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# Behind the Numbers on Energy Return on Investment

A full listing of the sources and references behind the calculations in this EROI infographic

Image: Oliver Munday

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When I proposed an article to Scientific American on energy return-on-investment, also known as EROI, I didn't realize how much legwork would be involved in gathering the numbers needed for an infographic to accompany the story.

On the surface, the measurement of EROI seems simple. It is just the energy output divided by the energy input. (For gasoline, for example, the output would be the energy in a gallon of gasoline, and the input would be all the energy required to make the gasoline—including oil exploration, drilling and refining.)

Despite the simple equation for EROI, however, there is a lot of complexity under the hood. One issue is that there is a range of EROIs in the literature for each energy source. In part this is because various researchers use different methods for calculating the number. The differences often reflect disagreements about how energy intensive various steps are in the process. To get numbers that I thought were reasonable, I consulted dozens of studies to get a sense of the range of EROI figures for each energy source, then figured out which ones seemed middle-of-the-road as well as computed in a way consistent with all the other EROI figures that I used.

Also, there's no single accepted way of calculating EROI, because it depends in part on what you count as an input. Two of the main types of EROI that researchers calculate are also known as the “net energy ratio” and the “external energy ratio.” For sources such as tar sands, there can be a large difference between these two measures because some methods of getting tar sands out of the ground derive a lot of the energy required for the processes from the tar sands themselves (see the paper cited by Adam Brandt below). The “net energy ratio” counts all inputs—whether diesel fuel for a truck or the tar sands themselves. The external energy ratio, on the other hand, only counts the energy that society puts in, and doesn't count what comes from the resource itself. This means the external energy ratio is always higher than the net energy ratio. Whenever possible, I used the external energy ratio because it is most relevant to the question of how much energy we get out, for the energy we put in. (For calculating greenhouse gas emissions, on the other hand, you would want to consider all energy inputs, and the total emissions from them.)

For biofuels, the EROI reported is usually the external energy ratio, and it doesn't include energy derived from, say, burning the stalks of sugarcane to help power the process of refining sugarcane juice into ethanol. So studies of biofuels will sometimes cite the “fossil energy ratio,” which is similar to the “external energy ratio.”

The external energy ratio number was not available for every energy source. For example, with conventional oil only the net energy ratio was available. The difference between these two types of EROIs, however, would likely be relatively small for conventional oil (personal communication, Charles Hall).

There are uncertainties in any EROI estimate, in part because energy companies usually don't report detailed information on their energy consumption. To calculate the energy input, researchers have to make an estimate based on the dollars spent on various processes and goods—such as the cost of steel to line an oil well. To keep the infographic as simple as possible, we did not attempt to show error bars or ranges on the estimates, and generally rounded them off to a single digit. This was meant to reflect the uncertainty in any single estimate as well as the fact that there is not a single, precise EROI for any energy source.

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1. 1. GRLCowan 11:34 AM 3/23/13

"Estimating life cycle greenhouse gas emissions from CANDU nuclear power plants", by Andseta, Thompson, Jarrell, and Pendergast, allows us to estimate the 2.8 petawatt-hours of nuclear electricity produced in 2010, if produced entirely by CANDU reactors, would have come with 9.0 million tonnes of CO2 emissions.

If we accept Inman's EROI estimate of 7 for natural gas, we must multiply by (8/7) the 337 million tonnes of CO2 that combined-cycle gas turbine power plants with 60 percent thermodynamic efficiency would have taken to produce the same electricity; result, 385 Mt.

This suggests nuclear electricity's EROI is about (385/9) times higher than gas's. About 300.

2. 2. sault in reply to GRLCowan 12:58 PM 3/24/13

CC natural gas plants can't get 60% efficiency. Under real-world optimum conditions, they can achieve around 50%. And NOWHERE NEAR 100% of the energy needed to make nuclear power possible comes from natural gas. The energy to run mining equipment might come from pitifully-low EROEI Tar Sands fuels, for example. And since the only nuclear plant to ever be even PARTIALLY decommissioned is Chernobyl, we have no idea how much of a pain it will be to return nuclear plants to a safe state at the end of their useful lives. I mean, how much energy will it take to keep old nuclear plants under lock and key basically forever? Or how much energy will it take to keep nuclear waste sequestered NEARLY forever? You know as well as I do that reprocessing doesn't make ANY sense until uranium is at least 10x the cost it is currently, so we're stuck with a lot of that waste forever. The MASSIVE subsidies the Socialist French threw at their reprocessing could have been better used to build up REAL clean energy instead of a dead-end and dirty reprocessing "industry".

