ueno_et_

Journal of Petroleum Science and Engineering 77 (2011) 200–208

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Journal of Petroleum Science and Engineering

j ourna l homepage: www.e lsev ie r.com/ locate /pet ro l

Constraining uncertainty in volumetric estimation: A case study from NamoradoField, Brazil

Juliana FinotoBueno a,⁎, RodrigoDuarteDrummond a,1, AlexandreCampaneVidal a,1, Sérgio Sacani Sancevero b,2

a Institute of Geosciences, P.O.Box 6152, University of Campinas, UNICAMP, 13083–870, Campinas, SP, Brazilb Roxar do Brasil Ltda, Rua Assembleia 10, Sala 2412 CEP 20011–910, Centro Rio de Janeiro, RJ, Brazil

⁎ Corresponding author. Tel.: +55 19 3521 4659; faxE-mail addresses: [email protected] (J.F

[email protected] (R.D. Drummond), [email protected]@roxar.com (S.S. Sancevero).

1 Tel.: +55 19 3521 4659; fax: +55 19 3289 1562.2 Tel./fax: +55 21 2222 1941.

0920-4105/$ – see front matter © 2011 Published by Edoi:10.1016/j.petrol.2011.03.003

a b s t r a c t
a r t i c l e i n f o
Article history:Received 13 August 2010Accepted 28 March 2011Available online xxxx

Keywords:Uncertainty analysis3D geological modelingVolumetric estimationNamorado FieldCase study

This paper describes the reservoir-modeling case of Namorado, an oil field located in offshore Brazil, theworkflow, tolls and benefits of a 3D integrated study with uncertainties. A geological uncertainty study wasinitiated to identify and quantify the input parameters of greatest impact in the reservoir model. In order torank reservoir uncertainties, a series of static models was built and a method to quantify the uncertaintyassociated with geological parameters was tested. The proposed workflow was developed in the Irap-RMSsoftware and comprised the following steps: construction of the structural model; construction of thegeological model; population of the geological model with petrophysical parameters, and uncertaintyanalysis. To construct the static reservoir model, the low, base and high cases of each uncertainty parameterwere defined and used, and all combinations of these parameters were tested. The uncertainties related to thechoice of parameters such as the variogram characteristics (type, range, and sill) involved in eachgeostatistical iteration were included into the workflow. The highest ranked contributors to uncertainty inStock Tank Oil Initially in Place (STOIIP) were oil–water contacts, range of variogram used to calculateporosity in possible-reservoir facies, and 3D water saturation. The uncertainties related to the mainparameters that affect the volumetric calculation were incorporated into the proposed workflow. Thehydrocarbon probabilistic volume established for the Namorado Field varies from 92.07 to 134.04×106 m3.

: +55 19 3289 1562.. Bueno),ge.unicamp.br (A.C. Vidal),

lsevier B.V.

© 2011 Published by Elsevier B.V.

1. Introduction

The available data for oil and gas fields are in general not enough tominimize the uncertainties related to the construction of reservoirmodels. The understanding of uncertainties involved in reservoirmodeling is an essential tool to support decisions in the petroleumindustry. The knowledge of uncertainty management related toprediction of hydrocarbon volumes has increased in the last decades,as a result of reliable 3D geological models made available byimprovements in computer processing. A successful geological modelshould represent the ‘real’ situation as accurate as possible. However,the ‘real’ geological situation is often unknown, and the modelrepresents an interpretation based on limited assumptions of what islikely to occur between data points (Lelliott et al., 2009).

When soft and hard data are not enough to define the distribution ofparameters between data points, stochastic algorithms can be used to

provide a measure of uncertainty by means of multiple realizationsinvolving lithofacies and petrophysical parameters. Despite the advan-tages of using deterministicmethods to calculate hydrocarbon reservoirvolumes in simple and understandableways, the uncertainties inherentto each input data set used to build 3D static reservoirmodels cannot beexpressed in a single deterministic realization.

