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    Presently available techniques for predictingquantitative reservoir quality typically are limited inapplicability to specific geographic areas or litho-stratigraphic units, or require input data that arepoorly constrained or difficult to obtain. We havedeveloped a forward numerical model (Exemplar)of compaction and quartz cementation to provide ageneral method suited for porosity prediction ofquartzose and ductile grain-rich sandstones inmature and frontier basins. The model providesaccurate predictions for many quartz-rich sand-stones using generally available geologic data asinput. Model predictions can be directly comparedto routinely available data, and can be used in riskanalysis through incorporating parameter optimiza-tion and Monte Carlo techniques.

    The diagenetic history is modeled from the timeof deposition to present. Compaction is modeledby an exponential decrease in intergranular vol-ume as a function of effective stress. The model isconsistent with compaction arising from grainrearrangement, ductile grain deformation, and brit-tle failure of grains, and accounts for the effects offluid overpressures and stable grain packing con-figurations. Quartz cementation is modeled as aprecipitation-ratecontrolled process according tothe method of Walderhaug (1994, 1996) andWalderhaug et al. (in press).

    Input data required for a simulation includeeffective stress and temperature histories, togetherwith the composition and texture of the modeledsandstone upon deposition. Burial history data can

    433AAPG Bulletin, V. 83, No. 3 (March 1999), P. 433449.

    Copyright 1999. The American Association of Petroleum Geologists. Allrights reserved.

    1Manuscript received August 14, 1997; revised manuscript received June19, 1998; final acceptance October 5, 1998.

    2Geologica, P.O. Box 8034, N-4003 Stavanger, Norway;

    3Statoil, 4035 Stavanger, Norway; e-mail: OWALD@statoil.noWe thank Esso Norge a.s and Exxon Production Research Company for

    providing the funding to implement and test Exemplar, and Stan Paxton,David Awwiller, et al., from Exxon Production Research for their valuableguidance in this work. Finally, we thank Linda Bonnell, Sal Bloch, AltonBrown, and Dick Larese for their thorough reviews of earlier versions of thismanuscript.

    Predicting Porosity through Simulating SandstoneCompaction and Quartz Cementation1

    R. H. Lander2 and O. Walderhaug3

    be obtained from basin models, whereas sandstonecomposition and texture are derived from point-count analysis of analog thin sections. Exemplarpredictions are consistent with measured porosity,intergranular volume, and quartz cement fractionsfor modeled examples from the Quaternary andTertiary of the Gulf of Mexico Basin, the Jurassic ofthe Norwegian shelf, the Ordovician of the Illinoisbasin, and the Cambrian of the Baltic region.


    Reservoir quality is one of the important uncer-tainties in wildcat drilling (Bloch, 1994a; Wilson,1994). Present approaches to reservoir qualityprediction, however, commonly are limited inapplicability, are difficult to apply, or are of unprovenaccuracy. The need for improved methods hasmotivated us to develop a model, known as Exemp-lar, that is designed to

    Consider the most significant porosity control-ling processes in sandstone lithologies that arecommon hydrocarbon reservoirs

    Make predictions that approach the measure-ment accuracy of available data

    Use input data that are commonly available, eas-ily obtained, or readily estimated in both matureand frontier basin settings

    Produce predictions that can be compareddirectly to petrographic thin sections

    Include a rigorous approach to uncertaintyassessment so that reservoir quality predictions canbe stated in probabilistic terms

    Be fast and easy to use on personal computersavailable to explorationists

    In our initial efforts we have targeted quartz-richsandstones because they are the most commonsandstone reservoir type and because their porositycommonly is controlled by just two classes of dia-genetic processes: compaction and quartz cemen-tation. In this paper, we review the models designand algorithms, give conceptual justifications forthe approaches we have used, and present some

  • example simulations. The model provides reason-ably accurate reservoir quality predictions forquartzarenites, sublitharenites, and subarkoses, andhas proven to be a useful predictive tool for bothmature and frontier regions. The model alsoappears to be well suited to porosity prediction ofductile grain-rich rocks, but more geologic data setsare needed for calibration before it can be confi-dently applied to reservoir quality prediction insuch lithologies.

