or connectivity of each medium, and (iii) thetime scale of flow interaction between media compared tothe time scale of fluid transport within a given medium.

If a quasi-static equilibrium, in terms of fluids saturation,pressure or composition, is established between the differentconstitutive media at any time and location of the reservoir,then the fractured medium can be represented as a singleequivalent medium. Such transfer conditions may be satisfiedin some densely-fractured media or in the presence of poor-ly-differentiated fractures and matrix, or also in single-phaseproduction conditions.

In other situations, the equilibrium between matrix andfractures does not follow any more the evolution of fractureparameters and flow conditions, and both media have to besimulated separately. That is, an homogenized single-medi-um model with averaged fracture and matrix properties canno more capture the flow features linked to a given medium.The well-known dual-porosity dual-permeability modellingapproach, introduced by Barenblatt et al. in 1960, is thenadopted assuming that matrix and fracture media behave astwo separate ‘continua’ or equivalent media. A simplifiedoption of this model, the dual-porosity single-permeabilitymodel, was proposed by Warren and Root (1963). Thismodel assumes that the matrix medium is made up of discon-tinuous blocks exchanging fluids with the fracture networkat any location of the reservoir. Warren and Root also adopt-ed the well-known representation of matrix blocks as sets ofidentical parallelepipeds in order to formulate matrix-frac-ture transfers more easily. However, poorly-connected frac-ture networks and/or a hydraulic continuity of the matrixmedium are frequent situations in practice. In those situa-tions, the dual-permeability approach is required and theideal representation of matrix medium as discontinuousblocks is no more valid at a local scale.

Single- or dual-medium modelling approaches require thedetermination of upscaled flow parameters of fractures andmatrix taken respectively as a unique medium or as separatemedia. Procedures to perform such an upscaling were notavailable for field-scale applications until recently. The onewe recently implemented (Bourbiaux et al., 1998) for dual-porosity models involves the determination of (i) equivalentfracture permeabilities from single-phase flow computationson the geological DFN at cell scale, (ii) equivalent blockdimensions from an image processing technique analogousto a simplified representation of matrix-fracture fluid trans-fers. The application of such procedures to large full-fieldmodels, up to several million cells in size, requires efficientmethods to assign equivalent parameter values to each cell.We recently implemented a multi-variable interpolation tech-nique which offers some flexibility in the presence of com-plex and large fracture models.

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Figure 5 Simulation of a build-up test on the discrete (geolog-ical) model of a fractured and faulted reservoir (tref: time atthe beginning of build-up).

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In the presence of a multi-scale fault/fracture network,one remaining question concerns the possibility to define anequivalent medium for the multi-scale fault/fracture net-work. Indeed, the Representative Elementary Scale (REV),beyond which the network behaves like an anisotropic con-tinuum, is generally far above the resolution scale of the flowsimulation grid, i.e. cell size. In such a situation, the direc-tionality of flow associated with large-scale conductiveobjects has to be preserved in the fracture upscaling proce-dure (Cosentino et al., 2001; Basquet et al., 2004).

Applying the previous procedure to our field example(Figure 6), the fracture/fault geological model was turnedinto a dual-medium simulation model in three steps. Firstly,the equivalent permeabilities of the diffuse fracture networkand the equivalent block dimensions were computed andinterpolated over the whole field. Secondly, the cell-to-cellfault transmissivities were determined taking into accounttheir direction with respect to the grid orientation. Finally,fault transmissivity values were converted into equivalentpermeability values which were added to those of the diffusefracture network to constitute the ‘fracture’ grid permeabili-ty input of the dual-medium flow model.

Challenges. Lumping the large-scale conductive faultsand the small-scale fracture network into a single fracturemedium may be responsible for inaccurate flow predictions,especially in the presence of a few major faults responsiblefor flow bypassing between wells in multiphase displacementprocesses. For this reason, the future trend in fractured reser-voir modelling is the adoption of multi-scale field flow mod-els combining a discrete representation of major objectscontrolling flows and one or several equivalent media. To beusable at field scale, such flexible models have to provideaccurate flow solutions at a minimum computational cost. Inthat perspective, we recently developed a multi-scale model(Henn et al., 2004) based on (i) the use of segregation con-cept to simulate flows within faults, thus avoiding the verti-cal discretization of these thin objects, and (ii) a couplingbetween faults and the surrounding medium avoiding gridrefinement nearby the faults, while keeping a good pre-dictability of the model (Figure 7).

