Linearize this...

Hubbert linearization of Middle East production from two sources (x-axis is Gb). Inset graph shows production versus time. Click for larger version. Source: American Petroleum Institute (courtesy J. Laharrere), and BP.

The other day, Alan posted this graph:

Hubbert Linearization of oil production according to Alan.

It shows a Hubbert linearization of oil production for the entire Middle East. The total URR from this plot is 828Gb, and the implied data of peak to make cumulative production to date match up is in 2017. A number of people suggested that this is inconsistent with the idea that the world is at plateau production now (though as we'll see, that's not actually true).

Anyway, let's take a closer look. Here I've reproduced Alan's linearization, but have focussed in on the area where most of the data is, and labeled various years that represent particular features of the graph. Also, I've inset the production versus time graph for comparison.

Hubbert linearization of Middle East production from two sources (x-axis is Gb). Inset graph shows production versus time. Click for larger version. Source: American Petroleum Institute (courtesy J. Laharrere), and BP. Cumulative production at start of BP series was inferred from API series.

As you can see, especially in the inset, the history is marred by massive shut-ins for various reasons (wars, revolutions, and OPEC's role as a monopolist maintainer of prices). It seems to me that this makes extrapolating this series a little problematic and I have less faith in linearization in the Middle East than elsewhere (recall the poor stability of the Kuwait linearization, for example, which I subjectively estimated might need an error bar of a factor of 2 on the URR).

For another view of the situation, here's the linearization with the vertical scale blown up some more, and with a kind of "stacked" linearization. I've plotted what each country's production adds to the y axis (P/Q recall - but all of them are divided by the same total Q for the entire Middle East). I've also marked some historical incidents that affected oil production so you can see how they play out.

Hubbert linearization of Middle East production broken down by key countries (x-axis is Gb). Bottom line shows the Saudi share of production, next line adds Iranian production and so on. All lines are divided by the cumulative production of the entire Middle East. Click for larger version. Source: American Petroleum Institute (courtesy J. Laharrere), and BP.

Finally, here's what two Hubbert peaks would look like in production versus time:

Production versus year for Middle East, together with two Hubbert peaks. Blue is Alan's with K=4.8%, URR=828 Gb, and peak half way through 2017. Grey has K=12%, URR=500 Gb, and peak in 1988. Click for larger version. Source: American Petroleum Institute (courtesy J. Laharrere), and BP.

The blue curve is Alan's 828 Gb, K=4.8% line peaking in 2017. As you can see, it fits the recent history (from about 1992 on) fairly well, but does a terrible job earlier. The gray line is an eyeball fit to the front of the curve. It has K=12% and URR of 500 Gb. The idea is maybe if production had continued unconstrained by oil shocks and price increases, it would have followed that path (peaking in 1988 and we'd be well on the downside by now). Presumably if that is what would have happened in an alternative universe with enthusiastically free-market Middle Eastern governments, then in this world we'd get to go for a little longer based on not having used the area between the gray curve and the actual data. We'd have about 200 Gb of Middle Eastern oil left.

What should we believe? I don't have a clue, to be honest. If I had to speculate, I'd guess somewhere in between.

One last thing worth noting: Alan's curve only rises by a couple of million barrels per day between now and its peak in 2017. It takes until 2009 to get another 1mbpd over 2005. So if non-OPEC production was peaking now, even in Alan's scenario, we might well be at the global plateau already (that is if non-OPEC production declines at least 1mbpd by 2009, and at least a couple of mbpd by 2017).

I think that horizontal drilling with controlled production has to mess up the linear projection. It permits constant production to well above 50% of URR followed probably by a very sharp drop when water cut reaches the horizontal "christmas tree". Any projection of such a curve, prior to drop-off will surely give a URR that is much too high.  Murray
In large regions where such aggressive techniques have been used extensively, like the North Sea, the Hubbert linearization correctly predicts the aggressive declines that result.
In a multi-field analysis, this effect will likely be small.

It shifts production under the curve to the left a bit, and distorts the curve, but when one aggregates all of the fields together the effect may be lost in the noise.  Or it may shift peak from Qt = 50% to Qt = 51%.

The reason is that for any specific year near the middle, some younger fields will produce more due to this effect and some older fields will produce less.

I agree with this.

If the ME fields diverge from a Hubbert linearization, it is more likely to be because the bulk of production comes from such a small number of fields.

IANAE (I'm not an expert), but I would suggest that this depends very much on the distribution of the fields. If the largest fields were discovered first and they were first to get the aggressive technics applied at, this effect will be much more significant.
Thanks very much Stuart.  I guess the main point among all the uncertainty is that at best ME production may only rise slowly, another couple of million barrels from here, not enough to compensate for falling production else where.

