Understanding EROEI

Introduction

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.

Likewise, I have heard people hand wave away the issue, suggesting it is really no big deal. Here’s an example that I saw yesterday in a thread at The Oil Drum:

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 fossil-fuel based the EROEI based only on fossil-fuel 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.

49 thoughts on “Understanding EROEI”

1. I tried to explain EROEI as well as some of the other important concepts in evaluating renewable energy systems in this essay.

OTEC has been a good example of even very trained people not understanding EROEI. The fact that in some locations there is almost unlimited seawater with a significant enough temperature differential to run a heat engine is true. The problem is that the energy required to pump the cold water to the warm requires almost all of that energy and construction/maintenance uses up the rest.

2. Bob, I have also seen it horribly misapplied to solar energy. To do EROEI for solar, you have to sum up the energy output over the duration of the panels. I have seen some try to do it differently and wrongly come up with a very low EROEI for solar.

3. I think these things sort themselves out if we kill the energy subsidies. It is a play of ROI and EROEI, and the market can figure that out.

4. Robert,

You mentioned in your comment that some estimates of EROEI for solar are likely lower than they should be. Do you have any idea what an actual EROEI is probably at with current commercial systems?

Also, how exactly do you get the units to match up when you’re not just comparing, for instance, gallons of gas in to gallons of ethanol out? What about a hydrogen producing system that requires various sources of input, with an output of gaseous hydrogen?

5. I think these things sort themselves out if we kill the energy subsidies.

To a point that’s true, but it gets convoluted with global markets. It might be profitable to get bio-oil, ethanol or silicon from a country where it is financially cheap and sell it in the US, but that doesn’t mean that it actually has a positive EROEI or that it lowers CO2 in the global picture.

wrongly come up with a very low EROEI for solar
I’m not sure I see people incorrectly understanding EROEI for solar as much as understanding the intermittent nature of the sun hitting the panel and importance of energy storage. A solar PV panel might output enough energy to recapture the input energy and have a positive EROEI in a few months to years, but did that energy come out when it was useful? Right out of the gate, using solar power for lighting is an oxymoron. Residential solar PV has the highest output when people are at work. It’s easy to calculate EROEI on a base load system, on an intermittent system you have to start looking at the electrical load and the user’s habits.

I think the major problem with renewable systems in general is applying base load terminology to intermittent systems. Seeing nameplate capacity on wind and solar systems doesn’t make much sense and appears to be a marketing gimmick. A standard like “kWh/year at location X,Y” would have some meaning, peak kW output means very little.

6. Do you have any idea what an actual EROEI is probably at with current commercial systems?

Kyle, I don’t know the process well enough to do one myself, but I have seen some attempts that got answers all over the map. Here is an analysis from the World Nuclear Association that shows EROEIs for solar PV clustering around 10. (See Table 2). That’s pretty good.

What about a hydrogen producing system that requires various sources of input, with an output of gaseous hydrogen?

The energy units themselves are all easily converted. The problem is sometimes figuring out where to draw the system boundaries.

Cheers, Robert

7. “it gets convoluted with global markets. It might be profitable to get bio-oil, ethanol or silicon from a country where it is financially cheap and sell it in the US”

That is true for all overseas externalities.

We try to cure them with encouragement, and sometimes with trade law.

hehe.. see softwood lumber

The USA isn’t going to impose anything in trade laws but local protectionism. Not that any other country would be different. If there isn’t some lobby group or local economy effected, there is no way a trade law is going to go in because of poor EROEI or carbon balance in some other country.

Or environmental impact in some other country. See Alberta Oil Sands. The oil sands are probably going to be the thing that turns Dr. Suzuki violent.

9. The USA isn’t going to impose anything in trade laws but local protectionism.

If we really believe that I can sell the Prius and get a Hummer right?

It’s the slope Robert was facing a little while back when he called GW inevitable.

If it truly is we can just part on.

