## When Does Hubbert Linearization Work?

Hubbert Linearization of Saudi Oil Production. Credit Jean Laherrere.

An interesting question is to know when does this style of Hubbert Linearization work? The empirical answer for a small non-random sample of five countries and one state is that it always seems to work as a pretty decent rough approximation once the graph has settled down into the linear regime. If anyone wants to post, or make, or suggest I make, a few more pictures, we can take this further. I would be particularly interested if anyone can come up with a country that has a decent section of linear regime that then goes substantially non-linear. The rest of the pictures are below the fold.

### United States

Credit Seppo Korpela.

### Norway

Credit Rune Likvern.

### Texas

Credit Jeff Brown.

Great!!!!!!!!!!!!!!!

Thanks again Stuart for this kind of analysis.

I think TOD should create a special page with this information, explaining the linearization method, with these plots and the world plot Stu posted a couple of days ago with BP data.

Peak Oil is not a theory is a mathematical interpretation of Mother Nature.

Is there any explanation on offer as to the conditions that produce this linearity (or the lack of same prior)?
Beyond Oil By Prof Deffeyes explains how the straight line is derived from a 'Hurberts curve'.
I'm skeptical about the tails of these graphs. It's clear from reading Aramco material that their production strategy is not to maximize near-term production. Rather, their strategy is to consistently plateau at a sub-maximal constant level, as they have been doing for years, and plan to continue in the future (e.g. at 12mbd).

For a producer following this strategy, the graph will take the non-linear form y=1/x, and foul up the linear extrapolation.

Also, has there ever been a case where the line actually hit the x-axis?

JD
I'm still getting my head around these graphs, but isn't the slope telling you how fast they are depleting their reserve?  Look at the Iran graph, very shallow slope compared to Norwegian.  Doesn't this mean that extraction rate becomes ever smaller with respect to cumulative removed if extraction rate is held constant?  Even a fixed rate of extraction for very long time will still have a negative slope estimating total reserve.  Only increasing extraction rate keeps the slope positive.

If extraction rate peaks than the slope gets steeper.  If I understand your post you say that SA is artificially holding production below their maximum rate.  They could increase extraction rate and shift the slope into positive territory or so flat intersection with the X axis is meaningless?  This is what the left side of all charts shows.  Extraction rate is increasing faster than cumulative.

But I am skeptical that after decades of pumping SA can increase their rate enough to change the slope very much. This would imply that very few of their wells have peaked and many have the potential for increased rate of extraction.  By increasing rates everywhere they could push the intersection to the X axis a bit to the right.  But this short term effect could be corrected later by steeper declines in extraction rate than previously calculated during the push for maximum extraction rate.

Am I on the right track here or just completely lost mathmatically?

Ah. That would explain why their existing production is depleting at 5% to 12% annually.
JD apparently knows nothing about the mathematical concept of an asymptote.

Oh, I forgot, asymptotes are features of junk science.

Seriously, it's like asking why log-log graph paper does not have any zero intercepts.

Speaking of log graphs, I was thinking that, as the wild swings in the curve for low cummulative output are exagerated (the ratio is more sensetive to chages in production for low cummulatives), the opposite might be true further out on the graph (the curve may not be sensitive enough to be enlightening for large cummulative values).  Perhaps putting these data on log paper, or some other non-linear scale, might be more illustrative.
Another (more tangential) point is this: the graphs don't take into account synthetic oil. As the U.S. reaches the extremities of it's depletion, it's inevitable they will turn to coal liquefaction, and that liquid will be classified as oil. It may not be possible for such synthetics to return the U.S. to levels of 10mbd again, but it will certainly be enough to keep the line from intersecting the x-axis for a long, sustained period. Even accounting for conversion losses, the U.S. currently has 3 times more oil in the form of coal reserves than its URR of conventional oil.

This too would lead to a y=1/x type curve.

Very cool graphs. We should definitely save these somewhere for future days/months to point people to.

Quote: "Energy markets are about to experience a seismic shift," Christopher Flavin, president of the Washington, D.C.-based Worldwatch Institute, said in a speech to oil executives and energy ministers in Johannesburg, South Africa, site of the 18th World Petroleum Congress. "The question for oil executives is whether you're in the oil business or the energy business."

The article paints a rosy picture of renewable energies, but one thing is clear: Peak oil awareness is entering the mainstream. We're still not being told the truth, tho, about the shock it'll mean for our society...

It is now their Most Popular Story (in terms of # of times e-mailed)

I'm skeptical about the use of this method to present production data because the relative error doesn't seem to be distributed uniformly. The relative error in the log domain of the vertical ordinates according to the logistic model is the following:

`D(ln(aP/Q)) = Dk/k - DQ/Q x Q / (1 - Q)`

where D stands for the greek symbol Delta, `Dk/k` and `DQ/Q` are the relative errors on k and Q which can be presumed constant. The error behaves has following:

• Production start Q -> 0:
`D(ln(aP/Q)) = Dk/k`
• Production Q -> 1 (total URR has been extracted):
`D(ln(aP/Q)) = -infinity`
Because we are in log domain, `D(ln(aP/Q)) = -infinity` means that deviation around the asymptotic line will tend toward zero! That's why, we observe these wild deviations aroud the line when production is starting whereas it seems to converge nicely when Q tend toward 1. This behavior can be misleading for an observer because it seems to reinforce that there is some inexorable mechanism at work pushing the production data around the line.
It's not a log plot. It's a linear plot of P/Q versus Q.
it doesn't matter! the log is applied here only to make the error analysis easier (multiplications become additions and absolute errors become reletive errors).
From what I've gathered about the math behind these curves, I don't think there are good answers to the concerns you are raising vis error analysis.

