Stratigraphic Well Correlations

AUTHORS

Jean R. F. Borgomano � Laboratoire deGeologie des Systemes et des Reservoirs Car-bonates, case 67, Universite de Provence, 3,Place Victor Hugo, F-13331 Marseille Cedex 03,France; [email protected]

Jean Borgomano obtained a Ph.D. in carbonategeology in 1987 from the University of Provencein Marseilles, France. In 1988–2003, he workedat Shell as a senior carbonate geologist in vari-ous exploration and production Shell compa-nies. He is currently a professor at the Universityof Provence and the director of the Geologyof Carbonate Systems and Reservoirs Labora-tory. His research focuses on the geological char-acterization and numerical modeling of car-bonate reservoir architecture and properties.

Francois Fournier � Laboratoire de Geo-logie des Systemes et des Reservoirs Carbo-nates, case 67, Universite de Provence, 3, PlaceVictor Hugo, F-13331 Marseille Cedex 03,France; [email protected]

Francois Fournier received his M.Sc. degreesfrom the Nancy School of Mines, France, andfrom the Institut Francais du Petrole and a Ph.D.in carbonate sedimentology from the Univer-sity of Provence in Marseilles, France. Aftera short experience in oil companies as an ex-ploration geologist in France and Angola, hejoined the Geology of Carbonate Systems Labo-ratory, Marseilles, France, as a lecturer in 2005.His research focuses on the relationship be-tween sedimentology, diagenesis, and seismicreflections in carbonate reservoirs.

Sophie Viseur � Laboratoire de Geologiedes Systemes et des Reservoirs Carbonates,case 67, Universite de Provence, 3, Place VictorHugo, F-13331 Marseille Cedex 03, France;[email protected]

Sophie Viseur is a numerical geologist workingas a researcher at the University of Provence.She received her Ph.D. from the Nancy Schoolof Geology in 2001. Her primary interests arein geostatistics for channel simulations and theirapplication to hydrocarbon exploration andproduction. In recent years, she has worked indeveloping methods for the integration of out-crop data and geological concepts into 3-Dcarbonate architecture models.

Stratigraphic well correlationsfor 3-D static modeling ofcarbonate reservoirsJean R. F. Borgomano, Francois Fournier,Sophie Viseur, and Lex Rijkels

ABSTRACT

The principles and purposes of stratigraphic well correlationin carbonate sedimentary systems are defined and discussedwithin the context of static reservoir modeling. The challengeof well correlations is to relate the heterogeneities measuredat core and well scales to the spatial heterogeneities at reser-voir and flow unit scales. The introduction of a priori knowl-edge in the process of stratigraphic well correlation is criticalto support the stratigraphic rules and to establish a coherentgeological and petrophysical concept. The links between wellcorrelation and geostatistics are discussed with regard to thestationarity hypothesis and property trend analysis. We stressthat wells are incomplete and biased samples of the geologicalreality, which is not dependent, unlike the dynamic reservoirbehavior, on the well numbers, location, and spacing. Strati-graphic rules are applied as a function of the well spacing rela-tive to the geological reality. A simple trigonometric method,combining angle of base profile, paleobathymetry, and wellspacing, is introduced to check the validity of the well cor-relation in carbonate ramp-like systems. Two models, basedrespectively on outcrop and subsurface with seismic data, arediscussed in detail to show the combined influence of the dataset, sedimentary systems, and diagenetic transformations onstratigraphic well correlations.

INTRODUCTION

This article discusses the principles of stratigraphic well cor-relations that form the foundation of most carbonate reser-voir models used in hydrocarbon flow simulations. The poor

AAPG Bulletin, v. 92, no. 6 (June 2008), pp. 789–824 789

Copyright #2008. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received July 13, 2007; provisional acceptance November 7, 2007; revised manuscriptreceived January 14, 2008; final acceptance February 21, 2008.DOI:10.1306/02210807078

reputation of carbonate reservoirs in term of flow predictabil-ity is directly proportional to the expectation that these reser-voir units behave like flowunits, asmost siliciclastic reservoirs.However, in carbonate reservoirs, the spatial correlations be-tween reservoir units and flow units (Amaefule et al., 1993)are commonly weaker than in siliciclastic reservoirs. Complexdiagenetic transformations and capillary forces are possiblecauses of these weaker spatial correlations (Figure 1). In addi-tion, the high degree of heterogeneity of carbonate rock prop-erties at all scales, as measured on well logs and core samples,for example, leads generally to the realization of subsurfacemodels characterized by a high-frequency variability that can-not be predicted nor correlated in the space between wells.The challenge in carbonate reservoir modeling is to relatethe heterogeneities measured at core and well scales to thespatial heterogeneities at reservoir and flow unit scales. Wellcorrelations and seismic data are the only possible links be-tween these two scales. The relevance of chronostratigraphicalwell correlations for siliciclastic reservoir modeling purposeshas already been discussed by Ainsworth et al. (1999). Thedeterministic method of correlating stratigraphic markers be-tween production wells implies spatial correlations betweenwell and seismic data and has an equal influence on the three-dimensional (3-D) reservoir rock property model and the seis-mic and geostatistic modeling methods. The intrinsic complex-ity of the carbonate reservoir at all scales (from pore networkto stratigraphic architectures) makes it necessary to concen-trate stratigraphic well correlation efforts on the level of res-ervoir heterogeneity, which matters in terms of reservoir andflow units.

The main objectives of this article are to (1) review the pro-cesses of stratigraphic well correlation in carbonate reservoirs,(2) discuss its impact on reservoir and flow unit modeling, and(3) present some recommendations adapted to specific strat-igraphic systems and reservoirs.

WHY CORRELATE WELL DATA?

Short-range variability has very limited influence on the over-all flow pattern (Jennings, 2000). Fluid displacement frontstend to follow the larger scale structures, such as strata and

sedimentary bodies, whereas small-scale heterogeneity, suchas pore networks, rock textures, and sedimentary structures,only smears the front of the flow. Such principles also holdwhen the short-range permeability variation is much largerthan the changes of the average permeability of larger scale

Lex Rijkels � Mærsk Olie og Gas AS, Espla-naden 50, DK-1263 København K, Denmark;[email protected]

Lex Rijkels is a reservoir engineer with MaerskOil in Copenhagen. He is interested in linkingfield development decisions to the resolutionof geostatistical and production data. He hasworked on fractured and carbonate reservoirs,faulted fluvial sandstones, tight gas-condensatechalks, and a range of primary to tertiary re-covery developments. He started his career atShell on the Carbonate Team and on a businessunit in Damascus.

ACKNOWLEDGEMENTS

The idea of this article was initiated during areservoir characterization project at Shell Re-search in 2000. It significantly benefited fromstimulating discussions with many staff memberson the Shell Carbonate Team and operationalbusiness units during the 2000–2001 period.We specially thank Cathy Hollis from the ShellCarbonate Team who gave constructive sug-gestions for the improvement of the manu-script. We thank Jean-Pierre and MuggetMasse from the University of Provence whocontributed to some outcrop mapping andLudovic Laugero who helped in finalizing thedrawings.

790 Well Correlations in Carbonates

structures. Jennings’ (2000) considerationswere inlinewithAraktingi andOrr (1993),whoalso studiedthe effect of heterogeneity on flow, for differentmobility ratios. They found that the difference influid mobility during water flooding may causefingering at lowheterogeneity, but that the viscousbypassing of oil becomes much less important formore heterogeneous samples. As a consequence, tounderstand the flowbehavior at the interwell scale,

one needs to identify the structures that are corre-latable betweenwells. Anything smaller than thosestructures is averaged out into the permeability ofthe correlatable units. This does not imply that onecan ignore all the detail below this scale.One needsa reliable measure of the permeability statisticswithin each unit to identify the representative aver-age properties. However, constructing a geologicalmodel at the smallest scale is not always necessary.

Figure 1. Comparison between flow units and reservoir units in carbonate and siliclastic marine sequences. Siliciclastic sedimentarysequences are characterized by simple correlations between grain size, mineralogy, porosity, and permeability. Rock properties can bedetected and correlated to stratigraphic sequences allowing the characterization of reservoir and flow units. These relationships aremore complex or nonexistent in carbonate sequences characterized by a high level of rock property heterogeneity. OWC = oil-watercontact.

Borgomano et al. 791

In principle, one should aim to construct the archi-tecture of the model at the scale of the correlatedstructures between wells and to use the measure-ment statistics made on smaller scales (e.g., coreplugs) for each structures. Very thin units (<1 m,3 ft) associated to extremepermeability values (highor low) can be retained in the model, provided theyare correlated between wells and can form flow con-duits or flow barriers.