10. That should have been “party on.”

(I guess I can ditch the small keyboard on this eee pc and switch to a quad-core xeon too!)

11. Good post, Robert — a pity that it is necessary. It is also rather telling that the human race does not even have a word for something as critical as EROEI/energy amplification.

The big implication is that the growth in gross global energy demand has likely been severely underestimated.

As we move away from prime fossil fuels, the energy demand of the energy supply industry will become one of the largest components of total energy demand. This is one of the Achilles Heel’s of most so-called “renewable” energy sources.

The world is currently using 15 TeraWatt power — with 2/3 of the human population under-served and relatively little power being used in the energy supply industry (high EROEI/energy amplification).

Even with good conservation, power demand to give every human being (including population growth in coming decades) a decent standard of living would push us to over 30 TW. Throw in lower energy amplification as prime fossil fuels get used up, and gross global energy demand could approach 100 TW — almost 7 times current level.

That is why we have to look at energy as a supply-side issue. There are viable technological solutions today, if we can ever get serious.

12. doggydogworld says:

I’m a big critic of EROEI. First, it is poorly defined. Your equation: EROEI = Energy Output/Energy Input, is inconsistent with other ROI calculations. If you put \$100 in a CD and get \$105 back a year later your financial ROI is 5%, not 105%. People often talk of negative EROEI, which is mathematically impossible using your definition. The term EO/EI is less ambiguous, but few use it.

Input definitions are another problem. Do you count the bagasse, as you noted? What about the solar energy falling on the panels, the crude oil going into the refinery or the energy used to grow the wheat to make the bread for the sandwich eaten by the janitor at the plant? Input definitions seem to depend mostly on the author’s desired outcome. This is how you get Patzek’s screwy ethanol numbers and Willem Storm van Leeuwen ‘proving’ nuclear ER/EI is below 1.

Second, ER/EI is not all that useful once you get above 2. If you must burn 1/3rd of an abundant resource (e.g. tar sands) to run the process your ER/EI is 2. You can run a society on that better than on a scarce resource with ER/EI=20.

Below 2 you don’t have an energy source, but a conversion process. Refineries convert crude to gas and diesel. The corn industry converts natural gas into ethanol, etc.

Another problem is EO/EI ignores time. An EO/EI=3 source which returns all the EO immediately can work, one which returns it over 30 years can’t. At EO/EI=3 PV would produce negative net energy as long as it grew faster than 10%/year. And if it grows slower than 10%/year it’ll never amount to anything. Energy payback time is the relevant metric here.

EO/EI also ignores externalities. If you include the energy required to extract carbon from the air and sequester it oil’s EO/EI drops way below 1.0. Fossil fuel industries depend entirely on free permits (i.e. subsidies) to pump sequestered carbon in the air.

EO/EI can help separate energy sources (EO/EI>2) from conversion processes (EO/EI near 1). But you have to do the calculation properly, which is rare, and even then the final number is often overwhelmed by other considerations such as resource availability, time scale, labor requirements, externalities, etc. I know of people who claim a proper EO/EI methodology will take all of this into account, but they are fools. You can’t reduce something as complex as energy to a single number.

13. If it truly is we can just part(y) on.

I don’t believe that, it’s just to learn from things like corn ethanol and not believe press releases from recent IPO’s. First Solar and CWT (TDP have a lot in common and investment in those companies is all driven by EROEI confusion.

Companies like First Solar put together enough technology and hype to drive their stock price from \$35 to \$207, but that doesn’t mean that they have a solution that will scale to be significant. First Solar has a valuable product, but solar PV won’t scale, regardless of which semiconductor material is chosen or how little of it they use. I am talking in scale to coal.

Uranium is another example. The earth has uranium out the wazoo, but only in a few known locations (one of them in my province) is it concentrated enough for the EROEI to be positive, or even the economics of extraction to be feasible with rising oil prices. This is exactly the reason why EROEI understanding is important. Uranium is very common and can be found in low concentrations almost everywhere. People some how take “plentiful” to mean there is some warehouse full of refined uranium that they can start shipping.

