Predicting the Past: The Hubbert Linearization
Posted by Robert Rapier on March 12, 2007 - 12:21pm
Topic: Supply/Production
Tags: hubbert linearization, hubbert peak, peak oil, saudi arabia, texas [list all tags]
Part I- Texas Myths
Like Cindy Crawford, I have done quite a bit of modeling in my career. However, mine has been in front of a computer. There are various types of models. They can be empirical, such that you curve fit data without having a clear explanation of the underlying mechanisms. Or they can be theoretical, in which the system is modeled according to the governing scientific principles and mathematical equations.
However, one thing is critical to keep in mind. If you are going to use the model for forecasting, the model must be tested. Testing the model is called “validation”, or sometimes “back-casting.” This involves feeding the model real data, and observing how well the predictions match up with the observations. If the predictions match up on a consistent basis, and any large variations are explainable, you have the makings of a predictive model. If you have not validated your model, or if you have attempted to validate it and found that the predictions were inconsistent, the model should be used with caution (if at all). In this essay I have done some back-casts on the Hubbert Linearization (HL) model and attempted to use it to make predictions using historical data.
Qt and Peak Production
I am unaware of a case in which a country has completely run out of recoverable oil and had Qt verified by the HL method. However, there are plenty of examples in which a region’s production profile follows the expected path determined by the HL. There are also many examples showing that a region’s production peaked at very close to 50% of Qt. Quoting from an article by Jeffrey Brown and Khebab:
With time, a HL data set starts to show a linear progression, and one can extrapolate the data down to where P is effectively zero, which gives one Qt, or ultimate recoverable reserves for the region. Based on the assumption that production tends to peak at about 50% of Qt, one can generate a predicted production profile for the region. The Lower 48 peaked at 48.5% of Qt.
Some areas have tended to peak at a higher % Qt than others. It is commonly claimed that Texas production, for example, peaked in 1972 at 57% of Qt (the reason for the qualifier will become apparent later in the essay). The fact that Texas peaked later than most regions is sometimes explained by the fact that prior to 1972 Texas was the swing producer, and production was regulated. This situation is similar to that of Saudi Arabia, so Texas is often used as an analog for predicting Saudi Arabia’s peak.
So far, so good. But the astute reader may wonder “Can the value of Qt change significantly over time?” If the answer is “yes”, then the inevitable follow-up is “Then how can I be confident in using the HL to predict a peak?” I will attempt to answer these key questions by looking at the evolution of the HL for Texas over time.
Evolution of the Texas HL
I have retrieved historical Texas oil production records and modeled a series of HLs at various time periods. According to a 1956 Hubbert paper, (1) Texas had extracted approximately 4 billion barrels of oil prior to 1935. Beginning in 1935, we have annual production statistics that take us through the end of 2006. (2) Therefore, we can construct a series of HL curves. To avoid any bias on my part, I had Excel extrapolate the line and make the forecast once there was a relatively smooth trend. Let’s take a snapshot from 1960:
Figure 1. Hubbert Linearization of Texas Oil Production Using Data Available in 1960.
As you can see, we have a nice trend. In fact, the latest 10 points are reminiscent of today’s HL of Saudi Arabia. The points have settled down and are staying pretty close to the line. So, what could we say in 1960? Qt as determined in 1960 from the intercept above is 42.5 billion barrels (Gbl). Texas crossed 50% of Qt in 1957, and by 1960 was at 56% of Qt – almost the same value as today. Surely peak was imminent. In fact, if you look at the data, Texas clearly peaked in 1956 at 1.079 MM bbl/day. By 1960, Texas was down to 892,000 bbl/day. It had undergone an annual decline of 5.5% for 4 years, and was well past 50% of Qt.
In 1960, we could have said “Texas oil production peaked in 1956, as predicted by the HL method.” But as we know, that’s not at all what happened. That would have been forecasting the peak 16 years too early. So let’s fast-forward to 1970:
Figure 2. Hubbert Linearization of Texas Oil Production Using Data Available in 1970.
