[WebHubbleTelescope]

$this->bbcode_second_pass_quote('jimk', '')$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')look familiar?

[jimk]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')I don't find it odd that R is actually the prey term. You have to remember that R is oil in reserve. Forget the "c" term you added. R will decrease to zero and the thing that looks like the production curve is P*R, which is the absolute rate of change in R according to your equation. Which means the PR curve you showed earlier is the correct one to use as the production curve.

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('jimk', '
')Anyway, thanks much for seeing the link to predator-prey, that is really interesting to think about. I will take some time to study your discovery / shock model next.

[jimk]

I like the general angle you're proposing with this discovery / shock model. I think the predator / prey equations are really assuming that geography doesn't count, that predator and prey are uniformly mixed.

Here are some additional factors... I wonder if you have thought about these or included them in your model...

Some oil is easily accessible, other oil is much more difficult. Probably depth is the key factor, under how much water and under how much rock. This accessibility will matter not just for discovery but also for depletion. Deeply buried oil will be harder to discover and harder to recover.

There is also the matter of flow rates, and probably quality of what comes out, heavy/light, sweet/sour, stuff I know nothing about, but it goes all the way to shale oil I suppose. Some oil will be easy enough to access but difficult to use effectively.

Both difficulties, of access and of use, can be abstracted as "net energy". To make a joule of energy available in e.g. diesel fuel, we will need to burn how many joules of energy in amortized exploration etc.

Another very interesting challenge that seems to be arising: To extract fuel, we not only need fuel to power the rigs etc., but we also need steel and whatever other materials. These other materials can also become scarce or expensive. Maybe we just don't have enough molybdenum or whatever to build enough pumping platforms to access all the deep oil fields we need in order to increase production to whatever rate.

It's not just a matter of scarcity. There is also an increasing energy cost to mine/produce the various materials. E.g. aluminum and concrete are not scarce, but are energy intensive.

What became clear to me in thinking through the equations that turned out to be a predator and non-renewable prey - how the peak and downslope of petroleum production looks, that depends a lot on what alternatives we develop or exploit. If we ramp up say coal-to-liquid so that energy scarcity doesn't hinder our efforts to extract petroleum, then the downslope will be relatively steep. Alternatively, the decline of petroleum could bring the decline of our ability to find and extract what's left, in which case the downslope won't be as steep.

What I am starting to see now is that energy scarcity is not the only factor. Water, of course, is huge, but that may be mostly indirect - oil can't be produced without humans, humans can't live without food, food can't be grown without water. Whereas the path to e.g. molybdenum could be shorter: oil can't be produced without steel, steel can't be produced without molybdenum. There must be many such potentially limiting resources. But as the next decades play out, we will not actually hit every possible wall. One or two walls will likely suffice to reduce our speed considerably! Which walls will those be? Or maybe we will innovate around every wall for centuries to come!!!

One thing that these kinds of models might be able to do is to help us understand which wall is going to be the main one that limits growth in consumption. It seems like such a model would have to include maybe the most likely dozen or so walls, and from there perhaps some kind of Monte Carlo set of simulation runs could winnow the contenders down to the most like champion/villain or two.

That's one thing that I think is useful in developing these sorts of models, is to be a bit clear on what one hopes to learn from the model. Given that reality is very noisy, the question of "when will we hit peak petroleum production" - that is hard to determine and actually not very meaningful, plus or minus a few years. Peak in 2005 or 2050, ok, that is plenty meaningful! More useful and meaningful, I think, is: what will the peak production level be? 85 MB/day or 95 or 105? Also, questions like: what will the production level be in 2020? 95 or 85 or 75 MB/day?

These questions of production levels are mostly useful from a consumer's point of view. If you're involved on the production side, it may be more interesting to get some kind of picture about: what rabbits must I learn to pull out of what hats, if I am to be producing effectively in 2010, 2015, 2020. How should I be investing today in order to be profitable in the future?

[jimk]

This non-renewable prey system does not end up recovering all the resource. The above is a plot of the asymptotic remaining resource as I tweak a couple parameters.

I leave constant a=0.00003; P(0)=1E-07; I vary b, the depreciation or death rate, which is correctly labelled in the figure. On the other axis I vary R(0) from 6000 to 12000. (Sorry about bogus excel axis labels. I don't know how to control that!)

The first wild thing that one can see - the more the initial resource, the less gets left behind. More intuitively, the faster the death rate of the predators, the more gets left behind. The greater initial resource allows P to build up bigger which then allows more resource to be recovered ultimately.

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('jimk', 'T')he first wild thing that one can see - the more the initial resource, the less gets left behind. More intuitively, the faster the death rate of the predators, the more gets left behind. The greater initial resource allows P to build up bigger which then allows more resource to be recovered ultimately.

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('jimk', 'H')ere are some additional factors... I wonder if you have thought about these or included them in your model...

[jimk]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')Or else what could happen is that the P term goes to zero rapidly, so that P*R also drops to zero, thus preventing R from depleting. But why this would depend on the intial size of R I don't know.

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('jimk', ' ')What a big initial R does is to feed the predators and let them grow, so that by the time the die-off starts, there are enough predators around to chew deeply into the remaining R.

[jimk]

Here is an R vs P trajectory plot for a=0.00003; b=0.05; so that (b/a) = 1666. Easy to see here how a larger starting R results in a smaller ending R.

[jimk]

$this->bbcode_second_pass_quote('ElijahJones', ' ') We don't need precise numbers to know that peak oil will happen within a window between 2002 to 2020.

[WebHubbleTelescope]

Would you agree the finite ending R is due to a "giving up" factor which occurs at the predator population can't sustain itself? I use "giving up" rather than "dying off" to keep it from devolving purely into population dynamics.

[jimk]

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'W')ould you agree the finite ending R is due to a "giving up" factor which occurs at the predator population can't sustain itself?

[Doly]

$this->bbcode_second_pass_quote('jimk', 'I')f the energy generated by the oil produced can't be used to support that labor and materials plus a litle profit, then oil production has become a losing proposition.

[jimk]

$this->bbcode_second_pass_quote('Doly', ' ')"economies of scale" depend on easy transport.