Sunday, October 21, 2018

Prieto's and Hall's Estimate of Solar EROI Is Very Outdated

Pedro Prieto and Charles Hall published a book a few years back entitled Spain's Photovoltaic Revolution. In that book they claim that solar PV has a drastically low EROI of less than 3. The reason for that low EROI is because Prieto and Hall calculate EROI differently from how it has generally been done. Prieto and Hall include things like labor expenses and first world salaries as energy investments (money is converted to energy by means of a formula). Those things are generally not included as energy investments for any sources of energy, but Hall and Prieto decided to include them for solar PV, drastically reducing its EROI all the way down to below 3.

However, that analysis is years old. Things change quickly in the field of solar PV. We must ask if that figure has improved. It is possible that the extended EROI of solar PV (including first world salaries) has improved considerably, not just because the EROI of the panels themselves has improved, but also because of improvements in foundations, frames, panel washing machines, and so on.

In this article, Prieto's and Hall's analysis will be repeated with more updated figures. This will be accomplished using monetary data taken from Lazard.

Prieto and Hall accomplished their task by adding up all the monetary expenses incurred by a solar PV plant, and then multiplying the resulting price by the energy intensity of the economy as a whole. This is what Prieto and Hall did for their PV plant in Spain and for the Spanish economy more generally. Their figures are summarized in a PDF presentation which Prieto gave recently (page 62).

I stress again that it's not necessary to track down and add up all these individual monetary expenses for a solar PV plant. That information is already available as the final levelized price of electricity for solar PV. Accountants have already added up all the monetary expenses for solar PV, along the entire supply chain, and have included all those expenses in the final levelized price. As a result, there is no purpose in duplicating the accountants' work and adding up prices for things like panel washing, security services, and so on.

Instead, we can easily re-calculate the extended energy investments for solar PV by just using the unsubsidized non-interest portion of the levelized price, then multiplying that price by the general energy intensity of the U.S. economy per dollar, similar to what Prieto and Hall did for Spain.

Let's do that procedure now. The levelized price of electricity for solar PV is $0.05/kwh (as per Lazard). If we assume half of that money is devoted to interest payments and energy investments already counted, that leaves $0.025/kwh for everything else. We can obtain an "energy intensity" for the entire U.S. economy by dividing the GDP by all energy usage, similar to what Hall and Prieto did for Spain. The US has a GDP of $19.39 trillion, and uses 97.7 Quads, which is 1.477 kwh/$1 (I just googled for those figures). Multiplying this by $0.025/kwh (from above) yields an uncounted energy investment of 0.037 kwh/kwh. If we assume an EROI of 14 for solar PV in a sunny region like Spain or the American Southwest, then the already-counted energy investment is 0.0714 (or 1/14), and the extended energy investment is 0.037 (above). Adding the two together yields a total extended energy investment of 0.108. Inverting this figure yields an extended EROI of 9.26 for solar PV in a sunny region.

That figure of 9.26 for an extended EROI is more than 3 times higher than the figure offered by Prieto and Hall, which was 3.0. At this point, we must ask why this newer estimate is so much higher.

Right away, it is clear that Prieto's solar plant is spending approximately 6x more money on these "extended" miscellaneous energy expenses than a more recent solar plant. Prieto uses a figure of 0.22 kwh/kwh for "extended" energy investments, which is 6x higher than the 0.037 figure we calculated above. In other words, the "miscellaneous" energy costs at Prieto's solar plant are vastly higher than at more recent solar plants.

The reason is fairly clear. Prieto's solar plant is a 1 megawatt solar plant, whereas newer plants are often 200 megawatts or larger. There is a large economy of scale when it comes to miscellaneous energy investments. Some of the energy investments which Prieto lists in his spreadsheet are fixed costs which would be reduced by a factor of 200 (per unit of energy delivered) for a larger plant. For example, a power plant which is 200x larger does not require 200 separate access roads leading to the plant, and so on.

