## Tuesday, May 08, 2012

### The IMF and Hubbert

The IMF just published a working paper with an eye-catching title The Future of Oil: Geology versus Technology. To my knowledge, this is is the first time a peak oil scenario, in the form of a Hubbert Linearization, is explicitly  injected into a econometric model. Based on the work of Hubbert, Deffeyes and Campbell, available supply is modeled by a Hubbert curve plus a marginal supply component sensitive to prices.

The Hubbert Linearization is a way to plot the annual production as a fraction of a cumulative production versus the cumulative production. If production follows a Logistic curve (aka Hubbert curve) then a linear relation can be observed

$\frac{q_t}{Q_t}= \alpha_s − \beta Q_t$

where $\alpha_s$ and $\beta=\alpha_s/URR$ are related to the logistic growth rate and the Ultimate Recoverable Resource respectively.  Figure 4 from the IMF paper shows the result of the Hubbert linearization following Deffeyes 2005 projection with an URR at 2.013 Trillion barrels.
 Figure 1. Oil Production Forecasts in the Deﬀeyes (2005) Model (Q in gigabarrels, q in gigabarrels p.a.). src: IMF, Figure 4.

The IMF correctly observes that total supply has been diverging from a straight line since 2004. There is some confusion on what definition exactly they are using for World supply. This is tricky of course because only conventional oil could possibly follow a geological peak whereas biofuels and NGL would follow different constraints. The IMF quotes the work of Deffeyes, however, Deffeyes was originally only looking at conventional crude oil. On the other side of the equation, demand is met by the total volume of liquid fuel available regardless of its origin. It is said that the model results are based on the IEA data for crude oil, condensates plus Natural Gas Liquids (NGL). It is a little bit strange because the IEA is publishing an estimate for World supply only for All liquids at least in the Oil Market Reports. Total supply usually includes Natural Gas Liquids, syncrude from tar sands, heavy oil such as raw bitumen, biofuels, refinery processing gains, etc.. The EIA database is giving  86.94 Mb/d for 2011 or 31.73 Giga barrels (see Figure 2 below). Considering only crude oil, condensates and NGL, we get 30.13 Gb/d for 2011. Looking at their forecast (Figure 10 page 30), the 2011 data point is clearly above 31 Gb so it seems to indicate they are considering All liquids.
 Figure 2. World Production (C+C= crude oil and lease condensates)

Since 2004, it is clear that supply growth is coming from unconventional sources and NGL while conventional oil production is basically flat.

 Figure 3. Supply growth per category (100= Jan 2001).
Looking at the residuals between the Hubbert Linearization and supply on Figure 1, there is a correlation between those residuals and real prices (excluding oil price shocks from the 70s).

It then follows that the deviation from the Hubbert line is interpreted as an increase in marginal supply due to high prices

$$\frac{q_t}{Q_t}= \alpha_s − \beta_1 Q_t+\beta_2 p_t +\beta_3 \frac{1}{3}\sum_{k=4}^6 p_{t-k}$$

more to come.