More on the Systematics of Hubbert Linearisation
Posted by Euan Mearns on September 12, 2007 - 10:00am in The Oil Drum: Europe
Topic: Supply/Production
Tags: coal reserves, discovered undeveloped, gas reserves, hubbert linearization, production capacity, yet to find [list all tags]
An empirical study of the impact producing at below capacity has on the Qt intercept of a Hubbert Linearisation (HL) shows exact proportionality. If a country produces at 90% of capacity, the Qt intercept is 90% of actual URR (ultimate recoverable reserves) and so forth.
On this basis the following methodology for applying HL is proposed.
Background
This post is aimed at bridging the gap between a face value interpretation of reserves based on the Qt intercept of a well-defined linear decline trend on Hubbert Linearisation and a more progressive interpretation that takes into account political and wider economic interference with resource exploitation.
Empirical approach
The actual crude + condensate + natural gas liquid (C+C+NGL) data for Norway as published in the BP statistical review of world energy are used to model the effect of producing at below capacity upon the HL Qt (URR) intercept.
The Norwegian data have been modelled at 100% (flush production), 90%, 80%, 70% and 60% of capacity and the results are shown below.
In advance of doing this exercise I was pretty sure that Qt would be reduced with below capacity production, but I was not sure about the nature of the relationship.
The experiment shows exact linear proportionality. If a country is producing at 90% of the built oil production capacity the Qt intercept gives a false low result for URR that is exactly 90% of actual URR and so forth.
Methodology
HL provides information on the developed resources in any given country. It says nothing about discovered undeveloped (DU) and yet to find reserves (YTF). In many countries, the size of the discovered undeveloped and yet to find resources are relatively small if the petroleum industry is mature. The majority of discoveries will be on production and most areas will be thoroughly explored. The HL for a mature country producing at capacity may provide an indication of that country's URR.
However, in countries where political interference has guided the resource development strategy, oil fields may not have produced at capacity and the full resource base may not have been produced following a single, commercial development cycle. In these instances the following methodology is proposed.
A correction should be applied for producing at below capacity. And allowance should be made for discovered undeveloped and yet to find reserves. I suggest this approach should always be followed but as already noted, in mature areas Cf will equal 1 and the size of DU and YTF are likely to be small. Hence the first order approach and this modified methodology will yield similar results in mature countries.
In countries that carry large volumes of DU reserves and which have produced for long periods below "capacity" it is very difficult to accurately estimate Cf and the size of DU reserves.
The variables of Cf, DU and YTF should always be taken into account when applying Hubbert Linearisation - be it to oil, gas or coal reserves.
Euan,
Excellent post I'm glad your working to improve the methodoogy of Hubbert Linearisation. I will certain use this type of equation in the future. I think it is a logical addtion to the existing knowledge base.
Best Regards,
David J.
"There is no silver bullet...to solve our energy crisis we will need, Solar, Wind, Nuclear, and Algae to Biodiesel."
It's an interesting approach. One suggestion, you might want to run a HL plot of total North Sea C+C production. My HL plot showed a rock solid pre-peak HL plot, with the production peaking right around 50%.
In regard to Texas, as we previously discussed, the only reasonable estimate of URR, using the pre-peak HL data, came from discounting the "dogleg up" just prior to the peak.
If memory serves, if we discount the dogleg up, it showed a URR estimate of 50 Gb or so. IMO, 66 Gb is the most accurate estimate of URR for Texas. If we used all of the "dogleg up" data, up to 1972, it produced a wildly inaccurate number, something like 110 Gb.
So, based on the Texas model, one could argue that the most accurate estimate of Saudi Arabia's URR comes from discounting the "dogleg up," but with an assumption that the resulting URR estimate will probably be on the low side, which may support your point.
One other interesting point about Saudi Arabia is that, dogleg aside, it showed a very stable linear pattern on the HL plot from about 1983 to 2001 or so.
This was the point of the Texas/Lower 48 article. I argued that the totality of the Texas HL data gave us a good idea of when Texas peaked--somewhere around 55% depleted--and the more stable Saudi data base allowed us to conclude that Saudi Arabia was at a similar stage of depletion, in the vicinity of 55%, in 2005:
Texas and the Lower 48 as a Model for Saudi Arabia and the World (May, 2006)
http://www.energybulletin.net/16459.html
In any case, regions with stable pre-peak HL plots seem to predict post-peak cumulative production quite well, e.g., the Lower 48 and Russia;
In Defense of the Hubbert Linearization Method (June, 2007)
http://graphoilogy.blogspot.com/2007/06/in-defense-of-hubbert-linearizat...
