A Nice Counterexample

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 intriguing - generally the UK is the poster child for the scariness of peak oil because it has had such high depletion rates recently. But just when we were getting used to it as a reliable method of scaring disobedient children into compliance, here it is messing up our nice simple-minded Hubbert theory. The basic problem becomes quickly clear when we look at the production versus time curve here:

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:

So now we need to know why did production not follow the same kind of general pattern that has worked so well for Texas, the US, or Romania? In the Russian case, it's reasonably clear what happened: society collapsed. Douglas Reynolds has argued, fairly plausibly, that the collapse was caused by the beginning of depletion in Russian oil production, but even if so, the decline would certainly have been greatly exacerbated by the resulting societal collapse. A lot of industry ground to a total halt, GDP was halved, life expectancy was sharply reduced, and the population declined. The subsequent partial recovery in production just goes to show that a societal collapse can actually cause oil production to drop even faster than geology alone dictates. At least, this is clearly so for communist economies: whether the lesson extends to capitalist economies could probably be (fiercely) argued both ways.

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!

Stuart, thanks for posting this.  Your work has greatly clarified
(at least for me ) the proper role of Hubbert analysis.
That graph is interesting. Unfortunately, it does not account for the huge tax increases on the oil industry introduced by the Chancellor of the Exchequer two or three years ago. With a lingering threat of windfall profits taxes.

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.

West Africa is one notch short of a war zone. It's a place no rational business person would set up shop without an incredibly good reason. The "risk" part of the "risk/reward" tradeoff is obviously huge (as in Nigeria in the last couple of weeks). So that suggests prospects are worse elsewhere right?
No, it suggests that West Africa is one of the few places where oil hasn't been nationalized.
OK, but why is nationalizing oil a Bad Thing, from this point of view?

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?

  1. Governments are fundamentally corrupt and inefficient.

  2. They know peak oil is coming, so they want to save it for later.

  3. ???
Good point. I personally believe that nationalized oil is a good thing because it leaves oil in the ground for later, causes higher prices, and will make the peak more of a plateau and gentle decline. If the OPEC governments could only be a little more incompetent and inefficient... then I'd be really happy!
I don't doubt depletion but I have a problem with the usefulness of Hubbert linearization. Take an oilfield that produces 1 (mbd) for ever. In a spreadsheet put 1 to 100 in column A. That's cumulative production. In B1 put =1/A1 and expand down to B100. That's annual production over cumulative production.  Now chart it.

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.

In your example, you don't get a straight line. It only looks approximately straight because of the large scale caused by the first few points.

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.


So fit that to the production curve to the most mature regions we have data for (like the US or Romania). It will suck - they don't look like hyperbolae. In general, for all you guys that want to propose other kinds of model - great, more power to you. But no-one's going to pay much attention to you unless you can show your model actually does a good job for some reasonable class of production regions. The reason Hubbert's model is famous is precisely because it has that property.

But no-one's going to pay much attention to you unless you can show your model actually does a good job for some reasonable class of production regions. The reason Hubbert's model is famous is precisely because it has that property.

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.

Actually, Campbell wasn't using the linearization method I don't think - I believe he was sticking in an explicit URR and constraining his fit to that. I wouldn't do that since our knowledge of reserves sucks. Our knowledge of production is imperfect (the different authorities differ as to the production numbers- maybe the Joint Oil Data Initiative is going to help here), but it's better than reserves.

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).

I still say that, on a linear scale, aP/CP plotted against CP will naturally follow something more like y=1/x than a line, thus making your predictions of 'zero' a little shy of the mark.
I agree. That UK graph reminds me of half-life decay in radioactive isotopes. I think a non-linear fit might give better predictive value.
But empirically that works very badly for the US, Romania, Norway, etc. So it doesn't seem interesting to push that model further.
I agree with the other commenters, you have to slow way down on this analysis.  I think you are violating Occam's razor by attributing something complicated and not physically possible (i.e. the logistic model) to something that can be explained away much more simply.

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:
and a more recent post showing how the math also describes the behavior of a simple electical RC circuit here:

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.

There's nothing physically impossible about the logistic model. It's obviously a simplification, but any model of an entire civilization is going to be a simplification. My perspective in such a situation is the more parameters we throw at it, the worse our predictions will be. You obviously differ, as you have a perfect right to do. I find your approach less persuasive than Hubbert's. I suggest you try it on partial histories for Romania or the US and see if you would have predicted the rest of the data better than the Hubbert linearization. If you can, that would get me to sit up and pay attention.

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.

Er, ok.  Looking at how you have been using the logistic model in the past --as a variant of the "pedator-prey" class of processes-- I think your modeling premise will have greater viability when applied to another pressing issue of today, that of the potential spread of avian flu. That is, if it firmly takes hold as some of the epidemiologists predict.

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.

Yes, the logistic equation is used in epidemiology - they call it the SI model (S=susceptible, I=infected). Essentially it is a model which is potentially applicable to any situation in which some initially exponentially growing process uses up some finite resource - whether it's a biological disease infecting a vulnerable population of animals, a computer worm using up a vulnerable population of computers, a new product spreading through a potential market, a new piece of information spreading through a financial market, or a civilization using up a finite pool of oil.

