Commentary
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For those who where wondering why the oil production from a oil well should follow a logistic curve, there is some interesting calculations performed by Danny Abrams (MIT Postdoctoral Fellow):
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Publicité
ETUDE DE L'EVOLUTION ECOLOGIQUE de la DESTRUCTION des ENERGIES FOSSILES . PETROLE .OIL.GAZ.GAS.RAREFACTION DU PETROLE .REPERCUSSIONS . EOLIENNES. NUCLEAIRE .NUCLEAR POWER.
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For those who where wondering why the oil production from a oil well should follow a logistic curve, there is some interesting calculations performed by Danny Abrams (MIT Postdoctoral Fellow):
Assuming an ideal pressurized container:
The volume of liquids getting out the container at time t is:
After some algebraic manipulations and assuming some numerical values, you get the following result:
I have indeed seen this analysis before, but I went through Abrams derivation and noticed that he made a specific assumption of the result he wanted at some point.
I do not understand why he did not just try to do the finite-element numerical calculation once he had the DiffEq. This is just a pure fluid dynamics calc much like that I collaborate on with people where I work. They solve these temporally all the time but know for a fact that this is all numerically calculated.
An important and intriguing find, but one that is frustrating to no end.
The problem I have with this approach is that the logistic curve is supposed to apply to things ranging from cell phone to whale bone. So this just raises a new question, how are whale stocks equivalent to a pressurized container?
I would be looking for a common feature of all these cases, rather than models specific to one case (unless there is an obvious way to show how they are equivalent). The common feature of the whaler and the oil driller is the profit motive. I think the model should (and can) be derived from that.
I think that the reason the logistic curve applies is mainly to do with economics, and little to do with geology. I realise this is pretty heretical. It's not really important though, as no model can capture the political and macro-economic factors, so Hubbert's model is close enough.
As an engineer, I think it would be nice to understand the causal mechanisms, even if there is a convincing correlation. But I certainly can't tell people oil production will peak shortly "because of Hubbert's curve", because that is like putting the cart before the horse.
My discussions about peak oil are with ordinary people, including science teachers and retired scientists, and they can't follow all the specialized technical jargon. Pointing out the basic facts, such as that we are using oil much faster than we are finding new sources of oil, and that new oil is getting much more difficult to find and expensive to produce (like oil sands, deepwater oil, etc.), is the best approach that I know of.
For people with little technical/scientific knowledge, I've also found that hitting the economic angle will at least get them thinking about it. The boom times are over, and it looks like we're heading into a recession (or worse), so people will start listening to economic (money-savings) arguments. There is enormous waste in this country, and a lot of money, and oil and other resources, can be saved without a lot of trouble. Building insulation is one area that I think doesn't get enough attention. It's an investment that keeps paying dividends(savings) for a long time. (Disclosure statement: my son-in-law is in the construction business). I remember back when the Alaska pipeline was first proposed, someone did a study and said that, if they took the Alaska pipeline money, and used it to insulate homes in New England, it would save as much oil as the pipeline would deliver. And you'd still have the oil!