The concept of energy return on investment (EROI), often called energy returned on energy invested (EROEI), is a simple and familiar one. Here is the short definition, from the Encyclopedia of Earth. To cite:
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Energy return on investment (EROI) is the ratio of the energy delivered by a process to the energy used directly and indirectly in that process.
For example given a process with an EROI of 5, expending 1 unit of energy yields a net energy gain of 4 units. The break-even point happens with an EROI of 1 or a net energy gain of 0.
A common related concept is the energy payback period. Every energy system has initial investments of energy in the construction of facilities. The facility then produced an energy out for a number of years until it reaches the end of its effective lifetime. Along the way, additional energy costs are incurred in the operation and maintenance of the facility, including any self use of energy. The energy payback period is the time it takes a facility “pay back” or produce an amount of energy equivalent to that invested in its start-up.
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Wiki also has a decent article about it, and it’s a source of much discussion on websites like The Oil Drum. In short, a simple concept, but fraught with debate. It is not my intention here to wade into the arguments on EROEI of individual energy sources — that would require many TCASE posts, and even after that, I’d be unlikely to get consensus. But feel free to hammer away on the ins and outs of EROEI in the comments.
What I want to do here is propose a simple method for estimating EREOI based on a life-cycle assessment of greenhouse gas emissions. This requires some assumptions, but is useful, I think, because LCA studies are readily available and widely cited, whereas explicit EREOIs via net energy analysis are harder to find and compare in a consistent way.
There have been many well-researched peer-reviewed studies looking at the life-cycle emissions of different energy technologies, expressed in terms of kilograms of CO2-e/MWh (commonly). For non-fossil fuel energy technologies, this is a useful benchmark for calculating EROEI, because their inputs mostly come from fossil fuels, yet they produce no CO2 when generating. So, let’s consider ‘clean energy’ EROEIs on this basis.
LCA on carbon emissions for nuclear (excluding weird outliers like SSL) is in the range of 5 – 80 kg CO2-e/MWh. This range is based on various assumptions about relative mixes of diffusion/centrifuge enrichment, embodied plant energy etc. (see WNA summary). For wind it’s ~30 kg CO2-e/MWh (without considering backup), solar thermal ~80 kg CO2-e/MWh, PV ~150 kg CO2-e/MWh. A more complete range of estimates, based on meta-analysis, are given here, in a detailed study by ISA (University of Sydney).
If we assume that about half the energy inputs comes from coal-fired electricity and the other half from oil (mostly diesel for mining) — a reasonable approximation, given the present fossil-fuel-dominated global economy — then the average emissions intensity for inputs will be roughly 900 kg CO2-e/MWh. With this number, we can then estimate the EROEI of various technologies:
Nuclear LWR = [900/5] to [900/80] = 180 to 11 EROEI; Wind = ~30, Solar Thermal = ~11, Solar PV = ~6, etc.
It is simple to then undertake a sensitivity analysis of the above, such as changing your assumption about the carbon intensity of the fossil-fuel inputs, and/or substituting different values you have for a nuclear/renewable CO2-e/MWh. For instance, if you assume 800 CO2-e/MWh for fossil-fuel inputs and a LCA of 50 for solar PV, the EROEI then becomes 800/50 = 16.
For a future closed-fuel-cycle nuclear technology, like the IFR, one can remove the inputs for mining, milling, enrichment and long-term waste management, retain those for plant construction and decomissioning, and add those for recycling of the fuel and short-term management of vitrified fission products. My rough estimate, using the breakdowns given here (Tables 1 and 2), is < 1 kg CO2-e/MWh, even if only fossil fuels are used for energy generation during the plant’s construction. There will be no direct emissions from fuel pyroprocessing, because it will be on-site, and so make use of the IFR’s power. Thus, the IFR’s EROEI is expected to be >900 — and it will be carbon-free, once fossil fuels are completely phased out.
With the EROEI to hand, energy payback time is a straightforward calculation. For example, if your technology’s EROEI is 15 and the power plant’s lifespan is 35 years, then the energy payback time can be approximated as 35/15 = 2.3 years or 28 months.
