The Hubbert Parabola

The logistic curve, and its derivative the hubbert’s curve, has been widely used to model population growth. And it has been applied to model oil production by M. King Hubbert. The model comes from the following differential equation:

dQ/dt=kQ(1-Q/URR)

where Q(t) is a function of time (measured in years) and it is defined as the cumulative production of a region until the end of year t. The parameter URR is the “Ultimately Recoverable Resources” or the maximum cumulative production that can be reached. K is the Malthusian parameter or the maximum cumulative production growth.

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