The Effect of Declining EROI on Industralized Countries

In the previous article, it was shown that any country can increase its energy supply exponentially with any EROI higher than 1. For example, with an EROI of 10, any investment of energy more than 1/10th of energy supply (or 1/eroi) will lead to exponential growth of energy obtained over time.

It was also shown in the previous article that a low EROI imposes a delay for civilization when accelerating exponential growth of energy obtained. For example, it was shown (using a simulation) that a low EROI of 10 imposed a delay of 6 years before a hypothetical civilization could accelerate growth from 0%/year to 4%/year.

However, some modern industrialized countries do not accelerate growth at all. In fact, they do not even grow their energy supply. Those countries are already fully industrialized. Once a country reaches a first-world standard of living, it voluntarily stops growing its energy supply. Citizens decide to spend any increase in their income on things like elaborate medical care, and not on setting their thermostats higher every year. This situation has already been reached in Japan and many places in Europe. It would have been reached in the USA, except the USA still has significant immigration.

What would happen to such a static country (in terms of energy supply) if it underwent a decline in EROI? Presumably, such a country wouldn't care about how fast it could grow its energy supply. It would care only about keeping the amount of net energy constant.

In such a country, any decline in EROI could be handled by initiating growth again, at a rate which is sufficient to compensate for the decline in EROI. Doing so would keep net energy constant.

As a result, we must ask how much net energy must be sacrificed by an industrialized country in the short term, in order to initiate growth and offset declines in EROI. Any acceleration of exponential growth requires a temporary sacrifice of net energy, in order to initiate the growth. How much net energy must an industralized country sacrifice to initiate growth again, sufficient to compensate for a decline in EROI?

This phenomenon can be modelled using a simple python computer program--even simpler than the last one, because this program has only 24 lines of code, excluding comments. (This phenomenon cannot be modelled using a simple mathematical formula, because generations of solar panels overlap, which resists a simple mathematical description).

In this paper, a simple python program will be proposed which simulates energy re-investment for an industrialized country over time. The program will execute in a single loop and will simulate energy re-investment, over and over again, each year. As before, we will assume a country which obtains all its energy from solar panels.

The program will simulate a decline in EROI. We can assume that the decline in EROI is caused by mineral exhaustion over time. The country used to build fancy Gallium-Arsenide solar cells with 40% efficiency and very high EROI, but the Gallium is running out. As a result, the civilization must start building silicon solar cells instead, which use far more abundant materials but have much lower EROI. Furthermore, the country has already filled its only tiny desert region with solar cells, and must now use worse locations, implying lower EROI for solar cells. As a result, the country undergoes a constant decline in EROI over years. This decline in EROI will be modelled in our program by increasing the energy investment required by some constant factor each year.

At the same time, the program will model the modest exponential growth which must be re-started in order to compensate for the decline. These two factors will operate simultaneously. Declining EROI will decrease net energy obtained, but exponential growth will increase it.

As pointed out in the previous article, any acceleration of exponential growth requires a temporary sacrifice of net energy for other purposes. How much of its net energy must an industrailzed country sacrifice, and for how long, in order to initiate exponential growth and compensate for declines in EROI?

When I implemented and ran the program, I obtained the following results. I tinkered with the input parameters, and I found that growing the total amount of energy obtained by 0.7%/year for a country is sufficient to compensate for a decline in EROI from 50 down to 6, over 37 years. In turn, the country had to sacrifice a small fraction of 1% of its net energy for 2 years in order to initiate that growth. The output of the program was as follows:

Original net: 0.98

year	total	retired	epbt	net	FracOriginalNet	eroi
0	1.000000	0.040000	0.500000	0.976500	0.996429	50.000000
1	1.007000	0.040000	0.600000	0.978771	0.998746	41.666667
2	1.014049	0.040000	0.700000	0.981080	1.001102	35.714286
3	1.021147	0.040000	0.800000	0.983429	1.003499	31.250000
4	1.028295	0.040000	0.900000	0.985817	1.005936	27.777778
6	1.042742	0.040000	1.100000	0.990713	1.010931	22.727273
8	1.057391	0.040000	1.300000	0.995769	1.016091	19.230769
10	1.072247	0.040000	1.500000	1.000988	1.021416	16.666667
12	1.087311	0.040000	1.700000	1.006372	1.026910	14.705882
14	1.102586	0.040000	1.900000	1.011922	1.032573	13.157895
16	1.118077	0.040000	2.100000	1.017641	1.038409	11.904762
18	1.133784	0.040000	2.300000	1.023530	1.044419	10.869565
20	1.149713	0.040000	2.500000	1.029593	1.050605	10.000000
22	1.165865	0.040000	2.700000	1.035830	1.056970	9.259259
24	1.182244	0.040000	2.900000	1.042245	1.063515	8.620690
26	1.198854	0.047049	3.100000	1.026987	1.047946	8.064516
28	1.215697	0.047148	3.300000	1.032025	1.053087	7.575758
30	1.232776	0.047248	3.500000	1.037203	1.058371	7.142857
32	1.250095	0.047350	3.700000	1.042522	1.063798	6.756757
34	1.267658	0.047454	3.900000	1.047982	1.069369	6.410256
36	1.285467	0.047558	4.100000	1.053585	1.075087	6.097561
38	1.303527	0.047664	4.300000	1.059333	1.080952	5.813953

As is shown above, the country needed to sacrifice a small fraction of 1% of its net energy for two years in order to initiate the growth necessary to outrun declines in EROI. After which, a decline in EROI from 50 down to 6, over 37 years, imposed no decline in net energy for our modelled industralized country.

(After the 5th year in the table above, I decided to print only every other year, in order to keep the table smaller. Not much changes from one year to the next at that point.)

(The label "epbt" refers to Energy Payback Time; net refers to net energy obtained; and"FracOrigNet" refers to the amount of net energy obtained relative to the original, for example, 1.0 implies no loss or gain of net energy compared to originally).

Of course, you can tinker with the input parameters and reduce the final EROI to below 6, or decrease the number of years the simulation runs, or increase the growth rate (and also the temporary sacrifice). I picked these particular parameters because they were the most pessimistic parameters I could imagine which were not just ludicrous. It is extremely unlikely that EROI will decline from 50 to 6 over 36 years. The EROI of 6 is far lower than almost any published EROI figures of any common sources of generating electricity. Furthermore, actual declines in EROI for our global industrial civilization have been FAR more gradual than simulated here. As a result, the parameters I picked were a kind of "drastic worst-case scenario" and should be interpreted as such.

Still, such a rapid decline in EROI imposed only negligible consequences for an industrialized country. The effect upon net energy obtained was to reduce it by a small fraction of 1% for two years.

Of course, this does not mean that consumers must actually reduce their energy consumption by a fraction of 1% for those two years. All industrialized countries in the world already have overbuilt their electricity grids. Industrialized countries have enough electricity generation to provide for the highest anticipated electricity demand in an entire year. Most of the time, they have excess generation capacity which is shut down or curtailed. As a result, the sub-1% sacrifice would only be imposed during the few hours per year when demand is highest and the electricity grid is fully committed. The actual sacrifice would probably mean shutting down some aluminum smelter plants for a few additional hours per year, for two years, and running a few gas turbines for longer the rest of the time for those two years.

From the above, we can conclude that it's easily within the capability of any industrialized country to compensate for any plausible decline in EROI, with no significant loss of net energy.

The source code for the python program is as follows:

# This is free and unencumbered software released into the public domain.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
# IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.
lifetime = 25
total = 1.0
initialEpbt = 0.5
epbtIncreaseFactor = 0.20
growthFactor = 0.007
yearsRun = 40
panelsYearly = []
initialNet = 1.0 - (initialEpbt / lifetime)

