Uncertainty Quantification by Using Stochastic

7/29/2019 Uncertainty Quantification by Using Stochastic

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PROCEEDINGS, Thirty-First Workshop on Geothermal Reservoir EngineeringStanford University, Stanford, California, January 30-February 1, 2006SGP-TR-179

UNCERTAINTY QUANTIFICATION BY USING STOCHASTIC APPROACH IN POREVOLUME CALCULATION, WAYANG WINDU GEOTHERMAL FIELD, W. JAVA,

INDONESIA

M. Asrizal, J. Hadi1)

, A. Bahar2)

and J.M. Sihombing3)

1): Magma Nusantara Limited Star Energy Ltd, 2): Kelkar and Associate Inc., 3) Schlumberger Information Solutions.

Magma Nusantara Limited Star Energy LtdWisma Mulia, 50

thflr, Jl. Jend. Gatot Subroto #42

Jakarta, Indonesia, [email protected],[email protected], [email protected],

[email protected]

ABSTRACT

This paper presents the application of a stochasticapproach and Experimental Design techniques to avolcanic geologic system in order to quantify theuncertainty of Pore Volume estimations for WayangWindu geothermal field in West Java, Indonesia. ThePore Volume is a key element when defining the totalresource available in the field. The uncertaintiesbeing addressed include (i) Geometry (top ofreservoir, intrusions and base of reservoir), (ii)Reservoir Continuity (rock type and faciesdistribution) and (iii) Petrophysical Properties(porosity).

The range of uncertainty for each of the parameterswas developed using information from varyingsources, including data from 30 wells, comparablegeothermal fields, Micro Earth Quake (MEQ)measurements, MT/TDEM surveys, etc. Faciesgroups were modeled based on distance of depositionfrom the volcanic center, i.e., Central-Proximal,Proximal-Medial and Medial-Distal. The model wascontrolled by the locations of present day volcaniccenters, XRF, age dating, etc. Each facies groupconsists of different proportions of 5 rock types;lavas, breccias, tuff breccias, lapilli tuffs, and tuffs.Porosity consistent with the rock type and faciesdistribution was generated within the 3D static modelcomprised of approximately 26 millions cells usingPetrel.

The uncertainty was quantified by evaluating theresults of multiple realizations through the Plackett-Burmann experimental design technique. The resultswere then used to generate a range of theoretical porevolumes via Monte Carlo simulation. From thisdistribution, low, medium and high cases wereextracted. The selected cases were upscaled and are

currently being evaluated through rigorous dynamicflow simulation modeling. The results show that thepore volume was most sensitive to the followingparameters (in order); base of reservoir, porosityvalues, rock type proportions, top of reservoir,intrusions and facies distribution.

INTRODUCTION

The Wayang Windu Geothermal Field is situated inthe West Java province of Indonesia, about 150 kmsoutheast of Jakarta (capital city of Indonesia) and 35km south of Bandung (capital city of West Java)(Figure 1).

Figure 1. Wayang Windu Geothermal Field Location

In geothermal development the estimated sustainableresource potential is the most important assumptionmade as this forecast naturally imposes constraints onthe type and scale of future developments. Currently,reservoir simulation is the most accurate method forassessing the power generation capacity ofgeothermal fields under production (PB Power,2000). Fluid reserves in a single or two phase systemsuch as Wayang Windu are believed to be storedwithin the porosity in the rock matrix. Understandingthe geologic framework of the reservoir, especially


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rock type and distribution, fault structure andalteration, is important in a geothermal reservoir.This framework governs key reservoir parameters forsimulation, such as porosity, connectivity andpermeability.

Interpreting rock types and distributions in a volcanic

setting is complex due to alteration and discontinuityof lava and pyroclastic rocks, however using anintegrated geological approach has led to thedevelopment of a consistent reservoir rockframework. A detailed geological model to betterrepresent the 3D distribution of petrophysicalproperties at Wayang Windu is important, especiallyfor estimating the porosity and permeabilitydistribution in the reservoir. One of the keyprocesses of this study is focused on identifying andunderstanding key drivers of pore volume (PV) andto include those uncertainties in a probabilisticresource assessment. Since PV is a key elementwhen defining the total resource available in the field,this overview will be focused on processes to assessthis critical parameter.

Because most geothermal fields are related to ageologic volcanic setting, Experimental Designtechniques should be employed as a standardworkflow in the geothermal industry to acquirereliable results during resource assessment.

