 | The Energy and Environment Round-Up: September 29th 2007 | The Oil Drum: Canada | The Finance Round-Up: October 2nd 2007 |  |
88 comments on Modeling Oil Production to Estimate URR - Saudi Arabia, Kuwait and World
Comments can no longer be added to this story.
| Show without comments | PDF version
88 comments on Modeling Oil Production to Estimate URR - Saudi Arabia, Kuwait and World
Comments can no longer be added to this story.
| Show without comments | PDF version
User login
Personnel
Archives
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- August 2008
- July 2008
- June 2008
- May 2008
- April 2008
- March 2008
- February 2008
- January 2008
- December 2007
- November 2007
- October 2007
- September 2007
- August 2007
- July 2007
- June 2007
- May 2007
- April 2007
- March 2007
- February 2007
- January 2007
- December 2006
- November 2006
- October 2006
License
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.
GAIA Host Collective
I have a problem with using this approach.
It seems to me that one very quickly gets to the point of "over-fitting" the data. If there is an underlying reason why production might follow the sum of seven (or whatever) logistic curves, I wouldn't have the problem with the methodology-- say seven different producing reservoirs, each rising and falling according to your model.
As it is, the fluctuations in production follow various external events - global recessions, conscious raising and lowering of production at less than maximum production. I have a hard time seeing how fitting multiple curves to the data gives predictive value going forward.
I will agree that we will have a time when demand exceeds supply, perhaps prior to real peak. I think this has been called "Peak Lite" before; you are calling it "Apparent Peak". This is a real issue - we are probably pretty much there.
More than that, it seems that all that was achieved in this extraordinary work was the finding of the last logistic bell detected in each scenario (KSA KWT WORLD), but we don't know if those are the last curves we are able to produce.
That is, it doesn't tell anything about the future, because it pressuposes that these bell curves are all the last bell curves the world manages to produce, which I think it is rather unlikely.
And if you want to check what I said, I have more homework for you. Take all your KSA KUWAIT and WORLD charts, wipe out like 30 years and then try to plot the futures of it according to your method.
I bet that you will fail miserably in all of your predictions (probably except for the world, which is much more stable), which renders your theory moot.
Nice try though. That's the spirit.
Clearly this method cannot predict that a new Ghawar will be found somewhere. It can only infer a URR for all past and currently producing fields. I think that the URR results predicted for Kuwait and the World from the BP data speaks to the validity of this methodology. As for predicting the future, we shall have to wait to see how it evolves.
Ghawar was found in the first decades of the century. He places bell curves well beyond 1980, even after 2000, so I don't know what you're talking about.
I don't reckon "ghawars" to have been found since, but north fields, and now tar sands, shale oil, perhaps helped making those bumps.
But there is a race towards artic oil, if I remember. And Angola is making huge increases.
Either way, doesn't matter. This is numerology, not science. It tries to see simple patterns on a very complex structure. How could it possibly go wrong? Correlation... you know what.
Even King Hubbert didn't calculate URR with his own HL curves. He was not that dumb.
Pff. Almost everyone agrees that we are close within the peak. So that's not rocket science. What science is this that creates a span between URR of KSA of between 160bb and 260bb?!? Is this thing even useful?
I also don't think so.
It's a good try though, and I commend the spirit. Not the results, not the science.
The comment regarding Ghawar has nothing to do with placing bell curves beyond 1980 or 2000. The least squares process determines the size and position of the logistic functions that are required to model KSA's multi-peak production profile.
The Ghawar comment was intended to indicate that I, along with many others, do not believe that a new oil field the size of Ghawar and capable of producing 6.0 M bpd or multiple queen fields will be found in the future.
As for Canadian Oil Sands, they are already accounted for and their rate of production increase will be slow. As for shale, that production may show up after the peak year.
On one hand you are looking at oil sands, arctic oil, and Angola making huge increases to perhaps helping to make additional production bumps. On the other hand, you say almost everyone says we are near the peak. What is your position?