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.

For Romania, say they had a single oil strike some time in the past. Therefore, the forcing function looks like a delta function, and the solution set is just the exponential function if you assume production is proportional to the amount remaining (i.e. the stripper well scenario). Then when you plot dQ/dt/Q vs Q you get exp(-kt)/(1-exp(-kt)) plotted vs (1-exp(-kt)). In the regime where the logistic graph appears linear and it gets close to 90%, so does the exponential. And the match gets better if you put a bit of a spread in the delta function. Therefore you cannot tell the difference and the exponential model wins out because it matches a real physical process.

I don't respect Lynch at all. I agree with many people that think he is intellectually dishonest.

The logistic will start working before peak, the exponential decline will only start working after peak (eventually, they look identical, as you note).
No, the logistic model does not work before the peak. It looks very susceptible to initial conditions. Looking right does not mean it is right.

The exponential model works over every regime. It just needs a  forcing function to create a spread in starting points.

Re: "Yes, the logistic equation is used in epidemiology - they call it the SI model (S=susceptible, I=infected). Essentially it is a model which is potentially applicable to any situation in which some initially exponentially growing process uses up some finite resource..."

VERY interesting.... Write a post about this.

No, you didn't. What I meant was the meaning of the linearization function in different domains (oil production, epidemiology, etc.), the intuitive generalization of the model in different domains. If this model has general applicability, then demonstrate it. Show that future oil production is modeled in the same way as the spread of the 1918 flu virus (in the worse case). What you have never expressed is the intuition behind the model. This is important.
The problem is that there is nothing exponentially growing. There is a cumulatively growing set of tapped reserves, which takes work and time to find. This is offset by a depletion activity which is proportional to the amount of oil in each new reserve tapped. Unfortunately this does not describe the logistic model, which is more suited to the epidemiological and ecological sciences, and also to some fairly arcane chemical growth models that I did my thesis work on in the 80's.  Trust me, no way does this model work for oil depletion. It just happens to give an empirical fit. And people have started building heuristics around this model. Bad idea.

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.

There is something (very roughly) exponentially growing - the amount of information, capital, equipment, etc applied to the region - go read the Mineral Economy.. Whether you like it or not, you are modeling a social process interacting with a physical process - both in the finding of the oil, in how quickly people choose to develop it, and in what kind of technology they apply to the extraction process (horizontal wells at the top of the oil layer are not likely to lead to an exponential dropoff, for example). Again, you can complain all you like, but until you show me your lower residual fits to a broad range of situations, you don't have anything. I at least am weary of discussing it with you for now since we do not seem to making any progress. Come back with your superior fits to the data.
In the logistic equation, you use the term "a" and "1-a" to refer to a quantity and its complement. Now you want to use "a" to refer to some some economic scalar that grows exponentially, while "1-a" to refer to the oil reservoir itself. That makes absolutely no sense from a mathematical point of view, as in mixing apples and oranges.  Unless someone establishes a physical relationship between "a" and "1-a", I wouldn't go near solving this equation. And if there were a relationship, it might not be linear.  In that case, the tidyness of the solution evaporates.

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?  

I meant to say superior predictions - you can always get superior fits by overfitting - the test is can you predict forward from partial histories with lower residuals.
Great post! thanks! so if I understand correctly, a discovery curve with a heavy tail will probably produce a multi-peak production curve which requires two separate Hubbert models. In the case of SA, there are a lot of very different estimates for the discovery curve. Too bad the graphic on SA shows only cumulative discoveries. It looks like that the UK discovery curve is a mixture of a gaussian centered on 1975 and a uniform distribution modeling the heavy tail.
There is a very simple explanation for the apparent conflict--time.  The other examples--especially Texas, Saudi Arabia and now the world--didn't enter the linear phase until the regions had decades, at least 20 to 30 years, of serious production.  

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

I agree completely. The UK North Sea was a very immature oil province. We should not expect another non-linear departure to happen there again. We might expect similar results for Angola (production started in about 1980 and off-shore is now in development). But we'll have to wait some years to see those results. Only recently developed regions will have noisy discovery curves at this point. Sudan is another example.
The drop in UK oil production in 1988 was caused by the Piper Alpha fire. IIRC they delayed further exploration and production for some time aftr that while they dealt with safety and enviromental issues.
The Piper Alpha Fire was in June 1988 by that time
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
Um, doesn't "near its...peak" imply that losses are showing up?
You could make a case that part of the drop after 2000 was due to the drop in exploration after the Piper Alpha fire in 1988 but Alun was suggesting that the drop in 1988 and immediately after was due to this.

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:-
and this has resulted in a fair boost in exploration. See:-

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:-

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

LE MONDE: the end of oil, a well kept secret

...According to the article, the big players use two main sources to evaluate reserves worldwide: the Oil & Gas Journal, which sends a yearly questionnaire to governments of oil producing countries, and publishes their (unconfirmed) replies, and IHS Energy, a Houston consultancy, which publishes a confidential database - the problem is that it's so confidential that even the price of the information is not public, but is rumored to be more than a million dollars... Total, which has access to the database, notes that the two sources come up with similar overall numbers (OGJ has 1,266 billion barrels of "probable reserves" from 94 countries, and IHS has 1,152 from 114 countries), but that each line (country per country) is pretty different...