Hubbert was not a mathematician or an econmist.  He drew his curves by hand, and calculated the areas underneath them by counting the squares on his graph paper and guessing.  He assumes logistic growth and decline, and some of the field curves look like logistic curves.

But I'm not seeing a lot of advanced statistical (or econometric) methods or models yet from the peakers.  Drawing and fitting curves is meaningless - its the equations the curves reflect and the relation of the variables in the equations to the facts in the ground that provide meaning.

Counting squares under a curve is not "guessing," it is measuring. It's the way things were done back in the days before computers.

If this non-argument is the best you can do, maybe the Peak Oil people are right.

Got it - it is certainly true that because of the Q term, the fluctuations are much smaller to the left than the right. However, that doesn't prevent the curve from diverging from the model if indeed the model is wrong. More tomorrow - I now have a couple of countries where it doesn't work that we can chew on.
Re: "I would be particularly interested if anyone can come up with a country that has a decent section of linear regime that then goes substantially non-linear."

Let's try to imagine under what conditions this might happen. Once P/Q over Q goes linear for a while for some country, it can only go non-linear (upwards) depending on the maturity of the country's production, where I'll define maturity as "% of URR in production". Maturity is obviously fuzzy. There are basically two cases:
1. maturity is high (some % = N1). The linear regime can not change much.
2. maturity is low (some % = N2). What can happen? The country ramps up production on some undeveloped big fields they've got laying around. But bringing new fields online happens gradually, production starts low and rises thereafter until the peak for each field. Meanwhile, suppose existing fields are depleting. All you can get is a "Prudhoe Bay" kind of bump as shown in the US graph (depending on N2). In the best case, existing fields are not declining yet, N2 is fairly low and some new big fields are being brought online at the same time. In this case, you could go non-linear for some amount of time but on the other hand, the country has not settled into the linear regime for very long either.
I am confident that there is no country in the real world meeting the conditions for the Hubbert Linearization to go non-linear as outlined in #2 above. It's more complicated than my simple description but I think the basic intuition is right.
By the way, when I said "In the best case..." above and since Saudi Arabia has just about doubled their URR numbers, Saudi Arabia is basically claiming that they mostly fit this best case (slightly modified) -- see HO's thread Debating to the numbers (or more on Saudi production). Therefore, they are saying they will go non-linear soon and for some time -- see Khebab's graph.

Thus saving the world and reasserting their premier position of control among the world's oil producers. And don't forget, we love the Saudi Oil Minister Ali Al-Naimi. It's all good.
I have a few questions and issues to raise:

First, what are some sources for the raw production data for states and countries? I'd like to try making some of these curves myself.

Second, what does the curve look like for the whole world, at present? Is the recent data on a line?

Third, is there a name for these kinds of curves? They would be helpful to look up references where they are discussed, particularly in the context of oil extraction.

Here is one reference which is skeptical about these curves, from Michael Lynch, http://www.gasresources.net/Lynch(Hubbert-Deffeyes).htm. His figures 4 and 5 show production curves for fields which don't fall into this nice pattern. He analyzed all of the UK's top producing fields and of the top 21, only 7 showed nice curves like those above.

My main problem with the curves is that the theory behind them is unsound. There is no reason to expect oil production to match a logistic or "yeast growth" curve. The fact that empirically it has done so for some oil fields in the past cannot be validly extrapolated forward into the future because conditions will be so different.

In the past, when one field was dry they would move onto the next. But in the future, as each field dies it means there will be that much less oil supply in the world. The price will rise and people will work much harder to draw oil from existing fields. This additional motivation and effort, which was not present in the past, will move production above the previous linear regime and create a departure from the predicted curve.

Because of this effect I can predict with high confidence that we will eventually extract more oil from these fields than the graphs above predict. It is impossible however to say how much more we will get.

Prices can't rise higher in the long term because the cost of making methanol and dme will continue to fall as the existing medium pressure catalysts are replaced by lower pressure catalysts, just as today's medium pressure catalysts replaced high pressure catalysts.
The lower the pressure, the lower the cost of making and fabricating the steel components for the synfuel plant. Oil well drilling will fall like a rock at some price and only the existing wells will continue to produce at a constantly decreasing rate.
I note this statement from Lynch's paper:
The primary flaw in Hubbert-type models is a reliance on URR as a static number rather than a dynamic variable, changing with technology, knowledge, infrastructure and other factors, but primarily growing. Campbell and Laherrere claim to have developed better analytical methods to resolve this problem, but their own estimates have been increasing, and increasingly rapidly.
That's interesting to me because in my post on this thread, I indeed assumed URR as a fixed number. Primarily growing? Just always getting bigger? Countries do tip over into decline, this does happen. One might assume their URR is primarily declining. I'm certainly willing to acknowledge that URR increases due to Lynch's factors are possible if he will acknowledge that in an increasing number of cases it goes the other way. Also, Lynch's Table 1 has China, Indonesia, Iran and Iraq with greater URR in 2002 than in 1997. I don't believe that and I'd love to be proved wrong. It's certainly not reflected in any actual production numbers I've seen. Finally, for OPEC in general, Lynch is right -- URR always seems to go up but is never offset by actual past production. Perhaps they could learn how to subtract as well as add.
There's a long thread on the peakoil.com forums where Lynch kindly discussed his views on the subject with the community there.