RESERVOIR CHARACTERIZATION

Reservoir Top and Bottom (Volume)

In geothermal field development, wells are targetedto penetrate zones with permeability and hightemperature. Downhole pressure-temperature (P-T)surveys indicate that the top of the reservoir ismarked by a change in temperature gradient andpressure within the reservoir. For most of theWayang Windu production wells, the point at whichthey penetrate the top of the reservoir is indicated bya distinct change in the temperature gradientreflecting a reservoir temperature of approximately

240C. The most reliable tool to interpret the top ofthe reservoir is from the downhole P-T survey,however temperature-dependent minerals, alterationand geophysics can be used to predict top of reservoir

both between the wells and outside of well control.

The bottom of the Wayang Windu reservoir waspreviously defined by the deepest drilled well in thereservoir (@ -700 masl (low case). A recent microearthquake (MEQ) survey however indicates seismicevents occurring 4 km below the surface suggestingthat defining the bottom of the reservoir based onwell control may be too conservative. Deep MEQdata interpreted to represent thermal stressproduced from cold injected fluid entering a hotgeothermal reservoir has been used to estimate

reservoir thickness at the Geysers. At Geysers thedeepest MEQ responses (at - 5 km) are usedtentatively to interpret the bottom of the reservoir(Stark, 1990).

Figure 2. 3D reservoir model shows top of reservoir,MEQ events, base of reservoir at -700masl (low case), at 1000 masl (base case)and at -4000 masl (high case).

In summary, the base case volume geometry of thereservoir follows the top of reservoir contouringusing well control and the bottom of the reservoir at -1000 masl. Deep MEQ events induced by waterinjection are used to define the high case reservoirbottom at 4000 masl (Figure 2).

Reservoir Geology Model (2D)

Rock Interpretation

Detailed review of all cores and cuttings from 4 deepcore holes and 26 wells was conducted, supported byFMS imagery analysis, to develop a consistent rockdefinition. However, the following order of priority(confidence level of data) was always used tointerpret the rock facies: thin section, coreexamination, FMS imagery and cuttings.

Surface Geology Interpretation

Surface geology mapping and air photo interpretationidentify eruptive centers and circular features in thearea that were active in the past and are the likelysource the Wayang Windu reservoir rocks. Most of

the eruptive centers observed are located on the northand east sides of the field (Figure 3).

The north eruption center with a distinct drainagepattern represents the Malabar volcanic complex andappears to consist of several nested caldera. Theeastern eruption centers are represented by thenortheast-southwest trending Wayang, Windu andBedil domes. Gunung Kencana, situated far to thesouth of the field, may have contributed to thereservoir rocks at the southern end of Wayang


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Windu. No obvious eruption center can be located tothe west.

Figure 3. Facies, rock types and eruption centers

Subsurface Rocks Distribution

For reservoir modeling purposes, 5 geologic crosssections were constructed through the reservoir tiedto wells with good rock data. Each cross section wasselected to minimize projections and properlyrepresent the fields complexity. Typical of manyvolcanic complexes, well to well correlations weredifficult; consequently it was found that theinterpretation was facilitated by grouping the rocksinto packets of similar origin facies. To correlatesubsurface rocks from wells, the facies model of astructurally undisturbed andesitic stratovolcano wasused (Bogie and McKenzie, 1998) (Figure 4). Themodel suggests that the occurrence of intrusive rocksand thick lava flows are associated with central andproximal facies compared to thick pyroclastics andlahars which are related to medial and distal facies.

Figure 4. Facies model used to assist subsurfacegeologic mapping.

The rock units encountered in the Wayang Windu

field were classified into 4 facies, namely, Central Proximal facies consisting of Lava and Breccias,Proximal Medial facies consisting of Breccias andTuff Breccias, and Medial Distal facies consistingof Lapilli and Tuffs. In the shallow reservoir section,wells in the northern part of the field intersected thicklava flows. In the middle section, wells in the centraland southern parts of the field are dominated bythicker lava flows and breccias (ProximalMedial).The deeper reservoir sections all wells penetratedthick pyroclastics (Medial-Distal). In general, only afew wells have indications of intrusive rocks at TD.

These observations postulated the occurrence ofseveral eruptive events; the lower parts of the wellsreflecting a medial-distal facies sourced from thesouth (Kencana), in the middle and shallow sectionsof the wells in the central and southern parts of thefield reflecting a facies group derived from the east(Wayang Windu) and the shallow section in the

northern part of the field reflecting an eruption sourcein the north (Malabar), (Figure 5).