The charts produced below are for C+C+NGL from BP data. The UK data contains some production from west of Shetland, the Irish Sea and south England and the Norwegian data contains some production from the mid-Norway, Haltenbanken province. It is a lot of work to back out individual fields from the full data set. The data I plot is dominated by North Sea production and by C+C - but it does contain NGL and data from these peripheral areas.
The first plot is for 5 years prior to the known peak year. Personally I'd be very, very reluctant to use ths data to forecast URR or peak production year.
This second plot brings us up to 2006. The peak year as documented by production data was 2000 when 6.38 mmbpd of C+C+NGL were produced. I'm fairly comfortable using this data now to say that the discovered developed (DD) resources may ultimately produce around 64 Gbs. With 47.8 Gbs already produced that leaves 16.2 Gbs of DD reserves remaining.
I'm also fairly comfortable with the notion that the N Sea has undergone flush production for much of its history. The UK had a spell in the mid-late 80s where some production was suspended and Norway withheld a little production during the late 1990s. But in the grander scheme of things, the North Sea has operated at capacity (Cf = 1).
In the interest of being cautious, I do know that there are a large number of small discoveries waiting to be developed in the UK and Norway (but I have not yet determined how much oil they contain) but will want to add these discovered undeveloped reserves (DU) to the 16.2 GBs. Furthermore, I know for sure there will be future discoveries. Maybe some large ones in Norway. And these too (unknown size) need to be added to any concept of URR for these countries.
The cumulative production to 2000 was 35.5 Gbs. That works out at about 55% of the indicated Qt of 64 Gbs for the DD reserves. This fits well with our notion that peak productin will occur post 50% of Qt owing to modern field developement practices.
Yeah, yeah — Hubbert math — Whoopee!
Did anybody notice that OPEC will raise their production 0.5 million barrels per day by November 1st? I guess that would apparently obviate any "peak now" nonsense, wouldn't it?
Funny, maybe TOD stands for "The Over-the-top Doomers".
Still, that does not remove us from a very likely peak by 2015 but probably 3 or 4 years sooner.
Have a good one, Euan.
Dave
Dave, please note that in response to the OPEC news, commodities traders raised the price of oil to within fifty cents of the all-time record of $78.77.
They are betting their careers against OPEC's word. My take on this is that a major disruption in petroleum distribution is expected in the next few months, rendering this quota increase moot.
I have a friend who works in a lumber yard. He regularly threatens to "start eating sawdust and crapping 2x4's" but I don't plan on building a house from his "output"
SW
Dave, I respect your posts greatly and value your wisdom, but I don't see how 500,000 barrels, if it is produced, changes anything yet. Most think SA has some spare capacity even if they are post-maximum peak, and the increase still won't break through the plateau we have had the last 1 to 2 years (depending on what liquids you are using and which data set). You are sounding like Hutter. I'm not saying you aren't right about 2012 or so, but this certainly doesn't tell us much one way or the other as far as I can see.
Eric
If you read his articles closely, Stuart Staniford does not believe that Saudi Arabia has any spare capacity.
Do you understand what I just said?
Stuart's view has become the mainstream view on TOD. Nobody else's view really counts. I see that PG believes Stuart's conjectures. HO, who I respect, does not. Look, if you want to deal with reality, read my columns over at ASPO-USA. If you want the doomer "end of the world" view, keep reading The Oil Drum.
Why do you think I resigned?
What makes you think they will actually be able to meet their production goals?
Um, to the best of my knowledge, they are raising the quota, not 'production' - OPEC's members have an extremely long track record of never producing within the set quota, it is at least possible to see this new quota as merely attempting to reconciling the numbers on paper with what is actually being produced. In Great Britain, the process is currently running in reverse - the numbers in such things as revenue for the government budget are being revised downwards - but the same trend can be seen. Reality is starting to overtake all the projections.
Of course, a lot of people here are over the top, and the looming American economic train wreck certainly plays its role in OPEC planning - except strangely, isn't this the sort of situation where traditionally OPEC would be cutting production, to ensure a stable price?
And yet, the price keeps rising, even as 'production' keeps rising.
A real puzzle - though some pieces are missing, it does seem as if a certain pattern can be seen - higher prices, no increase in real production from a number of former exporters (like the UK), and no noticeable increase in export production from countries like KSA or Russia (Russia remaining a puzzle wrapped in an enigma).
Of course, maybe Angola is the new Saudi Arabia, but I'm not holding my breath.