Well, that’s not very helpful. Our Texas HL in 1970 is much more muddled than in 1960. The 1956 record was broken in 1968 – twelve years after the 1960 analysis indicated a peak. We are starting to see some points rise above the line and extend Qt out further than was implied in 1960. The trend line that Excel drew is now forecasting 46.25 Gbl as our URR. That puts production in 1970 at 73% of Qt. The last 14 years had been spent well above 50% of Qt. But, the last 4 points – starting in 1967 – seem to indicate that Qt may end up being even further out than we thought. Now remember, it’s 1970. What exactly about this curve would indicate that we are 2 years from peaking?
Let’s jump forward now to 1980:
Figure 3. Hubbert Linearization of Texas Oil Production Using Data Available in 1980.
Qt continues to grow. Excel is now forecasting Qt at 55.5 Gbl. The trend toward a higher URR is evident. The last few points imply that the forecast will grow to 57 Gbl. If so, our 1980 HL would put Texas’ 1972 peak at 63% of Qt. So, not only do we see Qt growing with time, we see that the % of Qt when the 1972 peak occurred is getting smaller. So, can we forecast the 1972 peak by 1980? No. We have already seen a case where the 1956 production record wasn’t broken for 12 years. The % Qt during that time was well over 50%. The % Qt in 1970 had climbed to 73%. Yet that still didn’t enable us to call peak. On what basis could we have done so in 1980? We have now gone through 24 years in which we could say “peak might be here.” To suggest that we could have made any other forecast at that time is wishful thinking.
So let’s skip to present day – end of 2006:
Figure 4. Hubbert Linearization of Texas Oil Production Using Data Available in 2006.
Qt is now at 62 Gbl, but look at those last few points. They are once again pointing to a higher Qt. Some time in the 1980’s, as production continued to fall, we could have finally said “1972 was the peak.” But the % of Qt for the 1972 peak is still a moving target. Today, the 1972 peak clocks in at 58.3% of Qt – not far from the value in 1960. In 1980 it was 63% of Qt, and in 1970 it was 73% of Qt. Therefore, the claim of “no examples of large producing regions showing sustained, steady increases in production past the 60% of Qt mark” is clearly wrong. Texas showed steady production increases past the 60% mark of Qt, because it reached that level in the early 1960’s. Texas even showed production increases past 70% Qt, as it reached 73% two years prior to the production peak.
Implications for Saudi
So, is Saudi like Texas in 1956, or is Saudi like Texas in 1972? Or is it like neither? The HL can’t tell us that. This essay should make clear that confidently predicting a Saudi peak on the basis of the Texas HL is nothing more than an exercise in faith-based forecasting. The only reason that the Texas HL looks as it does is because we have decades of data points following the Texas peak. But what is missed is that the HL has changed greatly from the time Texas actually peaked. So the Texas HL at its peak looked nothing like the Saudi HL of today.
It is invalid to use three decades of hindsight for refining the Texas forecast, because we clearly don't have the same option with Saudi Arabia. Yet some argue that the Saudi peak can be forecast with confidence using the knowledge obtained from the case of Texas – a region in which the uncertainty of the method spanned almost 3 decades.
So, the HL has shown that it is good at forecasting the past, but can be very unreliable for predicting the future. In Part II, we will examine the evolution of the Saudi HL over time.
Note
For those who may be unfamiliar with my position, this argument in no way diminishes my belief that we need to take action right now concerning oil depletion. I am merely evaluating one of the tools that is used to forecast peak, and trying to determine whether that tool can give us any precision on forecasting a peak in Saudi Arabia. My conclusion is that it can’t, but we will look at the specific case of Saudi Arabia in Part II.
References
1. Hubbert, M. King. Nuclear Energy and the Fossil Fuels. Paper presented at an American Petroleum Institute meeting in San Antonio, Texas. March 7-9, 1956 p. 10.
2. Oil Production and Well Counts in Texas 1935-2005, Railroad Commission of Texas, Accessed March 2007 at http://www.rrc.state.tx.us/divisions/og/statistics/production/ogisopwc.html
Insofar as I know, I have never argued that the pre-peak Texas HL plot was stable, or that one could have accurately predicted the Texas peak, using the pre-peak data.
I have argued that we can--in retrospect--determine at what stage of depletion that Texas peaked. I have also argued that the Saudi HL plot is much more stable than the pre-peak Texas HL plot. The small change in deflection in recent Saudi data was also seen right before the Texas peak.