I still think that the whole data set may be distorted by the fact that production over the past 50 odd years has not captured the whole resource base but is heavily biased towards the biggest fields.

Frantic developement of a vast number of smaller fields now (some discovered some not) may lead to yet a third peak in ME production on the down curve.

Cry Wolf, to quote you...
"I still think that the whole data set may be distorted by the fact that production over the past 50 odd years has not captured the whole resource base but is heavily biased towards the biggest fields."

I think that's a pretty darn good read, and then of course we have to confront the "all liquids" issue again (for what, the 400th time this year?! :-), because NGL, GTL and the "dash to gas" are sure to accelerate as light crude oil gets harder to find, to get, and to afford.  This must also be combined with the various logistical issues  (my old distinction about "geological peak vs. logistical peak."

The problem is, we still have a problem.  I am amazed at how groups like CERA and other "bright and sunny types" can use the facts above, which indicate, even if not immediate peak, an obvious sense of chasing the treadmill on the part of oil and "liquids" fuel producers, as somehow an indication that "all's well".  This is not a comfortable situation no matter how you can piece together a "Rube Goldberg" technical/logistical house of cards to keep "official peak" at bay for one more, two more, three more, whatever (?), years. IF let us say, peak is in 2017 and not yesterday, ALL IS STILL NOT WELL.  Given where the oil comes from in the international community, and the CO2 issues, all is MOST CERTAINLY NOT WELL.

  As a nation and a world economy, it has the feel of slipping down an icy slope to the edge of a inch, one foot....and then you don't slide for an hour or two and call it victory, even though there you are still on the edge of the icy slope....then, one inch, one foot more.....but you rejoice, your still several feet from the edge!  How long do we want to go on that way without turning our heads about, and looking for a way off the slope, or at least, a way back up it?

One last concern:  in this seemingly eternal "death by a thousand cuts" inch by inch slide, there will be price and supply crisis, followed by relief, followed by deeper and more varied crisis.  After awhile, in one of the "relief" periods, and in sheer weariness of hearing that the "end is nigh", people will just wander off the topic, and the hope of gaining real momentum on energy conservation/efficiency/alternatives begins to wane....until it is too late.

Despite prejections by some "doom" peakers saying that TWSWHTF (the whatcha' stuff would hit the fan) by the first third or half of this year, and we would already be well in the full may be tomorrow, but wasn't yesterday....and we just crossed out of the sixth month.

I am more and more opposed to predicting a date for peak oil, which I have stated before is a very vague term, and would be all but impossible to prove until years or decades after it occured.  It becomes an argument about how many angels can dance on the head of a pin, and pulls us aways from real, big scale change, which is what we really need, peak yesterday, or peak 20 years from now.  

Roger Conner  known to you as ThatsItImout

I note the WTI price graph on the right side bar has climbed above $75.5.  A new record I think, WITHOUT anything much happening in Iraq, or in Nigeria, or in Venezuela, or in the GOM.  It seems to me that any big trouble in any such place could see us heading toward three figures.  I had been musing to myself what month would most likely see $100/barrel - surely that would hit the MSM in a big way - and opted for November '07.  Maybe too optimistic?  Any guesses!?
I still think that the whole data set may be distorted by the fact that production over the past 50 odd years has not captured the whole resource base but is heavily biased towards the biggest fields.

As I understand it, that's the kind of the point of Hubbert linearization.  The biggest fields are found first, and when you've found the biggest, you can project the rest.

Hello Stuart,

Very interesting analysis, thank you.

Now linearize this.....

Imagine about early '70s as M. King Hubbert's original '56 thesis was becoming confirmed for the first time and some really astute observers decided to use King's ideas to graph the burn rate and Hubbert curve for the MiddleEast.  They would be looking at your grey bell curve with the peak in 1988 and probably deciding, "Hell no, not on my watch!"

Kinda of boggles one's political mind--does it not?

Bob Shaw in Phx,AZ  Are Humans Smarter than Yeast?

That's exactly what I thought as well! And naturally I remembered the recent debate over whether H. Kissinger was somehow behind the first oil shock... On the other hand, I suppose the Saudis could have plotted it just as well; while it's common to say that the Saudis have been stupid and mismanaged their businesses, if I'm not totally mistaken Simmons pointed out several times in Twilight that the Saudis have been just as rational in their decisions as anybody.

