Monday, May 11, 2015

Six Errors in ERoEI calculations

The ERoEI ratio refers to the amount of energy which we must expend in order to obtain more energy. For example, if we must use one barrel of oil in order to drill for another three barrels of oil, then the ERoEI ratio of the oil we obtained thereby is 3:1, or just 3. As another example, it may take one bushel of coal worth of energy in order to mine 10 more bushels of coal, in which case the ERoEI of the coal we obtained is 10:1, or just 10.

Different sources of energy have different ERoEI ratios. Some sources of energy (such as coal) have high ERoEI ratios, typically more than 20:1, which indicates that coal requires very little energy expenditure to obtain it. Other sources of energy, such as oil, have much lower ERoEI ratios. Some sources of energy, such as corn ethanol, take as much energy to obtain as they will yield. They provide no leftover energy to society, and have an ERoEI of 1.

The ERoEI of various energy sources has been calculated throughout various papers on that topic. There are at least 30 papers calculating the ERoEI ratio for various sources of energy such as nuclear, coal, solar PV, and others.

Unfortunately, the reported ERoEI ratios for any given energy source are often widely divergent from one paper to the next. For example, Weissbach et al[1] report an ERoEI of 75 for nuclear power, whereas another study[2] reports an ERoEI of less than 1 for the same energy source. As another example, the ERoEI of solar PV is reported as 2.3 in Weissbach et al's paper[1], and the high 30s in another paper[3]. Those kinds of discrepancies are common throughout the ERoEI literature.

Much of those discrepancies are caused by errors in the calculation of ERoEI which I will detail here. Once these errors are corrected in the offending papers, the resultant ERoEI ratios for different sources of energy become much closer together.

The errors are as follows:

Error #1: Energy returns are repeatedly treated as energy investment

It's crucial not to count energy returns as energy investment, because they are different things. It would be incorrect to include energy returns as energy investment. It would yield the wrong result. However, this mistake is made repeatedly in the papers of Charles Hall and others.

As an example, the paper[4] from C Hall (What is the Minimum EROI that a Sustainable Society Must Have?) calculates the EROI of oil. However, it includes  the energy cost of freeways, automobiles, and so on. That is a mistake, because those things are energy returns, not energy investments to obtain energy. If I drive my car down the freeway, and I'm not doing so out of necessity for gathering coal, then it was because of energy returns.

If you include all energy returns as energy investment, then the EROI of every energy source is 1. This is an application of the first law of thermodynamics. It would be highly surprising if we got more energy out of an energy source than was present within it. As a result, it is not surprising that the EROI of any energy source will converge to 1, as returns are included in the denominator. However, that does not yield any useful information, because it does not tell us how much energy is left over after obtaining the energy to provide for consumption. That is just a roundabout way of testing the first law of thermodynamics--something which has already has been tested and which could be tested far more directly. If we wish to find how much energy is left over as a return, then we must exclude returns from the denominator.

Many of the conversions of money to energy, which are found throughout the EROI literature, are implicitly committing this mistake. For example, in Hall's papers such as Spain's Photovoltaic Revolution[5] and the accompanying presentation[6]. On pp 12 of that presentation, there is a conversion of money into energy units, in order to find the energy cost of things like accountants employed by solar companies, etc. The formula presented is "At 1 Toe = 42 GJ, this represents 5.12MJ/Euro" which is derived from dividing the GDP with all energy usage in the entire country (Spain). That is a mistake, because most energy usage in the country is energy returns, not energy investment. To correct this mistake, Hall et al should take the total energy return for the country as a whole and divide it by the ERoEI which prevails for the country as a whole.

Performing this correction (assuming an average EROI of 10 for the country), by will increase the reported ERoEI of solar PV for that paper from 2.79, to 5.22. The figure of 5.22 is much closer to other reported ERoEI calculations for solar PV. This correction was performed by dividing all values by 10 which were the result of a money conversion as found in the chart on pp 12 in the above presentation[6].

Error #2: Lifetime estimates are incorrect

Many papers wrongly assume that the lifetime of an energy source is identical to its warranty period. For example, Hall et al's book[5] indicated above, and Weissbach et al's paper[1], both assume that the lifespan of a solar PV module is 25 years because that is the warranty period.

It would be highly surprising if solar PV cells failed on exactly the day their warranty expired. For example, I bought a car with a 50,000 mile warranty, but it didn't cease working at 50,000 miles.

The reason manufacturers are offering a 25 year warranty on solar cells is because they expect the vast majority of cells to last longer than that.