...The article states that in a recent meeting with political leaders, Thierry Desmarets, the boss of French major Total, said that peak oil would happen around 2025, provided that there is a demand shock. Which means, obviously, that if we do not curtail our demand, the peak will be much earlier. This is very much compatible with the scenarios drawn by APSO's Jean Laherrère and Saudi Aramco's Al-Hussieni, who both expect that production will plateau very soon, with a bumpy ride on such plateau, marked by various shocks and price volatility. Laherrère expects the final decline by 2015, while Al-Husseini sees it closer to 2030...

Jerome a Paris at


Regarding SA. Consider the fact that SA had extra production capacity for many years. They may have kept on discovering new reserves without bothering to invest in the infrastructure to tap the new discoveries. Is this claim possible? What would it do to the linearization if SA suddenly decides to develop those fields and increases their annual output?

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?


While I'm sure there are going to be a lot of great responses that go well beyond what I'm about to say, here are the two biggest concerns I have about SA production.
#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.

A reasonable hypothesis if all we knew was what they tell us and the production history. However, and this is the case Twilight in the Desert makes pretty well IMO, their behavior in recent decades is not consistent with the idea that they have a bunch of fresh new fields lying around just waiting to tap into. They have been spending lots of $$ reworking old fields, developing very inaccessible fields in the empty quarter, developing fields with unrefinably contaminated oil, etc. They are now exploring EOR techniques in some cases (electric submersible pumps), and drilling in very deep water. In general, they are acting much more like people spending lots of $$ to extract the more difficult remaining parts of their reserves than like people who are still sitting on most of it.
They have been spending lots of $$ reworking old fields

I don't understand why this indicates a lack of new fields. Many of the fields being reworked were partly developed and then mothballed due to low prices. Why wouldn't the Saudis go back to them? What's the alternative? Just ignore them, and leave them there half developed forever? If they already have some infrastructure, it's economically rational to return to partly worked fields first even if they have plenty of other fields.

Have you read Twilight in the Desert? Simmons makes a pretty convincing case that SA doesn't have any significant fields waiting in the wings to replace Ghawar et al. I think Simmons would say that whatever fields SA could still bring online would have little effect on the linearized production graph.

Regarding production costs, I don't know if anyone outside Aramco really knows what they are, but given the extensive waterflooding and maximum reservoir contact (MRC) horizontal wells, I'm sure they're higher than $1.50. The bottom line here, though, is that production costs don't really impact what traders pay for a barrel of oil.

In regard to SA and the effect on linearization of suddenly increasing production, as others have pointed out it's probably not going to happen, but in any case Texas--the swing producer prior to SA--serves as a good model.  

In 1972, almost everyone (except Hubbert) assumed that Texas could increase production at will--just as most people assume today assume that SA can increase production at will.  

The Texas RRC went to 100% allowable right around 1972, the year Texas peaked.  Prior to that, the Texas RRC had controlled production in order to keep prices stable.  By the way, there were attempted Arab oil embargoes prior to 1973.  They failed because the Texas RRC flooded the market with oil.

Texas had a frantic drilling program after 1972 that did nothing to reverse the decline, even though the number of producing wells went up by 14% in the 10 years after 1972.  

But the bottom line is this.  The Hubbert method (assuming a peak at 50% of Qt) picked the Texas peak within two years.  This may be a little misleading.  If we assume that a more accurate prediction is at about 55% of Qt, the Hubbert method picked the peak year exactly.  SA is at 55% of Qt.  

Jeffrey J. Brown

There is also a thread on SA going on peakoil.com, here a good comment by antimatter:
I'm skeptical of the usefullness of the hubbert linearization applied to OPEC countries - their production has been demand driven since 1980 or so. OPEC production was as high as it is now in 1979. In any case, Aramco claims that only 130Gb of the 260Gb of reserves are developed, this is backed by the recently retired Al-Hussieni. The Hubbert linearization will only reflect the production of the developed reserves, if it works at all. Also keep in mind that Saudi fields are produced at low offtake/depletion rates, 1-3%/year for most fields. Shaybah was put online in 1998 at 500,000b/d from an 18Gb, depletion of 1%/year and would plateau at least 50 years at this rate, though its being bumped up to 800,000b/d soon. Compare to Prodhoe bay - 1.5mb/d from 13Gb at plateau. If they were really in trouble one would expect them to be draining the fields as fast as possible. In that case the 'super sucker' hysteria might actually have some basis in reality.
This is only an argument if you believe the things the Saudis say when they are trying to reassure you. I don't. In particular, there is very mixed stories on their depletion rates. The EIA quotes a different Aramco executive as saying depletion on their fields as 5%-12%. "Oh what a tangled web we weave, when first we practice to deceive." Shaybah is pretty new and should go for a long time. But it's no Ghawar.
No, that quote says that there is a 5% to 12% decline rate, not that depletion is at 5% to 12%.  Annual decline is how production falls from one year to the next; annual depletion is how much oil is produced as a percentage of proven reserves.  I'm not sure if it is calculated based upon remaining reserves, or original reserves.  If it is remaining reserves, then the depletion rate will actually rise as the field remains on a production plateau.