# Populate pre-existing panels
for year in range( 0, lifetime ):
  panelsYearly.append( total/lifetime )

# Run simulation
print ("Original net:", initialNet)
for year in range(0, yearsRun):
  epbt = initialEpbt * (1 + year * epbtIncreaseFactor)
  sumPanels = sum(panelsYearly)
  retiredYearly = panelsYearly.pop(0)
  yearlyToBeAdded = (sumPanels * growthFactor + retiredYearly)
  investment = (retiredYearly * epbt) + (sumPanels * growthFactor * epbt)
  net = sumPanels - investment
  panelsYearly.append(yearlyToBeAdded)
  print ("year:%i total:%f retired:%f epbt:%f net:%f frac_orig_net:%f eroi:%f"
% (year, sumPanels, retiredYearly, epbt, net, net/initialNet, lifetime/epbt)
)

EROI and economic growth

Introduction

A great deal of literature has been devoted to calculating the EROI of various energy sources. However, little explanation has been offered for why we should care, or what effect a lower EROI would have on civilization. Why even bother tracking EROI?

Some authors have speculated that declining EROI would imply less net energy for other purposes in the economy. For example, a decline in EROI from 100 down to 10 might imply a 90% loss of net energy for civilization. However, that conclusion was incorrect. EROI does not determine the amount of net energy obtained by civilization as a whole. This is because our global industrial civilization has been increasing the amount of energy (and therefore the amount of energy for investment) exponentially over time, and this effect has greatly outpaced any decline in EROI. For example, increasing the amount of energy (and energy investment) by a factor of 1.33 would compensate for a decline in EROI from 1 billion down to 4, with no loss of net energy. (An increase in the amount of total energy by 1.33x would allow 1/4th (or 0.33 / 1.33) of total energy to be devoted to obtaining the energy, yielding a net energy factor of 1.0 (or 1.33-0.33), or no change). Since the amount of energy for investment can increase exponentially, increasing it by a factor of 1.33 is obviously within the capability of industrial civilization, thereby more than compensating for any plausible decline in EROI. As an example, it has been pointed out repeatedly that the EROI of oil has declined from 100 in 1930 to less than 10 now, but there hasn’t been a decline in vehicle traffic by 90% worldwide since 1930. Quite the opposite, vehicle travel has increased tremendously since that time, because the amount of oil has increased by a such a large factor that net energy from oil increased, despite massive declines in EROI.

Other possible effects of lower EROI would include greater land usage for solar farms, or higher costs of energy. However, those effects would be minor, as a matter of arithmetic, as long as EROI remains above some very low threshold. For example, a low EROI of 10 would imply that a solar farm would need to have ~11% greater land area, compared to a solar farm with an EROI of 1000, in order to obtain the same amount of net energy ( (1-1/1000) / (1-1/10) ~= 1.11)  . Prices for solar panels would also be higher by a similar amount (11%), all other things being equal. However, the price of solar panels has dropped rapidly in recent years and is far below the price of electricity from coal-fired plants. The lower EROI of solar panels would have little effect on price compared to recent declines in price for other reasons.

One effect of lower EROI, which has not been investigated, is the effect on growth. A lower EROI implies a larger upfront investment of energy. A larger upfront investment of energy requires a greater sacrifice of net energy now in order to obtain a desired level of exponential growth. It will take time before exponential growth compensates for the original sacrifice of net energy to initiate that growth. As a result, a lower EROI implies a temporary sacrifice when initiating or accelerating growth.

A simple mathematical example may demonstrate this point. Assume a civilization which gets all its energy from solar panels with an EROI of 10 and a lifetime of 10 years. Also assume that generations of solar panels do not overlap; new panels are kept in a dark warehouse until old ones expire, at which point, all the old panels are replaced at once with new ones. In which case, our hypothetical civilization must invest 10% of its gross energy (or 1/eroi) on building new panels just to replace those that expire, leaving 90% of all gross energy for all other purposes. If that civilization decided to embark upon exponential growth, and double the amount of energy it obtains in each generation of solar panels, then it must double the investment energy from 10% to 20%, leading to a reduction of energy for all other purposes from 90% to 80%. This reduction would persist for one generation of panels (10 years) until exponential growth overcame it. Thus, our hypothetical civilization must undergo a temporary reduction of net energy by ~10% for 10 years, in order to accelerate exponential growth from 0%/year to ~7%/year. This reduction by 10% of net energy is determined by EROI. If the civilization had solar panels with an EROI of 100, then only a 1% reduction in net energy would be required to accelerate growth by the same amount.