    Exemplar simulates the evolution of sandstoneporosity and composition throughout the geologichistory of the modeled unit. In addition, it simulatesthe rates of porosity reduction due to compactionand cementation through time (output data typesare given in Table 1). Input data needed to conducta simulation include a description of the texture andcomposition of the sandstone upon deposition,burial history information, and parameter values forthe compaction and quartz cementation algorithms.Depositional sandstone texture and compositionaldata are derived from standard petrographic analy-ses of reservoir samples from nearby wells or fromlithologic analogs in frontier areas. Basin modelingresults for prospect reservoir intervals provide thenecessary temperature and effective stress historyinput (burial depth can be substituted for effectivestress for areas that have not experienced signifi-cant fluid overpressures). Finally, the appropriatecompaction and quartz cementation parameterscan be obtained from calibration studies. A listing of

    input data types that can be used by the model isgiven in Table 2.

    In addition to its utility for porosity predictionprior to drilling, Exemplar has proven to be a use-ful paleothermal indicator (Awwiller and Summa,1997; Lander et al., 1997a, b). Because quartzcementation is strongly controlled by burial history,the model can be used to constrain burial histo-ries by comparing model predictions with mea-sured values. Exemplar also may provide a moreaccurate depiction of reservoir quality variationsand heterogeneties within fields than do pure geo-statistical methods when it is used in concert withupscaling techniques; furthermore, the modelshould provide a more accurate basis for assessingthe evolution in properties of sandstones that act ashydrocarbon carrier systems than do current basinmodeling systems.


    Existing reservoir quality models tend to fall intotwo categories (Wood and Byrnes, 1994): effect-oriented models, such as statistical correlations ofporosity with other variables, and process-orientedmodels, such as geochemical reaction-path modelsthat are based on the thermodynamics and kinetics ofminerals, aqueous species, and gases. The statistical

    434 Predicting Porosity

    Table 1. Exemplar Output Results for Each Model Time Step

    Rock Fractions PorosityQuartz cementNonquartz cementIntergranular volumeQuartz grainsNonquartz framework grainsMatrix

    Rock Volumes (cm3) Bulk rock volumeQuartz cement (for current time step)Quartz cement (cumulative)Nonquartz cement (cumulative)

    Rates (cm3/m.y.) Quartz cementationNonquartz cementation Compaction

    Porosity Controls Coplabsolute porosity loss due to compaction (Ehrenberg, 1989)Ceplabsolute porosity loss due to cementation (Ehrenberg, 1989)ICOMPACT: copl / (copl + cepl) (Lundegard, 1991)

    Other Quartz surface area (cm2)Average overgrowth thickness (mm)%Ro (Sweeney and Burnham, 1990)

  • approach can be accurately applied to sandstoneswith less than 10% cement, but this approachbreaks down for more highly cemented sandstones(Bloch, 1991). An additional shortcoming to thestatistical approach is that accurate model predic-tions are constrained to sandstone compositions,textures, and geologic settings represented by thesamples included in calibration data sets (Bloch andHelmold, 1994). Thus, it is difficult to apply theempirical approaches to frontier areas with little orno data, to mature areas where statistical studieshave yet to be undertaken, or to depth ranges out-side that of an existing calibration data set.

    Geochemical models, such as those reviewed byMeshri (1990) and Wood (1994), are appealingbecause by using a first-principle approach to sim-ulating diagenetic reactions they should ideally bemore broadly applicable than empirical methods.Although reaction-path models provide importantinsights into diagenetic processes, in practice thepresent generation of models is difficult to applyto quantitative porosity prediction. Many suchmodels ignore compaction, frequently the singlegreatest cause of porosity reduction (Lundegard,1991), as well as the effect of diagenesis on thesurface area of reactive minerals. These models suf-fer from substantial uncertainties in kinetic andthermodynamic constants because many phaseshave not yet been characterized, and the extent towhich the existing data can be extrapolated fromlaboratory conditions to geologic time scales andenvironments is not always clear. Finally, mostreaction-path models do not explicitly distinguishbetween the detrital or authigenic occurrence ofminerals, making it difficult to compare predic-tions with petrographic data.

    The approach that we have taken to reservoirquality prediction attempts to synthesize effect-oriented and process-oriented methods. Althoughthe model predicts the result of diagenetic process-es, it does not employ a first-principle approach tosimulating these processes. Instead, our hybridsimulator [terminology of Wood and Byrnes(1994)] emplo