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Approximation of ERoEI for nuclear energy in the US

Alternative Energy

The importance of the ratio of Energy Returned over Energy Invested cannot be overstated; however, different researchers have included different items in the energy invested term. This may be satisfactory depending upon the use to which the concept is to placed; but, only the method recommended on this blog results in a ratio that can be used to determine sustainability of the technology*.

Sunday, November 24, 2013

Approximation of ERoEI for nuclear energy in the US

Jay Hanson’s America 2.0 Google group
The problem of estimating the ERoEI of nuclear energy has arisen once again.  In 2005, I read the MIT report and the University of Chicago report and, as part of a much larger project, wrote as follows:

Commentary Continued: The Nuclear Option

The positive characteristics of nuclear are easy to dwell upon if one is an exponent of growth such as John McCarthy or the late Julian Simon  On the other hand, they are likely to be ignored by Soft Energy zealots.
A Renewable Energy Resource
Regardless of the finiteness of uranium resources, nuclear energy must be considered renewable because of the existence of fast breeder reactors and the likelihood that their technological limitations will disappear over the coming decades.  Therefore, nuclear power should be admitted to the competition with wind, solar, biomass, and other sustainable technologies.  If there is some reason why nuclear energy is not sustainable, it has yet to be demonstrated.  (What is not sustainable is growth itself – not nuclear energy.)
The Hydrogen Economy
Suppose that we agree that the hydrogen economy means hydrogen from nuclear power installations (NPIs).  Suppose that we agree that the hydrogen economy means hydrogen from nuclear power installations (NPIs).  [However, see [] for a non-nuclear approach to the hydrogen economy.]  In their article “Large-Scale Production of Hydrogen by Nuclear Energy for the Hydrogen Economy” [], K.R. Schultz, L.C. Brown, G.E. Besenbruch, and C.J. Hamilton suggest that hydrogen can be produced with a 50% efficiency by thermal splitting of water using a Sulfur-Iodine cycle in conjunction with the Modular Helium Reactor (H2-MHR).  The efficiency of the H2-MHR bypasses the objections to using electricity as an intermediate step as discussed by Ulf Bossel, Baldur Eliasson and Gordon Taylor [].  Other drawbacks of  hydrogen have been addressed by Graham Cowan in his interesting paper Boron: A Better Energy Carrier than Hydrogen?  []
Also, associated with the hydrogen economy and whatever residual industrial tasks cannot be converted to electrical power are the huge changes in our technological and industrial infrastructure associated with conversion to the use of  hydrogen for fuel.  This will involve energetically costly re-tooling for the production of different types of industrial equipment.  Although the period of amortization can be prolonged, ultimately such costs must be charged to the energy invested in nuclear energy.
The cost of liquefying hydrogen might be paid in part at least by using hydrogen to facilitate transmission of electricity through ‘high-temperature’ superconducting transmission lines that might run through the middle of liquid hydrogen pipelines.  I do not know if this is feasible nor do I have a reference for it as I have no idea if it exists outside of my own imagination.  However, I have noticed that the fractional losses of electric power listed in the reference case from Annual Energy Outlook 2005 (Early Release) (AEO2005), published by the Energy Information Administration of the US Department of Energy (DOE), are rather large so that the potential savings, at least, are documented.  (See Appendix A of AEO2005Full.pdf.)  [Note.  The term ‘high-temperature’ means that, while the temperature is still cryogenic, it is well above absolute zero.]
Energy Returned over Energy Invested (ER/EI)
If the Energy Returned by NPIs is less than the Energy Invested, nuclear energy is infeasible.  Therefore, the frequently discussed ER/EI analysis is crucial to this discussion.  Probably, the ER/EI ratio for nuclear power is less than comparable ratios for fossil fuels, which is a drawback insofar as market penetration is concerned; however, so long as it exceeds 1.0 the introduction of nuclear energy is feasible.  There are a number of factors, however, that point to the possibility that ERoEI is less than 1.0.  In particular, elsewhere in this section, a number of requirements of  NPIs are mentioned that might be easy to overlook in an analysis of ER/EI.
The identification and quantification of every component, both direct and indirect, of the energy invested in nuclear power is not a simple thing to do.  In particular, if any such study of Energy Invested includes the ancillary business expenses, including the expense of doing the very study in question, I have not seen it.  But, in the American economy, for example, the energy consumed by commerce is 22% of the total energy budget.  This is corroborated by employment statistics.  (See [].)
Computation of Energy Invested by multiplying the sum of capital and operating costs by the ratio of Total National Energy Budget over Gross National Product (E/GDP) tabulated by the DOE provides an approximation to the correct value that does not omit the energy consumed by commerce.  (See “Energy Flow in a Mark II Economy” [Mark-II-Economy.html].)  Using cost data from the Shultz et al. study [], the University of Chicago Study [], and the MIT study [], I computed an ER/EI ratio of 4.63.