In an ideal case, let us assume that the rockproperties are measured in all available wells withmaximum resolution and precision. These are theonly direct measurements of the subsurface realityand are the foundations of the static or dynamicreservoir modeling and subsequent field develop-ment planning. With the exception of a dynamicwell test and production data that can give infor-mation on larger volumes of reservoir rock, awayfrom the borehole, thewell data only represent therock volume sampled within the bore hole. Thisvolume,which varies according to themeasurementmethods and the down-hole tools, is limited to theborehole (cores) and near borehole space (logs),representing a minute part of the reservoir rockvolume. To achieve a complete 3-Dnumericalmod-el of the reservoir parameters, all the available welldata are necessarily interpolated and extrapolated(Figure 2). This is justified because the dynamicbehavior of the reservoir ismainly controlled by thenonsampled rock volumes between thewells. In thecases of numerical modeling of sedimentary reser-voir rocks, the ultimate objective of stratigraphicwell correlations is to support the mathematical in-filling (or modeling) of the undrilled space betweenthe wells with realistic rock properties (Bashoreand Araktingi, 1994). The common mathematicalmethods used to infill the interwell space can begrouped under the general term of ‘‘geostatistics,’’which aims to characterize the intrinsic structure ofthe properties, allowing themodeling of reality andquantification of themodel uncertainty (Matheron,1989;Deutsch, 2002).Most of the geostatisticmeth-ods applied in oil industry are based on the station-arity hypothesis, which assumes that the processescontrolling the distribution of any rock propertiesare independent of space and time (Carle and Fogg,1996, 1997). This convenient mathematical as-

sumption is generally too simple to explain real-world processes (Coulibaly and Baldwin, 2005) andespecially in carbonate sedimentary systems, whichare driven by dynamic and interdependent geneticprocesses (biological, physical, and chemical) thatvary in time and space at all scales (Wilson, 1975;Schlager, 1999).Nonstationarymathematicalmeth-ods (Prokophi and Barthelmes, 1996) such as wave-let analysis or Fourier transforms are valid for theanalysis of the geological time series but are notadapted to spatial modeling of carbonate rock prop-erties from well data. The common and rather in-tuitive practice in the carbonate reservoir modelingworkflow (Figures 2, 3) is to increase the stationarynature of the systems (Bashore andAraktingi, 1994;Aitken and Howell, 1996; Weissmann and Fogg,1999; Ravenne, 2002; Tinker et al., 2004) by therealization of a stratigraphic framework based onthe well correlation. The main goal of the well cor-relation process is therefore to distinguish, at rel-evant scales, the correlatable from the noncorre-latable heterogeneities in space and to create subsetsof data in which stationary geostatistic methods canbe applied.

The key question is, therefore, What are thevalidwell correlationmethods to support themod-eling of the undrilled space at the relevant scales?This question needs to be answered within the con-text of the reservoir modeling workflow (Figure 3)and relative to the objectives of the reservoirmodel;for example, the estimation of the volume of thehydrocarbon in placewill favor themodeling of thereservoir units, whereas the planning of water-wellinjectorswill require themodeling of the flowunits.Dynamic simulation of hydrocarbon productionwill in general require the integration of reservoirunits (initial conditions) and flow units (productionbehavior).

A general carbonate staticmodelingworkflow,used for the Malampaya field in the Philippines(Neuhaus et al., 2004; Fournier and Borgomano,2007), is summarized in Figure 3. This workflowis a sequential and iterative workflow, where criticaldata are used for two main purposes: (1) establish-ment of a priori knowledge and geological conceptsand (2) input to the numerical reservoir modeling.The geological andpetrophysical concepts are used


to model the geobodies on the basis of determin-istic well correlation and seismic horizon interpre-tation. Specific facies are attributed to the geobodiesto condition the property simulation. The porosity

simulation results from a Bayesian mathematicalmethod (Omre and Halvorsen, 1989) that com-bined kriging (cokriging) of well and seismic po-rosity within the stratigraphic framework. Other

Figure 2. Typical reservoir modeling workflow applied in the petroleum industry (modified from Ravenne, 2002; reprinted by permissionof Institut Francais du Petrole). Well and seismic data are integrated in the first step of the workflow allowing the sequential realizationof facies and rock property models in 3-D. Stratigraphic well correlations are inferred but not explicit in this workflow.


methods integrating the seismic data such as col-located cokriging have also been tested (Xu et al.,1992). Background permeability is derived from theporosity cube, using poroperm transforms, whereasextreme permeability values (very high and very

low) are attributed to discrete geobodies. Propertycubes are exported to the dynamic simulator andare used as an input to the volumetric calculations.Note that this workflow is not integrating produc-tion data because the gas production had not yet

Figure 3. Reservoir modeling workflow integrating stratigraphic well correlation, seismic interpretation, and a priori geologicalknowledge in the third step of the workflow on the basis of a geological-petrophysical concept established by combining data analysisand a priori knowledge.


started at the time of the studies. In this carbonatereservoir modeling workflow, like in many othercases (see, among others, Kerans andTinker, 1997),stratigraphic well correlation is an early process inthe development of a field, on which the model-ing workflow is founded. Homewood et al. (1992)correctly stated that it is a critical working processthat deserves to be formalized within the contextof modeling carbonate sedimentary systems.

DEFINITION OF STRATIGRAPHICWELL CORRELATION

In practice, correlating well data in the subsurface(Figures 4, 5) consists of a combination of subjec-tive and objective processes based on stratigraphicanalyses, interpretations, and assumptions thatcan lead to a reservoir model with hidden uncer-tainties. Avoiding a common misunderstanding insubsurface geosciences concerning the stratigraph-

ic methods used with well data is important. Todate, the primary focus of geologists has been thechoice between sequence stratigraphy and litho-stratigraphy (chronostratigraphy, biostratigraphy,cyclostratigraphy, and chemiostratigraphy can alsobe considered), whereas the basic objective of wellcorrelation is mostly ignored and not well under-stood. When describing strata (drawing strata) oncontinuous outcrops and seismic data, all these strat-igraphic methods are valid and can be used in com-bination or alone depending on the objective of thestudy. Sequence stratigraphy is the stratigraphy ofthe depositional sequences, whereas lithostrati-graphy is the stratigraphy of the lithological units,chronostratigraphy is the stratigraphy of the timeunits, etc. In this respect, the process of well corre-lation in reservoir modeling is not a stratigraphicmethod sensu stricto (as opposed to seismostratig-raphy) but a deterministic interpolation methodbetween specific data points that are separated byvariable distance in 3-D (along the borehole andbetween thewells). These points, stratigraphicwellmarkers, deterministically selected along the bore-hole represent the intersection between the welltrajectory and possible 3-D stratigraphic envelopes.Because the ultimate objective of well correlation

in reservoir modeling is not to infill the interwellspace with sequences, lithologies, or times but toconstrain in 3-D the petrophysical and dynamicmodeling, the question is, therefore, What is themost reliable method to establish 3-D stratigraphicenvelopes and corresponding bodies from wells? Itcan be based on various correlation methods, suchas sequence stratigraphy, lithostratigraphy, chemio-stratigraphy, and biostratigraphy supported by theinterpretation of seismic reflectors.

SPATIAL RELATIONS BETWEENROCK PROPERTIES ANDSTRATIGRAPHIC CORRELATIONS

Before correlating wells, defining the degree of spa-tial relation between rock properties and possiblestratigraphic architectures (Figures 6, 7) as illus-trated is important, for example, in the cases of the

Malampaya field (Fournier and Borgomano, 2007),the Al Ghubar field (Smith et al., 2003), and theFahud field (Morettini et al., 2005). This is not aneasy task because the wells, in addition to their lat-eral spacing, sample the rock in one direction, intro-ducing a significant bias. A stepwise petrophysicalanalysis of the well data (Asquith, 1985) is recom-mended to establish the spatial relationships be-tween rock properties and stratigraphic architec-tures. This process includes geostatistical analyseswith several iterations based on various well corre-lation scenarios (stratigraphic, diagenetic, and struc-tural) and the introduction of a priori knowledgefrom analogs (Figure 3). At a higher hierarchicallevel, it can be considered that the distribution ofrock properties in most carbonate reservoirs is ei-ther conformable or not conformable to the sedi-mentary facies and the stratigraphic units (geneticstratigraphic units, sensu Homewood and Eberli,2000). In the conformable cases, the diagenetictransformations (from early to late and from shal-low to burial) overprint the stratigraphic architec-ture and the sedimentary facies, whereas the non-conformable cases are characterized by diagenetictransformations cutting through the stratigraphicarchitecture and the sedimentary facies, in rela-tion to fractures (Stearns and Friedman, 1972),


unconformities (Budd et al., 1995), depth trends(Ehrenberg and Nadeau, 2005), or karsts (JamesandChoquette, 1988). Distinguishing the two casesis critical, especially if they coexist in a single car-bonate reservoir. In this process, the early identifi-cation of genetic and spatial hierarchies is very im-portant where the two systems are mixed and notclearly stratified. One of the biggest sources of error

in 3-D modeling of rock properties is the early in-troduction in theworkflowof unrealistic stratigraph-ic well correlations not conforming to the diagenetictransformations and subsequent property distri-bution. Another common error is assuming thatdiagenetic transformations (and properties) con-form to the stratigraphic architectures and sedi-mentary facies at all scales and hierarchical levels.

