A Nice Counterexample
Posted by Stuart Staniford on October 1, 2005 - 1:21am
Topic: Supply/Production
Tags: hubbert peak, oil prices, peak oil, uk oil [list all tags]
Nick Rouse kindly provided me with an Excel spreadsheet with a Hubbert linearization of UK oil production (the only thing I added was the yellow line). As you can see, there was a long period when the curve looked linear and yet it would have totally misled you had you simply extrapolated it to the axis. You would have thought there was going to be about 11gb, but now it's headed for 28gb. So, things are more complex, and we must see if we can come up with some principle for dividing the Romanias (where this method seems to have worked with amazing success), from the UKs (where it would have been very misleading) before we can feel any confidence in our extrapolation of the Saudi graph or the world graph. More below the fold.
This is referenced from here. Clearly, production initially looks like a nice Hubbertian single peak, but then, whoops, a bunch more oil from somewhere is produced. And the initial (pink) straight line above only knows about the first peak, so when we get this second, superimposed peak it is not accounted for. However, we do go linear again, just with a different (yellow) line going to a much higher URR (28gb versus 11gb).
Clearly, we are likely to run into the same general kind of problem with Russian production, where James Williams shows:
In the UK case, economists will quickly be tempted by the idea that oil prices had something to do with it, since the second peak starts to go up again in 1993, a couple of years after the price spikes of the first gulf war. However, it's pretty clear that price does not cause too much deviation from the basic Hubbert model in the US or Romanian case, so we would be left trying to explain why price matters greatly in some places but not in others (especially challenging in the US, center of the free market religion). So this explanation doesn't seem too tempting to me (price seems to explain some of the noise about the basic Hubbert curve, but not the gross features of the shape of the curve).
Nick notes that Jean Laharrere has considered the possibility of discovery as an explanation. Here's Laharrere's figure plotting UK backdated discovery and production:
Clearly, we can see that this bimodal discovery curve looks like a good explanation of the bimodal peak in production. A lot of discovery initially occurs in the late sixties and seventies, and this powers production in the late seventies and eighties. But there's a second wave of discovery beginning after 1980, and this powers the second peak. There's not much of a third wave of discovery, so there seems limited prospect for much relief in UK depletion rates soon.
It's interesting to contrast the situation with that in the US. Laharrere again:
This time we have cumulative production plotted versus time. Pretty clearly, the nice sigmoidal logistic discovery gives a sigmoidal production curve 30 year later. What's different in the North Sea is that production comes on stream much faster - production is following discovery by only a decade or so, rather than three decades. Clearly the world was in rather a hurry to get that oil by this point in history (after the oil shocks of the seventies).
So, here's a new tentative working hypothesis:
Hubbert linearization is a decent approximate model for oil production unless production is interrupted by a societal collapse, or production is very closely following on the tails of a very noisy discovery curve.Clearly, further investigation is needed to support or refute this working hypothesis. In particular, if anyone knows or discovers other countries where linearization works well, or where it fails for different reasons, I'd love to hear about it. Hopefully our resident sceptics will go do some work and come up with some more evidence. But my final thought for tonight is just to look again at the Saudi situation.
Now the discovery picture there is somewhat unclear since we have wildly conflicting information about what their reserves really are. But Laharrere plots a variety of opinions:
Everyone agrees that all the discovery happened a long time ago - 90% of it was before 1970, and two thirds of it was before 1960. So it seems to me that our tentative hypothesis would suggest that linearization should work decently for Saudi Arabia (unless they were to collapse - never to be ruled out in the Middle East). The implications of linearization being pretty much true for Saudi Arabia again:
180gb of URR with 110gb produced already!
(at least for me ) the proper role of Hubbert analysis.
Those additional taxes made the UK, already a high priced exploration and production market (due to the environmental and regulatory climate) a difficult place to justify investment dollars. Big oil investment dollars go to the lowest risk/reward regions of the world. That is why offshore West Africa has exploded in production the last 5 years. Biggest bang for the buck.