This error has a large effect on calculated EROI. In Weissbach et al's paper[1], the EROI of nuclear is calculated as 75 but the EROI of solar PV is calculated as 3.8, partly because nuclear plants are assumed to last twice as long as their original rated lifespan based upon observations, but solar cells are assumed to fail the exact day their warranty expires.

Even worse, many EROI papers contain incorrect aggregations of lifespan estimates. For example, C Hall's book[5] includes energy costs for things such as access roads to the solar plant, metal fence posts around the solar plant, concrete in the foundation, steel frames for the solar cells, etc. These things are grouped together with the solar cells themselves and are therefore wrongly assumed to have the same lifespan as the cells themselves. Even if the solar cells spontaneously stop working the very day their warranty expires, the rest of the plant (access roads, fences, steel frames, canals, and so on), will certainly last much longer, and would be re-used.

Error #3: Not counting embedded energy which is recovered

Papers about EROI frequently include the "embedded energy" cost of components for an energy source. For example, calculations of the EROI for solar PV often include the "embedded energy" in the aluminum frames which support the solar panels in the field.

If embedded energy is counted on the way in, then it must also be counted on the way out. These papers uniformly fail to account for the energy which is recovered when the aluminum is recycled when the frames are dismantled. The recovered energy should be counted because the aluminum will be recycled. Almost all major corporations recycle structural materials such as aluminum because they save money by doing so.

This factor alone has a large effect on the reported EROI of solar PV. Much of the energy for solar PV is actually devoted to the aluminum frames which support the panels. About 75% of the energy for manufacturing those panels would be recovered when the panels are decommissioned.

In J Lundin's paper[7], there was some confusion expressed over how much recycled material should be assumed within incoming aluminum used to build solar frames. In my opinion, the incoming aluminum should be counted as 100% virgin, and the outgoing aluminum must also be counted, and should be counted as 100% recycled minus the energy costs of recycling. This is the only correct way. If recycled aluminum is used when a power plant is constructed, then the recycled portion is displacing the usage of that recycled aluminum elsewhere, which would require precisely that amount of aluminum to be made from raw materials for something else. Thus, 100% of the aluminum used for construction of the plant should be counted as virgin. However, 100% of the aluminum which is recovered should be subtracted from energy investments (not including the energy used to recycle the aluminum) because that is displacing aluminum which would have been made from virgin material elsewhere.

Error #4: Waste heat losses are counted as energy returns

This is a recurring problem throughout the ERoEI literature. Waste heat should not be counted as energy returns because it is not usable as energy to society. The only exception is when the waste heat is actually used for something (such as combined heat and power plants), but this is rare.

This factor is parcticularly important when computing the ERoEI of oil. Oil is refined and then used as transportation fuel within vehicles. Those vehicles have engines which convert the chemical energy in fuel to kinetic energy (movement). However, the engines lose about 70% of the energy in the fuel during the conversion. This must be counted as an energy loss. As a result, the EROI of oil is overstated almost everywhere by at least a factor of 3.

In fact, it might be useful to abandon the ratio "EROI" in these cases, and adopt the ratio "thermodynamic work over energy investment" or TWoEI. It is work which we want in the economy, not waste heat.

This factor is especially important when considering the oft-repeated figure that "oil had an EROI of 100 back in 1930". This comment is frequently repeated by the doomsday prepper sect. In fact, that EROI of oil back in 1930, does not include refinery losses, nor does it count losses in internal combustion engines which were even less efficient back then. If I perform a back-of-the-envelope calculation which takes into account those two factors (100*0.7*0.15), I obtain a corrected EROI of 10.5 for oil in 1930, not 100.

Error #5: Outdated figures are used

Frequently there are large discrepancies in the EROI calculations because different technologies are assumed when calculating energy inputs. For example, there are large discrepancies of the reported EROI of nuclear power. That is partly because some papers[1] calculate the EROI using gas diffusion enrichment of uranium, while other papers calculate the EROI using centrifruge enrichment[8]. Those different assumptions will yield very different EROIs for nuclear power, because centrifuge enrichment is so much more efficient. This factor is a large part of the energy investment for nuclear power, and so has a big effect on the resultant EROI.

When calculating the EROI of an energy source, we should use the most modern technology when calculating energy inputs. We wish to know the EROI of an energy source going forward, not the EROI of an energy source if we had built it years ago.

As an example, the paper by Weissbach et al[1], in its calculations of the EROI of solar PV, assumes the Siemens process is used to generate solar PV grade silicon. However, that process has been supplanted by processes which use only 40% of the energy[9]This factor by itself increases the EROI of solar PV in Weissbach's paper from 3.8 to 6.6.