Figure 4. Example oflayer-cake reservoir units(A, B, and C) in a giantcarbonate field in theMiddle East. (A) Log-based stratigraphic wellcorrelation of the mainlithostratigraphic unitsformed by alternatingporous limestones withlow gamma ray anddenser argillaceous lime-stones with higher gam-ma ray (from Alsharhan,1993; reprinted with per-mission from AAPG).(B) Cross-section show-ing the porosity modelbased on well and seismicdata (from Melville et al.,2004; reprinted by per-mission of the AAPGwhose permission is re-quired for further use).The tops of the reservoirunits A, B, and C corre-spond to seismic reflec-tors that allow a coherentstructural model of thereservoir throughout theentire structure. GR =gamma ray, N = neutron,OWC = oil-water contact.


Figure 5. Exampleof layer-cake flow unitsand mechanical units ina giant carbonate field(Fahud) in theMiddle East(modified from Morettiniet al., 2005). This figureshows how high-resolu-tion stratigraphical wellcorrelations (A) allow amechanical stratigraphicunit model to be estab-lished and implemented inthe static reservoir model(B) prior to flow simula-tion. (A) Log-based wellcorrelation of 3rd- and4th-order stratigraphicsequences that are inter-preted to control the flowunit architecture of thisfield on the basis of coreand well test analyses.Core and well analysesallow a concept of frac-ture distribution to beestablished in relation tothe stratigraphical se-quences. (B) The bed-bounded fracture modelof this reservoir is built onthe basis of the strati-graphic well correlationof the mechanical units.In this case, the regres-sive sequences are usedto populate the fracturesin the property model.Fractures are not associ-ated with transgressive se-quences (reproduced bypermission of GeoArabia).


GEOSTATISTICS AND WELL CORRELATIONS

As introduced above, the process of stratigraphicwell correlations must be supported by spatial sta-tistic analysis of rock properties (Sonnenfeld and

Cross, 1993; Pranter et al., 2004). The purpose isto identify and measure the property anisotropyand the spatial correlation between the data andpossible stratigraphic correlations (Goovaerts, 1997;Jennings, 2000;Gringarten andDeutsch, 2001). In

Figure 6. (A) Depth (in meters subsea) of the top Nido Limestone and location of wells Malampaya-1 (MA-1), Malampaya-2 (MA-2),Malampaya-5 (MA-5), and Malampaya-7 (MA-7). (B) Histograms of porosity (from well logs) within the SM2 sequence showingthe eastward lateral increase in porosity. (C) Correlation panel of depositional sequences and seismodiagenetic units between wellsMalampaya-1, Malampaya-5, and Malampaya-7, showing the eastward pinch-out of the SM2-IIIb tight unit (modified from Fournier andBorgomano, 2007; reprinted by permission of the AAPG whose permission is required for further use).


Figure 7. Spatial correlation betweenstratigraphic units and permeability inaMiddle East Cretaceous reservoir formedby carbonate platform deposits. Perme-ability data from 65 cores taken fromthe same reservoir unit throughout theentire field are depth-plotted relativeto a stratigraphic datum (the uppermostsequence boundary). The averagedthickness of the stratigraphic sequences(4th orders) and the lithostratigraphicunits interpreted from the cores areplotted on the right of the graph (A). Thevertical permeability trend is shown bythe variogram (B). Despite the difficultyto interpret it relative to the stratigraphicsequence, such a permeability trend hasto be taken into account in the strati-graphic well correlation process especiallyif the objective is to model the flow units.


fact, it allows the verification of the stationarity orthe nonstationarity of the inferred geological pro-cesses that controlled the reservoir rock properties.A typical inconsistency observed in carbonate reser-voir modeling is introducedwhere 3-D distributionproperties are controlled by diagenetic transforma-tions cutting through the sedimentary stratigraph-ic architecture (Fournier and Borgomano, 2007).Without accounting for this diagenetic control, thestratigraphic correlations result in unrealistic rockpropertymodeling. The idea is to establish a strati-graphic scenario that considers the spatial correla-tions between property and strata at specific scales,from the core plugs to the well interval. Commongeostatistic libraries such as the Geostatistical Soft-ware Library (GSLIB) (Deutsch and Journel, 1998)allow such analysis inmost commercial geomodelingsoftwares (Mallet, 2002). Trend analysis (variationas a function of direction, distance, and position) canhelp to establish the most valid correlation at theright scale and account for the nonstationarity of thegeological process. In carbonates, it is frequent toobserve vertical property trends relative to a strati-graphic datum (exposure surface, sequence bound-ary) (Figures 7, 8). Simple vertical variogram analysisandmoving averages canhelp to identify such trendsthat can deterministically influence the well corre-lations. Nonspatial and spatial correlations betweena primary continuous variable (permeability, poros-ity,. . .) and a secondary discrete variable (texture,grain size, facies,. . .), or two continuous variables(porosity and permeability) can also be addressedprior to the well correlation. Transition probabil-ities between facies (Weissmann and Fogg, 1999)can also be investigated within correlated deposi-tional sequences (Posamentier et al., 1988). Thisinitial statistical analysis is critical for the 3-Dperme-ability modeling and upscaling, which are the mostchallenging and uncertain processes in carbonatereservoir modeling for the four following reasons:(1) permeability is a tensor (not a scalar number),(2) its detection with seismic and log data is notaccurate, (3) averaging permeability (from core togrid cells) is problematic because of significant sup-port effects in relation to themultiscale heterogene-ities (core plug towell tests), and (4) the relationshipbetween porosity and permeability is nonlinear in

most carbonate reservoirs and interpolating perme-ability (i.e., kriging) fromwell data results common-ly in unrealistic and smooth realizations (Matheron,1989; Araktingi and Bashore, 1992; Bashore andAraktingi, 1994). In this respect, the early identi-fication of spatial correlation between permeabil-ity and strata or trend can be taken into account inthe correlation scenario. In carbonate reservoirmod-eling, it must be realized that well correlations canhave a greater impact on a 3-Dpermeabilitymodelthan on a 3-D porosity model (Jennings, 2000).

OBJECTIVES OF RESERVOIR MODELING

The last statement introduces the importance ofdefining the objectives of the reservoir modelingprior to the well correlation process. A commonworst practice in the industry is that the technicalgoals of reservoir modeling do not direct the (com-monly time consuming) well correlation processdespite their significant impact on themodeling out-comes. Obtaining high-resolution stratigraphic cor-relations becomes the primary goal and the causesof many technical arguments among geologists.Two typicalmodeling strategies are discussed belowwith the caveat thatmany other practices andmeth-ods are appropriate for varying situations.

� Modeling reservoir units and porosity distribu-tion for hydrocarbon volumetric assessment orappraisal well planning is based on stratigraphicarchitectures established from seismic interpre-tation matched to the wells, such as illustratedin the examples of giant fields in theMiddle EastinFigure4 (Alsharhan, 1993) andFigure9 (Munnand Jubralla, 1987). Thewell correlation focuseson stratigraphic envelopes that aremeaningful atseismic scale and can condition the seismic in-version (Melville et al., 2004). Well correlationconsists of picking the well markers that sepa-rate rock units on the basis of porosity, acousticimpedance, and lithological contrasts (Figure 1).When these markers are correlated betweenwells and are matched to seismic reflectors overthe entire structure of the field, they correspondto the primary envelopes of the rock units that


characterize a field: reservoir units, waste zones,and seals (Roehl and Choquette, 1985; Jardineand Wilshart, 1987).

