The Energy Trap

In this post I will address the issue called the "Energy Trap", which was explained well by Tom Murphy on his excellent blog post and re-iterated by oatleg in the comments to my prior post. Basically, the "energy trap" is a scenario where fossil fuels peak and start to decline, and we must start investing energy in building renewables in order to replace fossil fuels. But there is a problem, as follows: renewables require a large up-front investment of energy, but pay back that energy only gradually over many years. As a result, when fossil fuels start to decline, we must make large up-front investments in renewable power precisely when energy for investment is in short supply, leading to a temporary "energy deficit". For a fuller description of this phenomenon, I highly recommend reading Tom Murphy's blog post entitled The Energy Trap.

I decided to model this phenomenon of the "energy trap" by using a small computer program, which I wrote in python. Any reader can download the python interpreter for free and run the simulation on his computer (the source code is posted in the comments below).

For the simulation, I made the following assumptions:

1. Civilization gets all of its energy as electricity, generated from burning fossil fuels
2. All fossil fuels peak on the same day and decline immediately according to the right-hand side of a Gaussian curve
3. Fossil fuels start declining immediately without warning, and without any kind of production plateau
4. The Gaussian decline curve has a standard deviation of 30 years which is a very rapid decline. As a result, there is a 50% decline in all fossil fuel production in only 34 years.
5. There are no "unconventional" fossil fuels which will allow us to delay the decline or extend the decline curve
6. No preparation has been made. The investment in renewables beforehand was zero.
7. Investors and decision-makers do not begin investing in renewables until 7 years after the declines in fossil fuel production have begun, because it takes time to realize what is happening and ramp up PV production.
8. Investors use a very naive formula for determining how much PV to build. Once they realize what is happening, they start investing about 5% of electricity production per year to building renewables, later increasing the investment to 1/ERoEI.

Please note that these assumptions are all incredibly pessimistic. These were by far the most pessimistic assumptions which I could imagine but which were still at least somewhat plausible.

If I run my simulation with those parameters, what results do I get? Here are the results in tabular format:

year	gross_ff	gross_pv	gross_total	net_total	invest_pv	invest_ff	fraction_original_net
0	1.0000	0.0000	1.0000	0.9000	0.0000	0.1000	1.0000
2	0.9978	0.0000	0.9978	0.8978	0.0000	0.1000	0.9975
4	0.9912	0.0000	0.9912	0.8912	0.0000	0.1000	0.9902
6	0.9802	0.0000	0.9802	0.8802	0.0000	0.1000	0.9780
8	0.9651	0.0167	0.9817	0.8449	0.0500	0.0869	0.9388
10	0.9460	0.0500	0.9960	0.8608	0.0500	0.0851	0.9565
12	0.9231	0.0833	1.0064	0.8734	0.0500	0.0831	0.9704
14	0.8968	0.1167	1.0135	0.8828	0.0500	0.0807	0.9809
16	0.8674	0.1500	1.0174	0.8894	0.0500	0.0781	0.9882
18	0.8353	0.1833	1.0186	0.8934	0.0500	0.0752	0.9927
20	0.8007	0.2167	1.0174	0.8953	0.0500	0.0721	0.9948
22	0.7642	0.2500	1.0142	0.8954	0.0500	0.0688	0.9949
24	0.7261	0.2833	1.0095	0.8941	0.0500	0.0654	0.9935
26	0.6869	0.3167	1.0036	0.8918	0.0500	0.0618	0.9908
28	0.6469	0.3500	0.9969	0.8887	0.0500	0.0582	0.9874
30	0.6065	0.4000	1.0065	0.8519	0.1000	0.0546	0.9466
32	0.5662	0.4667	1.0328	0.8819	0.1000	0.0510	0.9799
34	0.5261	0.5333	1.0595	0.9121	0.1000	0.0474	1.0134
36	0.4868	0.6000	1.0868	0.9429	0.1000	0.0438	1.0477
38	0.4483	0.6500	1.0983	0.9580	0.1000	0.0403	1.0644

(Note: All values are fractions of the original gross amount of energy from fossil fuels; so an invest_pv column of 0.05 means that 5% of the original gross amount of energy is invested in PV panels)

As we can see, there is an "energy deficit" starting on year 8, because of the energy trap. At that point, civilization is only consuming 93.88% as much electricity as it used to. The reason is because year 8 is when investors have realized that fossil fuels are on a permanent decline, and start "investing" only 5% of yearly electricity in building solar panels. However, the 5% investment is all up front, with little payout this year, leading to an energy deficit of 5% this year plus a few more percent for the amount that fossil fuels had declined thus far. The energy deficit is brief, and civilization is back up to 97% consumption in 4 years.

Which raises the question: what will we actually do? Will we decide to forgo 5% of our electricity consumption now, as I assume above, in order to avert the gradual collapse of civilization over the next few decades? Or will we take the short-term view, and decide to "eat our seed corn" (so to speak) and cannibalize our energy infrastructure, leading to a small increase in our energy consumption now but the destruction of our civilization later?

Tom Murphy has this to say about it:

"Politically, the Energy Trap is a killer. In my lifetime, I have not witnessed in our political system the adult behavior that would be needed to buckle down for a long-term goal involving short-term sacrifice."

I disagree with that remark. These decisions are not made by our political system, but by investors in energy markets. Those investors routinely make short term sacrifices for larger payouts later. That is what investment means. For example, investors routinely carry out long-term planning and buy capital equipment (such as power plants) which will pay out over 30 years, but which require an up-front investment now. That is why we have power plants. Investors could always eat their seed corn and spend the money now rather than investing in the future. In general, they don't do that.

When fossil fuels start declining, the price of energy will skyrocket. Even a modest decline of a few percent of energy, could lead to a tripling of prices or more. At that point, the financial return of investing in renewables would be enormous and nearly certain. Any investment in renewables would promise vast payouts down the line, far higher than are obtained by any other investments. As a result, investors will transfer money from other investments in to this one. Investors are capable of outbidding consumers for that 5% of yearly electricity which is necessary to invest for the transition.

The energy trap is actually a fairly mild problem. Even using the incredibly pessimistic assumptions I outlined above, we will never face more than a 6.12% deficit of energy. The deficit starts decreasing right away and almost vanishes within 9 years after it begun. The energy trap is easy to overcome, with only modest and temporary sacrifices.

Furthermore, the deficit of 6.12% is almost certainly higher than what we will face in reality. We have begun transitioning to renewables decades before fossil fuels have begun declining. Furthermore, we get a large fraction of our energy now from sources other than fossil fuels (like nuclear and hydro-electric). What's more, the decline in fossil fuel production will be far more gradual than I modeled above. Also, there will be a production plateau lasting decades before fossil fuels start declining. Furthermore, investors will use a more sophisticated algorithm when determining how much PV to build, rather than just suddenly increasing PV investment from 0% to 5% (as I modeled above) which briefly worsens the energy deficit. When I run my model with more realistic assumptions that aren't so incredibly pessimistic, I find an energy deficit of less than 0.4% at its worst point.

In conclusion, the energy trap is easy to overcome with only modest adjustments. It requires modest planning--the kind which investment markets routinely carry out. As a result, the energy trap will be a minor problem which will impose only temporary and insignificant reductions in energy, in my opinion. It is also possible that civilization will transition to renewables before we reach peak fossil fuels, in which case the energy deficit will be zero.

(NOTE: The python source code is posted in the comments below)
(NOTE: I made minor changes to the wording of this article two days after initial publication. The values from the table have not changed.)

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.