Of course, reality is more complicated, for several reasons. First, generations of solar panels do actually overlap -- new panels are installed before all the old ones have expired. As a result, we cannot represent the compound growth with a simple exponential formula. Second, any real civilization obviously would not accelerate its growth from 0%/year to 7%/year overnight, because the sudden loss of net energy would be disruptive. Instead, any actual civilization would obviously ramp up growth more slowly, over a period of a few years, at least.

In this paper, a simple computer model is used to calculate the effect of EROI on growth of energy obtained. A simple python program is presented which repeatedly calculates re-investment of energy over time, and which ramps up growth slowly enough that net energy never falls below some threshold level.

The result is that even low EROI values (such as the EROI of 10 for solar panels) have only a modest effect on growth, as will be shown below.

The Model

The model is implemented as a simple python program which calculates energy re-investment over time. It executes in a single loop which calculates energy obtained and energy re-investment, over and over again, for each year. It takes input parameters such as EROI, target growth rate, and a minimum threshold for net energy. The minimum threshold parameter determines how low net energy can go (relative to the original value) before growth must be curtailed, in order to ramp up growth more slowly. When growth is curtailed (during the ramp-up period), all excess energy beyond the minimum threshold is re-invested for exponential growth.

When this program is run with an EROI of 10.0, a target growth rate of 4%/year, and a minimum threshold of 97%, we obtain the following results. The civilization requires six years of ramping up growth in order to reach the desired growth rate of 4%/year. During the ramp-up period, 3% of net energy is sacrificed in order to accelerate growth. During the ramp up period, all exponential growth is re-invested, according to the assumptions above. The output of the program is as follows:

Initial net:0.900000 minimumNetAmount:0.873000

year	total	retired	toBeAdded	net
0	1.000	0.040	0.0508	0.873
1	1.011	0.040	0.0551	0.873
2	1.026	0.040	0.0612	0.873
3	1.047	0.040	0.0696	0.873
4	1.077	0.040	0.0815	0.873
5	1.118	0.040	0.0981	0.873
STOP RAMPING UP
6	1.176	0.040	0.0871	0.959
7	1.223	0.040	0.0889	1.000
8	1.272	0.040	0.0909	1.045

As we can see, net energy must decline from 0.9 to 0.873, for six years, in order to initiate growth. After which, the civilization has enough surplus gross energy to grow at 4%/year with no further sacrifice.

The source code for the model is as follows:

# This is free and unencumbered software released into the public domain.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
# IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.

eroi = 10.0
lifetime = 25
targetGrowth = 1.04
minimumNetFactor = 0.97
total = 1.0
yearsRun = 30
#panelsYearly keeps track of the panels installed each year; one element
# per year. Each element refers to the amount of energy those panels
# will return EACH YEAR.
panelsYearly = []
oldSumPanels = 0.0
rampUpPeriod = True

# Populate pre-existing panels
for year in range(0,lifetime):
  panelsYearly.append(total/lifetime)

# Run simulation
originalNet = total - total/eroi
minimumNetAmount = sum(panelsYearly) * minimumNetFactor * originalNet
print("Initial net:%f minimumNetAmount:%f" % (originalNet, minimumNetAmount))
for year in range(0, yearsRun):
  sumPanels = sum(panelsYearly)
  retiredYearly = panelsYearly.pop(0)
  if (rampUpPeriod == True and oldSumPanels > 0
and sumPanels > oldSumPanels * targetGrowth):
    rampUpPeriod = False
    print("Stop ramping up")

  if (rampUpPeriod):
    investment = sumPanels - minimumNetAmount
    yearlyToBeAdded = (investment * eroi) / lifetime
  else:
    yearlyToBeAdded = sumPanels * targetGrowth - sumPanels + retiredYearly
    investment = (yearlyToBeAdded * lifetime) / eroi
  panelsYearly.append(yearlyToBeAdded)
  print ("year:%i total:%f retired:%f toBeAdded:%f net:%f" %
  (year, sumPanels, retiredYearly, yearlyToBeAdded, sumPanels-investment
  ))
  oldSumPanels = sumPanels

Conclusion

A decline in EROI worldwide down to 10 would impose a delay of 6 years when accelerating growth from 0% to 4% for the world economy as a whole.

