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