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).
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.
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.
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:
I'm not sure why your mapping the logistic equation back to oil itself I've not proposed this.
This statement completely contradicts your tautological statement preceding it. You, not I, are proposing this.
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.