Understanding EROEI
7 Mar, 2008 12:03 pm
The concept of energy return on energy invested, or EROEI, is terribly misunderstood. I have heard people argue that EROEI doesn't matter, only economics. This misses a very key point: EROEI is going to have a huge impact on economics, because it shows that in order to maintain current net energy for society, energy production must accelerate as EROEI declines.
Consider an EROEI of 20 with 10 units required; this means that 1 unit is invested to get 20 unit of output or if 10 units are required then .5 unit is invested. Add them together an you get a total of 10.5 units.
Try it with an EROEI of 10; 10+1=11 units
Try it with an EROEI of 3; 10+10/3=13.33 units
Try it with an EROEI of 1.5; 10+20/3=16.66 total units of energy.
(At a EROEI of 1.11; 10+9=19. But I don't know an energy process that runs that low)
So going from an EROEI of 20 to 1.5 raises the total amount of base energy extracted to maintain an output of 10 units would have to increase by only 59%(16.66/10.5)1.
The amount of low EROEI unconventional oil (for example) in the world is probably 2 times greater than conventional oil in the ground. There is still enough total energy to makeup for the drop in EROEI and still maintain the current levels of production given sufficent effort.
The object of energy production is to produce energy, not worry about EROEI.
That last sentence sums up the person's argument: EROEI is no big deal. Being a math type, I worked through his calculations and found that they are wrong. It took me a while to see his error, but I finally did see it. Work the problem in reverse at an EROEI of 1.5. If you produced 16.66 units of energy at an EROEI of 1.5, then the inputs were 16.66/1.5, or 11.1. The actual net is 16.66  11.1, or 5.56. He was trying to net 10 units, so he has vastly underestimated the energy inputs required for this. So of course he doesn't think EROEI is a problem. He doesn't understand the concept.
EROEI Basics
There are a couple of important EROEI equations. The first is that EROEI = Energy Output/Energy Input. In other words, if we have to spend 10 BTUs (Input) to extract and refine 100 BTUs of oil (Output), then the EROEI is 100 to 10, or 10 to 1. The second important equation concerns the net energy; that is how much energy was left after the energy input is accounted for. This equation is Net Energy = Energy Output  Energy Input. In our previous example, the net energy is (100 BTUs produced  10 BTUs input), or 90 BTUs.
A couple of points here. First, the break even for EROEI is 1.0. In that case, you have input just as much energy into the process as you got back out. In some cases, that may make economic sense. For instance, if you input coal BTUs but got back out ethanol or diesel BTUs, then you have converted the coal into something of greater value. However, if you input one transportation fuel and got another transportation fuel as output  as is mostly the case with corn ethanol (natural gas, diesel, and gasoline in; ethanol out)  then you are really just spinning your wheels. In a case like this, you should just use the inputs directly as a transportation fuel.
The same is true of Net Energy  it can be negative and yet still make economic sense. But an important point here is that society can't run for long on an EROEI of less than 1.0 or on a negative Net Energy. Doing so is equivalent to withdrawing money from a bank  at some point you have to make some deposits  or at least stop the withdrawals.
The EROEI of Brazilian Ethanol
The case of Brazilian sugarcane ethanol deserves special mention. It is often quoted as having an EROEI of 8 to 1. I have even repeated that myself. But this is misleading. This measurement is really a cousin of EROEI. What is done to get the 8 to 1 sugarcane EROEI is that they only count the fossil fuel inputs as energy. Boilers are powered by burning bagasse, but this energy input is not counted. For a true EROEI calculation, all energy inputs should be counted. So what we may see is that the EROEI for sugarcane is 2 to 1 (hypothetically) but since most inputs are not fossilfuel based the EROEI based only on fossilfuel inputs is 8 to 1.
What is overlooked by touting the EROEI of 8 to 1 and skipping over the true EROEI is an evaluation of whether those other energy inputs could be better utilized. For instance, that bagasse that doesn't get counted could be used to make electricity instead. Probably in the case of sugarcane, firing boilers is the best utilization. But the lesson from this digression is to be careful when people are touting very high EROEIs. They probably aren't really talking about EROEI.