I’d appreciate any comments on the validity (or otherwise) of the above short-hand method I’ve used here for estimating EROEI and payback. Indeed, in the spirit of ‘blog-science’ review, I’m happy to stand corrected on any of the above, and revise accordingly, if I’m in error.
Finally, I’d like to propose some open questions for discussion in the comments section, below. These were first asked of me by regular BNC commenter Douglas Wise, so the credit — as devil’s advocate — goes to him:
1) Why are EROEI assessments so monumentally variable?
2) Why don’t high EROEIs necessarily (currently) translate into high ERO$I?
3) Will high EROEIs ever translate into high ERO$I?
Here is an early answer I gave to Douglas via email, which covers some of these points, from my perspective:
The EROEI for nuclear varies a lot depending on the assumptions you make. Realistic assessments using current high grade ores put it at over 100:1 with centrifuge enrichment and a little higher again with CANDU. With low grade ores and diffusion enrichment, it can be as low as 10 to 20:1. The world average, according to some recent figures I’ve seen, is ~50:1. This has been worked out in a number of comprehensive studies, using real-world mine data (e.g. Rossing, Olympic Dam), enrichment SWUs from France, US and Russia, and plant construction and operating data. As always in such matters, the numbers are available, publicly, for you to crunch yourself, if you have the time and tools. Don’t take such matters on faith — a lesson from Mackay.
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Footnote: This article from EoE is well worth reading, Ten fundamental principles of net energy. Here are the headlines:
1. Net energy and energy surplus are important driving forces in ecology and economic systems
2. The size and rate of delivery of surplus energy is just as important as EROI
3. The unprecedented expansion of the human population, the global economy, and per capita living standards of the last 200 years was powered by high EROI, high energy surplus fossil fuels
4. The principal economic impact of a shift to a lower EROI energy system is the increased opportunity cost of energy delivery
5. Energy quality matters
6. Market imperfections that distort prices and cost also affect EROI
7. The methodologies to perform net energy analysis are well established
8. The relation between ‘peak oil’ and the EROI for world oil production is unknown
9. Technological change affects EROI just as it affects price and cost
10. Alternatives to the dominant energy and power systems show a wide range in EROI
Brave New Climate 
21 replies on “TCASE 8: Estimating EROEI from LCA”
It has been my observation that EROI calculations are more valuable comparing similar modes of energy production than they are making comparisons between different modes, simply because it is very difficult to establish a equivalent set of assumptions on inputs.
The method you are suggesting however goes a long way toward addressing this handicap and should be considered the only legitimate method to compare different types of energy production
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I appreciated this post because I am firmly of the view that ERoEI is an extremely important concept when attempting to discriminate between competing energy systems. If politicians saw things this way, they’d have to be very desperate to opt for systems with worse ERoEIs than those of fossil fuels.
We know that the ERoEIs of fossil fuels are declining and it is self evident that CCS coal will have a worse ERoEI than that of dirty coal. Why, then, devote time and money in researching capture and storage methods? The only justification I can see is if the techniques were applied to gas in its value added role of providing peaking power. With respect to solar and wind energy, only onshore wind looks to have potential from an ERoEI perspective but , as I have learned on BNC, this disappears as soon as one factors in back up requirements. Only if an important use for stranded wind could be found (ie where intermittency doesn’t matter), would it become sensible to contemplate it. Nuclear appears to be the only technology currently available to offer the potential to have a higher ERoEI than those of fossil fuels. However, as mentioned in the post, the antis have found it possible to come up with papers claiming truly disastrously low ERoEIs for nuclear (based, one assumes, on poor ore quality and expensive, energy intensive (now obsolete) enrichment. I believe nuclear proponents should attempt to get more realistic handles on nuclear ERoEIs and Barry has not only cited some relevant information but come up with his own,novel shorthand approach
By computing ratios as Barry has done with LCA figures, he is most certainly obtaining very useful information with respect to CO2 mitigation efficiencies. I am sure that the method also gives useful approximations of net energy gains in most instances as well. However, it is open to some criticism. For example, Barry writes, apropos the IFR, that “there will be no direct emissions from fuel pyroprocessing, because it will be on site and so make use of the IFR’s power.” Thus, if one bases one’s ERoEI calculation on the LCA of an IFR, it will look very favourable. However, were pyroprocessing to use up half the IFR’s power, net energy would be halved rather than left unchanged (still better than anything else, though).
