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Sunday, January 29, 2006

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.



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.

2 Comments:

Professor Anonymous Anonymous said...

lots of posts with no comments. amazing, given how great this blog is.

it's so lonely here, maybe i'll just blather a little. in july 2003 i was on vacation out in canyon country, thinking about the salons and bohemian cocktail parties to come, back in the big apple in autumn. a hot topic would be "why did we invade iraq?"

i had heard enough scruffy leftists say that "we did it for oil," and all they seemed to be saying was that we were going to go in and take the oil without paying for it. that didn't seem quite correct to me, but i thought it was time to learn enough to be able to argue the point.

at an enlightened little bookstore in a redrock town, i picked up michael klare's "resource wars" and read it in a few days. the book didn't talk about peak oil, but it left me thinking that it was time to figure out what was going to happen in 35 years or so when the oil straws started making that impolite gurgling sound as the stuff ran out.

i had gotten complacent a couple of decades earlier and slipped into the semiconscious belief that there was a plan, because there obviously had to be.

so now, i decided to find out what the plan really was. back home, some of klare's footnotes led me quickly to richard heinberg, whose footnotes led to matt simmons and jay hanson. the peak-and-decline concept stunned me. it was obviously correct, and i knew that the crisis was not 35 years away.

i suspected after a little reading that we were close to the peak, and i picked up on simmons' and others' fears of a rapid descent. this was speculative at the time, but i think it has become increasingly clear since then that we are going over the top now.

this blog seems to be quite focused on when and how high the peak will be, and how fast the decline. the writer seems to foresee a relatively benign energy descent, with life in minnesota (or thereabouts) not especially troubled in matters such as keeping warm. i should probably read the archives to check this perception.

i am not optimistic about how americans are going to take the decline. i am reading people like john michael greer and jason godesky, including some of the discussions on the anthropik site, getting oriented for an early departure from gotham.

but i'm keeping an eye on this site for some fine analysis of what the shape of the curve is truly going to be.

5:48 PM  
Professor Blogger WHT said...

this blog seems to be quite focused on when and how high the peak will be, and how fast the decline. the writer seems to foresee a relatively benign energy descent, with life in minnesota (or thereabouts) not especially troubled in matters such as keeping warm. i should probably read the archives to check this perception.

The writer doesn't worry about keeping warm with the current weather in Minnesota. Contrary to other years, I have hustled to work on my bike just about every day this winter. For this year at least, out of sight, out of mind. Who knows what next year will bring.

8:21 PM  

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