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Prieto's and Hall's Estimate of Solar EROI Is Very Outdated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