Figure 5. North-South cross section showingcorrelation of facies groups.

Validation of Geologic Model

Key samples were collected and X-Ray Fluorescence(XRF) analysis conducted to validate the geologicmodel. XRF analysis is frequently used by igneouspetrologists (SGS-Canada) to identify rock types andshow trends in the evolution of magmatic sources(eruption centers). Thirty-nine lava samples from thefield were collected for XRF analysis to confirm thefacies correlation within the field (Figures 5 & 6).

Figure 6. Rock Chemistry Analysis (XRF), the Zr vsTh and Zr vs SiO2 cross plots show samplegroups derived from North, East and Southsources.

The samples are all derived from a tholeiitic to calc-alkaline magma series where a parental tholeiitic(primitive mantle derived) magma erupts withvarying amounts of silicic andesites, which could bederived from a local magma chamber. Thisinterpretation verifies the facies correlation madebetween the wells.


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Reservoir Geology Model (3D)

The objective of constructing the detailed geologicalmodel is to create a 3D distribution of rock types andpetrophysical properties (porosity and permeability).

Interpreting rock types and their distribution within avolcanic setting is complex due to heterogeneity anddiscontinuity of the rocks. In these models, thestochastic approach, i.e., geostatistical methodologywas used within a 26 million grid cell model builtusing PETREL software. Using this approach,multiple models can be generated to quantify variousuncertainties that may exist. Additionally, theapproach also honors well data as well as the spatialrelationships between these data.

The technique used to complete the model includesFacies Transition Simulation, Sequential IndicatorSimulation (SIS) and Sequential Gaussian Simulation

(SGS). Facies Transition Simulation was used todistribute Facies (Central-Proximal, Proximal-Medial, and Medial-Distal). Subsequently, rock types(Lava, Breccia, Tuff Breccia, Lapilli and Tuffs)within each facies setting are simulated using SIS.Finally, porosity is simulated using SGS constrainedto the rock type within each facies. Using this methodthe result of porosity distribution is consistent with itsgeologic framework. Additionally, the method alsoprovides a way to quantify the uncertainty of theporosity distribution through multiple realizationmodels. With this information, better decisions canbe taken with respect to the future development of thefield.

The overall strategy used to evaluate the uncertaintyin the volumetric calculation is as follows: First, abase case was generated using most likelydescriptions for all parameters. Subsequently, usingthe Experimental Design technique, differentcombination of parameters (low and high scenarios)were used to generate multiple models, producing theprobabilistic estimates of the results and the ranges ofthe pore volume. Finally, representative modelswhich represent Downside, Upside and Most LikelyPore Volumes were then used as inputs to thedynamic reservoir simulation.

Model Overview

The reservoir characterization for Wayang Windu hasseveral hierarchies of data integrated withingeologically consistent 3D frameworks. Thehierarchies fall into 2 basic groups:

1) Overall container volume for the reservoir(geometry of the reservoir; Top of Reservoirsurface + Base of Reservoir, structuralconfiguration).

2) Rock types and Petrophysical properties(facies, rock type and porosity distribution).

The data in each of these hierarchies has significantuncertainties which can impact the metrics for theproposed Wayang Windu expansion (e.g. PoreVolume, production profile). In this study a keyobjective was to estimate the uncertainties in theinput data and to incorporate these uncertainties into

probabilistic estimates of the reservoir performance.This was accomplished by generating a suite of 3Dmodels which effectively sampled the range ofpossible characterizations constrained by theframework of the geologic model, the input data andthe associated uncertainties.

As described below, all of the 3D models hadcommon extents (areal, vertical and cell sizes) andused the same representation of the major fault planegeometries. These elements were held invariantthroughout the modeling. In contrast, the facies androck type proportions and the petrophysicalproperties distribution input to the 3D models weresystematically varied over ranges estimated from theuncertainties in the original source data. Thismethodology allowed probabilistic estimates of thekey reservoir metrics to be estimated and appropriatemodels to be passed through to the dynamicsimulation process for the probabilistic performanceprediction.