Perhaps another round of speculation is called for...? ;-)

Hello Jussi,

Thxs for responding.  I am grateful for this potential 20 year shift of the ME production profile peak from 1988 to 2006? 2008? 2010? by whomever, but it saddens one to think of those that have paid with their lives.  The turmoil, conflict, and wars as historically highlighted arrows in Stuart's graph clearly indicate that millions in the MiddleEast were sacrificed towards this peakshift program extending through to the present Iraqi War.  But billions & billions of barrels of crude can do strange things.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?

Can one of you smart people explain the Y axis on the first four graphs, for the profane?

P/Q ? Mind your P's and Q's...

Reading the Oil Drum generally makes me feel smart (ahead of the curve?)
Today I feel dumb.

In Hubbert Linearisation graphs, P is the rate of Production (i.e. X million barrels per day or year) and Q is Cumulative Production (i.e. the total amount of Oil produced to date).

The X axis is Q (not time as I first thought) and the y-axis is P/Q, or in other words, the percentage that the Production rate is of the Cumulative Production.

Take an example:
By the end of the first year of production from your oil well, you are producing at a rate of 1 million barrels a year and have cumulatively produced half a million barrels (you started  with no production at the beginning of the year). Thus, Q=0.5 and P=1, so P/Q=2 (or 200%), and a point at (0.5, 2) is plotted to mark the end of the first year.

By the end of the second year, you are producing at a rate of 1.5 million barrels a year and have produced a cumulative total of (say) 1.7 million barrels.  Thus, the P/Q value would be about 0.88 or 88%, and another point at (1.7, 0.88) is plotted.

This carries on and each point defined as (Q, P/Q) is plotted for each year.

It has been found that if production follows the usual Hubbert curve, then the Hubbert Linearisation graph tends to become linear after a certain period of production, and the linear extrapolation projects down to the x-axis to give the URR.

Of course, if the production curve does not fit a Hubbert curve exactly, then the linearisation also doesn't work very well either (as can be seen from Stuart's graphs above)

I've played around with fictional production curves and their linearisations and I've found that you can make graphs that look like the field has a higher URR. For example if the production keeps ramping up and up and then suddenly collapses, then the linearisation essentially 'drops off'.

I believe a lot of the current production is like that, and even areas like the North Sea will decline faster than the linearisation currently predicts.

Thank you Dunk... I believe I understood that a few weeks ago, or thought I did, but my mind is shutting down for the holidays.

In any case, that's an excellent nutshell.

Plotting the P/Q vs Q and linearizing part of it was easy once I had the data. How do you create the logistic curve from the URR and the linearization?
The logistic equation is Q(t) = URR/(1 + exp(-K(T-Tpeak)).  You can use that to build a series of Q(t)s.  Adjust Tpeak to match the model Q to some actual Q (eg at the end of 2005).  Then get P as the difference between successive Q's.
Solve the differential equation. P=dQ/dt, so dlogQ/dt=a(URR-Q). It has an analytic (that is, closed form) solution in spite of its non-linearity. Change dependent variable to Q=1/S (defn of S).
You seem to understand the calculus. Now, can you give it a try and explain the physical meaning of the equation in the context of oil depletion? So far no one has been able to do this without punting on the question and then relying on the heuristics of the fit as a rationale.
I am sorry to inform you that you cannot differentiate a discontinuous function.

For all intents and purposes, the consensus here on TOD seems to be that we are at the cusp of an age of discontinuity.

Thus I question the relevance of calculous, which was, after all, first invented by Newton to help describe and understand gravity and the motion of the planets.

Solar system astronomy is an atrocious model for trying to figure out petroleum geology, IMO.

You can describe a certain class of deternministic problems using calculus, such as trajectories, etc.  This enables us to follow the temporal behavior of a single particle acted on by physical processes.

Then we have stochastic calculus and strochastic differential equations which applies basically the same formulations to solve problems in probabalistic terms.  In simple terms this approach applies basic laws to aggregated sets of particles using mean values for rate determining factors. I don't think anyone studying the oil depletion problem seriously is trying to apply deterministic calculus to generate a solution.

And I think that is a huge problem in our greater understanding.  For one, I think we have a much better chance of creating simple formulations for oil depletion (and NG depletion, etc) than we do for other econometrics areas of study, which apply some of the same stochastic principles.  

However, if the proverbial "we" do give up, I will keep plugging away on this problem because it is certainly an interesting hobby and I have a tin-foil-free niche market to toil away in.

Sailorman's comment is a bit puzzling; the logistic curve (the Hubble linearization) is a continuous, differentiable function which may or may not match the measured (estimated?) production and production rates. It's no more arbitrary than satellite orbits, except we do know the law of gravity. (I believe that general relativity corrections to satellite orbits are measurable, so it's not just Newtonian, though.)

