## Sunday, June 19, 2016

### ERoEI is unimportant and is being used incorrectly

In this article I will show that ERoEI is unimportant by itself. It usually does not matter if ERoEI is increasing or decreasing. ERoEI provides no guidance about which sources of energy we should pursue, nor does it offer any guidance about how much net energy will be available to us in the future. By itself, ERoEI is a useless figure, unless it is lower than 1, which it almost never is. Although different sources of energy (such as coal or solar PV) have different ERoEI ratios, this means nothing important.

What is important to civilization (and to us) is the amount of net energy obtained from a source of energy. It is an amount of net energy (not a high ERoEI) which allows us to drive cars, fly airplanes, and so on. If we obtain 1 GWh of NET energy, then it does not matter if it came from a high-ERoEI source, or from a low one. What matters is the amount of net energy.

In turn, the amount of net energy depends upon two things: ERoEI AND the amount of gross energy. BOTH of those figures are required to determine the amount of net energy obtained. ERoEI by itself tells us almost nothing.

Let me provide an example, to demonstrate this point. Suppose you have a solar PV panel with an ERoEI of 3, which returns 1KW on average continuously for 30 years. In that case, the net energy provided by that solar panel is 175.2 MWh ((1*24*365*30)*(1-1/3)) over its lifetime. If, however you have ten such solar panels, then the net energy returned is ten times higher (1752 MWh), despite no change in ERoEI.

For the most part, the amount of NET energy we can obtain is determined by the amount of GROSS energy we can obtain, not by ERoEI. Usually, ERoEI is only a minor factor. This is because the difference in the amount of gross energy between sources of energy is so large that it completely overshadows any minor influence that ERoEI would have.

For example, suppose we had single 1KW solar panel, and the panel had a very low ERoEI of 4 (which is certainly an underestimate [1]). Even if you increased the ERoEI from the very low value of 4, all the way up to to infinity, so that no energy was required to replace that solar panel, it would make little difference--it would increase the amount of NET energy obtained by only 25%. On the other hand, if you could build 3 such solar panels, instead of 1, then you would triple the net energy obtained. In this case, building two more solar panels had 12x greater effect than increasing the ERoEI to infinity.

For the most part, the net energy obtained from solar power would be determined by the number of solar panels built, not by their ERoEI. In turn, the number of solar panels which can be built, is determined by non-energy factors like capital and labor, because those are the scarce factors which prevent the construction of more solar panels. Energy for investment is not scarce, because this planet is bombarded with 23,000 terawatt-years/year of solar radiation, which is vastly more than we will ever use. It is the scarce factors which determine how many solar panels we can build, and therefore, for the most part, how much net energy we will obtain. This point is complicated and requires further elaboration, so I will discuss it in a subsequent article. Suffice it to say, that the net energy of solar power is determined by non-energy factors such as capital and labor, and has almost no relation to ERoEI, because capital and labor (not energy) are the scarce factors which prevent the construction of more solar panels.

Generally speaking, the amount of net energy goes up as ERoEI declines, although it’s a weak correlation. This is because the amount of gross energy is vastly higher at lower ERoEI ratios, and the greater amount of gross energy more than compensates for any decline in ERoEI.

For example, solar PV could provide far more net energy than coal, regardless of its lower ERoEI. This is because solar radiation is so much more abundant that its lower ERoEI would be completely overshadowed by its greater amount. As a demonstration, suppose we could convert only 1% of solar radiation striking this planet into electricity using solar panels. In that case, we would obtain 40,000 times more electricity from solar power than we currently obtain from burning coal [2]. That figure does not take into account ERoEI, but it would make little difference. Even if solar PV had an extremely low ERoEI of 4 (certainly an underestimate), and coal had an ERoEI of infinity, it still would only reduce the maximum net energy of solar power by 25% relative to coal [3]. Since solar power is 40,000 times more abundant than coal, an ERoEI adjustment of 25% is not important. It would mean only that we could obtain 30,000 times more energy from solar power than from coal, rather than 40,000 times more [4].

Of course, if the ERoEI of some energy source were extremely low (like less than 2), then ERoEI would become an important factor. In that case, ERoEI would actually make a substantial difference, because it would cause a 50% or greater net energy loss. However, all common sources of generating electricity have ERoEI ratios far higher than that. With an ERoEI higher than 8 (which all sources of generating electricity have), the amount of energy spent obtaining more energy is only 12.5%, which is completely overshadowed by differences in gross amount between energy sources.