Calculations
Now for some calculations that show the challenge of energy production if the EROEI of our energy sources continues to decline. In the early days of oil production, the EROEI was over 100. Now, it has declined to somewhere between 10 and 20. So let's look at the implications as the EROEI declines from 20. Here is what it takes to get 10 units of energy (gross, not net) at various EROEI values.
A 20 to 1 EROEI it takes an investment of 0.5 energy units to get 10 out
At 10 to 1 it takes 1 energy unit to get 10 out
At 5 to 1 it takes 2 energy units to get 10 out
At 2 to 1 it takes 5 energy units to get 10 out
At 1.5 to 1 it takes 6.67 energy units to get 10 out
At 1.3 to 1 it takes 7.69 energy units to get 10 out
At 1 to 1 it takes 10 energy units to get 10 out
So, dropping from an EROEI of 20 to 1 down to 1.3 to 1 takes over 15 times the energy inputs (7.69/0.5) to output the same amount of energy.
Net Energy
But here is what so many  included that poster I quoted above  fail to understand. Look at the net energy.
At 20 to 1, an investment of 0.5 units got 10 back out. The net is 9.5 units.
At 1.3 to 1, it took an investment of 7.69 units got 10 back out. The net is 2.31 units.
At 1 to 1, an investment of 10 units got 10 back out. The net is 0 units  all you have done is converted one energy form into another. (And of course at less than 1 to 1, you have actually lost usable energy during the process).
If we wish to net 10 units, then at 20 to 1 we have to produce a total of 10.53 units (you are solving 2 equations here; EROEI = Out/In and Net = Out  In; For EROEI = 20, the solution is Out = 10.53 and In = 0.53). For an economy that requires 10 units of energy to run, we need an excess of 0.53 units to net that 10. (And if you want to pick nits, 10.53 is rounded from 10.5263157894737).
Now drop the EROEI to 1.3. We now have to produce a total of 43.33 – an excess of 33.33  to get the 10 we need to run the economy (Out = 43.33, In = 33.33; EROEI = 1.3 = 43.33/33.33; Net = 10 = 43.33  33.33). Thus, the requirement from dropping the EROEI from 20 to 1 down to 1.3 to 1 requires a production excess of (33.33/0.53), or over 60 times the high EROEI case.
Running Faster to Stay in Place
Therein EROEI illustrates clearly the challenge we face. As EROEI declines, energy production must accelerate just to maintain the same net energy for society. At an EROEI of less than 2, the amount of energy required to net our current energy usage far exceeds even the most optimistic proposals for our production capacity. Others have concluded much the same: The status quo can't be maintained if EROEI continues to decline.
Many don’t grasp this concept. If they did, they would understand why a falling EROEI is reason for concern.
Previously published on: RSqured Energy Blog

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If I've done this right, for bioenergy alone, the minimum tolerable EROEI is 800/1500, about 1/2.
I would have say the contrary ... that technology had improved oil production even with the increasing access difficulties, eneregy cost of transportation.
How could ROI increase and EROI decline ?
For more detail, look at the March 2008 Newsletter, titled ?The energyproduction peak?, of the blog http://thesmartcreature.blogspot.com/ . (I have recently proposed this article to scitizen). I have deliberately avoided talking of EROEI (for simplicity). It is easier, for most reader, to understand the phrase "cost of energy production".
http://www.oilism.com/oil/2008/04/01/whyeroimatters/
I have added the following comment, which complements my previous one at Scitizen :
? As an ordinary citizen, I sense intuitively that the EROI (or EROEI) is linked to the cost of producing energy : the higher EROI, the lower production cost. I also sense that the average cost of producing a definite amount of energy will increase in the future, thus slowing energy production growth (knowing that fast growth is greatly linked to energy produced at low cost) and in this way reducing the investment capabilities of increasing the world annual energy production. At some point in the future a threshold will be passed beyond which those capabilities will vanish. We will then reach (or will have reached) the energyproduction peak. What average value of EROEI corresponds to this threshold ? I have no idea but I sense it works this way. Are there any studies about it ? ?
http://www.theoildrum.com/node/3786
That, however, is inconsistent with the way we calculate EROEI for a refinery. In a refinery, the energy inputs are frequently derived from the fuel gas that is produced during the refining process. But we still count it against the process in the EROEI equation. If we didn't, the EROEI of refining could be something like 100/1.