S-Grid Geometry

The reservoir model grid in Petrel was designed toextend beyond the proven area of the field and toinclude the potential Northern and Western fieldextensions within the Wayang Windu concession. A

uniform 50m cell size was used to allow 3 or morecells between wells, resulting in a 219 x 291 cellareal mesh. The Petrel grid layers were distributedwithin each sequence such that the surface to the baseof the model at -4000m elevation was represented by412 layers. Placing the base of the model grid at theminimum postulated depth (based on MEQinterpretation) enabled the sensitivity of predictedfield performance to the base of reservoir depth to beevaluated by applying progressively shallower basedepths during the subsequent dynamic simulation.

All models used the same conceptual stratiformvolcano geometry for gross layering of the reservoir.

At Wayang Windu this subdivides the sequence into4 sequences, the deeper sequence referred to as the3SD facies group, overlain by the 2AE and 2BEfacies groups (Proximal - Distal facies) and the uppersection developed in the northern side of the fieldwas called 1NP facies group. The reservoir is almostentirely within the facies group of 3SD and 2BEsequence.


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Base Case Model

The Base Case model represented a plausiblescenario generated by using best-guess/most-likelyinputs at each hierarchy, with the notable exceptionof the porosity histograms. The porosity histograms

in the Base Case model were based only on the smalldataset of core porosities available in the study and,as a consequence of their distribution, are believed torepresent low side (conservative) estimates of theactual porosities in the reservoir. It is important tonote that the probability of the Base Case model andof the other models generated during the study werenot assumed (P50, P10, P90) as is often the case,however this was evaluated and is provided as part ofthe conclusions of the study.

Facies and Rock Type (lithotype) Modeling

For the Base Case model the facies picks in the wellswere matched to the interpreted facies boundaries

supplied as a set of digitized well-tie cross sections.These data were used as the basis for generating a setof consistent spatial distributions in 3D. Typicallysome of the 5 rock types are present within a givenfacies region. To simplify the model process, the rocktype proportions were combined for each faciesgroup and then populated geostatistically using SIS,where the distribution is constrained to the proportionand its spatial relationship (distance of volcaniccenter as source of rocks in the model), (Figure 4).

In the Base Case reservoir model approximately 78%of the reservoir pore volume is within Facies group3SD, 15% within Facies group 2BE and 7% withinFacies group 2AE.

Petrophysical (Porosity) modeling

Porosity data available for the study were derivedfrom core data. Porosity is a key component ofreservoir Pore Volume and hence of the resourcebase for the field. Although igh temperaturegeothermal fluids have resulted in the alteration ofportions of the reservoir, the porosity used for themodel was not constrained to the altered and freshrocks. Since the porosity defines the volumes ofmoveable geothermal fluids in the reservoir,measurements of the effective porosity of the

reservoir rock is also required. Fine-tuning of themodel will be conducted after effective porosity datais acquired during the next field development phase.The 3D distributions of porosity were simulatedgeostatistically using the SGS technique, constrainingthem to the rock type distribution according to thehistogram of porosity of the rock types (Figure 7).

Figure 7, 3D porosity distribution (right) showsconsistency with the corresponding rocktype distribution (left).

Fault Planes

The models grid was oriented to have a primary axis

oriented along the major fault trends at WayangWindu (Figure 8) with the aim of simplifying faultgeometries in the dynamic model. The faults wereinterpreted after integrating air photos, surfacemapping data and stratigraphic / facies correlations.The 6 major faults modeled in 3D were constrainedby surface traces, well penetrations, and faciescorrelations. The positions of fault planes were notvaried between models.

Figure 8. Fault planes used in the models.

Uncertainty AssessmentThe Base Case model was intended to provide themost likely scenario based on the current faciesinterpretation, core data and well production data.However, this was not known to represent the P50 orexpected case. For assessment of the range ofpossible outcomes for the Phase II expansion project,several scenarios were generated to capture theimpact of the key PV uncertainties in the modelbuilding.


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Key uncertainties in the static model were porevolume, whose variations can greatly impact the totalresource base for the project, and the connectivity ofthe reservoir, which will alter drainage areas and wellperformance predictions for the project. This secondarea of uncertainty was not investigated in the currentstudy. In combination these impacts strongly

influence plateau length for the field.

In the hierarchical approach to this study, theuncertainties were categorized at some basic levels:

Rock Volume Uncertainty

The gross rock volume uncertainty represents theuncertainty in the overall container volume(geometry of the reservoir; structural configuration +base of reservoir elevation + top of reservoir surface).The internal geometry of the model layering isconstrained by the Top of 1NP facies group. Asdefined by well penetrations, the major part of the

reservoir is within the 3SD facies group, so thevariations in geometry which impact the pore volumeare primarily a consequence of uncertainty in Base ofReservoir, rock type porosity, rock type proportionwithin facies groups and the Top of Reservoir (ToR).