According to Zabalza-Mezghani et al. (2004) the sources ofuncertainties, in reservoir engineering, can be classified as anywherewithin the reservoir modeling workflow. Such uncertainties areassociated with: the static model, upscaling, fluid flow modeling,production data integration, production scheme development, andeconomic evaluation. These authors classified the different uncer-tainty behaviors as deterministic, discrete and stochastic uncer-tainties. Lelliott et al. (2009) grouped the sources of uncertaintiesrelated to geological modeling into: data density (the density ofboreholes used to construct the model); data quality (quality of thedata used to construct the model, including borehole elevation,sample type, drilling method and logging quality); geologicalcomplexity (geological variability throughout the site); and modelingsoftwares. Mann (1993) suggested four main categories of uncertain-ty in geology: (1) variability: the inherent natural variability thatexists in geological objects; (2) measurement: uncertainty caused byimperfections in the measurement procedure; (3) sampling: uncer-tainty that arises from the process of making a measurement at a

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201J.F. Bueno et al. / Journal of Petroleum Science and Engineering 77 (2011) 200–208

specific spatial location; and (4) modeling: uncertainty associatedwith processing of data to create the model.

This work focuses on the uncertainties associated with stochasticstatic reservoir modeling of the Namorado Field, offshore Brazil.According to Beucher et al. (2008) large uncertainties in gross volumeestimation, and consequently in volumetric estimation, derive notonly from measurement errors, but also from the way the staticreservoir model is constructed.

The Namorado Field was the first giant offshore Brazil oil field andhas been productive since 1979 (Winter et al., 2007). The estimatedin-place oil volume is 669million bbl or 106×106 m3 (Guardado et al.,1989). Although the deterministic volumetric estimate of the field hasbeen known, the static reservoir probabilistic model and its associateduncertainties have not been well established in the literature. Despitethe importance of reservoir uncertainties to predict the recovery ofpetroleum volumes and flow performance, the results of uncertaintyanalyses carried out in some Brazilian oil fields are not always madeavailable by the oil companies, because these data are taken as con-fidential. According to Keogh et al. (2008), uncertainty studies con-cerning the analysis of all input parameters used to build a staticgeological model are not often performed.

This study focuses on the identification and quantification of un-certainties associated with the geological parameters used to modelthe Namorado Field static reservoir, the incorporation of these un-certainties into the proposed workflow, and the constraint of theprobabilistic oil volume estimation.

2. Field description

2.1. Geological setting

The Namorado Field is located in the Brazilian continental plat-form, in the central part of Campos Basin (Fig. 1). The area of CamposBasin is approximately 100,000 km2. More than 1600 wells have beendrilled for over three decades of oil and gas exploration. Campos is animportant offshore basin, encompassing more than 90% of theBrazilian reserves for oil and gas (Winter et al., 2007). The NamoradoField was discovered by Petrobrás in 1975, and has become the first

Fig. 1. A. Location map of the Namorado Field (offshore Brazil); B. Zoom of Fig. A showing the(black circles). (For interpretation of the references to color in this figure legend, the reade

giant offshore Brazilian oil field with reserves of more than 250million bbl (Mendonça et al., 2004).

The Campos Basin is a passive continental margin-type basinformed during the breakup of the Gondwana supercontinent,resulting in the separation of South America and Africa (Guardadoet al., 1989). According to geological and strategic criteria of oilproduction, this basin can be divided into three compartments:proximal, intermediate, and distal, with depths varying from 100 to3000 m (Schlumberger, 1998). The Campos Basin is composed ofseveral hydrocarbon producing fields of Oligo-Miocene ages. Sedi-ment starvation occurred in the basin from the Cenomanian to theMaestrichtian as a consequence of tectonic subsidence, eustatic sea-level rise, and a relatively low influx of terrigenous sediments(Guardado et al., 1989).