Error #6: Invalid Comparisons Are Made

The are actually different types of EROI depending upon where the boundaries are drawn for calculations. When calculating the EROI of oil, do you include refinery losses? Energy losses for the transport of oil? Waste heat losses from the car? And so on. Each one of those calculations represents a different type of EROI. Some EROI calculations attempt to include only energy inputs used for extraction at the mine mouth, whereas other EROI calculations attempt to include every energy investment in the entire economy, such as the energy investment for building rail lines to transport the coal. Those are different types of EROI.

EROI figures should not be compared if they draw the boundaries very differently. For example, there was a very famous graph from Charles Hall which makes such comparisons[9] (found here). That graph spread like wildfire throughout the peak oil community. However, that graph is repeatedly comparing different types of EROI figures which are not comparable.

For example, the comparison of the EROI of coal (about 70) to nuclear (about 10), taken from that graph. There is a big difference in the kinds of EROI for those two sources. The figure for coal is before waste heat losses are subtracted for generating electricity, whereas the figure for nuclear is after waste heat losses are subtracted. When a correction is made for that, coal has an EROI of about 24.5, compared to nuclear of 10. The discrepancy has been reduced considerably.

As another example from the same graph, oil from 1930 is reported to have an EROI of 100, whereas hydroelectric is reported to have an EROI of 30. However, the EROI of oil from does not include refinery losses and waste heat losses from interal combustion engines in 1930. Correcting these factors yields an EROI of 10.5 for oil in 1930, not 100. Of course, hydroelectric also suffers from electrical resistance losses which reduces its EROI to perhaps 25. However, the adjusted EROI ratio for oil has gone from much higher to much lower when an adjustment is made so the figures are comparable.


The six errors described above are widespread throughout the ERoEI literature. They are partly responsible for the wide discrepancy between reported ERoEI findings.

For example, Charles Hall et al's book[5]Spain's Photovoltaic Revolution, is committing errors #1, #2, #3, and #5. When I correct those errors and re-calculate, I obtain an EROI of 6.27 for solar PVnot 2.79 as reported.

Weissbach's paper[1] calculates an EROI of solar PV at 3.8. However, that paper is committing errors #2, #3, and #5. When I correct those errors, I obtain an EROI of 12.96, and not the 3.8 which that paper reported. Incidentally, that paper also calculates the EROI for solar in a cloudy site in Germany, and then generalizes that to the EROI of "solar PV" altogether. If I correct that factor also, and use the average insolation for the inhabited northern hemisphere, then I obtain an EROI figure of 22 for solar PVwhich is much higher than the reported figure of 3.8.

Finally, even the concept of EROI has problems. Perhaps net energy should be expressed or reported differently, using a different ratio. This is because EROI gives an exaggerated impression of the difference between energy sources. For example, assume a hypothetical energy source with an EROI of 10,000, and compare it to an energy source with an EROI of 10. The source with an EROI of 10,000 would require 0.0001% of its output (1/10000) to build another like it, whereas the source with an EROI of 10 would require only 10% of its output (1/10) to build another like it. In other words, a reduction in EROI of 99.99% led to a reduction of net energy output of only 10%. This is because EROI is less and less important as it becomes higher. Instead of using EROI, we should calculate net energy as 1-(EI/ER), and then express that as a percentage. For example, if natural gas has an EROI of 15 (everything included such as infrastructure), and solar PV has an EROI of 6.27 (everything included), then their inverted ratios are 93% and 84% respectively. This means that 7 percent of the energy from the gas plant is necessary to build another gas plant, whereas 16 percent of the energy from the solar plant is necessary to build another solar plant. The net energy available to society has declined by only 9% despite EROI falling by more than half. Thus, EROI figures give an incorrect impression, and should be calculated and reported differently.

When all the problems above are corrected, it's unclear if there is any significant difference in net energy between different methods of generating electricity. The highest EROI source (hydroelectric) requires 1.3% of its output to build another hydroelectric dam, whereas the lowest source (solar PV) requires 16%. This implies only that we would need to build slightly more solar cells (~15% more) to obtain the same net energy. Any EROI more than 5 or so makes little difference (20% at most). All common methods of generating electricity seem to exceed that threshold.

Certainly, we should investigate further into this matter. If any method of generating electricity has a disastrously low EROI (lower than 4 or so, everything included) then it would be very helpful for us to know about it. Hall's work is very useful in this regard, insofar as he attempts to include all energy investments, which will give us better approximations of relative EROIs. However, we must avoid the above mentioned errors in performing our calculations.

p.s. This paper should be seen as a draft. I will update it if any relevant objections are made.


