2_Basic Statistics_new

Petrel2011PropertyModelingBasicStatisticsPetrel2011PropertyModeling:SkillLevelCourseKrigingVs.GaussianSimulationScaleupwelllogsDataqualitycontrolFaciesModelingPetrophysicalModelingDiscreteDataanalysisIntroPetrelPropertymodelingObjectiveandworkflowGeostatisticsBasicStatisticsPropertymodelingdatapreparationStochasticFaciesmodelingStochastic&DeterministicPetrophysicalmodelingCountinuousDataanalysisUseofsecondaryinformationforpropertymodelingBasicStatistics:WhatisGeostatistics?Geostatisticsisabranchofappliedstatisticsthatplacesemphasisonthegeologicalcontextofthedataandthespatialrelationshipbetweenthedata.Geostatisticaltechniquesareindispensablepartofreservoirmanagementbecausequantitativenumericalmodelsarerequiredforplanningthefield/reservoirdevelopmenttooptimizetime,resourcesandeconomicgain.BasicStatistics:WhyuseGeostatisticsinReservoirmodeling?Veryfewdirectobservations.Analysisofvariablesinspaceanditscorrelation.Descriptionofthereservoirheterogeneity.Providemeansforpopulatinga3Dmodelinaconsistentandreproducibleway.Systematicwayofdescribingandhandlingreservoiruncertainty.Probabilityameasurementofthelikelihoodofanevent.(Measuredinpercent).Varianceameasurementofhowdifferentthemembersofacollectionarefromeachother.(Measuredinunitsofthecollection).Correlationawaytomeasurewhethertwoseparatecollectionsarerelated.(Measuredinpercent).Anisotropyawaytomeasurewhethervariancewithinacollectionofdataisdeterminedbydirection.(Measuredinazimuthandpercenteccentricity).BasicStatistics:DefinitionsStationarityissimplyanASSUMPTIONwhichismaderegardingtherulesofbehaviorofthepropertiesweanalyze,study,ormodelwithgeostatisticaltools.Inpracticaltermsitmeansthattheoverallmeanofaproperty(e.g.,averageporosity)isconstantanddifferencesfromthismeanareseenaslocalfluctuations.TheconceptisappliedinGeostatisticalalgorithmsandislinkedtoStandardNormaldistributions(throughNormalscoretransformations).BasicStatistics:DefinitionsClassesBasicStatistics:UnivariateAnalysisHistogramandProbabilityDistributionFunction(PDF)PropertyValuePDFHistogramisagraphicalrepresentationofthefrequencydistributionofaselectedvariable.BasicStatistics:UnivariateAnalysisCumulativeDistributionFunction(CDF)PropertyValue10ClassesCDFThehistogramclassesarerankedinascendingorderanddisplayedasacumulatedfraction.Histogram&CDFinaHistogramwindow1.OpenaHistogramwindow.2.Selectthelog/propertytoplot.3.SelecttheShowcdfcurveicon.4.Usefiltersifneeded.Histograminobjectsettings1.OpentheobjectSettingswindow.2.GototheHistogramtab.3.Usefiltersandintervals/incrementsasneeded.BasicStatistics:PDFandCDFinPetrel–HistogramNormalDistribution(bimodal)02468105678910111213141516MoreClassesNVFrequency0,000,200,400,600,801,00GammaDistribution0246810121451015202530354045505560MoreClassesGammaFrequency0,000,200,400,600,801,00LognormalDistribution024681012579111315171921232527MoreClassesLNVFrequency0,000,200,400,600,801,00Ahistogramisagraphicalhelptofindtheshapeofthedistribution(Normal,LognormalorGamma).TheDistributionshavespecificshapesandparameters.TheCDFcurveshapesaredependantontheshapeofthehistogram.BasicStatistics:TheoreticalDistribution222)(21),;(xexp00,020,040,060,080,10,120,140,160,180,20510152025303540ProbxProbabilityofaNormalDistributionwithMean=20andStddev=5(blue)andStddev=2(red)Mean:DescribesthelocationofadistributionVariance:Spread(averagedsquaredistance)ofdatafromexpectedvalue(Mean)Unit=squareoforiginaldataStandardDeviation:SquarerootofVariance(positive)Unit=sameunitasoriginaldataEquationforProbabilityofNormalDistributionNormaldistributionofavariablecreatesaSymmetricshape.Thisprovidesaconsistentuseinmathematicalalgorithms,butitmaybesensitivetooutliers.BasicStatistics:NormalDistribution22222)(21)1,0;(21),;(xxexpexpStatisticalconfidencelevelS=1-α(%)Riskα(%)Factorintermsofstandarddeviation68.331.71.00090.010.01.64595.05.01.96095.54.52.00099.01.02.57699.70.33.000Result:Transformationtableinbothdirections;dataaretransformedintoStandardNormalDistribution.BasicStatistics:NormalScoreTransformationBasicStatistics:NormalScoreTransformationBivariatestatisticsexplorestherelationshipbetweentwovariables:Correlationanalysistestingifasignificantcoincidencebetweentwovariablesexist.Regressionanalysisquantifiesanexistingcorrelation(herebyalinearformula).BasicStatistics:BivariateAnalysis–CorrelationCrossplotDisplaysthevaluesoftwovariablesmeasuredatthesamelocationRevealstheDegreeofCorrelation(-1to1)PositivecorrelationNegativecorrelationNocorrelationBasicStatistics:BivariateAnalysisCrossplotandCorrelationCorrelationsetup:1.OpenaFunctionwindow.2.Selectthepropertiestocrossplot.Threepropertiesmaybeplottedinthesamediagram(x,yandalternativelyzcanbeusedforcoloringthesamplepoints.Iftwopropertiesarewellcorrelated,thenonemaybeusedassecondaryinputwhenmodelingtheotherifthishasinsufficientdata(e.g.onlyafewwells).Alogscaleononeorbothaxisispossible.Selectwhethertoview3Dgrid,upscaledcellsand/orrawwelllogdata.CalculatetheCorrelationCoefficientbyusingtheMakelinearregressionfunct