Wednesday, January 9, 2008


Energy returned on energy invested (EROEI) is a measure of the feasibility of an energy source and so it should be useful for comparing different energy sources to try to pick which one to use. Here we are mainly concerned with real energy, but from time to time I get into discussions with people who feel that nuclear power is a good thing because it is suppose to have a high EROEI. They are deceiving themselves but they are being encouraged by the nuclear industry in this self-deception so lets look at the numbers. We won't do a full life cycle analysis, just find a few of the problems.

EROEI can be calculated as (net energy out)/(energy expended)+1. We can see that EROEI=1 is the break even point because if you are not getting any net energy out then you have zero in the numerator of the fraction and you are left with 1 in the sum. This is the situation where it takes just as much energy to get energy as you actually get. The classic example would be when an oil well needs a barrel of oil to extract a barrel of oil. Oil wells shut down before this happens. If an oil well gets two barrels of oil gross for every one used to run it then the EROEI(thermal) for the well is 2. We have pumped two barrels total to get one barrel net: 1/1+1. We are tagging the EROEI as thermal because that will be important later. Now let's consider an oil field where the output of half the wells are used to run the whole field. We'll consider this from the perspective of the oil input. The oil input produces itself in half the wells leaving an equal amount to take away (net). So, EROEI(thermal)=1/1+1, the same result as you might guess. For a similar system using nuclear power with half the reactors enriching uranium to power all the reactors we have net thermal energy from half the reactors (Eu/2) and energy input from half the reactors (Eu/2) so again we get EROEI(thermal)=(Eu/2)/(Eu/2)+1=2.

Now, we've introduced the tag thermal. This is important. The net energy is not really net until we figure out how its is used. For the example of nuclear power just now, we know that the power plants that are not used for enrichment will be producing electricity with a fairly low thermal to electric conversion factor near 30%. So, we should account for this by applying this to the net energy. We get EROEI(actual)=(Eu/2*0.3)/(Eu/2)+1=1.3. For the oil, it may be used in a furnace in which case EROEI(thermal) is just fine, or it may be used in an engine in which case we would have a similar conversion factor: EROEI(actual)=(1*0.3)/1+1=1.3. Or, it might be stored until fuel cells are available to use it in which case EROEI(actual)=1.7 might be about right. Because of this ambiguity, we want to know the scope of our calculation. Are we ending at the well head, at the furnace or at the wheels? In the case of electricity, we always end at the toaster so when comparing sources, this is where we want to set our scope.

Let's look at the EROEI of the French nuclear program. The French have 58 reactors of which three are devoted to uranium enrichment so we can estimate the EROEI(thermal)=55/3+1=19.3 and the EROEI(actual)=(55*0.3)/3+1=6.5. Because we are only looking at the energy input for uranium enrichment and ignoring the energy inputs for mining, ore processing, plant construction and decommissioning, and unmaking of the nuclear waste this is really an upper limit on the EROEI(actual) of the French nuclear program even if our method of estimating is a little imprecise.

We can use our estimate of the EROEI of the French nuclear program to make another estimate. Suppose that instead of enriching uranium from 0.7% U235 to 3% U235 for fuel, it is enriched to 25% U235 and then diluted this back down to 3% as the US is now doing. Since the US is using cold war enriched uranium, the process used in France, gaseous diffusion, is an appropriate model. Assuming that the depleted uranium that is a product of the enrichment process has a U235 content of 0.3%, Then one unit of natural uranium becomes about 0.14 units of 3% enriched uranium or 0.016 units of 25% enriched uranium with the remainder being depleted uranium. It takes about 1.55 times more energy to get to the higher level of enrichment. So, if France were following the US example, we'd have five of 58 reactors carrying out enrichment rather than three; EROEI(thermal) would be 53/5+1=11.6 and EROEI(actual) would be 4.2. Again, these are upper limits owing to neglect of other energy inputs.

The problem that we run into with the nuclear industry is that they will sometimes admit that the EROEI values they calculate are thermal values, but then they will compare these with actual values from real energy sources which power the toaster without conversion. So, if they calculate an EROEI(thermal) of 20 for nuclear power they'll compare this with an EROEI(actual) of 12.5 for silicon solar panels and say "Hey, nuclear is better!" But, as we have seen, the EROEI(actual) for nuclear power is less than 7 and thus lower than for the solar panels. We've noted before that extending the use of silicon to 100 years gives an EROEI(actual)=33 and recycling makes it approach 99 eventually. The reported values for the EROEI of wind power are also actual and they come in near 20 or above, again better than nuclear power.

