257 comments on Nuclear Britain
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257 comments on Nuclear Britain
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Hi Chris (mdsolar),
Your blog on Nuclear EROI is really good. Do you have a reference for the French enrichment numbers that you quote? (only thing I see missing from your great article).
So, essentially, the nuclear EROI values have been skewed by inputs from the cold-war era. H.T. Odum supports your position of low nuke eroi. And I notice that C. Hall also puts the value at the near 10 mark. Without a high eroi, then uranium really will run out by 2050 or so.
The estimate for France is pretty crude since it only uses numbers of reactors. The three reactors used for diffusion are at Tricastin. I see now 59 power plants in 2002 in France. A more careful calculation would include the size of the reactors and the amount of enriched uranium France exports, but since the calculation only looks at enrichment, it should still give an idea. The main point of the post is that even using centrifuges, nuclear power does not compare well with renewable sources. This is shown using industry supplied numbers in the table. I don't think that cold war uranium skews EROEI as much as I originally thought, it should still be above one I now think. But, cold war weapons grade uranium, taken together with actual EROEI numbers that are lower than for coal, makes it painfully obvious that nuclear power is primarily about politics, especially non-proliferation, rather than about energy generation. We may be able to keep it limping along if we use higher quality energy sources for the majority of our energy generation, but increasing its fraction of the whole would be impoverishing. I think there is a risk that even maintaining the current fraction of nuclear power could lead to plants being shut down before the end of their design lifetime owing to lack of fuel. This would tend to reduce EROEI since the energy cost of construction would not be carried over the anticipated period of operation. Shifting the associated finacial risk to pivate investors, as the UK is proposing, is a wise move I think. Proposed federal loan guarantees in the US seem like a problem.
Chris
It's not even numerate. I went through this in the previous thread, but it's worth a repeat just to show the disappointingly dishonest arguments Chris seems to think he's somehow justified in making.
In his blog article Chris use this formula to calculate EROEI:
(1) EROEI = (Net Energy/Ein) + 1
where Net Energy = Eout - Ein
This is where alarm bells should first have started ringing. Why does Chris use a more complicated formula to calculate EROEI when it is easily computed with Eout/Ein? We shall see in a minute when we consider the example given on his blog (my original thought experiment from the other thread). But first let's show that equation (1) is equivalent to EROEI:
EROEI = (Net Energy/Ein) + 1
= (Eout - Ein)/Ein + 1 (step 1)
= (Eout/Ein) - (Ein/Ein) + 1 (step 2)
= (Eout/Ein) - 1 + 1 (step 3)
= Eout/Ein
Thus equation (1) does indeed calculate EROEI and Chris is within his rights to use it.
Now on to the example. We consider a country whose reactors use uranium with an energy equivalent to Eu each year. Their only energy input is for diffusion enrichment which takes half the output electricity of the reactors and hence half the input uranium. In such a situation you might think the EROEI would be 2 (and you'd be right) but Chris calculates a value of 1.5. How does he do this? Here's his formula with all values inputted:
EROEI = (Eu/2)/Eu + 1
For net energy he uses Eout = Eu and Ein = Eu/2 (Eout - Ein = Eu - Eu/2 = Eu/2).
However, the value he uses for Ein in the denominator is Eu, the entire energy value of the uranium used by the reactors, not just that used to power the enrichment process. Thus he is using a different value of Ein in the denominator than in his calculation of net energy in the numerator. As can be seen above in step 2, this means that Ein/Ein does not equal 1 and therefore equation (1) is not equal to EROEI.
I pointed this out to Chris in this post and yet he repeats the same flawed argument here. Either he cannot comprehend simple mathematics or is blatantly attempting to deceive.
I think you need to read the blog again. For net energy I use Eu/2, the energy that can be converted to electricity for use by society. For Ein I use Eu, the energy that is expended. I think you have your ins and outs confused.
Chris
Chris:
And net energy = Eout - Ein, so if Eout = Eu then your Ein must logically be Eu/2.
