An ocean of ink has already been spilled on pros and cons of using Hubbert curves to model production from a large collection of wells in one or many reservoirs. In 2010, I published together with my last graduate student in Berkeley, Dr. Greg Croft, a
highly cited paper on this subject. I have also commented multiple times in this blog on the different aspects of the Hubbert curve analysis, its limitations, and predictive power.
Since I cannot out-talk or out-convince the numerous critics of this type of analysis, let me give you a simple example of its robustness. This particular story is as follows. At the end of the year 2010, Greg Fenves, at that time Dean of UT's Cockrell School of Engineering in Austin, asked me to make a presentation to the School's Engineering Advisory Board (EAB). Using the results of our recent paper with Greg Croft, I chose to speak about my new work on unconventional resources in the U.S. On April 09, 2011, I made the presentation, which was then internally published by the Cockrell School.
The first two Barnett shale plots shown below were based on the Texas Railroad Commission data through October 2010. In the presentation, I called these plots the "high production scenario." The Hubbert curve with which I matched the production data ending in October 2010, went right between the two local peaks of the data. Of course there was an element of luck, helped by two decades of my experience as a reservoir engineer. Such experience or - for that matter - any other knowledge of reservoir engineering is absent among the economists, political scientists and journalists, who are paid to criticize this type of work.
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| To see this image in full resolution, please click on it. The total rate
of gas production in the Barnett shale through October 2010, was matched
with a single Hubbert curve. 1 EJ/year ~ 1 trillion standard cubic feet
(TCF)/year. This "high production case" was presented in April 2011, at the Spring meeting of the Cockrell School Engineering Advisory Board (EAB) at the University of Texas in Austin. It was also made available electronically to the EAB members. |
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| To see this image in full resolution, please click on it. Cumulative gas
production in the Barnett shale through October 2010, was matched
with a single Hubbert curve (an integral of the bell curve shown above). The projected ultimate production was at
least 27 TCF. 1 EJ/year ~ 1 TCF/year. |
In fairness to lay people, the respected reservoir engineers who saw these curves in 2011, smiled at my naïveté and predicted 60, 100 plus, or more TCF of gas production from the Barnett. In short, most experts were also amused.
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| Cumulative drilling permits issued by the Texas Railroad Commission for (the mostly horizontal) wells in the Barnett shale. Note that the cumulative permit curve follows a logistic S-curve similar to the cumulative gas production above, only shifted in time. Peak wells (4,065 at the inflection point in 2008) were drilled ahead of peak gas production in 2012. We are beginning to see the ultimate "carrying capacity" of past drilling in the Barnett. To change this S-curve, we need a brand new Hubbert cycle of drilling. |
What did I do? I used a two parameter curve (height and width) to describe and extrapolate production from close to 20,000 wells in the Barnett. I knew two things: (1) this production could be matched with one Hubbert curve or 2-3 of them, and (2) I had to go above current gas production (overshoot it) because this production had not already peaked. The first observation is based on the Central Limit Theorem explained in
our paper, and the second one is an admission that more wells will be drilled and production will increase further, we just do not know by how much. Experience and intuition allow one to reasonably guess the size of this production increase. Guessing is an art and not all experts are artists.
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| To see this image in full resolution, please click on it. The total rate of gas production in the Barnett shale through March 2015, is matched with a single Hubbert curve. 1 EJ/year ~ 1 trillion standard cubic feet (TCF)/year. |
To see how good this December 2010 prediction was, fast forward five years. I should remind you that the Hubbert cycle
predictions of future production of a very large number of wells and/or reservoirs are remarkably stable - the Central Limit Theorem makes sure of this, but I would not be happy if I predicted gas production in the Barnett shale with a 50% error. Luckily, as the plot above shows, I was right on the money, and no corrections were needed. Nevertheless, I could not resist tweaking the peak almost imperceptibly and increased the ultimate gas production from the Barnett by less than 1 TCF. Call it a reservoir engineer's decease.