Furthermore, the costs listed in Prieto's spreadsheet are also subject to improvement and "learning by doing" over time, even without any economy of scale. For example, washing solar PV panels could be done by a machine, rather than by hand, which could greatly reduce the monetary cost. Newer PV plants usually do not have fences or canals surrounding the plant. Fairs, exhibitions, promotions, and so on (which are significant energy investments in Prieto's spreadhsheet) could just be cancelled, since the novelty of a PV plant has worn off, and we don't need an opening exhibition for every new solar plant. The "premature phase out of manufacturing equipment", which Prieto counts as a massive energy investment, will presumably be done less frequently as the technology matures. And so on.

In conclusion. Prieto's and Hall's estimate of the extended EROI of solar PV is obsolete and outdated. It uses data from an old, very small solar PV plant. Newer plants are much larger and correspondingly benefit from an economy of scale. As a result, newer plants have much lower extended energy investments. An updated analysis yields an extended EROI of 9.26 for solar PV, not 3.0.


One more thing. Prieto and Hall decided to include first world salaries, labor costs, and related discretionary energy expenditures as "energy investments", as mentioned above. Presumably, the same could be done for all other sources of energy. For example, if a Russian engineer at an oil company takes his whole family to the Bahamas, on a private jet rented with his salary, then that would count as an energy investment to obtain oil. In my opinion, those expenditures of energy should not be counted as energy investments.

However, those energy investments have been counted in this analysis. We have used to same method that Hall and Prieto used to estimate energy intensity, and have included labor, just as they did. The levelized cost of electricity from solar PV includes all labor costs along the entire supply chain, including first-world salaries for engineers, so it is included in the analysis above.

Still, such a broad definition of EROI made little difference. It reduced the EROI for solar PV from 14 to 9.26. In other words, the "extended" costs of solar PV have declined to such a degree that including them now makes only a modest difference.

Correction: The original version of this article contained an arithmetic mistake which I found several days after first posting it. The initial version of this post claimed an "uncounted" investment of 0.017 kwh/kwh, whereas the correct value is 0.037. This implies an extended EROI of 9.26 for the newer solar plant, not 11.32 as originally claimed.

Friday, October 19, 2018

Reports of Low EROI for Solar Power Are Outdated

A common claim within the energy decline movement is that renewables have much lower EROI than fossil fuels. For example, it is often claimed that coal has an EROI of 80 and oil has an EROI higher than 15, whereas solar PV has an EROI of only 10. Thus, solar PV is no match for fossil energy and cannot provide the same amount of net energy.

Such claims have been made repeatedly within the energy decline movement for more than 15 years now, and they rely upon data which is considerably older than that. Presumably, the EROI of fossil fuels has deteriorated at least somewhat, and the EROI of solar PV has improved at least somewhat, since those claims were first made. As a result, it's worth re-examining the issue and seeing what the respective EROI ratios of those sources of energy are now.

Gagnon et al (2009) published an analysis of EROI trends over time for both oil and gas combined. EROI for oil and gas had declined from approximately 30 in the early 1990s to approximately 17 in the mid-2000s. Gagnon et al also included a best-fit linear trend line of that data. Simply extrapolating from that linear trend line (visually using a ruler) yields an EROI for global oil and gas of approximately 13 now.

The EROI of solar PV, on the other hand, has been improving fairly rapidly. Leuwen et al (2016) examined the trend lines for energy payback studies of solar PV and found a consistent decrease in energy payback time over decades. The most recent studies (in 2014) indicate an energy payback time of approximately 1 year in areas of moderate insolation. This figure implies an EROI of approximately 25 for solar PV, assuming a 25+ year lifespan. The oft-quoted EROI of 10 for solar PV is two decades old and is seriously out of date.

