EROEI

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 Source	EROEI(actual)
Hydro	50, 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
Coal	12.2, 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	10.6
Solar PV	12-10, 7.5 and 3.7
Wind	12, 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.