Of course, the model above is simplified in some ways. The algorithm used to determine how to ramp up growth would almost certainly be more sophisticated in reality. In which case, the above model is sub-optimal. Results in reality would be slightly better.

Repeatedly throughout this paper, an EROI of 10 was assumed because that is the EROI of crystalline silicon photovoltaics, which has the lowest EROI of any common source of generating electricity. Still, such a low EROI imposed only a modest delay when accelerating growth. As a result, any plausible decline in EROI in the future would have only modest effects on growth.

Bardi's Universal Mining Machine

Introduction

A number of years ago, Dr Ugo Bardi published a very thought-provoking essay about the possibility of a universal mining machine (which I’ll refer to as “Bardi’s machine” from now on). Such a machine can take common dirt, melt it down, atomize it, and separate it into its elements, each in its own little pile. This would allow us to extract valuable elements from common dirt. It would also prevent us from ever running out any any elements, as I'll explain below.

Common dirt contains small amounts of all naturally occurring elements. You could dig up a cubic meter of dirt from behind your house, and it would contain trace amounts of every element which occurs naturally. If we atomized common dirt, using Bardi's machine, we would obtain all elements from any piece of earth fed into it. As a result, we would never absolutely "run out" of any element until we had exhausted all dirt on this planet.

Furthermore, the amount of rare elements available to us would be massive and practically inexhaustible. More than 99.9% of the rare elements (such as copper) exist as very low concentration deposits. The overwhelming majority of rare elements are found as an atom here, an atom there, spread out thinly throughout the earth's crust. If we could mine the low-concentration deposits, then we would increase the total supply of rare elements by more than a factor of 1,000x.

What's more, we would no longer be "running out" of rare elements at any rate. Once we began mining common dirt, the amount of all elements available to us would be constant, and would not diminish over any time period. When we throw away old smart phones, or we build structures that rust away, they would just return to being common dirt (eventually) and could easily be re-mined. As a result, the amount of materials available to us would not diminish over time.

Presumably, we will eventually be forced to use Bardi's machine at some point. If we continue mining and dispersing the concentrated deposits of rare elements, as we are doing, we will eventually exhaust all of them. At some point, far in the distant future, we will have exhausted all concentrated copper deposits, all the concentrated rare earth deposits, and so on. At that point, only common dirt will remain. If we wish to continue mining the rare elements at that point, we'd need to use something like Bardi's machine.

The problem with mining common dirt is that it takes so much energy to do so. Lower concentrations of elements require higher amounts of energy to mine them. The lower the concentration, the higher the energy requirement. For example, it takes 10 times as much energy to mine an ore which is only 1/10th the concentration. The problem is, the concentration of rare elements is extremely low within common dirt. As a result, it would be energetically extremely expensive to obtain any particular rare element from common dirt. From Bardi’s article:

"Consider copper, again, as an example. Copper is present at concentrations of about 25 ppm in the upper crust (Wikipedia 2007). To extract copper from the undifferentiated crust, we would need to break down rock at the atomic level providing an amount of energy comparable to the energy of formation of the rock. On the average, we can take it as something of the order of 10 MJ/kg. From these data, we can estimate about 400 GJ/kg for the energy of extraction. Now, if we wanted to keep producing 15 million tons of copper per year, as we do nowadays, by extracting it from common rock, this calculation says that we would have to spend 20 times the current worldwide production of primary energy."

That is a valid point. It seems to rule out the possibility of mining undifferentiated crust.

However, one of the commenters for that article pointed out that mining undifferentiated crust would allow us to obtain all the elements at once, not just copper, for the same expenditure of energy. In other words, that expenditure of 400 GJ would yield not just 1 kg of copper, but many kilograms of many other elements also.

Bardi wisely made a concession to that point. In his subsequent book, he calculates the energy expenditure of mining undifferentiated crust while obtaining many uncommon elements thereby.