EROEI education is very important for good decisions.

14. Thinking about the uranium statement I just made, I’m wrong. I think uranium extraction energy compared to the output energy is probably not as significant as the energy required to build and maintain the power plant. Nuclear power suffers a receding horizon as it becomes more difficult to find concentrated uranium, but the EROEI of uranium extraction would still be very positive for an existing plant. The question that comes up is that if we tried to scale nuclear to replace coal would it have a positive EROEI as it becomes more difficult to mine.

15. But you weren’t making a technical point (and neither was Robert before), you were stating a social expectation.

16. Your equation: EROEI = Energy Output/Energy Input, is inconsistent with other ROI calculations. If you put \$100 in a CD and get \$105 back a year later your financial ROI is 5%, not 105%.

No, those calculations are completely consistent.

If I put 100 BTUs in and get 105 back out, then my EROEI is 1.05, but the energy return is 5%. You do exactly the same calculation for your financial example.

Remember, EROEI is a ratio, just like your money out over money in is a ratio. To calculate your %return, you always have to subtract out and divide by your initial investment.

17. doggy said: “EO/EI also ignores externalities. If you include the energy required to extract carbon from the air and sequester it oil’s EO/EI drops way below 1.0.”

Except we wouldn’t do it that way. Extacting CO2 from the air at 400 ppm would be very expensive. We would rather take the O2 (20%) out of the air and then combine it with fuel to create a concentrated CO2 stream we could then sequester. At large industrial size plants the EROI would still be way above 2. You would be right for liquid transportation fuel.

18. Hawkshaw says:

Here’s a simple way of understanding EROEI.

Any system with an EROEI of greater than one could power itself.

The US Patent Office tests all the perpetual motion machine proposals they receive with a simple proposition: “If what you say about your machine is true, please connect the output to the input and let’s see if it keeps running.”

The Patent Office test would easily debunk the corn ethanol industry. If farmers and ethanol plants had to rely on only the ethanol they make as their source of energy, the corn ethanol production process would quickly grind to a halt.

19. Benny "peak Demand" Cole says:

Finally, I disagree with RR about something.
I think it is worth distinguishing energy derived from, say, bagasse, from energy derived from fossil fuels.
The bagasse is relatively cheap to burn. It is (one could argue) the conversion of solar power into liquid fuel.
The Brazilians thus import less crude oil, have better balance of trade, and are not as vulnerable to the whims of Thug Oil states.
I think that we will have lesser EROEIs in biofuels, but if the energy is essentially captured solar energy in plant form, then not to worry (too much, anyway).
In any event, the price mechanism is divine at sorting these things out. The Brazilians seem to making a go of it.

20. EROEI should technically be:

(energy out / energy in) – 1

but no one seems to do it that way, so I don’t try to swim upstream.

21. Jerry Unruh says:

Robert – Thanks for the post. It made me think more of how to calculate EROEI and I came up with what I think may be a more general approach which allows the energy input to come from energy at any EROEI. Using 1.5 as an example. In order to obtain 1.5 units one as to input 1 unit. However, that unit of energy has to contain the energy to get it out, etc, etc. Using 1.5 as the example, the energy input is 1 + the integral of(1/1.5)**n from zero to infinity. The answer works out to be 1 – 1/ln(1/1.5) = 3.466. Therefore, to obtain 1.5 units of energy one has to input 3.466 units and the total energy ultimately expended is 4.966.

The beauty of this approach is that it is general for the energy input having a different EROEI than what is being obtained. Again if the EROEI of a system is 1.5 but the energy input comes from a source with a 10:1 EROEI than the energy input is 1 -1/ln(1/10) = 1.434 or total energy ultimately expended is 2.934.