Lynch's point about URR is that URR is partially an economic assessment of the ultimate amount of oil that will be recovered, similar to "proven reserves".  Whereas "proven reserves" are the amount of OOIP that is economically recoverable under present economic and technological conditions, URR is an estimate of total future recovery based on projected economic and technological conditions.  Even if we can only get 35% of the oil today, we might estimate that ultimate recovery rates will be 50%.  Lynch argues that over time estimates of ultimate recovery rates have risen, thus raising URR.

As prices rise higher then we previously thought they'd go, and as technology improves faster than we previously thought it could, projected future final recovery rates rise.  That implies URR should continue to increase relative to OOIP.

Dr. Tanstaafl  ---  aka "Silent E"
There Aint No Such Thing As A Free Lunch

As prices rise higher then we previously thought they'd go, and as technology improves faster than we previously thought it could, projected future final recovery rates rise.  That implies URR should continue to increase relative to OOIP.

I think this is the crux of what separates "peakoilers" and cornucopians. It's obvious that the URR will grow according to the current/technological conditions. However, it cannot grow forever and will reach an asymptote (75%-80% of the OOIP?). The application of enhanced oil recovery methods is also highly dependent on a particular oil field history/features and cannot be generalized across all fields. The need for new extraction methods reinforce the fact that oil is getting harder to get and more economically expensive which is exactly the point of "peakoilers".
You've got Lynch's paper, so you know what he says.

And although they claim their methods yield reliable, stable URR estimates, this is far from true. Not only have they repeatedly increased their estimates of URR (from 1575 in Campbell 1989 to 1950 in Campbell 2002), but on an individual country basis, the amount of discovered oil now exceeds their 1997 estimates of URR for 30 out of 57
countries! (Table 1) If these estimates do not prove valid for as short a time as five years, how can they be expected to hold true for the long term, as claimed?

His point is that Campbell's own numbers indicated URR rose over that 5 year period.  That's where Lynch got the data for the chart!  But Campbell never makes an effort to explain why the factors that drove reserve increases won't operate over the next 15 years as well, raising URR once again.

I think this is mainly a problem if you fit in the P vs t domain and constrain the area under the curve to meet some a-priori idea of the URR. The nice thing about the linearization method is no a-priori assumtions about URR are required. And it least in some cases, it works like a dream (Romania - where you'd have been getting basically the same answer for decades using this method.)
I think that depends on where the fields are.  As we have discussed in earlier posts, when the fields are deep offshore, when they reach a certain point the plug is pulled and its over.  It is easier with onshore wells (Texas,  Oklahoma etc) to put in stripper production and perhaps come back later to do EOR.
First, what are some sources for the raw production data for states and countries?
BP Statistical Review of World Energy 2005
Second, what does the curve look like for the whole world, at present? Is the recent data on a line?
Another Way of Looking at CERA
My main problem with the curves is that the theory behind them is unsound. There is no reason to expect oil production to match a logistic or "yeast growth" curve.
There are other models that have been studied by David Roper for the modeling of the depletion of nonrenewable resources:
The Verhulst model is a generalization of the logistic model:
`P/Q=k/n(1-(Q/URR)^n)`

It gives the following fit (k= 0.0312, n=5.5635e-006,  URR= 309 Gb):
picture
The maximum production rate is given by:

`Pmax=kQ/(n+1)^(1+1/n)`

which gives 3.55 Gb (9.7 mbpd).
Mmmm. Extra parameters rarely help models that are only "rough, good to 10%" sort of fits anyway - you just end up overfitting to the noise, which looks like what's happening here. Try it on Romania. Also, how'd you do your fit - the residuals don't look balanced.
I agree, the Verhulst model is usually hard to fit, I'm not sure that P/Q vs. Q is also the best space to perform the fit. its main interest is the possibility to obtain asymmetric curves (n=1 is the symmetric case). There is a thread on peakoil.com dedicated at this issue (Updated Verhulst model).
Have you read Kaufmann & Cleveland's paper assessing Lower-48 oil production with a more detailed model?  They conclude: "Hubbert got lucky."

