MCM ICM 数学建模优秀论文 石油资源模型.pdf

ThePetroleumArmageddon163

ThePetroleumArmageddon

JonathanGiuffrida
PalmerMebane
DanielLackek
MaggieWalkerGovernor'sSchool
Richmond,VA

Advisor:JohnBarnes

Summary
Wedescribethedepletionofpetroleum,avitalnonrenewableresource,over
thenextfewdecades.Petroleumisafossilfuelthatfuelsourindustries,heats
ourbuildings,andpowersourautomobiles;plasticsandfertilizersarealso
derivedfromoil.Theproductionofnonrenewableresourcesthatcannotbe
returnedtotheenvironmentisgenerallyconsideredtofollowabell-shaped
curve;asinterestanddemandincrease,therateofproductionlikewisein-
creasesuntiltheworldisproducingatcapacity,whencetheratedecreasesas
theresourceisslowlyexhausted.
Ourmodelassumesthatproductionandconsumptionareequivalent;this
doesnotaccountforstockpilesofoilorthedelaycausedbyshippingand
distribution.Wealsoassumethattotaldiscoveriesofnewreservesandtotal
productionfollowlogisticcurves;thisisheavilysupportedbyprofessional
opinionandbyourdata.
Ourappr6achincludesfourmajorfunctionsoftime:totalproduction,total
knownoil,totalremainingoil,andtotaldemand."Total"meanscumulative;
thederivativesofthesefunctionsaretheproduction,discovery,anddemand
ofoilatanytime(exceptfortotalremainingoil).Theequationsincltidepa-
rametersforproduction,discovery,anddemand,whichallowourfunctions
tofollowhistoricaldata.Thefunctionfordemandisbasedheavilyontotal
production,inaccordancewiththelawofsupplyanddemand,whichinturn
dependsontotalknownoil(asacarryingcapacity)andondemand.,
Byvaryingtheparameters,themodelisflexibleenoughtoprovidefortech-
nologicaladvance,economiclimit/incentive,naturalormanmadedisaster,and
increaseord6creaseindemand.Themodelalsoincludesamanagementpol-
icyforfutureproduction,involvinggovernmentlimitsonproductiontoenable

TheUMAPJournal26(2)(2005)163-174.@Copyright2005byCOMAP,Inc.Allrightsreserved.
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