Newsletter No 3 September 2010

Modeling fossil fuel availability and price

Dr. Frédéric Reynès & Sam Okullo, MSc.

oil_ee_9_10The price and supply of fossil fuels are two key issues that are inter-related in the climate change problem. The extent to which fossil fuels will be extracted greatly determines the potential of the future anthropogenic CO2 emissions whereas price greatly determines the rate at which low carbon substitutes — such as hydrogen technologies — are used.

Over the last decades, models attempting to predict fossil fuel production and prices have been subject to many empirical and theoretical controversies. Empirically, researchers disagree on the date of the peak of production, on the amount of extractable reserves, and on the impact of technology on future supply. Theoretically, models differ on their representation of the production process and on the role and objectives of economic agents. These differences, including the uncertainty involved in simulation, make it difficult to provide decisive conclusions about future supplies of fossil fuels and their prices. Nonetheless, the undertaking remains worthwhile given that more realistic models for the production process are continuously being realized and that these models give useful insights for the evaluation of sustainable policies.

Broadly classified these models fit in two categories: technical models and economic models. Largely inspired by the geo-engineering models used at the well level, the technical approach is symbolized by the famous Hubbert (1956) model. This approach assumes that the level of production is mainly driven by geological, physical and technical factors and can reasonably be approximated by a bell-shaped mathematical function. Production should as a consequence grow from initially low levels, to peak and decline thereafter. The technical approach has the advantage of simplicity and is also known to be consistent with several production profiles (see e.g. Brandt, 2007). The approach has, however, failed to predict OPEC production and has generally been criticized for neglecting economic variables (Pesaran and Samiei, 1995). Given the current changing economic environment, predictions from these models could thus be debatable.

The economic approach of oil production is largely symbolized by the famous Hotelling (1931) model of exhaustible resources. In this approach, the optimal level of extraction of a non-renewable resource maximises the intertemporal profit (i.e. the cumulated profit over a given period of time). Consequently producers’ choices about extraction in the present are influenced by their anticipation of future developments. Compared to the technical approach, the economic approach has the advantage of sound economic foundations but, in basic form, has the disadvantage of failing to explain the often observed peaked production profiles and the largely non-increasing fossil fuel prices that has been observed historically.
Whereas these two approaches are often seen as antagonistic, our research aims to reconcile them. In a theoretical contribution (Reynès et al., 2010), we investigate how economic theory explains the Hubbert peak oil model. We argue that the economic approach encompasses the technical approach by showing that a technical or geological constraint can be reinterpreted as a cost constraint and thus incorporated in the economic approach. More generally, we show that production curve trajectories over time reflect changes in profitability, that is, mainly changes in costs and price.

We confront this theoretical intuition empirically by developing a complete economic model of the crude oil market. This model is calibrated for 11 oil producers (among them 5 OPEC regions) using real data for production, reserve, price and production costs. In a first application, we investigate to what extent new reserve discoveries in old crude oil regions can attenuate the peak oil (Okullo and Reynès, 2010). Results from the model indicate that substantial reserve additions will be required in mature crude oil regions if an inexorable decline in non-OPEC crude oil production by 2030 is to be avoided. We also find that new discoveries in OPEC do not affect the global peak in production: because of their rather large reserve holdings, OPEC countries base their production decision more on strategy than on resource depletion.

The model is currently being extended to incorporate several other important features of the fossil fuel market such as regional demand markets, production capacity constraints, endogenous reserve additions, strategic buyers. The development of this model is founded by NWO as part of the ACTS Sustainable Hydrogen program ( As a component of the project on “The Feasibility of the Hydrogen Economy as a Function of Developments in Global Energy Markets and Climate Change Policies”, the fossil fuel model will be ultimately coupled with the bottom-up TIAM model of European energy system transitions in order to explore the socio-technical conditions that are most likely to enhance the economic feasibility of a hydrogen economy.

Contact information: Samuel Okullo.  


Brandt, A. R., 2007. Testing Hubbert. Energy Policy 35 (5), 3074-3088.

Hotelling, H., 1931. The Economics of Exhaustible Resources. The Journal of Political Economy 39 (2), 137-175.

Hubbert, M. K., 1956. Nuclear Energy and Fossil Fuels. Drilling and production practice 23, 7-25.

Okullo, S. J., Reynès, F., 2010. Can Reserve Additions in Mature Crude Oil Provinces Attenuate Peak Oil? SURED 2010 Conference. Available at

Pesaran, M. H., Samiei, H., 1995. Forecasting ultimate resource recovery. International Journal of Forecasting 11 (4), 543-555.

Reynès, F., Okullo, S., Hofkes, M., 2010. How does economic theory explain the Hubbert peak oil model? IVM Working Paper 10/01. Available at