Again: net energy available is a function of BOTH EROEI AND AMOUNT. Either one of them by itself cannot be used to calculate net energy. If we wish to use a “rule of thumb”, then we should assume that MORE net energy is available at lower ERoEI ratios, but the correlation is so weak that it can’t be relied upon. In any case, ERoEI is not generally an important factor.

Unfortunately, ERoEI theorists do not realize any of this. Over and over again, they wrongly assume that ERoEI is somehow proportional to net energy. They assume that a higher ERoEI somehow implies more net energy obtained. This is a severe mathematical error, but it’s repeated endlessly throughout the ERoEI literature, across decades.

Let me provide some examples which I read just a few days ago:

“Look [at a] Cheetah… That beautiful and ultra efficient machine, needs an EROI of about 3:1... That’s a metabolic minimum EROI for mammals.Being the minimum EROI for any live being (mammals in particular) 2-3:1 in average, to be kept alive as species and for the couple to successfully breed their offspring (minimum of 2-3 per couple), probably Charles Hall is very right to state that a minimum EROI of 5:1 is required to have a minimum (very primitive and elemental) of civilization, beyond us living as naked apes.”
No, because that wrongly assumes that greater amounts of net energy are obtained at higher ERoEI. That is a basic mathematical error. Frequently, using a lower ERoEI source of energy will obtain more net energy than a higher ERoEI one.

The Cheetah example is also mistaken in other ways. The Cheetah doesn’t just have a low ERoEI; it also has TOO FEW prey which it can catch. If the Cheetah could eat prey every 5 minutes, then it would have a vast excess of energy even at an ERoEI of 1.5. The problem is that many animals eat only once per day and some animals (such as crocodiles) eat only once per week or so. The problem is amount, not ERoEI. If they eat only 10,000 kilocalories per week, then increasing the ERoEI wouldn’t matter much (even increasing ERoEI to infinity in this case would only gain the animal another 3,300 kilocalories). What would help is to catch MORE prey.

Here is another example of the same mistake:
We can take our ERoEI 20 FF and invest them in ERoEI 50 sources and make a huge energy profit. Or we can invest them in <5 and make a loss. Our policy makers have lost their heads electing to promote loss making activities.”

No, because that is confusing ERoEI with an AMOUNT of net energy. If an ERoEI were an amount, then spending fossil fuels with ERoEI 20 on solar panels with ERoEI 5, would imply a loss of 15. However, you cannot subtract the ERoEIs of different sources of energy, because they are not AMOUNTS which can subtracted. The correct mathematical operation is to multiply those two numbers, not subtract them.

If you take ERoEI 20 fossil fuels, and invest them in ERoEI 5 solar PV, then the aggregate ERoEI is 100 (invest 1 unit of fossil fuels initially, obtain 20 units of fossil fuels with ERoEI of 20 thereby, invest each of those 20 units in solar panels with ERoEI 5, then obtain 100 units at the end of it for an initial investment of 1).

Here is another example:
IMO, the only thing that could delay the bad impacts of declining high ERoEI FF is to introduce to the global energy mix an energy source that has higher ERoEI than the fuels they have to replace. Introducing low ERoEI energy sources simply makes things worse.”

No, because (again) that is confusing ERoEI with an AMOUNT of net energy. The “bad impacts” are caused by TOO LITTLE net energy, not a low ERoEI. Adding any source of energy with an ERoEI higher than 1 increases the total amount of net energy available. Only an ERoEI lower than 1 would make things worse. If the source of energy is cheaper per unit of net energy (as solar power actually is) then it is easier to obtain more net energy that way, regardless of its ERoEI.

…All three of the above quotations are taken from leading figures in the ERoEI literature, all published within the last few weeks. Granted, the ERoEI movement is a tiny fringe movement, but these people are among the leading figures of it. Over and over again, they wrongly assume that ERoEI and net energy are somehow proportional, and that higher ERoEI implies more net energy. That is a basic mathematical error. Frequently, the opposite is the case.

What matters is the AMOUNT of NET energy available to civilization, and that amount is far higher for renewables than for any other source, regardless of ERoEI.

* NOTE: In this article, I am using the term "ERoEI" to by synonymous with "EROI" and other spellings. I am referring to the amount of energy obtained for an investment of energy. If ERoEI for some energy source were extremely low (like lower than 3) then ERoEI would start to become more important, since we'd need to build significantly more power plants to generate the same net energy. Since all common sources of generating electricity have an ERoEI much higher than that, ERoEI is not important in any real-world scenario.

I revised this article on August 18, two months after its initial publication, to improve the flow of the text.