Copyright 1999, Society of Petroleum Engineers, Inc.

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AbstractThe onshore Barua Field, near the southeast edge of LakeMaracaibo, is a highly faulted structure producing from theEocene Pauji and Misoa intervals. This mature field hasundergone significant depletion from approximately 30 wellssince 1958. A classical, deterministic reservoir characterizationstudy followed by reservoir simulation history matching wasconducted. Prior to completing the history match, a stochasticreservoir characterization, including multiple realizations, wasperformed. Barua’s Eocene interval of near shore littoral barenvironments can be modeled using a variety of geostatisticaltechniques. A pixel-based method was selected over objectmodeling due to the long continuous nature of the reservoirsands and shales, and the absence of any definitive local geneticdepositional facies geometries. Understanding the petrofaciesand lithofacies and their relationship in the depositionalenvironment was key to creating a representative stochasticreservoir characterization. This modeling process is described.The process of integrating seismic, well logs, depositionalconcepts, and facies data is also described.

The comparative reservoir simulation results between thestochastic and deterministic approaches, and the resulting impactfrom an engineering perspective on the history matching processprovide insight into the different methodologies. A discussionof the differences and benefits is provided.

IntroductionAn integrated (geophysical, geological, petrophysical, andengineering) study was conducted to (1) develop a geological-petrophysical model covering the field area and formations ofinterest, (2) evaluate past reservoir performance, (3) predictfuture performance under various operating plans, and (4)prepare appropriate recommendations for field development and

operations. Initially, the study plan called for a deterministicapproach to reservoir characterization. Subsequently, theoperator elected to develop the reservoir description usingstochastic methods. Flow simulations were carried out usingboth the deterministic and stochastic reservoir descriptions.

General Information and Field HistoryThe Barua field is located onshore near the southeast edge ofLake Maracaibo. It is south of the Mene Grande field and westof the Mototan field, Fig.1. Production is from the Eocene Paujiand Misoa formations at depths ranging from about 3,100 m tomore than 4,200 m. Figure 2 is an example log showingsequences and parasequences within the two formations. Figure3 is a generalized facies cross section, again illustrating thesequences and parasequences. At least 24 sands have beenobserved to contain by hydrocarbons in some area of the field. The field contained numerous faults, some with throws ofseveral hundred feet. Figure 4 is a structure map on the topMisoa. A 3-D seismic survey covered the area.

Production was initiated in 1958, but development wasrelatively slow and production low until the mid-1980s. Mostwells were completed in multiple zones. Production logs in afew wells generally indicated uneven profiles with some zonesnot contributing. RFT pressures in a number of wells drilledfrom 1993 to 1998 indicated large differentials, both areally andvertically throughout the field. The reservoir fluid was highlyundersaturated initially, but pressures are now below thebubblepoint pressure in some zones in certain areas. The mainproduction mechanism has been fluid and rock expansion. Mostwells are on some form of artificial lift.

Reservoir Description DataIn addition to 3-D seismic data and normal open hole loggingsuites at the times the wells were drilled, the following itemswere available for use in developing the geological-petrophysical model.

Detailed core descriptions including standard faciesclassifications in four wellsThin section descriptionsRoutine core analysesSpecial core analysesImage logs on four wells (one cored)Dipmeters on seven wells

SPE 56656

The Barua Field, Venezuela: Comparison of the Results and Process of Deterministicversus Stochastic Reservoir CharacterizationA. Carnes, SPE, J. Yarus, Smedvig Technologies, P. Cordova, SPE, M. Delgado, H. Rodriguez, PDVSA, P.J. Black, R.L.Brown,SPE, K. Kramer, K. Yang, and L.D. Green, Smedvig Technologies