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| To see this image in full resolution, please click on it. Cumulative gas production in the Barnett shale through March 2015, is matched
with a single Hubbert curve. The projected ultimate production is at least 28 TCF. 1 EJ/year ~ 1 TCF/year. |
In summary, given the current number of wells in the Barnett shale (over 25,000 drilling permits by now) and the already traversed peak of gas production, it is unlikely that I will have to adjust this prediction in the future, but let me play devil's advocate.
The Barnett shale is most unusual in that it has two sets of fractures in the hydrofractured rock surrounding horizontal wells. One set is formed by the stress relief cracks from shear rock failure during hydrofracturing. Think of these cracks as being almost parallel to main hydrofractures and extending some distance away from both sides of these hydrofractures. But the Barnett shale is also likely to have another set of critically stressed (ready to pop), cemented natural fractures perpendicular to the hydrofracture planes. Together these two sets of fractures link during hydrofracturing and form large complex fracture systems that also communicate with the main hydrofractures. Thus, one
could use this wonderful property of the Barnett mudrock, not replicated in other major shales, to create in the future many better and cheaper wells in the Barnett. If this happens, I will add a new Hubbert curve to my Barnett shale production model to account for the new wells, and happily report a significant increase (but
not by 50%) of gas production there.
It's great when experts are correct and economists(and various other snake oil salesmen and charlatans) are proven wrong. Bravo Sir!
ReplyDeleteThe charlatans are richly paid and publicly praised for misleading and lying to the public. They give lectures at big conferences, publish in premier journals, and have faculty positions at top U.S. schools of public policy, economics, and management.
DeleteThe big energy game attracts all kinds of unsavory people.
Nice prediction.
ReplyDelete1. what is implicit (during the runup) or explicit price assumption? [The field produces more at high price than low. It is shale drilling, high decline, so they adjust rapidly to economic incentives. Not even a crit, just checking.]
2. Leaving yourself an out for 50% increase seems like a fair amount of wiggle room. If it happens, can't really still say the 2010 call was so eerily prescient.
3. Did you predict the Marcellus increase? The Utica? BTW, they are takeaway limited now. [Not saying you have to do everything. Just want to know if you were always so accurate. If this example is representative.]
4. Give me enough parameters and I fit an elephant. Possible crit of the multi bell curve models.
-civilian, non-professor
@Nano.
Delete1. The Hubbert curve approach is a purely statistical analysis of arbitrarily complex decision making processes that result in random outcomes (random variables) with arbitrary distributions but finite variances. If these variables are not correlated or only weakly correlated, as production from individual wells in the Barnett would be, the outcome is a Gaussian. This is the powerful Central Limit Theorem you saw in action in the Barnett. This theorem is one of the beautiful laws of mathematics that reflect the complex actions of nature and humans, who are a part of the same nature but forget about it.
2. The notion of a 50% increase was purely rhetorical. If you see the various predictions of future production from the Barnett, they can be off by over 100% five years into the future. In reality, there cannot be a 50% increase of production rate in the Barnett. There could be a significant increase of cumulative production over several decades, but the incremental gas would be produced at a low rate uneconomic for today's producers.
In fact, the 2015 outcome shows that there was not a large increase of the total rate, and production went through the peak as predicted 5 years earlier.
3. I have not touched the Marcellus as a play because of the incredibly low quality of reporting. Compared with Texas, Pennsylvania has a production reporting scheme that belongs in the 19th century or is designed to obfuscate and mislead. Where I could get proprietary company data on production, I saw the best shale wells I have ever seen, but they exist over two limited geographical areas, one in the NE. I have not analyzed the Utica shale.
4. You are in denial. :) How about 3 parameters for 25,000 drilling permits? (Width, height, and timing of the peak.) The usual economic models have dozens or hundreds of parameters, and almost zero predictive capability more than 3 months into the future.