The World Nuclear Association has put together a table (2) of estimates of EROEI from a number of sources but they are comparing thermal figures with non-thermal figures in many cases. Let's summarize their table here making the following corrections: for nuclear power we'll use a conversion of 30%, for coal, 40% and for gas 60% assuming a combined cycle:

Power SourceEROEI(actual)
Hydro50, 43 and 205
Nuclear (centrifuge)18.1, 18.4, 14.5, 13.6 and 14.8
Nuclear (diffusion)6.0, 6.7, 5.8, 7.9, 5.3, 5.6 and 3.9
Coal12.2, 7.4, 7.32, 3.4 and 14.2
Gas (piped)16
Gas (piped a lot or liquefied)3.4, 3.76 and 4
Solar PV12-10, 7.5 and 3.7
Wind12, 6, 34, 80 and 50

Here we also have corrections to their table 2 to be consistent with their table 1 for their own calculations. Their calculations are the first listed in each nucelar row and the rest are taken in the order they give them as well. I have not checked that they copied correctly from the references they cite (they left the referernces out) but the solar PV values look familiar and are somewhat out-of-date now. In all, nuclear power does not look as good as wind, even with centrifuge enrichment and with current solar EROEI for thin film PV around 30 in 2009, it does not look good in comparison there either. If the row marked just solar is concentrated solar thermal power, then a commenter below has kindly provided a reference which did not fear to look at conversion to electricty, finding an EROEI of 27 with thermal storage and 34 without (this last is a correction spotted by Brad F at TOD). And, it should be remembered that silicon can get to 30 if you are willing to wait just a little longer than the warrantee duration. It is notable also that present day coal does better than present day (diffusion sourced) nuclear power in most estimates. In all, the renewable sources of electricity, hydro, wind and solar do better than the non-renewable sources, which is pretty much what you would expect since they don't need fuel.

There are some, particularly nuclear power proponents, who might object to my procedure here saying that EROEI should only be applied to the energy source itself and not compared with other sources in this manner. We can easily overcome these objections by subtracting one from each of the numbers in the table. This gives us a new measure which we can call Energy Delivered on Energy Expended (EDOEE). For this measure, break even occurs at the value zero (it was at the value 1 previously). This allows us to look at another set of issues. Two sources in the table require primarily electrical energy be expended to make them work. For nuclear power, enrichment is done using electricity and for solar power refining silicon is also done in this manner. This means that the mix of generating sources is essentially the same for both. Nuclear proponents will often try to hide this by saying that enrichment of uranium is done using nuclear power, but electricity is fungible so this is quite dishonest. But, since both produce electricity, they have the potential to change the mixture of generating sources. Which can do this producing the least amount of emissions? Here we are talking about future growth so we should use the high numbers for nuclear power (around 14) since enrichment capacity is currently inadequate to supply even the current set of nuclear reactors to the end of their design lifetimes so new enrichment facilities would need to be built. Enrichment causes deaths owing to criticality accidents. And, we should take at least the EDOEE for thin film solar (29) (which also uses electricity) since competition will drive out the low EDOEE producers. By taking the ratio, we see that solar power can make electricity generation free of carbon dioxide emissions with half the associated emissions to get the job done. For a utility scale solar installation at an average US location, the two are about equal.

The emissions associated with either are not that large though, and so the largest gain comes in doing the job quickly so that fossil fuel use for general consumption is eliminated. Here, wind has an advantage. 20 GW were installed in 2007. For nuclear power, it is not clear that new construction can keep up with the retirement of existing reactors. With 30 reactors under construction and a ten year construction timescale, that comes to about 3 GW/year of new nuclear power without accounting for retirement of old reactors. So, the pace of nuclear energy is slow. In fact, it is even slow compared to solar which produced 3.8 GW of new capacity in 2007. With growth rates for wind at 30% and solar at 50% annually, both are faster off the block than the essentially replacement level activity in nuclear power. Now, these are all nameplate capacities and we do need to look at the capacity factors which are 82% for nuclear power worldwide, about 35% for wind and about 20% for solar, so wind is ahead of solar by a factor of nine. New nuclear power, not adjusted for retirements, is ahead of solar by a factor of three or less and wind is ahead of nuclear by a factor of three or more. At the present rates of growth, solar will match wind in adding capacity factor adjusted new capacity in 15 years at which point is would be adding 1920 GW of namplate and 384 GW of adjusted capacity. It seems unlikely that that nuclear power will be adding that much capacity in fifteen years while the growth of solar power seems sustainable over the next decade or so owing to the rapidly falling cost of production.

