Deterministic facies model using lithotype proportion ......proportion matrix, nonstationary case (Yarus, et. al, 2012). Figure 2: LPM showing a user-defined region of better quality

Deterministic facies model using lithotype proportion mapping and plurigaussian simulationguided by seismic attribute.

Tadeo Ditia*, Andrean Satria, Geovani Christopher Kaeng, and Adeline Susanto, Halliburton

[email protected]

Keywordslithotype proportion mapping, acoustic impedance,facies modeling

Summary

Modelers are faced with a variety of challenges whenbuilding geocellular models. One significantchallenge centers on facies modeling. Practitionersare driven by the depositional models theyunderstand, but all too often the mathematicalmethods they use are less understood. The selectionof a simulation algorithm and the methods used tointroduce trends and conceptual geologic informationare two potentially significant areas inwhichproblems canarise. To address these issues, theauthorspropose common facies simulationsalgorithms be combined with the use of a lithotypeproportion matrix (LPM).

LPM allows the geomodellers to map the reservoirboth vertically and laterally using well proportiondata. Acoustic impedance(AI)data will be treated asguidance to the trend of the reservoir interval. AIdatawill be blocking to the 3D geocellular grid and usedas the calibration to the model. By using thecombination of seismic blocking, LPM, andplurigaussian simulation (PGS), themodeler will haveobjects control (facies) in their pixel-based modelsequence model.

The implementation of a LPM and seismic attributein combination with pixel-based methods,such asPGS provides a workflow that is both powerful andeasy to use.

Introduction

Geostatistical methods have their limitation whenapplied in complex geological settings. In somecases, the reservoir architecture presents complexfacies transitions, which cannot be simulated withmono-Gaussian techniques. However, modelers arepresented with a plethora of challenges whenattempting to produce models based on real data,including honoring depositional facies boundary

conditions and their proportions, honoring the data inpresence of numerous or closely spaced wells.

The simplest and frequently used method for faciesmodeling is sequential indicator simulation (SIS).This algorithm is very straightforward and able tohandle anisotropy of maximum continuity direction.However, the algorithm cannot regulate thetransitional rule between lithology laterally.

On the other hand, object-based modeling solves thismajor problem faced by SIS because it can rule thelithology transition laterally. This algorithm canproduce a deterministic model. This means thisspecified algorithm is lack of randomness(stochastic). It usually fails for the very large wellcounts. Because it usually preserves the object model,it cannot preserve the probability distributionfunction of input wells in the process.

The plurigaussianapproach has the ability to handlecomplex facies relationship both vertically andlaterally in a pixel simulation. The one powerfulcombination of methodologies is the use of LPM withplurigaussian algorithm. TheLPM counts fornonstationary casesfor each facies with every layerand interval.

Lithotype Proportion Matrix

The LPM consists of lithology curves representingthe facies proportions lithotypes (grouped facies)locally for every blocked layer throughout the model.For the stationarity case (Figure 1A), a singleproportion curve is calculated from the pooled set ofwell control. In nonstationary cases, local proportioncurves are created from grouped wells (Figure 1B)located near one another that share similar faciesrelationships. These are referred to as groupedproportion curves. The LPM (Figure 1C) is computedby interpolating the grouped proportion curves to thegeocellular grid. The result is essentially a suite ofhundreds of trend maps; one for each lithotype ineach layer throughout all layers and all intervals.

The purpose of the LPM is to introduce secondaryinformation, minimally, the various trends in the data.

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Facies simulation algorithms combined with lithotype proportion mapping

For example, Figure 1C shows the evaporite facies(blue) increasing in proportion to the east (right) andthe siltstone facies (yellow) increasing to the north(up). If a practitioner chooses to modify these trendsor insert a geometric pattern of facies related to theconceptual geologic model, the grouped proportioncurves canbe edited and copied to desired locations as“pseudo” proportion curves. Thus, when the LPM isrecreated, this updated secondary information iscaptured and ready to be used in subsequentsimulations. Figure 2 illustrates a modified LPM,which captures a high permeability feature bymodifying the proportions to include better qualityreservoir in a channel-like feature.