3. 3. davekimble 06:34 PM 3/24/13

All true enough, but nowhere near sufficient to analyse what should be done about our energy predicament.

ERoEI boils down a whole lot of information, called the energy budget, to just one number. If ERoEI is < 1, you would think the technology is a non-starter, but if the EI is coal, and you have plenty of that, and the ER is a petrol substitute, which is in short supply, then an ERoEI of < 1 can make a certain kind of sense.

Also the ERoEI will vary for things like solar, wind and hydro, because the location of the project will have a big effect on the ER.

Also some of the EI has to be spent a long time before you get the ER - almost all of it in the case of solar PV. To boost the production of panels, you first have to build a factory, and fill it with complex machines which work in especially clean air, and vacuum chambers, and produce more bulldozers and trucks to mine the silica sand. Once set up, you would hope you are then ready for 30 years of production and the panels themselves will produce the ER for 30 years, spreading the ER out over say 3-63 years from the start of the project.

In the early years, there is a lot of EI and very little ER, so the project is a drain on the nation's energy budget, which has to be met by the very fossil fuels we want to reduce.

And if, after building your PV factory, you then build another PV factory, and another, and another, and another two, the ER will not outweigh the EI until you have built all the PV factories you need and stop building them, and then wait some more time for all the EI to be paid back. Only then does the entire project start to make an energy profit - decades down the track.

So the simple ERoEI figure can be grossly misleading.

4. 4. twayburn 10:06 PM 3/24/13

I went to a lot of trouble to show Dave that the front-loading of the energy investment in solar energy from photo-voltaic cells is a difficulty that could be overcome in Australia where he lives. Some of this discussion can be found at http://dematerialism.net/pv.htm .

Mason Inman read the wrong references for EROI (or ERoEI) if he was concerned about greenhouse gases, for example, because the calculations he cited could give EROI > 1.0 but the technology might result in more fossil fuel being consumed rather than less; that is, the technology might be subsidized by fossil fuel.

The rest of this comment can be found at http://dematerialism.net/eroeistar.htm .

5. 5. twayburn 05:20 AM 3/25/13

I should add that Dave Kimble and I do not agree as to who showed who what in our little debate. Both sides think they won. Nevertheless, the diligent (and interested) reader can look at http://dematerialism.net/pv.htm and adjudicate the dispute. Of course, pv.htm was written from my point of view.

6. 6. PeteW 01:45 AM 3/28/13

A thought provoking article, as you note getting good numbers is difficult.
After a career working with CANDU reactors I find that your estimate of an EROI of 5 for nuclear is suspect. Based on a CANDU burnup of 180MWH/kg of uranium and a mining and milling requirement of 100GJ/T from your reference (Life cycle energy and greenhouse gas emissions of nuclear energy: A review), the EROI for the fuel alone is 6,480. If you divide this by 3 as you do for coal to allow for losses at the plant, then you get about 2000. From this we would have to deduct the cost of construction, which will be two or three times that of a coal plant, but I cannot see how this would reduce 2000 to 5 when coal gets 8.7? Other reactor types would be lower because of the costs of enrichment, but this is offset by getting a significantly higher fuel burnup.

7. 7. leontis 10:39 AM 4/11/13

What about Large-Scale (District-Wide) Geothermal for Heating and Cooling? Why is this not discussed? Why do we continue to burn natural gas to heat large buildings (universities, hospitals, industrial plants and warehouses) when geothermal is available almost everywhere?

8. 8. sethdiyal 02:39 PM 4/12/13

Another low information post from our resident illiterate who thinks himself an expert on all things. Never any backup from reputable sources for his outrageous claims.

There have been scores of reactors decommissioned which the NRC uses to establish a fee of .1 cents a kwh.

The cost of decommissioning and nuke waste storage is covered by a per kwh fee from the NRC with \$55B collected to date and kept in a fund administered by the DOE/GAO. Since the nuke waste is very valuable fuel for Gen IV reactors like India's new unit first of 5 to 2020 and a nuke site will always be a nuke site those funds are being lent out to Obama's pals in the renewable business to build wind and solar plants on the taxpayers dime.

