Backdating and reserve growth

In the USA, the government prohibits speculative estimates of the remaining oil in a field.

Operators in the United States are required by law to report only those reserves that are known with high certainty to be available for production, thus excluding resources that are at all speculative. It follows that one component of reserve growth is the difference between early estimates of recoverable resources, which in the presence of limited data are required to be conservative, and later estimates based on better knowledge of the field.

This means that oilers can't use the reserve estimate outlined in the previous post. That technique, which empirically demonstrates a growth of 10x or more from the initial estimate after 90 years, apparently ranks as a speculative estimate (blue curve below, assuming an initial growth estimator of 0.1). So, instead of coming up with an estimate based on established heuristics, the field operators always undershoot the actual amount, to safely remain below the "speculative" point.

That means that all the original discovery curves need continual updating, commonly referred to as backdating in the oil industry. I double-checked how well the oil-shock model (red curve above) tracked the average A&R reserve growth algorithm. The fit looks decent, with the cumulative production hanging below the parabolic growth at all points. If in fact my curve showed more than an order-of-magnitude tracking difference, I would worry that I seriously erred in my own parameter estimates and/or that the discoveries got backdated incorrectly. As formulated, the long lag in extraction comes about from the serial application of the fallow, construction, maturation, and extraction phases. These combine to a 1/e time constant of about 30 years, leading to the s-shaped curve shown.

The big problem with the A&R parabolic growth law remains unanswered. Although it does not show compound growth, neither does it show any signs of abatement -- as it should continue to grow for years according to the formula. As you can see, the oil shock model does hit a normalized limit at about the 90 year mark. I have only seen results for the A&R model up to the year 1991, with initial data from 1900. Which means it could show signs of abatement should anyone get the nerve to present more recent data from the last 15 years¹. How about it USGS?

The Kuwaitis learned from the best in applying their own reserve growth estimates. I salute you, good ol' USA, for educating our foreign pupils. What a mess we have created.

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¹ This transcendental function follows a parabolic growth law initially, but then goes on to from an asymptotic limit, effectively stopping further growth.

df(t)/dt = K/f(t) - C*f(t)

I haven't checked the literature, but the parabolic growth law for oxidation should follow this behavior for very thin substrates where the source of materials limits out physically.