A dynamic model for liquid fossil fuel production based on gross product/ERoEI coupling

Since 1940, many attempts to model oil production have been proposed. These approaches, using increasing complexity, consider growing and decay of production independently of external, time-varying, causes. It is here proposed to extend the production equation by a dynamic dependency between oil and Energy Return on Energy Invested (ERoEI). The model is based on mass and energy conservation and can be applied to all extracted liquid fossil fuels. After comparison with oil extraction and ERoEI dynamics, it highlights the existence of an external, controlling parameter: the investment rate, which account for the re-investment in newly operated liquid fuel sources. Its dynamic provides explanations about the oil shock and some explanations about the peak prediction issues of the Hubbert model. Studying this evolution suggests an attempt to control the oil production in order to sustain a globally linear production, starting around 1943: at short time scale (shorter than 28–36 years), the investment rate evolved linearly. However, in order to keep a linearly growing production at long time scale, the investment rate had to evolve exponentially: this was achieved through a piecewize linear control, where the investment rate and its derivative doubled every 28–36 years. The link between this control and the oil shocks suggests the next oil shock will occur around 2035–2040. The model also allows to highlight a major issue in liquid fossil fuel production: even if gross product can be controlled and keeps growing linearly, net product, which account for the energy delivered by the oil industry to the consumer, can decrease before the gross product peaks, due to the decay of ERoEI. At this point, the energy benefit of the oil industry will inevitably decrease and oil production will slow down. Based on the present model and a sensibility study on its parameters, this tipping point will happen between 2026 and 2039. Net product of fossil liquid fuels could therefore keep growing linearly until this point, where a steep decay is expected. Hence production will be strongly asymmetric regarding the peak, contrary to the prediction suggested by Hubbert's model. Production will finally be close to zero around 2063–2072.