Ponte and Asmus (1976) proposed the division of the CamposBasin into three sedimentary megasequences from base to top: (1) acontinental megasequence related to the rift phase, (2) a transitionalmegasequence related to the initial drift, and (3) a marine mega-sequence related to the late drift phase. Each sequence correspondsto a distinct depositional environment and crustal rifting phase(Guardado et al., 1989).

The Campos Basin stratigraphic sequence includes the Campos,Macaé, and Lagoa Feia Formations (Guardado et al., 1989, 2000). Theinstallation of the marine environment started with carbonatedeposition in shallow-water conditions, followed by the siliciclasticsof the Macaé Formation. The Campos Basin encompasses dozens ofoil-producing fields, and Namorado is a major field in this basin.

The reservoir of the Namorado Field occurs at depths between−2900 m and −3400 m, and is composed of the Namoradosandstone (Meneses and Adams, 1990). The Namorado sandstone iscomposed of turbidite sands deposited during the Cenomanian/Turonian and is intercalated with shale and carbonates. The axis of thedepositional paleochannel strikes NW–SE. The Namorado field is afaulted structure separated into five blocks by normal faults. The mainhydrocarbon producing block is at the center of the field. Hydrocarbonaccumulation is controlled by turbidite sandstone pinchout, andstructural features. The reservoir seals are marbles and shales of thehemipelagic sequence (Guardado et al., 1989). The turbidite sand-stones are up to 115 m thick, and usually massive, medium-grained,

Namorado Field; C. Zoom of Fig. B showing the Namorado Field and the location of wellsr is referred to the web version of this article.)

Fig. 2. Workflow diagram used in the uncertainty study.

202 J.F. Bueno et al. / Journal of Petroleum Science and Engineering 77 (2011) 200–208

arkosic, and locally conglomeratic (Guardado et al., 1989; Menesesand Adams, 1990; Barboza, 2005). The porosity of the sandstones liesbetween 20 and 30%, and the permeability is higher than 1 darcy(Guardado et al., 1989; Meneses and Adams, 1990).

2.2. Database

The Namorado Field is covered by a 3D seismic survey, fromwhichstructural and sedimentological information was derived for reservoirevaluation. A total of 55 wells drilled and logged between 1975 and1986 were used in this study. The well logs presented in the datasetare: density (RHOB), gamma-ray (GR), resistivity (ILD), neutron po-rosity (NPHI), and sonic (DT). Eight wells were cored and qualitativepetrographic description is available. The dataset is currently availableby the Brazilian National Agency of Petroleum (ANP).

3. Workflow

This study was conducted in the Roxar Irap-RMS geostatisticalframework, using stochastic modeling techniques to build thegeological model based on geometrical, geological, and petrophysicalproperties of the reservoir. The workflow set up is a scenario-basedworkflow where high and low cases around the base case are definedto each of the parameters under investigation. For each parameter thehigh and low cases were relative to the mean value of the variabledistribution, the multiple stochastic realizations were run.

In Irap-RMS, the workflow consists of a series of IPL (InternalProgramming Language) scripts that execute a routine of modelingjobs. The parameter under investigation is varied, while the otherparameters are kept to the high-, base- and low-case scenarios (Keoghet al., 2008). This kind of investigation is known as a ‘three levels fullfactorial’ experimental set-up. Each IPL workflow job involves thebuilding of a full model, from structural modeling, to grid building, tofacies modeling, to petrophysical modeling, and finally to volumecalculations, in order to give the response variable for that particularscenario.

The workflow (Fig. 2) comprises the following steps: (1) con-struction of the structural model; (2) construction of the geologicalmodel; (3) population of the geological model with petrophysicalparameters, and (4) uncertainty analysis. Theworkflow used tomodelthe Namorado Field consisted of three phases, each progressivelymore complex. The initial phase comprised steps 1, 2 and 3 so that thehigh, base and low-cases of the static model were defined. The seconditeration was carried out to address the uncertainty of the parametersused to construct the static model. In the third iteration, the highest-ranked contributors to uncertainty were used to constrain the oil fieldvolume.