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The infamous Storm van Leeuwen publication wasn’t based on assumptions about lean ores and gaseous diffusion enrichment – it was simply based on totally nonsensical methodology and accounting.
It’s possible to look at life-cycle analysis of nuclear energy from light-water reactors, assuming enrichment via gaseous diffusion and lean uranium ores – and still get consistent numbers from different sources which still are totally inconsistent with van Leeuwen.
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Barry – I’ve thought about EROEI for some time, after reading about it at “The Oil Drum” several years back. I believe it is a fundamentally flawed metric because it leaves out the time factor – both forward and back (how far back do you count “inputs”?) – i.e. as long as EROEI is greater than 1, any technology will produce growth, and the rate of growth is then determined by the time scale, not by the EROEI number in itself.
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That publication was only commissioned on the basis that mud always sticks (aka malevolent memetic engineering). Therefore I like to name it as above, so that persons eager to be deceived can’t so easily find it.
(Boron: A Better Energy Carrier than Hydrogen?)
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A troubling feature of EROEI estimates is the way we apply them to chalk and cheese situations. We can have a rate of return on both a fuel like NG and on a low fuel technology like wind power. It gets more complicated for a coupled system like gas-backed wind power when the two technologies may have different plant lifetimes. I suggest a weighted average may be a reasonable approximation for a coupled system. Suppose wind has 25% c.f. and an EROEI of 20 while combined cycle gas has an EROEI of 8. Then the weighted average is .25(20) + .75(8) = 11 an intermediate figure closer to the larger weighted component. Note commentators like Euan Mearns on The Oil Drum believe a system average EROEI of about 8 represents the shoulder of a cliff from which we will never return if we fall below it.
Perhaps those weights should sum to more than unity to allow for transients such as ‘powering up’ for the gas plant. I’m not sure about using CO2 intensity as a proxy variable. I thought renewables utopians envisage concrete, steel and silicon being one day made entirely from renewable energy. By then fossil fuel burning will be a distant memory.
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With LWR fuel recycling, the EROEI for either the LFTR or the IFR should be excellent. Currently there is something like a million tons of spent uranium that can be used to fuel IFRs, and tens of thousands of tons of thorium in mine tailings, and it only takes a ton of thorium to provide a Gw year of electricity. If only the pyroprocessing system did not manage to loose 3% of fuel plutonium every time the fuel is reprocessed.
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Thanks for the post Barry.
Personally, as you and others are talking about a phased introduction of IFRs at the other end of a process beginning with AP1000s or other suitable LWRs and allowing the anticipated movement of the fuels-hazmat between the plants perhaps a more useful calculation would be one that considers the entire fuel complex as a system.
So then the EROEI on an LWR that was built with GenIV technologies as the target of its hazmat would spread the initial embedded energy and feedstock energy harvest cost across the whole lifecycle. That way the IFR’s payback cost time goes up but the LWR’s payback time goes down.
Of course, an IFR built simply to harvest existing hazmat and extract further energy could keep its unique marginal EROEI.
Part of the problem mof course is at what point you start the calculation. If you use mine tailings, or perhaps coal slag — both waste products — then you can legitimately ignore the energy input that produced them, since this was not contemplated at the start of the operation. It is a given. OTOH, if a mining operation is part of a process of nuclearFF energy production in which the tailings are a feedstock or the LWR for example produces feedstock for the IFR, for example, then maybe the calculation ought to reflect this.
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The question of the power consumption of pyroprocessing has come up before, and I’ve wondered about it. There’s no instance of the process available so there’s no data, so I decided to try and estimate it.
In IFAD3, Barry reports a 1 GW IFR would require about 13.5 tonne per year of metal fuel to be run through pyroprocessing. Thats about 56250 mole, assuming an atomic weight of 240.
As I’ve said previously, aluminium production by electrolysis in a molten salt is a great comparative system for understanding pyroprocessing. Its obviously a highly developed process that would operate on a much larger scale than an IFR module, but its a real world process we can draw from.
Aluminium is currently produced by electrolysis for an electrical energy cost of about 50 MJ/kg, or about 1.35 MJ/mol (atomic weight of Al is 27). That’s about 50% theoretical efficiency – pretty good.
