A Different Way to Perform the Hubbert Linearization
Posted by Khebab on August 18, 2006 - 11:34am
Topic: Supply/Production
Tags: hubbert linearization, logistic, urr [list all tags]
A quick post about a different manipulation of the logistic differential equation. By using the first derivative, we get a new way to perform the Hubbert linearization. Some results are given on Norway and the US oil production.
[Updated by Khebab on 08/18/2006 at 02:36 PM EDT] After some thinking, I came up with a simple way to combine the two linearizations (see text below).
[Updated by Khebab on 08/18/2006 at 02:36 PM EDT] After some thinking, I came up with a simple way to combine the two linearizations (see text below).
The
logistic differential equation relates the production P
to the cumulative
production Q
as following:
Fig. 1- Standard Hubbert linearization (top) and resulting logistic curve (bottom). The peak date is determined by matching cumulative productions for the last year. (data from BP 2006, all liquids excluding refining gains). Click To Enlarge.
Fig. 2- Hubbert linearization on the production annual increase (top) and resulting logistic curve (bottom). The peak date is determined by matching cumulative productions for the last year. (data from BP 2006, all liquids excluding refining gains). Click To Enlarge.
Fig. 3- Standard Hubbert linearization (top) and resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
Fig. 4- Hubbert linearization on the production annual increase (top) and resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
A few comments:
Fig. 5- Hybrid Hubbert linearization combining the production annual increase (blue points) and the standard P/Q representation (black points), the resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
Other stories on TOD about the Hubbert Linearization here. The Datasets used in this post can be found here.
P=dQ/dt=KQ(1-Q/URR)
dP/dt=(dP/dQ)(dQ/dt)=(dP/dQ)P=K(1-2Q/URR)P
(dP/dt)/P=K(1-2Q/URR)
Fig. 1- Standard Hubbert linearization (top) and resulting logistic curve (bottom). The peak date is determined by matching cumulative productions for the last year. (data from BP 2006, all liquids excluding refining gains). Click To Enlarge.
Fig. 2- Hubbert linearization on the production annual increase (top) and resulting logistic curve (bottom). The peak date is determined by matching cumulative productions for the last year. (data from BP 2006, all liquids excluding refining gains). Click To Enlarge.
Fig. 3- Standard Hubbert linearization (top) and resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
Fig. 4- Hubbert linearization on the production annual increase (top) and resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
A few comments:
- this approach is much more sensitive to noise because of the use of the production first derivative and seems to give more reliable estimates for the URR than for K.
- the data representation is more symmetric compare to the standard HL approach which is very sensitive to noise for low cumulative production values (therefore, early production data points are generally excluded).
- the two HL techniques could be combined.
Fig. 5- Hybrid Hubbert linearization combining the production annual increase (blue points) and the standard P/Q representation (black points), the resulting logistic curve (bottom) for the US. The peak date is determined by matching cumulative productions for the last year. (data from the EIA, crude oil only). Click To Enlarge.
Other stories on TOD about the Hubbert Linearization here. The Datasets used in this post can be found here.
P(2013)= 83.62 mbpd
P(2005)= 81.1 mbpd
Pumping the fear factor out of oil
As more production comes online over the next few years, prices may ease by as much as $20 a barrel.
http://money.cnn.com/2006/08/18/news/economy/oil_fear/index.htm
Peak Oil Passnotes: Supply 'Cushionitis'
By Edward Tapamor
18 Aug 2006 at 11:49 AM EDT
PARIS (ResourceInvestor.com) -- You have seen what Resource Investor was mooting about the oil market last week, basically come true. Oil has actually fallen a little faster than we expected - to around $71 - but it still has an important couple of barriers to break before it goes really wild to the downside. So let us take a little look at some recent history and see if we can figure out why.
On April 21st the Nymex WTI price reached $75.17 on the back of worries over Iran and general supply tightness. By June the Nymex WTI was at $69 before it set off on its latest run. In other words it had hit a strong high before falling back. It then surged back once more to hit $78.40 on July 14th before dropping off once again. Then we reached an odd moment a few days ago, on August 7th when some genuine myopic hysteria set in around the crude markets.
Brent crude had broken up past the WTI by August 7th as supplies of Brent became constrained by declines and increasing seasonal demand, pushing up past its historically higher-priced relative. The price was spurred by a number of reasons, not of which were crystal clear. One being the Israeli attack on Lebanon, others being the problems in Nigeria and the first signs of the difficulties for BP [NYSE:BP; LSE:BP] at Prudhoe Bay.