You ask the question “What science is this that creates a span between URR of KSA of between 160bb and 260bb?!?”
First off lets consider the real world situation. Saudi Aramco claims 259.8 B barrels proven oil reserves at the end of 2005 on its website and describes its expansion plan of increasing production capacity to 12.5 Mb/d by 2009. Many TOD participants and others believe that that the KSA reserves are closer to 160 B barrels. Isn’t it amazing that this “numerology” gives two answers, one in the 160 B barrel range and the other in the 260 B barrel range, that reflect the current debate occurring in the real world.
This numerology also indicates what to look for in future KSA production to get an indication of the real URR. For the 260 B barrel estimate to have credence, the numerology shows that KSA production would have to exceed 10.5 M b/d to 11.0 M b/d in the next 2 years. With the IEA indicating that world demand is increasing at around 2% per year, KSA’s ability to increase production to its claimed levels may be tested soon.
You have looked at the KSA results and question the value of the two results. At the same time, you have chosen to ignore the accuracy of the Kuwait and BP results. The projection of a URR of 45B barrels for Kuwait is spot on with Dr. Nader Al-Awadhi statement that traditional methods would produce 45 billion barrels. The BP results, which show a range of 2460 B barrels to 2600 B barrels for world URR, are also in close agreement with the latest projections from Hart and Skrebowski on world URR of 2420 B barrels and the varying projections in the range 2500 B to 2600 B barrels in ASPO newsletters #73 to #80.
As I mentioned in my reply to Gail the Actuary, I am following in the footsteps of many TOD participants who have gone before me looking at past oil production to get some insight into future production. Since others have also been making models and projections on TOD, I am trying to understand the nature of your concerns.
Are you addressing the use of analysis in general? Are you addressing the value of analysis that uses a number of logistic functions to model multi-peak production profiles, such as the use of loglets in the Fischer-Pry decomposition, which is a challenge for many curve fitting techniques? Are you addressing the use and ability of the “least squares method” to fit a number of logistic functions to model multi-peak production profiles?
And my comment was intended to indicate that the lack of appearance of new "ghawars" was definitely not a reason for the lack of future production bumps, as if that was the case being, then there would be no bumps in the 1990's and 2000's.
I look at the world, not at my crazy numbers and a way to correlate them nicely into a chart. I look at the world and see further bumps that would add to your final big bump in the future, so that the final curve would be the sum of those future bumps and that last bump of yours. It could even be another negative bumps, like those you've used.
I see then that these predictions are worth zero, they only indicate a good correlation in past summed curves. The only way this theory could be of any use would be if one could know if further bumps are possible and produced, and how much. THEN, one would HAVE to add those curves to the last one in blue in all of those charts.
You would by then have your own PREDICTION.
OTOH, I say we are almost or past the peak. That is obvious and doesn't come from this analysis, rather from many others that didn't depend on curve fitting (HL comes to mind), numerology or astrology.
Amazing indeed. But it is rather like watching the horoscope that says that it is about to rain, but then again it may not rain. How that kind of knowledge is worth anything is beyond me. I couldn't care if it was astrology or numerology, if it told me exactly what was going to happen RATHER than telling me exactly what I want to hear, then I would gladly accept it. But it doesn't.
STILL, it is only numerology. Period. Even stopped clocks give always too good answers (160 and 260?) everyday.
...Which renders your theory, among many others moot. You are not considering many things, like politics, specific geological problems, human error, worldwide actions/reactions, wars, etc. You just plot the line and tell us "if x doesn't reach y in z time, then abracadabra". That's nonsensical analysis. Even if your numerology is somehow based on a much more fundamental phenomenon, you can only aspire to a certain curve fit that doesn't wipe out the noise. And this noise could falsely trace you to the final URR between 160 and 260. This means that even from two years now you can't tell final URR of KSA. You can only guess, or aspire to know.
You could eventually be very wrong.
Which is to say that a newly created theory has achieved to bring on the same results that we've already known / suspected. Brilliant. That is not enough. Learn more of Scientific Method: that is not enough.