In which case, the EROI of solar PV is already nearly twice as high as the EROI for gas and oil worldwide. As a result, the notion that fossil fuels have much higher EROI ratios than solar PV is badly outdated and is exactly the opposite of the true situation; in fact, solar PV has an EROI ratio which is considerably higher than oil and gas worldwide.

Granted, the EROI for coal in the United States (80) is still much higher than the EROI for solar PV. However, the United States is an outlier insofar as its coal deposits are larger and more easily accessed than anywhere else in the world. As a result, the United States is not a good comparison for solar PV in areas of average insolation. Instead, we should compare the EROI of average solar to the EROI of average coal for the world.

In which case, the EROI of solar PV is higher than the EROI for coal worldwide. In my opinion, China is a good comparsion for coal, because China mines and uses more coal than the rest of the world combined. Hu et al (2103) published a historical trend line for the EROI of Chinese coal and found steady declines over decades. The trend line indicated an EROI of 27 for Chinese coal in 2010. A simple visual extrapolation (again using a ruler) indicates an EROI of approximately 22 now. As a result, the EROI of Chinese coal is already lower than the EROI of solar PV in areas of moderate insolation, and the gap is presumably widening over time.

Extending the boundaries of EROI analysis will simply reduce the EROI of fossil fuels by more than for renewables. Coal fired electricity in particular has far more "uncounted" energy investments, which are reflected in its much higher price (as shown here). Any conversion of money into energy, as was done by Prieto and Hall (2013), will reduce the EROI of fossil fuel electricity by more. This implies that extending boudaries will increase the EROI advantage which solar power already enjoys.

This analysis makes no attempt to compensate for energy quality. Even if we count the waste heat losses from cooling towers at coal power plants as "energy returns", which artificially inflates the EROI of coal-fired electricity, the EROI of global coal is still worse than the EROI of solar PV in areas of average insolation.

It should also be mentioned that the EROI of solar PV continues to improve and this trend shows no sign of stopping. New kinds of solar panels are being introduced, such as perovskite and organic solar cells. Those panels have an estimated energy payback time of a few months or less. If the lifetime of those panels can be improved to 20 years, it implies an EROI of 60 or higher for areas of average insolation.

It is possible that the EROI from 4th-generation, thin film solar cells deployed in desert regions near the equator will exceed the EROI from any fossil fuels anywhere, ever. If EROI were actually an important metric (which it is not), then global civilization could simply relocate its most energy-intensive manufacturing (such as aluminum smelting, or solar panel manufacturing) to desert regions near the equator, which could afford them higher EROI than any fossil fuels have ever provided.

In conclusion. The idea that solar PV has very low EROI, is simply outdated and is based upon obsolete data. The EROI of solar PV has been improving ever since that claim was first popularized around 2005. By now, the EROI of solar PV matches or exceeds the EROI of all fossil fuels, except coal in a few ideal locations. The EROI advantage which solar PV enjoys is likely to increase in the future because the EROI of solar PV continues to improve and shows no sign of stopping, whereas the EROI of fossil fuels continues to decline.


Gagnon, N., Hall, C., Brinker, L. 2009. A preliminary investigation of the energy return on energy investment for global oil and gas production. Energies 2 490-503.

Louwen A., van Sark W.G.J.H.M., Faaij A.P.C., Schropp R.E.I. 2016. Re-assessment of net energy production and greenhouse gas emissions avoidance after 40 years of photovoltaics development. Nature Communications 7

Hu, Y., Hall, C., Wang, J., Feng, L., Poisson, A. 2013. Energy Return on Investment (EROI) of china's conventional fossil fuels: Historical and future trends. Energy 1-13.

Prieto, P., Hall, C. 2013. Spain's Photovoltaic Revolution. Springer.

Wednesday, October 17, 2018

Hubbert Curves Would Never Have Worked

Everyone who followed the peak oil story is familiar with Hubbert curves. A Hubbert curve is a bell-shaped curve which is claimed to represent oil extraction for a region over time. It is claimed that all oil extracting regions will follow such a curve or approximate it.