  1. A fuel with an EROI of 10 would require 1,000 times the effort of a fuel with an EROI of 10,000. This was pointed out in the first paragraph of the Weissbach paper you cited:

    The EROI answers the simple question ”How much useful energy do we obtain for a certain effort to make this energy available”

    (Emphasis mine.)

    Thus, the EROI figure gives a correct impression of relative cost in terms of something people actually care about: effort. Fuel is free. That's why people, rightly, don't care how much of it they have to burn to get more. What isn't free is effort -- and people, rightly, do care about that.

  2. No, that's wrong, in my opinion.

    This was pointed out in the first paragraph of the Weissbach paper you cited: "The EROI answers the simple question ”How much useful energy do we obtain for a certain effort to make this energy available”

    I think you're misinterpreting him. I think that's a mistranslation or a language issue in Weissbach's paper. Nothing in that paper is measuring "effort", such as the amount of labor necessary to obtain a given amount of net energy. I think he just means "effort" as another word for "energy". I think it's a language issue. There is nothing in the paper which measures effort, anywhere. Everything in that paper is an EROI calculation.

    If he does actually mean what he says, then it's just factually wrong. EROI does not measure how much energy we obtain for a given amount of "effort". It measures how much energy we obtain for a given amount of energy invested. The denominator of ERoEI stands for "energy invested" and not "effort invested".

    A fuel with an EROI of 10 would require 1,000 times the effort of a fuel with an EROI of 10,000.

    No, definitely not. That just doesn't follow at all. EROI is not proportional to effort, and there is no way to derive from it the amount of effort required. A good example of this is the EROI of some tar sands and shale fuels, where some of the fuel itself is burned underground to make the rest accessible. This requires very little "effort" for a huge investment of energy (the fuel was there already, and we're just setting it on fire without even extracting it).

    Another example is coal mining. By any estimation, modern coal mining requires far less "effort" than mining by British coal miners in the 19th century, yet the ERoEI is far lower, not higher.

    Don't get me wrong, I think you're on to something. I've considered this issue quite a bit already. I think that another ratio (other than EROI) would be far more useful. It should measure the amount of net thermodynamic work we obtain for a given amount of capital/labor invested (not energy invested).

    However, it is not possible to derive that from an EROI ratio. EROI would be part of it, but it would require a new calculation and additional data. It's definitely not the case that "effort" is just inversely proportional to EROI or something like that. It depends on a lot of things.

    -Tom S

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  4. I found your article very interesting, but also confusing in some places. Here are some comments that may help you (and your comment may help me in return):

    First I was wondering what you mean by “energy consumption” and “energy investment”. How would you choose to define the two? This is altogether not very clear, and I wonder if I am missing the point here. In energetic terms there cannot be anything called “energy consumption” because energy cannot be consumed or used up as I am sure you are already aware of. It seems to me that what you call energy consumption is actually a matter of energy dissipation/conversion, and that energy investment is also, in fact, a matter of energy dissipation/conversion. What is truly important is causality, or system boundaries, where you make plain what particular processes of energy dissipation can be said to be foundational for a particular fuel. Accountants are, like it or not, needed to maintain businesses that provide such a foundation, and they do not run on nothing. The energy they “consume” is therefore an investment in that particular fuel (if you set the system’s boundaries in such a fashion). But how do we know how much energy an accountant requires in order to complete his/her daily tasks as an accountant? Money is one way to arrive at an estimate, and although it may not be very accurate it still provides a rough figure.

    Because I fail to see the difference between your “energy consumption” and “energy investment” I also fail to see why it is important to divide a country’s energy expenditures with its EROI. Come to think of it, I do not even know how to calculate the EROI of a country. Has this been done? No doubt trade would be very important. I am interested in the idea, and the results would be very interesting I think.

    My second comment concerns your suggestion to include “embedded energy recovered”. The headline alone sends me warning signals because the same energy that has dissipated cannot be expected to be recovered, as a result of the second law of thermodynamics. More to the point, what you are suggesting is that we treat infrastructures as capturers of energy. Speaking of recycling as an energy capturing processes is simply a case of misplaced concreteness because no such recovering ever takes place. There is no “recovering” of energy in a recycling process, only energy expenditures. To introduce a model saying that there are such “recoverings” is theoretically laudable, but it would be incorrect and make matters more complicated in my opinion. From my point of view, it is more correct, and easier, to work out the percentage of material that is recycled/not recycled and base the calculations on the associated energy expenditures of the composition of the structure in question. Over time the aggregation of these types of studies will provide with an accurate account of the energy savings you are talking about. Embodied energy/energy memory/emergy, or as you term it “embedded energy” is by definition a ‘what-has-happened’ concept, not a ‘what-will-happen’ concept. The former is data, the latter is prediction.