Chris:
So you admit your Ein's are inconsistent leading to an incorrect calculation of EROEI?
Seriously, Chris, this is getting ridiculous. I'm a proponent of nuclear power, believing it vitally necessary to help us cope with climate change and fossil fuel depletion. However, I can honestly say that in all the words I've written about nuclear and renewables I've never knowingly tried to deceive anyone with a lie. Anyone with even small mathematical ability can see that your calculation of EROEI is flawed, designed to produce an artificially low value that tells you nothing about its energetic sustainability. Did you really expect to get away with this on TOD where there are lots of people far brighter than either of us?
Your really are confusing yourself I think. Ein is Eu, not Eout. If Eout were Eu, then EROEI(thermal)=1 not 1.5. Obviously Eout is Eu/2 to be converted to electricity for use by society plus Eu to be used for the process next year, just as you originally proposed. Thus, EROEI(thermal)=1.5. If you take Eout to be Eu then you have not bothered to enrich any uranium.
Chris
If Eout = Eu/2 and Ein = Eu then
Net Energy = Eout - Ein = Eu/2 - Eu = -Eu/2
and
EROEI = Eout/Ein = (Eu/2)/Eu = 1/2
The reason we get these nonsensical values is that you include all the energy of the uranium as an input. If we were talking about oil, for example, were you got a 100 barrels back for every one you invested, it would be like pretending that Ein was 100 instead of 1. This is why you use this equation:
EROEI = Net Energy/Ein + 1
in order to hide the fact that you are using different values of Ein to suit your purposes. However, as I've shown above, when doing so, this equation no longer calculates EROEI.
Read what I wrote again. Eout is both the energy going to society and the energy in the enriched uranium to be used during the next refueling. The net energy is what is available to convert to electricity for use by society. You seem to be confusing yourself by not reading carefully.
Chris
Chris:
I've read everything you've written very carefully, Chris, and the fact that you can't admit your mistake and stop trying to deceive is increasingly painful.
EROEI = Eout/Ein
and also
EROEI = Net Energy/Ein + 1
If you are correct, Chris, then you should be able to explicitly state your Eout and Ein and get the same value of EROEI using either equation. We both know you can't do that.
Better read again. I've stated what Eout in both my last two posts since this seems to be where you are getting stuck. Divide that by Eu and you'll get 1.5. I thought your example would give two before converting to electricity by analogy with oil but it doesn't. I tried rather hard to make it come out to two because I was somewhat surprised. Perhaps it would help you to try to carry out the calculation yourself.
Chris
Chris:
Very well.
Thought Experiment
A country has nuclear reactors and uses half the output to enrich the uranium for next year. The other half is used to power factories, homes, etc. There is no other energy input but that used to power the enrichment process. The energy used to mine the uranium, build the reactors, deal with the waste, etc, is assumed to be zero.
Energy Content of Uranium = Eout = Eu
Energy required to Enrich uranium = Ein = Eu/2
Net Energy = Eu - Eu/2 = Eu/2
EROEI = Net Energy/Ein + 1 = (Eu/2)/(Eu/2) + 1 = 1 + 1 = 2
Thus giving the obviously correct answer. This would be the same for oil, gas, coal, etc if half the output were used to mine/refine the input. It is no different for uranium.
This is helpful because it shows where you are confused. The energy expended is obviously Eu rather than Eu/2. The energy produced is also clearly Eu in enriched uranium plus Eu/2 in thermal energy that can be used elsewhere. You are undercounting both the input and the output. The net energy is indeed Eu/2, but you must calculate this as (Eu+Eu/2)-Eu rather than the way you have done. You don't get that net thermal energy unless you use the whole system. Confining your analysis to half the system is what is steering you wrong.
Chris
And this is helpful in showing where you are 'confused'.
Chris:
No, the energy produced by the inputted uranium Eu is Eu/2 to enrich next years uranium, Eu/2 thermal energy to be used elsewhere, and Eu embodied in next years uranium. This sums to 2Eu, hence net energy is Eu and EROEI = Eu/Eu + 1 = 2.