Hubbert, using some mathematical methods (estimating the area under a production rate versus time graph, which is what HL does), stated, in 1956 that the Lower 48--inclusive of Texas--would peak in 1966 if URR was 150 Gb and in 1971 if URR was 200 Gb. A one third increase in URR only delayed the estimated peak by five years.
The post-1970 cumulative Lower 48 production (again inclusive of Texas) through 2004, using only the production data through 1970 to generate the model, was 99% of what the HL model predicted it would be.
This is the method that can't be used to predict the Saudi decline, even as production is declining as predicted?
http://www.energybulletin.net/16459.html
Judge for yourself how stable the following HL plots look (all done by Khebab, all on the same vertical scale):
Khebab's HL plots:
Texas:
http://static.flickr.com/44/145149303_e59bbf9890_o.png
Saudi Arabia:
http://static.flickr.com/52/145149302_924470eaa7_o.png
Lower 48:
http://static.flickr.com/45/145149304_a4a72211e6_o.png
World (C+C+ NGL):
http://static.flickr.com/54/145149301_b930ef7bc4_o.png
(GreenMan tiptoes through a minefield in attempting to comment)
If I am understanding your point, you are saying that a stable HL plot is necessary before it has predictive ability?
The Texas HL, as analysed by Robert, did not have predictive ability until well after peak, at which point the HL plot stabilized, and can be used to predict future production and Qt?
Do we have a mathmatical definition of the requisite "stability"? Could we give some metric of "stability quality" to a particular data set as a way of expressing confidence in its predictive ability?
Of the four plots you offered, Texas, KSA, Lower 48, and World, the Texas HL was unstable prior to actual peak, the other three seem to be stable, but the peak of KSA and World are debatable, in fact, the primary topic of debate. That leaves only one data point, Lower 48?
Robert ended his essay saying his next target would be HL plots of KSA. Perhaps we need a similar analysis of Lower 48, since that now seems to be the sole case in which we had both stability prior to peak and clear (in hindsight) peak?
I suppose we could throw the North Sea in there, as well, though you did not mention it in your list. I think we are all comfortable saying that the North Sea is past its peak. Did its HL plot prior to peaking exibit stability? How far in advance?
Is there a suitable data set for Prudhoe Bay? Or is that folded into the data for the rest of the US? Or can it be obtained by subtracting Lower 48 from total?
Is instability in an HL plot solely a factor of having been a swing producer, or are there other factors? For example, could we hope to do a predictive HL analysis on Iraq given its history of war and sanctions?
I guess the point of this is trying to answer the question "for a given data set, how confident can we be in the predictions it makes", and can we come up with a definite mathmatical expression of that confidence?
Do we have a mathmatical definition of the requisite "stability"? Could we give some metric of "stability quality" to a particular data set as a way of expressing confidence in its predictive ability?
Exactly the right question to ask. I think Stuart is looking at this. We have been discussing this essay some via e-mail, and I sent him my Texas data set so he could look into it.
I guess the point of this is trying to answer the question "for a given data set, how confident can we be in the predictions it makes", and can we come up with a definite mathmatical expression of that confidence?
Bingo! Give that man a cookie!
Could you come up with a non-linear, asymptotic formula that would fit better with the observed increase in URR toward the end of the cycle? It's been many years since I saw the inside of a math classroom, so it's just a thought.
It never gets much consideration IMO is the impact of technology. I fully understand the law of diminishing returns but some of the most productive improvements had to come into play at some point.
I don't understand how this would not add both to peak production and URR as what ever the (____)became widely accepted. The increase in production should generate somewhat of a addition to the curve.
I'll venture into hand slapping territory and speak on DelusionaL's point.
If there is a impact of new technology on the HL result for Texas, wouldn't this impact come into play earlier on a Saudi HL and result in an increased stability of the curve compared to the Texas HL? Am I correct in thinking that Saudi oil came 'that much' later in the game?
A kid with a question should also show up with a toy in hand, so hope this at least is new:
http://www.energyandcapital.com/consumption.php
Very cool! Thanks.
Stuart has done some work on stability analysis, but as you can see from the four plots, it's not hard to find the HL plot that was pretty noisy prior to its peak (and again, all four regions are--at present time--showing overall declining crude oil production). So, I wonder why Robert focused on that one plot--especially when Hubbert accurately predicted the approximate time frame for the Lower 48, inclusive of Texas?