I know nothing about Fischer-Pry. I am addressing to your charts and to this simple reasoning: you took all of your charts and fitted bell-shaped curves with "least squares method". Fine. You then, show us your bell curves, they are a lot. Then, you plot a final one, blue painted, which is always given as the final curve, the final bell shaped curve, and yet you don't give any reason for us to take that blue curve as the final curve of history in oil production, you took that from granted. That's what I question and what seems to me as the greatest flaw.
Because, you see, a great way to see if your theory has any predictive value, is if you do what I challenged you to do: wipe out years to your plots (in several different charts), trace back your curves, and let us see if your charts always tells the same story. I bet they don't, I bet they always tell a different URR, a different story and different bell curves.
I am not against "analysis in general", as I commended the spirit of it. I like what Hubbert made. But he made a different approach. He didn't use curve fitting to predict URR. He made the other way around. That's why I called this "numerology".
I think that we are going to have to agree to disagree on the merits of this post.
I am following in the footsteps of many TOD participants who have gone before me looking at past oil production to get some insight into future production. I would agree with you that external events affect the production profile. However, countries have been producing oil for many years and I guess some of us believe that external events should not dissuade us from the challenge of analyzing past production to predict the future. Check Khebab’s latest post on September 22, 2007 to see the range of analysis and predictions. Also, while the external events have a large effect on a single country, they have a much smaller effect on world production.
Previous posts on TOD have attempted to model past production using different approaches, i.e. loglets, successive Fischer-Pry decompositions, etc. All of these approaches result in a number of logistic functions fitting past production to gain some insight into plausible future outcomes. Being familiar with least squares, I decided to try a different approach, i.e. directly fitting a number of logistic functions to the production history using the well known least squares approach and Excel. I also was interested in seeing whether the results would provide greater insight into the HL method and when it can be used.
As you have noted, one can over fit the data. On the other hand, one can also under fit the data. It is a decision that to some extent is determined by the variation in the data being fitted. The KSA and Kuwait data were quite variable, very non-logistic, and I used 6 and 7 logistic functions to model these cases. The more critical issue, as discussed in the post, is how accurately to treat the later years. Some of the results speak for themselves. The projection of a URR of 45B barrels for Kuwait compares well with Dr. Nader Al-Awadhi statement that traditional methods would produce 45 billion barrels.
Looking at the results, you will note that the early logistic functions are small and decay quickly. Their main purpose is to unload the last logistic function so that it can do a better fit on the later years.
For the EIA and BP world production data, I addressed the question of over fitting and under fitting by showing results using 6 and 2 logistic functions. For the BP case, the difference between the two results was 5.6% on the URR and a shift of 20 months in the peak. This gives an indication of the low sensitivity of the results to the number of logistic functions used when the production profile is close to being logistic. The two and six logistic BP result are interesting because they are in close agreement with the latest projections from Hart and Skrebowski on world URR of 2420 B barrels and the 2600 B barrels projection in the ASPO newsletter #80.
My ultimate aim was to study the relationship between the annual supply rate of change (ROC) relative to the annual demand ROC near the peak to see whether we might see an apparent peak, or as you mentioned “Peak Lite” (New to me). For 2007, the results indicate that we should be seeing a supply ROC of less than one percent. Looking at the latest IEA data, I will be surprised if the 2007 production is more than 0.5% larger than 2006.
I do quite a lot of non-linear least squares fitting and I try to stick with Bevington's CURVEFIT as often as possible because the systematics are understood by quite a few people. I'd be interested to know the genetic relation between this program and the one you use.
I have to agree with Luis, that if you know that the main current production comes from a field that was recently discovered, you would do best to include this in some way. Before I read his post, I had been thinking that you might want to add a technologically learning curve enabled huristic by insisting that the widths of you curves decrease with time. People know how to suck a field dry faster as they gain experience. With non-linear fitting you can do all sorts of things like this and you don't need to actually work out the partial derivatives any more because of how fast computers run now. (I expect that this is what your program does.) On the other hand, adding in interesting constraints can introduce degeneracies that inhibit convergence or make it impossible using a stright forward gradient approach. To deal with this I will go to the AMOEBA program given in Numerical Recipes which will not sucumb to this problem. I expect that you could make the width of your functions a simple function of their time centers or simply rescale the time axis and use fixed width functions in the rescaled axis and you would not see large issues with degeneracies.