Any lingering uncertainty about the efficiency of the estimation results or the identification of the cointegrating relations does not affect the conclusion that the accuracy of Hubbert's original forecast for oil  production in the lower 48 states is fortuitous (e.g., Ryan, 1965; Harris, 1977). The cointegration analysis indicates that oil production in the lower 48 states shares stochastic trends with the decomposed price series, average costs, and prorationing decisions by the TRC. These stochastic trends are not present in the deterministic bell-shaped curve, therefore the first difference of the bell-shaped curve drifts away from the annual change in oil production for extended periods (Figure 3). For example, production in the lower 48 states stabilizes in the late 1970's and early 1980's, which contradicts the steady decline forecast by the Hubbert model. Our results indicate that Hub'bert was able to predict the peak in US production accurately because real oil prices, average real cost of production, and decisions by the TRC co-evolved in a way that traced what appears to be a symmetric bell-shaped curve for production over time. A different evolutionary path for any of these variables could have produced a pattern of production that is significantly different from a bell-shaped curve. For example, if the TRC did not shut in production, or did not favor high cost producers, production may not have followed a bell-shaped curve for production and production may not have peaked in 1970. In effect, Hubbert got lucky. Thus, the ability of the Hubbert's model (and its variants) to forecast production Oil Production in the Lower 48 States in the lower 48 states accurately, probably cannot be extrapolated to other regions, as done by Campbell and Laherrere (1998).
Since this method also gets pretty lucky in Romania, Norway, and a number of other countries I think we need a deeper understanding than that. It is somewhat mysterious to me why it often does as well as it seems to empirically.
Not only that, but people who talk like this
The cointegration analysis indicates that oil production in the lower 48 states shares stochastic trends with the decomposed price series, average costs, and prorationing decisions by the TRC.
can't be taken seriously.
A critical reading of the Lynch paper will reveal several problems, the major one of which is the failure to quantify his statements. To look at only one example, let's take his last table. He refers to the number of countries for which the URR has increased, but fails to mention that some have decreased. He then shows us an increase in the total from 1995 to 2002 of 7%, which, given the accuracy of the data available, is close to trivial. In the figure of growing asymptotes, ignoring the first curve which is relatively early data, the growth is about 10%, and the rate of growth is declining. In (was it fig 6?), where he claims the straight line decline has been violated, one can go back several data points and get a trend that goes to the x axis at 48, or use all of the data and get an intercept at 49. All Lynch has shown is that the data is not real good, and changes a little bit with time. If we assume that the famous 2000 Gb URR is really 2200 (which would accomodate all the errors that Lynch has been able to illustrate) we postpone the peak by about 3 years, and maybe raise peak production by a percent or so. Big deal! I think Lynch has demonstrated that the Campbell/Laherrere work is quite valid, especially given Campbell's oft repeated statements that the data is far from accurate and reliable. I wish I had time to parse this paper in detail, but the above should be enough to guide the discerning reader through Lynch's artful misdirection.  Murray
wow this is stunningly good stuff.  as you can see, SA is already in linear decline.  AS simmons put it, the world peaks when OPEC has peaked and OPEC has peaked when SA peaks.

clearly, clear as i dont know what, SA is in decline and this should be published on every newspapaer, frontpage on every news website.

For the sake of the discussion, I added al-Naimi scenario (12.9 mbpd in 2009):

you can see that you can estimate a second logistic line which  gives an URR near 570 Gb.

That's a great graph.  It demonstrates that these charts are dependent on a arbitrary starting point for the linear regime that only can be recognized with a large number of datapoints.

Also, they seem to be creating more confusion than benefit.  A negative slope does not mean that production is necessarily in decline, as Khebab earlier pointed out.

One more observation - as production declines for a country, unless it completely stops, it will never reach the x-axis.  However, it also won't reach an asymptote.  Instead, datapoints will cluster closer and closer together, nearing the x-axis but never making it there.

As Defeyes explains, this is a tool to extrapolate the ultimate (cumulative) production or Qmax, the x-axis intercept.  Knowing Qmax, one knows peak cumulative production (Qmax/2).
Simmons did a great job, but ME future production remains difficult to estimate. Non-OPEC countries (the US, GB and Norway, etc) had no limits on production, so found and produced all that was economically feasible as quickly as possible; it is logical that their peak and subsequent decline would be similar. Some off limites areas (former USSR) now being produced are following suit.

OPEC, however, has until recently been quota limited. With over capacity due in part to large non-OPEC production increases, the ME made little attempt to further develop its reserves after around the mid-eighties, and certainly not at a maximum clip. Indeed, their existing output could not be utilized. Accordingly, and because they followed their own economic rules, their curve is likely to be different from other countries. Consider Russia, with an earlier peak, followed by a decline, and then climbing to a new peak under a different political and economic environment.

Most have been surprised by the sharply growing Asian demand over the past few years. SA and others are only now responding to the high prices by looking to increase production. This effort is helped by their substantial increase in income, without which they would have anyway been unable to fund the effort. Simmons may be right that increased production will damage the fields, but it seems likely that production will nevertheless increase for a time.

The statement that the world peaks when SA peaks is not obviously correct. Increases in SA production, if realized, may offset worldwide decline, or perhaps not. And, future Siberian output, and its timing,is also murky.

I am delighted that Stuart is addressing this topic.  What I find compelling about the method is that it is (almost) totally objective and that it uses the two knowns (current production and cumulative production) to predict the unknowns: approximate date of peak production and estimated total cumulative production (Qt).

In the real world, I think that the approach works because after decades of drilling in a given region--Texas; Saudi Arabia and now the world--there aren't many surprises left.

Here in Texas, the method predicted the peak of production (in 1972) within two years (assuming that peak production is at 50% of Qt).  Texas peaked at 54% of Qt.  Saudi Arabia is currently at 55%.

Another interesting analogy.  The method gives Texas recoverable reserves of 66 billion barrels (Gb), and the method gives Saudi Arabia 180 Gb.  Peak production in Texas was 3.5 MMBOPD.  If you divide 180 by 66 and multiply times 3.5, you get:  9.5 MMBOPD, which is precisely what the EIA currently estimates as the Saudi's oil production.  (By the way, note that 180 Gb is almost exactly the number that Matt Simmons cited as Saudi Aramco's estimate of recoverable reserves in 1970's).