3.1. Stage 1: construction of the structural model

The data consist of a set of depth markers measured along thewells, which give the true vertical depth at the intersections of thewell with the sedimentary units, and seismic horizons recorded attime units. Three depositional sequences labeled 3, 2 and 1 werefound in the 3D seismic data. The reservoir top and bottom weredefined in OpenDtect software. These depositional sequences hadalready been identified in previous works such as Johann (1997) andSouza (1997) as a succession of sandstones and shales. After con-version of the seismic horizons picks into depth units, the reservoirtop was used as the reference surface for the reservoir organization.All interpreted surfaces are approximately parallel to this referencesurface.

The construction of horizon surfaces was divided into two steps. Inthe first step the deterministic horizon surfaces were built using theLocal B-spline algorithm. This algorithm calculates the amplitude to afamily of bell-shaped functions (B-splines) using a local heuristic

approach (de Boor, 1978; Soleimani et al., 2008). The sum of thesefunctions defines a function in (x, y) that approaches the input data.These surfaces were used as input for the horizon simulation in thesecond step. In the second step, the horizon simulation around thedeterministic ones was used in order to introduce laterally varyinguncertainties into the simulation. This allows performing realisticuncertainty analysis since depth uncertainty is often a function of thewell density. The algorithm used for horizon simulation was ordinarykriging.

The eight faults mapped in the reservoir area were used to buildthe structural model (Fig. 3A). The fault model created was used toconstruct the structural model for the high-, base- and low-casescenarios. Fault F3 divides the Namorado field into two smaller blocks:the high-block (left of Fig. 3B) and the low-block (right of Fig. 3B).The fault model was not incorporated in the structural simulation,because correctly honoring varying fault locations in RMS is not easilyautomated.

3.2. Stage 2: construction of the geological model

The facies were defined by means of the weighed k-nearestneighbors (wk-NN) algorithm, which is a method for classifyingobjects based on closest training examples in the feature space. Thewk-NN is a type of instance-based learning or lazy learning, where thefunction is only approximated locally and all computation is deferreduntil classification is concluded (Hechenbichler and Schliep, 2004). Inthe wk-NN classification the class determination of each point notonly takes into account the classes of k nearest neighbors among thepoints from the training set, but also the distance of each of theseneighbors to the point in question.

Twenty-nine lithofacies were identified from the core samples,from clean to shaly sandstones, shales, conglomerates, diamictites andcarbonates. They were grouped into three major lithotypes accordingto their overall character, and petrophysical properties: coarse- to

Fig. 3. A. Structural model for the Namorado field; B. Structural division of the field into high and low blocks.


medium-grained sand (reservoir), shale and mixed lithotypes (non-reservoir), and shaly sands (possible-reservoir). These three newgroups were used as training examples in the wk-NN classification,and the validation showed that 92.8% of the core samples wereclassified correctly by the wk-NN triangular weight function.

In order to capture the reservoir heterogeneities, a grid cell re-solution of 50×50×1 m was defined. The facies log defined in wellswith the wk-NN algorithm was scaled and discretized to this gridresolution without any loss of heterogeneity.

A deterministic grid model can be described in terms of pro-portions by building the global vertical proportion curve (VPC). TheVPC gives the proportion of each lithotype per level in the flattenedspace, integrated laterally over the whole field. It reflects the verticalvariations of the lithotype proportions and confirms the depositionalprocess that governed the facies distribution (Ravenne et al., 2002).For each horizontal layer of the grid, the probability of occurrence of afacies can be extracted from the VPC and transferred as a 2D vectorialproperty. When these 2D vectorial properties are stacked vertically, a(one dimension) proportion curve representing the vertical evolutionof facies proportions is obtained, i.e. facies evolution with depth(Fig. 4A) (Labourdette et al., 2008). This deterministic grid model canalso be described vertically. Each single column of the model can bedefined by the proportion of each facies it contains (Fig. 4B). Fig. 4Bshows a higher content of the reservoir facies in the NW–SE direction,which represents the direction of the paleodepositional channel, and adecrease of the reservoir facies in the eastern portion of the Namoradofield. According to stratigraphic division of the field, the zone belowsequence 3 shows a higher content of the reservoir facies (Fig. 4A).