The North Sea (EIA, C+C), on my HL plot, started showing a rock solid linear progression in 1988, until it peaked in 1999 (between 48% and 52% of Qt, just like the Lower 48), and production has precisely followed the predicted downward trend. Note that this was empirical. I did not predict a North Sea peak (although Matt Simmons did, using his own data).
According to Matt Simmons, the top oil companies working the North Sea--using the best data and personnel available--were predicting that the North Sea would not peak until after 2009.
All of the following regions have shown peak or plateaus, (with stable HL plots prior to the 50% mark) in close proximity to their respective 50% of Qt marks: Lower 48; Russia; North Sea; Mexico and now, the world.
Remember Khebab's prediction that Mexico would peak in 2006?
The two post-peak cumulative models we did were quite supportive of the method. The post-50% of Qt cumulative Lower 48 production through 2004 was 99% of what the HL model predicted (using only data through the 50% mark) and the post-50% of Qt cumulative Russian production through 2004 was 95% of what the HL model predicted (using only data through the 50% mark).
If our period of stability started in 1988, how much later was that stability evident? Are two years of stable data enough to establish stability? Three? How much is enough to say "we have stable data, now let's make some solid predictions"?
Perhaps another way of asking the same question might be "in what year, using only the data available up to that year, would we have been able to correctly call the peak?", with subsequent production data falling substantially onto the predicted curve.
The North Sea is a nice case to consider since, as far as I know, there were no above ground factors in its development.
As I noted in a separate post to robert, I see mexico as a better example for sa than texas. In addition to what I said there that, to me, shows sa/mexico to be more like each other than texas:
high tech simultaneous secondary and primary production
ultimate resort to high tech horizontals
each country has an old super giant field that dominates, rapid loss of which results in unavoidable peak
there is a further point, also different from texas, that is both are gov run and are, compared with what would have been done had they been exploited by private companies, starved of investment.
For all of these reasons, comparing the HL plots of sa/mexico may be informative. Can you resurrect and post the two?
And, I have a separate question; does the data suggest that the 'dog leg' up following a stable regime is predictive, not of higher Qt but, rather, that peak is nigh?
Thanks
We saw small deflections in the Texas and Lower 48 plots, right before the they peaked, much like the small deflections in the Saudi and world plots, right before they (IMO) peaked.
WT do you have the OIP numbers for Texas and can you give me
the % recovery factors based on the HL analysis ?
Thats the plot we need.
Mike, the problem with using recovery factors based on Texas is that we gutted many of our early-discovered giant fields with overproduction.
Secondary and tertiary production and Maximum Efficient Rate (of recovery) were all invented by my homies in the oil patch around here. As a consequence the is a recovery factor of the oil in place of about 1/3rd, while the mid-east and North Sea are getting about 50% of the original oil in place.
The Bureau of Economic Geology at the University of Texas should have the exzact figures you are looking for.
Right I forgot about this. We really damaged our fields early on. In a sense its a blessing since fixing the damage is probably what keep us going. I don't think Texas by itself is all that useful as a model past a certain point because of this.
For all of these reasons, comparing the HL plots of sa/mexico may be informative. Can you resurrect and post the two?
And, I have a separate question; does the data suggest that the 'dog leg' up following a stable regime is predictive, not of higher Qt but, rather, that peak is nigh?
Mexico did the dogleg up in 1995 resulting in a new stable regime with a Qt roughly twice what the previous data was pointing to, see my post from two month's ago:
http://www.theoildrum.com/node/2149#comment-144998
Thanks for the link. SO, mexico's HL is not a good predictor for sa, or at least not if sa has peaked.
Mexico, sa, kuwait, maybe china remain special cases with a super giant that dominates overall production; for each of these, the question is, when will the super giant go down? HL is probably silent on this issue. Ghawar and cantarell were produced with the latest high tech, meaning that the decline, when it comes, will dominate production and almost certainly signal that peak is here. We know about cantarell and mexico, daqing and china, burghan and, probably, kuwait. Ghawar remains veiled because of sa stonewalling, but precipitous decline would neatly explain sa production profile over the past year.
The early HL plot for Mexico showed a P/Q intercept of about 13%. While it is not impossible, 13% is unlikely.
Compare it to the P/Q intercepts on the four HL plots I have shown above.
Yet another example of a region: (1) Declining and (2) As predicted (by Khebab in this case).