The Base Case for the reservoir was generated at -1000 masl where MEQ events predominatlyoccurred. The downside for the model is constrainedby the deepest drilled well at -700 masl. The upside isdefined by the deepest MEQ events at -4000 masl(Figure 2).

Figure 9. High case, base case and low case TORsurfaces used for modeling.

The Base Case ToR surface incorporates the wellpicks (PT data), the hand contoured ToR maps,isotherm map at sea level and the MT contour data(Figure 9). In the uncertainty assessment the wellpicks for Top of Reservoir (measured from PT data)remained fixed while the MT contours werediscarded. The optimistic (high case) ToR surfacewas generated in Petrel based on the well picks andapplying flattened, hand contoured trends on theflanks of the field. A pessimistic (low case) ToR

surface also used the well picks as control nodes, butused a steeper, hand contoured ToR map to constrainthe flanks.

Facies Group and Rock Proportion Uncertainties

As described above, the main facies group

components of the Base Case model in terms of PoreVolume are facies groups 3SD (78%), 2BE (15%)and 2AE (7%) respectively. Uncertainty in theproportion of these key facies groups within thereservoir was captured from alternative interpretationof the well-tied cross sections which providedoptimistic and pessimistic versions for the spatialdistribution of Proximal to Distal facies boundaries.These distributions were used to redefine the extentof facies group 3SD and the complementary faciesgroups of 2AE and 2BE.

Within each facies, an assemblage of rockproportions comprised a rock types, and the facies

were characterized by the proportion of rock types.The basecase model used rock types proportion foreach facies which were identical to those observed inthe wells and honored the statistical nature of rocktype distribution (Figure 10). However, the actualrock type proportion within each facies is uncertainsince the observed data is biased as a consequence ofthe restricted location of the wells. In this studyuncertainty was capture by alternative proportionsinto the analysis including the variogram. In terms ofPore Volume, optimistic cases have higherproportions of the pyroclastics (tuff breccias, lapillituffs, and tuffs) where is higher porosities rock typeand whereas pessimistic cases have greater

proportion of lavas and breccias (lower porositiesrock type).

Figure 10. Rocks Type distribution was simulated byhonoring variogram, lavas have a lower

range than tuffs.

Petrophysical Property (Porosity) Uncertainties

The porosity distributions in the Base Case modelwere based on sparse (core sample) data andtherefore they have significant uncertaintiesassociated with them. In terms of analyzing the porevolume, porosity distribution within the reservoir wasconstrained to rock type proportion in each facies byhonoring the statistical nature of the parameter usingSGS method. In the model, there is no differentiation


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between altered and fresh porosity. Uncertainty in theporosity value was captured from the alternativevalue of the rocks and the statistical nature of theparameter. To capture the porosity uncertainties inthe models the characterizations used the core-onlyhistogram (Figure 11) for the Base Case, the broaderhistograms (with the higher mean porosities) for the

high porosity cases and the lower histograms (withthe lower mean porosities) for the pessimisticporosity cases.

The matrix permeability and saturations will beevaluated as part of the history matching in thereservoir simulation phase of the study.

Figure 11. Porosity histograms of lavas and lapillituffs have unique distributions used inthe model.

Assessing the impact of uncertainties

As describe above, there are several potentiallysignificant uncertainties which impact the modelspore volume. Traditionally, to assess the uncertainty,a Monte Carlo simulation was run, sampling theindependent parameters based on statistical

distributions, ignoring the geologic model as describeabove. In order to properly quantify the distributionof the pore volume based on 3-D geologicalmodeling and the interaction effect of the propertiesinside the model, an experimental design technique isapplied.

Experimental Design process

Experimental design (ED) is an approach techniqueto investigate the effect of the various variablessimultaneously in a series of experimental runs (inthis case a multiple realization of the 3-D geologicalmodel). A specific combination of properties (inputvariables) at different levels (low, mid and high) thatmake up multiple realizations of the 3-D geologicmodel was set up in a predefined pattern toinvestigate the experimental pore volume response.The results were analyzed to obtain the relationshipbetween the input variables (properties) and theoutput responses (pore volume). These relationshipsact as a proxy function for the pore volume in the 3-Dgeologic model. A pore volume probability curvewas then generated using the Monte Carlo techniquebased on this proxy function.