This is how peak looks - we will know if it is in a couple of more years, regardless of anyone's opinions.
The news made it quite clear that they are raising the quota by 1.4 million, and raising production by 500,000 to meet the new quota. So no, they are not just raising the quota and keeping production flat. I sense that they don't intend to raise production by this amount, however.
I haven't the interest to wade through the thickets, but does the statement's details include Angola being brought into the system (or how Angola's expected ramp up in production is to be accounted)? How about Iraq's declining production, which is not subject to quota? Or Saudi Aramco's now confirmed reduced output?
There is a lot of very imprecise data, and much of it is not readily accessible anyways - the call for transparency is actually just the start of beginning to actually figure out what is going on, and then how to deal with it.
However, rising price in the face of flat production does seem to indicate certain shifts in the oil market, ones best explained by geology, in my opinion.
I have little attachment to any particular model or method - to me, peak oil is measured by what is coming out of the pipeline, and these days, it is less than a year ago, and not significantly higher, even as the price seems to have undergone an approximate doubling, since the amount of oil being produced flattened 2005.
In Iraq the oil pipeline meters have been shut off since the invasion, so nobody can say how much oil has left Iraq or where it went. But I bet America had a hand in deciding how much and where.
So far, the data support a peak last year. Until production exceeds that peak, it's impossible to know that peak will happen a few years down the line.
OPEC agreed an increase but that doesn't mean they will produce an increase.
The latest IEA report shows a near 500,000 bpd drop in production last month.
Incredibly, the IEA are forecasting average consumption, this year, of 85.9 mbpd. From memory, I don't think production has ever reached this figure this year (and last month's production was way below that) and yet the report also shows a slight increase in stocks. I don't have all of the data with me but unless last month's figure is an abberation, stocks cannot increase when consumption exceeds production. Can it?
I think OPEC has consistently demonstrated that its production quota announcements are meaningless.
James Hamilton documents this at Econbrowser, and says: "I see the primary role of OPEC today as one of orchestrating political theater."
Khursaniyah was expected online in December of 2007--I expect it will be online in November instead. It is expected to produce 500,000 barrels per day. I expect we'll see a temporary increase of fewer barrels per day than that in overall Saudi production.
Moe - the role of OPEC is a price fixing cartell. For much of its history it existed in a world with over-supply of oil. Quotas were set and members cheated and the oil price bumbed along bottom for decades.
Now the rules have changed - but only recently - and I think OPEC are still playing catch up. I presume they are in favour of as high a price as the world economy can sustain without causing a crash that would reduce demand. They are trying to second guess what demand is in a rapidly changing world (BRIC etc). Some of their members import oil, others are pumping flat out, others want to mess with guest OECD companies (Venezuela) others are being messed up by invading armies (Iraq) and civil / tribal unrest (Nigeria). This is a complex tapestry.
Khursaniyah is indeed due onstream - and yes I'd bet that Saudi production may rise by around 250,000 bpd. Their heritage supergiants are tired and will benefit from rest. But remmeber that Khursaniyah is just the first in a line of new developments.
Didn't the discussions over Ghawar, earlier in the year, point to other new developments that came on stream previously? Stuart's analysis showed that these new developments just caused a blip in a generally declining trend. So Khursaniyah is certainly not the first, and won't be the last, but the question is how much will it affect the overall decline?
What decline? According to the IEA, Saudi oil production has been within 0.08mb/d - 1% - of 8.35 since the beginning of the year.
As much as we may not trust them, Aramco's production has been perfectly in line with their claims all year, and has totally failed to match any of the decline-based predictions made while Saudi production was falling. Like it or not, the available evidence suggests that Saudi production declines were voluntary.
Mmm, perhaps you didn't read Stuart's analysis; it showed that the decline during last year was on an 8% curve and didn't show the mathematical signature of voluntary declines. A quick check of the IEA figures shows 2007 production currently running at an average of about 8.35 mbpd, as you say. This is 6.5% below the average production for 2006. Their levels in the first seven months of the year were 8.42, 8.32, 8.27, 8.33, 8.43, 8.35, 8.35. This seems to indicate that they've halted the decline for now after continuing declines for the first three months. If you'd rather see no decline, that's up to you, but I don't think one can categorically point to an end to the trend. Let's see if they can raise production later this year, and what the final end of year average is.
I read it; he was just wrong.
There's nothing wrong with that - it was a speculative hypothesis, and I believe he said as much. But there is no indication of decline in the last 7 months of production (the slope of the linear regression is positive, meaning the best-fit line is a tiny but statistically-insignificant increase over time) and every indication of production being held in compliance with a quota.