However, I wish to continue with the commenter’s line of thinking. I wish to explore the possibility of mining undifferentiated crust (dirt) and using all the elements obtained thereby, including the common elements such as iron, aluminum, silicon, oxygen, and so on. That is the purpose of this article: to explore the energetic effects of mining undifferentiated crust and using all the material obtained thereby, or at least using as much of that material as possible.

Can we mine undifferentiated crust?

If we started mining undifferentiated crust, using Bardi’s machine, then the elements emitted from it would not correspond to our needs for them. For example, almost 80% of the material emissions from Bardi’s machine would consist of silicon, oxygen, sodium, potassium, and magnesium, which only could be used for making glass, at least in those quantities. Another 18% or so of the material emissions would be common metals such as aluminum, iron (for steel), titanium, and so on. Less than 1% would be the “uncommon elements” such as copper, nickel, rare earths, and so on. We must use the elements in precisely those proportions if we wish to avoid throwing away any elements emitted from Bardi’s machine.

It’s necessary to avoid throwing away materials, because that’s what would determine how much energy would be required for Bardi’s machine, per kilogram of materials mined. If we used everything emitted from Bardi’s machine, in the proportions in which they were emitted, then the amount of energy used for mining undifferentiated crust would be 10 MJ/kg, as per Bardi’s quotation above, which is a modest amount of energy and is similar to what we use for mining today. If, on the other hand, we mine only copper from undifferentiated crust, and throw everything else away, then the energy expenditure is 400 GJ/kg, which is 40,000 times higher.

Since we wish to avoid throwing away material, we must align our mining of undifferentiated crust with our usage of materials. Presumably, only a fraction of all mining could be done using Bardi’s machines. Some of the common elements (like aluminum and iron) would still be mined using traditional methods, so only a fraction of our mining would use Bardi’s machines. That fraction must be low enough that no materials are emitted from Bardi’s machine in greater quantities than are used by that civilization. In that manner, Bardi’s machines would displace the energy which otherwise would have been used to obtain materials for glass, steel, and so on, using traditional mining methods. We would get the common elements “for free” from Bardi’s machines, as a side effect of trying to obtain the rare ones, which would reduce the energy expenditure for mining elsewhere in the economy. As a result, the net effect of using Bardi’s machines would not increase the energy requirements for mining as a whole, at least not by very much. The advantage of using Bardi’s machine is that it would also emit small quantities of all the uncommon elements, so we would never run out of them over any time scale.

Let’s suppose that civilization has exhausted all ores and all concentrated deposits, of all rare elements, everywhere. All that remains is undifferentiated crust for uncommon elements. Also assume that civilization wishes to use Bardi’s machines as much as possible to obtain uncommon elements from that point forward. We’ll assume the civilization uses the same proportions of common elements (such as silicon, iron, and so on) as we use today.

In which case, Bardi’s machines could be used to mine all the materials for all glass produced by that civilization. Glass would be the material which was relatively most over-supplied from Bardi’s machines (almost 80% of the material emitted could only be used for making glass). As a result, if there was enough demand for all that glass from Bardi’s machines, then there would also be enough demand for all the iron, aluminum, calcium (for cement), and so on. Little material would be thrown away. All other glassmaking operations in civilization could cease, thereby saving the energy that had been expended on it. Also, some of the mining for bauxite, iron, and so on, would also be displaced by Bardi’s machines. The amount of energy used by Bardi’s machines would be on the order of 10 MJ/kg, which is not higher than civilization was already expending upon glass, aluminum, and so on.

It would be possible to make glass directly from the output of Bardi’s machines, by mixing together the necessary elements while they were still molten, and cooling the result quickly enough that glass is formed. This would displace the amount of energy used for glassmaking elsewhere in the economy, which is on the order of 15 MJ/kg of glass. Of course, we would also make some steel and some aluminum from the output of Bardi’s machines.

This strategy would reduce the amount of energy required for mining undifferentiated crust. The amount of energy for mining altogether would not be much higher than today. Furthermore, we would get all of the elements which occur in the Earth’s crust, as long as mining continued.