RR
To make my explanations easier, I will use the following symbols :
n = net energy required ;
i = energy investment required to get the net energy n ;
t = total energy required to get the net energy n ;
e = EROEI = t/i = (n+i) / i = n/i + 1 {definition 1}.
As e ? 1 = n/i and t = n + i , we get :
t = n [ 1 + 1/(e ? 1) ] = n e / (e ? 1) {formula 1}
The ratio n/t equals (e ? 1) / e = 1 ? 1/e ; it gets ever closer to zero when EROEI gets ever closer to 1, as we approach the breakeven point.
But formula 1 is not the one you have used in your calculations. Instead, you have used this one :
t = n ( 1 + 1/e ) {formula 2}
Here the ratio n/t equals e / (e+1) ; it gets ever closer to zero when EROEI gets ever closer to zero, corresponding to the following definition for EROEI :
e = n / i {definition 2} , where the breakeven point correspond to EROEI = 0 instead of EROEI = 1 .
Using formula 2 and with n = 10 energy units you got the results t = 11 units, t = 13.33 units and t = 16.66 units, respectively when EROEI takes the successive values 10 , 3 and 1.5 (whereas formula 1 gives the results 11,11 units, 15 units and 30 units with the same numerical values).
I believe definition 1 is the right one, but I have read definition 2 on some websites. Thus there seems to be some confusions about it.
Notice that EROEI(def 1) = EROEI(def 2) + 1 . Thus your calculations correspond to EROEI(def 1) with the three successive values 11 (instead of 10), 4 (instead of 3) and 2.5 (instead of 1.5).
Regards.
There is definitely disagreement  even in the literature  about proper EROEI accounting. This is clearly demonstrated by the reported EROEI from Brazilian sugarcane ethanol. However, I don?t believe there is any incoherence at all in my calculations. They are quite straight forward.
If I try to work through your calculations, then it looks to me like your e is my EROEI, your t is my Energy Output, your i is my Energy Input, and your n is my Net Energy. In this case, my equations would be:
e = t/i
n=ti
Now plug in any of my examples; for instance use the one with EROEI of 1.3. You will find that if you plug those terms into your Formula 1, you get an equality. If you plug into Formula 2, you get an inequality (10 = 17.7). Thus, Formula 1 is consistent with the method I am using.
I started to work through to see if I could figure out the disconnect, but I have gotten interrupted several times. I have a feeling that there is some difference in the way we have both defined terms. But if t=i, we have an EROEI of 1.0 and a net energy of zero. Thus, e approaches 1 as net energy approaches zero.
Cheers, RR
I see we share the same definitions concerning i, n, t and e , as well as the same equations e = t/i and n = t ? i .
But then I do not understand your following assumptions :
?Try it with an EROEI of 10; 10+1=11 units
Try it with an EROEI of 3; 10+10/3=13.33 units
Try it with an EROEI of 1.5; 10+20/3=16.66 total units of energy.?
Let us consider your second example, with EROEI = 3. I suppose it means that
n = 10, t = 13.33 and i = 3.33 . Hence our common equation e = t/i gives the result 13.33/3.33 = 4 (instead of 3).
If my supposition is right, your three above assumptions show that you have applied the equation
t = n + n/e = n(1+1/e) = n (e+1)/e .
With that you get a ratio n/t = e/(e+1) , showing that e = 0 (instead of e = 1) when n = 0 (breakeven point).
Now, when e = 1 and n = 10 , that same equation leads to t = 2n = 20 and i = n = 10 . In this case we invest 10 units and we get 20. Out of those 20 units we get a net energy of 10 units and we reinvest the remaining 10 units into the production to keep it going on at the same level. Do I get it straight ? If that is the case, then I find that the EROEI you have used is defined by the equation e = n/i (instead of n = t/i).
Coming back to an EROEI of 3 and the definition e = t/i = (n+i) / i , I believe the right figures associated with
n = 10 are i = 5 and t = 15 (Checking : 3 = (10 + 5) / 5 ) .