Since all oil producing regions supposedly follow a Hubbert curve, such curves could be used to predict oil extraction for any region. We can just look at the production profile from a region, and see how far along its bell curve it happens to be. For example, we can draw a bell curve through the past production profile of some region, then extend the bell curve out into the future. In so doing, we would predict the future oil extraction from that region over time. We could also predict the total future amount of oil extracted by adding up the area under the curve we had extended. These procedures are done mathematically, not visually, but Hubbert's very earliest paper relied upon a simple visual extrapolation.

Presumably, Hubbert curves are based upon a statistical phenomenon. With a consistent amount of effort devoted to discovery and extraction, production will follow a fairly consistent pattern. The largest oil deposits are discovered first and are depleted as quickly as possible. New oil wells are drilled at a certain rate. At first, new wells more than compensate for depletion of old ones. Eventually, there are more and more "old" oil wells, and the newer ones get smaller and smaller, until depletion of old wells overcomes extraction from new ones, leading to a peak and then decline. The end result is a bell-shaped curve for the region as a whole.

However, that behavior is a statistical phenomenon which relies upon certain conditions being met. In particular, it requires a constant amount of effort devoted to discovery and extraction. If the resources devoted to discovery and extraction increased exponentially over time for a region, for example, then we would expect the resulting curve to be negatively skewed, with the peak further to the right. More oil would be extracted toward the end of the production profile, and the drop-off would be fairly rapid. On the other hand, if discovery and extraction were exponentially decaying, then we would expect a rapid ramp-up and a gradual decline. In both cases, the curve would not be symmetric at all, and Hubbert curves would no longer work.

In my opinion, Hubbert curves would only work in regions where there is a consistent amount of effort devoted to extraction. In other words, there must be a consistent amount of money and resources devoted to discovery, drilling, and so on. Only then would Hubbert curves work at all. Otherwise, Hubbert curves would not work at all, because the underlying forces which cause the statistical trend would no longer be operating.

This explains why Hubbert curves failed for Saudi Arabia, Kuwait, the Emirates, Iran, Iraq, and Russia. All of those countries were presumed to be entering terminal decline in the 2005-2010 period, but none of them actually did. The reason is because the effort devoted to extraction has changed drastically over time in those countries, which would render Hubbert curves completely useless. For example, Iraq was subject to sanctions for decades. Russia underwent a collapse. Saudi Arabia, Kuwait, the Emirates, and Iran voluntarily curtailed their oil production as part of a cartel strategy, in order to control prices. Once those events have occured, Hubbert curves will be useless at that point, and cannot be used to predict oil production going forward.

Curtailment is a phenomenon which requires special consideration. The Middle Eastern countries with large oil deposits all curtailed their production as part of a cartel strategy, starting in the early 1970s. Doing so will push the date of geological peak way out into the future, but will make the peak of a Hubbert curve appear much closer. Curtailment would cause an inflection point on the production graph, which Hubbert curves would misinterpret as a sign of imminent geological scarcity. In fact, curtailment pushes geological scarcity further away. In this case, a Hubbert curve would indicate the opposite of what is really happening. Thus, Hubbert curves will not work at all for a region which was greatly curtailed its oil production.

This implies that Hubbert curves would not have worked for the world as a whole, either. The Middle Eastern countries (for which Hubbert curves are not applicable) represent approximately 70% of the conventional oil deposits on Earth. As a result, any Hubbert curve for the entire world would include the 70% of deposits for which Hubbert curves are not applicable.

There is also good reason to believe that Hubbert curves would stop working when the price of oil has considerably increased. Any large increase in the price of oil would lead to an increase in drilling effort, which would invalidate Hubbert curves from that point forward. For this reason, the peak of conventional oil, excluding the Middle East and Russia, has not followed a Hubbert curve either. A Hubbert curve actually did predict the peak of oil outside the Middle East and Russia, but the peak for such a large region will increase prices, and thereby cause increased discovery and extraction, which will invalidate the Hubbert curve from that point forward. For that reason, Hubbert curves did predict the peak for oil outside the Middle East and Russia, but the decline was offset by increased drilling and discovery caused by increased prices.

