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By Robert Rapier on Mar 5, 2008 with 10 responses

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.

  1. By Chris Harries on April 7, 2011 at 7:35 pm

    I have been wondering for some time if an enterprise that has, in effect, a negative EROEI – that is, it consumes more energy than it produces – can be viable.

    For instance, if in extracting oil from tar sands an enterprise uses 10 units of energy to produce 8 units of useful energy then why is that not possible?

    Horribly inefficient, I know, but the owner of the tar sands fields ends up delivering some energy even though the majority of the energy produced by the field is used up in the production process.

    If 10 units of energy was bought from external sources in order to deliver 8 units of energy for sale, then the enterprise would have to fail. But as a closed loop, then the only factor preventing a viable concern would be one of cost. So long as the sums add up the the enterprise may be commercially viable.

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  2. By Robert Rapier on April 7, 2011 at 9:19 pm

    Hi Chris,

    Yes, and I have pointed this out in other posts. If, for example, you could take X BTUs of coal worth $1 and turn that into 1/3 X BTUs of a liquid fuel worth $2, then of course you do it. Economics will dictate you do it, but it is of course highly unsustainable and will deplete resources much faster.

    RR

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  3. By Robert Rapier on April 8, 2011 at 12:48 pm

    Chris, here is an article that I wrote that went into some of the details you allude to above:

    http://www.consumerenergyreport.com/2010/07/07/fun-with-numbers-the-new-usda-report-on-corn-ethanol/

    RR

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  4. By Balint Simon on December 13, 2011 at 5:10 am

    Hi,
    unfortunately the rules of economy never will be similar to the rules of ecology :( I don´t find it really sound thing, but the economy is the boss (yet).

    Regard

    B.

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  5. By John Clarkson on May 14, 2013 at 8:32 am

    This makes no sense. Think about the cost of turning the tarsand into oil and selling the oil. The input energy will be more than the output energy cost so it will never be profitable.

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    • By Robert Rapier on May 14, 2013 at 1:56 pm

      It could still be done if the energy inputs are cheap and the outputs a worth more. For instance, it might be economically attractive to turn 2 BTUs of coal into 1 BTU of liquid fuel. Not a good idea from an environmental viewpoint, but economics could trump EROEI in that case.

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      • By Franz von Rintelen on June 2, 2013 at 8:21 pm

        Economics unfortunately can never triumph physics or mathematics. The physics of doing this make it very expensive in order to replace all oil consumed per year. But let’s say you are right, and they do it, how long would it last? Exponential growth in demand would quickly out do it. Is this a sensible use of coal? Why not burn it and convert it to electricity and charge up lithium batteries for transport instead?

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    • By TimC on June 3, 2013 at 12:27 pm

      At Shell’s Pearl GTL plant in Qatar, the cost of the natural gas feedstock is practically zero. Converting $0/MMBTU gas into $30/MMBTU liquid may prove to be very profitable, even if the EROEI is poor.

      The confusion over energy balance, I think, arises because for fossil fuel production, EROEI is calculated without accounting for the energy in the raw feedstock. If the heating value of crude oil or tar sands is included, then EROEI of fossil gasoline or diesel production can never be > 1. For consistency in comparing renewable to fossil fuel production schemes, I think that all energy inputs should be included in the EROEI calculation, regardless of the costs of the inputs. Or am I wrong?

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      • By Robert Rapier on June 3, 2013 at 1:04 pm

        “For consistency in comparing renewable to fossil fuel production schemes, I think that all energy inputs should be included in the EROEI calculation, regardless of the costs of the inputs. Or am I wrong?”

        First, you are correct that there is confusion around the issue. When you see someone say that the EROEI of corn ethanol is 1.3 and that of gasoline 0.8 they are comparing an EROEI to a process efficiency. The former is a measure of how much energy was consumed in the process of producing the fuel, and the latter merely measures how much energy was lost given the energy value of the inputs. By an apples to apples comparison, the EROEI of gasoline would be around 5 or 6 to 1.

        The other confusion is that sugarcane ethanol producers don’t count the bagasse as energy inputs. So they come up with EROEIs in the range of 8 to 1. What that really is reflects the fossil fuel inputs consumed. The actual EROEI that would consider all of the energy inputs is probably down in the range of corn ethanol, but corn ethanol is using natural gas and sugarcane is using biomass.

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        • By TimC on June 3, 2013 at 2:34 pm

          Thanks for the clarification, RR. I’m no EROEI Expert (EROEIE), but I have noticed that EROEI values are used to obfuscate energy discussions as often as inform. Outside of this website, of course.

          It seems what is needed is a quantity that expresses the amount of fossil energy required to produce an energy output, maybe Fossil Energy Input Per Energy Output (FEIPEO). While EROEI indicates if a process is a net energy source or sink, FEIPEO would indicate if the process is renewable. A truly renewable process would have FEIPEO of zero, meaning no fossil inputs required. Many current biofuel processes would probably have FEIPEOs close to 1, showing that they are really just fossil fuel conversions, not renewable energy sources. Something like tar sands-to-gasoline might have FEIPEO over 2, revealing very poor leverage of a fossil resource.

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