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.

Conclusion

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 PV, not 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 PV, which 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.