[smallpoxgirl]

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.

[Novus]

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.

[emailking]

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.

[smallpoxgirl]

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.

[emailking]

$this->bbcode_second_pass_quote('Novus', '
')
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

[turmoil]

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)

[WebHubbleTelescope]

Here is my version of the proof marked-up:


EROIE reinvestment calculation

[turmoil]

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'H')ere is my version of the proof marked-up:

EROIE reinvestment calculation

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('turmoil', '')$this->bbcode_second_pass_quote('WebHubbleTelescope', 'H')ere is my version of the proof marked-up:

EROIE reinvestment calculation

[turmoil]

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'W')hy 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?

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('turmoil', '
')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!

[turmoil]

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'Y')our problem is that you are way too sensible! Thinking about our future, and all that extraneous stuff.

[0mar]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '')$this->bbcode_second_pass_quote('turmoil', '')$this->bbcode_second_pass_quote('WebHubbleTelescope', 'H')ere is my version of the proof marked-up:

EROIE reinvestment calculation

[ohanian]

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'H')ere is my version of the proof marked-up:

[bdmarti]

$this->bbcode_second_pass_quote('Novus', ' ')This graph is the visual interpertation of the math I have shown before.

[Novus]

For those who disbelieve the corollary to net oil you seem to be tripping over semantics.

I am not saying EROEI = EROEI - 1

That does not make any sence. I am talking about compond EROEI which is something I have not really defined. You must remember that these fields are finite in size. What I mean by compond EROEI really talking about a concept of Net URR where URR is Utimately Recoverable Reserves.

The formula for Net URR = (EROEI -1)/EROEI

So if well 'A' has a URR of 10,000 units of energy and EROEI is 1.9 I will still be able to recover all 10,000 units of energy. However, only 4700 units of that URR will be Net Oil. The other 5300 units of energy will be spent recovering that energy from well 'A'.

That is the corollary to Net Oil and I know it is correct. The graph from before only woks in terms Net URR which is the real heart of the Net Oil theory.

[turmoil]

Novus,

(EROI - 1) / EROI = Amount of energy used in each iteration

Example:
(2 - 1) / 2 = 1/2 of the produced energy was used to produce it

URR is how much you can produce, regardless of how much energy investment it requires. It is an estimate based on how fast you think EROI will fall. The reason you can't produce more than the URR is because EROI is dropping to 1.

If
ER = Energy Returned/Recovered
EI = Energy Invested
ES = Energy Start (the kick start energy)

then
SUM ER = URR = Ultimate Energy Returned
SUM EI = Total Energy Invested
Net Oil = Net URR = SUM ER - [(SUM EI) - ES]

Example:

In this example we will reinvest all the energy gained in a well that loses EROI really fast (since we are really greedy and dumb).

Total Oil in Place = 1,500 barrels
Starting EROI = 1.9

1: 100 -> 'A' -> 190

EROI = 1.5

2: 190 -> 'A' -> 285

EROI = 1.1

3: 285 -> 'A' -> 313.5

On the next iteration EROI would less than or equal to 1.

SUM ER = URR = 190 + 285 + 313.5 = 788.5
SUM EI = 100 + 190 + 285 = 575
Average EROI = SUM ER / SUM EI ~1.37

To calculate Net Oil, leave out the "kick start" energy and find the difference.

Net Oil = Net URR = 788.5 - (575 - 100) = 313.5

With EROI > 1:
% of total produced = 788.5 / 1500 = 52.56%
% of URR reinvested = 475 / 788.5 = 60.24%
% of URR that is Net = 313.5 / 788.5 = 39.76%

Check out this page. They have a great interest analogy, as well as some cool graphics.

Edit: made some corrections. Forgot to take out the "kick start" energy

[ohanian]

$this->bbcode_second_pass_quote('Novus', '
')That does not make any sence. I am talking about compond EROEI which is something I have not really defined. You must remember that these fields are finite in size. What I mean by compond EROEI really talking about a concept of Net URR where URR is Utimately Recoverable Reserves.

The formula for Net URR = (EROEI -1)/EROEI

[WebHubbleTelescope]

The only thing I don't like about using the financial interest analogy is that it includes a time component to the equation. This tends to stump people a bit because they think in terms of compound interest and when a doubling in initial investment, for example, occurs. Nowhere does EROEI really discuss how fast things proceed. It is definitely more of a limiting kind of analysis. And more to the point, people are more likely to reinvest all their interest in comparison to oil companies, who have to continuously siphon off non-reinvested energy that an ordinary investor would typically keep compounding in an IRA, for example.

I wonder if that is what Novus is trying to get at? More precisely, what is the empirical fraction that gets siphoned off, and therefore not available for reinvestment? I'm saying empirical because it has a lot to do with profits. I would make an analogy to the tree farmer that has to resist cutting down his saplings for Christmas trees, because he can't wait for a mature stand of potential lumber.

I don't think this would be too hard to show mathematically, just take a fraction off the energy reinvested every cycle. Then, if say, half of this gets used for its intended purpose of powering NASCAR races, then Novus has a point. Which means an EROIE of 1.9 is nonsustainable, unless you have more of the patience of a tree farmer, and decide to defer gratification and not siphon off as much per cycle. Note that this only works for Novus if he assumes a value of half. I think the amount you can siphon off per cycle is <= (E-1)/E if you want to keep this sustainable.

So for large E, it is not hard to avoid oversiphoning but for smaller and smaller E, it becomes more and more difficult to resist temptation and thus decide to go for the immediate gratification, and eschew sustainability with your captive, essentially "free", source of energy.

Overall, I believe that Novus is looking at a "knee in the curve" type of analysis which provides a heuristic for a rough energy self-sustainability measure.

Basically, I am willing to hear Novus out, and try to walk myself through his thought process.

[turmoil]

Yes, indeed. There is a huge difference between keeping a country going and keeping a well going. I posted a theory a while ago stating that how efficiently a society uses its energy dictates what EROI is sustainable. The Energy Invested could be viewed as the total energy use of the country plus the required reinvested energy. I'd guess that you'd get EROI = 1 every time though, since supply is close to demand, if not equal.

EC = Energy used by the Country

ER / (EI + EC) = 1

For EROI of 1.9: 190 / (100 + 90) = 1

If the country uses 100 units then an EROI = 2 is the minimum "sustainable" EROI for the country, not the resource. But as with oil, the price goes up when there is scarcity. So EC would fall to meet what the resource can provide, in this case.

200 / (100 + 100) = 1
190 / (100 + 90) = 1
180 / (100 + 80) = 1

Note: this is all within a "closed" system with one resource. The world uses more than one resource. But I guess you could get an average EROI for every resource and then calculate the maximum EC and minimum EROI.

Edit: meant minimum "sustainable", not maximum "sustainable", lol....it was getting late I guess.