Mathematical Modeling of the World Oil Production Peak

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Mathematical Modeling of the World Oil Production
Peak

• S. Korte (P. Berg)
• Aug. 10, 2005

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Hubbert Model

• M. King Hubbert in1956, predicted U.S oil
  production will peak in 1970 using the basic
  model

http//dieoff.org/page191.htm
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Extension to Hubbert Model
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Extension SupplyDemand Model
Features
i) As b,m , Hubbert model is recovered
ii) D increases if production gt
demand D decreases if production
lt demand
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Phase Plane
Region I - No Oscillations Region II III -
Oscillations
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Hubbert vs 2-D model
Note All numerical calculations preformed by
fourth order Runge-Kutta Method
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Extension
Supply-Demand-Reserves Model 1
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Supply-Demand Reserves Model 1
Four Reductions

• c , becomes Supply-Demand model
• b , becomes Supply-Reserves model
• b,c , becomes Hubbert model
• a , becomes Demand-Reserves model
• There exists a curious limiting shape for demand
  as a

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Supply-Demand-Reserves Model 1
Limiting Shape
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Supply-Demand-Reserves Model 1
3-D vs. Hubbert
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Supply-Demand-Reserves Model 2
Q Are there different models which would also
fit the data that Hubbert fitted his model to?
- No reduction to the Hubbert model is possible
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Supply-Demand-Reserves Model 2
3-D Model II vs. Hubbert
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Possible Future Work

• Look at world oil data and estimate the constants
• Make a justifiable prediction for the worldwide
  oil peak production