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88 comments on Modeling Oil Production to Estimate URR - Saudi Arabia, Kuwait and World
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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.