Fossil energy resources - IMACLIM

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Model Documentation - IMACLIM
Corresponding documentation
Model information
Institution Centre international de recherche sur l'environnement et le développement (CIRED), France,, Societe de Mathematiques Appliquees et de Sciences Humaines (SMASH), France,
Solution concept General equilibrium (closed economy)
Solution method SimulationImaclim-R is implemented in Scilab, and uses the fonction fsolve from a shared C++ library to solve the static equilibrium system of non-linear equations.
Anticipation Recursive dynamics: each year the equilibrium is solved (system of non-linear equations), in between two years parameters to the equilibrium evolve according to specified functions.

Modelling the long-term dynamics of oil markets

The IMACLIM-R framework includes the following four properties of oil markets in dedicated bottom-up modules describing the dynamics of oil supply and demand:

(a) A small group of suppliers benefit from market power; Middle-Eastern countries (ME) at the core of the Organization of the Petroleum Exporting Countries (OPEC)) can dictate (Granger cause) world oil prices (Gulen, 1996)1 until such time as they approach their depletion constraint.
(b) The geological nature of World oil reserves dictates that oil supply has a limited adaptability to demand. Total production is constrained by the amount of economically exploitable reserves and by technical constraints that lead to inertias in the deployment of production capacities. The former depends on producers' response to price-signals whereas the latter affects the conversion of economically exploitable reserves into actual production.
(c) Oil demand depends on agents' microeconomic trade-offs. This concerns both agents' decisions affecting their oil consumption, as well as incentives aimed at increasing the production of alternatives to oil based fuels (biofuels, Coal-To-Liquid). Those price-driven decisions will determine the short term oil demand, as well as the long-run oil-dependency of the economy.
(d) Uncertainties on the technical, geopolitical and economical determinants of oil markets alter agents' expectations. Four such forces are presented: increasing demand over time; exogenous decrease of production costs due to technological change; incentives for further exploration given by the inverse relationship between marginal extraction costs and reserves; and increases in aggregate production capacity due to production at newly developed sites. The assumption of perfectly optimizing isolated agents, which remains a useful analytical benchmark, fails to provide a good proxy for the oil economy.

Oil supply

Imaclim-R includes seven categories of conventional and five categories of non-conventional oil resources in each region. Each category (i) is characterized by an amount of recoverable resources (Total resource of a given category is the sum of resources extracted before 2001 and recoverable resources); and by a threshold selling price above which producers initiate production. This price is a proxy for production costs and accessibility. ??? gives the inhouse numerical assumptions made on the amount of ultimate resources in the main groups of regions. The figures are consistent with conservative estimates (shale oil excluded) made elsewhere (USGS, 20002; Greene et al., 20063; Rogner, 19974). Due to the specificities related to the exploitation of shale oil and the associated high production costs, we consider shale oil as an alternative to oil instead of a new category of oil.

<figtable id="tab:resources">

Assumptions about oil resources in the central case (Trillion bbl)
Resources extracted before 2001 Recoverable resources beyond 2001§
Conventional oil Non-conventional oil (Heavy oil and Tar sands)
Middle East RoW Canada Latin America Row
0.895 0.78 1.17 0.220 0.38 0.4

§"recoverable resources" are 2P reserves (Proven+Probable) remaining in the soil, which has been identified as the relevant indicator to investigate global oil peak (Bentley et al, 2007)5

Each oil category is subject to geological constraints (inertias in the exploration process and depletion effects), which limit the pace of expansion of their production capacity. In line with (Rehrl and Friedrich, 2006)6, who combine analyzes of discovery processes (Uhler, 1976)7 and of the 'mineral economy' (Reynolds, 1999)8, the maximum rate of increase of production capacity for an oil category i at date t, ΔCapmax(t,i), is given by:


The parameter bi (in t-1) controls the intensity of the constraints on production growth: a lowbi means a flat production profile that represents slow deployment of production capacities whereas a high bi means a sloping production profile which represents the opposite effect. We retain bi=0.061/year for conventional oil as estimated by Rehrl and Friedrich (2006)6 and, for the sake of simplicity, the same value for non-conventional oil in the median case. The parameter t0,i represents the date at which production capacities of the concerned oil category are expected to start their decline due to depletion effects. It is endogenous and varies in time since it depends on the amount of oil remaining in the field given past exploitation decisions.