Nice call Tad!
ReplyDeleteBut there should be no surprise when we find a nice Hubbert Curve. Take a look at the graphs at the bottom of this paper by John Hallock, myself and others. We had predicted oil production for some 35 major oil producing countries back in 2002 using Hubbert curves and low medium and high (USGS) estimates of EUR (Ultimate return).
We then revisited our earlier predictions in 2013, with some 10 additional years of production.[Note to Mr. citizen: during a time of increasing energy prices). The data (i.e. the red or blue circles) for the overwhelming majority of the countries have followed a clear, clean HUbbert pattern, mostly following our low EUR predictions. While there many or may not be some ambiguity in the "undulating plateau" of GLOBAL conventional oil there is no question that we have observed the Hubbert curve in the data from dozens of countries. There is no question that Hubbert was right on the mark for the vast majority of countries. in this case 30 of 33 countries (with a few "too early or ambiguous to tell") definitely show a pretty much classic Hubbert curve (with mostly one but occasionally two peaks, as Hubbert said could happen) compared to three that do not (yet anyway). At least 90 percent accuracy. How many economic analysis can say that?
Charlie Hall
Hallock Jr., John L., Wei Wu, Charles A.S. Hall, Michael Jefferson. 2014. Forecasting
the limits to the availability and diversity of global conventional oil supply:
Validation. Energy 64: 130-153. (Article 12 in:
http://www.sciencedirect.com/science/journal/03605442/64/supp/C
http://www.sciencedirect.com/science/journal/03605442/open-access
Dear Charlie,
DeleteYes, the Central Limit Theorem (CLT) acts like a big spring attracting all production from all fields on the Earth to a normal distribution. Since confusion on this complex subject abounds, soon I will write a tutorial on the emergence of Hubbert curves.
The CLT is the reason why King Hubbert was right 16 years ahead of the peak of production of conventional crude oil and associated condensate in the U.S., and 49 year ahead of the global production peak. I sketched these two seminal contributions by Hubbert here:
http://patzek-lifeitself.blogspot.com/2011/10/peak-oil-nonsense-says-daniel-yergin.html
http://patzek-lifeitself.blogspot.com/2012/04/world-is-finite-isnt-it.html
What you, many others, and I are doing is reconfirming the omnipresence of CLT in oil and gas production. Since logic behind the CLT is multi-step and complicated, most people simply deny the emergence of peaks of production of anything with their own faith-based, ad hoc arguments. As life goes on more peaks emerge...
Prof Patzek,
ReplyDeleteRegarding the results of your paper on coal, I appreciate that it's only a few years since the publication data, but how would you say the prediction is holding up so far? BP stat review 2015 seems to have energy production from coal somewhat stable over the last few years, but I would assume this might be within your error bounds?
Secondly, regarding the Hubbert analysis. One criticism of the curve fitting techniques which are used (such as hubbert linearisation) is that they tend to be somewhat pessimistic, as they don't adequately capture things like reserve growth. There was a paper about this in the recent royal society Phil Trans A special, which looked at the future of the oil supply ( http://www.researchgate.net/publication/259115321_Using_growth_curves_to_forecast_regional_resource_recovery_approaches_analytics_and_consistency_tests ). Do you think there's much weight to this criticism?
Dear Sam,
DeleteSince China produces about 1/2 of world's coal, and some of the steep growth in Chinese coal production is unexplainable, it is difficult to say what is happening with the world coal production rate.
I was born and grew up in the largest coal mining region of Poland, called Silesia. Several mine shafts and coal unloading facilities were within a few kilometers from my home. Therefore, I know for a fact that in a command economy, where mine managers are ordered to produce more coal each year, they do, whether the overburden rock they load on trains has plenty of coal mixed with it, or not so much.
My guess is that much of the explosive growth of coal production from the Chinese mines before 2010, was imaginary. With better accounting of what constitutes coal, plenty of rock production will disappear from the statistics.