Simulation of multiphase fluid transfers in a multi-medium field modelIn many porous fractured reservoirs, the long-term productionand recovery are controlled by matrix-fracture transfers whichtake place in the multiphase conditions resulting from deple-tion or the implementation of secondary/tertiary methods.Therefore, fractured reservoir simulators have to incorporatereliable formulations and algorithms in order to correctly rep-resent the physics of multiphase transfers between the consti-tutive media, matrix, fractures, and/or faults. Considered on ageneral basis, the problem is complex as multiple physicalmechanisms can be involved in those transfers, including pres-sure diffusivity, capillarity, gravity, viscous drive, moleculardiffusion, and thermal conduction.

The single-medium approach offers far less flexibility thanthe dual-medium approach to simulate matrix-fracture trans-fers. Actually, pseudo-parameters, especially pseudo relativepermeabilities (kr), have to be assigned to the cells of the sin-gle-porosity model in order to represent both the large-scalefluid transport in the fractures and the local exchanges withthe matrix medium. Except in extreme situations (Van Lingenet al., 2001), pseudo-parameters can hardly be determined asthey depend on all factors controlling matrix-fractureexchanges which, in addition, are history-dependent. Such dif-ficulties constitute one of the main reasons justifying thechoice of a dual-porosity simulation approach, which will alsobe a dual-permeability approach if large-scale matrix flowshave to be simulated.

Thanks to a separate representation of flows taking place ineach medium, the dual-porosity concept enables a better under-standing and simulation of flow interactions between contrast-ed media. However, one major difficulty remains, whichconcerns the formulation of multiphase matrix-fracture trans-fers because matrix blocks are generally not discretized in such

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Figure 6 Turning the geological fault-fracture model into adual-porosity flow model: upscaling fracture network flowproperties - populating the full field dual-medium modelwith flow-equivalent parameters.

Figure 7 Coupling explicit and dual-porosity models formulti-scale fractured reservoir simulation.

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models. Two constraints have to be satisfied, in priority the pre-diction of the final equilibrium of matrix blocks in terms ofpressure, saturation, and composition, and also a satisfactoryprediction of the transient states of the matrix block if transfersare delayed compared to the transport phenomena taking placein the fracture medium. Until now, most proposed solutions tosimulate multiphase transfers is through the use of modifiedforms of the Pseudo-Steady-State (PSS) equation that was pro-posed by Warren and Root (1963) to interpret the wellborepressures recorded during transient well tests of a fracturedreservoir. This equation simply assumes a linear relationshipbetween the overall matrix-fracture flux per unit volume ofmatrix, q, to the pressure difference, pm - pf , between matrixand fracture media modelled as two continua, that is:

(1)

where km is the matrix single-phase permeability, µ the fluidviscosity and s the well-known shape factor accounting formatrix block dimensions and shape.

Modified forms of this PSS equation involve variousshape factor expressions and/or tuned multiphase pseudo-functions however their range of validity remains most oftenrestricted to the reservoir parameters and multiphase flowmechanisms and history under consideration. Actually, mul-tiphase flow situations (Figure 8) involve ‘directional’ mech-anisms, gravity forces at first and also viscous drive due tofracture flows in fractured media with low matrix-to-frac-ture permeability contrast, which combine their effects with‘diffusive’ mechanisms, like capillarity, pressure diffusivity,sometimes also molecular diffusion and/or heat conduction.Furthermore, the thermodynamical coupling between phaseshas to be taken into account in compositional gas-oilprocesses involving swelling or vaporisation of the matrix oilphase.

Being aware of this complexity, our preferred approach(Quandalle and Sabathier, 1987) implemented in our reservoirsimulation software, consists in splitting the matrix-fracturetransfer into the contributions of each involved physical mech-anism, and assigning them scaling factors.

That is, the matrix-fracture transfer flux of a given phase pis expressed at cell scale as:

(2)

with DX,DY,DZ the cell dimensions, li (lx, ly, lz) the lateraldimensions of the equivalent parallelepiped matrix block, Ai thecross-section area of each of the 6 matrix block lateral faces i (i=x-, x+, y- y+, z-, z+) and λi

p specific phase mobility function. It is worth mentioning that this formulation does not require

any shape factor input but directly incorporates the equivalentmatrix block dimensions determined at cell scale from geologi-cal discrete fracture network images.

∆Φ ip represents the potential difference, in phase p across

exchange face i, between fracture and the representative matrixblock of the cell:

(3)

where Dp is the matrix-fracture pressure difference in a givenreference phase and Dpcp the capillary pressure differencebetween both media. Gi (i= z-, z+) represents an averagevalue of the gravity head applied on the matrix block anddpf the viscous pressure drop applied on the block in thedirection considered. Ccp, Cgp and Cvp are scaling factorsreferring respectively to capillarity, gravity and viscous flowmechanisms. By setting those scaling factors to 0 or 1, onecan assess the role of capillarity, gravity and viscous drivein matrix-fracture exchanges. In addition, for typical trans-fers governed by capillary and gravity forces alone, the scal-ing factors can be expressed analytically in order to satisfythe vertical equilibrium of fluids at the end of transfer(Sabathier et al., 1998).