Of course, the decline referred to in Abdullah Saif's statement could be the equivalent of Skrebowski's "Type 1" decline: certain wells are declining, but production is maintained by drilling new wells or increasing flow rates from other wells at the same fields.  In other words, production would fall 5% to 12% in a year at existing fields if they weren't worked on.  However, if total production from those fields is actually falling at that rate and can only be replaced by new production at other fields ("Type 2"), that is alarming.  Unfortunately, "Type 2" decline may be the correct interpreation of Abdullah Saif's statement.

Hmmm. A quick check around the net finds people using "depletion rate" both in the sense you define it here, and also in the same sense I use it (synonymous with decline rate). Eg here's Skrebowski
Currently, world oil depletion is running at 4-6 percent, according to ExxonMobil. Taking 5 percent of 2004 production of 82.5 million barrels per day (mn b/d) gives a depletion rate of 4.1mn b/d per year. This sounds huge but is in fact correct.
He clearly uses it as I do. But here's Campbell clearly using it as you suggest:
Depletion Rate is a given year's production as a percentage of the remaining reserves at the end of the preceding year
Oups! these two definitions are quite different and could produce very different numbers for the same situation!
Yep! I guess we all need to get careful about defining our terms (I do, anyway).
This is only an argument if you believe the things the Saudis say when they are trying to reassure you. I don't.

Hate to be blunt, but this is the very definition of conspiracy theory.

It's also self-serving that you claim the Saudis are liars, and then immediately proceed to quote a Saudi official to support your point. Isn't Abdullah Saif a liar too? Surely he was at the meeting where the Aramco executives pored ashen-faced over the data and decided they had to lie to the world. How do you explain the fact that the truth leaked out?

Or is this just a case of cherry-picking? I.e.: When the Saudis say negative things about their production, that's true; and when they say positive things about their production that's a lie.

The Saudi government is an authoritarian government. Governments of that class are not known for their truthfulness, nor for their tendency to tolerate their citizens freely expressing whatever opinion the citizen might hold. I think the Saudi government is misleading the world about it's reserves (for reasons I've articulated at length in recent days). That is not a conspiracy - it's simply a common way for governments of that kind to operate. That's different than believing that a seemingly democratic country such as the US is really operating primarily according to the presciptions of some hidden set of conspirators.

I do not know which if any Saudi statements are true. I was pointing out that one set of Aramco personnel in one context claimed they were managing their fields for 1% to 4% decline and that we should be reassured by this as to the future performance of their production, while a different official in a different context stated that they were already experiencing 5% to 12% decline in their fields. This seems like an inconsistency, and a severe one, on something that really matters. At least one of these statements must be misleading. Similarly, one set claim they had 700gb of OOIP, gradually increasing from 570 twenty five years ago, while almost simultaneously, al-Naimi is saying there's 1200gb of OOIP. I don't see how they can both be truthful statements of their best understanding.

I tend to think there is somewhat more likelihood of things they say that are contrary to their interests being true. But really, having concluded that they are not committed to providing accurate information to the world, I prefer to reason as much as possible with information that doesn't come from them. You yourself have stated that you believe Sadad al-Husseini, which presumably implies that you do not believe the official Saudi position that they can produce 15mbpd for 50 years.

Thanks Stuart. I agree with you wholeheartedly about reasoning with objective data. Otherwise, I think we both understand each other's position, so there's no need to rehash.

The deeper issue is this: We always talk about transparency in the context of Saudi Arabia. Simmons pays lip service to transparency for everybody, but he invariably hammers the Saudis. In fact, I don't think I've heard him, or anyone, explicitly go after a country other than Saudi Arabia.

How about transparency for Venezuela, for instance? The U.S. currently imports almost as much crude from Venezuela (41 mb in July) as from the Saudis (46 mb in July). Why doesn't Simmons hammer Chavez? Are we getting the truth from Petróleos de Venezuela?

Take it a step further. Suppose we inspect Venezuela. We send in the third party inspectors, and they determine that Venezuela indeed has plenty of reserves. The problem isn't the lack of oil; it's the lack of a favorable investment/production environment. Chavez is scaring away all the big oil companies, giving investment the short shrift, and funneling all the oil revenues to the poor, Cuba etc.

What's the verdict then? I'm afraid the answer will inevitably be: get rid of Chavez, we need that oil now. Oil is essential for our economy and our military, and doing nothing is not an option.

I don't want to see things go that way. My agenda is to leave as much oil in the ground as possible, for as long as possible. Anything which hinders oil production is good IMO because it's good for the atmosphere, and it accelerates the process of adapting to less oil. So I think it's counterproductive to support a campaign like transparency because it's an attack on the prerogatives and sovereignty of nationalized oil.

That is why I don't care whether the Saudis are lying. The Saudis aren't the problem. Peak oil is a problem which must be solved on the demand side, not the supply side.

I agree with much of your goals JD, but if the true situation were clearer, the price of oil would go up a lot and tend to bring about the things you want sooner. It would also help society adapt with less pain, and pain tends to differentially fall on the poor.
I agree with much of your goals JD, but if the true situation were clearer, the price of oil would go up a lot and tend to bring about the things you want sooner.