This is another reason why Hubbert curves would never have worked for the world as a whole. Hubbert curves have worked fairly well for individual regions, but a peak for the world  will change prices, which would cause Hubbert curves to stop working.

As a result, we can conclude that Hubbert curves would never have worked for the Middle East or for Russia, which collectively have more than 70% of worldwide conventional oil deposits. Nor would Hubbert curves have worked for the world as a whole. Nor would Hubbert curves have worked for the regions except the Middle East and Russia, once the peak has been passed.

Interestingly, Hubbert curves did appear to work fairly well when the condition of constant effort was actually met. The peak of conventional oil, outside the Middle East and Russia, for a given price, did actually occur in 2005. That is exactly what Hubbert curves had predicted, and I don't think it was a coincidence. Hubbert was actually on to something here.

However, Hubbert curves need to be applied far more judiciously and sparingly than they have been in the past. When we see an inflection point on a curve, we must ask why the inflection point occurred. Is drilling being curtailed in that region for political reasons? Has the price of oil changed greatly? Has a cartel formed? Is there some kind of political disruption or turmoil that would interrupt drilling or curtail output? If so, Hubbert curves will no longer apply.

These considerations imply that Hubbert curves will not work for predicting future coal production for the United States or for the world. The United States has faced inadequate demand for coal, going back to the 1970s. All industrialized countries have stopped growing their per-capita energy production because of inadequate demand. Growth was purposefully curtailed. In the case of the United States, this happened long before the geological peak of coal. As a result, Hubbert curves will greatly underestimate the amount of coal which could be extracted there, because they will misinterpret that inflection point as an indicator of approaching geological scarcity, when it actually indicates that scarcity is being pushed further into the future. In my opinion, this is the reason for the drastic discrepancy between USGS estimates for coal in the United States and Hubbert curves applied to the same region. Hubbert curves are inapplicable there, and would drastically underestimate the amount of coal that could be extracted. Since the United States coal deposits are such a large fraction of global coal deposits, Hubbert curves won't work for global coal production either.

In summary. Hubbert curves are based upon a statistical regularity. As such, they'll only work when certain conditions are met. They work when there is a constant amount of effort devoted to discovery, drilling, and extraction. In all other circumstances, they fail badly.

As a result, Hubbert curves cannot be used to predict oil production for the Middle East or Russia, nor can they be used to predict oil production for the world as a whole. Furthermore, Hubbert curves cannot be used to predict coal production for the United States or the world. In all those cases, Hubbert curves will greatly underestimate the amount of oil or coal that could be produced.

Friday, September 21, 2018

Extended EROI


Some EROI authors have suggested that renewable sources of energy have much lower EROI ratios than generally believed. The reason is that published EROI figures do not include all of the energy investments which were incurred. There are many small energy investments which are difficult to count, for example, the energy investments for smelting aluminum used to build metal fences around a power plant. Those tiny energy investments are omitted from EROI analysis. As a result, the EROI ratio is overstated for renewable sources of energy.

There are many small energy investments for any source of electricity, which are too numerous and too minor to count. For example, the EROI of solar power (commonly quoted as 10) does not include the energy investments to replace truck tires which wear out during the delivery of solar panels to solar farms. Nor does it include the energy investment of the steel-making equipment used to manufacture the steel for parts for that truck. And there are thousands of other little uncounted energy investments, such as energy investments for fences around the power plant, roads to the plant, security cameras, replacement of transportation equipment, electricity used in the plant office, and so on. Any one of those energy investments might be quite small, but taken together, they can add up to a lot, because there are so many of them. When those little energy investments are added up, the EROI of renewable electricity will be reduced considerably.