Applying our workflow to the field example consideredhere, a 20-year water injection history was simulated on thefield sector shown in Figure 9. For injectivity/productivitypurposes, both vertical injection and production wells arecompleted in the mostly-fractured middle reservoir unit.Note the presence of numerous faults in this field sector,but located at a certain distance from each well. Water sat-uration maps of the fault/fracture grid after two and 10years of injection show that the highly-conductive fault sys-tem is rapidly invaded by water via the diffuse fracture net-work. However, diffuse fractures themselves remain at anintermediate water saturation level during several yearsbecause of the oil transfer from the matrix medium to frac-tures that occurs gradually with time.

Challenges. Despite recent progress made to simulatecomplex transfers, in particular multiphase compositionalones (Lacroix et al., 2004), the prediction of matrix-frac-

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Figure 8 Different types of physical mechanisms involved inmatrix-fracture transfers.

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ture transfers in field flow simulators remains an openproblem because it involves unsolved up-scaling problemsat the matrix block scale. Methods involving a local-scalemodelling of transfers on discretised matrix blocks (Famyet al., 2005) are worth being reconsidered as the ever-increasing capacity of computers offers enlarged calcula-tion possibilities.

The near future: further integrationThe availability of methods and tools to turn geologicalfracture models into consistent flow models opens the wayfor further integration of static and dynamic modellingsteps. The methodology consists in directly calibrating thegeological fracture/fault models to flow data (Jenni et al.,2004). Indeed, most often in practice, many parameters ofthe geological model are poorly defined.

This is, for instance, the case of the locations and lengthsof sub-seismic faults. Hence, the resulting field flow modeldoes not generally reproduce the observed dynamic data.

The multiple adjustments of the geological model bytrial and error and the subsequent rebuilding of the fieldflow model are hardly practical.

With the proposed methodology, the position and/orconductive properties of the stochastically-generated faultscan be gradually altered within a history matching proce-dure involving multiphase flow simulations on the geology-inherited field flow models.

Thus, the geologist and the reservoir engineer can effec-tively integrate, in a consistent manner, the geologicalobservations and the flow data into a unified model. Thismethodology constitutes a major progress in terms of inte-gration, because the geological modelling of fractures isnow driven by the field dynamic behaviour.

The key for integrating the previously-reviewed modellingsteps is the capability to gradually alter the poorly-definedproperties or the location of geological objects like faults whilerespecting other well-defined parameters of the geological/geo-statistical model (Hu, 2000).

ConclusionsThanks to the recent development of integrated and flexi-ble modelling methods and software, an integrated work-flow can now be implemented to model naturally-fracturedreservoirs, starting with the geological analysis of fracturesand ending with the reservoir simulation of multiphase pro-duction profiles. The development of hydraulic characteri-zation tools and of reliable upscaling methods based ongeological DFN models was a major breakthrough thatenabled the effective integration of geosciences and reser-voir engineering. The consistency between geological/staticobservations and flow/dynamic data can thus be preserved.

The implementation of such a workflow takes benefitfrom all the observations and measurements that are avail-able to assess the presence of fractures and their impact onproduction. The approach is all the more rewarding asavailable fracture-related data are abundant, of comple-mentary nature and well distributed over the field. At thesame time, the larger the amount of data, the higher the com-plexity of the data integration and reconciliation process.

Therefore, both the availability of fracture-relatedinformation and the capability to integrate diverse datasources remain challenges for a more widespread adop-tion of integrated workflows in fractured reservoir stud-ies. In that respect, a significant progress is expected inthe coming years from:■ additional fault/fracture modelling constraints derived

from geomechanical concepts and from 3D/4D seismicsurveys designed for fracture characterization;

■ an improved reliability of field-scale flow simulatorsthrough the proper integration of multi-scale flow hetero-geneities by means of mixed models coupling discrete andhomogenized representations of geological fault/fractureobjects;

■ and also, the capability to drive the geological modellingof faults and fractures by efficient flow history matchingprocedures.

Hopefully, the development of flow-constrained geologicalmodelling techniques in the near future will further recon-cile the geoscientist and reservoir engineer representationsof fractured reservoirs, and thus reduce prediction modelsuncertainty for the sake of optimised productivity andreserves.

ReferencesBarenblatt, G.I., Zheltov, Iu P., and Kochina I.N. [1960] BasicConcepts in the Theory of Seepage of Homogeneous Liquidsin Fissured Rocks, J. Appl. Math, 24, 1286.

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Figure 9 Simulation of water injection on the dual-mediumflow model of a field sector.