Anyway, the Hubble formula says when production begins, it grows exponentially (compound interest): growth is proportional to the amount produced. I could make up a story about why that might be true, but it would just be a story. Of course, this part doesn't fit the very early data, which show oscillations before P/Q settles down.

The model also says that the production rate is proportional to the amount remaining (URR-Q). Makes sense, I guess, when you're nearly out of unproduced oil. That's the whole model: rate= aQ(*URR-Q)

It's a very simple pair of assumptions, and it's surprising to me that it fits so well so many situations. (The Fermi function of describing the energy of electrons in metals at finite temperatures is a form of this function.) I hope this helps.

Excuse me! I meant "Hubbert" not "Hubble," of course. Senior moment, I guess.
Most interesting!

Just eye-balling the production curves - the area under the grey curve looks to be a lot less than the area under the blue curve.

It seems that finding the URR by the HL method is unlikely to work for the Middle East at this stage. So I wondered if there is a formula to deduce the area under the curves from the parameters you have drawn and so give estimates for the URR? Maybe this would give us the upper and lower estimates of the URR for this region.

Thanks for your great work!

As stated in the article the gray area has an URR of 500 Gb and the blue area has an URR of 828 Gb.

So a substatial difference.

As usual, good work Stuart.  Some comments:

A key point is that the ME has the best remaining oil reserves in the world, and it looks like all of the key countries are showing strong HL behavior.  Iraq probably has the best remaining exploratory potential, and oddly enough that is where we have 135,000 troops stationed.

Note that the two largest producing oil fields in the region, Ghawar and Burgan, are both almost certainly declining.

An interesting exercise would be to try to model the Yibal Field in Oman, which was redeveloped--like Ghawar--using horizontal wells, and which had a severe, and unexpected, production crash when the water hit the horizontal wells.

But my key point is that the world is at the 50% of Qt mark, and world crude + condensate production is down 1% since December.  Based on these HL plots and based on the fact that the two largest oil fields--accounting for about one-fourth of total production--are almost certainly declining, I don't expect the Middle East to do much to reverse the decline.

Another factor:  in the past couple of years, oil consumption in the Arab countries in the ME has been going up at the rate of close to 6% per year.  And many countries in the ME have huge populations of young people.  

The twin devils of rising population and rising per capita consumption in the remaining oil producing countries is going to be very challenging to our world economic and diplomatic regimes. I have looked around for examples of where weaker exporting countries (of any valuable resource) have negotiated successfully with militarily more powerful importing countries and I really don't find any. That may be because of reporting bias- we tend to study wars, not trade agreements, in high school and college history classes. Or it may be because it really hasn't happened.
Switzerland and Sweden traded reasonably well with Germany during WW II.  Ball bearings and weapons were some of the trade items.
Germany was somewhat preoccupied then. Even Hitler would hardly want to start a 3 or 4 front War.
Roumanian oil was regarded as a vital resource at the outbreak of WW2. In 1939, the UK bought almost all Roumanian oil. After France fell in 1940, it looked as though Germany would control all Europe and Roumania negotiated with Germany eventually joining the Pact Of Steel (Germany, Japan, and Italy) in Noveber 1940. Germany paid market prices for all Roumanian oil. Perhaps the special feature is that Hitler did not want to invade Roumania because he feared that invasion would lead to damage and destruction of the oil industry that he needed so much.
I'm skeptical about HL's predictive abilities for members of OPEC. I suspect their restraining production to maintain prices results in a predicted URR that is too low.
For example, using HL on the only OPEC member that is clearly beyond peak, Indonesia, shows that it went into decline when it was close to 50% of URR. Unfortunately the only data that fits the linearization well is from after it went into decline. If you try to force a fit of the data shortly before peak ( the 80's ) it looks like it was beyond 70% of URR when production peaked.
I apologize for my basic question here but I have wondered about this since reading Deffeyes: why is the line you drew starting in '89 more valid than a line drawn starting in '74?  If that line had been been drawn in 1983, wouldn't we all have been saying they had URR of 200B barrels which obviously would not have been correct.  So why is the line we draw now more valid than the line we would have drawn then?  Doesn't this give the appearance (at least to those of us who don't understand the math) of simply picking the numbers that support our position?
There is of course a subjective element, but we tend to see a "noisy" set of data, and then a consistent HL pattern.

For models, my personal "rule" is that a region should have been producing about 2 mbpd for about 20 years.

Khebab and/or I have several HL themed articles on the Energy Bulletin: h

At my request, Khebab took only the Lower 48 production through 1970, and used it to predict future Lower 48 production.  Actual post-1970 cumulative production was 99% of what the HL method predicted that it would be.  IMO, the world is now where the Lower 48 was at in 1970.