Your mistake, Chris, is in ignoring the energy used to enrich the uranium as an output. You seem to be conflating net energy and gross energy. You do have a penchant for apples/oranges comparisons. They're seldom valid, you know.
Before you were undercounting, but now you are overcounting. The energy used to enrich uranium is used up. All you get is the enriched uranium as an output. You are kind of wanting to keep your cake and eat it at the same time. Hope this clears things up for you now.
Chris
Oh things are now very clear. Let's recap:
The Mdsolar Patented Way to Calculate Nuclear EROEI
1) Take as Ein all uranium used Eu, not just that for enrichment.
2) Eout is now the energy in next years enriched uranium, Eu, plus the thermal energy not used for enrichment.
3) EROEI can now be calculated with Net Energy/Ein + 1.
This accurately describes the method you use to calculate EROEI in my original thought experiment, in which half the reactors were powering the enrichment process, leading to a value of 1.5.
Okay, now the fun part: we vary the original assumption of the thought experiment and see what happens.
Enrichment uses only 1/10th reactors output
Ein must still be Eu
Eout is now the energy is the enriched uranium, Eu, plus the thermal energy not used for enrichment, 9Eu/10.
Therefore Net Energy = 9Eu/10
and EROEI = Net Energy/Ein + 1 = (9Eu/10)/Eu + 1 = 1.9
Hmmm, very strange. We've reduced the power needed to enrich the uranium by 5 times, and yet our mdsolar approved EROEI has only increased from 1.5 to 1.9.
Okay, let's really go mad:
Enrichment uses only 1/1000th reactors output
Ein = Eu (of course!!)
Eout = Eu + 999Eu/1000
Net Energy = Eout - Ein = 999Eu/1000
Therefore EROEI = Net Energy/Ein + 1 = 1.999
Curiouser and curiouser. Only one fivehundredth of the original energy is used for enrichment but our EROEI still hasn't breached 2.
Hmm, wonder what would happen in the case were no energy at all was used in the nuclear lifecycle. Surely Chris's foolproof method will give us an infinity for EROEI, as it must. Let's see:
Enrichment uses none of reactors output
Ein = Eu
Eout = Eu + Eu = 2Eu
Net Energy = Eout - Ein = Eu
Therefore EROEI = Net Energy/Ein + 1 = 2
That's right, Chris, in the event were there are no energy inputs your method calculates an EROEI of 2. May I humbly suggest you are mistaken.
Reductio ad absurdum. I was puzzled by that result. Thanks.
Chris
And if I weren't so dense that I actually read what you wrote rather than assuming, we'd have got to this point ages ago.
I've corrected the blog and added an acknowledgement as a comment. I think you'll agree that the thermal/actual terms help to clarify what we were discussing in a previous thread, but let me know it you disagree.
Chris
mdsolar:
I know you'll be just delighted to find out I have other problems with the blog entry, Chris. I'll concentrate on the next one.
We've finally come to an agreement that in the thought experiment were half a country's reactors are used to enrich their uranium - and there are no other inputs - then EROEI = 2 in terms of primary energy input to output.
You then go on to calculate EROEI in terms of electrical output to primary energy input using this formula:
EROEI = (0.3*(Eu/2))/Eu/2) + 1 = 1.3
However, this is incorrect. The point I was erroneously making in our discussion above about inconsistent Ein's is ironically valid when discussing this calculation. Essentially you're multiplying the net energy by 0.3, which leads to a different Ein in the numerator than in the denominator. If we multiply the equation out we shall see that it does not equal the traditional definition of EROEI:
If EROEI = (0.3*Net Energy)/Ein + 1
then EROEI = (0.3Eout - 0.3Ein)/Ein + 1 = 0.3Eout/Ein - 0.3 + 1 = 0.3Eout/Ein + 0.7
If your equation was truly calculating EROEI(electric) then it would simplify to 0.3Eout/Ein. Also, reductio ad absurdum, if Eout = 0, EROEI = 0.7 not zero.