Unfortunately, higher EROEI fuels are also of higher quality, i.e., natural gas and, therefore, it is foolish to upgrade a poor quality fuel with a high quality fuel. This is exactly what is being done to upgrade tar sands using natural gas as the hydrogen source.

I also saw a comment about the EROEI of PV. The easy way to determine this is to go NREL’s website (www.nrel.gov). They have calculated the years a panel has to operate to pay back the energy input. Thin film panels are expected to have about a 1 to 3 year energy payback. Since they are being guaranteed for 25 years, one can assume the payback is about 8 to 25:1 (there may be issues with the way they calculated the payback). If Nanosolar’s process is successful, I assume their payback could be even better.

22. One more note on bagasse — Robert mentions that the stuff could be burned for electricity generation as an alternative to ethanol production. True, but the bagasse they’re burning is (as I understand) tied to the sugarcane — it wouldn’t even *exist* unless they were growing the sugarcane to make ethanol in the first place. I.e. they wouldn’t grow sugarcane just to take the bagasse and burn it; that would, I’d guess, be economically infeasible.

So as Benny says, it may be better to count bagasse as like the sun hitting solar panels — maybe leaving it out of the equation is the correct thing to do.

(Of course, none of this considers the emissions created by burning that stuff.)

23. Optimist says:

I’m with Doggy on this.
As EROEI declines, energy production must accelerate just to maintain the same net energy for society.
Who says society needs the same net energy? As energy gets more expensive, society will figure out how to make do with less net energy, believe you me. As Benny keeps reminding us, is it already happening in the US.

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.
That’s a bit hypothetical. Other than corn ethanol, do we know of any process that has an EROEI of less than 2, you know without counting the energy in the janitor’s sandwich, etc.?

Others have concluded much the same: The status quo can’t be maintained if EROEI continues to decline.
Why are you stuck on the status quo?

Many don’t grasp this concept. If they did, they would understand why a falling EROEI is reason for concern.
It only becomes a case for concern once EROEI starts to approach unity. The drop from 100 to 10 is a mere inconvenience, especially when there is plenty of feedstock available.

I think Odograph is right: remove the subsidies and the markets will sort this out.

24. Optimist says:

Using 1.5 as an example. In order to obtain 1.5 units one as to input 1 unit. However, that unit of energy has to contain the energy to get it out, etc, etc. Using 1.5 as the example, the energy input is 1 + the integral of(1/1.5)**n from zero to infinity. The answer works out to be 1 – 1/ln(1/1.5) = 3.466. Therefore, to obtain 1.5 units of energy one has to input 3.466 units and the total energy ultimately expended is 4.966.
Jerry,
Maybe I’m being slow here, but I find this a tad confusing. You seem to be using both an EROEI of 1.5 and a (net?) energy output of 1.5. Would you mind showing what the calc would look like for say an EROEI of 1.5 and net energy out of 10?

25. Finally, I disagree with RR about something.

I think it is worth distinguishing energy derived from, say, bagasse, from energy derived from fossil fuels.

But you aren’t disagreeing with me, because I never said that it isn’t worth distinguishing. I am just pointing out that when the EROEI from sugarcane is mentioned as 8/1, it isn’t really an EROEI. I also said that firing the boilers with bagasse probably is the best usage in the case of Brazil. So I am not really sure what your disagreement is.

26. Who says society needs the same net energy?

Not me. I have consistently said we need to reduce energy consumption. What I am showing is why it will be difficult to keep the same net – not that we need to do it.

Other than corn ethanol, do we know of any process that has an EROEI of less than 2, you know without counting the energy in the janitor’s sandwich, etc.?

Cellulosic ethanol. Biobutanol. Oil shale. You know, the ones everyone is talking about.

Why are you stuck on the status quo?

Why would you think that? I am trying to call attention to a problem by telling people that the status quo can’t be maintained. I am not saying we must maintain the status quo.