Comparing EROEI(actual) or EDOEE shows us that less effort is needed to eliminate fossil fuel use in electricity generation using wind and solar power compared to nuclear power. This probably partly explains why both wind and solar are doing so much better than nuclear power in getting the job done. It also tells us how much of our time we'll be spending on paying our energy bill rather than say educating our children or improving our health. Those sources which require more effort will be more expensive and a greater drain on our resources. Since nuclear power appears to have little to contribute to accomplishing what we need to do to reduce fossil fuel emissions, it can be viewed as a wasted effort which hinders that accomplishment. Such wasted efforts generally lead to financial losses so it would seem prudent to avoid placing public money at risk in such ventures.

On critic of this entry (mcrab) has proposed a Virtual EROEI (VEROEI) which, instead of adjusting the output of thermal sources of electricity by their conversion efficiency to electricity, one would multiply the outputs of the electricity only sources, hydro, wind and PV solar by factor of three to make a comparison. This is an interesting suggestion and it would provide a fair comparison of relative EROEI between the thermal and more direct sources, giving simliar results to what we have just done using EDOEE. In a way this is a fair thing to do since, if we are to electrify transportation, a wind mill only needs to put in a third as much energy as a gas pump. So, the virtual thermal energy returned is quite a bit more. And, it is true that one can get 4 times as much low grade heat with electricity as with, say, heating oil using a heat pump. But, we can only get a one-to-one conversion when we make fuel using electricity and then only if we have a use for the process heat. Further, to intercompare thermal sources, VEROEI is not all that useful since gas produces twice as much electricity as nuclear power for the same thermal input (one does not want the nuclear fuel to melt). VEROEI may be useful for comparing oranges to oranges, but for apples-to-apples, the method adopted here seems clearer and more physical.


Chris Dudley said...

I am indebted to a commentator at (Mcrab) for pointing out a calculational error in an earlier version of this entry.

Anonymous said...

The EROEI for utitily scale solar thermal electric plants looks pretty good:

The concept of carbonROI is also used which may be relevant with respect to emissions impact.

Charles Barton said...

chris, you failed to consider the effect of centrifuge technology on reactor EROEI. Centrifuges are 50 times more efficient than gaseous diffusion enrichment. The fundamental flaw in your thinking is stems from your failure to understand than the efficiency of nuclear technology can be improved. Since United States plans to open its first centrifuge enrichment plant in 2010, and its current gaseous diffusion plant is only supplying one customer, you ought to to asses the impending transition on nuclear EROEI. Beyond that you ought to look at preposed new nuclear technologies. Since thermal efficiencies as high as >50% are possible with some proposed reactors and nuclear breeding also greatly adds to reactor fuel efficiency, future reactor technology could blow the top off the EROEI chart. Not only are new reactor designs far more efficient, they simly eliminate the supposed problem of nuclear waste.

Chris Dudley said...


Thanks for your comment. If you look at the table, both centrifuge and diffusion enrichment are considered. The limit on thermal efficiency now in nuclear power stems from the need to protect the fuel. In a gas turbine, you need to protect the blades, but you can use more refractory material. In a reactor, you don't want the fuel to melt, and uranium has a melting point 450 C lower than iron. This limits delta T and thus the efficiency.

Breeder reactors are not legal in the US. A breeding program would rather obviously produce even more fission products than we already produce, and these are among the most dangerous portions of the nuclear waste since their corresponding natural isotopes are part of our biological makeup. A first step to solving our nuclear waste problem is to stop making it I think.

Charles Barton said...

Oh Chris but I do want the fuel to melt. In fact a reactor with a molten core has many advantages. If you read my blog youo will know why!

Anonymous said...

Chris, I'm afraid you've fallen into what seems like a common trap. Your EROEI equation is correct as far as it goes, although I would expand it slightly so that (net energy out) = (Energy out) - (expended energy). This is the same equation, with the terms clarified. It gives numbers that are slightly different, but comparable to what you used.

I presume (and correct me if I'm wrong) you will agree with me that doubling the efficiency of a process should result in a doubling of the EROEI. For instance, doubling the conversion efficiency of a solar panel will result in a doubling of EROEI, all other things being equal. What happens to your EROEI(thermal) equation if, in your French nuclear example, we double the thermal efficiency of the 58 reactors? The Tricastin diffusion plant won't require any more electricity for enrichment, so the energy used is cut in half to 1.5 plants. With your math (56.5*.6)/1.5 = 22.6, which is a quadrupling of EROEI for a doubling of efficiency. This demonstrates that your attempt to account for the thermal efficiency has resulted in an equation that is not mathematically consistent with what we expect. There's a problem with it.