It is worth remembering that daily production is likely to be very correlated so that your number of degrees of freedom may be much lower than the number of data points would indicate.
If you need help including constraints in your fitting, I'd be happy to try to assist.
Chris
I think for the first time I'm actually clearer maybe :)
I think a simple linear weighting is enough at least for a first pass. I like how your saying decrease the widths of later curves but don't you get the same result by using a global linear weighting that weights early data above late.
The slope of this line is effectively increased product rate vs enhanced URR. I'm suggesting that 2:1 is a reasonable guess.
Its effectively the same and simpler.
From the article:
a = constant affecting the height to width ratio of the logistic function
If you make a=a(Tp) then you can constrain the width to be a function of time. It seems to me now that reparameterizing t will leave you leave you with a curve that is not the logistic curve in actual time. So, to keep it a sum of logistic curve you'd have the width vary by a factor of two or three perhaps.
As you can see from the equation for P (there is a closing parentheses missing in the numerator), ingnoring the constants, it peaks at a value of 0.25. The half width therefore occurs at a value of 0.125. Application of the quadratic equation give -a(t-Tp)=ln(3+2sqrt(2)) or ln(3-2sqrt(2)) so a=2*ln(3+2sqrt(2))/delta_t year^-1 where delta_t is the desired half width. If we assume that drilling equipment in a country is obtained at a constant rate and is repairable so that the capacity to drill increases with time then we might be motivated a little to rise to peak at least on a shorter timescale as more equipment is accumulated.
I don't think weighting would act as much of a constraint on the halfwidths of the components.
Chris
Okay got you.
I agree with you thats a nice analytical way to do it.
Non-linear least square regression programs I'm familiar with let you apply weighting functions a number of ways.
The weighting function would be this ?
So the weight is increased drilling equipment and better technology which can be treated as the ability to drill more wells since this model is not taking into account the physical limitations of how closely spaced well are this is in the data.
So its a linear increase in well drilling capability to start with we could simply use rig counts. Later this saturates and then technical advances make a rig more powerful but for a first pass a simple analysis using rig counts makes sense.
So a normalized weighting by rig count seems pretty reasonable.
Note this goes right to my assertion in the past the the logistic fit is arising from the birth and death of wells.
If this is true a dependency on the "birth mothers creators" or oil rigs makes sense.
This correct will correctly discount later drilling efforts around the peak and post peak since more of the URR will be correctly weighted back on the earlier well data.
The only flaw is you have a undercount past peak where rig count stays constance or declines but technological boosts continue. The earliest data when their are few rigs may also be noisy.
Is the number of active rigs available for the US and is split between gas and oil ? My understanding is a lot of the data does not differentiate between gas and oil drilling.
If not I bet we have good numbers for the North Sea ?
Data anyone ??
I think we have demonstrated that the use of Logistic-styled curves precludes us from ever trying to model the generated profile in terms of real-world analogies like rig count. As Khebab put it succinctly in other posts, we can either (1) curve fit or (2) use a model.
This post by Apparent Peak is impressive but it remains curve-fitting.
I will bring this up again, but the minute you invoke a birth-death model on oil production via rig count you will run into the contradiction of Current Carrying Capacity != URR. Deaths in the birth-death model remove entities from the Current Carrying Capacity but they cannot remove anything from the URR because URR is cumulative (while carrying capacity is not).
See this post, "Logistic Model for HL purely a Birth Model"
http://mobjectivist.blogspot.com/2007/09/logistic-model-for-hl-purely-bi...
Its all a matter of matching variables if the focus is on wells and well production when a well is capped the carrying capacity is reduced. I.e the field cannot have more wells.
