A series of models, based predominantly on the logistic product, is presented. The models contain an endogenous technological learning index which gives rise to an enlarged not yet occupied niche, and thus, to an asymptotically enlarged resource basis. The learning effect is formulated in terms of powers of the cumulatively depleted resource. The combination of the resource depletion process and the accompanying technological learning effects form an environment where a multiplication of an originally assumed reserve can emerge. Some light is shed on the non-linear mathematics behind this scenario. (C) 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.