Of course, the same holds true for all sources of energy. The EROI of coal-fired electricity, for example, does not include the energy investments of building roads to the coal power plant, building a railway to the coal power plant, replacing locomotives which have worn out delivering coal to the power plant, and so on. Those energy investments could be considerable and could greatly reduce the EROI of coal-fired electricity.

As a result, EROI is overstated for all sources of electricity. The only way to get an accurate EROI value is to include all the small uncounted energy investments, or at least try to estimate them.

Dr Charles Hall has referred to this as "extending the boundaries" of EROI analysis. Prior EROI analyses have not included indirect energy investments such as degradation of transportation equipment. It was considered outside the scope of the EROI analysis. As we extend the boundaries of EROI analysis, we include more and more energy investments that occurred further up the supply chain.

The purpose of this article is to extend the EROI boundaries all the way, and to include all energy investments for each source of energy, no matter how minor or indirect. This will be done for coal fired electricity, nuclear power, solar PV, and wind power. The result is a convergence of EROI values for different sources of electricity, as will be shown.

Method of estimating extended EROI

The great difficulty with extending EROI boundaries is that it becomes more and more difficult to gather the information needed, the further you extend the boundaries. The uncounted energy investments become more numerous and smaller. As an example, a coal-fired power plant requires a railroad connection. That railroad connection requires railroad ties, which are made out of wood, which were taken from a tree, which was chopped down using a chainsaw, which has a plastic gasoline tank, and the plastic was made out of oil, which was extracted by an oil well, and the oil well was made out of steel, taken from a blast furnace. How do we account for the energy investment for the degradation of the blast furnace, which is fully seven degrees removed from the top of the supply chain?

At some point, the energy investments are so far removed, and there are so many of them, and they are so little, that it becomes difficult to add them all up. It would be nearly impossible to track down all this information.

Hall and Prieto attempted to extend the EROI boundaries for a solar PV plant[1]. They accomplished this by adding up all the monetary costs for things like roads to the power plant, security cameras, fences, and so on. Prieto was a manager at a solar power plant, so he had access to the relevant accounting information and added up the prices for everything. Hall and Prieto then converted those prices to energy by means of a formula (6 megajoules per dollar, if I recall).

It was a good idea to estimate uncounted energy investments by looking at prices. That was a significant contribution of Hall's and Prieto's book.

However, it is not necessary to add up the prices of all these little things like roads to the plant, security cameras, and so on. All of those things are already included in the final levelized price of wholesale solar electricity. For that matter, all monetary expenditures, along the entire supply chain, no matter how minor or indirect, are already included in the final levelized price of solar electricity.

The price of something includes all the monetary costs, along the entire supply chain, to obtain that thing. Each supplier in the supply chain keeps track of all its monetary costs, and passes along all those expenses to the supplier above it in the chain. All companies keep careful track of money and pass along all of their expenses. There is an army of accountants, spread throughout the economy, who do this. They pass along all monetary costs, no matter how indirect. As a result, the final price of a thing, is a kind of summary of all prices paid to obtain it, throughout the entire supply chain.

Because of this, we can estimate the uncounted energy investments for a source of energy by just looking at the price of it. The price of electricity from solar PV, for example, includes the price of everything needed to obtain it.

Thus, we can estimate the extended EROI of a source of electricity using the following algorithm:

  1. Obtain the levelized cost of electricity for a source (from Lazard[2], for example).
  2. Subtract the top-level interest expense, which is not an energy investment.
  3. Also subtract the money which was spent on obtaining energy for the counted energy investments. This can be done using published EROI figures. Those energy investments have already been counted, and we don't want to double-count them.
  4. What is left is the amount of money spent on everything else. We'll call this "miscellaneous expenses". It includes things like profits, salaries, taxes, interest paid on transportation equipment like trucks, and everything else, for every contractor and sub-contractor and supplier, up the entire supply chain. It also includes all money spent on obtaining energy, throughout the entire supply chain.
  5. We must estimate how much of this "miscellaneous" money was spent on energy, and how much was spent  on everything else, using a factor. We'll refer to that factor as the "uncounted energy investment factor".
  6. We must multiply the uncounted energy investment factor by the amount of money spent on miscellaneous expenses.
  7. We then add that "uncounted" energy investment to the energy investment from published EROI figures. After which, we can calculate an "extended EROI" by just performing the division again using the energy investment with extended boundaries.