� Modeling flow units (Amaefule et al., 1993), tosupport field development, a water flood plan,for example, is based on 3-D high-resolution pe-trophysical modeling that is generally beyondseismic resolution (Morettini et al., 2005). Estab-lishing the degree of spatial correlation betweenseismic scale geobodies and potential flow units

(Araktingi and Bashore, 1992; Yao and Journel,2000; Fournier and Borgomano, 2007) is impor-tant; for instance, howdoes the permeability thatcontrols the well flow correlate to the acousticproperty detected in the seismic data? A com-mon error is to assume that the correlation be-tween these two parameters is high withoutproperly checking the relevant scales. Importantparameters inmodeling flowunits are the sweep-ing radius of each well and the communication

Figure 8. Sequence-stratigraphic correlations between two cored intervals in a carbonate reservoir formed by carbonate platformdeposits. The core-plug permeability and the pore types indicate that the three vertical permeability trends are overall correlated tothe three sequences that should be correlated between the wells. The stratigraphic correlation of the off-trend high permeabilityvalues (related to vugs) is, however, questionable: are they isolated and randomly distributed in space or are they representative ofhigh permeability thin beds? The answer might come from the detail analysis of many cores and will have a very high impact on theflow unit model. This virtual example shows the impact of stratigraphic well correlation on reservoir modeling.


between producing or injectorwells. Prior to thestratigraphic well correlations, the interpretermust identify the permeability trends and thelow-frequency spatial heterogeneities that are

correlatable between wells (Figure 8). Noncor-relatable, high-frequency spatial heterogeneitiesare in reality averaged out by the flow and donot affect the flow interference between wells

Figure 9. High-resolution stratigraphic correlations in the Bul Haninefield, Arab D member, Qatar (modified from Munn and Jubralla, 1987).This graph shows the spatial relationships, in a flat carbonate shelf systemsuch as the Arab D, between time lines and rock units. The two setsof correlations are overlapping or conformable with each other. Suchstratigraphic correlations will result in a stratified, layer-cake, reservoirmodel. The challenge will be to preserve in the dynamic model theextreme property values that are stratigraphicaly correlated and have thepotential to form barriers or conduits to flow. GR = gamma ray, FDC =density.


(Araktingi and Orr, 1993; Jennings, 2000). Acommonmistake is to force thewell stratigraphiccorrelations on the high-frequency variability thatis observed at well and core scales (in responseto local diagenetic transformations for example)but is not necessarily correlated between wells(Figure 8). This process will inevitably increasethe impact of the noise in the final numericalmodel (Coulibaly and Baldwin, 2005). The chal-lenge is, however, to link such high-frequencyvariability to genetic stratigraphicunits (sequences,sedimentary, or diagenetic bodies) that can be cor-related in space and to apply geostatistics tomodelthem within each unit. These static models arevery sensitive to well spacing; their dynamic sim-ulation allows the identification of the most effi-cient and economic well spacing according to thespatial heterogeneity and the fluid properties.

WHAT TO CORRELATE?

The previous paragraphs summarize the scope andmain objectives of the process of stratigraphic wellcorrelation that forms the foundation of manycarbonate reservoir models. It is therefore impor-tant to distinguish three main types of critical rock

units that coexist in each carbonate field and canbe correlated betweenwells: geological units, reser-voir units, and flow units. The degree of spatial cor-relations between these three units can range fromvery low to very high and from field to field (Roehland Choquette, 1985; Moore, 2001). A general butcritical observation is that reservoir units and flowunits always correspond to geological units but notnecessarily the same ones and not necessarily theones we interpret from the data set. The main pur-pose of this distinction is to focus the attention of theinterpreter on the fact that despite the high resolu-tion of the stratigraphic correlation scheme and thetime spent to achieve it, the result could well beuseless, or even worse, introduce major hidden er-rors regarding the 3-D property modeling and theflow simulation. A typical error is to assume thatthe 3-D distribution of porosity and permeabilityis exclusively related to stratigraphic sequences andsedimentary bodies, whereas, in reality, they cor-

relate to diagenetic transformations that more orless conform to the stratigraphy (Fournier and Bor-gomano, 2007). Typical mistakes include corre-lating noise and forcing stratigraphically valid, butunrealistic, from a well-spacing viewpoint, correla-tions. Such misunderstandings will have little im-pact on the initial hydrocarbon productions fromimmature assets but could have significant negativeconsequences on long-term field developments andultimate oil recovery from mature fields (Chilin-garian et al., 1992). During the initial phase of themodeling workflow (Figure 2), the interpretersmust distinguish the three main categories, geolog-ical unit, reservoir unit, and flow unit, according tothe available data set. It is, however, expected that,at an early stage of a field appraisal, when data arescarce and production has not yet started, they can-not be separated.

Geological Units

Generally, a geological unit (geobody) can be con-sidered as a volume of rock material bounded byenvelopes genetically related to a set of specific geo-logical processes. In general and in carbonate sys-tems in particular, they are not necessarily equiv-alent to units with specific reservoir propertiessuch as porosity, permeability, and elastic properties

(Figure 1). The body envelopes, which could corre-spond to genetic stratigraphic surfaces (HomewoodandEberli, 2000), are commonly pickedon the basisof well-log responses (Schlumberger, 1972, 1974;Asquith, 1985) and used as correlations betweenwells (Homewood et al., 1992; Sonnenfeld andCross, 1993). The relation between stratigraphy, es-pecially high-resolution sequence stratigraphy, andcarbonate geobody can be confusing, for example, ifthe geometry of the sedimentary, diagenetic, or rockproperty body does not conform to the time surfaces(Figure 10). Four main types of geological objectsare commonly correlated in carbonate reservoirs:

� Stratigraphic sequences: themost common geo-logical units that are correlated in carbonate fieldsare sequence-stratigraphic units formed by setsof various sedimentary and diagenetic objects,which are genetically related (Posamentier et al.,


1988; Sarg, 1988; Van Wagoner et al., 1988;Pomar, 1993; Schlager, 1999). They have to beinterpreted in a hierarchical system (2nd to 7thorders) and are topped by sequence boundaries,which are considered to be time surfaces (Vailet al., 1977) and therefore equivalent to paleo-sedimentary profiles. The sequence boundarieswill become an important parameter when ana-lyzing further the relationships between wellspacing and stratigraphic well correlations. Max-imum flooding surfaces can also be identifiedand correlated within the sequences. Sequence-

stratigraphic correlations are not too sensitive tofield-scale well spacing in the case of wide andflat sedimentary profiles (e.g., a carbonate shelf )such as the Natih Formation in the Middle East(Van Buchem et al., 2002) that is illustrated inthe well correlation of the Fahud field (Morettiniet al., 2005) (Figure 5). Similar considerationscan be applied to the Jurassic Arab Formation(Figure 9). In the case of fields located on gen-tle carbonate slopes, for example, around theLower Cretaceous Bab Basin in theMiddle East(Boote and Mou, 2003; Droste and Steewinkel,

Figure 10. Differenttypes of spatial correla-tions between correlatedtime lines and simplesedimentary objects. Thesedimentary objects aredefined by sharp (A) orgradual (B) facies changesthat are characterized bydifferent degrees of spa-tial correlation with thetime lines. Stratigraphicwell correlations of suchsedimentary objects willbe influenced by well lo-cations, well spacing, anda priori knowledge onthe objects. In both cases,the grainstone objects,which would be criticalfor the reservoir model,are not entirely conform-able with stratigraphicenvelopes.


2004), the well spacing will influence the wellcorrelation depending on the paleoslope anglethat controls the stacking of the stratigraphic se-quences (Figure 11).

� Sedimentary bodies: these bodies can be consid-ered as continuous volumes of carbonate sedi-

ments (biostrome, bioherm, bank, patch reef,channel, lobe, mound, dune,. . .), resulting froma single set of depositional processes (Borgomanoet al., 2001) occurring in specific environmentsof deposition (Scholle et al., 1983). In theory,their envelopes should represent time surfaces

Figure 11. Well corre-lations of reservoir unitsin Middle East Cretaceouscarbonate platform sys-tems, based on sequencestratigraphy. These cor-relations display low-angle paleotopographies(clinoforms) that can bevery critical for the dis-tribution of reservoirproperty at basin and res-ervoir scales. They arenot easy to pick in wellswithout integrating high-resolution sequence stra-tigraphy and seismostra-tigraphy. (A) The ShuaibaFormation in the Safahfield (modified from Booteand Mou, 2003; repro-duced by permission ofGeoArabia) and (B) theNatih formations (modi-fied from Droste andSteewinkel, 2004) in northOman. Such clinoformsrepresent progradingtrends expressing the lat-eral accretion throughtime of the platform sed-imentary profiles.


that can be correlated between wells within asequence-stratigraphic framework. Sedimentarybodies can also be formed by stacked diachronousdeposits of the same nature, which can be assem-bled into objects bounded by composite surfacesor gradual changes (Figure 10). Dimensions ofcarbonate sedimentary bodies, such as the Cre-taceous rudistid bodies common in Middle Eastreservoirs, vary significantly even in a single plat-form system depending on their environments ofdeposition (Borgomano, 2000; Borgomano et al.,2002). In this case, well correlations can be verysensitive to well spacing (Figure 12).

� Diagenetic bodies: these bodies can be consid-ered as volumes of carbonate rock material trans-formed or formed by diagenetic processes (ce-mentation, dissolution, recrystallization, anddolomitization) and confined to a discrete spatialentity (bed, lens, etc.) (Budd et al., 1995). Suchbodies can be defined by envelopes that can bepicked in the wells or by gradual changes moredifficult to correlate. Diagenetic bodies can con-form or not conform to sedimentary bodies de-pending on the types and timing of diagenetictransformations (see, for example, Fournier andBorgomano, 2007). It is therefore important toestablish the relationships between these twogenetic types of bodies when they coexist in asingle reservoir. Diagenetic bodies can also con-form to structural deformation (faults, fractures,and folds).