However, it is not clear that all ancillary costs have been included, e.g., desalination of sea water, remediation of environmental change, etc.  A pro-rata share of the costs of providing and maintaining railways to carry heavy equipment, fuel, and waste, highways to transport workers, conduits to transmit electric current, pipelines to transport hydrogen, and easements through which electrical power lines and hydrogen pipelines can be run must be charged to the plant.  Some locations for NPIs are unsuitable for this necessary infrastructure, and, therefore, unsuitable for NPIs.
At the start of this exercise, I considered the notion that I might be able to determine the feasibility of nuclear by looking at the energy balance for France.  (  France produces about three quarters of her electricity from nuclear, but France has to import about half of its energy.  Is it possible that nuclear power consumes more energy than it produces?  Despite the inclination to prove the affirmative, I have not been able to determine the answer to this question by looking at the available data.  In fact, France seems to be doing rather well insofar as energy is concerned; and, therefore, is much less of a problem for the rest of the world than is the United States.
Finally, and we shall have to await a more thorough discussion of this topic, the author wonders if the cost of restoring the land and the water employed by NPIs to its pre-nuclear condition should be charged to the Energy Invested even if  there is no possibility that the land will ever be used for any other purpose than nuclear power into the foreseeable future.  Clearly, decommissioning costs must be included, but does decommissioning include restoring the land to its original condition as a beautiful, natural, wildlife habitat?  Quite frankly, I believe that it does.
Although the capital costs of NPIs are sufficiently high that market penetration under the standard short-sighted micro-economic model might be prohibitively difficult, as a fraction of the projected Gross Domestic Product they are quite manageable by a society that possesses the political will to manage them as we shall see in the sequel.  The final irony might be that a capitalist-style market economy can be maintained under a centrally-planned socialist energy economy and only under such an economy.
Many people believe that the United States economy is in such bad shape, principally because of the trade deficit and the national debt, that it could not possibly support the massive spending necessary to install a hydrogen economy.  If the government continues to run a deficit, the public costs of such a project might very well multiply that deficit by a large factor.  While this may be true, it does not necessarily represent the prohibition of the Apollo Plan, so long as American workers are willing to accept government debt in the form of fiat money as payment of wages.  This study shows that capital costs are well within the capabilities of the US economy.  The results are presented as the final two computations done on the spreadsheet explained in the body of this report.
Unfortunately, nuclear facilities are operated sometimes for the personal profit of their owners, managers, and other stakeholders who might be inclined to place their personal interests ahead of other considerations such as good engineering practice and safety.  Mere prudence dictates that we be suspicious of enterprises run for profit.  Since it will require huge investments by the federal government to penetrate a market economy with current nuclear technology, the federal government might just as well own and operate whichever nuclear plants it chooses to subsidize.  The Apollo Plan amounts to some sort of Socialism; hopefully, it will not be Corporate Socialism, i.e., Fascism.  Thus, the evils of the profit motive can be avoided, but only by compromising Capitalism.  However, as critics of Socialism will be quick to attest, this does not necessarily protect society from incompetence.
Nuclear Power Installations (NPIs) need fresh water.  Many experts believe that we are even closer to Peak Water than we are to Peak Oil if we are not past both.  Since some experts disagree, this must be regarded as an open question.  If fresh water is used as cooling water, it must be returned to the environment at the original temperature with all contaminants removed and all nutrients restored.  If fresh water is split to produce hydrogen, it may end up as atmospheric water only part of which will return to Earth as fresh water, in which case the losses in our fresh water supply will have to be replaced somehow.  If some of our NPIs are used to desalinate sea water, the energy expended must be subtracted from the Energy Returned in computing ERoEI.
As an example of water use by an existing nuclear power facility, nuclear Plant Hatch in Georgia withdraws an average of 57 million gallons per day from the Altamaha River and actually “consumes” 33 million gallons per day, lost primarily as water vapor, according to the U.S. Nuclear Regulatory Commission (  Plant Hatch, consisting of two 924 MWe reactors each with a capacity factor of 0.8453, consumes water at the rate of 3.2903 x 1011 kgs/emquad.  Thus, if every NPI in the year 2100 used water at the rate Hatch Plant did in 2000, we would need 1.1442 x 1015 kgs of water per year to satisfy the modest economic growth assumed in my Reference Case for the Conservation-within-Capitalism Scenario.  According to, we have about 3 x 1015 kilograms of renewable fresh water total.  Thus, power plants would use more than one-third of all of our renewable fresh water.  According to, the US has 2.5 trillion cubic meters of water or 2.5 x 1015 kgs, which corroborates the previous estimate.  Also, see