So I would say capping a well can easily be mapped to a death and whats lost is the capacity of the field as far as how many wells can be drilled.
If its really about wells which it seems to be its more about how you can extract the oil. In time the number of places you can drill a new well drops and thus the carrying capacity drops.
The terms used in the Logistic equation URR/Production rates are simply proxies for the underlying physical real logistic process of well creation death and loss of places to drill or carrying capacity.
I'm not sure why your mapping the logistic equation back to oil itself I've not proposed this. I don't think it has anything to do with oil it has a lot to do with exploitation of a resource in the case of oil this is wells and prospects for drilling more wells.
I'm mainly interested in a fitting method and applying constraints. When I saw the shape of the data, it seemed to me that a narrow function with large amplitude might do something that looks a little like the recent data, and after reading Luis comment that a big field was tapped recently and seeing the video saying that the same field is in decline I thought a constraint that makes production from new fields faster than production from historic fields might have a physical motivation. I don't have a big stake in the idea that this might be predictive. I'm willing to accept Richard Gott's method of prediction. We've been using oil for about 80 years so there is about a 75% chance that we won't be using it in 240 years. And, I think that there is real predictive power in looking at the pattern of discoveries of oil fields. My comments, though, are more about trying a few things in fitting.
Chris
Let me parse one of the statements you make:
You say the "terms used in the Logistic equation ... are simply proxies for the underlying physical real Logistic process". This reads like a tautology. Did you really mean to say this? Because when I read it, it looks like you are saying that the real physical process follows the Logistic equation.
But then you say this, in responding to me:
This statement completely contradicts your tautological statement preceding it. You, not I, are proposing this.
Good catch and a sharp eye for noticing that missing bracket Mdsolar.
Thanx
No sweat. When you said it was the derivative that was info enough. It is kind of a pretty function. Symmetric without the heavy handedness of the Guassian. I use the error function to fence parameters sometimes to get well behaved convergence but implementations are dicey because it is an indefinite integral. I might switch to the logistic curve for this purpose.
Chris
This is my first crack at non-linear curve fitting and I am not familiar with Bevington's CURVEFIT and do not have access to any high powered NL programs. I just set the program up in Excel using equation 2. Having the predicted values and the actual values I calculated the SS and then launched the “Solver” algorithm in Excel and let it find the minimum.
I had to use different initial guesses to obtain an idea of the stability of the solution and in general there appeared to be a lot of local minima over a relatively flat range. When I added an initial guess with a small negative logistic, which converged to -1.2 B barrels, as shown in Fig 6, there was a staggering drop of approximately 100 B barrels in the URR and a major reduction in the SS. This then raised the question of how accurately to fit the later years?
From the short description given in Excel, the Solver algorithm appears to be a type of relaxed gradient approach. While I understand gradient methods, I am not familiar with their intricacies and pitfalls. I was just thankful that such a powerful tool was available in Excel. How does Bevington handle multiple valleys? Does it search for the lowest one?
I will review the comments from the other TOD participants regarding the addition of a technology component. As you can see, there are already concerns being expressed regarding over fitting.
With regard to the comment “I have to agree with Luis, that if you know that the main current production comes from a field that was recently discovered, you would do best to include this in some way.” I am not aware of any data set that is available from a recently discovered field that could be subtracted from the world production and treated as a separate sub-data set.
I would be interested in having further discussions regarding this methodology and how Bevington could add to it. Send an email to Stoneleigh, the publisher of this post and who has my gmail address and then we could communicate off line.
Like Gail I am worried about over fitting.
A test of whether this close fitting has any predictive superiority over a single logistic is to truncate the time sequence at some point in the past, produce a fit of the remaining data and see if it produces a better prediction of the truncated data.
My shared caution about over-fitting is in part due to the fact that Fourier analysis will give a fit to any continuous finite single valued function. This includes a set of time functions that are identical up to a certain point (which could be the present time) and thereafter diverge strongly.