� Structural objects: these objects correspond tothe volume of rock bounded by the structuraldiscontinuity of tectonic origin such as faults orthrust planes. Carbonate reservoir architecturesbased on the well correlations of tectonic dis-continuities are rare.

Reservoir Units

Reservoir units in carbonate rocks correspond tostorage units characterized by specific porositiesand pore entry pressures that control the distri-bution of hydrocarbon within the trap (Chilingaret al., 1972; Jardine andWilshart, 1987; Roehl andChoquette, 1985; Chilingarian et al., 1992). Cap-illary or static seals formed by specific lithologies

such as shale, salt, anhydrite, and dense carbonatesbound the reservoir unit. Pore volume is the pri-mary parameter that controls porosity. Faults canalso provide effective seals. From a storage point ofview, the most complex carbonate oil fields canbe characterized by long transition zones, mul-tiple and tilted oil-water contacts, and vertical andhorizontal pressure compartments. The identifi-cation and mapping of such reservoir heterogene-ity at an early stage of the field development (basedon 3-D seismic data associated with appraisal wells)are the foundation of a successful economic devel-opment. This first level of heterogeneity controlsthe hydrocarbon volume in place in the carbonatefields but not necessarily the dynamic behaviorof the reservoir. In carbonate systems, hydrocar-bons are commonly stored in all the carbonaterock units (limestone and dolomite) indepen-dently of the grain size, unlike in siliciclastics res-ervoirs (Figure 1). For example, chalky reservoirswithmicroporosity are typical in carbonate petro-leum provinces as a result of favorable entry pres-sures and capillary forces. Interbedded noncarbon-ate units, such as salt, anhydrite, or shale, form thenonreservoir, the seal, or the waste zones. Corre-lating reservoir units in carbonate systems consistsgenerally of separating carbonate from noncarbo-nate units or porous from nonporous carbonates,using core and well logs (Asquith, 1985), withina consistent stratigraphic framework (Figures 4,5, 9, 11). In addition to noncarbonate units, well-cemented and nonporous carbonates can form non-reservoir units, which have to be discounted fromthe reservoir units. In giant carbonate fields, reser-voir units are generally easy to correlate betweenwells and to imagewith seismic reflection as conse-quences of their wide development at a regionalscale, combinedwith their significant rockpropertycontrastwith nonreservoir units (Eberli et al., 2004;Neuhaus et al., 2004; Fournier and Borgomano,2007).

Flow Units

A flow unit, or hydraulic flow unit (Ebanks, 1987;Amaefule et al., 1993), is defined as the represen-tative volume of total reservoir rock within which


geological properties that control fluid flow, fromthe reservoir into the wells, are internally con-sistent and predictably different from propertiesof other rocks. A flow unit is a discrete rock unitthat is in flow communication in a field with atleast onewell.Unlike reservoir units, flowunits haveno meaning as a subsurface object without phys-ical connection to wells (producers or injectors).Flow units can also vary according to the dynamic

conditions applied to the reservoir. Their geolog-ical properties are a function of pore geometry,pore throat, and pore distribution that are, in turn,controlled in carbonate rocks by the depositionaltexture, the grain mineralogy, and the diagenetictransformations. In this article, we restrict our defi-nition of flow units to units of ‘‘absolute perme-ability’’ defined as the permeability of a rock to afluid when the rock is 100% saturated with that

Figure 12. Spatial rela-tionships between welldistribution and sedimen-tary systems. Hydrocar-bon fields are generallysmaller than the entiresedimentary system.The well spacing, loca-tions, and numbers de-termine the samplingpattern of the facies het-erogeneity and determinethe stratigraphic rules ap-plied for the well correla-tions. If the well spacingis more than the averagedimensions of the sedi-mentary objects, only se-quence-stratigraphic cor-relations can be applied tocondition object-basedor pixel-based facies mod-els. If the well spacing isless than the average di-mensions of the sedimen-tary objects, sequence andlithostratigraphic correla-tions can be combined tocondition pixel-based fa-cies models.


fluid. In this manner, only rock properties are con-sidered to control the flow units. Instead of abso-lute permeability, it is possible to consider ‘‘effec-tive permeability,’’ defined as the ability of a rockto flow a particular fluid when another immisciblefluid is present in the pore space. Effective perme-ability, which is always less than the absolute per-meability, is therefore dependent of the pore satura-tion (oil and water), introducing a fluid componentto the definition of the flowunits. Effective perme-ability units might be investigated in case of a com-plex fluid distribution in the reservoir, especiallywhen gas, oil, andwater aremixed following a longperiod of production and reservoir stimulation (wa-ter flooding, gas injection, etc.).

The identification of flow units relies on thepermeability detection in the subsurface, which isvery limited and uncertain in carbonate systems forthe following reasons: (1) direct down-hole mea-surements of permeability (as a physical property)are not routinely acquired by logging tools, unlikeporosity or water saturation; only nuclear mag-netic resonance (NMR) logs proved to be success-ful in some sandstone reservoirs (Kenyon, 1997;Coates et al., 1999); (2) the seismic reflectionmeth-od is not capable of detecting permeability hetero-geneities, especially within carbonate rocks withhomogeneous porosity and acoustic impedance(Anselmetti and Eberli, 1993); (3) depending onthe depositional and diagenetic factors, flow unitscan be very thin (<0.5 m, 1.6 ft) compared to res-ervoir units (Lucia, 1995, 1999) and beyond seis-mic and log resolutions. In practice, it should beconcluded that seismic and logging methods donot allow the straightforward detection of per-meability and flow units in carbonate reservoirs.The only two methods supporting without equiv-ocation the detection of the permeability are(1) laboratory permeability measurements oncore samples and (2) well tests. In practice, flowunits will be assessed by an integrated petrophys-ical and geological numerical approach based ona core-calibrated petrophysical log evaluation, in-cluding borehole image, resistivity, NMR, and pro-duction tests. The spatial and genetic relation-ships between flow units and geological units mustbe established prior to attempting the well correla-

tions, especially in uncored wells (Morettini et al.,2005). A typical worst practice in the industry isto correlate directly flow units from well logs, asstratigraphic units, without integrating all the prev-ious data. Figure 8 shows an example of flow unitcorrelations based on core data. In this syntheticexample, only the vertical permeability trends, cor-responding to the stratigraphic sequences, havebeen correlated.

WELL SPACINGS ANDSTRATIGRAPHIC CORRELATION

The ultimate objective of stratigraphic well corre-lation is to support and condition rock propertymodeling for simulation and prediction of fluidflow in hydrocarbon fields. One of the most funda-mentals laws of hydrocarbon reservoir engineer-ing is the famousDarcy law that clearly states thatspatial dimensions are critical parameters of thefluid dynamics in porous media (see, among others,Dake, 1978). To simplify, for a given rate of totaloil production at field scale, the spacing of produc-ing wells would increase with increasing rock per-meability and decrease with increasing oil visco-sity. Well spacing is also equally critical to theprocess of modeling rock properties (Figures 2, 3),with geostatistic methods involving variograms(Armstrong, 1984). Although it might be intui-tive tomost geologists that flow rates and propertymodeling at field scale are a function of well spac-ing, it is not a certainty that this critical parameteris correctly taken into account when correlatingstratigraphic markers between wells. The paradoxis that the recent and fundamental introduction ofhigh-resolution sequence-stratigraphic concepts inthe well correlation process (Kerans and Tinker,1997; Homewood and Eberli, 2000) is potentiallymisleading as it consists of the correlation of a timeseries intrinsically independent of the well spacing,especially at field scale.