It only becomes a case for concern once EROEI starts to approach unity.

No, it starts to become an issue at less than 5. In fact, I think it was Cutler Cleveland who argues that a modern society can’t be maintained at an EROEI of less than 5. I don’t necessarily believe that, but I understand why he makes that argument.

27. bc says:

The great bit about a complex thing like energy is that you *can* reduce it to a single number, which is why we have everything from steam engines to iPods. If it like the climate and not reducible to simple numbers we would still be using abacuses.

I have a smattering of engineering, so EROEI seems patently obvious to me. You have get out more than you put in. This is a simple concept, it’s the same as running a business. You have to get out more money than you put in. What is complicated about that? Sure, there is some ‘creative’ accounting, and often insolvent companies last longer than they should, but as a general rule it’s inescapable.

A good graphic associated with EROEI is the EROEI cliff, which I don’t have to hand but it’s been posted on TOD. It really brings home the impact of declining EROEI.

28. I think I understand why my intuition with PV doesn’t agree with the published numbers (besides the real world example at Toronto’s Horse Palace not agreeing with the published numbers). Doggydogs comment about time and growth.

From the resident’s point of view, let’s say that both the EROEI and financial ROI return at 3 years on their fancy new thin film PV system. If they are actually using the power when it’s produced (or really lowering their grid load for a real ROI) the PV owner is happy after 3 years and sailing along on “free” power until the panels wear out.

Globally were not happy until PV is no longer a growth market. We are taking electricity and other energy and perpetually tying it up in an intermittent power source. If storage is added, the EROEI and ROI drop way over the horizon.

As the market grows and more semiconductor and PV factories are built, they are continually adding load to the global grid.

Is the load on the grid being lessened by as much? No. Not until the market is saturated or the price of cadmium, tellurium or silicon jumps as demand increases and the panels become unaffordable. At that point when the factories are shutdown, globally we wait 3 years and then we sail along on “free” power until the panels wear out.

If you really want to help the environment, move to Manitoba where 98% of their power is hydroelectric.

29. Weather for Winnipeg, MB, Canada …
5°F, Clear

(ouch, though I think I might have kin there)

30. Since the subject of Brazilian sugar cane ethanol came up, I’d like to ask about how the inputs are calculated. Specifically, I read somewhere (IHT, I think) that about 20% of the sugar cane operations are mechanized, which means that human cane cutters do about 80% of the harvest. It’s relatively easy to figure out fossil fuel inputs because you just say we used X liters of diesel fuel to harvest X hectares of cane, etc. But how do you calculate the energy of the cane cutters? Where do you set system boundaries? Also, I understand that the cane cutters work at a furious pace, and that some of them damage themselves physically. Are there social costs that should be considered?

31. But how do you calculate the energy of the cane cutters?

Modern North American farming practices are a big part of the low EROEI on ethanol. I am convinced that agriculture can be moved to renewable electricity from diesel relatively easily compared to the transport fleet. Canola oil grown with electric farm equipment has potential.

My grandpa made ethanol from barley with absolutely no fossil fuel inputs and a low capital investment distillery powered by firewood. They didn’t have cars to burn it in, but being resourceful people they found other uses for it. Owning a smart horse meant that they always had a designated driver. 🙂

32. Jerry Unruh says:

Optimist:

Jerry,
Maybe I’m being slow here, but I find this a tad confusing. You seem to be using both an EROEI of 1.5 and a (net?) energy output of 1.5. Would you mind showing what the calc would look like for say an EROEI of 1.5 and net energy out of 10?
——————————————
After reading Robert’s post it seemed clear to me that if the EROEI was 1.5:1 and the input energy came from the same source, then the energy required to obtain the 1 unit of input also had to be obtained. That is, 1/1.5 = 0.67 is needed to generate the 1 unit. Then the 0.67 had to be accounted for (0.67/1.5 = 0.44), etc. Essentially a summation of all the energy input is required and this can be done by integrating (1/1.5)**n from 0 to infinity. The solution to the integral is: (1/1.5)**n/ln(1/1.5). At n= infinity this becomes zero and at n= 0, it reduces to 1/ln(1/1.5). Obviously, this can used to calculate any EROEI and the input energy does not have to be the same as the output. Does this answer the question?