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Basquet, R., Jeannin, L., Lange, A., Bourbiaux, B., andSarda. S. [2004] Gas-Flow Simulation in Discrete Fracture-Network Models, SPE Reservoir Evaluation & Engineering,October, 378-384.Bourbiaux, B., Cacas, M.C., Sarda, S., and Sabathier, J.C.[1998] A Rapid and Efficient Methodology to ConvertFractured Reservoir Images into a Dual-Porosity Model.Revue de l’Institut Français du Pétrole, 53, 6, Nov-Dec,758-799.Bourbiaux, B., Basquet, R., Cacas, M.C., Daniel, J.M., andSarda, S. [2002] An Integrated Workflow to Account forMulti-Scale Fractures in Reservoir Simulation Models:Implementation and Benefits. Paper SPE No 78489, pre-sented at the 10th ADIPEC, Abu Dhabi, Oct. 13-16.Cacas, M.C., Daniel, J.M., and Letouzey, J. [2001] NestedGeological Modelling of Naturally Fractured Reservoirs.Petroleum Geoscience, 7, S43-S52.Cosentino, L., Coury, Y., Daniel, J.M., Manceau, E.,Ravenne, C., Van Lingen, P., Cole, J., and Sengul, M.[2001] Integrated Study of a Fractured Middle EastReservoir with Stratiform Super-K Intervals - Part 2:Upscaling and Dual Media Simulation. Paper SPE 68184presented at the Middle East Oil Show, Bahrain, 17-20March.Daniel, J.M. [2004] See http://www.ifp.fr/IFP/en/researchindustry/explorationreservoir/Facet4D.htm.Famy, C., Bourbiaux, B., and M. Quintard [2005] AccurateModelling of Matrix-Fracture Transfers in Dual-PorosityModels: optimal sub-gridding of matrix blocks. Paper SPE93115 presented at the SPE Reservoir SimulationSymposium, Houston, 31 Jan-2 Feb.Henn, N., Quintard, M., Bourbiaux, B., and Sakthikumar,S. [2004] Modelling of Conductive Faults With aMultiscale Approach. Oil & Gas Science and Technology –Rev. IFP. 59, 2, 197-214.Hu, L.Y. [2000] Gradual Deformation and IterativeCalibration of Gaussian-Related Stochastic Models. Math.Geol., 32, 1.Jenni, S., Hu, L.Y., Basquet, R., de Marsily, G., andBourbiaux, B. [2004] History Matching of StochasticModels of Field-Scale Fractures: Methodology and CaseStudy. Paper SPE 90020 presented at the SPE Ann. Tech.Conf. & Exh., Houston, 26-29 September.See also: http://www.ifp.fr/IFP/en/researchindustry/explorationreservoir/Calfrac.htm.Lacroix, S., Delaplace, Ph., Bourbiaux, B., and Foulon, D.[2004] Simulation of Air Injection in Light-Oil FracturedReservoirs: Setting-Up a Predictive Dual-Porosity Model.Paper SPE 89931 presented at the SPE Ann. Tech. Conf. &Exh., Houston, 26-29 September.Lange, A., Basquet, R., and Bourbiaux, B. [2004]Hydraulic Characterization of Faults and Fractures Using aDual Medium Discrete Fracture Network Simulator. PaperSPE 88675 presented at the 11th ADIPEC, Abu Dhabi, 10-13 October.

Quandalle, Ph., and Sabathier, J.C. [1987] Typical Featuresof a New Multipurpose Reservoir Simulator. Paper SPE16007 presented at the 9th SPE Reservoir SimulationSymposium, San Antonio, Tx, 1-4 Feb.Rasolofosaon, P.N.J. [2005] Fracture characterization in anAlgerian gas reservoir using seismic azimuthal anisotropy.Presented at the 2nd North African/Mediterranean Petroleum &Geosciences Conference and Exhibition, Algiers, 10-13 April.See also http://www.ifp.fr/IFP/en/researchindustry/explo-rationreservoir/FracAnis.htm.Sabathier, J.C., Bourbiaux, B., Cacas, M.C., and Sarda, S.[1998] A New Approach of Fractured Reservoirs. PaperSPE 39825 presented at the SPE Int. Pet. Conf. & Exh.,Villahermosa, Mexico, 3-5 March.Sarda, S., Jeannin, L., Basquet, R., and Bourbiaux, B.[2002] Hydraulic Characterization of Fractured Reservoirs:Simulation on Discrete Fracture Models. SPE FormationEvaluation, April.Van Lingen, P., Daniel, J.M., Cosentino, L., and Sengul, M.[2001] Single Medium Simulation of Reservoirs withConductive Faults and Fractures. Paper SPE 68165 present-ed at the Middle East Oil Show, Bahrain, 17-20 March.Warren, J.E. and Root, P.J. [1963] The Behavior ofNaturally Fractured Reservoirs. SPE Journal, Sept, 245-255.

first break volume 23, September 2005