Elemental Scarcity

As a result, we could use Bardi’s machines to a limited degree, and could obtain all elements indefinitely, without ever increasing the energy we use for mining. We would just have to limit the use of Bardi's machines so that they don't produce much more of any elements than were otherwise mined.

The problem is, the amounts of uncommon elements would be emitted in fairly limited quantities. We’d never run out of uncommon elements, but the amounts produced per year of copper, nickel, and so on, would be fairly limited, assuming we don’t wish to “throw away” anything, and thereby increase the amount of energy devoted to mining intolerably.

At present, global civilization produces about 70 million tonnes of glass per year. If all that glass were produced from materials from Bardi’s machines, then the following amounts of rare elements would also be obtained:

Copper (70 megatonnes * 70ppm) = 4,900 tonnes/year

Nickel (70 megatonnes * 90ppm) = 6,300 tonnes/year

Lithium = ~1,800 tonnes/year

"Rare Earth" elements = ~20,000 tonnes/year

As a result, we would mine 0.7 grams of copper per person per year, and also 0.9 grams of nickel, worldwide, and similar or smaller amounts of all the other uncommon elements per person each year. Doing so would never require more energy than is expended on mining now. We could mine those rare elements, in those amounts, from undifferentiated crust until the sun explodes. We would never run out of them, and would never expend any more energy on mining than we do now.

Conclusion

As a result, our civilization could always have enough of the uncommon elements for things like smart phones, flat screen televisions, computer chips, and so on. Many of those devices use less than one gram of uncommon elements, per device. We could always mine enough materials for those purposes, even after billions of years.

We would also have enough uncommon elements for "massive" uses of them, such as electric cars, as long as we enforce high rates of recycling. For example, we would have enough lithium for electric cars indefinitely, provided that the batteries are sealed from the environment and the recycling rate is 99% or higher. If we assume that an electric vehicle has 30 kg of lithium in its batteries, the batteries are sealed from the environment, the car lasts 20 years, and 99.9% of the lithium in electric cars is recycled, then an average electric vehicle would require a net of 1.5 grams of lithium per year to be mined. That amount is on the order of what would be emitted from Bardi's machines, with no additional expenditure of energy. As a result, we would have enough lithium (and other uncommon elements) for "bulk" uses, indefinitely, as long as we enforce high rates of recycling.

We would not, however, have enough rare elements for “bulk” usages that are just thrown away. Some day, we will not have enough uncommon elements to allow people to throw away larger than single-digit gram quantities of rare elements per year. At some point, careful recycling will be required for devices (such as electric cars) which use large quantities of uncommon elements.

A few caveats are necessary here. It's possible that we won't have enough lithium in the future to build additional new electric vehicles. We would have enough lithium to sustain the peak number of electric cars indefinitely, but not enough to build additional new electric cars. Also, it is quite possible that we will simply substitute other elements when rare ones become scarcer, in which case, we would not pursue the diffuse deposits for those elements.

However, we will never "run out" of any element over any time period. The conclusion is that we can mine undifferentiated crust, in limited amounts. It is energetically feasible to do so. As a result, we will never run out of any element over any time period. We may have much lower extraction of some elements, far in the future, but extraction will never be zero for any important element. All uncommon elements will always be available, at tolerable energy expense.

NOTE: I made two changes to this article the day after it was published, as explained in the comments below. I also added the "caveats" paragraph shortly after this article was first published.

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.

Energy decline theory is pseudoscience

Here is a response I wrote on a forum:

I'm sorry, but there's just no science happening here. It's not sufficient to say the word "science" and to use scientific-sounding terms like "biophysical". Those kinds of things are also common within pseudoscience.

What is required are specific, falsifiable, risky predictions of things which weren't happening anyway. Then those predictions must be confirmed by subsequent evidence. That is the first step toward actual science, and it has never happened and is not happening within this group.

This group has all the hallmarks of pseudoscience. It has never produced any risky, falsifiable predictions which were confirmed by subsequent evidence, not even once. There have been massive failures of prediction, over and over again, but the theories remain totally unchanged, and the failures of prediction are not even addressed. Failures of prediction are handled by making the theory less and less falsifiable ("there is now a long descent which is difficult to see", see John Greer). Members do not respond to criticism, and leave errors uncorrected when they are pointed out. Notably, this group is ignored by legitimate researchers. There is almost no interconnection between this group and actual legitimate fields of study, and this material is rarely cited outside this group. Notably, it appears that this group settles its conclusions in advance ("civilization is about to collapse"), then generates theory after theory which all lead to that conclusion, but then the predictions all fail.