The purpose of this paragraph is to illustrate theimpact of well spacing on stratigraphic well cor-relations and to indicate some practical approachesto improve the validity of the correlations and avoidunrealistic reservoir models (Figures 11–17). In the


process of stratigraphic well correlation, it mustbe clearly considered that production wells andwell spacing determine the fluid flow and influ-ence the property modeling but have no impacton the geological reality. Wells are random or de-terministic samples of this geological reality,whichcould even overestimate reservoir and flow unitsif they target the best areas on the basis of conceptsandmodels. In fact, the process of stratigraphic wellcorrelation is introduced in the reservoir modelingworkflow to compensate for the lack of interwellgeological information and improve the validity ofthe geological and numericalmodels (Figures 2, 3).The conceptual representation and the numericalmodeling of the reservoir depend significantly onhow accurately the wells are sampling the subsur-face reality. Thus, it is not a straightforward exercise

to estimate the validity of the well sampling relativeto an uncertain geological reality in 3-D and fur-thermore to compare the well spacing against thelateral heterogeneity of the reservoir (Figure 12).The knowledge of the geological reality is basedon the subsurface data, including the wells them-selves and the seismic and the dynamic data. Themajor problem, generally addressed by geostatis-tics (Matheron, 1989), is that the optimized in-tegration of those three sources of information givesonly an approximation of the geological reality, es-pecially if the information is not representative. Acommon practice is to validate the stratigraphicmodel and the subsequent geological reservoirmodel by production dynamic data (Bashore andAraktingi, 1994; Jennings, 2000). This is a prac-tical and valid approach, especially inmature fields

Figure 13. Spatial rela-tionship between welldistribution and strati-graphic trends in carbon-ate platform systems. Thisfigure illustrates threetypical stratigraphic archi-tectures with a differentfacies partitioning andsedimentary profile expres-sing the regression of thecarbonate platform system:ramp (1), flat-toppedshelf with a low-angle slope(2), and flat-topped shelfwith steep slope (3). Thestratigraphical correlationof vertical trends in wellsis strongly influenced bythe position and the spac-ing of the wells relativeto the geometry of theplatform system especiallyto the zones of prograda-tion and aggradation. Dis-tinguishing these threearchitectures in the sub-surface, especially if theyare beyond seismic reso-lution, is commonly achallenge (see well spac-ing sensitivity analysis inFigure 14).


Figure 14. Well spacing sensitivityanalysis for stratigraphical correla-tion. The purpose of this figure is toillustrate the influence of well spacingand well density on the stratigraphiccorrelation of the three architecturesof carbonate platform systems illus-trated in Figure 13. Well correlation ofaggrading zones is not sensitive towell spacing and to stratigraphic rules:sequence stratigraphy and lithostratig-raphy can be indifferently appliedand have identical results. Well cor-relation of prograding zones is, how-ever, very sensitive to well spacing andto stratigraphic rules: sequence stra-tigraphy is better adapted in this situ-ation. Correlation of the ramp system(A) is less sensitive to well spacingand to stratigraphic rules than thetwo flat-topped shelves (B, C). In thesetwo cases, the correlation of the pro-grading zones is strongly dependent ofthe well spacing. In the three cases (A, B,C), when well spacing exceeds mostlya threshold, equivalent to the averagelateral dimensions of the facies zones(A4, B4, and C4), the well correlationswill be unrealistic and uncertain forany stratigraphic rules. In these cases,well correlation of different strati-graphic architectures can look identi-cal for any stratigraphic rules (A4 = B4 =C4). Only seismic images could helpto differentiate the three cases.


with a long production history. It needs, however, tobe funded on realistic geological scenarios and strat-igraphic models to avoid a random validation of thedynamicmodels, which could have a significant neg-ative impact on longer term field development.

The suggested approach for the static (geolog-ical) data is to integrate a priori stratigraphic knowl-edge, compare thewell information to stratigraphicand reservoir analogs, and carry out several iterations(Figure 3). This approach formalizes the intuitive

Figure 15. Trigonometric relationships of carbonate sedimentary profiles. (A) This simple prograding carbonate ramp system isformed by stacked shallowing upward sequences that can be detected in wells by the analysis of vertical sedimentary trends (triangles).(B) Well correlations of such stratigraphic sequences can help to establish the geometry of the carbonate ramp as a simple sedimentaryprism (triangle) characterized by a thickness (E), a length (L), and an angle (A) relative to a given horizontal stratigraphic datum.(C) Assuming that L is the distance between the correlated wells, a simple trigonometric relationship between this distance, the angle (A),and the thickness (E) is seen. Such a relationship can be used to check the validity and the self-coherence of the well correlation asexplained in Figures 16 and 17. In specific cases, it can also be assumed that E is equivalent to the maximum paleobathymetryalong the sedimentary profiles. This parameter can be interpreted from the core analysis and introduced in the validation of thewell correlation as explained in Figures 16 and 17.



approach typically applied by geologists in thewellcorrelation process. Our purpose here is to discussthe impact of well spacing on stratigraphic well cor-relations in the simple cases of carbonate platformsand ramps (Read, 1985),which are hosting themostprolific hydrocarbon reserves (Carmalt andSt. John,1986; Jardine and Wilshart, 1987).

Sedimentary Bodies

In fields where it is established that reservoir andflow units are controlled by discrete sedimentarybodies (sand shoals, rudist banks, etc.), it is criticalto compare their dimensions relative to the wellspacings and to the field extension (Figure 12).

Figure 16. Trigonometric relationships for the well correlation of carbonate ramp systems. (A) The diagram displays two successivesedimentary profiles or base profiles (BP) consequent to a regular increase in accommodation without differential subsidence. Thesuccessive sea levels are noted as SL. Assuming the paleobathymetry of the two couples of stratigraphic markers that are correlatedbetween the wells, a simple trigonometric relationship between the well spacing (L), the base profile angles (a, b), and the sedimentthickness (E1, E2) is observed. (B) The diagram displays two successive base profiles consequent to a differential increase inaccommodation (rotation or differential subsidence). The equation, derived from the previous one, expresses the trigonometricrelationships between the well spacing (L), the sediment thickness (E1, E2), the base profile angles (a, b), and the angle of rotationbetween the two base profiles (g). This angle is referenced to as a horizontal datum (dashed line, SL b) parallel to the sea level.

Figure 17. Crossplot showing theoretical trigonometric relationships between well spacing (L), base profile angles (A), andpaleobathymetric differences (N) calculated along the base profile between two correlated wells. The curves show the relationbetween sedimentary profile angles and spacing of two correlated wells for various paleobathymetric differences along thesedimentary profile between the two wells. Based on the simple trigonometric relationship (tanA = N/L), similar to the equation inFigure 15, such plots could help to check the geometrical self-coherency of the stratigraphic correlations given the paleobathymetricinterpretations in the wells.


Deterministicwell correlation of such sedimentarybodies must be based on the valid assumption thatwell spacing is less than the lateral extent of thebodies (Borgomano et al., 2001). This assumptionshould be validated at the regional and global scaleswith the support of an analog database. If well spac-ing is greater than the lateral extent of the bod-ies (Figure 12), the deterministic well correlationof sedimentary bodies will force unrealistic sedi-mentary architectures and subsequent reservoirmodels. In such cases, the recommended approachis to correlate sequence-stratigraphic units, whichcomprise the bodies, and model the sedimentarybodies with stochastic methods (Dubrule, 1993;Goovaerts, 1997). The two main stochastic meth-ods that can be applied are pixel-based (KoltermannandGorelick, 1996) and object-based (Deutsch andWang, 1996; Viseur, 2001). The pixel-based meth-od simulates a facies property in a 3-D grid whiletaking spatial statistical parameters and availabledata into account (Suro-Perez and Journel, 1990).To capture and reproduce facies spatial repartition,most of these approaches rely on the variogram,which is a two-point statistic and cannot detect com-plex shapes. The object-basedmethod aims to, first,define template objects that mimic sedimentarybody geometries and, second, to distribute themstochastically in themodeled volumewhile account-ing for available data and facies proportions (Viseur,2001). Most of these approaches integrate in thesimulation processes geological rules to generate3-D models that look geologically sound.

Sequence-Stratigraphic Systems

In hydrocarbon fields hosted by extensive andflat carbonate ramps or platforms, the sequence-stratigraphic architecture is commonly the key tothe reservoir and flow models (Kerans and Tinker,1997; Homewood and Eberli, 2000). Where thespatial and genetic relationships betweenpetrophys-ical trends and stratigraphic sequences are clearlyestablished (Figures 6–8), sequence-stratigraphicwell correlations become one of the most criticalsteps of the reservoir modeling workflow. Ideally,the well correlation should be founded on a coher-ent stratophysical concept integrating thedata (wells

and seismic) and a priori knowledge (analog data-base and regional trends) (Figure 3). At this stageof the workflow, it is critical to compare the wellspacing and the spatial heterogeneity of the strat-igraphic systems (Figures 12, 13). In such flat andextensive systems, subtle changes of sedimentaryprofiles will affect the rock property and faciespartitioning (Figures 11, 13). Therefore captur-ing this depositional architecture from the seismicdata and from the well correlation is critical. Al-though it is generally admitted that the sequence-stratigraphic well correlation is the most reli-able method, it is important to consider the wellspacing relative to the stratigraphic architectures(Figures 13, 14). In the aggrading parts of the sys-tems, well correlations are not sensitive to wellspacing and to correlation methods: lithostrati-graphic and sequence-stratigraphic correlationsresult in the same stratigraphic architecture inde-pendently of the well spacing (Figures 13, 14). Inthe prograding parts of the systems, well correla-tion is very dependent of well spacing, and litho-stratigraphic methods should be avoided. Thisprinciple should also be applied to transgressivesystems. This sensitivity analysis shows also thatthe sequence-stratigraphic method does not re-store realistic stratigraphic architectures if the wellsare not sampling the spatial heterogeneity of thestratigraphic systems (A4, B4, and C4 in Figure 14).The lithostratigraphic method would be equallywrong in this case.