    My third comment concerns your idea that heat losses should be taken into consideration when calculating the “energy return to society”. This entails an analysis of what the particular fuel is going to be used for, and then calculating how much exergy is provided to that particular service, e.g. internal combustion. But this cannot be attributed to the EROI of oil, because oil can be used in many other industrial processes than internal combustion. What you are calculating here is arguably not the EROI of a fuel, but the energy expenditures of different societal sectors and potentially the energy investment in another/or the same fuel.

    Finally, I think that your article is interesting and it has made me think more about the “return-to-society-side" of the EROI model. I will continue to explore this dimension of the topic. Thank you for a well-needed inquiry into the errors of EROI calculating.

  5. Hi Arthur,

    Thanks for your interesting and thoughtful remarks.

    "In energetic terms there cannot be anything called “energy consumption” because energy cannot be consumed or used up as I am sure you are already aware of."

    Sure. All of these terms ("energy investment", "energy returns", "energy consumption"), and so on, are fairly loose ways of talking. If I "consume" the energy in a gallon of gasoline, the energy still exists. It becomes waste heat in the outside atmosphere from the radiator of my car and from my brakes. The waste heat is useless to me. The energy isn't really consumed; it's relocated and it changes form, so it no longer provides any useful service to society.

    Of course, it's not possible to have an EROI higher than 1:1 for any source of energy, because that would violate the first law of thermodynamics. You can never get back more energy than you put in. In this case, "energy returns" refers to the amount of energy minus energy losses of obtaining the energy. Here, "energy losses" refers to waste heat from oil refineries, drilling equipment, and so on.

    "My second comment concerns your suggestion to include “embedded energy recovered”. The headline alone sends me warning signals because the same energy that has dissipated cannot be expected to be recovered,"

    Sure. By "recovered" is meant that the material is recycled, so that additional embedded energy is displaced or not necessary. Again, it's a loose way of talking.

    If we want, we could just throw away old steel frames and so on, rather than recycling them. In both cases, the energy is still there, but in the second case, it's useless to us, because it's in the ground and the steel is being oxidized by natural processes which provide no services to society. In this case "recovered" means that the material is not thrown away so we don't need to expend more coal making more steel.

    "Accountants are, like it or not, needed to maintain businesses that provide such a foundation, and they do not run on nothing."

    Sure, absolutely. The energy expenditures of accountants should be included. I will address this is a subsequent article.

    "This entails an analysis of what the particular fuel is going to be used for, and then calculating how much exergy is provided to that particular service, e.g. internal combustion. "

    Sure. With coal this is easy to do, because well over 95% of it is used for electricity generation. With oil, you would need to find out how much is used in cars, how much in large trucks, how much in marine engines, etc, and generated a weighted average. Large marine diesels are much more efficient than gasoline engines in cars.

    "But this cannot be attributed to the EROI of oil, because oil can be used in many other industrial processes than internal combustion."

    If oil is used to make plastics etc, then that oil has an EROI of zero. The term "EROI" should be used only when discussing energy used to obtain energy, in which case, only the oil which is used as a fuel should be counted.

    "Come to think of it, I do not even know how to calculate the EROI of a country. Has this been done?"

    No, but you could come up with a reasonable estimate. Almost all the energy in society consists of coal, gas, oil, nuclear, hydro, wind, solar, biomass, and geothermal. You could determine the EROI ratios of each of those and then perform a weighted average.

    -Tom S

  6. Hi Arthur,

    Because of your helpful remarks, I slightly re-worded the first part of the article, to make it clearer. I removed all instances of "energy consumption" and replaced them with "energy returns".

    I think it would be clearer to use as little terminology as possible here.

  7. Thanks Tom for your clear explanations. I did have to concentrate to grasp the distinctions re- energy returns contrasted with energy invested. It seems to me that you are contrasting the amount of initial energy invested to gain the energy later 'consumed' or 'returned' by society to run the economy itself. In which case it does seem strange that someone would add the two together to contrast with GDP.
    I came here from an article about the Prieto and Hall book, which article had a strong smell of anti-solar from the start, which served to stimulate my critical facilities. So it was good to see your erudite critique. Thanks.