The facies model (Fig. 5A) was built using the Sequential IndicatorSimulation (SIS), the vertical trends being obtained with verticalproportion curves (Fig. 4A). SIS is an algorithm used to generate adiscrete 3D facies parameter for the current realization. To each cell inthe parameter a facies code is assigned, defining the facies (reservoir,possible-reservoir and non-reservoir) present in that cell, based onprobabilities calculated from well data and user-defined input(Srivastava, 1994; Seifert and Jensen, 1999). Although SIS does notdefine geological bodies, the elongation direction can be imposedthrough use of the variogram model (Martin, 2008). The indicatorvariogramswere calculated for parallel, normal and vertical directionsin relation to the NW–SE direction of the paleochannel in theNamorado field (Fig. 4C), and for all facies (i.e. possible-reservoir,reservoir and non-reservoir) in the reservoir. For all reservoir layers,the percentage of each facies within the low, base and high cases(Fig. 5B) honored the fieldmean percentage of that facies preserved inwells (Fig. 5C).

3.3. Stage 3: population of the geological model with petrophysicalparameters

Water saturation was defined for all 55 wells using the Archiemethod for the reservoir facies, and the Simandoux method for thepossible-reservoir facies.

Two oil–water contacts (OWC) were defined according to themain fault (F3) that divides the Namorado Field into high and lowblocks. For each block OWC was defined at the depth where watersaturation first reaches, or is close to, 100% in the reservoir facies,which corresponds to the free water level (FWL) (Fig. 3B). Accordingto this criterion OWC were defined at a −3100 m depth in the highblock (Fig. 6A), and at a −3155 m depth in the low block (Fig. 6B).

Porosity and water saturation curves calculated from well datawere used to model the properties of the reservoir and the possible-reservoir facies of the Namorado field. Porosity and water saturationdata were scaled up to grid resolution without loss of heterogeneityand checked for trends related to depth. Variograms were developedin all direction for each facies from blocked well data. SequentialGaussian Simulation (SGS) was then used to populate grid cells. SGS isa kriging-based method in which unsampled locations are sequen-tially visited in a random order until all unsampled points are visited(Deutsch and Journel, 1992; Kelkar and Perez, 2002). The spatialcorrelation of the porosity, after transformation into the Gaussianscale, is fitted in the sedimentary system where the simulations areperformed. The results are then back-transformed to the initialstructural system before volume calculations. Porosity (Fig. 7A) andwater saturation are then simulated, reproducing per-facies distribu-tion as derived from the blocked well data.

An interval average porosity cut-off N20%was used to calculate thenet-to-gross (NTG) ratio of each interval. This number was obtainedfrom percentile 10% of porosity distribution in the reservoir faciesafter simulation (Fig. 7B, C). NTG was then calculated for thegeological models in each of the three reservoir layers from blockedwell data.

3.4. Stage 4: uncertainty analysis

One-hundred realizations for the complete model were generatedby varying seed number only. In this first iteration, parameters wereranked by STOIIP (Fig. 8A) and P90, P50, and P10 cases (Fig. 8B) werepicked as low-, base- and high-case scenarios for structural, grid,facies, porosity, water saturation and net-to-gross models.

In the second iteration, uncertainties associated with parameterswere addressed in iteration 1. The Bo factor was not included in the

Fig. 4. A. Global vertical proportion curve representing the vertical distribution of facies. B. Well data distributed along columns defined by the proportion of each facies they contain.C. Indicator variograms along the wells per lithotype. Experimental variograms are represented by dotted lines and the models by thick lines.


uncertainty analysis, because a previous PVT study had reported abase-case Bo factor around 1% uncertainty. In this step, the parametersthat are actually influential on the production were identified. Low-,base- and high-case models were used to address uncertaintiesassociated with 3D porosity, water saturation, and net-to-grossparameters. To address uncertainties associated with variographicparameters like range, azimuth and direction, a normal (Gaussian)distribution was adopted. Using this option for each realization, thevalue of the uncertainty is sampled to the defined normal distribution.This type of distribution was used in this stage, because it consumesless time than the low, base and high cases, and theoretically andempirically a normal distribution best represents the uncertaintyassociated with any new sample of a geological parameter (Quirk andRuthrauff, 2008).

