06美赛建模论文.docx

06美赛建模论文.docx

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06美赛建模论文

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2005MathematicalContestinModeling（MCM）SummarySheet

（Attachacopyofthispagetoeachcopyofyoursolutionpaper.）

Typeasummaryofyourresultsonthispage.Donotinclude

thenameofyourschool,advisor,orteammembersonthispage.

Summary

Thispaperaimstopredictthedepletionofcrudeoilreserve.Inourprediction,weanalyzetherelationshipbetweenproduction,reserveandsomeexogenousfactorsindetail.AnalyzingthedatafromwebsiteofOrganizationofPetroleumExportingCountries（OPEC）andU.S.EnergyInformationAdministration（EIA）,weproposethreemodelstoforecasttheannualpetroleumproductionandpeakproductionyears.

Ourfirstmodelisashort-termpredictionforregionalannualproduction.BasedontheHubbertmodel,weobtainadifferentialequationforthecumulativeproduction.Usingtheleastsquaresfits,weobtainthevaluesofparametersforthedifferentialequation.Solvingtheequation,wegetaroughpredictionoftheoilproduction.

Thesecondoneisusedforlong-termforecast.Firstly,wemodeltheaccumulativediscoverybylogisticregression;thenweintroducethereserve-to-productionratioconcepttodescribetherelationshipbetweenthereserveandproduction;finally,wedesignarecursionoftimetopredicttheproductionyearbyyear.Accordingtothevariationofreserve-to-productionratio,weconsidertwoscenariosandfindthepeakyearofproductionis2010and2015respectivelyandeventilltheyearof2100,theannualproductioncanbeatthelevelof5.5billionbarrels.

Thethirdmodeltakessomeexogenousfactorsimpactingproductionintoaccount.Wedividethosefactorsintothreecategories:

Supplyfactors,DemandfactorsandModulationfactors.Choosingfourmainfactors,wefiguredouthowtheyimpactproductionbyNeuralNetworkmethod.Thenwecheckthetrendofproductionvariationandthepeakyearofthismodel,andfindthatourpredictionagreescloselywithJeanLahrrere’spredictionaswellastheforecastofthesecondmodel.

Basingonourmodel,weproposerecommendationstoensurethesustainableusageandsecurityofoilresource.Finally,wedesignpoliciestocontroltheenvironmentaleffectsandtoencouragethenewenergyandenergy-efficiencyresearch.

Thefutureof“blackgold”

电子科技大学

林杰220210301叶蔚2206202012夏斌2202405030

Introduction

Petroleum,orcrudeoil,isavitalexhaustibleresourcefoundtrappedincertainrocksbelowtheearth'scrust.Itisadark,stickyliquidwhich,scientificallyspeaking,isclassedasahydrocarbon.Crudeoilishighlyflammableandcanbeburnedtocreateenergy.Alongwithitssisterhydrocarbon,naturalgas,crudeoilmakesanexcellentfuel.

Beingviewedasthelifelineofthemodernindustrialcivilization,willpetroleumproductionkeepupwiththeincreasingdemand?

Toanswerthisquestion,adetailedanalysisonproductionandreservesofpetroleumisneeded.Petroleumproductionisdeeplyinfluencedbyexogenousfactorssuchasglobaleconomy,politics,populationandenvironment.Soweshouldtakethesefactorsintoaccount.Ourgoalistopredictthedepletion—declineinproduction—ofpetroleumthroughouranalysis,andfindtheconnectionsbetweenthoseexogenousfactorsandpetroleumdepletion.Withourprediction,wecananswerthequestion:

whetherpetroleumwillbeexhaustedinthefuture,orweneedn’tworryaboutit.

SymbolsUsed

P

Theannualproductionofpetroleum

Thecumulativeproductionofpetroleum

R

Thereservesofpetroleum

Accumulativediscoverytillthej-thyear

Annualdiscoveryofthej-thyear

TheratioofR/P

bn

Billion（109）

b

Barrel

ReviewofLiterature

1OPEC

OrganizationofPetroleumExportingCountries（OPEC）isaninternationalorganizationofelevendevelopingcountries,whichareheavilyreliantonoilrevenuesastheirmainsourceofincome.ThecurrentmembersareAlgeria,Indonesia,Iran,Iraq,Kuwait,Libya,Nigeria,Qatar,SaudiArabia,theUnitedArabEmiratesandVenezuela.

OPEC’selevenmembercollectivelysupplyabout40percentoftheworld'soiloutput,andpossessmorethanthree-quartersoftheworld'stotalprovencrudeoilreserves.

2TheEnergyInformationAdministration（EIA）

TheEnergyInformationAdministration（EIA）,createdbyU.S.Congressin1977,isastatisticalagencyoftheU.S.DepartmentofEnergy.Theyprovidepolicy-independentdata,forecasts,andanalysestopromotesoundpolicymaking,efficientmarkets,andpublicunderstandingregardingenergyanditsinteractionwiththeeconomyandtheenvironment.