My answer to this has been to perform stability analysis where one varies the start and end date and looks at how much difference it makes.  Only if there's a broad region of stability can the answers be trustworthy.   See a US analysis for example.  Generally, I don't think it's very trustworthy for OPEC countries.  It also tends to fail if there's a double peak structure in the discovery curve and production is following fairly hastily on discovery (as has been getting more and more true).

In short, Hubbert Linearization is likely to be better than astrology, but needs to be applied with great caution and only as one part of an overall evaluation of the situation.  You can't just linearize and treat the answers as gospel.

Both Westtexas' and your responses and accompanying links were helpful (although ultimately I still have to simply defer to and rely upon the expertise of you and the other more mathematically-inclined posters).  Thanks.
Ummm...I know this is off-thread, but why are we already breaking records this morning?

Light Crude Oil - High - 75.78 ergy Futures&iFSQfields=desc,month,last,netchg,open,high,low,exchg,time

"Geopolitical tensions" would be my guess.
Well, since you asked, I do have this theory about net export capacity. . . (groans from the audience)

I predict that we will see the following pattern over and over again (sort of like my posts on net export capacity):

(1)  Net exports drop;

(2)  Oil prices go up, and the remaining net export capacity is allocated to the high bidders and the low bidders do without (generally developing countries at this point);

(3)  We have a period of stability, and then the cycle starts all over again.

I think that we had one complete cycle earlier this year, and I think that we are at the start of another cycle right now.   We will proceed through progressive cycles of demand destruction.  The irony of Americans complaining about high gasoline prices is that high prices are the only thing keeping the gas stations supplied.

This is actually a fairly accurate synopsis for the price increase.

UPDATE 4-Oil hits record $75.78 on strong demand 5_2006-07-07_12-55-10_SP136390

Basically, they are saying it's due to higher demand in the US and supply worries.

This pretty much fits what we discuss here at TOD.

...why are we already breaking records this morning?

Here's what the MSM are saying about it.

Why record prices this morningg? Maybe some of the speculators saw this.
The gray line is an eyeball fit to the front of the curve. It has K=12% and URR of 500 Gb.   ...   We'd have about 200 Gb of Middle Eastern oil left.
One interesting thing to point out is that if the grey curve was the correct one--where URR is 500 GB and we have produced 300--then the ME would have "peaked" years ago, where "peaked" means 50% of URR has been produced.  We would then have "peaked" while production was way below its highest level.
If production capacity is significantly greater than actual production, you can have this scenario easily. I think this has probably actually happened. The estimate of around 5 mbpd of OPEC spare capacity at the start of the decade shows the leeway available. Much of that is now being produced, and we could easily have produced though the capacity peak without even knowing it. This happened in Norway when they did voluntary cutbacks in 2003 to support oil prices. Halfway through the year they realized they couldn't even produce up to their targeted production cutback level. Depletion had overtaken their ability to produce during the time they had deliberatly held production back, and has continued to fall since.

Excellent analysis.  I still remain skeptical of the predictive value of these linearization plots.  It appears from your eyeball curve fit that an HL prediction would fail using pre-1974 data.  What if it were 1984, and we used the 1972-1984 data for our fit?  

What convincing evidence is there that the past 15 years are predictive of the future, whereas all of the years prior that are not?  

For example, do we need to account for the effect of Iraqi production shut in by the Gulf Wars?

As I indicated above, I don't think it's very reliable at all as applied to OPEC countries where production has been subject to a lot of constraints.  Empirically, it seems to work amazingly well in regions where there's been more of a free-market "have at it" approach to the resource (eg the US, the North Sea).  However, we don't, at the moment, have a very good theoretical understanding of exactly why, so there remains room for doubt about whether it will continue to work as well in the future.
However, we don't, at the moment, have a very good theoretical understanding of exactly why, so there remains room for doubt about whether it will continue to work as well in the future.

You say this deep in some comments and it doesn't raise any eyebrows. When I say essentially the same thing regarding why the logistic curve should theoretically map to any oil depletion model at all, I just about get my head taken off.

It might come down to the way I say it. At work, my boss describes me as edgy. I have set off fireworks by simply calling someone's work "ornate".  Some would call it a skill.


In addition to the communication style issues, a difference in position that I perceive is that you appear to think that the lack of a solid theoretical understanding is a reason for everyone to forget the whole project and do something else. While I'm all in favor of pursuing other approaches too, I think HL (and similar approaches) are worthwhile and we ought to continue to try to deepen our understanding of it, both because it has a proven track record of making useful predictions (something that can be said of no other approach AFAIK), even though certainly not a 100% track record, and more deeply it seems to me quite surprising that the US production record is so Gaussian, and my intuition is that there must be a good reason for it, even though we don't know what that reason is today. The question is of profound practical importance, since the difference between a symmetrical gradual drop-off in world production, as the logistic/gaussian approaches suggest, and a Yibal style production collapse, could easily be the difference between civilization making it past peak oil and not.
The problem is that the US does not match a Gaussian profile across the entire time span. It fails in the first few years, showing no apparent "starting point" and a kind of spontaneous combustion in production output.