At the time we pointed out that although significant these events were underpinned by the - now seemingly age old - supply cushion absence. As there was no supply cushion the market had driven itself into hysteria. The Prudhoe Bay outage was not that significant although it was not helpful. Lebanon did not produce oil even though indirectly the invasion was about energy being a proxy war between the U.S. and Iran. Nigeria was going on the same as it has been in recent months.
Brent boomed up to an all time record of $78.64 intraday and $78.30 at the close with the WTI chipping in at a healthy $77.05 at the end of trading.
Now just 10 days or so later Nigeria actually seems to have got worse, armed men stormed a bar in Port Harcourt (who calls a bar Goodfellas in a place like that?) although the short-term outage at Nembe Creek of around 180,000 barrels per day has been restored. Meanwhile the Lebanon situation is still not really impacting oil and its supply. BP on the other hand has managed to keep somewhere around half of its Prudhoe Bay output online, even so you will note that is a loss of some 200,000 barrels per day. A loss is after all a loss.
Yet we are seeing the WTI hit exactly $70 intraday, some seven dollars off its high in around eight days active trading. Brent is around $72. A big, big move to the downside.
There is one other reason, Goldman Sachs. They are not excited about the new gasoline contract for - cough - reformulated gasoline blendstock for oxygenate blending or RBOB. New regulations in the U.S. have meant that RBOB is replacing methyl tertiary butyl ether (MTBE) in gasoline. Sachs are not about to risk a load of cash on this new contract so they have simply stopped playing.
The result of such a big player leaving the table is that there is no liquidity - or relatively little - in the gasoline market. This has pulled down the price of gasoline which has impacted on the price of crude. So the combination of events, Lebanon ceasefire, Prudhoe Bay, staying half-online, Nembe Creek being repaired and RBOB illiquidity have stuck a knife in the gut of the oil price. Then we hear stuff like this.
"Some of the factors and disruptions that helped drive us to very high levels have been resolved now," according to a statement by from Eoin O'Callaghan at the French bank BNP Paribas.
No they have not.
Lebanon is not resolved, Nigeria is not resolved, Prudhoe Bay and BP's general behaviour is not resolved, Iran is still awaiting the outcome of its nuclear enrichment programme and demand is still healthy. What has happened is the market has seen a great time to take a big chunk of profits. A breather. That is all.
If we were smart guys we would open a book on the first "Oil Makes Dramatic Surge" headline. No doubt you will see it in the next sixty days. We will be told all the stories about collapse, markets imploding, frenetic activity on the trading floor and `peak oil freaks' will be telling us to ride Oxen to work. Then we will do the same dance all over again. Isn't energy great?
Did we burst your dreamy life? Have you read just enough about it to be only scared? Do you really think that CNN is not selling ads to : car, insurance, housing, bank and oil company so they can stay "impartial"
They dont want to tell you the truth, you cant handle the truth, the economy and those company either.
Oil = finite ressource
No matter what you think.
Hubbert Linearization is technique developped in 1956 and used since then to calculate the production of whole region or country.
Oil at 20$ may be next door but in that case we will have suffer a very deep, profond and large depression.
Unless you dont have some math background, you cannot increase oil consumption very much because of exponential growth. I suggest that you take a look at this presentation by prof Albert Bartlett you will see what we mean.
Again, we are very sorry to have woke you.
You should have taken the blue pill.
ohhhhhh, it's the great CNN conspiracy that has allowed oil prices to fall...somebody thank thme for me....and the Bloomberg conspiracy I bet kept them from going to....where...$200, $150 a barrel this past summer as was predicted by so many of the catastrophephists....somebody REALLY thank them for me! (By the way, as much as I admire them, why don't you all have a field day of ridicule when Simmons or Pickens blows predictions at least as bad as Yergin does? Fair is fair....this year everybody blew it....)
Yes oil is a finite resource, but that frankly don't tell us shiit...(quick,name something on Earth that is not a finite resource except for hungry mouths of beasts to feed, including us....ain't that a paradox?), but just being finite does not tell us HOW MUCH is out there, now does it?
"... we are very sorry to have woke you." Cute and humorously snide, but don't worry about waking us....some of us are a helll of a lot more awake than you give us credit for....