Sedimentary Profiles

In extensive and flat carbonate ramps or platforms,volume partitioning of sedimentary facies is main-ly controlled by the evolution through time of thebase profiles, or sedimentary profile (Quirk, 1996),in response to changes of accommodation spaceand sedimentary fluxes (Robin et al., 2005). Faciespartitioning is in turn expressed by the evolutionof the sedimentary profiles as illustrated by outcropsand subsurface data in modern and ancient carbon-ate sedimentary systems (Pomar, 1993; Adams andSchlager, 2000; Boote and Mou, 2003; Droste andSteewinkel, 2004; Pranter et al., 2004). It impliesthat the reservoir model should be based on facies


distribution consistent with the spatial evolution ofthe sedimentary profiles. In theory, this consisten-cy is guaranteed by the well correlation of strat-igraphic sequences, assuming that the correlatedsequences are representative of the sedimentaryprofiles (Figure 15A, B).

The validity of the well correlation is there-fore dependent of the well spacing relative to thesedimentary profiles (Figure 15C). Flat and widecarbonate ramps or platforms are characterized bylow-angle-average sedimentary profiles that are be-yond seismic resolution at field scale (Boote andMou, 2003;Droste and Steewinkel, 2004). Theonlymethod to estimate the average angle of the sedi-mentary profiles is to integrate the paleobathyme-try of the correlated well markers and the wellspacing (Figures 15, 16). The introduction of thepaleobathymetry parameter (inferred from biotaand sedimentary structures) in the correlation pro-cess of carbonate platforms and rampswas implic-it in the Neptune modeling reservoir modelingworkflow (Massonat, 2001). It infers the existenceof a horizontal datum sea level, allowing simple tri-gonometric calculations to assess the validity of thecorrelation (Figure 15C). Although the quantifica-tion of the paleobathymetry in wells is uncertain,this method should be used to estimate the inter-nal coherency of the stratigraphicmodel. The cross-plots in Figure 18 illustrate the relationships be-tween the average angle of the sedimentary profileand the well spacing for a given paleobathymetricgradient betweenwells. Such graphs could be usedin principle to estimate the range of possible cor-relations depending on the well spacing and theinterpreted paleoenvironments (Figure 13). Thegraphs could also support the validation of low-angle clinoforms interpreted from seismic data(Schwab et al., 2005).

The previous trigonometric calculations in-volved a single sedimentary profile correlated be-tween wells. Actually, the sequence-stratigraphiccorrelation process infers multiple and stackedsedimentary profiles that are spatially and genet-ically related to each other. Two cases have beeninvestigated without and with differential subsi-dence or tectonic unconformity (Figure 16). In thistrigonometric calculation, we are trying to relate

critical parameters to assess the validity of the wellcorrelation. In the first case without differentialsubsidence (Figure 16A), a simple relationship be-tween the thickness (decompacted) between thetwo markers (E), the interwell length (L), and thetwo successive sedimentary profile angles (a and b)is observed. In the second case with differentialsubsidencebetween the twowells (Figure 16B), thetrigonometric calculation introduces the angle oftectonic rotation (c). These oversimplified calcu-lations, which apply only to ramp profiles, indicateclearly the possibility to assess the validity of wellcorrelations on the basis of sedimentary profilesand paleobathymetric estimation.

EXAMPLE OF OUTCROPSEQUENCE-STRATIGRAPHICCORRELATION AND FACIES MODELING

The following paragraph illustrates the impact ofsequence-stratigraphic well correlation and wellspacing on stochastic facies modeling on the basis ofan outcrop example (Figures 18, 19). This sensitivityanalysis is based on a Lower Cretaceous outcropexample studied in the south of France and repre-sents typical marine carbonate platform systems.

At the scale of the studied outcrop (4 km2,1.5 mi2), the internal architecture of this 25-m(82-ft)-thick sedimentary system corresponds tothree correlated shallowing upward sequences. It isdominated by grainstone bodies (submarine dunes)that are generally connected and wackestone bod-ies, formed belowwave base, that are not connectedas a result of the erosive nature of the grainstones.This sedimentary system can be represented bythe deterministic correlation of 14 pseudowellsresulting in a well spacing ranging between 68 and648 m (223 and 2126 ft) with an average of 243 m(797 ft). The body dimensions exceed the wellspacing at any location, but the mudstone bodies(300–700 m, 984–2296 ft) are characterized byoverall smaller dimensions than the grainstone bod-ies (0.5–2 km, 0.3–1.2mi) and a lower net-to-grossratio (0–30%).

No or limited stratigraphic interpolation wasinvolved in the representation of this sequence.


Figure 18. Impacts of different stratigraphic correlation rules on facies interpolation between two wells. The gray shades in the twologs represent the three main carbonate facies. The workflow includes four main steps (1–4): the first step represents the higherlevel of stratigraphical correlation that could be based on seismic reflectors. The second step illustrates the two possible correlationscenarios based, respectively, on lithostratigraphy and sequence stratigraphy. The third step corresponds to the restoration of thestructural deformations whereas the fourth step displays the facies interpolation within the correlated units. Lithostratigraphy forcesthe lateral correlation of facies between the two wells and the realization of layered reservoir architectures with a strong polarizationof the spatial correlation of the properties. Sequence stratigraphy allows lateral facies variations (sharp or gradual) within correlatedunits and the realization of more complex and heterogeneous reservoir architectures.


Facies units and sequence boundaries were walked-out on the outcrop. Facies are distributed accord-ing to a sequence-stratigraphic framework thatresults in the development of pinch-outs and sharpchanges between facies. Gradual changes, for ex-ample, between wackestones and grainstones, havenot been observed.

The 14 pseudowells, the facies, and the se-quence correlations were imported in a numericalgeomodeler. The main objective of the sensitivityanalysis was to test the impact of the sequence-stratigraphic correlations and of the well spacingon the stochastic facies modeling. A standard pixel-based stochastic method, founded on facies pro-portion curve and variogram (Ravenne, 2002), wasused with or without constraints on object dimen-sions and shapes.

The workflow in Figure 18 illustrates the dif-ferential impact of sequence-stratigraphic correla-tion and lithostratigraphic correlation on stochasticfacies modeling. Lithostratigraphic correlation im-plies the spatial correlation and the lateral continuityof facies between the wells, whereas sequence-stratigraphic correlation allows gradual or sharplateral facies transition between the wells. In thiscase, lithostratigraphic correlation is intrinsicallynot compatible with stochastic facies infilling be-tween wells. It can be applied if the overall spatialheterogeneity of the sedimentary system is sam-pled by the wells (Figure 19A). When this is notthe case (Figures 13, 14), applying a high-resolutionsequence-stratigraphic correlation is recommended.The correlation of the three sequences between the14 wells results in a stochastic facies model veryclose to the reality (Figure 19B). The high preci-sion of the proportion curves and variograms, whichare established for each sequence, is controlled byhigh well numbers and small well spacing. Wellspacing and well numbers are nevertheless insuf-ficient on their own to guaranty a realistic modelwithout the correlation of the three sequences(Figure 19C). It just confirms that the determin-istic correlation of the three sequences improves,for this particular data set, the quality of the pro-portion curves and variograms. Despite the corre-lation of the three sequences, the great spacing be-tween the wells would result in a nonrealistic facies

model unless facies body dimensions are intro-duced in the modeling workflow (Figure 19D).In a subsurface case, such knowledge would comefrom reservoir or outcrop analogs. High net-to-grossand thick facies (grainstone) are less sensitive to wellspacing and sequence correlations than the low net-to-gross and thin facies (Figure 19B, C, D). Thesethin objects, which could act as a flow barrier, mustbe deterministically correlated between the wellsby a lithostratigraphic method, which shows thatsequence-stratigraphic and lithostratigraphic cor-relations can be complementary in the same res-ervoir modeling workflow.

EXAMPLE OF SUBSURFACE WELLCORRELATIONS (MALAMPAYA GAS FIELD,TERTIARY, PHILIPPINES)

The Malampaya oil and gas accumulation is locatedin the deep-water Block Service Contract 38, off-shore Palawan (Philippines), at a depth of 3000 m(9840 ft) below present sea level, within a northeast-southwest–oriented carbonate buildup. Like sev-eral hydrocarbon accumulations in the north Pala-wan block, the Malampaya field is situated withinthe upper Eocene to lower Miocene Nido Lime-stone (Sales et al., 1997;Williams, 1997). Variousmodels of carbonate buildup growth history wereproposed (Grotsch andMercadier, 1999; Fournieret al., 2005) using 3-D seismic data,well logs, cores,and sidewall samples.