Seismic Attribute Blocking and SeismicCalibration

Calibrating seismic properties, such as AI tolithologies is not a clear-cut process. Ideally, eachlithology would correspond to a different range of AIvalues; unfortunately, this rarely occurs and there ismore often an overlap between the lithologies and therange in AI (Figure 3).

The calibration involves the use of the crossplot,where the seismic attribute value lies on X-axis withthe Y-axis as probability (Figure 4).

Seismic attribute blocking is used to block a 3Dseismic attribute volume onto a grid. The purpose ofseismic blocking is to calibrate the attribute value toidentify which facies are associated with a particularrange value of amplitude. This process will averagethe value of the seismic attribute and assign the valueto every cell in3D geocellular. The preferred methodis using the same number of samples to calibrate therelationship between the seismic attribute and thefacies. This method will give the result of probabilityof seismic attribute class in relationship with facies.Seismic attribute blocking and calibration can beused to quality control (QC) the facies changinglaterally and vertically.

Seismic data will help the geomodeller define thecontinuity of the facies because of lack of well data.With the combination of LPMand seismic attribute,the geomodeller can easily interpret the distributionof particular facies for particular layering of themodel.

Sequential Indicator Simulation

Sequential simulation techniques explicitly calculatethe conditional distribution at each point and samplefrom this distribution. SIS will require an indicatorfor

each modeled interval. By constraining therandomness, spatial distributions vary fromrealization to realization;yet, always honor the dataand variogram.

Plurigaussian Simulation

Plurigaussian method assumes a logical ordering ortransition between lithologies controlledby LPM, thedata, and variogram.The results also show the sameordering in the lithologies. PGS can use twovariograms; one for each of the two lithology sets.

Case Studies

In a West Texas field located on the eastern edge ofthe Central Basin platform in the West TexasPermian Basin (Figure 5), production is from theGrayburg Formation (Permian,Guadalupian), whichis transitional between the previously more openmarine conditions of the San Andres Formation andthe more arid sabkha and siliciclastic eolian dunefield environment of the younger Queen Formation.

Lithologically, the Grayburg Formationis composedof alternating dolomite and siltstone for a totalthickness of 140 m. Dolomites range from anhydriticskeletal wackestones tomudstones. Porosity is moldicor vuggy and can be extensively plugged byanhydrite. The siltstones are dominantly angular tosubrounded quartz grains with angular feldspathicgrains, which commonly alter to clay often pluggingpore throats. Siltstone porosity is intergranular. Thisformation has a characteristic shoaling-upward,prograding sedimentary motif, ranging from shallowopenmarine to tidal flat/sabkha sediments. The silt isbelieved to be of eolian origin, reworked bystrandline processes into a series of thin, offlappingshoals. Progradation of the carbonate shelf wasapproximately from west to east. Structurally, thereservoir is a north-south-trending asymmetricalanticline, dipping gently eastward into the MidlandBasin. The Permian climatic regime was similar tothe Plio-Pleistocene with major periods of glaciation.The carbonates formed during interglacial periods ofrelative high sealevel, whereas the eolian siltstoneswere most likely deposited during low sea levelglacial periods with a source from the present daysoutheast New Mexico.

Results and Discussion

Two different LPMs were created: one allowing thegrouped proportion curves to be interpolated with nomodification or introduction of pseudo-proportioncurves, and one with modifications to introduce a



continuous geometric zone of better reservoir quality(siltstone, thief zone) known to be present. Each LPMwas used with two different modeling methods: SISand PGS respectively. For SIS, a simulation is shownwith no introduction of secondary information todemonstrate the general effect LPM has on thisparticular method. The results are shown below.