The simplest ED methods are the 2-level designswhich consider only High and Low values for eachfactor and ignoring the non-linear response. If this isinadequate, a 3-level design (full factorial design)using Low, Mid and High values for each factor maybe necessary to capture the non-linear response.

To reduce the number of experiment runs, afractional factorial design such as Placket-Burman(P-B) is applied to investigate the effects of the maininput variables. For the simple case of 7 factors(variables) and 2 levels (high/low only) the fullfactorial requires 128 scenarios, whereas P-B onlyneeds 12 scenarios to be generated. For largernumbers of factors the differences rapidly increase.

For the Wayang Windu Base Case reservoircharacterization, the key variables selected forinclusion were:

1) Facies geometry2) Rock types proportions3) Porosity Histogram/Variogram4) Top of Reservoir surface5) Base of Reservoir surface6) Intrusion bodies7) Seed number

See (Figure 12) for Plackett-Burman design matrixand Base Case runs.

Experimental Design results and discussion

The Experiment Table data determines the analyticalresponse surface. The associated Pareto chartindicates that the most significant factors for Pore

Volume are the geometry of the base of reservoir andthe porosity histograms (Figure 13).

Figure 12. The Experimental Design table resultsversus Base Case model.

The final step in the Experimental Design method isto evaluate the analytical response surface over therange of possible input parameters using a MonteCarlo process. This provides a probabilistic summaryof outcomes for the model (Figure 14).


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Figure13. Pareto chart showing significance rank of

the input variables to Pore Volume.

From Figure 14, the P10, P50 and P90 Pore Volumeestimates based on this analysis are 5.7, 10.2 and 16.8km

3respectively.

Figure 14 . Probabilistic Pore Volume Calculation viaMonte Carlo process. Note that Base Casewas sited at P17 (6445 10

6m

3) instead of

P50 (10,200 106

m3).

Note that in the S-curve from the Monte Carloanalysis, the Base Case model lies below the P20estimate.

CONCLUSIONS

1. All XRF samples indicate Wayang Windu isrelated to a tholeiitic to calc-alkaline magmaseries derived from the same parentalmagma.

2. Age dating, tuff-soils and XRF data supportwell to well facies correlations.

3. The reservoir rocks consist of medial-distalfacies, dominated by higher porositypyroclastic rocks.

4. The primary factors controlling PoreVolume uncertainty in the model are base ofreservoir and porosity histogram. Secondaryfactors are rock type proportion and top ofreservoir.

5. The Base Case model was conservative asindicated by P17 on the S-curve.

6. The Base Case at P17 shows that theparadigm of Base Case at P50 is misleading

and possibly not capturing the upsidepotential.

7. In order to recognize the upside potential ofgeothermal fields, Multiple Realization /Experimental Design techniques should beemployed as part of the standard workflowin the geothermal industry.

ACKNOWLEDGEMENT

We thank the Management of Star Energy Ltd. Magma Nusantara Ltd., for their support of the workand permission to present this paper. Special thanksgo to the many colleagues in SE-MNL for theirassistance.

REFERENCES

Bahar, A., Ates, H., Kelkar, M. and Al-Deed, M.,Methodology to Incorporate Geological Knowledgein Variogram Modeling, SPE 68704, presented at

the SPE Asia Pacific Oil and Gas Conference andExhibition, held in Jakarta, Indonesia, 17-19 April2001.

Bogie, I., and Mackenzie, K. M, The Application ofa Volcanic Facies Model to an AndesiticStratovolcano Hosted Geothermal System at WayangWindu, Java, Indonesia, presented at 20

thNZ

Geothermal Workshop, in New Zealand, 1998.

F. Friedmann, A. Chawathe, D. Larue, UncertaintyAssessment of Reservoir Performance UsingExperimental Designs, presented at the PetroleumSocietys Canadian International Petroleum

Conference 2001, Calgary, Alberta, Canada, June 12-14, 2001.

Hadi, J., Harrison, C., Keller, J., Rejeki, S.,Overview of Darajat Reservoir Characterization: AVolcanic Hosted Reservoir, presented at the WGC,held in Antalya, Turkey, 24-29 April 2005.

White, D. C.,, Experimental Design as a Frameworkfor Reservoir Studies, SPE 79676, presented at theSPE Reservoir Simulation Symposium, held inHouston, Texas, U.S.A, 3-5 February 2003.

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Uncertainty Quantification by Using Stochastic