Let's try extending the boundaries for a typical solar PV plant.  We'll assume that the levelized cost of wholesale electricity for solar PV is $0.05/kwh (as per Lazard), that 50% of that money is spent on interest (which is common for projects which involve almost the entire cost upfront and which last decades), and that the EROI of solar PV is 10. In which case, the amount of money for miscellaneous expenses for solar PV is $0.02/kwh (interest was $0.025, and counted energy investments were $0.05, and subtracting both of those leaves $0.02 remaining for miscellaneous expenses). Let's assume, as an initial estimate, that 10% of the miscellaneous expenses are payments for energy. We'll also assume that the price of the energy for investment is $0.01/megajoule.  With a conversion factor of 0.10, $0.002 of the wholesale price was spent on uncounted energy investments. At $0.01/megajoule, that translates into 0.2 megajoules, or 0.0556 kilowatt hours. Thus, the counted energy investments for solar PV were 0.1 kwhinvest/kwhdelivered (or 1/eroi), and the uncounted were 0.0556 kwhinvest/kwhdelivered, leading to a total extended energy investment of 0.1556 kwhinvest/kwhdelivered, or an extended EROI of 6.43 for solar PV.

If we perform the same procedure for various sources of energy, we obtain the following extended EROI ratios:

SourceExtended EROINotes
Coal5.29(assumes EROI of 20 after waste heat loss, $0.10/kwh, 40% interest)
Nuclear6.22(assumes EROI of 30, $0.10/kwh, and 50% interest)
Wind9.00(assumes EROI of 20, $0.04/kwh, and 40% interest)

Of course, the above figures are dependent upon an uncounted investment factor of 0.10. In other words, we assumed that 10% of miscellaneous expenses are devoted to buying energy products. However, the choice of 0.10 was little more than a guesstimate.

At this point, we could estimate an accurate uncounted factor by looking at the economy as a whole. We could examine a first-world economy which gets most of its electricity from coal-fired plants and try to estimate how much of its energy expenditure is devoted to the energy industry itself, then subtract the the energy investments which had already been counted.

I suspect that the factor of 0.10 was too high. If coal-fired plants, for example, consume 18.9% of the energy they produce, then this would have been obvious in Sankey diagrams of the US economy back in the 1970s and 1980s. As a result, let's use a different factor of 5%. In which case, the extended EROI ratios for different sources of electricity are:

SourceExtended EROI

We can use different estimates for the uncounted energy investment factor. With smaller factors, the EROI ratios of all sources of energy increase, and the ratios for coal and nuclear power increase by more.

Interpretation of Results

Right away, it is obvious that the extended EROI ratios for different sources of electricity are fairly close together. This is totally unsurprising. The monetary prices of those sources of electricity are also somewhat close together. Any conversion of money into energy would cause the EROI ratios for different sources of energy, of the same price, to converge.

Furthermore, the high-EROI sources of electricity (such as coal-fired electricity and nuclear power) are also moderately more expensive. This implies that the "uncounted" energy investments are higher for those sources of electricity than for renewables, using any consistent conversion of money into energy. As a result, extending EROI boundaries will reduce the EROI ratios for high-EROI sources of energy (such as coal and nuclear) the most. In turn, that will cause the EROI ratios of different sources of energy to converge even more strongly.

The result is no large difference between the extended EROI ratios of different sources of electricity.

