[bdmarti]

$this->bbcode_second_pass_quote('Novus', '
')1st iteration: 100 -> 'A' -> 190 units of energy
2nd iteration: 100 -> 'A' -> 190 -> 'A' -> 361
3rd iteration: 100 -> 'A' -> 190 -> 'A' -> 361 -> 'A' -> 686
4th iteration: 100 -> 'A' -> 190 -> 'A' -> 361 -> 'A' -> 686 -> 'A' -> 1303

Net energy return for each iteration:

1st iteration Net = Revenue(190) - Cost(100) = 90
2nd iteration Net = Revenue(361) - Cost(100 + 190) = 71
3rd iteration Net = Revenue(686) - Cost(100 + 190 + 361) = 35
4th iteration Net = Revenue(1303) - Cost(100 + 190 + 361 + 686) = -34

[arocoun]

I just checked. bdmarti is right. Novus subtracts the investment from the energy returned, where he shouldn't. And EROEI of 1.9 doesn't mean that you invest (lose) 100, get 190 in return, but then lose 100 again, leading to only having 90. Rather, it means you invest (lose) 100 once, and get 190 back, plain and simple.

So, a new example to explain what I mean:

Start with 100 total, our starting energy.
Invest 100, we now have 0 total.
We get back 190. We have 190 total.

We don't subtract 100 again, since we've already lost that before, by investing it before.. Unless, of course, we wish to invest 100 more, in which case:

Start with 190, our current total.
Invest 100, we now have 90 total.
We get back another 190. We now have 280 total.

And thus, there is no need of outside investment, necessarily. Still, good job on the other stuff, Novus!

[Terrapin]

Good post Novus. It got a number of folks thinking, and the slide rules sliding. The concept is far from new here as it is usually cloaked as EROEI (energy returned on energy invested) which is actually a more accurate term, because, as several folks have mentioned; the “energy returned” is often in a different form than the “energy invested”.

One of the most glaring examples of this came to my attention a couple months ago in a paper presented in Science (abstract) which analyzed the efficiency of several corn>ethanol refineries in the Midwest. Although they were more or less a wash EROEI wise, since most of the energy was used in the refining process, and it came from coal/nuclear generated electricity., basically it is a scheme to turn coal/nuclear energy into ethanol/petroleum energy (with a little pork thrown in for the farm belt). Surprising little energy was used in the form of diesel in the harvesting/transport processes.

[Novus]

$this->bbcode_second_pass_quote('', 'Y')ou now have 90 more units of energy than you started with.

You can take those 90 units of energy and re-invest them into the pump, or you can spend those 90 units of energy doing something else, it doesn't matter. What does matter is that even after spending your 90 extra units of energy, you still have enough energy left (100 units) to do the whole thing again.

Why would one want to spend 100 units of energy to get only 90 units of "spendable" energy? Well, because it's repeatable of course.

[JustinFrankl]

We are all missing in a post-peak world that with each iteration EROEI will fall. You won't continue to get 90 barrels out at even the second iteration. What's more, there is no more growth in the oil extracted that goes to soccer moms, etc.

[emailking]

I still don't follow that Novus. For these purposes, you can call the surface earth the closed system, with the caveat that it gets to interact with the oil under the surface.

Suppose I have 100 units of energy available, say 100 MJ...perfectly reasonable. I extract, refine, transport the oil, etc. Now I have 190 MJ of energy available, as dictated by the EROEI of 1.9 = (190 MJ)/(100 MJ). Notice the the 100 MJ were already lying around somewhere (from oil already on the surface if you will...or from solar or something else if that makes you feel better). I didn't get the 100 MJ from the 190 MJ I just extracted today. Now I can use 100 MJ of my newly created 190 MJ to start the process over again. I can bank the 90 MJ left over. The process was worth it as this can continue. Even if I never extract another drop of oil for the rest of my life, it was worth it for me to scrounge up those 100 MJ of energy as I now have 190 MJ to live on for however long that will last me. This is independent of the earth being a closed system because the oil we extracted wasn't in the system before. Now it is.

Seriously, with all the books that have been written on these issues, I think someone would have mentioned by now that it cuts off at EROEI at 2 rather than 1.