Norway's depletion can be viewed in the same way. It is by far the most restrictive place to drill on the planet. We know where the oil and gas is. It is currently not economically viable, given the restrictions in Norway, to drill there.
If I understand correctly, it's because governments don't invest in enough capacity to get the oil out of the ground fast.
Why not?
What you get is an asymptote that always starts at 1 (first year production/cumulative) and approaches the x axis but never gets there.
The chart for the UK and many others looks more like the chart for a `perpetual' oil field than a straight line. There aren't enough data points to distinguish between them so either could be true.
So what you've discovered is that not all curves produce a straight line at all. In fact this seems to strengthen, not weaken the theory slightly, since the curve you identified that doesn't produce a straight line is also impossible in real life.
Chris
It obviously doesn't do a good job for the world as a whole -- as demonstrated by Colin Campbell's failed predictions.
The only value which the linearization method might have is its ability to predict peak oil. Now, IIRC, Deffeyes predicts peak oil for Thanksgiving Day 2005 based on the linearization method, so that's the reality check.
Also, the method isn't objective until you specify an objective algorithm for selecting the line, and apply it uniformly in all cases. Otherwise, it's just subjective voodoo.
I agree with you that the predictions of the world peak are a good check. However, Deffeyes used a particular oil data series (and I don't actually know which one!), and it's only fair to do comparison to whatever series he was fitting too. Also, obviously there's significant noise, so it could well be off by a few years either way (as it was for the US). But I don't believe it's going to be decades off. We need to get to some error analysis here soon to tighten that up (but one thing at a time).
The more I look at it, the more I dislike plotting aP/CP against CP. I once was told a story long ago by my father who described going to a talk by another engineer who was very excited about this great correlation he found in his data set. The data points were very well aligned, all falling along a straight line. Well, as it turned out, the engineer had plotted X against X!
And that is part of the problem. We ought to not contaminate one already dependent variable onto the axis of the other variable -- unless you are relatively sure that this fits some realistic behavior (c.f. the "drunk looking for his keys under the streetlight" scenario). And I think the non-linear behavior we consistently see rules out the logistic model.
I have a post up describing the quasi-hyperbolic behavior that likely fits better here:
http://mobjectivist.blogspot.com/2005/09/oil-shock-model.html
and a more recent post showing how the math also describes the behavior of a simple electical RC circuit here:
http://mobjectivist.blogspot.com/2005/09/rc-circuit-analogy.html
But I also have to agree that the extra bump provided by new discoveries in North Sea oil tends to once again flatten out the slope. After all, every earlier discovery accomplished the same thing!
And don't take this criticism wrong. If you tried publishing this in any scientific journal as I and many others are accustomed to, you will have to be prepared to go through the ringer in your analysis. It's just that referees are much less common on the internet than in academic circles, as it doesn't come with the job description and it won't help anybody get tenure.
I have significant experience getting modeling work published in scientific fora, some of which has been very influential - scholar.google me for details. But these posts are work in progress (as I think should be obvious). No doubt publication will eventually follow when I think I have the story figured out to my own satisfaction.
So is that really how Hubbert, Deffeyes, and others set up the original peak oil math? By using a "predator-prey" model? Oh my, no wonder that people like Michael Lynch and company are having a field day in dissembling these kinds of models. It's common practice in those circles to simply trash another's model (i.e. policy); Lynch then doesn't even have to come up with his own. Look at how well this strategy works in today's political circles.
Fundamentally, it is an empirical question whether or not the model applies to oil production. No-one would claim it's going to be a perfect fit (or no-one with any sense, anyway!) but it has done a reasonably decent job in the very mature production areas (but not in the early stages). Stare at Romania again:
But there are certainly regions where it could mislead you without care (eg the UK). I'm engaged in trying to develop insight into where we might expect it to work, and where we might not.