Some of the energy produced can be used to desalinate sea water for reactors on our East, West, and South coasts where the population is dense and fresh water dear.  Moreover, energy from ocean waves can be used to assist desalination.  []  Let us compute a lower bound for the energy cost of desalination of sea water to make the case against nuclear as conservative as possible.  According to Allan R. Hoffman (GlobalWater.htm), “energy requirements, exclusive of energy required for pre-treatment, brine disposal, and water transport, are: reverse osmosis: 4.7 – 5.7 kWh/m3and multi-stage flash: 23 – 27 kWh/m3”.  To establish a minimum, I shall use 4.7 kWh/m3 to obtain
i.e., an increase in Energy Invested of 1.6% of the Energy Returned, which should not present a problem.  However, if the higher value for multi-stage flash were the best one could do, the costs would soar to nearly 9% of the Energy Returned.  If the ratio of Energy Returned to Energy Invested (ERoEI) were 5.0, the energy costs would increase by 44.9% and the ERoEI would be reduced to 3.45, which would certainly be an unwelcome surcharge on nuclear power.  In addition to the costs of pre-treatment, brine disposal, and transport, the cost of desalinating water to be split into hydrogen and oxygen would have to be borne.  The cost of transport might be considerable if sea water were needed in Minneapolis, say, but the scarcity of fresh water is most acute in places much closer to the ocean.  The calculation of these additional costs shall be postponed to some future study.
The final limitation upon economic growth is the area of the surface of Earth.  NPIs require a smaller fraction of Earth’s surface per unit of power generated than any of the competing technologies, namely, wind, solar, and biomass – despite the fact that solar and wind power installations can coexist with other land uses.  Even if every other obstacle to growth were removed, ultimately we should run out of space – unless some means of miniaturizing NPIs, for example, should be discovered such that the rate of increase of power density could keep pace with growth.  (If emquads per square meter increases at the same rate as emquads, we would be able to produce the energy budget of the future in the space we use now.)  Even in the unlikely event that NPIs could be stacked, a limit would be reached after which they could be stacked no further without the expenditure of more energy than an NPI can produce during its lifetime.  Also, there are limits to power density that, if none other could be found, would be set by the atomic nature of matter – although, admittedly, if the concentration of the space per unit of power were limited by atomic considerations alone, growth might continue for a very long time.  Probably, though, by the time the individual Earthling could wear an NPI strapped to his wrist like Dick Tracy wore a radio, we shall no longer be living on Earth, a situation to be deplored for other reasons as stated previously.
To return, for a moment, to more realistic considerations, the land needed for NPIs includes not just the plant sites and infrastructure for transportation and power transmission but also the space occupied by facilities for mining and enrichment, fabrication, maintenance, recycle, hydrogen compression and liquefaction, waste management, sea water desalination, fresh water remediation, and the ubiquitous office buildings that seem to be a necessary part of every enterprise engaged in the pursuit of profit.  Engineers and scientists will need workplaces; and, if I am not mistaken, the greater the complexity of our energy economy the greater the superstructure of command and control, which, in the case of nuclear, must be multiply redundant.  Moreover, many areas on the face of the Earth are not suitable for NPIs, namely, the tops of mountains, earthquake zones, crowded cities (perhaps), and, if we wish to observe the ethical treatment of animals, wildernesses, swamps, prairies, etc. – in short, any place where humans have not yet evicted animals from their natural habitats, which, for all practical purposes, amounts to saying that future nuclear installations may be placed nowhere.  Finally, it must be decided whether the space occupied by outmoded and obsolete facilities can be reused for new facilities or if it must be restored to the pristine condition in which Nature bequeathed it to us.  If the latter, the energetic costs will very likely overwhelm the Energy Returned in the ratio (or difference) represented by ERoEI, which brings me to the next point:
Quite obviously, while operating as designed, nuclear power plants do not contribute directly to Global Climate Change nor air and water pollution regardless of the effect of their ancillary facilities, e.g., mining, etc.  When nuclear facilities are operated properly, the dangers are rather minimal; nevertheless, nuclear radiation is extremely dangerous.  In addition to radiation poisoning, nuclear plants have a non-zero, but very small, probability of exploding; but, if there are many of them, the probability of explosion increases accordingly.  Admittedly, there is no physical reason why the problems associated with pollution, radiation, explosions, waste, and decommissioning cannot be solved, however they must be solved; and, to the extent that they have not yet been solved, they represent impediments to the introduction of nuclear power and the hydrogen economy, which brings us to the next topic.