There are many functions beside sinewaves that can be used for such fitting. Logistic curves may not have the required orthonormality to fit any curve but they can fit a great many.
In reply to a previous comment about over-fitting Stuart Staniford described it is as "pure epicycles" recalling the efforts of early astronomers trying to fit the motions of the planets to a earth centred universe by fitting epicycles onto epicycles onto epicycles.
Making a assumption of the logistic curve for fitting in the first place is claimed to be over fitting by many :)
I think this approach has merit and the number of knobs to turn can be reduced once we have a good reason to reduce them.
Right now it has a constraints problem that needs to be solved. We have no way to constrain the number of curves. So its not clear how to back down from the "over fit" condition.
In other posts we are suggesting one constraint based on active rig count.
So first lets see if a few reasonable constrains can help reduce the "over fit".
As I have set up this methodology, I can select from 1 to 7 logistics to model the production history. For the strongly variable non-logistic cases of KSA and Kuwait, I have tried 6 and 7 logistics. For the closer to logistic cases of world production, I have shown solutions for 2, 5 and 6 logistic fcns.
As I have noted in the post, my big issue is how to treat the latest years, average them or fit accurately. At this time, I believe that averaging is more realistic since in a few cases the accurate fit gave an unrealistically low URR. See Figure 17.
I tried one logistic fcn and it was very bad because I did not have sufficient data before 1960 to anchor the left hand side of the logistic fcn. Clues on where I can get earlier data on world production would be appreciated since I would like to see what one logistic can do. Also I am looking for data on Russia.
The early logistic fcn are small relative to the last one and decay quickly. As far as I can figure out at this time, their main purpose seems to be to unload the last logistic function so that it can do a better fit on the later years.
Yeah it has some problems but also quite a bit of merit.
Although it is curve fitting the key to curve fitting is generally to use real variables to control the constraints and as data filters.
My suggestion is to center your logistics on wells drilled per year. This is fairly close to some of your better fits.
As the price of oil drops drilling activity drops and future production "declines".
I really think your on to something with your approach and it seems to be suggesting and additional factor is at play.
1.) The obvious reduction in immediate output during embargos or price collapses.
2.) The secondary effects on drilling and investment activity and thus future production. So a short term event echo's for quite some time through the production profile.
3.) This leads to a rise and fall in production capacity and rate of expansion which determines future production rates.
4.) The depletion effects fields no longer worth drilling this increases linearly with time so the number of wells drilled decreases naturally as you simply run out of places to drill.
In any case if you agree its all about well which makes sense since the cost of a well is constant regardless of its production rate. Dry holes do not come with a discount. The actual oil/gas production rates are just proxy data for well drilling activity and success rates.
Its really not the oil and gas industry its the oil well and gas well industry. The don't call the mining industry the metal industry. We have no problems focusing on the expense of extraction for other materials like coal and metals but for some reason for oil the mining costs are swept under the table and the focus is on the production rate.
In any case thats for your work its given me more to think about which is why I can't resist the oil drum.
"My suggestion is to center your logistics on wells drilled per year. This is fairly close to some of your better fits."
Wells drilled is not an independent variable. Tautology alert?
As I mentioned in my response to Gail, one can over fit the data as well as under fit. It is a decision that to some extent is determined by the variation in the data being fitted. The goal is to find the right balance. In the case shown in Figure 17, it was obvious that over fitting was the case since it gave an unrealistically low URR.
The more critical issue, as discussed in the post, is how to treat the later years. Based on the results in Figure 17, I think that averaging is the more appropriate approach.
However, some of the results speak for themselves. The projection of a URR of 45 B barrels for Kuwait compares well with Dr. Nader Al-Awadhi statement that traditional methods would produce 45 billion barrels. Also the BP results for 2 and six logistic fcns, which show a range of 2460 B barrels to 2600 B barrels for world URR, are also in close agreement with the latest projections from Hart and Skrebowski on world URR of 2420 B barrels and the varying projections in the range 2500 B to 2600 B barrels in ASPO newsletters #73 to #80.