For the second iteration, 243 realizations of the workflow wererun. The three levels full factorial algorithm was used in this iteration.By using this algorithm, all combinations of high, base and low valuesfor each sensitivity were tested (Montgomery, 2001). In addition, thecombination with all sensitivities at base value was tested. LatinHypercube was used as sampling method, which prescribes asubdivision of the distribution into N equiprobable intervals. Then, anumber is randomly selected from each of the N intervals, in order toachieve a better representation of the underlying distribution (McKayet al., 1979; Xu et al., 2005; Maschio et al., 2010). Tornado style plotwas used for ranking each parameter in terms of its contribution tothe total uncertainty range in STOIIP (Fig. 9A). The highest-rankedcontributors to uncertainty were (Fig. 9B): (1) oil–water contact inthe high block, (2) oil–water contact in the low block, (3) range of

Fig. 5. A. Base-case scenario for the Namorado field 3D reservoir model showing facies distribution. B. Facies distribution using the Sequential Indicator Simulation (SIS). C. Faciesdistribution per well.


variogram used for porosity simulation in parallel direction in thepossible-reservoir facies, and (4) 3D water saturation in the oil zone.

In the third iteration, the four highest ranked parametersdetermined in iteration 2 (Fig. 9B) were used for addressinguncertainty in the high-, base- and low-case models. The low/base/high algorithm is typically used in sensitivity studies, where the aim isto investigate the effect of the different uncertainties/sensitivitiesrelated to each other, or alternatively, the effect on the total un-certainty. The purpose of the third iteration was to address theuncertainty associated with the main parameters ranked in thesecond iteration into the proposed workflow and consequently toconstrain the hydrocarbon volume of the Namorado field. In thisiteration the three levels full factorial algorithm was used and 81realizations of this workflow were run, combining all low-, base- andhigh-case parameters.

4. Results

The STOIIP obtained after the third iteration was: 92.07×106 m3

for P90, 109.11×106 m3 for P50 and 134.04×106 m3 for P10 scenarios(Fig. 10A, B). The P50 volume is close to that shown by Guardado et al.(1989) of 106×106 m3.

Fig. 6. Water saturation vs. depth diagrams showing oil–water conta

The two highest ranked contributors to uncertainty were oil–watercontacts in high and low blocks (Fig. 9B). Oil–water contacts weredefined based onwater saturation, and two OWCwere found accordingto structural model of the field, one at a −3100 m depth in the highblock, and another at a−3155 mdepth in the lowblock (Fig. 7A). Thesevalues are close to those found by Meneses and Adams (1990) around−3200 m to −3100 m. In the proposed workflow it was defined thatOWC correspond to FWL, but this relation could be in reality quitedifferent. Probably the oil–water contact in the high and low blocks isnotflat in thefield.As a single value for this contactwasadopted for eachblock, this caused a large impact in the uncertainty analysis.

The third major contributor to uncertainty was the range ofvariogram used to simulate porosity in the parallel direction to thefield paleo-channel in the possible-reservoir facies (Fig. 9B). Thevariogram model describes the spatial correlation between the pa-rameter of interest as a function of distance. The possible-reservoirfacies and its petrophysical properties can have an erratic distributionalong the wells in the Namorado field causing its impact in theuncertainty analysis.

The fourthmain parameter that affected the volumetric calculationwas the 3D water saturation, and this may have been caused byseveral factors, such as the choice of algorithm used to simulate thewater saturation in the whole field or the method used to calculate

cts (OWC) for the Namorado Field: A. high block; B. low block.