I do agree that the electrical output is the proper measure of (energy out) when looking at nuclear electricity generation; however you accounted for the energy input to the gaseous diffusion process incorrectly. The energy input is the electrical consumption of the diffusion plant, not the thermal output of the reactors. The only thing this approach neglects is the EROEI of the electricity source. If we have an electrical source with an EROEI of 50, then when the energy is used as an input to another process, its contribution is the electrical energy used, plus the 2% embodied energy required to generate it. This additional 2% does not dramatically change the result, which is also a relatively high EROEI.
A thought experiment to illustrate the point: If you change the boundary of the system from "France's nuclear plants", to "France's electrical system" which includes a fair amount of hydro, and the French declare that they are dedicating their hydro resources to uranium enrichment, then there is no thermal conversion efficiency to confuse the issue. The electrical output of all reactors is able to be used elsewhere, and we both agree that the electrical output is what counts.

More later. I have to get to work now.

Chris Dudley said...


Sorry to take so long to respond.

If we look at the thermal EROEI for a doubling on conversion efficeincy, then 1.5 reactor are providing power to enrich uranium for 58 reactors and we get EROEI(thermal)=56.5/1.5+1=39 or about twice 19 as you expect. What seems to be bothering you is the behavior of the EROEI(actual) which is 56.5*0.6/1.5+1=23.6 which is 3.6 times larger than 6.5.

The behavior that is bothering you goes away if thermal energy is converted to electricity perfectly. So, if we are 3.3 times more efficient the EROEI(thermal)=57.1/0.9+1=64 which is the same as EROEI(actual). And, in the case where the efficiency is so low that we need all the reactors to power the enrichment plant, we get identical results. We can't go any farther than these two extremes with this example. So, yes, in some sense, to get the actual result of the the effort, the electricity out to society, we need to apply the efficiency twice.

Now, your solution to this is to say forget the reactors and just look at electricity in and electricity out. But, that ignores that what is being produced is thermal energy. To see why this is important, supose we powered all of our electricity use with either solar PV or nuclear. Both are delivering electricity and both have actual EROEIs of 10. How much energy needs to be produced to keep each system going? For solar you need 10% more panels producing 10% more energy and for nuclear you need 3% more reactors producing 10% more energy. The amount of extra energy production is the same. Looked at the other way, if we use EROEI(thermal)=30 for nuclear and system life over energy payback time for solar=30, we only need to produce one third the energy to keep the solar powered system going as for the nuclear powered system. So, using EROEI(actual) helps us to put things on the same scale. It indicates how much more or less messing around we have to do with the different options. The electricity only sources can have a lower EROEI(actual) than the EROEI(thermal) of the other sources and still lead to less extra energy production to keep the whole show going.

But, I think that the EDOEE measure can be used also if the EROEI picture seems too mixed.

Anonymous said...


You were careful with your capacity factor for nuclear, but the capacity factor for wind is a fair bit lower than 35%.

The link shows wind capacity factors at a minimum of 22% to a max of 26.6% in 2005 and a minimum of 21.8% to a max of 26.2% in 2006 among IEA Wind countries, which account for 83% of installed capacity worldwide. The min/max ranges are due to the large amounts of capacity being installed in each year. Not all the new capacity is generating for the full year, so in the absence of specific connection dates an average of the 2 values seems appropriate, say 24%.

Anonymous said...

Those low capacity factors include older, smaller windmills. The new larger ones are getting higher capacity factors. And since we're building new ones, mostly big ones, that seems like a better figure to use.

Also, with larger amounts of wind installed, the economics of wind and electric transmission favour better but remote wind locations over suboptimal locations that are closer to the grid.

Typical capacity factors of modern large ~2 MWe turbines in good to very good locations is about 30-40%. This already includes some downtime for maintenance.

Anonymous said...

"Now, these are all nameplate capacities and we do need to look at the capacity factors which are 82% for nuclear power worldwide, about 35% for wind and about 20% for solar, so wind is ahead of solar by a factor of nine."

Cyril, Chris was comparing what *is* a measured capacity factor for nuclear plants and so a measured capacity for what wind power is providing today is appropriate.

If you want to discuss what *might be*, then I could point out that the US nuclear industry has achieved a 90% capacity factor for several years running, and the design capacity factor for new baseload nuclear plants is 90% or better.