33. Jerry’s approach gets to the heart of why the guy at TOD made the initial error: He treated his inputs as free energy. Jerry integrated to get all of the required energy inputs. But it also works to solve the two equations for Net Energy and EROEI.

34. Kinuachdrac writes:
As we move away from prime fossil fuels, the energy demand of the energy supply industry will become one of the largest components of total energy demand. This is one of the Achilles Heel’s of most so-called “renewable” energy sources.

But from the website that RR mentioned
http://db.world-nuclear.org/info/inf11.html
The EROEI for Solar is on par with LNG. Wind is on par with Coal. Hydro is on par with Nuclear. Seems to me that if renewables have an EROEI problem, then so would these others. But you do have a point about storage. Right now most EROEI studies don’t include the storage within the system boundaries, and there probably should be more studies that include with and without storage. Sometimes you’ll see the PV studies with storage listed as “off-grid”.

35. Anonymous says:

I don’t think Robert really touched the biggest problem in EROEI. The important point when calculating it is that the energy input and energy output are inputs and outputs to the system. However, the system can be defined in various way, affecting the inputs and outs – often there is not even one correct way to define it. Also important to notice is that warying the defintion of the system has often larger effect on the resulting number than the actual performance of the system. Almost alway when someone calculates EROEIs, they fail to explicitly say the definition of the system, resulting in very strange numbers.

It is also apparent in this comment:

But you aren’t disagreeing with me, because I never said that it isn’t worth distinguishing. I am just pointing out that when the EROEI from sugarcane is mentioned as 8/1, it isn’t really an EROEI.

Both 8/1 and 2/1 are correct EROEI, they just use different definitons of the system. For 8/1 the system is considered to contain everything from the start of growth of the sugarcane to the final product. The bagrasse is just moving energy inside the system, not affecting the EROEI at all. For 2/1, you consider only the actual sugar-part of the cane to be part of the system, and the bagrasse is exteranl input.

However, I do have a problem in defining the system so that you get 2/1 as the EROEI. If you consider bagrasse as external input, then you have to also calculate the bagrasse going “out” from the system. After all, the bagrasse is a byproduct of that very same process.

To illustrate that, let’s say that the bagrasse is burned to electricity (with the same efficiency as in the boiler), and oil is used in the boilers instead. Now the etanol process would look the following:

N units input to grow the sugarcane and other associates processes.
3N units of bagrasse output to electricity generation.
3N units of oil input to fire the boilers.
8N units of etanol produced.

Now, to get the EROEI of 2/1, you need to ignore the output of bagrasse produced together with sugarcane, which seems a bit silly.

36. Jerry Unruh says:

Optimist:

After I posted last night, I realized I didn’t answer your question. Using the 1.5:1 EROEI, I added the input to the 1.5 units to show the total energy required to obtain 1.5 units of usable energy. Thus 3.466 units were required to produce the 1.5 units used to fuel a car, heat a house, etc. The total energy ultimately burned is 4.966. To obtain any other amount e.g., 100, multiply 4.966 by 100 and divide by 1.5.

37. However, the system can be defined in various way…

This is a big problem, which I touched on above as the boundary problem. Where do you draw system boundaries? EROEI can be subject to a lot of manipulation that way.

For 2/1, you consider only the actual sugar-part of the cane to be part of the system, and the bagrasse is exteranl input.

