101 comments on The Shock Model (Part II)
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101 comments on The Shock Model (Part II)
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Khebab this is surelly precious stuff. While I’m still diggesting it tell me something, does that definition of reserve growth include discovery?
It seems to me that the definition of URR growth used by CERA, USGS, et al. includes what we call discovery. If so aren’t you including discovery twice in the model?
No, it's not included twice. Reserve growth does not include discoveries, reserve growth is measuring how your initial discovery estimate is changing over time (it's a growth factor). The final URR is the total discovery volume + reserve growth. The problem is that the ASPO discovery curve is including some amount of reserve growth. That's why I introduced the parameters t_start and t_init in order to better control when the reserve growth factor should start.
We have to watch out on these reserve growth laws however. In the case of parabolic growth, i.e. a square root of time growth dependence, the amount of reserve growth is infinite !!!!!
see here:
http://mobjectivist.blogspot.com/2006/12/conun-drum.html
It is easy to prove this as all you have to do is look at the growth value for Time = infinity. But the most amazing insight that you can see from this and Khebab's curves is that even though we have infinite reserve growth, we still see a peak in a few years! You read that right:
Even though we have infinite reserve growth, we will still see peak oil in a few years time. Has that sunk in?
No one that I know of is mentioning this mathematical reality that extraction and production can not keep up with reserve growth, even though there is an infinite supply.
But we know that the growth has to limit itself at some point in the future.
http://mobjectivist.blogspot.com/2006/01/self-limiting-parabolic-growth....
Which makes the infinite supply consideration a moot point anyways.
Well, Web, you may have actually done the undoable....prove that no matter how much oil there is....there is actually no oil! :-)
(that's a kick....I once had a math teacher who proved that the length of a coastline was always infinite! If you looked at it from space, you had one length, but as you moved closer you would be able to view more inlets and tiny curves and jagged edges you would see...the closer you got, the longer the coastline got, so the only thing limiting it's length was how close in the magnification was...in other words, how close you were looking....(!!)
(gee, I love the precision of mathematics...:-)
RC
Remember, we are only one cubic mile from freedom
Another coastline paradox often discussed in college science classes. How fast does an oblique wavefront propagate as it hits the shore at a more and more perpendicular attitude? It actually approaches an infinite speed at the limit. However, the professor would be smart to add that this is purely a phase speed that carries no information content whatsoever.
Likewise, your contribution adds absolutely no informational content to the discussion :-) :-) :-) :-) :-)
I know, but it was fun! :-)
RC
re: Even though we have infinite reserve growth, we will still see peak oil in a few years time. Has that sunk in?
Agreed. Reserve growth is great material for spin-doctors! you can actually claim to have a forever growing URR which of course is mostly irrelevant to the problem of increasing flow rates.
I have limited growth to a maximum of 95 years (see Figure 6) but you're self-limiting parabolic growth could be a good substitute.
It's not hard to analytically solve the power-law forms (unlimited growth) but the self-limited foms need numerical solutions. In lieu of solving numerically, I have had good success modeling this limiting behavior with two damped exponentials, which essentially mimics the hM(t) and hG(t) terms that you have in Eq. 7. The following is an impulse response to a delta discovery @ T=1900:
from http://mobjectivist.blogspot.com/2006/02/decomposing-reserve-growth.html
It looks like this when put on top of a real reserve growth curve:
Whether this is worth doing, and whether this is mathematically valid, I have to ponder a bit. But since you essentially came up with this idea independently of me, I think it is worth pursuing.