The temporal dynamics are what I am interested in, and neither the gaussian or logistics curve effectively address this shortcoming, i.e. how does everthing kick in.
Again, I find your insistence that the model explain the exact number of barrels in 1860 and 1861 strange - in general the extreme tails of things are often governed by a different process than the rest of the distribution. To my eye, the fit is extraordinary across almost four orders of magnitude in a social science/economics problem like oil supply where we would not expect any model to fit very precisely.
My fit is also extraordinary and includes real physical mechanisms.
and how many free parameters?
Quadratic growth in discoveries until the peak (a scale-free parameter) followed by a linear decrease in discoveries, which essentially tracks the discovery data. The free parameter is a 4th-order gamma distribution rate of 12 years per phase.

The quadratic growth is a "gold-rush" behavior often observed. The 4th-order gamma is determined by the fallow/construction/maturity/extraction behavior that gives a lag between discoveries and full scale production.  

So it's one parameter with supporting data, but like I said, I am not into some simple empirical formula that would give me a solution without any physical understanding.

In contrast, if you look at how a Gaussian could be generated off a rate equation, it means solving the following partial differential equation:
dP/P = K(T1 - t)

where P is production, t is time, T1 is the peak time, and K is the width of the Gaussian. I suppose I can read that as exponentially growing production with the throttle linearly pulled back through to where it switches sign at the peak.  However, the T1 number looks suspiciously preordained as opposed to coming out of some intuitive process.

On the other hand, I could look at the gaussian from the law of large numbers approach, which would mean for me to give up and punt, while waving my hands wildly.

I agree with other posters that HL plots may not necessarily be good predictors of either future production or URR.

However, IMO, the HL plots are more likely to be too optimistic.

Let me illustrate this with an example of a fictional oil producing country called "Sudia".

In this example, Sudia is blessed with a fair amount of oil in a small number of super giant and giant, shallow oil fields. The initial estimates of these fields predicts a URR of about 170Gb.

Here is the complete graph of the 30 year history of Sudia Oil Production:

Here's what happened:

Initially, production was ramped up fairly quickly due to the shallow wells and initial high pressure in the fields.

By year 8 production has reached almost 6Gb/yr, but pressures are dropping and by year 10 production appears to be plateauing.

At this point the Sudians discover water injecion and the pressure in the fields is maintained. Production from smaller fields is added in the following years allowing production to grow to over 11Gb/yr in year 22.  

All this time the oil columns in their super giant fields are getting smaller and smaller, but by managing the water injection carefully, the Sudians keep the production at what appear to be indestructible levels.

But in the 22nd year of production (when they are at their Peak), disaster strikes as most of the largest Sudian fields completely water out as their oil columns disappear.

Sudian oil production then collapses as only the very small fields are left, and by year 30 it's all over.

Now the HL plot of this entire production would look like this:

But let's assume we are only looking at the graph up to their peak in the 22nd year (Q=140Gb).  The line I added to the graph would appear to fit the HL plot up to that point, and seems to predict a URR of 400Gb (which the Sudians themselves believe and publicly announce that their reserves have actually 'grown' to this new figure).

However, the sudden collapse of these fields means that the actual URR ends up being only 180Gb.

The trouble I have is that most of the 'mature' HL plots (ones that plot fields that have gone to completion) are based on production that has had only very late help from advanced EOR techniques. I believe that these techniques produce non-symmetrical production curves with sudden collapses. This is essentially what Matt Simmons in predicting.

If the bulk of the world oil supply is coming from fields that will exhibit this behaviour, then the world HL plot could be misleading us into thinking that we've still got a fair amount of oil to extract.

Anyway, I'd be interested in peoples thoughts on this.  I'm going to bed now (3am), so I'll check back tomorrow.

Very good analysis!

The HL result can be biased if the production curve is asymmetric. In the case of your virtual country, peak production is at 140/200= 70% of the URR. The HL works well when the production is symmetric (peak at 50% of the URR) which means that the growth and decline rates before and after the peak are similar (in your case you have K= 14% and K around 50% before and after peak respectively).