It's just wishful thinking to say anything else at this point. You can speculate about all kinds of reasons why Saudi production is not declining right now, but the fact is that it is not.
Not really wishful thinking, just looking at the data. Wishful thinking would be that SA are not in decline. Of course, that thinking may be correct but, so far, 2006 shows a year on year decline over 2005 and 2007 shows a year on year decline over 2006. The data are not clear but I guess it all depends on how one is hoping that the production trends are going. Until the Saudis can increase production and keep it there (or further improve on it), they would appear to be in decline and struggling to hold production level in a period when oil prices are very high.
No, that would be statistics.
The linear trend of monthly 2007 production values from KSA is positive, but is statistically indistinguishable from zero (F = 0.009, P > 0.97). KSA is showing - statistically speaking - neither a growth nor a decline trend in its 2007 production levels.
Declines happened - for whatever reason - in 2006, but they are no longer happening.
It is wishful thinking because declines have only apparently been halted in the last few months. Last year's decline continued into this year but the production curve has now flattened. It is wishful thinking to say that this means the declines are over. As I've pointed out, year-on-year average production figures continue to show a decline. You may choose to believe that the plateau will continue indefinitely (or for the rest of this year) but if the figures start down again soon (say within the next 6 months), the recent plateau will almost be unnoticed when looking back at the production curve in a few years.
The last 7 months of production data show a statistically verifiable lack of relationship between time and production level; i.e., no decline. You can dispute this all you want, but you are verifiably incorrect. Run the stats yourself if you don't believe me.
KSA's production did decline in the past, but has not been declining recently, and that is the more salient data for predicting production in the immediate future.
You're reading in something I haven't written.
What I have said is that KSA's production this year has not been in decline, and that that lack of decline is statistically verifiable.
I have not said what their production will do in the future, other than to note that since they appear to be in voluntary control of production levels now, it seems reasonable to assume they will have some level of voluntary control over production levels in the near future.
Based on that, my guess is that they'll fulfill their increased production quota starting in November. If they couldn't, I don't see why they would have allowed the quota to be increased; news reports suggested that KSA was the main voice in favour of a quota increase, strongly suggesting they could have nixed it if they'd wanted to.
"I read it; he was just wrong." Wrong in that it wasn't declining at 8% at the time? It certainly was. Or wrong in projecting it to continue indefinitely? I made no such claim and specifically pointed out that Saudi production was unlikely to continue to decline at that rate indefinitely. Would you care to point to a specific statement I actually made that you think is wrong?
"didn't show the mathematical signature of voluntary declines" is the claim I'm saying appears to have been wrong.
I don't recall whether you explicitly made that claim, much less a claim about continuing declines, although both I and the previous poster got that sense from your articles. If you didn't make either claim, then my apologies for suggesting you had.
Both claims do seem to be widely-believed and incorrect, though, regardless of who bears responsibility for making them.
EDIT: ahh, found the speculative hypothesis I was referring to. From Saudi Arabian oil declines 8% in 2006:
You made the speculative hypothesis that KSA production is in decline - from the phrasing, you appeared to be saying permanent decline - and appear to imply that it will decline at a rapid rate. You reinforced that hypothesis at the beginning of A Nosedive Toward the Desert:
i.e., KSA is currently undergoing rapid decline. As in, that is a present and continuing situation as of March 2007.
Obviously, I disagree with that hypothesis: KSA was not in the middle of a decline - rapid or otherwise - in March of this year, as the 2007 production numbers show. Moreover, I disagree with your other hypothesis:
2006-2007 production has been a sharp decline until reaching the quota level, and then no decline at all thereafter. That is just what one would expect from a voluntary decline, but it seems unlikely that an involuntary decline would conveniently stop at a chosen quota level.
"Declines are rather unlikely to be arrested, and may well accelerate." was clearly wrong and an overhasty extrapolation. By the next piece, I was more careful, saying "has entered rapid decline of their oil production, at least for the time being". I also in that piece pointed out that "However, it's very hard to believe that declines would continue at that rate. Eg, if they continued all the way to zero after ten years, that would only be another 16 billion barrels of oil production. No-one is that sceptical of Saudi oil reserves. Eg Hubbert linearization suggests there's about another 80gb or so of oil there. ASPO estimates 170gb still to produce (though based on a fairly generous recovery factor)."