The reduction potential of Al(3+) -> Al is 1.66 V. The production cells run at a potential difference of 3-5 V, and currents of about 300 kA. This gives a cell power consumption of about P = VI ~ 4V x 300kA = 1.2 MW.
The cell production rate is therefore ~ 1 mole per second (1.2 MW / 1.35 MJ/mol), or about 100 kg/hr.
Thats aluminium.
Going to uranium, the electrochemistry is, coincidentally, almost identical: U(3+) -> U at 1.66 V. There are differences (different half cell reaction at the cathode, its a mix with plutonium, different mobilities for U vs Al, etc) but assuming the same cell parameters as for Al will be pretty good.
So we can assume a similar energy cost of ~1.35 MJ/mol for the IFR fuel and be in the right ballpark. In an Al-class electrolysis process, producing 1 mol/s, thats 860 kg/hr at 1.2 MW.
So you could process 13.5 tonne of IFR fuel in 15.6 hours at 1.2 MW. Call it 20 MW.hr for annual pyroprocessing power consumption.
For a 1 GW reactor, thats nothing. Even if you assume a much lower efficiency due to smaller scale and a less developed process, its still nothing. Which is as you’d expect, since we’re comparing the energy required to push around outer shell electrons to the energy available from fissioning the nucleus.
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I wonder whether I could ask those with appropriate knowledge for more information about the economic prospects for and environmental impacts of underground coal gasification plus CCS? Although the subject may be somewhat OT, I think it may have some relevance if what its advocates say of it is correct.
If one accepts the thesis that renewables are not the way forward and that oil and gas reserves are depleting, one is left with coal as the only serious competitor with nuclear. It has been repeatedly stated here that nuclear’s success can be best achieved by ensuring that it can compete with coal on economic grounds.
Enthusiasts for UCG claim that it is a far cheaper and cleaner way to obtain energy from coal than is conventional mining. They also claim that the process facilitates CO2 capture and will thus make CCS more affordable. If they are to be believed, one might suppose that, in future, clean energy from coal might be no more expensive than is the current energy from dirty coal (ie it’s ERoEI might not be adversely impacted). If this is really likely to be the case, it would be wonderful news for mankind and the planet, not that it would in any way weaken the case for rapid deployment of nuclear power (except in the minds of dyed-in the-wool anti nukes).
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DW I see a problem with UCG + CCS immediately. The sedimentary basin that gets lanced and burned up should be somewhat pliable. OTOH the underlying or nearby sedimentary basin that gets CO2 storage should be as tight as a drum, an unlikely coincidence. If the CCS basin is a saline aquifer that property is undesirable in the UCG basin since damp conditions inhibit combustion. Note underground partial burning will produce additional NOx, SOx (from pyrite) and CO2 that will need to be scrubbed at the surface after second stage burning. The gas from underground already contains fire retardants so the energy penalty of additional CCS will then be substantial. This is oddly similar to granite geothermal; lack of control over underground plumbing combined with a not very hot surface process.
I think UCG enthusiasts could be mining subsidies which politicians seem willing to dish out to anything that isn’t nuclear.
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Just subscribing to this threat too, thanks.
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John Newlands
Thanks for the reply. I thought that all in the UCG garden might not be as rosy as its supporters claim.
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It’s really time to discard any fission lifecycle study results that assumes diffusion enrichment, when discussing future considerations of nuclear power. Low EROI figures can often be traced to this historical relic. Present-day nuclear with efficient (centrifuge/other) enrichment should have a lifecycle EROI of 50 at least. Options for more efficient use of fuel or fuller use of uranium (or thorium) probably push the figure well north of 100 and possibly much higher.
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I have some major objections to the usefulness, if any, of EROEI.
A bad map can be worse than none at all. There are people who are firmly convinced that going from an EROEI of 100 to an EROEI of 1000 is an important improvement. Expressed as EIOER this is merely going from 0.01 to 0.001, from negligible to completely irrelevant.
There is a strong tendency to focus on EROEI as if it was a shorthand for the economics/practicality or the environmental costs of a form of energy. The correlation is weak even for low EROEI sources(e.g. you can easily do 100 times more damage by draining a peat bog to plant oil palms than planting them somewhere sane).