The trouble I have is that most of the 'mature' HL plots (ones that plot fields that have gone to completion) are based on production that has had only very late help from advanced EOR techniques. I believe that these techniques produce non-symmetrical production curves with sudden collapses. This is essentially what Matt Simmons in predicting.
That's a possibility, Cantarell is maybe a good example. In that case, you need to go down the Parabolic Fractal ladder and develop a lot of smaller fields to  soften the blow from the big fields' decline.
Also consider that, as swing producer, SA peak is anyway expected to occur sometime after 50%, similar to Texas and asymetric by definition. So, combining the unusual swing status with eg multiple horizontals for (by now) several years could mean SA is well past 50%, maybe past 60%, and that post peak production decline will be precipitous. They may well be looling, but there is no evidence that a multitude of medium sized fields are about to take the place of the tottering giants. (The bigger they are...)
Khebab, thanks for your comments.

The question that is really bugging me is this: How much of the daily global supply of oil comes from fields that could behave like Yibal? If there is a significant proportion of the major fields that have had extensibe EOR techniques applied to them to maintain their production?

I guess we would need to expand our 'top 20' field list to include details of what EOR methods have been used on the fields and for how long.

Unfortunately, I wouldn't even know where to start looking for such data.

Still, I'm glad if my post has provoked some thought.

Other people have said similar things but have not made the case quite as clearly as you have just done. Thank you for that effort. I happen to worry that EOR techniques may produce exactly the effect you are describing but so far, I am not aware of any large fields that have produced the kind of production profile that you are proposing. Your comments are appealing in an intuitive way. What remains is to see if any fields ultimately behave as you speculate they might. At the moment, this sudden dropoff effect is just a speculative worry, lacking substantial data to support it. I share your concern but am not sure if there is any way to "prove" it short of it actually occurring, at which point we're in much bigger trouble than we previously thought.
I just realized that there is a candidate field for evaluating this - if we can get full production numbers for Yibal. Yibal crashed dramatically like this and is down about 2/3rds from it's late 1990s (1997?) peak.

I did some quick Google searches but I have been unable to locate annual production data about Yibal. Does anyone else have such data or know where we can get it?

Laherrere must have it.  He made this graph (PDF warning).
Woa! the decline started at 1300/1800= 72% of the URR!
Some Ghawar Asssumptions: original oil in place of about 172 Gb; Cumulative production to date, about 60 Gb.

From Matt Simmons:

Retired Aramco Executive's best case for Ghawar:  70 Gb--now at 86% of URR

World best case history for similar reservoirs:  77 Gb--now at 78% of URR

Anyone have a production graph for Ghawar?

Note that the Saudis are raising oil prices for light, sweet--which is what Ghawar produces.

Good Ghawar article, linked at Deffeyes' website:

Trouble in the World's Largest Oil Field-Ghawar
Copyright 2004 G.R. Morton  This can be freely distributed so long as no changes are made and no charges are made.


One of the things to keep in mind as you look at the model below is that the original oil column was 1300 feet thick.  Today, the green layer is less than 150 feet thick.  One must draw the necessary conclusions that most of the oil has been removed from Ghawar.

You can see for yourself, that the area occupied by oil is not very large compared with where the initial injectors were placed. One friend, a reservoir engineer, to whom I showed this picture said "It's over! Kiss your life-style goodbye!"

Holy shit!  That document is scary!

It's exactly like my Sudia fictional country. Half their production comes from this one field which has been very carefully managed to keep the oil flowing, but the oil column is down to 1/10th of the original size.

As that engineer said (in 2004!) "It's over! Kiss your life-style goodbye!"

Well there we have a confirmation of thesis. Now the question is does this apply to Ghawar, Burgan, and Cantarell?

And yeah, Khebab... that graph is a gigantic "OH CRAP!" moment, isn't it?

To DuncanK, I have quoted you over at forums and wanted to provide a link to that in case you want to followup the discussion. Since it is a slightly different audience there, I was interested in seeing their response to this discussion.
Grey Zone, thanks for all your comments.

See also my reply to Khebab above.

You have a copy of that 'top 20' field list, don't you?

How can we expand that list with information about how aggressively EOR techniques have been used on these fields.

Thanks also for the heads up about the cross-posting to  I'll keep watching the comments there, too.

As has been mentioned on TOD before (eg. Cantarell, Greater Burgan, Ghawar?), we may be fast approaching the fictional Sudia "tipping point" for some of the world's largest and mature fields.

Your main point as I see it, that EOR may change the linearization analysis, is well taken. Cantarell (nitrogen injection) would appear to be the best test case. But we're basically all waiting around to see what happens. IMHO, we will know within a few years. Until then, we'll just have to wait it out.