Let's see, what's the score so far?
Notice a developing trend here?
Notice the escalating attacks as the reality of a near term peak becomes more apparent?
Notice the escalating attacks as the reality of a near term peak becomes more apparent?
You are taking this far too personally. I am not attacking you. I am pointing out that in the case of Texas - which you have indicated is reflective of Saudi - the HL performed very poorly at the time of peak. So, I am pointing out that we can't then have much confidence in using the HL to predict Saudi's peak. In turn you have resorted to "Who's right!" Come on.
You would have been right had you predicted Texas peak in 1956. You would have been right for 12 years. But you would have ultimately been wrong because you used a tool that is not very reliable for what you are trying to use it for.
On the other hand I think Stuart's work was very interesting, and this is by no means an answer to his posts. I still don't think the world has peaked, but the HL gives me absolutely no useful information one way or the other. The kind of analysis Stuart did gave me more to think about though.
So, one of us predicts the peak, and he is so far right, but you criticize the work, even as the Lower 48, Saudi Arabia, Mexico and the world are declining as predicted, based on Hubbert/HL models, and as the North Sea is following the HL model.
The other one observes that Saudi Arabia has peaked, and his work is more valid?
(BTW, Stuart posted an article last year, to the effect that we were probably at or past world crude oil production).
Somehow, I get the feeling that you are getting ready for the following admission:
"Saudi Arabia has probably peaked, but by God, Jeffrey's methodology was wrong."
Cut to new Titanic Scene:
Jeffery the problem is everyone that has confidence in HL has paired it with other data to develop that confidence and its not just QT.
In the case of KSA its the fact that
1.) HL is showing a peak about now.
2.) They are out of easy oil look at how they are drilling now and what they are producing.
3.) Ghawar has a rising water cut and is in decline.
They peaked.
You only need HL plus some other information and you can pick the right HL plot with almost 100% confidence.
I assert you need no more information.
WT
I'm just curious why the vehement tone in the responses to RR? It is possible to come up with the right answers using a wrong methodology. I keep reading the exchange between you and RR and I really don't get the impression that he thinks your answer is either right or wrong, but rather he has taken you to task about the path you took to arrive at your conclusion.
Ultimately you can argue that you are right in that dependence on fossil fuels needs to end ASAP, and the difference between now or 5 years from now or 50 years from now will in the grand scheme of things be a trivial detail.
Given the evidence I too think we are pass/at peak, but I understand from an academic point of view why models should be tested, analyzed and refined, and from what I read that is what RR appears to be doing.
You however seem fixated on being right, just for the sake of being right. Perhaps it is just a personal thing, but I like to be right including as to why I was right. And in RRs case I think he wants to be right down to the details in his methodology because he has the fear that crying wolf too early could cause resistance to a Peak Oil warning if this turns out to be a false Peak.
The media constantly bombards those "Peak Oil Nuts" as being whacks because from the beginning of oil there have been those claiming it will end tomorrow. Given the climate surrounding Oil and the competiveness surrounding this commodity today, this type of debtate takes on even more importance. RR has stated previously that his big fear is in crying Peak too early and giving ammunition to the opposing side which will in turn make it that much harder to convince people when the real peak will occur.
I can understand RRs hesitation and from a academic standpoint admire his humility and skeptism used in his efforts to forcast oil related events. RR has the mark of a true researcher, one who does not rest on his laurels claiming he has found the answer, instead he takes what he thinks is right, and subjects to even further scrutiny. Its an excercise I think is well worth doing, because if it turns out that this is a false peak, this community had best have moral fortitude and academic honesty to go back and admit they were wrong and review WHY they were wrong. During that process, it will mean that methodologies will need to be picked apart.
Amen
I totally agree - Robert's approach is IMO entirely correct, and he is to be highly commended in taking the line he has.
Beautifully put.
:)
That is funny....
Robert: "We sank in 2 hours, 23 minutes and twelve seconds and your math was wrong".
The early HL plot for Mexico showed a P/Q intercept of about 13%. While it is not impossible, 13% is unlikely.
Russia's HL also has a P/Q intercept over 10%. Its predicted Qt is also likely to be inaccurate.
Notice a developing trend here?
The trend I've been noticing is the tendency for HL to produce false alarms 10-15 years before peak.