There are other good analogies.  The largest oil field in Texas, and in the Lower 48, is (or was) the East Texas Field.  The first production peak in the East Texas field was in the Thirties, before the Texas RRC curtailed production.  The final peak was in 1972--exactly when overall Texas oil production peaked.  The East Texas Field is to Texas as the Ghawar Field is to Saudi Arabia.

We have had roughly 70 years of regulated oil production.  From about 1935 to 1970, Texas served as swing producer. From about 1970 to 2005, Saudi Arabia served as swing producer.  There is no longer a swing producer.

The production history in the 10 years after the Texas peak also serves as a cautionary model for the next 10 years.   In the years following 1972, oil prices in nominal terms went up by 1,000%; the state saw the biggest drilling boom that we will ever see and the number of producing wells went up by 14% in the 10 years following 1972.  It made no difference.  Texas production declined by about 30% in the 10 years following the peak. We are currently down by almost 75%, 33 years after the peak.

By the way, based on some estimates I have made, since Katrina hit the world has used--from fossil fuel + nuclear sources--the energy equivalent of the entire recoverable reserves of the East Texas Field, about 6 Gb of oil.  We use about one Gb equivalent every five days.

Jeffrey J. Brown

I neglected to read your excellent post, Jeffrey. I hope Stuart saw it as well. When you say
Here in Texas, the method predicted the peak of production (in 1972) within two years (assuming that peak production is at 50% of Qt). Texas peaked at 54% of Qt. Saudi Arabia is currently at 55%
where is a reference for the Texas prediction using Deffeyes (and Stuart's) function (P/Q)/Q?
Oh, sorry, it's right here. I spaced that out.
That's your graph, of course, and I was thinking about countries.... I used to live in Texas -- Austin -- but then again Texas is a country, isn't it?
Since Texas production was controlled by a production-setting body, how can a Hubbert curve reflect market conditions?  If OPEC no longer has spare capacity, their ability to set prices vanishes.  And so does any applicability of the Hubbert model...
Since demand for oil is so inelastic, it doesn't take too much adjustment to production to cause wild change in price. Thus we generally see (in many countries) the price signal is sort of secondary noise on top of the basic trend.
Re: "goes substantially non-linear..."

I am wondering what Brazil, Angola and Nigeria would look like. In the short-term (up to 2013 or so), they might go non-linear but since most of the new stuff is from deep-sea drilling, there would be a steep drop-off afterwards.
The Cornucopian Slippery Slope

Michael Lynch's assumptions about new supply as a function of price & technology were discussed above. This reminds me of a slippery slope. I'll explain. From the wiki page:
1. Event A has occurred (or will or might occur); therefore
2. B will inevitably happen. (slippery slope)

And instantiating the argument:

A = Oil supplies are becoming scarce with respect to demand
B = New technology and higher prices will increase supply to make oil plentiful again with respect to demand.
The connection between A and B is an historical one, so this looks like an induction (eg. the sun has always risen in the morning, therefore it will rise tomorrow). Everytime A has occurred historically, B inevitably follows. This is the article of faith.

However, the reasoning is flawed because conditions have changed, specifically
• Each time B occurs, more easily recoverable oil has been extracted and such (conventional) oil is ultimately limited by geology.
• Each time B occurs (ie. each time you go to the well, so to speak), you need more oil to make the resource plentiful with respect to demand than you did last time (eg. demand has never been at 84/mbd -- obviously demand can go down, but not much, certainly not to previous historical levels like 1982, the last time we faced this problem).
Now, the simple conclusion is that, from an historical perspective, the world has changed. Previous draws on oil and higher demand figures have changed it. You can not infer that Michael Lynch's B dynamic is always going to work. He thinks oil will never peak (or at least for a real long time). But there are limits to growth. As Dr. Tanstaafl --- aka "Silent E" said, there's no free lunch. Lynch seems to think that there is a free (actually low cost) lunch into indefinite future. I've got to disagree.
He [Mike Lynch] thinks oil will never peak (or at least for a real long time).

Lynch is on the record stating that peak oil will happen after 2025 -- which is comparable to the forecasts of many other commentators (Total, Exxon/Mobil, IEA, EIA, BP, Laherrere).

There is no one who claims that oil will never peak. The idea that there are such people is a straw man, and it baffles me why peak oilers keep talking about these  dissenters who do not believe in peak oil. I challenge you to produce even one person who seriously claims that oil will never peak.

Maybe Lynch is changing his mind, I don't know. Look at Table 1 of this summary of the Hirsch report by Robert L. Hirsch, SAIC, Project leader; Roger Bezdek and Robert Wendling, MISI.
That quote by Hirsch et al. is misleading. They state Lynch's position as "no visible peak" -- i.e. no visible peak will ever occur.

What Lynch actually says in the referenced article is:

The controversy will no doubt continue, but for upstream companies, there is a clear choice inherent in the two schools of thought. If the Hubbert modelers and their colleagues are correct, then the appropriate strategy would be to assume much higher oil prices soon, hire and hoard geologists and engineers, sign long-term rig contracts, and invest in high-cost production, including gas-to-liquids, and even oil shale. Borrow against future elevated revenue and buy reserves whenever possible.