[Novus]

emailking, when looking at oil production the surface of the earth is not a closed system. There is: nat gas, nuke, coal, low EROEI wells, and high EROEI wells all interplaying with eachother. The high EROEI systems all give a hand up to the low EROEI systems. A lot of authors mention how subsidies distort EROEI. This is the mathematical proof of the distortion that those authors could never quite nail down.

In a true closed system the starting energy is actually zero. From a modeling prespective this does not work because the sum of zero and any number is still zero. To run my model of a closed system I input 100 units of energy then imediately take it back. Taking the energy back only restores the closted system from its initial input. The net still has to be calculated after the energy is taken back. It gives the apearance that I calculated the costs twice as you say. The purpose of adding the energy input and then taking it back is to give the model a running start yet preserve the appearance of a closed system.

This first iteration shows missing step in the process.

1st: (kick start 100 -> 'A' - 100) -> 190 NET=90

My well still consumed 100 units of energy to produce its 190 output and then I took back the kick start energy which leaves me with a net of only 90.

[Rich7]

$this->bbcode_second_pass_quote('Novus', '')$this->bbcode_second_pass_quote('', 'Y')ou now have 90 more units of energy than you started with.

You can take those 90 units of energy and re-invest them into the pump, or you can spend those 90 units of energy doing something else, it doesn't matter. What does matter is that even after spending your 90 extra units of energy, you still have enough energy left (100 units) to do the whole thing again.

Why would one want to spend 100 units of energy to get only 90 units of "spendable" energy? Well, because it's repeatable of course.

[Rich7]

$this->bbcode_second_pass_quote('Novus', 'e')mailking, when looking at oil production the surface of the earth is not a closed system. There is: nat gas, nuke, coal, low EROEI wells, and high EROEI wells all interplaying with eachother. The high EROEI systems all give a hand up to the low EROEI systems. A lot of authors mention how subsidies distort EROEI. This is the mathematical proof of the distortion that those authors could never quite nail down.

In a true closed system the starting energy is actually zero. From a modeling prespective this does not work because the sum of zero and any number is still zero. To run my model of a closed system I input 100 units of energy then imediately take it back. Taking the energy back only restores the closted system from its initial input. The net still has to be calculated after the energy is taken back. It gives the apearance that I calculated the costs twice as you say. The purpose of adding the energy input and then taking it back is to give the model a running start yet preserve the appearance of a closed system.

This first iteration shows missing step in the process.

1st: (kick start 100 -> 'A' - 100) -> 190 NET=90

My well still consumed 100 units of energy to produce its 190 output and then I took back the kick start energy which leaves me with a net of only 90.

[emailking]

$this->bbcode_second_pass_quote('Novus', 'e')mailking, when looking at oil production the surface of the earth is not a closed system. There is: nat gas, nuke, coal, low EROEI wells, and high EROEI wells all interplaying with eachother. The high EROEI systems all give a hand up to the low EROEI systems. A lot of authors mention how subsidies distort EROEI. This is the mathematical proof of the distortion that those authors could never quite nail down.

In a true closed system the starting energy is actually zero. From a modeling prespective this does not work because the sum of zero and any number is still zero. To run my model of a closed system I input 100 units of energy then imediately take it back. Taking the energy back only restores the closted system from its initial input. The net still has to be calculated after the energy is taken back. It gives the apearance that I calculated the costs twice as you say. The purpose of adding the energy input and then taking it back is to give the model a running start yet preserve the appearance of a closed system.

This first iteration shows missing step in the process.

1st: (kick start 100 -> 'A' - 100) -> 190 NET=90

My well still consumed 100 units of energy to produce its 190 output and then I took back the kick start energy which leaves me with a net of only 90.

[pilot]

Net exported oil is even worse. OPEC and Russia will have a drop in net exports even worse than implied by net oil production. Oil importers are facing a world of hurt.

[turmoil]

Novus, I will reply to your post but I'm curious about where you got Net Decline = EROEI/2 from. Also, I don't see how that factors into your iterations.