The actual calculation of EROEI(electric) is:
(Using a factor of 1/3 to account for conversion to electricity and make the maths prettier)
Net Energy = Eout - Ein = (1/3)*Eu - Eu/2 = Eu/3 - Eu/2 = -Eu/6
Therefore EROEI = Net Energy/Ein + 1 = (-Eu/6)/(Eu/2) + 1 = -1/3 + 1 = 2/3
Which brings us right back to the motivation for the original thought experiment: to show that EROEI(electric) is a poor measure of energetic sustainability, giving a value of < 1 for a process that produces an energy profit.
I want to consider two cases. The issue we are dealing with here is scope because I want to compare what it takes to run an electric toaster given EROEIs in various forms. So, how do we handle scope?
Let us say we have an oil well with EROEI(well head) =2 and a refinery at some distance. The oil company has two choices on how to transport the oil. It can use a sail boat with the strange property that 70% of the oil transported during the journey evaporates, or it can use a tanker that burns 70% of the oil. To calculate EROEI at the refinery terminal rather than the well head the way I am doing it, I want the evaporation case so net energy is 0.3*(net energy at the well head) and I get EROEI(terminal)=0.3*1/1+1=1.3. You object to this because you want to retain the difference in the net energy calculation and apply the conversion also to oil that was used to pump I think. In the case of the tanker I think we would both say that Eout=2 and Ein=1.7 so that EROEI=1.176. Net energy is the same in both cases, 0.3, but in one case we just lost the oil while in the second case we used it so that it affects the denominator.
Based on this, we might account for waste in conversion as though that energy were actually used as an input. So, if X is a reported thermal EROEI and Y is the conversion efficiency then 1-Y is the fractional loss which is applied to the original net energy. This is (X-1)*Ein. So, we write (1-Y)*(X-1)*Ein as the additional term for the denominator. X=Eout/Ein and without loss of generality we can set Ein=1 so that Eout=X. This then gives:
X'=X/(1+(1-Y)*(X-1))
Where X' is the desired effective EROEI for X greater than 1.
If Y=0 then X'=1. If Y=1 then X'=X. If Y=0.5 and X=1.05 then X'=1.024. If X=10 and Y=0.5 then X'=1.8 and at higher X we approach 2, just as you pointed out to me earlier. In the case of actually burning the oil, this would make sense since we are seeing the limiting case of the tanker using half the oil it transports. When Y=0.3 then X' approaches 1.43 (1/(1-y)).
But this is not really sensible when we are considering losses because we do expect improvements in X to lead to improvements in X' that are quasi-linear.
So, I think that we need to work on the numerator.
I am indeed multiplying net energy by 0.3, so now X'=Y*(X-1)+1. If X=1 then X'=1, if X=0 the X'=0, If Y=0, then X'=1 and if Y=1 then X'=X. If X=10 and Y=0.5 then X'=5.5. Now, I think you criticism is not so strong because I am looking for a way to carry forward from the net energy, and what it's composition was beforehand does not seem to me to be all that important. It is the net energy which undergoes a loss. But I do notice is that taking X to the limit gives an asymptotic behavior with successively lower X' going to a limit of 5 for Y=0.5 and this is not transmitting improve initial EROEI.
So, I think that there is a way to compare thermal sources with those that provide electricity directly and it looks something like 0.3*Eout/Ein in its behavior, but I'm not sure yet what it is.
Chris
Oh dear, you have constructed a house of cards, Chris. You concoct this oil analogy and consider it to be essentially equivalent to our earlier uranium thought experiment, only it isn't. In our earlier discussion all the uranium - i.e. the gross Eu - was converted to electricity at an efficiency of 0.3. In this example only the net energy is subject to conversion.
Also the EROEI in your example is 1.3 regardless of whether the tanker or sail boat is used. Why?
Beginning of Process:
Ein = 1 unit of oil
End of Process:
Eout = 1 unit of oil at well head + 0.3 units at terminal = 1.3
Therefore EROEI = Eout/Ein = 1.3/1 = 1.3
This is true for both transport methods.