Nuclear power is the key to a much larger and complicated economy with much greater opportunities for unanticipated environmental catastrophes both because it makes a larger economy possible and because it makes a more complicated economy necessary to supply an energy budget that is growing exponentially.  Now, the economy is sufficiently complicated in 2005 that the average person must necessarily depend upon the opinions of experts to determine which public policies are in his best interests and which are not.  Moreover, experts disagree.  The average man or woman is held hostage to the complexity of the economy, and this situation is not conducive to democracy.  Soon enough, under a scenario of modest growth, this situation will be exacerbated many times over.  The interests of ordinary private individuals will be taken out of their own hands almost completely.  Presumably, a technocracy is better than a plutocracy (unless technocrats become plutocrats); but, in either case, it represents social degeneration – not progress.
As one can see, this was written before – but just before – I began to consider ERoEI by drawing my control surface around an entire community, a community living in an Autonomous Alternative Energy District as in  However, without repeating the earlier computation, one can take new data such as (1) the Energy Information Agency’s cost per kilowatt-hour (electrical) of electricity from nuclear energy of $0.108 in 2013 from; (2) the Gross Domestic Product of the United States in 2012, which is close enough to 2013 for our purposes, of 16.25 Trillion US Dollars; and (3) the Total Energy Budget of the US, which was 95.14 quads.  Thus, since most components of the energy investment contribute a corresponding component to the monetary cost, we can compute an upper bound for the ERoEI of  0.54.   Wow!  I must have made a mistake.   I haven’t got time for Microsoft’s equation editor; so, I had better scan a pencil calculation and include it as a jpeg.  I will place this on-line in case Google doesn’t print equations or figures.  See .  The actual ERoEI* must be less than this because society does not require some of the measures that would have to be taken to achieve genuine sustainability; however, the technology is infeasible as it is.
The mistake is in the conversion of quads/year to terawatts.  It should be 0.0334372 NOT 0.334372.  Thus, Dilip Kale is right and I thank him.  The ERoEI of nuclear is no greater than 5.4, which agrees with my 2005 paper.
Alexander Carpenter is rather skeptical about this computation because the levelized cost represents the amount that nuclear energy would have to sold for to just break even.  I believe that the break-even price includes all obligatory payments to investors and lenders.  We don’t care if the industry makes a profit or not; but, if it does make a profit, the additional energy consumption of those who earn it must be charged to the technology.  This is accounted for by the price.  The energy associated with every single component of the price including the taxes collected must be reflected appropriately in the energy investment term.
This, then, is a slightly edited version of my reply to him on the America 2.0 forum:
Rather than re-send the post I sent earlier tonight from the wrong email account, I would like to ask Alexander to take a moment to read this carefully.  Obviously, he has a great deal to contribute to this discussion; but, I am not interested in ROI.  I may not understand what GDP means nowadays; so, I will tell you what I think it means with the hope of being corrected if I am behind the times: GDP is supposed to be the sum total of  all goods and services purveyed and purchased domestically during a given year.  It is the flow of money through the economy as in Odum’s famous diagram, which was first rendered when the US GDP was only 1.4 trillion USD/year.
Next, I need to be sure what the levelized cost is and how it is intended to be used.  I think that’s where Alexander got the idea that I am after ROI.  I think I should use the average price to the consumer regardless of sector because this is how much money enters the economy when one kilowatt-hour of electricty is sold regardless of origin.  This was 0.1045 USD according to which is assumed to be a reliable source of raw historical data.  In my experience, these bureaus are staffed by serious, competent people who would rather not be pushed around by unscrupulous businessmen.  I don’t think these people are much influenced by political pressure, which is exerted much farther downstream in the dissemination of data.  Are they not tenured?  I have had serious discussions with the people who supply my data and they have had a lot to teach me.  In addition, they seem to be pleased to show the general public how useful they are. It doesn’t matter to us if the average price to the consumer is affected by subsidies; however, since it does not reflect things like environmental reparations that should be done but are not done, the figure I come up with delineates feasibility rather than sustainability as I defined these terms at in the post of August 14th, 2013.  Finally, I believe we are in agreement on the total energy budget, E.  The ratio of E to GDP is the quantity of energy flow through the economy counter-current to one USD of monetary flow. The new value of ERoEI is higher, then, by the ratio of levelized cost to the average price to the consumer or 0.108/0.1045 X 5.4 =  5.6.  This result is subject to the determination that 1 KWH(e) is really 1 KWH and not a third of a kilowatt-hour, the electric energy generated by the expenditure of 1 KWH of fuel at the conventional power plant.  I would like some input on that question.
To make absolutely clear what I mean by this technique, I illustrated it for the Mark II economy in where it is crystal clear how each term was computed and, therefore, what it means.
Tom Wayburn, Houston, Texas