Fig. 7. A. Base-case scenario for Namorado field 3D reservoir model showing porosity simulation and division of the field in high and low blocks. Porosity distribution per facies:B. reservoir facies, and C. possible-reservoir facies.


water saturation. The lack of certain petrophysical parameters, such ascapillary pressure, may be another factor that could have generatedthis impact of water saturation in the calculation of uncertainties. Ifcapillary pressure data were available, other methods could beapplied to calculate the water saturation, such as the J-function, inwhich cell permeability is a proxy for capillarity (Beucher et al., 2008).

5. Conclusions

The workflow used in this study successfully integrated all thegeological uncertainty scenarios, and produced significant results. Amodeling workflow has been established to handle both multiplescenarios, and multiple realizations of a given scenario. The sources ofuncertainties related to the inaccuracy of the measurements were nottaken into account.

The combination of different parameters: depositional facies,porosity and water saturation, net-to-gross ratio and oil–watercontact uncertainties, resulted in 243 hydrocarbon volume estima-tions, and in the ranking of the impact of these parameters in volumeestimation. The ‘top 4’ contributors to the total uncertainty range in

Fig. 8. A. Histogram showing the total uncertainty range in STOIIP; B. Statist

STOIIP were identified and the corresponding uncertainties were usedto build the low, base and high-case scenarios to the Namorado Field.

The major contributors to uncertainty were oil–water contacts inboth high and low blocks, followed by range of variogram used tocalculate porosity in the parallel direction in the possible-reservoirfacies, and 3D water saturation.

After 81 realizations of all combinations of low-, base- and high-case scenarios and ‘top 4’ parameters, the hydrocarbon volume of theNamorado Field was established as varying from 92.07 to 134.04×106 m3. The value obtained for STOIIP at P50 was 109.11×106 m3,

which is very close to the deterministic value of 106×106 m3

presented by Guardado et al. (1989).The limitation of the proposed workflow is that structural

modeling is restricted because the fault model was not incorporatedinto the simulation. In the Irap-RMS, fault modeling was notautomated, limiting the rebuilding of grids where fault patterns havechanged due to interpretation. As this study focuses on staticmodelinguncertainties, this limitation is not significant, as has been shown byKeogh et al. (2008)who conducted a staticmodeling of the Glitne Field(North Sea). The impact on the calculation of gross rock volume was

ics for STOIIP before uncertainty analysis of the P90, P50 and P10 cases.

Fig. 9. A. Tornado-style plot ranking each parameter in terms of its contribution to the total uncertainty range in STOIIP. The most significant parameter at the top and the leastsignificant parameter at the bottom; B. List of the ‘top 4’ contributors to the uncertainty range in STOIIP as identified in the Tornado plot.


less than 1% between the grids constructed with not-faulted andfaulted grids. Fault modeling does not represent a serious problem instatic modeling; on the other hand, should dynamic analysis beemployed, the uncertainty in fault modeling must be accounted for.

Despite the limitation described above, in the proposed workflowall the sources of uncertainties were considered to quantify thevariability linked to the construction of a reservoir in the static model.Not only all the steps from geometry to flow parameters werefollowed, but also the variability linked to the choice of the parameter.The uncertainties in the choice of parameters such as the variogramcharacteristics (type, range and sill) involved in each geostatisticalprocess were also considered.

The main focus of this work was to identify, quantify, andincorporate all uncertainties involved in the construction of a staticmodel for the Namorado field, and this purpose has been successfullyreached. A step forward is necessary, with focus on the understandingof the behavior of the highest-ranked contributors to uncertainty inSTOIIP, so as to minimize their impact on the geological model.

Fig. 10. A. Histogram showing the total uncertainty range in STOIIP; B. statis

Acknowledgments

The authors wish to thank Petrobras for the financial support, andRoxar for providing the Irap-RMS reservoir modeling software. MoacirCornetti is greatly acknowledged for his useful suggestions. Webenefited from the positive comments of two referees.

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