If, however, the arguments here and elsewhere that there is no peak visible for non-OPEC oil production (absent a price collapse), let alone global production, and volatility will remain high, then keep a low debt level, focus on low-cost projects, and maintain flexible inputs (personnel and equipment) so as not to be caught with high expenses when the occasional price collapse comes. That most companies are following such a path suggests that they have already judged the issue.

Clearly, what Lynch is saying is that no imminent peak in non-OPEC oil (or global oil) was in sight at the time the article was written, not that there will be no visible global peak.

Well, Yergin (CERA) is reluctant to admit that there will ever be a peak after 2025 rather an undefinitely long plateau without visible peak.
The CERA position:

The CERA analysis rejects the current fear that a near-term "peak" in world oil production and a coming exhaustion of supply are near.  The report indicates that the "inflexion" point will come in the third or fourth decade of this century.  Moreover, rather than a "peak," it will be an "undulating plateau" that will continue for several decades.

http://www.cera.com/news/details/print/1,2317,7453,00.html

This is an admission of peak oil. The peak will be a long plateau, lasting several decades, but it will definitely end.

Like I said, no one believes peak oil will not occur, not even the most extreme optimists. The person who "doesn't believe in peak oil" is a myth, like the unicorn.

JD, sometimes you post unproductive remarks. Questioning the things said here can be positive, but comeon!, saying "The person who doesn't believe in peak oil is a myth" is simply ridiculous.

Two years ago NO-ONE of the energy companies and institutions, and much less economic institutes believed in or spoke about Peak Oil. Only in the last year, as it has become evident that supply is not infinite, are analysis starting to accept there will be one. And only in the last months do some economist abandon the flat-earth belief. But, I'm sorry to say, predicting a peak in 2035 and then a decade-long plateau is nearly as much as saying there won't be one.
If 2005/6 is the PO year, in 2010 everyone will make predictions with a peak in 2005/6, and you will probably kindly point to us all the studies that, o wonders of wonders, admit the peak. In the USA of the late 70s, you would probably have said that nobody thought that Hubert was wrong.

Please, stop making that kind of inflammatory comments, and stop only answering to the questions easy to attack, and ignoring the ones that debunk you.

Only in the last year, as it has become evident that supply is not infinite, are analysis starting to accept there will be one.

Mike, if you can supply even one quote from someone who seriously claims the supply of oil is infinite, I will grant your point.

Speech by Kenneth T. Derr Chairman of the Board and Chief Executive Officer Chevron Corporation
To the National Association of Petroleum Investment Analysts New York, New York Nov. 30, 1999
"At various times in the 20th Century, we've seen confident geologic extrapolations that told us production would peak -- but it hasn't. We had the \$100-a-barrel price outlooks of 20 years ago -- now mocked by the long parade of flat-price years. We had subsidized synthetic-fuel projects to help rescue America from costly oil imports - but as things turned out, imports rescued us from a costly dependency on synfuels! "
...
"A history of ingenuity
Given the supply/demand outlook, I think it's fair to ask whether new technology can overcome old geology forever. "
A forecast
Geopolitics and Energy
Key Trends: 2000-2020 Anthony H. Cordesman Arleigh A. Burke Chair in Strategy Center for Strategic and International Studies July 2002
1990 1998 1999 2000 2005 2010 2015 2020
Oil 134.9 149.8 152.2 157.7 173.4 195.4 219 241.8
It doesn't go further than 2020, but the trend is exponential growth with no PO mention.

EIA oil supply forecast from 2004: http://www.hubbertpeak.com/us/eia/oilsupply2004.htm
Scroll down to see figure 2. Yes, they finally recognise Peak Oil, but I repeat, saying that the expected PO year is 2037 is like saying: yes, production will peak... sometime in the far, far future. So we have half a century of slightly more expensive oil. Completely ridiculous.

I could go on and on, but as of September 2005, it is not so easy anymore to find flat-earth statements as it was just a few months ago (somebody knows more blatant flat-earth statements please help with this stupid argument).

And hell, if you had said: "In the course of the last few months, on the face of rising oil prices, and the supply problem becomming evident, nearly everyone has at last acknowledged that there will be an Oil peak", then I wouldn't have said anything. But your statement was simply not true, and you should know it. I see it already comming, a few years after PO, everybody will be saying: "But we never ever said oil production will grow forever". And after their ridiculous 2020+ PO dates (they only adopted after about the year 2000) have been proven false, they will point at their past years forecast (witch of course will have been made after PO happened) and say "you see, we are in decline, like we said".
Given the supply/demand outlook, I think it's fair to ask whether new technology can overcome old geology forever.

That's a question. He's not making a commitment one way or the other. He's said "it's fair to ask", not "here's the answer".

It's also taken out of context:

Given the supply/demand outlook, I think it's fair to ask whether new technology can overcome old geology forever. And it's logical to worry about decline and depletion.

http://www.chevron.com/news/archive/chevron_speech/1999/1999-11-30.asp

Why would it be logical to worry about decline and depletion if oil is infinite and will never peak?

The "Geopolitics and Energy" forecast numbers are from the IEA. Oddly enough, their figure for 2005 is too low. They predicted 82mbd, and it's closer to 84.