Not exactly. You get 2/1 by considering all of the energy inputs that were actually consumed in the process. Bagasse was consumed by burning it. This is exactly how we calculate the EROEI in a refining process. The fuel gas generated internally gets counted against the EROEI. If you didn’t count it, you could come up with an outrageous – potentially almost infinite EROEI for making gasoline. But if you focus on what was actually consumed to make the final product, 2/1 (or whatever the real number is) is correct for sugarcane, and 8/1 would be a fossil fuel ratio – but not EROEI.

RR

38. Optimist says:

Jerry,
Thanks for the explanation.

I have to disagree, though. I think you are overcomplicating the calculation.
That is, 1/1.5 = 0.67 is needed to generate the 1 unit. Then the 0.67 had to be accounted for (0.67/1.5 = 0.44), etc.
This the bit I disagree with. EROEI = 1.5 means you put 1.0 units in and you get 1.5 units out, not so? (You net [1.5 – 1.0 =] 0.5 units; you need to put [1.0/0.5 =] 2.0 units in for every net unit out needed) There is nothing left to be accounted for.

Thus 3.466 units were required to produce the 1.5 units used to fuel a car, heat a house, etc. The total energy ultimately burned is 4.966. To obtain any other amount e.g., 100, multiply 4.966 by 100 and divide by 1.5.
In this case EROEI would be 1.5/3.466 = 0.43, or am I missing something?

BTW, Robert, should your definition be expanded, for clarity? The first is that EROEI = Energy Output/Energy Input not including energy in the feedstock? If you include energy in the feedstock, you are simply calculating efficiency, right?

Question: Do we need both EROEI and efficiency? Aren’t they just different ways of calculating the same thing?

39. Jerry Unruh says:

Optimist:

I can understand your concerns. Here are my answers. First, in the 1.5:1 example without correcting as I have, 2.5 units of energy will ultimately be expended; the 1.5 to heat a house, etc. and the amount that went in to producing the 1.5 units. The problem with stopping there is that the 1 input unit would be “free” by your approach, i.e., there was no energy cost to produce it. if you focus on how that energy was produced you will ultimately come to the conclusion that this is a power series just like accumulating interest in a savings account. The difference is the power series is less than 1. Consider that 1.05**-n is the same as 1/1.05**n.

The approach I am suggesting is flexible in that it allows separation of the output energy and the input energy. For example, as I stated in another example the energy input from the 1.5:1 case could come from any source, perhaps one that has an EROEI of 10:1. Then the power series shows that much less total energy is needed.

Using my 1.5: example, the way I calculated shows how much energy is needed to produce 1.5 units for heating a house, etc. If you divide the total number by 1.5 one obtains the amount of energy required/ unit of energy, i.e., (3.466 + 1.5)/1.5 =3.311/ unit of useable energy. From there you can get the amount of energy required to obtain any amount of usable energy you wish.

40. doggydogworld says:

If I put 100 BTUs in and get 105 back out, then my EROEI is 1.05, but the energy return is 5%.

But financial people who put in \$100 and get \$105 back do not say their “ROI” was 1.05. Their definition of “R” differs from yours — theirs is net return while yours is gross.

I don’t mind that EROEI is defined differently than financial ROI, I merely note the difference. And I further note that people who talk of negative EROEI obviously use a different definition than you.

41. Optimist says:

Jerry,
I think we are talking two fundamentally different approaches here: I am interested in EROEI as it relates to a specific process, something I can draw a box around. What enters from outside the box is not my concern. At least not while I’m calculating EROEI.

Your approach seem to be to look at a closed system where nothing leaves (or enters) the box, it must all be accounted for inside the box, i.e. within the definition of EROEI.

So, when you say: The problem with stopping there is that the 1 input unit would be “free” by your approach… I have to disagree. It’s not free, it’s just that it came from outside the box of interest.

Considering which approach is more useful I have to say I think my method is, because closed systems are rare. Even the planet is not a closed system i.t.o. energy, with all that sunshine that keeps the natural world going.

At least, that’s the way I see it.