If my memory serves me right, Poland lost close to 1/2 of production rate of real coal when communism fell. Again, there were other economic factors at play, not just better accounting.
To complicate things further, the slowing Chinese economy and the runaway air pollution must slow down real coal consumption in China and, therefore, the global coal production rate.
Then there is a lot of new coal in Mongolia, Botswana and Australia. This new coal - if produced in large quantities - would have to be captured by separate Hubbert curves.
So that fact that the global rate of coal production has stalled or decreased has many associated confounding factors. Thus, a lively discussion of whether the coal production has peaked on the Earth or not will continue for another several years.
Thanks for the time to respond to numbered questions.
ReplyDeleteOne example of non Hubbert behavior is the Canada rise in oil with the tar sands. Another is the rise in US oil with shale. both cases with an apparent hubbert peak that then deviates.
You may say this is two populations, but so what. It just goes to the point that the initial Hubbert curve was not covering all Canada or all US oil. It's an indictment of that Hubbert approach.
I think Hubbert was aware of this issue. In his 1956 paper he discusses the issue of multiple peaks with respect to Indiana, where seismic enabled multiple peaks. But then says it is unlikely to happen again in general (but he was wrong, look we got LTO in the US).
Note also, that both tar sands and shale were enabled by $$$. An approach that might have better predicted them would have been based on the cost curve (amount of resource at different prices). This shows you thinks Hubbert peaks don't.
Gaussians bell curves occur in a lot of distributions. That is where there beauty lies. But you are on the wrong dimension to extend that to time series just out of beauty or all the places where they function well in iid statistics (shooting arrows at a target is not the same thing as...height versus age of a man).
Keep the bell curves for electrons in orbitals or factory deviations or speeds of molecules or sizes of grains in mineral or the like (and even then watch out for log normal).
[Gotta get back to some red blooded American football...too much geeky math talk with liberals.]
Dear Nony,
DeleteI think that I have work cut out for me to show why eventually Gaussians emerge when you sample at random any arbitrary probability distribution with a finite mean and variance. That probability distribution expresses the past, current, and future production from all wells past, current and future in a fixed set of hydrocarbon-bearing formations. An added twist may be that this underlying probability distribution itself may be changing with time. How does one restrict this time evolution? What difficulties will arise from introducing memory into the model?
Nevertheless, if annual production from all wells in many fields is summed up, then year-after-year these random sums (total annual production each year) form a Gaussian.
The well populations that never belonged to the original set (Prudhoe Bay and North Slope, deep and ultradeep offshore GOM, shales, Canadian tar sands, etc.) obviously must be handled through a separate summation or summations.
The Hubbert curves are not magic but a statistic and have many limitations of course. I just described the important one: No Hubbert curve carries any information about wells and fields that are not in it.
What amazes me though is that people shrug their arms at gross failures of complex econometric models, including the stock market models, but are put off by a simple Hubbert curve underestimating the world oil production 60 years into the future by a factor of two, while capturing the timing of the peak. That it does so well for the whole world is nothing short of amazing. We need to appreciate gifts the Central Limit Theorem (CLT) gives us almost for free. This free thing is especially important now when a good chunk of our imaginary equity wealth has just evaporated.
OK, enough of fraternizing with the conservatives. I need to go back to constructing a demo of how the CLT works for oil and gas fields on this beautiful planet of ours.
Natural gas is below $2. We have over 30 TCF/year. And have gone down from a (relatively LOW) level of 350 rigs at beginning 2015 to a 100 now. That is kicking the Red Queen's butt. Those are not "small wells". When you consider they do decline fast, they must be very large indeed.
DeleteShale gas is incredible. I love it. USA! USA! USA!
https://www.youtube.com/watch?v=8gfD134ED54
Great Blog !!! I like the way you written the post. Post is informative and very easy to understand.Project economic courses | Reservoir engineering courses online
ReplyDelete