Of course, we may have chosen an uncounted factor which was still far too high, even after revising it downwards. In which case, extending EROI boundaries would make little difference for solar PV, and published figures are already fairly accurate. Using very small factors will result in less than a 10% adjustment of published figures for solar PV.

It is just not possible that solar PV has a drastically low extended EROI ratio while other sources of electricity have much higher extended EROI ratios. Solar PV is much cheaper than alternatives, so any attempt to extend boundaries will cause a strong convergence of EROI values. This implies one of two things. If extending boundaries makes little difference, then the EROI of solar PV was fairly accurate beforehand and is above 9. If extending boundaries makes a large difference, then the EROI ratios of other sources of electricity will be reduced by more, and all sources of electricity will have similarly low extended EROI ratios. There is no possible factor for uncounted energy investment which would yield a very low extended EROI for solar power and very high extended EROI ratios for other sources of electricity. The higher the factor, the more the extended EROI is reduced for coal and nuclear power compared to solar PV. Making assumptions of extremely high uncounted energy investments will result in lower extended EROI ratios for coal and nuclear power than for solar PV.

One other conclusion from the above figures is that coal-fired electricity has much higher "uncounted" energy investments than other sources of electricity. This is also totally unsurprising. It has frequently been pointed out that solar PV plants require fences and security cameras, which incur energy investments that had not been counted. That much is clearly true. However, coal-fired plants require a railroad connection with a mile-long train full of coal arriving every few days, for the entire lifetime of the plant. That imposes massive "uncounted" energy investments, including fuel usage by locomotives, degradation and replacement of locomotives and rail cars, wear on the national rail network, and so on. Those energy investments are massive and ongoing, and would obviously outweigh the trivial energy investments of installing cameras or fences once. Those much higher "uncounted" energy investments for coal-fired electricity are reflected in its higher price.

One final point bears mentioning. The extended EROI ratio of solar PV (indicated above) is considerably higher than that estimated by Hall and Prieto. Their analysis was useful, but it's years old. The field of solar PV moves quickly. Hall's and Prieto's estimate has fallen out of date.

Hall and Prieto estimated the extended EROI of a 1-megawatt solar plant. However, newer solar plants are much larger, frequently larger than 100 megawatts. There is an economy of scale when it comes to uncounted energy costs. Solar plants which are 100x larger do not require 100x as long of a road leading to the plant, or 100x as many employees, or 100x as long of a fence surrounding the plant, and so on (in fact, a solar plant which is 100x larger would require only 10x as long of a fence surrounding the plant, if we assume that all solar plants are laid out in a square shape, which implies a 90% reduction in energy investment for fences, per kilowatt-hour). As a result, Hall's and Prieto's analysis is out of date, and the actual extended EROI of solar PV would be significantly higher now, as indicated in the table above.

Summary and Conclusion

Extending EROI boundaries as far as possible, while also assuming high uncounted energy investments, causes the EROI values for different sources of electricity to converge strongly. The result is no large difference between EROI values for different sources of electricity. If we assume that uncounted energy investments are extremely low, then published figures for the EROI of solar PV are already fairly accurate.


[1] Spain's Photovoltaic Revolution, Charles Hall and Pedro Prieto, Springer, 2013

[2] Lazard Levelized Cost of Energy, version 11.0.

This article was originally published with a minor arithmetic error which was corrected several hours after the initial publication.

Wednesday, September 5, 2018

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

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.
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
  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)

Monday, September 3, 2018

EROI and economic growth


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

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.

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):

# 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
    yearlyToBeAdded = sumPanels * targetGrowth - sumPanels + retiredYearly
    investment = (yearlyToBeAdded * lifetime) / eroi
  print ("year:%i total:%f retired:%f toBeAdded:%f net:%f" %
  (year, sumPanels, retiredYearly, yearlyToBeAdded, sumPanels-investment
  oldSumPanels = sumPanels


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.

Thursday, October 19, 2017

Bardi's Universal Mining Machine


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.


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.