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  • Reservoir Characterization Using Expert Knowledge, Data and Statistics

    Prepared with assistance from:

    Peter Corvi, Head of Effective PropertiesKes Heffer, Head of Reservoir DescriptionPeter King, Senior Reservoir Engineer,

    Effective PropertiesStephen Tyson, Computing ConsultantGeorges Verly, Senior Geostatistician,

    Effective PropertiesBP Research Sunbury-on-Thames, England

    Christine Ehlig-Economides, ReservoirDynamics Program Leader

    Isabelle Le Nir, GeologistShuki Ronen, Geophysics Integration

    Program LeaderPhil Schultz, Department Head Etudes et Productions SchlumbergerReservoir Characterization DepartmentClamart, France

    Patrick Corbett, Research AssociateJonathan Lewis, Conoco Lecturer in GeologyGillian Pickup, Research AssociatePhillip Ringrose, Senior Research AssociateHeriot-Watt UniversityDepartment of Petroleum EngineeringEdinburgh, Scotland

    Dominique Gurillot, Sr. Research Engineer, Reservoir Engineering Division

    Lucien Montadert, Director of Exploration and Production

    Christian Ravenne, Principal Research Associate,Geology and Chemistry Division

    Institut Franais du Ptrole Rueil-Malmaison, France

    Helge Haldorsen, Assistant Director, InternationalField Developments

    Norsk Hydro A.S. Oslo, Norway

    Thomas Hewett, Professor of Petroleum Engineering

    Stanford University California, USA

    Accurately simulating field performance requires knowing properties

    like porosity and permeability throughout the reservoir. Yet wells provid-

    ing the majority of data may occupy only a billionth of the total reser-

    voir volume. Transforming this paucity of data into a geologic model for

    simulating fluid flow remains an industry priority.

    January 1992

    The simplest representation of a reservoir isa homogeneous tank with uniform proper-ties throughout. Characterizing such a sim-plified model requires merely enough datato define its volume and basic petrophysicalproperties. This information can then beused to help forecast reservoir behavior andcompare possible production scenarios.

    But efficient exploitation of reservesrequires a more sophisticated approach.Reservoirs have been created by complexsedimentary and diagenetic processes, andmodified by a history of tectonic change.Rather than resembling simple tanks, reser-voirs are heterogeneous structures at everyscale. The need for accurate characteriza-tion is vital for oil company economic plan-ning (next page, top).

    In the past, geologists have used expertknowledge to interpolate between wells andproduce basic reservoir models. However,during the last ten years, this effort has beentransformed by statistical modeling offeringinsight into the effects of heterogeneity.

    This article details how reservoir descrip-tions are developed and is divided intothree stages (page 27):Defining the reservoirs large-scale struc-

    ture using deterministic dataDefining the small-scale structure using

    statistical techniquesgeostatistics Rescaling the detailed geologic model to

    be suitable input for a fluid-flow simulator.

    Cray is a mark of Cray Research Inc. MicroVAX is a markof Digital Equipment Corp.1. Weber KJ: How Heterogeneity Affects Oil Recovery,

    in Lake LW and Carroll HB Jr (eds): Reservoir Charac-terization. Orlando, Florida, USA: Academic PressInc. (1986): 487-544.

    Defining the Large-Scale StructureThe first stage aims to construct as detailed ageologic description of the reservoir as mea-surements will allow. The available informa-tion includes a structural interpretation fromseismic data, static data from cores and logsand dynamic production data from testing.To these, the geologist adds expert knowl-edge on geologic structures, obtained fromfield experience and outcrop studies (seeGathering Outcrop Data, page 28).

    The first step is to recognize depositionalunits and then, if possible, correlate thembetween wells. It helps to know the generalshape and order of deposition of the units,and ideally the relationships between width,thickness and length for each unit.1 Well-to-well correlation is made using traditionalhard-copy maps and logs or, today, interac-tive computer workstations. Workstationsallowing simultaneous visualization of seis-mic, log and other data enable easier recog-nition of subtle correlations.

    In most cases, this large-scale characteri-zation results in a conventional layer-cakemodela stack of subhomogeneous layers.There is no doubt that many reservoirsshould be characterized by more complexarrangements of depositional unitssuch asthe jigsaw and labyrinth models (nextpage, bottom).2 The ability to use thesemore complex models routinely remains anindustry goal (see Trends in Reservoir Man-agement, page 8).

