An energy-economic oil production model

An energy-economic model for global oil production is presented. By combining a production function for economic output with an expression for oil supply, a system of differential-algebraic equations is derived whose solution contains oil production, referred to as Hubbert curves, and the price of oil. The system of equations is solved numerically with several methods whose accuracy can be validated against an analytical solution that arises for one distinct scenario. The graphs for oil production break the symmetry of the well-known bell-shaped Hubbert curves and predict a much steeper decline past peak oil production. This supports increasing evidence that large decline rates might indeed materialize for global oil supply. This contribution also provides some ideas of how dynamical systems theory might be applied to more complex energy-economic modelling in the future.