There are no engineering issues on waste storage. We've being doing it for years without problem at WIPP and the locals want to more - a lot more. The only problem with Yucca is not engineering but corrupt politics -Harry Reid. Finland uses the Yucca method of waste storage without issue.

There are no long term security costs if the not "waste" was simply buried in an abandoned uranium mine.

According to Areva the cost of Purex processing once established as in France is about the same as new uranium. Pyroprocessing promises to be much cheaper.

All parts of the nuke energy input could be powered by natural gas or nuke electricity.

9. 9. mhfskibum 10:08 AM 4/13/13

Would ANY of these industries exist without tax incentives and governmental supports of all kinds? This seems to me to be the easiest test.

10. 10. peterbrm in reply to davekimble 10:16 PM 4/13/13

Set up costs apply to all energy types. If we followed you costing method then we would not have learned how to flake flint as the cost of learning the skill was temporarily greater than the cost of looking for naturally occurring sharp stones.
Our investment in existing technology is often the enemy of adopting a newer technology, even when it is obviously better in the long term (this > 5 years for some people - especially politicians and accountants).

11. 11. paldao 02:02 PM 5/1/13

the substantial energy required to construct and safely decommision a nuclear plant, would probably bring the eroi down to below reasonable.rob paldao

12. 12. sbwoodside 08:50 PM 5/10/13

13. 13. Cliff Claven 09:05 AM 5/18/13

This article does a good job of introducing a very complex subject, but a bad job of actually comparing alternatives. As the author lays out, there are EROIs, FERs, EERs and other measures of energy balance that all have different boundaries and tell a different story. One cannot cherry-pick one source's EROI to compare with another's EER. It is long past time, but the physics community is finally getting involved. There is an excellent paper just published that goes the furthest yet in developing a rigorous, apples-to-apples comparison of electrical power generations alternatives (Weißbach et al. “Energy Intensities, EROIs (energy Returned on Invested), and Energy Payback Times of Electricity Generating Power Plants.” Energy 52 (April 1, 2013): 210–221. doi:10.1016/j.energy.2013.01.029). The key they have found is to normalize not just across power quantity, but also quality. A key aspect of quality is "usability," which is the degree to which the supply of power matches the real-time demand. Intermittent and invariable baseload power sources must be adjusted for the amount of buffering necessary to match their output to the real world of variable demand. The study authors did this by requiring each source to have the overcapacity and storage necessary to be compatible with a large international European grid scenario, and they used pumped-hydro power storage parameters since it is today's most cost-effective option for storage and buffering. The study is behind a paywall but the results have been posted online and are being updated as newer data is reviewed (https://docs.google.com/spreadsheet/ccc?key=0Aux2QwQckeWEdE9UbHNKR3l6THItNi1RTUdxa1RrdUE#gid=0). In their analysis, they found that a minimum EROI of 7:1 was necessary for economic viability. With that in mind, here are their results:

PV solar 2.3:1
Biomass Boiler: 3.5:1
Onshore Wind: 3.9:1
CSP Solar : 9.6:1
Natural Gas: 28:1
Coal: 30:1
Run-of-River Hydro: 35:1
PWR Nuclear: 75:1

14. 14. Bob Wallace 04:36 PM 5/25/13

Perhaps we need a new EROEI. Let's call it the ERO(non-sustainable)EI, ERONsEI. Until someone comes up with a better name.

In 2012 we had enough solar panels on our grid to produce all the electricity we used to manufacture solar panels during the year. The same has been true for wind turbines for some years.

Let's take the sustainable part out. We can make electricity with solar, wind and other renewables. EROEI concerns us mostly because we are using up a finite resource, oil/gas, in order to extract more oil/gas.

We aren't going to run out of sunshine or wind for a few billion years.

We can extract iron ore and the other raw materials for solar panels and wind turbines using electricity (from renewable sources). We can refine and transport them using renewable electricity.

We have the ability to make EROEI/ERONsEI irrelevant, except as a guide to creating more efficiency.

15. 15. sidmun 01:34 PM 10/24/13

Very good article.
<a href="http://www.shawn-bartholomae.blogspot.com/">Shawn Bartholomae</a>

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