I don't disagree that the capacity factor for wind is capable of rising, if most new wind turbines are installed in the best locations. But the capacity factor is still low, and there will still be (hopefully small numbers of) turbines installed for greenwashing purposes in visible, but non-ideal locations to bring down the average.

To reiterate, the comparison was for *what is*, not *what might be*.

C W Magee said...

Has anyone calculated the EROEI for candu or other heavy water reactors that do not require any fuel enrichment?

Also, the melting point of uranium is not relevant, as reactor fuel is uranium dioxide. This is a refactory ceramic that melts at around 2800C, although the zirconium metal fuel rods will fail at a substantially lower temperature.

Anonymous said...

Brad F: what's your point? There's not much to improve from 90%. Just can't go much higher. 100% is the theoretical maxiumum. Wind can improve relatively more. One caveat is due here as well. The average capacity factor for all electric generators in the US is less than 45%. Moreover, it is dynamic - it fluctuates during the day (diurnally) as well as over the year (seasonally).

What this means is that 90% capacity factor nukes isn't as useful as one might think, especially when you realize that flexible nuclear powerplants are commercially completely unproven. France, for example has had issues with large amounts of nuclear power on the grid, and is only able to do it because of shutting the plants down during weekends and because of flexible hydro-electric plants but also because of exporting significant amounts of nuclear power abroad to European countries. Of course, that has diminishing returns if all countries in Europe go mostly nuclear, same for the US case. Who's going to buy power from the US? Canada already has loads of nuclear plants. Mexico maybe, but it's not a lot compared to the US use. And the US has relatively less flexible hydro potential because of it's much higher electricity consumption. Well there's your problem!

What we really need is flexible load following powerplants. Correlation with the load is one of the best measures for this. Wind isn't too good, even high capacity factors are generally less than 20-30 percent correlated (or so, don't remember the exact figures and it depends on which grid). Solar thermal with heat storage, for example is really good in this respect, so there's a very high limit to how much of such plants can be put on the grid with only a modest backup needed for the occasional rainy day or week (literally).

Now, a nuke running at theoretical 100% capacity factor would have perhaps 45% correlation with the load. Reasonable, but not great. We'll end up building more natural gas capacity than nuclear capacity just to be able to follow the load.

On the topic of this post, nuclear ERoEI will suffer from tuned down capacity factors due to higher penetrations of baseload nuclear. The reason is fairly straightforward: lower capacity factor means less energy out, lowering ERoEI.

Vehicle-to-grid offers a lot of potential to solve these issues, both on the nuclear as well as on the renewables side.

Sarah said...

Your post is very similar to a project I am currently doing. I would love to be able to site your World Nuclear Association information, but your link doesn't work at the moment. Could you possibly update this? It would be much appreciated!
Thank you!

Anonymous said...

All the arguments you apply to nuclear down rating its ERoEI also apply to solar PV.

And others I have seen peg the ERoEI of PV as 1, once you add back in the bits "conveniently" left out by the people doing the calcs.


Anonymous said...

What is the EROEI for Solar Cells?

heavyweather said...

Considering the low EROI of nuclear power it is already dead. Fast Breeders are nothing but a pipe dream.
Nuclear plants are too much of a risc considering that they can be rendered useless in a matter of seconds. (Japan has powered down a 8.7GW plant due to an Eartquake for over 2 years...) Thats wasted money and resources.

Furthermore there are wind technologies with a C-factor of 5000-7000h/a and an EROIE of 375.

Also we must consider adapting usage to production by automated load balancing. Peaks can be lowered by 20-30%.
Thats much more efficient than puffering electricity in any form.

Here is what you are looking for:

27MW are built in the province of Asti right now...should go to grid by end 09...producing power for 5cent or under 60€/MWh (lower than fossile..which is the obvious target.)

Nuclear stays dirty no matter how you put it.

Even in the US you are trying to catch up with Europe now...

In ship propulsion we have already won :)

dragonpolaraxis said...

Hi, I'm doing a research project on whether green technologies are actually green and I found your page content really interesting. Is there any way I could get information on EROEI numbers/the energy used to make the product as well? I have not seen any sites with information like this, but I'm not sure if this is credible or reliable information for my project (if you have some references, I would love to know)

Krista Hiles said...

It great to read post like this which includes topic like EROEI, i.e. Energy returned on energy invested. EROEI is a measure of the feasibility of an energy source and so it should be useful for comparing different energy sources to try to pick which one to use.
Professional Power Project