(now I am just waiting for that great MSNBC conspiracy to kick in so the prices will really come down....how'd a thought that bringing prices down could have been this easy? :-)
Roger Conner known to you as ThatsItImout
-best
But that does not seem to be of concern at TOD, 99.98% of the posts are about, when THIS particular Peak Oil will happen, brainstorming about technical "solutions" by mostly technologically ILLITERATES, anecdotes and gossip about life in the US (not so bad, entertaining at least) and endless haggling by Peak Deniers.
"Of course the only true problem is GROWTH in a finite environment!"
Maybe, but at the end of the day, that's biting off more than I can chew.
If I ruled by fiat, and everyone would obey my command to cease fornication (because after all, birth control pills require energy to make!), then maybe growth would cease.....but since I don't and everyone won't, it's a bit of a moot point, isn't it? Growth, like change, has probably been going on too damm long....but nobody knows how to make either one stop.
You say, "99.98% of the posts are about, when THIS particular Peak Oil will happen, brainstorming about technical "solutions" by mostly technologically ILLITERATES. That's actually not a bad overview. I have learned a couple of things since I came here:
- Everybody's a damm physicist! I didn't know we had so may physics genuises in the country, until every other post I read ended every debate about all the things that could not be done (half of them already being done somewhere) with the flat and knowing assertion, "the physics proves it" or "it's in the physics"....that second one has the cool resigned detachment of the old Bruce Hornsby song..."That's just the way it is....some things will never change.....", and then he takes the counter point, "but don't you believe it..." I prefer to take the counterpoint.
- Despite the fact that no one knows exactly how much oil and gas there is, or exactly how to define it, everybody knows to the day when we are going to peak! Astounding that! Both the optimists and the pessimists have this in common! Even the Dan Yergin's, despite having no idea whatsoever how much gas and oil is actually out there, completely relient on other people's word, says, we have plenty for the next decade! While the pessimists like Deffeyes who says that HL (Hubbert Linearization) is holy writ, even though Hubbert Linearization is based entirely on known URR (Ultimate Recoverable Reserves) when confronted on lack of any real knowledge of world URR by anybody, he changes gears and says, "Well, it's production that counts, reserves mean nothing! You can't pull up to the pump and fill up you car with reserves!" What do the optimists and the pessimists have in common? Despite having no idea how much is there, and what exactly counts (crude oil, all liquids, which of course makes nat gas interchangable with crude oil....despite another poster on TOD who recently shut his ears "hear no evil" fashion, "I have heard too much about bottled gas, there seems to be bottled gas everywhere!"...yep, the world is a confusing place!
- Despite everyone, EVERYONE saying "peak is not "running out!", when they talk you can hear they all have a mental picture of running out, right to the last drop!
Someone says "perhaps we can build windmills", they reply, "that takes oil" as though there won't be a pint left! Someone says, "perhaps we can build electric cars", they reply "that will take oil to produce them and the batteries".....what, won't there even be a few gallon?" Medication? "Big dieoff is coming, medication takes oil." Now, exactly how many tons of the oil consumed in the world, exactly what percent of the total tonnage goes to production of medication? (I am leaving aside the fact that many medicines and chemicals are made with natural gas processing for the moment, I love it when people on here will scream about how oil is used to make fertilizer! Well, actually, it's natural gas....but back to the point....) You mean that if we reduce the waste burning of crude oil, there still won't be even enough for medicines that actually use it in their production?You mean if everyone drove a 2 cylinder tin box like a Citreon 2CV, we would still run clear out, and be as Deffeyes says, "Stone age by 2030", or thereabouts? Does "Peak Oil" really mean a Fred Flintstone world?
The view of the world is sometimes childlike....growth is the problem, tell them to stop! and they will.....Technology? Go home and tell you daddy technology is BAD! It is a BAD THING!! If he is trying to develop technology, he is a BAD MAN! Don't let him fool you, and say it's efficient, it is still technology, and will use energy, and we will be OUT, it's BAD! He is an evil DENIER! Life in the U.S., it is a BAD THING!! It must stop, many must die! Then some will go on and do the right thing....with no TECHNOLOGY, the BAD thing that messed up the world!!
As you say, not so bad, entertaining at least, or at least it would be if it were not so sad, and the problem is far too serous, too complex, too much in need of sophisticated acceptance of real ideas, real modern maturity.
We are not as much paying the price for wasted energy, we are paying the greater price, as we knew we someday would, for wasted talent, preperation, mental ability to design, to concieve of more than yes/no, and to think in terms of multiple, interlocking options and confluent ideas. We are frankly stumbling in the dark, blind but hoping to pass ourselves off as "seers" who will lead the "ILLITERATES", the "screaming monkeys" and the "sheepies" out of the dark. Such are the terms we use to win over our disciples. That alone should tell you volumes.