Maybe. There's also a good chance that transparency will reveal the situation to be just what Al Husseini says it is, and that might put minds at ease and lower prices. You shouldn't rule that possibility out. You're operating on incomplete information, and the outcome may surprise you. It's rational to consider and hedge for that possibility.

Someone might try producing the curve for Egypt. In this reprint of a Science article (June 2, 2004 Science Magazine 21 MAY 2004 VOL 304 1114-15) Oil: Never Cry Wolf--Why the Petroleum Age Is Far from over, the author Leonardo Maugeri (working with Lynch) claims that Egypt (started production in 1960) is a counterexample to a standard Hubbert curve.
Will do.
This article looks very fishy to me, the Egypt production curve looks like almost a perfect gaussian! check the ASPO newsletter (article #199) Newsletter  30 for the country assessment. The source for the figure  in the article is a document from Lynch!
I see what you mean. Somebody put in an extra factor-of-10 adjustment.
As I wrote above in the comments, this is the kind of information that Lynch and his disciples use to push their agenda.  If you don't have a good model for what they are showing, it doesn't matter that they don't have one either -- it suffices to make you look bad.

On the other hand, when I look at the Egyptian production curve, it looks like the global one, with OPEC oil shocks placed in the same locations on the time axis.

The current working model is:
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.
What is meant by "discovery"? Here is the BP Oil Reserves page, which defines their terms.

At the top level, URR = the sum of three variables
  1. cumulative production
  2. discovered reserves
  3. undiscovered resources
Going further, #2 is defined as
  1. proved reserves, P > 90%
  2. probable reserves, P > 50%
  3. possible reserves, P in a low range, also known as P10, P20 reserves
I would define "discovery" as the sum of (undiscovered resources, possible or probable)
proven, assuming that only proven reserves go into full-scale production.

So, when considering countries (oil provinces?) that may or may not give a good Hubbard Linearization "fit", it is prudent to ask whether they are candidates for a "noisy" discovery curve where discovery is as defined here. This will depend on various factors including how long they've been in production of any kind and how fully geologically vetted their resources have been -- their maturity as oil producers. The more mature an producing region is, the fewer discoveries (as defined here) I would expect, ie. there is less noise possible in the curve.

Finally, the historical UK and Texas in 1935-45 are "exceptions" because discoveries were not all in. Saudi Arabia is asserting that they are an exception -- some of us do not believe them. Some countries like Angola are not mature because they are in the early stages of production (offshore exploration continues) and new proven fields are just now in development.
My understanding of what Laharrere is doing for discovery curves is looking at 2p reserves (proved+probable), and backdating them to the initial discovery of the field. As Lynch has pointed out, that probably produces some systematic under-estimation of recent portions of the discovery curve which haven't had the chance to experience most of their reserve growth yet (Laharrere has argued that reserve estimation has become much better these days so this doesn't matter - I don't know the truth of that, but it shouldn't matter so much in areas like Saudi Arabia where it's pretty undisputed that all the discovery is old). I agree completely with your observations the importance of the maturity of the region.

On the "exception" thing - I think that what exacerbated the UK situation is that production was following so closely on the heels of discovery - there was much more separation in the US case - presumably because the industry was growing itself there, while in the UK case there was already a large hungry global oil industry ready to pounce on a new medium-sized province.

I'm going to have to think about the Laharrere/Lynch dispute ... it's not clear to me what's going on there. You might say more about that (with references).

Re: the "exception" thing -- Time is the variable. The UK production curve was compressed in time, the US case was not. Historically, things have changed. In all future cases, it will look much more like the UK where production follows closely on discovery (however defined). After all, demand grows, we need more supply to meet that demand and in the end we have doubts about that supply because, afterall, this is the Peak Oil site :)

I have a suspicious feeling that a lot of that "notchy/spiky" behavior in the plots that Laharrere provides is due to incorrect initial estimates of the cumulative production at time T=0. For example, if you apply the correct estimate for cumulative oil as of 2004 to the global model matched at TOD several days ago:
and if you adjust to the currently accepted global cumulative, you get
The data looks more hyperbolic and the straight line part of the data is less pronounced. TOD had 1050 bbls and the current estimate is 950 bbls.

Is someone massaging the data to fit the logistic model? As I will continue to say: there is no need to do this, as you can stay intellectually honest if you just get away from the dang logistic model and use something that matches a simple physical process!

I documented what I did and why. It's an admittedly imperfect procedure since Deffeyes wasn't using the same data series as I - I don't have his data series, and I don't have a cumulative total for before the BP series. However, I did play around quite a bit with that assumption to make sure my analysis wasn't too sensitive to it: I didn't get anything that looks like what you have. Can you email me exactly what you did and I'll try to reproduce your curve?

I'm getting the feeling you don't understand the basis for why the logistic model is a reasonable thing to do here. Have you read the Wikipedia?

Deffeyes has cumulative production through 04 a shade less than 1 trillion, but the BP production numbers are a few percent higher than his. Thus I think that would largely explain the discrepancy about the current cumulative production numbers. You have to realize that the various authorities that publish production stats do not agree on the numbers to better than 5% or so.
Re: "use something that matches a simple physical process!"

