logistic model

This study reviews a variety of growth curve models and the theoretical frameworks that lay behind them. In many systems, growth patterns are, or must, ultimately be subjected to some form of limitation. A number of curve models have been developed to describe and predict such behaviours. Symmetric growth curves have frequently been used for forecasting fossil fuel production, but others have expressed a need for more flexible and asymmetric models.

A number of examples show differences and applications of various growth curve models. It is concluded that these growth curve models can be utilised as forecasting tools, but are do not necessarily provide better predictions than any other method. Consequently, growth curve models and other forecasting methods should be used together to provide a triangulated forecast. urthermore, the growth curve methodology offers a simple tool for resource management to determine what might happen to future production if resource availability poses a problem. In the light of peak oil and the awareness of natural resources as a basis for the continued well-being of society and mankind, resource management should be an important factor in future social planning.

Published in: Natural Resources Research, Volume 20, Issue 2, June 2011, Pages 103-116
Available from: Global Energy Systems or SpringerLink

The logistic function has been used to describe the discovery and production of oil and natural gas at the national level. This type of functional representation provides a direct approach for estimating the available supply of the resource and the time at which that supply will be essentially depleted. The mathematical characteristics of the function imply restrictions, which are not necessarily applicable to natural resource-production patterns. We examine these restrictions in the context of crude-oil production at a regional level. We attempt to show that statistical estimates of the functional parameters based on actual crude-oil production could satisfy the mathematical restrictions inherent in the logistic function.

Published in: Energy, Volume 9, Issue 7, July 1984, Pages 565-570
Available from: ScienceDirect

The United States has a vast supply of coal, with almost 30% of world reserves (BP, 2008) and more than 1600 Gt (short) as remaining coal resources (Ruppert et al., 2002). The US is also the world’s second largest coal producer after China and annually produces more than twice as much coal as India, the third largest producer (BP, 2008). The reserves are concentrated in a few states, giving them a major influence on future production. Historically many states have also shown a dramatic reduction in recoverable coal volumes and this has been closely investigated. Current recoverable estimates may also be too high, especially if further restrictions are imposed. The average calorific value of US coals has decreased from 29.2 MJ/kg in 1950 to 23.6 MJ/kg in 2007 as U.S. production moved to subbituminous western coals (Annual Energy Review, 2007). This has also been examined in more detail. This study also uses established analysis methods from oil and gas production forecasting, such as Hubbert linearization and logistic curves, to create some possible future outlooks for U.S. coal production. In one case, the production stabilizes at 1400 Mt annually and remains there until the end of the century, provided that Montana dramatically increases coal output. The second case, which ignores mining restrictions, forecasts a maximum production of 2500 Mt annually by the end of the century.

Published in: International Journal of Coal Geology, Volume 78, Issue 3, May 2009, Pages 201-216
Available from: ScienceDirect
also available from: Global Energy Systems