Roger Conner known to you as ThatsItImout
You may prefer starving to choking but both are an ugly death.
every other post I read ended every debate about all the things that could not be done
"every other", yes, but the OTHER half was all about the miraculous solutions.
Just as unsubstanciated, illiteracy comes both ways.
The view of the world is sometimes childlike
To the point, but nobody is compelled to share so much optimism.
growth is the problem, tell them to stop! and they will...
Of course not, this is my point, telling won't do :
- Enforcing, not politically correct and LOTS of trouble, struggle, strife, unanswerable messy arguments.
- Die-off...
Go home and tell you daddy technology is BAD! It is a BAD THING!!
Are you speaking to me?
I thought I cleared up this in our previous discussions.
to pass ourselves off as "seers" who will lead the "ILLITERATES"
TPTB have been doing a hell of a job leading the illiterates , too bad the looming difficulties are WELL BEYOND THEIR SKILLS, in spite of the high appraisal they have of their capabilities.
we are paying the greater price, as we knew we someday would, for wasted talent, preperation, mental ability to design, to concieve of more than yes/no,
A "price", yes, ignorance can be remedied AT A COST, stupidity cannot.
What is the ratio between these 2 impediments, and, hoping for the best, can we bear the cost?
Todd
As an aside, I will be giving 2 conferences september 23 in Metabetchouan (Lac Saint-Jean). One in the morning regarding peak oil and one in the afternoon regarding solutions.
I know it's gone a be a bit far from you, but I wanted to let you know.
The local newspaper is going to produce a series of articles also. I hope regional, then national will pick it up.
Anyway, it's gona be fun.
We know that the old method was 99% accurate (using only production data through 1970) in predicting post 1970 cumulative Lower 48 production, through 2004. How about if you did the same thing with the second method?
For the Lower 48 case history that I cited, Khebab just used the production data through 1970 to generate a predicted post-1970 production profile (using HL method #1). The cumulative post-1970 Lower 48 production was 99% of what the HL method predicted that it would be.
Since the world is now about where the Lower 48 was at in 1970, this has obvious implications for world oil production.
One of the problems with the conventional way of graphing the HL fit is that the y axis variable (P/Q) is a function of the X axis variable (Q). This is why the variability in the data appears to smooth out with increasing Q. This alternate way of graphing the data does not have this problem and so we see the variability seems much greater but uniform. That is actually a good thing if you are performing a least squares fit. I've never delved too deeply into how people are doing a hubbert linearization fit, but it is not strictly apropriate to use the least squares fit on the P/Q versus Q data.
So good work Khebab, this alternate graphical form of the logistics curve does show the actual variability inherent in the data and is thus a much more informative graphical representation of the hubbert logistics model.
The standard least-square fit assumes gaussian distributed residuals which is not the case for the HL (probably a more heavy tail distribution). I always use a robust fit technique based on robust statistics which is recommended in case of contaminated residuals by outliers.
I am struck by similarity of both equations:
(dQ/dt)/Q=K(1- Q/URR)
(dP/dt)/P=K(1-2Q/URR)
I understand all the details, but somehow I know that there is something deeper that escapes me. I'll think about it.
I have some questions/comments:
What do you use dP/dt=P(t)-P(t-1) or dP/dt=(P(t+1)-P(t-1))/2? (you favor the second one so I suppose that's the one, don't you?)
It is really nice to combine both methods in the same picture for comparison. But, what I would favor is to draw two lines, one for each method.
To combine all points of both methods and then draw only one line (your hybrid method) seems odd. I understand why you want to do this: you want to compensate the low sensitiveness of the tail of the first method with the noisy second method. But you put too much weight into the left side of the plot, where most of the points are. Anyway, its a very nice idea worth considering.
Well, I also wanted to tell you that I really like your plots: the text is of the right size, the legend is very clear and informative, the dots are just the right size. I mean, I really dig your plots. What program do you use? Do you have to fiddle a lot to make each one? Or is it quite automatic?
I love plots. I am a very visual person. I use Mathematica but I don't like the style it outputs and so I have to export the plot into wmf and then change font size, the labeling, etc with Flash or Power-Point. Very time consuming. At some point I have to customize the style of the plots Mathematica outputs into something I like. But it is not trivial.
Thats all for the moment.