Dream on while you still can.
As I stated before if production was with 5-10% of peak 10-15 years before peak its not a false alarm. Its a good prediction.
The fact that we feel 20 or more years at peak is a long time is simply applying how we feel about time to a process.
Put it this way a mountain say spends say 30% of its lifetime within 10% of its maximum height this could be millions of years. But I think mountain weathering and HL are closely correlated and behave the same way. Other factors have to be taken into account to do a better prediction of when a mountain will reach its peak these are the filters I speak of.
But its the same problem and you can see HL is not something you discard.
Its not a personal attack. Stay focused.
I guess what I am trying to express is the contribution of "above ground factors" to noise in the production data.
For example, was Prudhoe Bay production ever limited by the throughput of the Trans-Alaska Pipeline? For how many years? By how much? Would that have contributed to false predictions from the HL plot? Or is it small enough that we would get good predictions anyway?
Would we get better results if we simply discard data points during points which are strongly impacted by above ground factors, such as for Iranian production during the Iran-Iraq war?
While not a mathmatical process, it could be documented. "I started with data set A, removed data points B2, B7, B8 due to clear above ground factors, and did my HL on the remaining points. The data points C1 through C12 exhibited stability quality XYZ, and I have used them to make the following predictions". Something like that.
Well, let's consider the two most stable cases, with essentially no material restrictions on drilling or constraints on production (other than as noted below): the US Lower 48 and the North Sea.
Both regions peaked in close proximity to their respective 50% marks, after showing solid linear progressions on their HL plots.
Within the Lower 48, Texas produced at less than capacity, i.e., it was the swing producer. This was the basis for using Texas and the Lower 48 as a model for Saudi Arabia and the world. Not to belabor a point, but Saudi Arabia and the world are declining as predicted (EIA, C+C).
Because of political problems, there have of course been huge swings in production, e.g., the Iranian revolution and the collapse of the Soviet Union.
But again, consider the Lower 48 and North Sea--developed by private companies, vastly different producing regions--yet they are both following the predicted downward production curve after peaking in close proximity to the 50% of Qt mark.
So, absent political/technical problems, IMO, large producing regions tend to show linear HL patterns and to peak and then decline in proximity to the 50% of Qt mark.
Westexas points at this HL for Saudi Arabia by Khebab:
Notice how the last 3 green dots are up a bit and are dragging the fitted line up. Suppose we had done this plot 3 years earlier, and didn't have those last 3 dots? Then the red line would have gone through just the other green dots, which are very close to a line. Looking at the chart, this would give a Qt of more like 150, compared to about 180 today. And that would mean that production as of 2002 would have been an even higher percent of Qt than what the chart shows in 2005! Probably over 60%. Especially coming after a couple of years of decreases, we would have had an even stronger case 3 years ago of saying that 2002 was the peak than we do today for 2005 or 2006, based on HL analysis.
So, even if true, we are talking about a 20% increase in URR?
Hubbert estimated that a one-third increase in URR only delayed the Lower 48 peak by five years. If the math is roughly the same for Saudi Arabia, we are talking about a difference of three years.
In any case, Saudi Arabia is declining as predicted.
This whole exercise is roughly akin to passengers arguing over how soon the Titanic will sink--even as water laps at their ankles.
In any case, Saudi Arabia is declining as predicted.
I think the whole point of this essay still eludes you. Texas declined as would have been predicted in 1956. It continued to do so for 12 years before breaking out to new highs. So, how can you tell where we are with respect to Texas production on the basis of the HL? You can't.
This whole exercise is roughly akin to passengers arguing over how soon the Titanic will sink--even as water laps at their ankles.
You keep saying that, but it isn't. I am still telling people to get on the lifeboats. I am just trying to figure out how much time we have to load the lifeboats. What I am trying to avoid is telling people we are going to sink in 2 hours if it's going to be 6 hours, because people might start jumping in 2 hours.
Robert,
---would have been predicted in 1956.
Did it get more predictive in 1969-70? WT has maintained that we are at/past peak at KSA then the question in my mind is how well did HL work at or near peak. Did it tell peak? IMHO this will tell us if we need to man the life boats so to speak. I will go back and reread your post looking for this.
I find it very difficult to believe that oil co.'s fly by the seat of thier pants, something isn't right here IMHO.