The IEA admits that oil is finite and will peak:

In the Summary, the IEA states: "Production of conventional oil will not peak before 2030 if the necessary investments are made". But we find in Chapter 3 that a peak on this date is premised on the USGS Mean estimate of 2626 Gb (billion barrels) for remaining conventional oil (IEA include NGL, Natural Gas Liquid, in conventional oil), adding that if this estimate should prove too high, the peak of production would come by 2015 or before  . It is very important to note that the IEA now accepts the notion that there is a peak in oil production, even if there is uncertainty as to the date. The range is from 2015 to 2033, coming even sooner if all the assumptions are not fulfilled.

http://www.peakoil.net/uhdsg/weo2004/TheUppsalaCode.html

As you note, the EIA recognizes peak oil, and thus is obviously not stating that oil supplies are infinite.

I could go on and on,
Yes, but you're just spinning your tires. You're not producing anyone who believes the supply of oil is infinite and will never peak. I'm telling you, no matter how far back you go, you will never find a person who seriously claimed that the supplies of oil located in the crust of the earth are infinite, and that oil production will continue growing forever in an exponential fashion. There is no such person. Anyone who puts 5 minutes of thought into it knows that oil is finite, and therefore must eventually peak. People just had it on the back burner for a while because they didn't believe it was close enough to worry about. Putting peak oil on low priority is a completely different thing from explicitly stating that it will never occur.

But your statement was simply not true, and you should know it.
You haven't refuted it yet. You still haven't produced even one person who says crude oil will never peak. That's because there is no such person. Please, think about it. The earth is finite. Therefore any material good produced from it must eventually peak. It's not rocket science. Everyone understands that, and always has. The only person you will find to disagree with that is someone who is mentally defective.

a few years after PO, everybody will be saying: "But we never ever said oil production will grow forever"
Yes, and they will be completely correct in saying that because no one ever did say oil production will grow forever. If you disagree, please dig harder and find one person who said: "oil production will grow forever".

And after their ridiculous 2020+ PO dates (they only adopted after about the year 2000) have been proven false,
Colin Campbell's PO dates have been proven false on two or three occasions and it didn't affect his credibility.

You're not producing anyone who believes the supply of oil is infinite and will never peak.
WTF?. In contrast to interesting energy articles, I don't save the links to articles that say such stupid things, and like I said it is difficult to find some TODAY. But how about all the abiotic guys? (Thomas Gold et all) how about all the flat-earth economists I've had discusions with and that write articles on how the only problem is the lacking investment and out there lies all the oil you may ever want?. Of course not very often comes someone and says "oil is an infinite resource" because that is such blatant nonesense, but it was implied in the thinking of a good many economists (at least untill last year).
Colin Campbell's PO dates have been proven false on two or three occasions and it didn't affect his credibility.
Peak Oil could probably be 2005/6, but even if it doesn't come till the end of the decade, that's a couple of years. Even 10 years is not that much for people who made predictions at the end of the past century. But the IEA forecast I meant (from August), gives the range 2026-2047, with the expected value 2037, witch is absolutely bogus. In the link you give, two months later, the IEA already puts the range sooner, 2015-2033, but 2030 (if the investments necesary are made) is still ridiculously late (and what a fast change! surely trustworthy). Not even if the new Saudi numbers were true could such a date hold. So don't mistakenly compare some 5 years error (Campbell) with decades later (IAE).
Campbell first predicted peak oil for the late 1980s.
http://sepwww.stanford.edu/sep/jon/world-oil.dir/lynch/figure3.gif

And we don't know how far off he is yet. You seem to be convinced that we are peaking right now (or will peak next year), but that is just a prediction, not a fact.

Anyway, only time will tell.

...or a quote from someone who seriously did claim, 2 years ago or earlier, that the supply of oil is infinite...
How about Julian Simon, p178 of Ultimate Resource 2, Revised Edition. "But our energy supply is nonfinite, including oil as an important example."

"Then there is the oil we that we might produce, not from fossils, but from new crops--palm oil, soybean oil, and so on. Clearly, there is no meaninful limit to this source excep the sun's energy (land and water are not limits -- see chapters 6 and 10). The notion of finiteness is making ever less sense as we proceed)."

And "After our sun runs out of energy, there may be nuclear fusion, or some other suns to take care of our needs. We've got seven billion years to discover solutions to the theoretical problems that we have only been able to cook up in the past few centuries of progress in physics. It's reasonable to expect the supply of energy to continue becoming more available and less scarce, forever."

Professor Simon was a professor of Business Administration at the University of Maryland. The book quoted above was published by a major university press (Princeton), and thus presumably peer-reviewed.

thanks Stuart
But our energy supply is nonfinite, including oil as an important example.

You might have me there, Stuart, but I'd have to see the context to be sure. We've already seen a couple of cases of selective quoting on this tangent. What's Simon's rationale for saying that oil is nonfinite?

As for energy, I agree with Simon. I personally believe the human destiny is to intensively harvest the energy of the sun using space power satellites, space mirrors and other forms of space solar power. That's a lot of energy out there, and when we get done with that there is a whole universe humming with massive power flows. This has nothing to do with oil, however. Peak oil and peak energy are two different things. Peak oil is inevitable, peak energy isn't.

Simon's comments on vegetable oils are perfectly correct. There is no meaningful limit on the cumulative volume of those oils produced.

The rest of his comments pertain to energy, not oil, and thus are irrelevant to the challenge of producing a person who believes oil will never peak.

