A Simple Interpretation of Hubbert’s Model of Resource Exploitation

Abstract

Abstract:The well known "Hubbert curve" assumes that the production curve of a crude oil in a free market economy is "bell shaped" and symmetric. The model was first applied in the 1950s as a way of forecasting the production of crude oil in the US lower 48 states. Today, variants of the model are often used for describing the worldwide production of crude oil, which is supposed to reach a global production peak ("peak oil") and to decline afterwards. The model has also been shown to be generally valid for mineral resources other than crude oil and also for slowly renewable biological resources such as whales. Despite its widespread use, Hubbert's modelis sometimes criticized for being arbitrary and its underlying assumptions are rarely examined. In the present work, we use a simple model to generate the bell shaped curve curve using the smallest possible number of assumptions, taking also into account the "Energy Return to Energy Invested" (EROI or EROEI) parameter. We show that this model can reproduce several historical cases, even for resources other than crude oil, and provide a useful tool for understanding the general mechanisms of resource exploitation and the future of energy production in the world's economy.

Mind Sized World Models

“…Thus, if a model has to help human minds in understanding the future, a fundamental factor is that it must be testable on a real-world system. The results obtained for the two-stock model on an economic system that went through a complete exploitation cycle of mineral or biological resources (10) gives us confidence that -mind sized‖ models can be trusted as tools for understanding what the future may have in store for us.…”

“…In a recent study [10], it was shown that the model could quantitatively describe a number of historical cases of economic systems based on the exploitation of non-renewable or slowly renewable resources. Among these systems, we have gold mining, whaling in the 19th, century, and oil extraction in some of the world's regions.…”

“…If we consider the threestock model (termed here also the -Seneca model‖), so far, it has not been quantitatively fitted to historical data, but from a qualitative viewpoint, we find some examples of asymmetric, forward-skewed production curves, such as in the production of Caspian sturgeon [14]. It is likely that it will be possible to describe the historical data by a curve-fitting procedure similar to the one used in [10] for the two-stock system, However, the experience with the two-stock model shows that a quantitative fitting is complex and it becomes difficult to manage already with a small number of parameters. It is not known, at present, if it would be possible to find unique sets of parameters for these more complex systems.…”

“…However, as that stock is also gradually dissipated, the system evolves toward a lower rate of dissipation (production) from one stock to the other. The overall result ( Figure 5) is a bell-shaped curve, as described in [10]. In this form, the two-stock model can be seen as equivalent to the empirical -Hubbert model‖ [11] that describes a number of cases of oil extraction in large productive regions.…”

Rethinking Economic Growth Theory From a Biophysical Perspective

“…Bardi and Lavacchi (2009) have shown that the famous Lotka-Volterra equations (which are usually used to model predator-prey dynamics) can be adapted to model the resource exploitation process:Ṙ…”