Energy Returned over Energy Invested

10 Comments on "Approximation of ERoEI for nuclear energy in the US"

  1. Arthur on Mon, 25th Nov 2013 2:03 pm 

    Did not read this intensively but did get that nuclear EROEI is 5 or less. Well then, so wind and solar are better? Oh, and they actually work NOW, without significant hazards. So how about installing a solid renewable energy base first, with an economic lifetime of 25 year (solar) or 30 (wind) + hydrostorage and then contemplate if there are maybe other solutions, like thorium or fusion?

  2. Kenz300 on Mon, 25th Nov 2013 2:21 pm 

    The current estimate is that it will take 30 – 40 years to decommission Fukishima and clean up the disaster. There is no estimate as to the cost to store the nuclear waste FOREVER.

    Nuclear energy is too costly and too dangerous…….

    There are safer, cleaner and cheaper ways to generate electricity.

  3. noobtube on Mon, 25th Nov 2013 3:44 pm 

    The reason why the United States and Europe are so determined to keep nuclear energy is because they want the ability to murder brown people with nuclear weapons.

    It is this racial madness, that you find in the minds of the racist garbage in the United States/Europe/Israel, that will doom the Northern Hemisphere and maybe the world if these race maniacs actually use nuclear in their “national interests” against the brown people of the world.