2 A. Carnes, et al. [SPE 56656]

Deterministic ModelThe structure at top Misoa (Fig. 4) was based upon seismic, wellcontrol, and available dipmeter data. The fault interpretationwas almost entirely from the seismic. The structural surface wasexported to commercial mapping software where depthmatching at the wells was ensured. Zone thicknesses werededuced from well control and seismic and contoured using themapping software. Zone thickness grids were then added orsubtracted from the top Misoa grids to develop the structuralframework. Nine lithofacies were identified in the core descriptions, four ofwhich were interpreted as being of reservoir quality by oilstaining as well as porosity and permeability ranges and fluidcontents. After adjustment of core depths to log depths, acorrelation was developed which related certain log responses tothe lithofacies from core descriptions. The correlationconsistently separated reservoir from non-reservoir facies. Theprediction also was quite good in the four wells having imagelogs. After investigating other methods of determining net rock(porosity cutoff, etc.), the facies predictor was considered to bethe best approach. A correlation also was developed for predicting permeabilityfrom log data. It involved a two-step process. The first was tocorrelate log responses to the Flow Zone Indicator (FZI)¹ whichwas derived from core data. The second was to calculatepermeability using log porosity and the corresponding value ofFZI. Figure 5 is a graph of calculated permeability vs corepermeability on one of the cored wells. The correspondingdepth plot is presented on Fig. 6. The next step in preparing the deterministic model was to applythe facies discriminator to the 0.25-ft log analysis results in eachwell/zone and calculate net thickness and average values ofporosity, permeability, water saturation, and hydrocarbonthickness. Finally, well values of the various parameters wereinput to the computer mapping program. The contouringalgorithm was constrained to broadly honor the conceptualgeological model through the use of pseudo well control pointsas well as the estimated oil-water contact where appropriate.

Stochastic ModelThe stochastic model began with much the same input data asthe deterministic model. In general, the work flow used tomodel heterogeneous reservoirs consists of five steps: constructthe structural framework, construct the stratigraphic framework,model the facies, model the petrophysical properties, andupscale the results for flow simulation.

Structural Framework. Twenty-four maximum floodingsurfaces defining the parasequences along with faults and faultpolygons were used to define the structural framework. Fivesurfaces were added to provide greater resolution where thickshales were present in some of the main reservoir intervals. Allsurfaces honored the well tops. The zonation is illustrated onFig. 2.

Stratigraphic Framework. The stochastic model used a gridwith a fine scale resolution. Each parasequence was discretizedinto 10 layers using proportional gridding. Proportionalgridding was used to emulate the stratigraphic thinning andthickening associated with typical Type II sequences.2,3 Thus,the internal fine grid structure consisted of approximately 290

layers with a horizontal resolution of 100m x 100m, and avertical resolution varying between <0 .33m to 1.5m. The finalfine scale model consisted of 8,000,000 cells.

Facies Modeling. Facies modeling is important because itprovides information about the vertical and lateral relationshipsbetween the various reservoir and non-reservoir rocks,ultimately constraining the distribution of the petrophysicalproperties. Each sedimentological facies has variable directions,geometries, and petrophysical properties that must beconsidered. Lithofacies derived from petrophysical analyses donot guarantee a geometrical distribution pattern that can beunderstood in geological terms. Thus, it is preferable to modelthe sedimentological facies patterns to the extent that they can bedefined.

The sedimentological facies in the Barua Field are wellunderstood. The reservoir zones consist of shallow marinedeposits in stacked Type II parasequences. The sands appearcontinuous in each progradational parasequence; and localvariation in sand thickness is gradual, giving rise to broad sandbars or ridges. Widespread thin shales between and within thereservoir sands indicate a uniform and periodic sedimentologicalprocess.

The seismic attribute, instantaneous frequency was generallycorrelated with the depositional facies. In fact, this attributealong with net sand isopachs were used in the deterministicmodel to develop a set of generalized facies distribution maps(Fig. 7). Integrating such attribute maps into the model is oneway to honor the depositional facies pattern and constrain theensuing petrophysical model. The attribute was extracted foreach parasequence conformable to the defined flooding surfaces(horizon slices, Fig. 8). Instantaneous frequency was used as anexternal trend4 or pseudo-facies.

Petrophysical Modeling. Variogram models were constructedfor each zone using the petrophysical data. In general, the dataindicated a W-NW anisotropic trend with the maximumdirection of continuity 1.5 times that of the minor direction.Variograms were modeled with a either a spherical orexponential function and small nugget (less than 1% of the sill).Figure 9 depicts a set of typical variograms for x, y, and zdirections.

Figure 10a depicts one layer of the fine scale porositydistribution. Porosity values and the other petrophysicalvariables were distributed using a Sequential GaussianSimulation algorithm5 constrained by instantaneous frequency.Note the similarity in the distribution patterns between Figs. 10aand 8.