EROEI completely ignores the quality of energy. Can I have it when and where I want? Is it portable? Is it thermal, mechanical, chemical or electrical energy? How efficient is that form of energy in doing what I need it to do?
My second major criticism to EROEI is that it’s illdefined. Do you include ESelf? To what extend do you include ESelf?
E.g. In a combustion turbine some large fraction of the mechanical energy produced by the turbine is consumed by the compressor stage. If you include this as a component of ESelf into EROEI you will never get an EROEI above low single digits for combustion turbines.
E.g. In a nuclear plant some 5% or so of electricity produced is consumed internally to run the various pumps associated with the cooling and steam cycle. If this is included in the ESelf component the EROEI is at most 20, if it’s not included it is ~100, if the input energy was expressed as electricity(because that’s what e.g. coal is converted to when used for enrichment) you get an EROEI of ~200. From the economic point of view, the ESelf component just means you consume a tiny amount more of uranium(which is not included in energy invested because it is “free” in the same way coal is for coal plants or sunshine is for PV plants) and the plant is slightly more sturdily built.
(see the EPD for Forsmark nuclear plant, not far from where I live: http://www.environdec.com/reg/021/ . The conversion from grams of fuels to kWh of thermal or electrical energy is trivial with reasonable precision and I won’t elaborate on it here).
Where does legacy infrastructure and losses fit into EROEI?(e.g. the prior investments in electrical grid and the line losses)
Does a solar farm in a desert in the middle of nowhere pick up the energy invested tab for the powerlines even if they were built by the tax payer in order to support solar development?
I reject the notion that EROEI is a useful concept other than for political gameplaying and obfuscation.
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@Soylent, – While I agree wholeheartedly that the concept is abused shamefully, it is nonetheless of some use comparing apples to apples.
If the modes are the same, and the ‘EI’ input sources are the same, a good comparison can be made, for example, between different designs of NPPs or hydro dams, storage battery types and such.
The problem, as you pointed out, are when it is used to compare apples to oranges, particularly when there is no constraints put on the set of input sources.
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Soylent
While you raise some interesting objections to EROEI, it is a basic metric in energy feasibility. Not the only one, but one that is a starting point for examination.
Yes, energy quality matters. So does scaleability. So does the wider footprint of the energy. So does opportunity cost, and relative cost per unit of output and whether the energy technology can be reproduced in the setting needed. But it is still a useful measure.
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I personally would like to see an international body that defined what the heck we are meant to be discussing with ERoEI.
As Soylent rightly asks, do we include the power lines that shove the power from deserts into cities?
Do we include construction of the roads, which maybe 1/100 thousandth of their lifespan was used up by the construction of the power plants?
Do we include the breakfast that the widget factory worker was digesting that morning in the factory that made the screws that were used on the power plant?
These are all issues that various peak oil doomers (like Mike Stasse of ROEOZ) have tried to put to their various equations to try and make anything non-petroleum have ridiculously low ERoEI’s. It’s not science, but catechisms of their faith, and they don’t bother actually measuring out these things but just summarise: “With all these things in mind, there is no WAY anything measures up to the energy density of oil”.
So while that’s an example of the extremes the ERoEI term can evoke in people, it does still seem to be a subject of varying definition, and every Life Cycle Analysis / ERoEI study seems to have a very long list of terms and definitions and scope of their studies, as this is still an evolving field.
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[…] https://bravenewclimate.com/2010/03/08/tcase8/ […]
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Workers’ breakfasts may be totally negligible in calculating eroei, but tell that to anyone who has to go to work without theirs, and see how well he or she performs during their 8 hour shift….
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I’d love to resurrect this conversation about ERoEI and ask what nuclear’s ERoEI would be once the higher grade ore bodies run out? Ultimately, ERoEI asks if something is even an energy source, which is sometimes debatable in cases of various ethanol crops. What would the ERoEI be of uranium from seawater? I know that could be as far as 50,000 years away, and who knows what we’ll have by then. (Space solar? Fusion?) But I like to argue that IFR’s are already the ‘forever machine’ that could run our world for 10’s of millions of years if nothing else comes along. It would be great to know the ERoEI from seawater for this purpose.
Regards!
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