42. Optimist says:

RR,
Allow me to phrase this in terms of mathematics, and see if you agree. You mentioned that:
EROEI = Energy Output/Energy Input, or
EROEI = Eo/Ei (1) and
Net Energy = Energy Output – Energy Input, or
En = Eo – Ei (2)
Substitute (1) in (2) and eliminate Eo so that you get:
En/Ei = EROEI – 1 (3)
which is innocent enough. The trouble starts when one focusses on Ei, as RR tends to do:
Ei = En/(EROEI – 1) (4)

All of which leads me to believe that as EROEI drops we will have to start conserving on a huge scale, or else…

43. Hey Robert,

This is an excellent post. It’s that net energy that people never seem to think about.
I am new to your blog, so perhaps you may have mentioned this before, but what average EROEI would you say modern society needs to keep running?
Have their been any studies done on this?

44. Jerry Unruh says:

Optimist:

The problem as you state it is why I think Robert posted the piece in the first place and is summed up by the paragraph I lifted from his original post.
—————————————
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 usable energy at a 20:1 EROEI is 93.7% while the usable energy from 1.5:1 is only 30.2% (as calculated by my method). Therefore, the calculation as stated above and as you would like to do it greatly underestimates the amount of energy required to maintain a given usable energy output as the EROEI decreases. Therefore, we can be lulled into a false sense of security or be led to unsound energy solutions (e.g., ethanol from corn or biodiesel from soy). We are going to have enough problems dealing with all of this in the future without lying to ourselves.

Your analogy of closed and open systems seems irrelevant. In fact, I think you have the concept turned around. Closed systems draw arbitrary boundaries in order to make them easier to deal with. One of the prime reasons so many people thing that life is a refutation of the second law of thermodynamics is that the earth is viewed as a closed system without considering input from the sun, etc.

45. Optimist says:

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.
OK, but that’s not I’m saying. Take eq (4) from above, assume that En needs to stay constant. As EROEI drops from 20 to 1.5, Ei increases from 0.053 (per unit of En) to 2.0, or by a factor of 38. If you go from 20 to 1.3, Ei increases by a factor of 63, the same result RR got.

The usable energy at a 20:1 EROEI is 93.7% while the usable energy from 1.5:1 is only 30.2% (as calculated by my method).
My head’s spinning again. Usable energy (net energy?) as a percentage of?

Therefore, we can be lulled into a false sense of security or be led to unsound energy solutions (e.g., ethanol from corn or biodiesel from soy). We are going to have enough problems dealing with all of this in the future without lying to ourselves.
I think RR does a good job of pointing out that the pro-ethanol crowd uses efficiency when discussing oil (Eff = En/Ei, RR?), but switches to EROEI when discussing corn ethanol (more than 100%, see!). And that argument can’t be won, I believe.

Anyway, corn ethanol (and all food-based fuels) will be killed in the marketplace, as is already happening. Unfortunately, we all have to live with high food prices (but not high inflation, you’ll be glad to hear), while this works its way to the scrapheap of Washington’s dumbest ideas…

46. Anonymous says:

Robert,

I have been buying drilling stocks such as PTEN and PDS for the past year because: A. They are cheap on P/E basis and B. It would seem to me, as EROEI declines, drilling activity will have to increase exponentially. Am I thinking correctly?

Tom

47. Tom, I think that logic is correct. The oil field services companies are in the position of the corn farmer: They profit from higher prices whereas the producer doesn’t always profit because of loss of margin.

I think oil field services will continue to be profitable, and I think your logic is correct.

48. BTW, Ethanol from Brazil is greater than 2 to 1 as Brazil loaned Ethanol Distillers money to put in co-generation equipment to add electricity to the national grid. Bagasse returns a lot more energy than is needed to make Ethanol.

Distillers only use about 25% of the electricity generated and the balance goes in the grid which pays off the loans and gives distillers a second source of income. Source: “Alcohol Can Be a Gas” by David Blume