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.

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.

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.

I still don't understand

okay using your analogy, A company makes $190 but hasn't spent a dime doing anything, they then spend $100. They have $90. ???

I somehow get 190 units of energy but in the process spent 100 units of energy getting that. so that means I had the 100 units to begin with and I ended up with 90 units. That seems more like a EROEI of .9 and not 1.9

So why coudn't you use the 90 units of energy to create 171, why would you have to subtract another 100 from it? Even on a closed system I still dont see why 100 units of energy is subtracted in every input.

Well then, your model doesn't reflect reality. The earth is not a closed system the way you see it. We get energy from the sun. At the very least we have plenty of refined and ready to go oil already on the surface to start extracting oiil with an EROEI of 2.

If at some moment we literally had 0 energy available, then there would no longer be life. Any energy excess over what is needed to live can be pooled together to start extracting oil.

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.

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.

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.
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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

Novus, I understand closed systems just fine. That isn't the issue.

The issue is that you are making your "kickstart" energy dissapear into thin air.

Start with 100 units of energy ( we don't care from where ), and use your 1.9 EROEI pump to generate 190 units of energy.

You now have 190 units of energy. You then say that you "take back" the starting energy. Take it back to where? does it leave your closed system? How can something leave a closed system?

the fact is, the closed system that you proposed now has 190 units of energy, and that's greater than the 100 units it started with, no matter how you slice it.

It's true that we have only a net GAIN of 90 units of energy, but it's still a gain.


I would equate your methodology to something like this:
We build a building.
Start with 1 floor.
Given the first floor, we can build a second, so now we have 1 second floor and no first floor. With a second floor, we can build a 3rd floor, but now we have no second floor.

this is what it looks like when you use all your reinvested energy on the COST side of an equation, but don't also include that energy in the PRODUCED side of an equation.

EROEI is simple to understand. It's a ratio. It's a slope of a line. If you graph a line with a slope of 1.9, the line will go up for ever. The slope must be less than 1 for the line to go down.

Fine, your closed system now has 90 units of energy after you bizzarely take away energy. You use that enrgy in the pump.

Your closed system now has 171 units of energy, which if you didn't notice, is 71 more units than you gave to the system in the first place.

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...

A neat little site:

www.eroei.com

I would just like to add that while I think Novus' math/proof is not correct, I do agree that declining EROEI is a very bad thing.

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.

Further, I think that an EROEI rate near 2, while again sustainable, would undoubtedly mean massive restructuring of society and economies. You would have to spend literally half of your economy producing energy, while today producing energy is (I believe) less than 10% of world GDP.

If we get to the point that oil has an EROEI of anything close to 2, we're in for a world of hurt.

What does that have to do with it?

I think we agree EROEI of 2 will devestate the economy and that oil will peak and not be pumped as fast afterwards. EROEI will certainly go down past this with time too.

We're saying it still makes energetic sense to recover oil with such a return. If it wasn't doable for whatever reason (infrastructure costs too much, or possibly even symptons of global warming at some point) that would be reflected in an EROEI of less than 1.