Historical rates of consumption of coal, oil, and gas are used in the FeliX model to project likely future demand. In the plot below, the model-generated market shares of coal, gas, and oil are plotted along with historical market share (defined as a fraction of primary energy supply) from the IEA publication Key World Energy Statistics 2013. This data is used to calibrate energy market parameters, including most importantly the price elasticity of demand (PED) for each fuel.
PEDs for natural gas and oil are calibrated to historical data, and are consistent with meta-analyses of long-term price elasticities of demand .
Over the course of the century, the market share of fossil fuels is projected to fall from nearly 100% of primary energy supply in 1999 to 56% in 2100. During this period, total annual primary energy supply also doubles, implying that absolute production levels stay roughly constant (coal) or peak and fall (oil & gas) over this period, as shown in the plots below.
A Note on Peak Oil: The BAU scenario of the FeliX model may overestimate fossil fuel reserves in order to avoid externalities like severe Peak Oil in projecting future development. The baseline is premised on the notion that global agriculture, energy, and development continue (muddle) along, more-or-less as they have been. A corollary of this assumption is that it is possible to just continue along, something that Peak Oil precludes. Similarly, specific and transformational technological developments such as fusion or a breakthrough GMO are, though possible, externalities which distract from consideration of the ultimate consequences of business-as-usual.
 Espey, M.: Gasoline demand revisited: an international meta-analysis of elasticities. Energy Economics 20, 273–295 (1998)