Sequential Indicator Simulation

If the modeler is SIS without a secondary constraint,such as LPM (Figure 6A),the results are noisy, thereis no control over facies boundary conditions, andfacies occur in areas where they do not belong.Figure 6B illustrates the improvement of the modelwith the introduction of the LPM. With the pseudo-proportion curve, themodeler can introduce amoregeological concept and generate a cleaner faciesmodel (Figure 6C).

AI calibration wasused as a background to thesimulation. Based on the seismic blocking andcalibration, the value AI ranges between 3.89 and0.61 will result ineolian facies in the model (Figure7).

Plurigaussian Simulation

PGSmethod assumes a logical ordering or transitionbetween lithologies controlled by LPM, the data, andvariogram. The results also show the same orderingin the lithologies. PGS can use two variograms: onefor each of the two lithology sets (Figure 8). In thisstudy, one variogram controls the geometry of twosiltstone facies, and the other variogramcontrolsgeometry of carbonate facies. Figure 9Ashows a model using unedited LPM generateshighlyoptimistically simulated connectivity of high-permeability zone (red). Whereas, Figure 9Bintroduces the pseudo-proportion map to the modeland generates a more geologically reliable model.

The PGS results model fits with the AI calibrationbetter and also provides more reliable lithologycontact vertically (Figure 10).

Conclusion

There is no stochastic modeling method that isuniversally best for all possible petroleum reservoirproblems. As stochastic modeling becomes moreaccepted in the petroleum industry, and as morestochastic modeling techniques are developed, themost successful case studies will be those that viewthe growing assortment of methods as a tool kit ratherthan as a set of competing methods.The seismic

attribute can provide guidance becausethe well gap inbetween the well allows the model to makemoregeological sense. PGS as the algorithm has theflexibility to give two variograms in one interval eachfor every lithology set.

The implementation of a LPM and seismic attributein combination with pixel-based modeling,such asplurigaussian simulation provides a workflow thatgenerates a more geologically reliable model.

References

Srivastra R.M., 1994, An Overview of StochasticMethods for Reservoir Characterization; CA 3:Stochastic Modeling and Geostatistics, Chap 1.Tulsa, Oklahoma, AAPG.

Yarus J.M., Chambers R.L., and Maucec M.2012,Facies Simulation in Practice: LithotypeProportion Mapping and PlurigaussianSimulation, a Powerful Combination;Paperpresented atthe Ninth International GeostatisticsCongress, Oslo, Norway, 11–15 June.P-014.

Yarus J.M., and Chambers R.L., 1994, StochasticModeling and Geostatistics; Tulsa, Oklahoma,AAPG.



Figure 1: Interval 2 proportion curves and matrix:(A)vertical proportion curve, stationary case; (B)grouped proportion curves;(C)lithotypeproportion matrix, nonstationary case (Yarus, et. al, 2012).

Figure 2: LPM showing a user-defined region of better qualityreservoir relating to high permeability (Yaruset al. 2012).

Figure 3: AI probability value.

Figure 4: Crossplot diagram showing AI value (X-axis) andprobability (Y-axis).

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Figure 5: Study data location.

Figure 6: (A) SIS result with no LPM model; (B) raw LPM model; and (C) using the pseudo-proportion curve model.

Figure 7: (A) 3D view of SIS QC model with AI calibration (purple marked AI range value 0.38 to 0.61) showing the distribution of eolian faciesthrough the model;(B) Crosssection comparison between AI (left) and SIS facies model (right).

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Figure 8: Two variograms model for plurigaussian facies simulation.

Figure 9: (A)PGS result with no LPM model;(B)raw LPM model.

Figure 10: (A) 3D view PGS QC model with AI calibration (purple marks AI range value 0.38 to 0.61) showing the distribution of eolian faciesthrough the model;(B) crosssection comparison between AI (left) and PGS facies model (right).

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Documents

Deterministic facies model using lithotype proportion ......proportion matrix, nonstationary case (Yarus, et. al, 2012). Figure 2: LPM showing a user-defined region of better quality