06美赛建模论文.docx
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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
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