    25

    2. Weber KJ and van Geuns LC: Framework For Con-structing Clastic Reservoir Simulation Models, Jour-nal of Petroleum Technology 42 (October 1990):1248-1253, 1296-1297.

  • nHow heterogeneity affects productivity. In this example developed at BP Research,Sunbury-on-Thames, England, two different models have been interpolated between apair of hypothetical wells. The lithologies are identical: only their spatial correlationhas been altered. The graph shows how the pore volume recovered versus pore volumeinjected varies for the two models. After one pore volume has been injected, the differ-ence in recovery between the two models is about 0.1 of a pore volume.

    26

    nDefining reservoir type. Current large-scale characterization tends to result in a sim-ple layer-cake model. However, efforts are being made to use more complex modelslike the jigsaw and labyrinth models shown.

    Heterogeneity case A

    Hypothetical well data

    Heterogeneity case B

    12345Shale Barrier

    Lithology

    Pore volume (PV) injected

    PV

    re

    co

    vere

    d

    0.5

    0.4

    0.3

    0.2

    0.1

    00 0.2 0.4 0.6 0.8 1.0

    Case BCase A

    Predicted oil recovery

    Layer cake Jigsaw Labyrinth

    Tidal channel

    Barrier footTransgressive deposit Barrier barBarrier bar Crevasse splay

    Distributary channel fill

    Defining the Small-Scale Structure UsingGeostatistical ModelingOnce the shape of the reservoir and itslarge-scale structure have been described,the next stage focuses on defining hetero-geneity within each depositional unit. Thisrequires more detailed interwell measure-ments than are currently available. Boreholeseismic data typically cannot span wells.Although surface and cross-well seismicdata do reach everywhere, there is insuffi-cient knowledge relating seismic data tophysical rock properties, and explorationseismic data have insufficient resolution. Inaddition, well testing data often lack direc-tional information. Therefore nondetermin-istic, or geostatistical, methods are required.3

    Large-scale reservoir models typicallycomprise a few thousand grid blocks, eachmeasuring about 100 m square and morethan 1-m thick [about 1000 ft2 by 3 ft] Butmodels that take into account small-scaleheterogeneity use smaller grid blocks1million or more are often needed. The sheerquantity of input data required to fill somany blocks also favors geostatistics.

    Geostatistical techniques designed to pro-vide missing data can be classified in twoways: by the allowable variation of theproperty at a given point and by the waydata are organized. There are two classes ofproperty variation, continuous and discrete.Continuous models are suited to propertieslike permeability, porosity, residual satura-tion and seismic velocity that can take anyvalue. Discrete models are suited to geo-logic properties, like lithology that can berepresented by one of a few possibilities.4

    Data organization has developed alongtwo paths depending on how the modelsare built up. One is grid based. All theproperties are represented as numbers on agrid, which is then used for fluid-flow simu-lation. The second is object based. Reser-voir features such as shales or sands aregenerated in space and a grid then superim-posed on them.

    Grid-Based ModelingOne of the key geostatistical tools used ingrid-based modeling is krigingnamed aftera pioneer of rock-property estimation, D. G.Krige, who made a series of empirical stud-ies in the South African goldfields.5 Krigingis designed to honor measured data andproduce spatially correlated heterogeneity.The heart of the technique is a two-pointstatistical function called a variogram thatdescribes the increasing difference (ordecreasing correlation) between sample val-ues as separation between them increases.

    Oilfield Review

  • Stage 2: Defining small-scale structure

    Stage 1: Defining large-scale structure

    Core plugs Whole core Well logs Well testing

    Borehole geophysics Surface seismicsOutcrop studies

    Geologists expert knowledge

    Kriging minimizes the error between theinterpolated value and the actual (butunknown) value of the property.6

    For a given property, a variogram is con-structed from pairs of data generally mea-sured in wells. In the oilfield, criticism ofkriging centers on the low density of welldata when compared to mining. To over-come this problem, variograms can alterna-tively be constructed from data measuredon outcrops or in mature fields where bettersampling is available.

    Although variograms are commonly usedto infer the spatial continuity of a singlevariable, the same approach can be used tostudy the cross-continuity of several differ-ent variablesfor example, the porosity atone location can be compared to seismictransit time. Once constructed, this cross-correlation can be used in a multivariateregression known as cokriging. In this way,a fieldwide map of porosity can be com-puted using not only porosity data, but alsothe more abundant seismic data.7

    Kriging and cokriging d

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