Non-Middle-Eastern producers are seen as 'fatalistic producers' who do not act strategically on oil markets. Given the selling oil price poil, they invest in new production capacity if an oil category becomes profitable: they develop production capacities at their maximum rate of increase ΔCapmax(t,i) for least-cost categories of oil (poil>p(0)(i)) but do not undertake investments in high-cost categories (poil<p(0)(i)). If prices continuously increase, production capacities of a given oil category follow a bell-shape trend i.e. the reach a point of capactity saturation, whereas their deployment profile passes through a plateau if prices decrease below the profitability threshold.

Middle-Eastern producers are 'swing producers' who are free to strategically determine their investment decisions and, until such time as they reach their depletion constraints, to control oil prices through the utilization rate of their production capacities (Kaufmann et al, 2004)9. This possibility is justified by the recent temporary reinforcement of their market power due to the stagnation and decline of conventional oil sources in the rest of the world. They can in particular decide to slow the development of production capacities to below their maximum rate of construction in order to adjust the oil price according to their rent-seeking objectives.

Total production capacity at date t is given by the sum over all oil categories with different production costs (captured by different threshold). This means that projects of various merit orders coexist at a given point in time, consistent with the observed evidence and theoretical justifications. For example, low-cost fields in Saudi Arabia and high-cost non-conventional production in Canada are simultaneously active on oil markets. In addition Kemp and Van Long, (1980)10 have demonstrated that, in a general equilibrium context, the lowest-cost deposits are not necessarily exploited first. Holland, (2003)11 even demonstrates that least-cost-first extraction rule does not hold in a partial equilibrium framework under capacity constraints, like those envisaged for geological reasons here.

Formation of oil prices

The oil price which forms in static equilibrium reflects the level of tension between supply and demand. The price formation equation is:

The regional prices thus correspond to the addition of the average regional production costs and a margin that encapsulates Ricardian and scarcity rents at the same time. The swing producer uses this equation to anticipate the level of capacities that will make it possible for them to reach their goal on the basis of projections of total oil demand and production in other regions.

Other fossil fuels

Coal and gas reserves are a priori subjected to less important availability constraints on the market than crude oil. In the present version of the model, the treatment of production capacity evolution of these two sectors as well as the mechanisms of their price formation are thus more simply treated.

Natural gas supply

In the model the evolution of worldwide natural gas production capacities meets demand increases until available reserves enter a depletion process. The distribution of regional production capacities in the 'gas supply' dynamic module is made using exogenous weights calibrated on the output of the POLES energy model (LEPII-EPE, 2006)12, which captures both reserve availability and the capacity of regional production facilities. Gas markets follow oil markets with an elasticity of 0.68 of gas to oil price. This behavior is calibrated on the World Energy Model (IEA, 2007)13 and is valid as long as oil prices remain below a threshold poil/gas. At high price levels reflecting tensions due to depletion of reserves, gas prices are driven by production costs and the increased profit margin for the possessors of the remaining reserves.

Coal supply

Unlike oil and gas markets, cumulitive coal production has a weak influence on coal prices because of large world resources. Coal prices instead depend on current levels of production through specific elasticity coefficients. To represent the asymmetry in coal price response to production variations, we consider two different values of this elasticity, ηcoal and η-coal. The former corresponds to a price reaction to a production increase while the latter corresponds to the opposite effects. Tight coal markets exhibit a high value of ηcoal (i.e the coal price increases strongly if production rises) and low value of η-coal (the price decreases only slightly if production drops).

[1] Four such forces are presented: increasing demand over time; exogenous decrease of production costs due to technological change; incentives for further exploration given by the inverse relationship between marginal extraction costs and reserves; and increases in aggregate production capacity due to production at newly developed sites.


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