There was no good evidence of stabilization in March. The data available at that time would only go through Jan-Feb, and all series were still dropping. I continue to believe the declines in 2005-2006 were largely or entirely involuntary and likely reflected at least in part depletion in North Ghawar. However, I also continue to believe that there is a sizeable fraction of reserves remaining in Saudi Arabia, and the declines probably reflect a failure to anticipate the depletion of Ghawar (and maybe other fields), and not a complete lack of anything else to develop.
Yes, of course. I'm not saying you did anything wrong - as I said, you made a speculative hypothesis, and it turned out to be incorrect, and there's nothing wrong with that. Happens all the time when people are trying to figure out something tricky. All I'm saying is that current evidence suggests that hypothesis was not correct. No biggie.
It's not yet clear, though, what the nature of last year's decline was. I'd argue that 2007 production gives strong evidence that at least some of it was voluntary, but we don't know whether all of it was. There's probably a good chance you're right that some of it was involuntary - your analysis of North Ghawar was very solid, although it's somewhat speculative how heavily KSA was relying on the region - but there's also a good chance we'll never know.
Wikipedia on Signal to Noise Ratio.
I like HL but I think it only makes sense to apply it to resource where there are Geological reasons for thinking we're close to using a large fraction of the resources, say above 0.2 minimum.
HL derives it's power from it's simplicity:
dQ/dt = Q(1-Q)
Where Q is the fraction of the total resource consumed. The equation above describes the growth of bacteria in a petri dish. At small Q, the growth is exponential. As Q becomes reaches 0.5, diminishing returns set in and the growth rate becomes negative. Of course in the real world, many effects can interfere with this but it's hard to beat the fundamental first order effect you get from the equation.
If you apply it to many minerals you get no predictive power from the extrapolations because we're so far away from exhausting supply. ie Q << 0.2. For this reason I don't think it works for coal production.
Sorry for the low quality graphs. I haven't put time into prettying them up. The data are for the period 1900 - 2004 from the the United States Geological Survey.
The hard part was obtaining the production prior to 1900, for which I pent a fair bit of time web surfing. I'm pretty confident of gold, copper and silver. But for tin I just scaled the copper production prior to 1900 by the production rate post 1900.
HL is more applicable to oil IMHO because oil is:
1) liquid. the easy stuff was under pressure on land, even.
2) sold in its natural state.
3) the source of energy for its own exploitation, and the exploitation of all other resources, including all metals
The limiting factor - the bottleneck of oil production - is geology. Copper, Tin, Silver and Gold however must be mined and smelted. Even when geology is good, metal production is limited by the availability of energy sources required for mining, smelting, and transportation. Energy sources such as oil.
Metal production in the ancient world rose and fell on the availability of cheap wood, and in today's world it rises and falls on cheap oil.
If you'd like to explore the efficacy of HL I invite you to apply it to primary energy sources and not metals, or PlayStations, or pork bellies, all of which are made of cheap oil.
Wood and coal should be good targets, but you'd need to look back at when they served as primary energy sources - before the age of oil.
I think you have hit the nail on the head BMCNETT.
Given a limitless amount of free Energy Q would tend to zero for most extracted commodities...
This would explain the long term commodity downtrend even as demand has risen.
There are metals that should be more highly correlated to underlying energy costs: Aluminium and Lithium come to mind.
Regards, Nick
Prices and Production over a complete Hubbert Cycle: the Case of the American Whale Fisheries in 19th Century
http://www.energybulletin.net/3338.html
What's your reasoning to apply HL to metals?
Try to apply it to whale oil, that would be interesting.
A few reasons. Firstly to demonstrate the limits of the HL method. You can can't use HL to predict URR and the peak production time if a large fraction of the resource has not been produced.
Secondly there is a second order theme on this site that we're close to peak production of various other resources.
The data above suggest we're nowhere near close to this.
Thirdly because a lot of economists confuse Oil with other mineral commodities. The four metals I showed have been mined for over 5000 years. Some economists appear to confuse metals with Oil and think that if we just keep trying harder we'll find more Oil, like we have for copper, gold, silver and tin for the past 5000 years.
So I'm also trying to demonstrate that there is a fundamental difference between fossil Oil and minerals.
Recycling is a significant part of metal usage. A large fraction of the iron used now is recycled. I think you need to adjust if you can metal production for the recycling effect.
In general most oil products are not recycled.
But is not recycling like a birth/death model? For instance, the materials die and then come back to life as they get recycled. If what I am reading here is that Hubbert Linearizing is a form of birthing and dying, then it seems like it should work even better for recycled materials.