Two levels ofwell correlationswere definedwith-in the Nido Limestone: (1) sequence-stratigraphicwell correlations individualizing time-correlatableunits and (2) reservoir unitwell correlations definingrock volumes characterized by specific diageneticpatterns and petrophysical properties. Figure 20 pre-sents the overall workflow of the well correlationas well as the spatial relationship between reservoirunits and depositional sequences.

Sequence-Stratigraphic Well Correlations

Decameter-scale depositional sequences have beenidentified in wells, within the inner shelf, on thebasis of (1) the vertical evolution of depositional



facies, (2) the vertical evolution of meteoric diage-netic features, and (3) the presence of major uncon-formities associated with a significant time hiatus(Fournier et al., 2005). The sequences and bound-ing unconformities have been correlated betweenwells using (1) the chemiostratigraphic (Sr isotopes)and biostratigraphic constraints (large benthic for-aminifers), (2) the well-to-seismic data tie, and(3) the sequence stacking pattern. Inner shelf se-quences are mainly composed of mud-rich shallowwater deposits (mainly wackestone to packstonetextures). The upper part of the sequences is al-ways characterized by a strongmeteoric overprintrelated to repeated phases of subaerial exposures.

Reservoir Unit and SeismodiageneticUnit Well Correlations

On the basis of cores and well logs, the Nido Lime-stone was subdivided into 20–70-m (66–231-ft)-thick units characterized by specific pore-typediagenetic patterns and petrophysical properties(= reservoirunits).Thealternationbetween tight andporous units is mainly controlled by meteoric dia-genesis (leaching and pedogenesis) and by late buri-al cementation and leaching (Fournier and Borgo-mano, 2007). The correlation between wells of thesereservoir units rests on a detailed well-to-seismicdata tie using synthetic seismograms. Figure 20shows the spatial relationship between rock prop-erties, pore type, and reservoir units. Seismodia-genetic units (sensu Fournier andBorgomano, 2007)are carbonate rock volumes whose petrophysicalproperties (porosity, permeability, density, and sonicvelocity) are dominantly controlled by diagenesis

and whose boundaries display acoustic impedancecontrasts that are high enough to generate inter-pretable seismic reflectors. In 3-D seismic data,seismodiagenetic units whose thickness exceeds thevertical resolution of seismic data can be accuratelyrelated to reservoir units and can be delineated in3-D by picking selected seismic horizons. In Ma-lampaya, most of the tight burially cemented unitscan be imaged in 3-D. The resulting low-resolutionpetrophysical model can be used for guiding thefurther porosity inversionof the seismic amplitudes(Neuhaus et al., 2004).

Relationship between Depositional Sequences andReservoir Units

Figure 6 shows the relationships between depo-sitional sequences and reservoir units. In Malam-paya, the tight units are formed by burial-relatedcemented lenses that progressively pinch out fromthe western to the eastern margin of the buildup.In contrast, the depositional architecture displays anaggradingpattern andconsists of a stackof sequencesof constant thickness that are bounded by flat un-conformities. As a consequence, the boundaries ofthe reservoir units are not necessarily parallel to de-positional surfaces and to sequence boundaries.

Impact of Well Spacing on Well Correlations

Previous studies (Fournier et al., 2004, 2005) haveshown that despite the significant effects of syn-sedimentary tectonic deformation, theMalampayabuildup developed mainly as an aggrading flat-topped shelf, with very low lateral variations of

Figure 19. Well spacing and correlation sensitivity analyses for facies simulation of an outcropping carbonate shelf. (A) The realityof the stratigraphic architecture (mapped from the outcrop) is obtained by the deterministic correlation of the two main facies withinthree correlated shallowing-upward sequences between 14 pseudowells. (B) This simulation is realized with 14 wells and the threecorrelated sequences. In this case, the facies are not correlated. The stochastic facies infilling, based on facies proportion curvesand variogram, is closer to the reality because of the well density and spacing relative to the object dimensions (minimum wellspacing < minimum body dimensions) combined to the sequence correlations that improve the quality of the proportion curves andvariograms. This model could be improved by introducing constrains on the object shapes and dimensions. (C) Same as B withoutthe correlations of the three sequences. The high net-to-gross facies (grainstone) is not sensitive to the sequence correlations asopposed to the low net-to-gross facies (wackestone). The spatial correlation of the less abundant and thin wackestone beds must bedeterministically imposed by the interpreter. (D) Same as B with only four pseudowells. In this case, probalistic discrete objects (coralwackestone for example) are introduced on the basis of the proportion curves and a priori knowledge. This compensates onlypartially for the well decimation.


Figure 20. Workflow of sequence-stratigraphic and seismic-based well correlation in the Malampaya carbonate reservoir (depths are in true vertical depth subsea, TVDSS). Steps1a to 1d show the definition of a sequence-stratigraphic framework based on larger foram biostratigraphy (letter-scale classification), Sr-isotope stratigraphy (the step-like shape ofthe Sr curve indicates significant hiatuses), and vertical changes in depositional environment. The water depth trends are dominated by keep-up intervals, meaning that thecarbonate sedimentary system is able to grow despite the increase in accommodation. Steps 2a to 2d present the process of seismic-based well correlation and seismodiageneticunit definition, integrating diagenetic interpretation of cores, well logs, and petrophysical measurements, and well-to-seismic tie. Step 3 establishes the spatial relationship betweendepositional sequences and seismodiagenetic units, and therefore specifies the chronostratigraphic or diagenetic significance of correlation surfaces. TVDSS = true vertical depthsubsea; Tf1 = Upper Burdigalian; Upper Te = Aquitanian-Lower Burdigalian; Lower Te = Chattian. (Fournier et al., 2005)

820

Well

CorrelationsinCarbonates

depositional facies. In such a layer-cake depositionalsystem, the well spacing will not significantly in-fluence the stratigraphic framework of the reser-voir, within the shelf deposits. In addition, exceptfor few cemented lenses (e.g., SM2-IIIb unit),mostof the large-scale seismodiagenetic units (20–70 m[66–231 ft] thick) can be picked continuously using3-D seismic. As a consequence, a higher density ofwells is not expected to have a significant impacton the reservoir model at this scale, within theMa-lampaya shelf, but it can help to better characterizesmaller scale heterogeneity.

Further modeling of the build-up flanks, wheredepositional facies (andpossibly petrophysical prop-erties) are expected to change laterally within ashort distance, could be more sensitive to well spac-ing. Specific diagenetic environments, such as themeteoric-marine mixing zone, combined with tran-sitional shelf-to-slope environments of depositioncould increase the lateral heterogeneity of the res-ervoir rocks and justify a much denser well spacingfor realistic reservoir modeling.

The combined use of detailed stratigraphic inter-pretations of well data and a synthetic seismogramto tiewells to seismic data allows one to answer thethree following questions that are commonly en-countered in reservoir case studies involving 3-Dseismic and well data: (1) the spatial relationshipbetween stratigraphic sequences, depositional bod-ies, seismodiagenetic units, and reservoir units;(2) the geological significance (chronostratigraphicversus diagenetic) of seismic-based correlations;and (3) the relevance of sequence-stratigraphic andbiostratigraphic well correlations for the construc-tion of reservoir models. Such an integrative ap-proach linking sedimentology, diagenesis, petro-physics, and seismic data is therefore recommendedfor carbonate reservoirs that have undergone in-tense diagenetic alteration, in a meteoric and/orburial realm (Zampetti et al., 2005; Fournier andBorgomano, 2007).

CONCLUSIONS

The process of stratigraphic well correlations is verycritical for carbonate reservoir modeling and the

stratigraphic method must be adapted to the goalof the reservoir model. The main objective of thewell correlation process is to distinguish, at the rel-evant scales, the correlatable from the noncorrela-table heterogeneities in space and to create subsetsof data in which stationary geostatisticmethods canbe applied for the reservoir modeling. The strati-graphic well correlations must therefore be guidedby consistent geological and petrophysical conceptsthat are established on the basis of data analysis anda priori knowledge. The ultimate objective of thecorrelation is to capture in the model the correlat-able petrophysical heterogeneities that matter forthe definition of reservoir and flowunits. The largesterror is introducedwhen the stratigraphic rules forceunrealistic spatial correlations of random noise sam-pled in the wells. Stratigraphic rules are chosen onthe basis of the geological factors that control thedistribution of the rock properties, the spatial het-erogeneity of the reservoir, the well spacing, andthe objectives of the reservoirmodel. If the averagewell spacing is less than the lateral dimensions ofcritical sedimentary objects, then lithostratigraphicrules can be applied. If, on the contrary, averagewellspacing is far beyond these object dimensions, thensequence-stratigraphic rules are more valid. Wellcorrelation of the time series is, however, not sen-sitive to well spacing but it does not necessarilyrepresent a valid correlation of rock properties.In the case of sequence-stratigraphic correlationsof base profiles, several genetic assumptions can bemade that allow the validation of the correlationsbased on simple trigonometry.

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