As to Lynch et al. Critics serve a very valuable purpose in noting the holes and driving the improvements that need to be made. However, it's always much easier to criticise than make some constructive proposal oneself. No-one remembers the critics - they remember the people who make developments that actually improve the state of the art. Hubbert will be remembered far longer than Lynch, even though I respect Lynch as Hubbert's best critic: he has done some actual hard work and made critiques that serve a useful purpose.
And again - if you can develop a better model, more power to you. But the proof of that is showing that you can predict forward with smaller residuals for a broader class of situations.
I don't respect Lynch at all. I agree with many people that think he is intellectually dishonest.
The exponential model works over every regime. It just needs a forcing function to create a spread in starting points.
VERY interesting.... Write a post about this.
Now knowing what the basis of the logistic model was before today, I keep wanting to imagine little Pac-man oil molecules gobbling each other up. I will probably have nightmares over this tonight.
In the normal predator-prey relationships, you can get away with this stuff because you are ony dealing with discrete entities that have at least an empirical relationship. For example, it takes N rabbits to sustain a single fox. Or one virus to infect one unprotected computer. Or an anion and a cation to generate a molecule. But where does this relationship come up here?
Note that the initial UK peak was only about 10 years after the onset of serious oil production. This would be analogous to just looking at Texas data from 1935 to 1945. If you just focused on 1935 to 1945, the plot of Texas data would have given you a similarly erroneous result. Hubbert made his Lower 48 prediction about 27 years after the East Texas Field was discovered.
The answer to the apparent conflict is that the initial data points don't provide sufficient data to make an extrapolation.
Again, in my opinioin this technique works in the real world because--after decades of drilling--the industry has a pretty good idea of where the big fields are.
Jeffrey J. Brown
monthly production had already fallen by 25%
over its peak in January 1985. It undoubtedly
caused a direct loss in production but any losses due
to a reduction in exploration would have shown up
10 years or so later about 1998 when production
was near its second peak
Dave suggested that he would not expect another non-linear deviation but this is not sure.
Contrary to what Mad Oilman suggested, In 2003 the Chancellor of the Exchequer, Gordon Brown announced tax changes in favour of North Sea exploration. See:-
http://www.ukbudget.com/prebudget2003/Prebudget2003_companies.cfm
and this has resulted in a fair boost in exploration. See:-
http://thescotsman.scotsman.com/business.cfm?id=102472005
There are still forecasts that production will rise for a couple of years before starting to decline again although some only hope that it will slow the decline down. Whether this will happen to any large extent is open to doubt. There are some very interesting graphs here:-
http://www.worldoil.com/Magazine/MAGAZINE_DETAIL.asp?ART_ID=2655
Fig 1 shows the modest increase in the number of exploration and appraisal wells that have been dug (not including the expected increase in 2005 given in the Scotsman reference). However fig 3 shows the strong decline in the success rate of exploratory wells dropping from 43% or so for much of the 1980's to 20% in 2004. It would be interesting to see comparable figures for other parts of the world.
The forecast part of the production figures in Fig 3 seems optimistic in the near term as the show a slight increase in 2005 and output has fallen 17.5% in the first 5 months of this year
I read that actual oil production costs are around $0.50 to $1.50 per barrel. Is this true? If so, then tapping smaller 'more expensive' fields after the giant SA fields begin dwindling would raise the price to what? Even $3 to $8/barrel wouldn't really impact current prices. Am I missing something?
H
#1 They have peaked in light sweet production (according to their own journal) which means additional production increases will only come in the form of heavier, sourer grades that are harder to refine, etc.
#2 The infrastructure to drill the wells, build the pipelines, etc. is just not nearly as far along as in the US. If we want to lay down a ton of wells, etc. in a field, there are all sorts of people to do it. For most of SA production history the oil has been flowing from a relatively small number of wells considering the size of the fields.
And I'm also loathe to believe that the recent upward reserve revisions are based in anything remotely approaching reality.