    American Exceptionalism and Racial Superiority.

    Such contributions the United States/Europe/Israel have made to mankind.

  4. shortonoil on Mon, 25th Nov 2013 4:53 pm 

    For a supposed academic article – incredibly ignorant! The Second Law assures us that an EROEI of less than 1:1 can not be used to produce work usable energy). It even informs us that an EROEI of 1:1 can not produce work. Entropy production (which is a Second Law mandate) in the system requires that some of the system’s energy must be given up as waste heat to make the process go forward.

    Conventional crude now has an ERoEI (at the well head) of 9.6:1, with a breakeven point a little less than 7:1. The entire system will stop working at that point.

    This article is a cross between Grimm’s Fairy Tales, and Wish Upon a Star!

  5. solarity on Mon, 25th Nov 2013 5:15 pm 

    This write-up is so full of gobbledygook it is difficult to read and comprehend (did anyone?). The author’s misplaced ardor, and lack of knowledge in several disciplines (Econ., GAAP, and English Comp., et.el.) render the prose almost un-readable. Reminds me of a book I read in high school: ‘How to lie with statistics,’ or in more modern and common parlance: baffle with BS.

  6. Mike on Mon, 25th Nov 2013 8:32 pm 

    If you support nuclear you need to be put to death asap as you’re a danger to the species. It’s that simple.

  7. Others on Tue, 26th Nov 2013 2:43 am 

    1 ton of Uranium has as much energy as 10,000 tons of Oil or nearly 20,000 tons of Coal. So the EROEI of nuclear power should be much higher in nuclear’s favor.

    Problem is the high capital cost. That’s why Chinese are building Gen 4 plant which will be lot more simpler and cheaper. Once that comes to market, the nuclear power will become lot more cheaper and safer as well.

    Compared to fuel oil, nuclear is lot cheaper, that’s why countries like UAE, Iran, Russia are building more nuclear power plants.

  8. Norm on Tue, 26th Nov 2013 7:47 am 

    It took me so long to scroll from top to bottom, that my arm is getting tired. imagine how long it would have taken, if i had actually read some of it.

    Seems like EROEI of standard water-filled nuclear reactor isn’t the problem. The problem is it doesn’t work worth beans, then it blows up in your face scattering plutonium dust all over your countryside.

    Noticing i have never seen anybody, not ever, be capable of comprehending what i am about to say (ameri-duhh is too stupid) There is a ratio of about 15:1 on energy efficiency of power plants. For example, pebble-bed vs standard pressurized water filled. Coudl that factor of 15 affect your EROEI computations ?? Naaah, factor of 15 doesn’t make any difference, doesn’t matter if you get 10mpg or 150mpg, duhhhhh.

  9. ulenspiegel on Tue, 26th Nov 2013 8:52 am 

    “1 ton of Uranium has as much energy as 10,000 tons of Oil or nearly 20,000 tons of Coal. So the EROEI of nuclear power should be much higher in nuclear’s favor.”

    The interesting parameter is how much fossil energy is required to produce this 1 ton of uranium.

    According to other academic papers the amount depends strongly on the uranium content of the ore.

    Thefore you see EROEI for NPP from 20 up to >100.

  10. Norm on Tue, 26th Nov 2013 3:51 pm 

    As much energy as 20,000 tons of coal. Really? In what reactor device? In a water pressurized vessel,with rods? In a pebble bed? Since there us a 15:1 ratio difference, then clearly its 20,000 tons energy, no matter what equipment built to react it.

    This is indeed similar to cars. All cars get 20 mpg. All gallons of gas go 20 miles. The mpg parameter is a physical constant of the fuel. You cannot change the mpg by building a different car. Because all gasoline is 20 mpg. As such, you should only build F-150 trucks, cause they get 20 mpg.

    Same for nuclear. You should only build the 3 mile style of reactor, so that it gets the correct fuel economy, since improvement in fuel output is not possible. Same with cars, no car can get more than 20 mpg.

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