If you guys want to start doing science, then you need to respond to criticism without badly misreading it, modify your theories in light of failed predictions, and make falsifiable, risky predictions which are confirmed by subsequent evidence. Those things would be the first steps toward actual science, but those things are just not happening here.

----

Here is another post from the same thread:

George, you said:
"I'm talking about net free energy per capita, not raw energy produced... The numbers you quote do not take into account the amount of that energy it took to obtain that amount...So with slowing net energy increase and increasing total population the amount of usable energy for the economy per individual is in decline."

No, that's clearly wrong. Let's do the math. According to the EIA's numbers, world energy consumption has increased from 480x10^15 to 524x10^15 btu, between 2009 and 2013 (inclusive). At the same time, world population increased from 6.83x10^9 to 7.08x10^9 people (http://www.geohive.com/earth/his_history3.aspx). That means that per-capita energy consumption has increased from 70.27x10^6 btu/capita to 74.01x10^6 btu/capita in that time. In other words, per capita energy consumption increased by 5.3% in 4 years, which is a compound growth rate of ~1.3% per year.

Now let's look at the prior 29 year period, from 1980-2009 (inclusive), using the same sources of data. Per capita energy consumption increased from 63.63x10^6 btu/capita to 70.27x10^6 btu/capita over 29 years, which is an increase of 10.4% over 29 years or only ~0.35% per year.

In other words, per capita energy consumption is not only increasing, but the rate of increase accelerated. The growth in per capita energy consumption was much faster during the period of 2009-2013 than during the prior 29 years.

Those figures are not EROI adjusted. It's impossible to find reliable statistics on worldwide average EROI.

However, it's totally implausible that average EROI worldwide has dropped by an amount sufficient to erase that acceleration in energy consumption. Even if EROI had been stable and had not declined at all over 29 years, and then suddenly dropped from 30 to 15 (a decline by half, which is totally implausible) in only the 4 year subsequent period, the EROI-adjusted per capita energy consumption still increased faster (0.5% vs 0.35%) during the period from 2009-2013 than during the prior 29 years.

The straightforward conclusion from this, is that per capita energy consumption is increasing, and the rate of increase has sped up, no matter what you think happened to EROI (within reason).

I don't know how you arrived at the conclusion that "usable energy ... per individual is in decline". Your statement is not compatible with the data which hitssquad just presented.

This is exactly the opposite of what energy doomers had predicted. They had confidently predicted a sudden collapse of civilization in the late late 2000s and rapid declines in energy consumption. What happened was the opposite of what they had predicted, yet again.
The consistent and severe failure of prediction from these theories implies that there is something seriously wrong with them. It's long overdue to start asking what is wrong.

---

Here is another post from the same thread:

Hi Harry,

I just read through the comments again, and came across yours. You said:

"Could you be very kind and point me to some of those suggestions? I am about to radically decouple!"

Harry, are you going to radically decouple because you expect civilization to collapse soon? If so, you're about to throw your life away. Civilization is not collapsing for these reasons. The most recent collapse predictions from this group are no more scientific, and no better founded, than any of their other collapse predictions over the prior decades.

This material is just totally wrong. It's littered with severe errors that invalidate its conclusions, it's ignored by almost all relevant experts, it does not meet the minimal criteria of a valid scientific theory, and it's characterized by massive, repeated failures of prediction without any corresponding correction of the underlying theories.

There have already been many people who moved out into the wilderness circa 2005 in expectation of a drastic collapse of civilization, for these reasons. They wasted ten years of their lives on a fringe doomsday theory. Do you really want to join them? Of course, you can do whatever you want, but you should clearly envision what you will feel like when five or more years have passed and civilization hasn't collapsed and not that much has happened other than you living in the middle of nowhere.

The original conversation is here.

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.