Ten porosity realizations were made for one of the primaryreservoir intervals to evaluate the variation in stochasticmodeling by the approach selected in this study. Observation ofthe multiple realizations shows that the general pattern ofpetrophysical distribution remained the same and variations arelocalized. A typical example from another realization is shownin Fig. 10b.

[SPE 56656] [THE BARUA FIELD, VENEZUELA:] 3

To further evaluate the variation in volumetrics, a part of thefield was selected for pore volume calculation. The differencesfrom realization to realization are very small, usually less than1% (Fig. 11). Upscaling is described in the Flow Simulationssection.

Comparison of Two Models. Net thickness, porosity, and permeability maps from one of thezones were selected to illustrate the differences in reservoirdescription obtained using the two different models. The mapsshown here are the upscaled versions for the flow simulations,but they clearly demonstrate the results of the two differentapproaches. Figures 12 and 13 are the respective deterministicand stochastic net/gross maps for the same zone. Figure 14through 17 are the corresponding maps for porosity andpermeability. The contrast in results from using the twodifferent approaches is obvious. Permeability probably is themost dramatic. One has to believe that the stochastically derivedpermeability distribution is more realistic than one which lookslike a smooth surface constructed by a mapping program.

Flow Simulations The same 34 x 45 areal grid system was used for bothsimulation models (Fig. 18). Grid lines conform to faults whereconsidered feasible. The stochastic reservoir description was upscaled using thesame layering as in the deterministic model. Net thickness(net/gross ratio) and porosity upscaling are straightforward.Permeability upscaling has several options. A commonly usedoption for horizontal permeability is the combination ofharmonic and arithmetic averaging. When this was applied,there were a sufficient number of low values in the stochasticmodel grid to cause the upscaled value to be lower than the zoneaverage value at the well, sometimes much lower. As a result,arithmetic averaging only was used in the upscaling. Theresulting values were more in line with those at the wells. Ahistory run with each upscaled permeability furtherdemonstrated the need for the higher values. Vertical permeability was assigned rather than computed,because the shales between the sands were considered to besealing, unless indicated to be otherwise during the matchingprocess. Reservoir volumes for the two models are very similar.Unfortunately, it can not be concluded which reservoirdescription provided the better starting point for the historymatch. The main reason is that the degree of communicationamong layers at faults is the single biggest factor affecting fieldand well performance. History matching using the deterministicmodel was abandoned, but a satisfactory history matchultimately was obtained using the stochastic reservoircharacterization.

Conclusions1) Reservoir characterization of the Barua field was anevolutionary process. It is very unlikely that the same procedurewould be followed again. If the study were to be started now, itseems probable that the stochastic approach to reservoircharacterization would be followed. An added benefit is that theflow simulation grid and the grid data arrays can be generatedwith the stochastic modeling software in formats competitionwith commercial simulators.2) In stochastic reservoir characterization, consequences of

using the selected permeability upscaling method(s) should beinvestigated thoroughly. In our model, the upscaling schemeused was rather simple. More sophisticated methods areavailable, some of which may prove valueable.

AcknowledgementsMany colleagues of the authors participated in various aspects ofthe study. Their contributions are acknowledged andappreciated. Thanks also are due Helga Ehrhardt of Smedvigwho typed the manuscript.

References:1. Amaefule, V.O., Altunbay, M., Tiab, D., Kersey, D,G.,

and Keelan, D.K: “Enhanced Reservoir Description UsingCore andLog Data to Identify Hydrandic (Flow) Units and PredictPermeability in Uncored Intervals/Wells.” SPE 26436 (1993).

2. Van Wagoner, J.C., Mitchum, R.M., Campioun, k.m., and Rahmanian, V.D.: Siliciclastic Sequence Stratigraphy in Well Logs, Cores, and Outcrops, AAPG Methods in Exploration Series, No. 7, American Association of Petroleum Geologists, Tulsa (1996) 55.3. Deutsch, C.V. and Meehan, D.N.: “Geostatistical Techniques Improve Reservoir Management,” Petroleum Engineer International, (March 1996) 21.4. Goovaerts. P: Geostatistics for Natural Resource Evaluation, Oxford University Press,New York (1997) 483.5. Deutsch, C.V. and Journal, A.G.: GSLIB Geostatistical Software Library and User’s Guide, Oxford University Press, New York (1998) 369

SI Metric Conversion Factorsft x 3.048* E-01 = m

* conversion factor is exact.