Throw in a few oil shocks just for realism and now you're talking.

best, Dave

This would help explain the discrepancy between the HL model above (300 out of 800 GB Middle East oil used up, with roughly 60% remaining), and what we are seeing (Saudi output apparently going into decline; Kuwaiti production from its primary field "exhausted", Matthew Simmons' "Twilight" analysis, etc.).

It is difficult to deduce where this remaining "60%" could be hiding.

Thanks for the posting.

Probably not a problem for some, eg russia/China. Only SA, Q8, Mexico, North Sea, US deep GOM are/were primarily giant fields developed in ways likely to face rapid declines near term. Probably true of all deep off shore ramping up off W africa/Brazil.

As an aside, even if SA has multitudes of smaller fields that could be developed, they won't have the hundreds of rigs/crews necessary to exploit them any time soon. Going from 4000b/d/well to 2000b/d not so bad, just double the number of rigs from 50 to 100, but dropping down to 100b/d means a lot more holes if you want to maintain production. In the US, 10b/d is no longer considered a 'dry' hole, but a useful investment; four of these produce $1mm/year.

Where HL works well (eg the US), it seems to be because the production curve is close to Gaussian.  Presumably there is some kind of central limit theorem "adding lots of random variables together" or "random walk through oil exploration space" kind of reason for this.  If so, the asymmetry of individual field profiles may not necessarily give rise to an asymmetric overall shape.  However, since we lack a clear and persuasive account of why the Gaussian shape arises, it's hard to say.
"the asymmetry of individual field profiles may not necessarily give rise to an asymmetric overall shape"

Stuart, I really hope that this is true.

As I said above in response to Khebab, it would be nice to know how many of the top 20 or top 50 fields have had aggressive EOR activities, and for how long. Since Canterell was the last super giant found and it starting to decline after EOR has already been used, then what chance do the other major fields have that were discovered before it?

Is there a way we can quantify how many of these big fields could fit this collapse profile?

Speaking as a logician, unless you can get damn good data there is no way.

The essential problem is NOT with the models. The root of the problem is lack of data, and there is no mathematics than can elegantly get around this problem.

IMO the least bad way is to use the techniques propounded by L.J. Savage (and others) more than fifty years ago to use subjective probability.


Thanks Stuart. I have been looking forward to this post because with all the posts and comments claiming Saudi Arabia and the middle east are at or near peak and that we are currently at peak I had assumed one claim rested on the other. I figured if the middle east wasn't at or near 50% of URR then we couldn't be at peak oil now. This however gives me something to think about.

One last thing worth noting: Alan's curve only rises by a couple of million barrels per day between now and its peak in 2017. It takes until 2009 to get another 1mbpd over 2005.
So if non-OPEC production was peaking now, even in Alan's scenario, we might well be at the global plateau already (that is if non-OPEC production declines at least 1mbpd by 2009, and at least a couple of mbpd by 2017).

Peak oil in the near future and the middle east peak more than a deacade away is the last thing I would want to see. 25 years from now most of the world would be far beyond peak while the miile east would still be producing at near 90% of its peak. If alternative energy sources were not developed quickly we could end up with the middle east countries, or whoever was able to occupy and control them, essentially owning the world.

Almost makes you want to invade one or more before somebody else does.
I see two competing factors here

  1. Shut-ins disrupt the typical HL so there is likely more oil the ground than would otherwise be predicted.

  2. Dependence on a few large fields and advanced recovery techniques argue that we have gotten more of it out than HL would otherwise predict.

What are the arguments for why one factor is more important than the other?
Another analysis following the same idea:

Big fields have been developped first in the middle east for obvious economic reasons. The first production peak in 1975 is probably 90% based on a small group of 15-20 giant and super-giant fields that constitutes 50% of the total URR. In 1984, there is a cumulative production at 150Gb. Assuming that the reserves are 387 Gb (ASPO) which gives an URR at 700 Gb for the Middle East. Following Norway example, half of the 700 Gb is coming from the big fields (i.e. 350 Gb).

That could mean that the big fields may have reached 150/350=  43% of their URR already in 1984!

Thanks Stuart,
I've been hoping you might explore this issue ever since I posted that link to Drollas's analysis here where he also compares two production peaks as you have done.
Hello Mheisler,

Thxs for this link to Drollas's analysis.  I found it to be a fascinating alternative discussion to much of what Stuart and others have posted.  As to it's validity regarding his Hubbert Curves and where he thinks we currently are on his Peakoil path-- I think he may be too optimistic, but I am no expert.  Hopefully Stuart & other TOD data freaks will analyze this more.

Bob Shaw in Phx,AZ  Are Humans Smarter than Yeast?

totoneila, just in case you're interested in previous comments on this pdf, search for drollas in this thread