I often give the URL of your article, when I give explanations about the meaning of EROEI, using it as a reference and borrowing the image of Aliceinwonderland?s red queen running ever faster just to keep in the same place. This is why I want to be sure that I have elucidated all ambiguities.
Regards,
Andr?
I now see the problem. When you write "I do not understand your following assumptions", those are not my assumptions. Those were the assumptions of someone I was quoting, and I was pointing out that they had done the math wrong. Look at the paragraph right after that section and you will see. What I think you are saying is that the quoted portion has the math wrong, which was exactly my point!
Your example at an EROEI of 3/1 is exactly correct. Input of 15, output of 5, net energy of 10. The person I quoted came up with 13.33, which overestimated EROEI.
Cheers, Robert
Cheers, RR
Now, I understand the misunderstanding ! How silly of me !
When I read your article from beginning to end, I did not find anything abnormal. So I suppose I had got it right.
But I just have focalized on this three assumptions, this time, without looking elsewhere, assuming they were yours, just after having given your URL in one comment following my article Des limites ? la croissance ? Chut ! published on the blog Imago (a translation in French of the one I posted on Scitizen). As I had given some explanations in this comment, I wanted to check if they were similar as yours ? and of course I found that they were not !
That is the explanation ?
Please, excuse me.
Cheers,
Andr?
I come again, first to add a little rectification to the last sentence of my previous comment (just to make it clearer for the readers) : Of course I have found out, in the end, that the explanations I give to my audience are in full agreement with your?s ?
After having sorted out the misunderstanding, I had a look to that thread at the Oil Drum and found that the author (named majorian) gives the definition :
EROEI ? 1 = (Eout ? Einv)/Einv
With such presentation, it should be clear that Eout is the total energy and (Eout ? Einv) the net energy. But the following calculations are coherent with Eout = net energy instead of total energy, so maybe majorian just made such interpretation. If that is the case, it means that the EROEI he used is the one I have named EROEI(def 2) in comment [8], whereas you and I use the one I have named EROEI(def 1).
As EROEI(def 1) = EROEI(def 2) + 1 , the set of values (10 ; 3 ; 1.5) adopted by majorian is to be transposed in the set (11 ; 4 ; 2.5) when using EROEI(def 1). Do your own calculations with this second set and you will find the same set of results concerning the total energy required for getting 10 units of net energy, that is : (11 ; 13,33 ; 16,66).
Regards
After having analysed majorian?s calculations, I conclude that he understands very well the fundamentals of EROEI, namely : ? as EROEI gets lower, we need to increase production to get a required amount of energy. (In other words, we need to run faster just to keep at the same place, as you say in your conclusion.) And he is also correct when he writes ?There is still enough total energy to make up for the drop in EROEI and still maintain the current levels of production given sufficient effort?, as we know that there are still plenty of concentrated resources left underground as well as plenty of diffused renewable energy sources around us.
But he does not seem to have grasped that ?giving sufficient effort? (in other words : investing more and more in energy production just to obtain the same net energy) will become ever more costly (hence ever less sustainable in the long run) and that the concentrated resources left underground or the diffused renewable energy sources will not help us very much if harvesting them becomes (for the former) or remains (for the latter) too expensive. I think we agree on this point.
Since 1945 and until around 2003, the exceptionally fast growth our world has experienced (with the help of high EROEI concentrated energy resources) has been fed by energy produced al low cost and sold at low price while having simultaneously remained able to satisfy growing demand. But we have entered into a new world, in the course of the last five years, as it seems now that our aptitude to increase year after year the annual production of cheap energy has come to an end or is about to end. From now on, as EROEI is expected to get ever lower (getting ever closer to the break even point), the cost of producing a given amount of energy will become ever higher (as will also get the footprint on the environment), hence diminishing the pace of growth and as a consequence the financialsystemmoneylending capability feeding the investment capability of world economies. At some point, we will no longer be able to increase our annual energy output and will probably have to face contraction. But as this prospect looks very painful, most people do not want to hear or talk about it ? and this is perhaps why many educated people (including politicians, economists, journalists and even scientists) do not want to understand what EROEI really means ?
Regards.