**Peak Oil**

**Geology**

Way back in 1956, a petroleum geologist named M. King Hubbert predicted that US lower 48 crude oil production would peak in 1970 and decrease thereafter, never to rise again. In fact, it did. Hubbert's hypothesis is applicable to any geographic region that contains oil fields because oil is a non-renewable resource and one that exists in discrete pockets. The conclusion is that at some point in time, world oil production will peak and decline just as it did in the United States. Because the mathematics is pretty consistent, the time of the peak can be predicted through a variety of methods based on the annual net reserve addition and the amount of oil in the Earth that is ultimately possible to recover. A crude back-of-the-envelope calculation shows that oil production should peak sometime in the decade between 2000 and 2010. Various petroleum geologists predict a spread of numbers that look something like this: 2007, 2009, 2011, 2016, 2025. Geologist Kenneth Deffeyes believes production peaked in May, 2005.

There are several different types of oil reserve estimates for a given field; they're named after the certainty that there is that much oil in the ground, kind of like weather forecasting. The P90 (or P95) estimate gives the oil that geologists can say is in the ground with 90% (or 95%) certainty. The P50 estimate, by the same token, gives what geologists can claim with 50% certainty; and the P10 estimate is the amount that's in the ground with 10% certainty. So, for example, a new field might have P90 reserves of 500 million barrels, P50 reserves of 750 million barrels, and P10 reserves of 2 billion barrels of oil. There's a 90% chance of 500 million barrels, a 50% chance of 750 million, and a 10% chance of 2 billion barrels of oil in the ground.

The general consensus on the total amount of oil that can ever be recovered, the Ultimately Recoverable Reserves (URR), is in the neighborhood of 2 trillion barrels of conventional oil (this does not include heavy oil substitutes; there may be as many as 1.8 trillion barrels of oil shale in the central US alone, although it is not all recoverable). Note that there is a significant (10% either way) uncertainty in conventional reserve numbers largely thanks to the OPEC cartel and their reserve numbers, which many believe are fudged so they can sell more oil (according to OPEC policy, sales must be directly proportional to reserves; upon the adoption of this policy, of course, member states' reserve numbers jumped dramatically and have not changed in the ensuing decade despite record levels of oil production).

**Economics**

Note that oil production peaking does

*not*mean that oil will just dry up and go away in a matter of days or months or even years. This is a common misconception. Rather, it means that the

*rate*of production will decrease permanently as total recovered oil approaches ultimately recoverable reserves. Because the quantity of oil demanded is very inelastic and follows an exponential growth curve, the price of oil will rise considerably as production goes all out and then begins to decrease. The economic effects will come chiefly from the skyrocketing price of oil, the time lag before mitigation efforts come into effect, and a phenomenon known as the Land Export Model.

Oil prices will, of course, increase dramatically as quantity supplied plateaus and begins to decrease. In the past, every single significant oil price spike has been followed by a recession of the US economy. Since this price spike will be more severe and will last infinitely longer, it is safe to conclude that the ensuing depression will be correspondingly greater in severity. Think the 1970s on crack and doped up with heroine.

There is a general consensus that economy-wide efforts will eventually mitigate the high fuel prices and wean the world economy away from oil, although some people here maintain that peak oil in tandem with global warming spells the end of industrialized human society. However, though there's a light at the end of the tunnel, you still have to walk the mile in darkness to get there. The Hirsch Report, linked below, points out that if mitigation efforts do not begin until the peak occurs, the US will be facing liquid fuels shortfalls for at least two decades, if not more.

Oil substitutes do exist; however, most optimistic projections, as outlined in the GAO report linked below, predict just 34% of projected oil consumption replaced by 2030, and only 4% of projected oil consumption replaced by 2015.

Finally, the Land Export Model predicts that as demand for oil in net oil-exporting countries rises, their exports will drop to zero. This is a result of the inelastic demand curve for oil. Consequently, after the peak, the United States will experience a precipitous drop in oil imports; combined with currently-declining US oil production, it will lose approximately 1/3 of the energy it consumes. This will correspond to a 1/3 drop in GDP over that period, between six and ten years after peak, in addition to the drop caused by declining domestic production.

**Math**

The logistic curve, defined by the differential equation dP/dt = rP(1-P/U) describes in particular the cumulative production of a finite, nonrenewable resource. P is the cumulative production, U is the total recoverable material. The solution to the differential equation is P = U/(1+exp[r(t-t_m)]), where t_m is the inflection point of the curve. It is also the point of maximum production where the derivative peaks. The production curve is as follows:

[1] dP/dt = rU/(2+2cosh[r(t-t_m)]) = P_m/(1+cosh[r(t-t_m)]),

where P_m = rU/4 is the peak production.

The key insight to Hubbert's model is this: production will follow discovery by a constant amount of time. That is, the cumulative production curve

*is*the cumulative discovery curve shifted to the right by a constant. The difference between production and discovery is a quantity known as

*reserves*-- i.e., the amount of oil known to be in the ground but not yet extracted. Thus,

[2] D - P = R,

where, of course, D is cumulative discovery, P is cumulative production, and R is amount of reserves. An illustration.

If we are interested in the rate of change of production, we may differentiate [2] with respect to time, arriving at

[3] dD/dt - dP/dt = dR/dt.

Because dD/dt is essentially the same as dP/dt, separated only by a constant time C, we can crunch out a formula for dR/dt:

[4] dR/dt = P_m{cosh[r(t-t_m)] - cosh[r(t-t_m+C)]}/w(t),

where w(t) = (1+cosh[r(t-t_m)])(1+cosh[r(t-t_m+C]) is a long, nasty product of coshs.

*A priori*, though, we can determine that dR/dt will peak at some point t_m-C and will vanish at t_m-C/2. An illustration is here.

**References**

- US Department of Energy Annual Energy Review. A US government publication that covers US energy use and has a section dedicated to petroleum, including current and historical world production.
- The Peaking of World Oil Production: Impacts, Mitigation, and Risk Management [Warning: .pdf file]. A report prepared in 2005 for the US Congress. Commonly known as the Hirsch Report. Focuses on impact and mitigation by substitutes.
- Giant Oil Fields - The Highway to Oil: Giant Oil Fields and their Importance for Future Oil Production. A Doctoral Thesis from Uppsala University in Sweden. Contains information on the Hubbert Curve.
- CRUDE OIL. A report from the US Government Accountability Office regarding the federal government's work (or lack thereof) in preparing for peak oil.

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