I would be happy to know, given the uncertainties, what that "something" is.

Dave, I remember you from a previous thread mocking "the something" I did use. Oh well, if you want to take a look again, go here:
If I did, maybe I wasn't justified. I will take another look at the links you provide at mobjectivist.... Do you have a link to my previous skepticism?

I don't believe you or Stuart or me are in serious conflict about Peak Oil issues, I believe we're all on the same side.... we're arguing about details (that matter) but still, merely details....

best, Dave

I agree with Dave, there are no major differences between the approach proposed by Stuart and the more sophisticated models developped by WebHubble. They both give the same position in x-ordinates for the URR so I don't think that matching the first years of production is that important. The only drawback with the logistic model is that it imposes a symmetrical production curve which is not necessarely approriate for all fields.
If you just subtract 100m cumulative off what I did, you get that in 1965 the world's cumulative production was only 75m barrels till then - almost certainly horribly wrong. If anything, my cumulative production input should probably be higher, since the BP data series seem to be a little higher than whatever Deffeyes was using. But the qualitative conclusion from his series and mine are basically the same: looks linear after 1983, and it just shifts the peak a couple of years. So you'll need to accuse both of us of "intellectual dishonesty" :-)
What you can do in order to correct for post 1965 production is to take the ASPO country assessment and take their cumulative prodution and then add an offest to the BP cumulative production.
OK, so if I understand your reasoning, it goes like this:

  1. Claim is that an oil region (or other phenomenon) subject to (wannabe) exponential growth will produce in a sigmoid function.

  2. The derivative of a sigmoid can be graphed to make a clean straight line that shows (in this case) the total oil to be produced.

  3. Graphs of mature oil regions do tend to show the straight line.

  4. Therefore, they're probably sigmoids, and the graph can be used to deduce total production. (And with a bit more work, peak production rate and post-peak production decrease.)

So far, I'm with you. I plotted a sigmoid for the Saudi data, and it did in fact fit very closely to the linear data--not only in the slope, but in the number and spacing of data points.

But to apply this method to nations and the world, you need to make a further assumption: that if you take the sum of several oil production baskets, you will still get a sigmoid.

In fact, the sum of sigmoids is not generally a sigmoid. The first paragraph of section III of http://hep.ucsb.edu/people/ascott/fermilab-conf-90-94.pdf (p. 6 or 7) implies that almost any function can be represented by a sum of sigmoids.

So to use this method for baskets of oil fields, you have to explain why in this case the sum of sigmoids is a sigmoid. I did a bit of Googling and couldn't find anything about the conditions that would make that true. If you have a power-law distribution, of course, you may have one or two oil fields dominating the curve--in which case you're calling all the rest "noise."

I could sort-of believe that the sum production of oil fields found in a single political and geographic area formed a sigmoid--though UK shows that even that isn't necessarily the case.

Perhaps we have to specify: sum production of oil fields found in a signle political and geographic area at approximately the same time. But then I find it very hard to believe that this method can be used for the world, and it must be used with care even on single nations.


Thank all of you for this discusion of modeling.  I suggest that an 'ideal model' needs to be made for the purposes of comparison.  Assume production in year t as f(t), where f is a gauss curve.  What does this look like?
So to use this method for baskets of oil fields, you have to explain why in this case the sum of sigmoids is a sigmoid. I did a bit of Googling and couldn't find anything about the conditions that would make that true. If you have a power-law distribution, of course, you may have one or two oil fields dominating the curve--in which case you're calling all the rest "noise."
I think this is a remote consequence of the central limit theorem which states that a sum of independent random variables is gaussian distributed. I made a Matlab simulation and I can show you that this is indeed the case.
I'm not 100% sure of the terminology, but I think the sum of independent random distributions is Gaussian. Sigmoid isn't a distribution; it goes from 0 at far left to 1 at far right.

Production rate (derivative of sigmoid) is a distribution, and maybe that's what you're talking about. So I guess you're saying that the production rate from a basket of oil (wells, fields, nations) is Gaussian.

Is the integral of a Gaussian a sigmoid? I couldn't find that on Google.

The sweeping under the rug is that the "0" at the far left cannot truly be zero.  It has to have a finite value to meet the requirements of causality. And where it starts makes a huge difference on how "fast" the sigmoid evolves.

That's one of the features that Michael Lynch scoffs at when he looks at these models. He doesn't say it in exactly this way, but assuming gaussians in particular breaks causality. He extends this to sigmoids when he sees the long negative tail. While I don't agree with this completely, as you typically start the sigmoid at some finite value, no one has ever articulated where it should start.

In nature, when you use the logistic model, it starts with a small population of discrete entitities, and you let it proceed to (consume/infect/kill/bond) one entity. Then you can sit back and watch as the reaction propagates.