[WebHubbleTelescope]

Consider the case that the energy needed for extraction comes from the energy produced:

if E=EROIE
and
if P=Fraction of Energy put to use elsewhere

then
P = (E-1)/E

Notice that when E=2, it indicates that exactly half the energy is wasted.

Anything greater than 1 means that the process can sustain itself. The problem is the huge "burn" rate that comes about when you get closer to one.

This has implications for global warming and the tremendous pressure on non-renewable resources, which hastens depletion as shown in the graphs.
[hr]
Another way to look at this mathematically is to look at the energy reinvestment series (as other posters have been doing by hand). This actually converges quite nicely using properties of geometric series.

Energy Reinvested = SUM ( E[sup]i[/sup] ) for i=0..N-1
Energy Produced = E[sup]N[/sup]

ER/EP = 1/E * SUM ((1/E)[sup]i[/sup]) for i=1..N

The sum term converges to the value 1/(1-1/E) for large N

so ER/EP = 1/(E-1)

so the fraction "produced" over total energy is :
P = EP/(EP+ER)=1/(1+ER/EP)=(E-1)/E

[bdmarti]

$this->bbcode_second_pass_quote('Novus', '
')This first iteration shows missing step in the process.

1st: (kick start 100 -> 'A' - 100) -> 190 NET=90

My well still consumed 100 units of energy to produce its 190 output and then I took back the kick start energy which leaves me with a net of only 90.

[bdmarti]

$this->bbcode_second_pass_quote('Novus', '
')
This first iteration shows missing step in the process.

1st: (kick start 100 -> 'A' - 100) -> 190 NET=90

My well still consumed 100 units of energy to produce its 190 output and then I took back the kick start energy which leaves me with a net of only 90.

[clifman]

Yeesh, this was a long way 'round. I'm not a math whiz, but this EROEI thing is big, and I again thank Novus for the original post, but this open/closed system debate has detracted from the main point. I think bdmarti just made this point, but I'd like to try to clarify:

Take 100 units of energy from "outside" the system.
Burn it up to extract 190 units of energy from the ground.
Okay. Give that 100 units of initial energy back to the "outside".
Take our net 90 and burn it to produce 171.
Take the 171 and burn it to produce 325.
Take the 325 and burn it to produce 617.

See how now that we're staying in the "closed" system, we keep gaining energy? So as long as the EROEI is greater than 1, we can keep producing net energy. We can sell whatever fraction of that 171, 325 or 617 we deem prudent to the "outside" and reinvest (burn) what we need to to extract more. Gee, it almost sounds like an EROEI of 1.9 is nothing to fear. Well, quite the contrary. I am absolutely with you, Novus, on the point that declining EROEI is gonna bite us like we can't imagine.

Here's the essence of it to me. At 10:1, we have 90% of the gross extraction available to us for use other than extraction. Not as good as the 99% we had early in the 20th century, but still not bad. But as we fall to 5:1, we have only 80% of the gross available, at 4:1 we have 75%, 3:1 - 67%, 2:1 - 50%. Below that, less than half, and the decline continues to accelerate. From 10:1 to 7:1, the available net drops only by a percent or two for each point drop in the ratio. But below that, it starts to drop by chunks. I've seen estimates as to where we are now that range from 15:1 (or higher) to as low as 2.5 or 3:1. I don't know. But it ain't going up, and just as we're either at or approaching peak extraction, we're also either at or approaching the point where declining EROEI really starts to take meaningful bites out of the net available to us. Put those two together with an increasing population increasingly dependent upon the black goo, and that's the world of hurt I see coming. To say nothing of the fact that we're in similar position regarding so much else - fish, water, soil...

[Raxozanne]

A neat little site:

www.eroei.com

[bdmarti]

$this->bbcode_second_pass_quote('clifman', 'G')ee, it almost sounds like an EROEI of 1.9 is nothing to fear. Well, quite the contrary. I am absolutely with you, Novus, on the point that declining EROEI is gonna bite us like we can't imagine.

[emailking]

$this->bbcode_second_pass_quote('bdmarti', '
')I also think that while in theory an EROEI > 1 might be perpetually maintainable; such a thing doesn't exist in the context of fossil fuels. One can't remove fossil fuels from the ground forever at the same rate.