3HubbertPeak

Hubbert'sPeakisthenamesometimesgiventothehighestpointonthecurveofanOilProduction-Timegraphforacountry,regionortheworld.ItisnamedafterDr.MKingHubbert,thegeologistwhoin1956predictedtheoilproductionpeakoftheUSAin1971（hisactualpredictionwasthemid-1970s）.Othershaveattemptedtodothesameforthewholeworld,especiallysincethelate1980s.Theconsensusisthatitwillhappenbytheendofthisdecade.Infact,itcouldhaveoccurredalready,in2000or2003,oritcouldbeoccurringrightnow,in2004.

4TheLogisticEquation

Thelogisticgrowthmodelassumesthatapopulation

ofindividuals,cells,orinanimateobjectsgrowsordiffusesatanexponentialrateuntiltheapproachofalimitorcapacityslowsthegrowth.Thismodelcanbeexpressedmathematicallybythefollowingordinarydifferentialequation,whichspecifiesthegrowthrate

isproportionaltotheproductof

and

where

istheupperbound

:

5NeuralNetwork

Neuralnetworksaredesignedtoworklikeanervecellsystem,similartotheworkingsofthehumanorbiologicalbraininitsphysicalform.Artificialneuralnetworksarepowerfultoolsforuseinclassification,empiricalmodeling,predictionandpatternrecognition.Neuralnetworkswillneverreplaceconventionalmethodsinsometasks;butasagrowinglistofapplications,theneuralarchitecturewillprovideeitheranalternativeoracomplementtotheseothertechniques.

Thesourcesofdata

GiventhatOPEC’smemberspossessover75%ofworld'stotalprovencrudeoilreserves,weconsiderthedataonpetroleumofOPECasworldwide.Allofthiskindofdatacomesfrom“OPECannualstatisticalbulletin2003”.However,allelevenmembersofOPECaredevelopingcountries;consequentlytheirgrossdomesticproduct（GDP）amount,populationandemissionsofgreenhousegasescannotrepresentthewholeworld’slevel.Sothedataonabovefactorsareofthewholeworld,whichcomesfromEIA.

Methodology

Petroleumproductionisdeeplyinfluencedbymanyexogenousfactors,suchaseconomy,politics,environmentandpopulation.Forexample,theGulfWar,whichbrokeoutin1991,decreasesIraqiandKuwaiti1991’sannualpetroleumproductionby86.6%and77.9%respectively[AnnualStatisticalBulletin,OPEC,2003].Petroleumproductionisalsoaffectedbytheestimatesofreserves.

Topredicttheproductionandreservesofpetroleum,wemustexaminethoseexogenousfactors.Herewelistsomemajorexogenousfactorsasfollows:

●Time

Petroleumisanonrenewableresource,sotheproductionofpetroleumcanstaythesameallthetime.Itwillvarywithtime.

●Reserves

Theamountofreserveslimitswilllimitstheproductionofpetroleumtokeepsustainable.

●Population

Petroleumisanessentialofourdailylife.Forexample,ourcarcannotmovewithpetrol.Sopopulationwillaffectpetroleumproductionwithoutdoubt.

●GDP

Thegrowthofeconomydependsonenergybadly.SoGDPcantosomeextentreflectthedemandforenergy.Alargeproportionofenergycomesfrompetroleum.Therefore,GDPisaimportantfactorwhichinfluence

●Emissionof

isakindofgreenhousegas,theemissionofitisconcernedbythewholeworld.Thegovernmentswilllimittheuseofpetroleumtocontroltheemissionof

Combiningallexogenousfactors,wecanfigureouttherelationshipbetweenthosefactorsandproduction:

WherePdenotestheannualproduction;t,R,POP,G,andEdenotetime,reserves,population,GDP,andemissionof

respectively.

Tofacilitaterepresentationofthedataandasmootheranalysis,wefirstlyfindouttheinfluenceofoneortwofactors,thentakeotherfactorsintoaccount.Wedivideourpredictioninto3models:

1.Firstly,wejustconsiderthetimefactorwithalltheotherfactorsremainingunchanged.

.Wecanusethismodeltopredicttheshort-termlocalproduction.

2.Secondly,wetakethechangeofreservesintoaccount.So

.Weusethismodeltopredictthelong-termproductionwithrespecttotheexpansionofreserves.

3.Thirdly,wetakeotherfactorsintoconsideration.Hence,

Thismodelisusedinthelong-termandglobalprediction.Andwecancomparetheresultsofitandthesecondone.

Model1Short-termPrediction

1.Dealingwiththedata

Assumingthatallfactorsremainunchangedexcepttimeinthisperiod,weneeddatahavethecorrespondingfeature—stable.WefindthatthedataofallOPECortheworldisn’tverystableduetothelargeareaofthem.Soweselectthedataofalocalarea.SaudiArabiahasthelargestreservesofpetroleumintheworld（25%oftheprovedreserves）[www.cia.gov].SaudiArabiaalsoranksasthelargestpetroleumexporteraroundtheworld,andplaysaleadingroleinOPEC.SoSaudiArabianpetroleumproductioncanroughlyrepresentthewholeworld.Moreover,SaudiArabiahasarelativestabledomesticenvironment.Therefore,wechoosethedataofSaudiArabiatocreatethe