Excellent post Novus. Couple of things though: 1. You can never scare a real doomer. There are people here that would see a hoarde of zombie heading towards their house and say "See honey! I told you this was going to happen!" 2. As several others pointed out, your math is off. The problem with your business analogy is that you started the day with nothing, paid all your bills, and still had $90 left over. That $90 doesn't have to be reinvested. You can use it to buy dinner, pay your rent, whatever. Tomorrow you just show up and get another $90.

In a closed system the available energy after n itterations is startingenergy*EROI^n. Fraction of energy which is available for use though is 1-1/EROI which drops of quite dramatically with EROI's below 10.

The whole theory basically falls apart without the corollary. If we were to graph the logic that anything with an EROEI greater the one could be exploited sustainably then falling EROEI would have little impact on peak oil. The system would basically take it in stride as this graph shows.



The corollary theory is what causes the trend lines to turn negative on the graph below. This graph is the visual interpertation of the math I have shown before.



It is all in the math. Look back to the 4th iteration where the break point ocures.

100 -> 'A' -> 190 -> 'A' -> 361 -> 'A' -> 686 -> 'A' -> 1303

How much oil energy was pumped on the forth iteration and of that total how much was net and how much was cost?

190 units came out of the well
361 units came out of the well
686 units came out of the well
1303 units came out of the well
------------------------------------------
2540 total units came out of the well

Now break the total into cost and net. The cost was 1237 and net was 1303. The Compond EROEI after four iterations is only (1303/1237) = 1.05

There is no sence in me pumping any more units out of this well.

I know I am right...I have just not explained it in clear enough terms.

If your whole theory falls apart on this point, then I say your whole theory original theory falls apart.

Still, I thought your original point was that EROEI is not usually taken into account, and it makes things much worse. Well, that's still true. It's just not as bad as you thought.

Just a point about that lower figure. The shape of the net resource curve shown in blue doesn't have to look like that. It's determined mostly by what curve you assume EROI will take. I reproduced the figure assuming EROI to be a declining log scale function. My lower curve is pretty symetric (i.e. it doesn't have a squenched to the right look with the cliff-like drop off.) Also the pink region is exagerated in the first part of that curve. For an EROI of greater than about 50, the difference between the two curves is imperceptible.

The problem, IMHO, with the arguement that EROI doesn't matter, is that there really aren't any energy systems in existance that aren't pretty well stressed. Natural gas is North America and Europe is probably in worse shape than oil. Coal is significantly declining in EROI. Nuclear energy requires huge start up costs, operates via electricity which is incredibly inefficient to transmit, and the recoverable amounts of uranium are not very big. (Yeah, I know, seawater uranium, Buck Rogers, blah blah blah.) EROI wouldn't be a huge problem if there was an energy source that could replace oil, but there's not.

You only put 100 units of your *own* energy into this process. The rest of the inputs came from the well itself. You have netted 1303 - 100 = 1203.
1203/100 = 12.03

You have multiplied the energy you started with by 12.

Novus, you are right to assume that EROEI decreases with each iteration, but as smallpoxgirl alluded to, how fast it falls depends on the resource.

Let's say that between an EROI of 1.9 and 1.8, Oil EROI falls at about 1%(1 - 1.88/1.90) each iteration. Please excuse the rounding errors...

1 (EROI=1.90): 100 -> 'A' -> 190 = 90
2 (EROI=1.88): 101 -> 'A' -> 190 = 89
3 (EROI=1.86): 102 -> 'A' -> 190 = 88
4 (EROI=1.84): 103 -> 'A' -> 190 = 87

In 4 iterations our little well A, which happens to be losing EROI with each passing day, has produced 760 (190*4) units with an input of 406 units, at an average EROI of 1.87.

Each iteration you are adding to the cost of producing the oil. Each time you take a little bit more from the energy you got back, but thats all you are doing because you are actually getting 'free' energy with any resource over EROI = 1. But you are right, EROI does not stay constant, which I did assume for 4 iterations. But how fast EROI falls, as we can see with Oil, depends on how much is left.

(again, sorry for the edits)

Here is my version of the proof marked-up:


EROIE reinvestment calculation

Nicely done.

...I had to stare at it for about 30 minutes

...but I still don't get it why you are reinvesting everything...why not use the energy for something else?

Why reinvest everything? Good question. Why did we shoot every last passenger pigeon in North America until they went extinct?
Answer: Basic human greed, pure and simple.

Let's say you found a broken slot machine in Reno. You put in $1.00 and out pops $10.00. It happens three times in a row. Would you keep putting in the coin until someone stopped you? Or would you walk away with only $30.00?

Hmm, well, lets say I was the leader of a semi-intelligent species. If I knew that there was only $365,000 in the machine and the basic needs of my species cost only a dollar a day, I would maintain population and go back every 10 days for more. That way my society would have the benefit of technological and cultural growth for a thousand years, and by then we would be getting our 'money' from the sun.

doh!

Your problem is that you are way too sensible! Thinking about our future, and all that extraneous stuff.

yeah, it's a mental disorder called idealism

don't worry, it will pass...

None, because Reno sucks dick. Let's go to Vegas instead ^^

http://static.flickr.com/54/128287988_3298bfe793_o.png

Novus,

The graph you supplied shows that there is a net gain for energy reinvestment all the way to EROEI = 1. See the little z* on the graph? It is only after z* that the blue area of the graph, or the net profits if you will, goes to zero. at all points above EROEI = 1, there is a profit to be had.

emailking has it right when he's telling you that your net is 1303 (currently available) - 100 (starting) = 1203 units.

You will have 12 times your starting energy after 4 iterations of reinvestment.