Have you done on EROEI analysis on space solar power? I haven't, but somehow, watching the shuttle take off makes that seem an implausible source of energy...
The energy required to launch payload into orbit is modest:
One important consideration in planning space power is the expense of putting a satellite into orbit. Right now, it costs a thousand times more to put an object into space than to fly it across country by commercial airliner, even though the two jobs require roughly the same amount of energy--about 10 kilowatt-hours per kilogram of payload. Two factors account for the extra cost: the army of engineers and scientists required for a successful space launch, and the practice of discarding much of the launch vehicle after each flight.

Source

The following link ("Why are launch costs so high") is detailed and interesting:

2. Propellant costs.
This is silly. If it takes 100 lbs of kerosene and LOX to put a pound of payload in orbit, with propellants on the order of \$0.20/lb, this only accounts for \$20/lb. of payload, out of something like \$5,000-10,000/lb. That was the way I initially thought about the cost of the space program when I was 10 years old, so I tend to describe this as a ten-year old's view of launch costs.

http://www.ghg.net/redflame/launch.htm
I think it fairly straightforward to understand the asymptotic behavior. Mathematically, consider that the differential equation governing extraction is driven by a forcing function (i.e. discoveries) that have largely occurred sometime in the past. To a good approximation, extraction is proportional, first order, to how much is left (see stripper wells for the realization of this). So taken far enough to the future, the forcing function looks like a delta function, and the solution set is just the exponential function. Then when you plot dQ/dt/Q vs Q you get exp(-kt)/(1-exp(-kt)) plotted vs (1-exp(-kt)).

This has the asymptotic property of "appearing" to intercept the Y-axis at zero.  However, it never gets there.  The behavior is correct, but it has nothing to do with the logistics function. It's more like a very thin man walking toward a wall, every second going halfway there, and then realizing mathematically that he will never hit the wall.

And then notice how the curves match best when we are deep into depletion (i.e. Texas). At that point, there is really no use figuring out URR; to use an electronics analogy, we are just discharging the capacitor in an RC circuit.

Good stuff, but as you know, I like to get the maximum insight out of the model that I can.

Zeno's Paradox? On the y-axis, in the real world, there is indeed a last barrel of oil that actually gets extracted in any given oil province and therefore a final URR number. It does hit zero. Of course, we're all dead then and who will tally the final numbers? This reminds me of the poem Ozymandias by Shelley:
I met a traveller from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert. Near them, on the sand,
Half sunk, a shattered visage lies, whose frown,
And wrinkled lip, and sneer of cold command,
Tell that its sculptor well those passions read
Which yet survive, stamped on these lifeless things,
The hand that mocked them, and the heart that fed;
And on the pedestal these words appear:
"My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair!"
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away.
Not mathematics and not TOD style, I know, to quote a romantic poet. But apt nonetheless.
Fascinating stuff web. With all that sophistication, I bet you've honed right in on the date of peak oil. Care to share it with us?
Thanksgiving 2005, perhaps? That's the answer Deffeyes got when he plugged into the formula.
I have always been fascinated by Peter Huber's position on energy.  If pressed, he will admit that conventional oil production will eventually peak, but he believes that non-conventional oil production is virtually limitless.  And after non-conventional oil, he asserts that human ingenuity will cause our energy supply to essentially increase forever.

What I find fascinating about his position is that he is saying that while individual (nonrenewable) sources of energy will peak and then decline, our overall supply of nonrenewable energy--which is after all the sum of individual sources--will never decline.

This is exactly analogous to saying that while individual oil wells in a field will peak and decline, but the overall production from the field--which is the sum of the production from individuals wells--will never decline.

In regard to conventional versus non-conventional oil production, the history of Texas gas production again offers a cautionary lesson.  Texas gas production peaked about the same time as oil.   Gas production has not declined as much as oil, partly because of non-conventional sources such as shale gas.  However, we are still significantly below our peak gas production level in the Seventies.  In other words, non-conventional gas only served to slow the rate of decline of total gas production.

In my opinion, we will see the same pattern regarding oil, i.e., non-conventional oil production will only serve to slow the rate of decline of total oil production.  By the way, according to the EIA, total Canadian oil production is down year over year.  In other words, tar sands production is not even keeping up with the decline in conventional Canadian oil production--let alone doing anything to offset declines elsewhere.

Jeffrey J. Brown

A lot of people, like Huber, refer to the vast reserves of non-conventional oil, but they fail to address recovery rates. Tar sands are great, but the recovery rate is now about 1Mb/d light crude equivalent, may get to 3 Mb/d sometime between 2015 and 2020, and is unlikely to ever exceed 7 Mb/d, vs current world demand of 83-84 Mb/d. the non conventional stuff assures that we will not be forced to zero in the forseeable future, but does nothing to delay the peak and little to slow the decline rate.  Murray
What formula are you talking about?
Interesting analysis, Stuart.

For me the million dollar question is:

How does the peak year predicted by these analyses compare to the actual peak year for each of these countries? This does not seem to be addressed here.

It would certainly help, to give some insight as to the likely accuracy of current predictions for the world peak using this method, by yourself, Deffeyes and others.

The fairly consistent pattern seems to be that regions are peaking at around 55% of estimated cumulative production.  This suggests that Saudi Arabia is peaking this year.  The world probably in a year or two.

Jeffrey J. Brown