That's one of the features that Michael Lynch scoffs at when he looks at these models. He doesn't say it in exactly this way, but assuming gaussians in particular breaks causality. He extends this to sigmoids when he sees the long negative tail. While I don't agree with this completely, as you typically start the sigmoid at some finite value, no one has ever articulated where it should start.
The argument of causality is bogus to me, because gaussians/sigmoids have an infinite support (they extend from -infinity to -infinity). But this is an asymptotic behavior  which will be never observed in teh real world. In reality gaussians are convoluted with a rectangular function which limits their temporal support.  
Well, the right terminology is "the sum of independent random variates which have an arbitrary probability density function has a limiting cumulative distribution function which approaches a normal distribution." . The sigmoid and its derivative are neither probability density functions. They are deterministic functions with random parameters (URR, slope, half time period, etc.).

This problem reminds me of the non parametric density function estimation techniques used in statistics for the estimation of a probability density function from a limited set of observed random samples (x_i, y_i):

f(x)=sum_i(y_i x K((x-x_i)/h_i))
where K() is the kernel function. In our case, f(x) would be the country total production and x_i, y_i, h_i would be the peak production date, peak production and depletion rate respectively for each oil field i. K() would be the normalized Hubbert function.
Is the integral of a Gaussian a sigmoid? I couldn't find that on Google.

kind of, it's called an erf function ( "error function").
Thanks for your answer. Good to be talking with someone who knows how math works.

I was going to ask whether Hubbert linearization will work on an "erf function" or not.

But before I ask that... it sounds like we can't expect the curves to add to a Gaussian anyway, since they're not a probability distribution.

So let me ask again the more direct question: Under what conditions is the sum of sigmoids a sigmoid? And, are these conditions approximated by oil-field baskets?

If you are interested, I've just started a thread on this subject on peakoil.com:

A Statistical Model for the Simulation of Oil Production

So let me ask again the more direct question: Under what conditions is the sum of sigmoids a sigmoid? And, are these conditions approximated by oil-field baskets?

You can't add sigmoids directly (cumulative productions) because they are not temporally related (each field does not reach the same cumulative production at the same time). The right question is Under what conditions is the sum of sigmoid first derivatives a mono-peak function. From the simulation I made, it looks like it depends strongly on the shape of discovery distribution.
Well, the sigmoids would be offset in time, of course. It's obvious that there are many sums-of-sigmoids that are not sigmoids, not even approximately. The question is, do oil-field baskets happen to be one of the sums-of-sigmoids that does approximate a sigmoid?

Your single-peak derivative criterion is too weak. The point of a sigmoid is that the "linearized graph" of its derivative produces a straight line that points at total production. For other shapes of derivative, even if they have a single peak, they won't produce that nice useful straight line.

And this makes me suspicious that linearized graphs of derivatives of baskets only produce straight lines accidentally or when one pulse of exploration dominates the basket. That would make "Hubbert linearization" not generally useful.


Yes, the predator prey relationships work best on homogeneous populations. Another, but not the most important, reason to stay away from it. If you really want to see what kind of trouble you can get into using the sigmoid, go to this Java applet:

Scroll down to small values of P and R and you can see how touchy the whole thing is.  Touchy too on initial conditions, which is always conveniently swept under the rug in these discussions.

Actually the explanation is both more complicated and simpler than what we have above. First lets deal with numbers and labelling. The y axis on the linearized hubbert curve for the UK is mislabelled as they only get to a bit less than 3 Mb/d at their peak. To help the confusion the 2 peak UK production curve shown next is in Mcu.ft/mo, not  a very useful measure for us, even if it does clearly illustrate the 2 peaks. The Laherrere annual production curve is in Mb/d which is much more helpful.

Now, at 1980 the UK production is 1.8 Mb/d or 660 Mb/yr and the cumulative is 2100 Mb. So the annual is 31% of the cumulative. In 2004 we are back to about 660 Mb/yr on 21300 cumulative or 3%. The first big problem is that the curve doesn't really tend to linearize until the annual production is a small % of the cumulative production. At a fixed annual production it doesn't linearize then either, it just looks linear on the scale we are using. Saudi Arabia for example is producing about 3.5 Gb/yr on a cumulative 105 GB or a little over 3 %, so they look pretty linear.

 If you just take a case where production is constant at 1 x/yr, for the first year production over cumulative is 100%, on the second year it is 50%, on the third year it is 33% etc, and you have to get out about 15 years and below 7% before the increments are small enough to start to look linear.If you are increasing production you will have a flatter slope depending on the rate of increase. It takes only a little effort to understand that to project URR you have to be past the peak and you have to have unconstrained production at the optimum rate that does not damage the field. If these 2 conditions are not met the projection will give a false URR. I suspect you have to also have something pretty close to a logistic curve, but I am not mathematician enough to explain that.

The UK curve is past the second peak now as of 1999 and is probably in irreversibla decline.  The decline so far has been at an absolute rate of about 70 Mb/yr/yr, which on a 1999 production of 1070 Mb was 6.5% and in 2005, on a 2004 production of 730 Mb is 10%.

In the case of Saudi Arabia we have constrained production below the peak due to lack of world refinery capacity for their sour crude. As a first order approximation, if their production were declining at a rate of 50Mb/yr/yr they would show a URR of about 190 GB, essentially what we see. If production is constant at 3.5 Gb/yr the apparent URR would be about 240 Gb. If production were still growing at 50 Mb/yr/yr the apparent URR would be 320 Gb. This last would be the case if they can bring on enough new production to offset declines and if increasing world refinery capacity lets them sell an incremental 50 Mb/yr of sour crude each year until they get to annual production of near 4 Gb/yr or 11 Mb/d.

We saw some weeks ago that SA light sweet crude peaked somewhere between 2000 and 2004. If their light sweet crude is unconstrained and is declining at about 50 Mb/yr/yr, then the Laherrere URR projection may be valid for light sweet crude only, which to me seems like a pretty likely case. That could still leave their total URR more like 260 Gb without straining my credulity. My guess is that their present frantic efforts to increase drilling is precisely because their light sweet crude is in decline.

The last kicker comes in because I think that using maximum reservoir contact wells blows the whole Hubbert picture. It allows near peak production well beyond 50% depletion, but will almost surely result in a precipitous decline when the peak is passed. In the case of SA, when the water cut reaches the MRC wells, production will fall off a cliff. I think their MRC wells are pretty recent, and that they may have intentionally constrained production somewhat below the possible peak rate for these wells, so they may not have visibly distorted the curve yet.

I would expect the curve to begin moving to a less steep slope soon, and then after a few years get very steep, probably with an X intercept for light sweet crude pretty close to the Laherrere projection. Of course all this last bit is just speculation on my part. Murray

The constant depletion hyperbolic view works if you use the Taylor series approximation y/(x+dx)  ~ y/x*(1-dx/x) when the year-to-year cumulative increase is much less than the total. But more importantly, the linearity improves when you add in that the extraction being proportional to the amount remaining. That part of the analyis I have no problem with. But otherwise I agree with you, it's the early stuff I have heartburn with. The logistic formulation just happens to work when you start fitting past peak because of the strong decline component.  No one can prove that it works early on because of a weak premise and the fact that for some reason the plots get filled with "noisy" data in that regime.  I believe it looks way more hyperbolic than the data that Laherrere and company suggests.
I'd once again, if you haven't looked at it, recommend:

Oil Production in the Lower 48 States
Kaufmann & Cleveland, 2001

They use a modified Hubbert model, including political and economic factors to account for oil production behavior, including the decisions of the Texas Railroad Commission (analgous to OPEC on the world scale).

They conclude that Hubbert was very lucky - the factors which are most salient to the 1970 peak outcome were the non-geologic ones he had the least ability or information to predict, and which have no support in his model.

Data mining for coefficients from the looks of it.
That's a rather pejorative description of published research - especially research that is explicitly backward-looking.  How nice that it means you don't have to address their findings or conclusions.  I suppose you could characterize all the work being done by Stuart, Khebab, and even yourself as mere "data mining."  Indeed, the same would go for every statistician or economist anywhere...
Data mining is good. It maps out the human genome. It goes through plant life, looking for agents that could cure cancer.   I hope they find what they are looking for.
Sorry - I misunderstood your meaning.

Any final conclusions?

As best that I can tell, there do not seem to be any counterexamples of regions showing--once they have established substantial oil production over period of 20 to 30 years--significant deviations from a downward linear slope.  

My conclusion is that we all need to be looking into starting organic gardens and/or farms and moving to much smaller more energy efficient homes closer to where we work, preferably along mass transit lines.

Jeffrey J. Brown

Your first paragraph I agree with based on our empirical exploration so far, but I think we should look at more countries and also develop a deeper insight into why it works as well as it does. No-one who is proposing a different model seems yet to have done any work to establish that their model is predictively better, so I await that with interest. Right now the Hubbert model, imperfect as it undoubtedly is, seems to predict better than anything else, once there is enough of a track record as you say.

As to what to do, I'm not sure I understand all the options well enough to have developed a solid position yet.


I ran across this paper a while back, and it may be useful to you.  One thing to look at is the effect that excess production can have on a Deffeyes plot.


I think the graph for the entire world production will follow a perfect Hubbert curve far more precisely than the curve's of individual nations because a nation is by definition a political entity and not per se a geological unit and therefore a productioncurves of individual nations exaggerates political influences. E.g. The Persian Gulf is a geological unit yet Iraqs production curve typically has a lot of political infuences in it. Yet a drop in production in Iraq would be mitigated by a rise in production in other Gulfstates. The result will be that the productioncurve for the entire Gulf would be far more "smoother", will fit a Hubbertcurve far better then would be expected if one were only to look at Iraqs production curve.

In other words, if you would want to exclude political influences the thing you should not do is look at individual nations curves.  

Stuart - I think you're too quick to dismiss prices as at least a partial driver for the UK and Russian production cycles illustrated here. Note that '93 was a significant cyclical trough in oil prices. I remember vividly the Economist cover trumpeting "The Case for $5bbl Oil".  (A better contrarian indicator may only be the cover of Time.) So at least in this case, prices and production came down in parallel, post-GW I.

Obviously the Russian production increase in the last 10 years is mostly a result of the para-capitalist structures coming into place, so less related to prices. (It'll be fascinating to me see how rapidly Putin screws it up and provides attribution-error peak-oil fodder.)

Anyway, I'd love to see some of these production charts overlayed with prices.