Sunday, July 25, 2021

Railroads to the Rescue!

One of the main claims of the Energy Decline movement is that trucks will suddenly stop running once diesel becomes scarce. There was a book written about this problem, entitled When Trucks Stop Running.

Since that time, battery-powered trucks have been introduced by Tesla and other manufacturers and are commercially available now.

The problem with battery-powered trucks is that they have a 200 mile range or so. That range is insufficient for long-haul trucking. However, that range IS SUFFICIENT if we use inter-modal transportation. I am proposing that we could switch some of the truck traffic to rail as diesel becomes scarcer. Instead of using long-haul trucking, we would use short-haul trucks to deliver the cargo to the nearest railroad, and then use other short-haul trucks to deliver the cargo from the railroad to its destination. In which case, the range of battery-powered trucks is sufficient.

Take a look at this map of the railroad network in the United States. You will notice that almost everybody lives within a 200 mile radius of a railroad. There are some rural areas in Nevada, Idaho and Wyoming which are not within 200 miles. However, those areas are extremely sparsely populated, consisting of very small towns spread far apart. I would estimate that approximately 99.9% of the population of the continental US lives within 200 miles of a railroad (the proportion is certainly higher in Europe and Asia, which are more densely populated). The one major exception is western Florida, but a railroad could be built there if necessary.

Thus, we could simply switch modes of transportation and use rail more often. A combination of current railroads and 200-mile trucks is sufficient to reach almost everywhere in the country.

Railroads do not require diesel for their propulsion. About 30% of the railroads in the world are powered by overhead electricity lines, and many countries have electrified their entire railroad networks in less than 20 years.

The only reason long-haul trucking is used at all is because it’s often cheaper than using trains part of the way. If you want to use a train part of the way, then you must drive the truck to the nearest railroad, offload its cargo onto a train, offload the cargo from the train and back onto another truck, then drive that truck to its final destination. The added step of loading and offloading takes time and money. Oftentimes, it’s cheaper just to drive a truck the whole way. Furthermore, the route is sometimes more direct by just driving a truck the whole way.

However, that calculus changes when diesel is more expensive. Suddenly, it becomes cheaper to use rail part of the way despite the additional step of loading and offloading. As a result, long-haul trucking could become much rarer as diesel becomes more expensive.

Of course, there are a few rare circumstances where long-haul trucks would be irreplaceable. Think of those isolated towns in rural Nevada. In those rare cases, we could use biofuels or synthetic fuels for long-haul trucking. I would estimate that less than 0.01% of freight delivery in this country is not amenable, at all, to rail or inter-model transport. Although biofuels couldn't scale up to power everything, they could certainly scale up to power those rare cases.

Finally, I should point out that the industrial revolution and first-world countries were built using railroads, not trucks. Back in 1910, the US had a railroad network about 3x longer than today, and long-haul trucking was non-existent. Anything possible in 1910 is still possible now. Long-haul trucking is not really necessary at all. I once lived in a tiny isolated town of a few hundred people, which still had an old railroad depot (long since abandoned). This is common almost everywhere in rural America.

Thus, the solution to diesel becoming more expensive is to use electrified rail more often.

All of this assumes that hydrogen fuel-cell trucks are impossible, as was widely assumed in the energy decline movement (here). However, long-haul fuel-cell trucks were introduced late last year and Hyundai is scaling them up. In which case, long-haul trucking could continue without diesel.

Response to Pump Up The Storage

In this article I will briefly respond to Dr Murphy’s article entitled Pump Up The Storage. In that article, Dr Murphy shows, through straightforward calculations, that pumped hydropower storage is nowhere near sufficient to compensate for the intermittency of renewables. He assumes that renewables need 7 days of backup power to compensate for prolonged overcast wind lulls. He then calculates the amount and size of dams necessary to provide 7 days of storage and finds that it would take triple the annual concrete used in the United States and would be much larger than any construction project completed so far. As a result, Dr Murphy concludes that it would be impossible, or at least very difficult, to use pumped hydro storage to compensate for the intermittency of renewables.

In his article, Dr Murphy provides all kinds of calculations and physics. However, he makes some assumptions too. In this article, I will make different assumptions and see the results.

First and foremost, I will assume we use a combination of storage mechanisms. I will assume that we use pumped hydropower for the first 12 hours of storage (nighttime) so that solar power is essentially a 24-hour energy source on sunny days. Of course, this would not be enough for long overcast periods. For longer periods of storage, hydrogen would be used. As a result, I will assume 12 hours of pumped hydro storage, not 7 days, which means only 1/14th the amount of storage is required from pumped hydro. I will address the inefficiency of hydrogen later.

It makes no sense to use a single form of storage for all purposes. Instead, storage would be divided into short-term and long-term solutions. The short-term storage is used every single night, so we would use a more expensive, smaller, and more efficient form of storage for that (like pumped hydro). The long-term storage is used only occasionally but is prolonged, so we would use a less efficient form (like hydrogen) which allows large volumes of storage.

Second, I will assume that the dam size needs only to be 5% of the size which Dr Murphy assumes. In his simple physics model, Dr Murphy proposes constructing a dam right through the middle of the reservoir. This is never done in practice. A simple physics model will not suffice here. We need to dig into the details of dam construction and siting. Dams are not built haphazardly. Instead, a crew of surveyors will spend years finding a naturally-occurring “choke point” or narrow section between mountains or in a valley. For example, the Hoover Dam is not built through the middle of Lake Mead. Instead, it is built in a tiny choke point, so it's much narrower. I obtained the figure of 95% narrower by looking on Google Maps, observing the three largest dams in North America (Daniel Johnson, Hoover, and Glen Canyon) and then estimating the width of the dam versus the width of the reservoir using a ruler. Those three dams would be more than sufficient by themselves for 12 hours of storage for the whole country.

Next, I will assume that electrification reduces total energy demand by approximately 50%. Electric vehicles, heat pumps, and so on, are far more efficient than their fossil fuel counterparts. For example, an electric vehicle travels almost triple the distance per unit of energy as a gasoline-powered car. As a result, I will assume a 50% reduction in energy usage from electrification.

Finally, I will assume that the dams are built in a staggered fashion over 50 years. Dr Murphy calculates that it would take triple the annual concrete production in the United States to build his dams. However, the dams wouldn’t all be constructed in a single 3-year period.

If we use the assumptions above, then the dams would take 0.01% of concrete production continuously (3/50/20/14/2 = 0.01%). This would be sufficient for 12 hours of storage for the whole country, until the sun comes up again.

Incidentally, far more dams have already been constructed than would be needed for this purpose in North America. It would be necessary to increase the maximum power of those dams by adding turbines. However, the size of the dams is already sufficient.

I should also point out that we could use any combination of short-term storage technologies, including pumped hydro, compressed air, sodium-sulfur batteries, iron-air batteries, flow batteries of various chemistries (vanadium, iron, organic, and others), pumped heat, gravimetric, and others. Storage is only an unsolvable problem if all of the above solutions combined are insufficient. However, it appears that any one of these solutions by itself is sufficient to provide our 12-hour short term storage.

Finally, this scheme relies upon a long-term form of storage also (hydrogen). This kind of storage is necessary to keep the lights on during prolonged wind lulls when it’s also overcast in the desert. Dr Murphy points out in another article that hydrogen has large round-trip energy losses, so he subsequently dismisses it. However, those large round-trip losses would be incurred only occasionally. Periods when it’s overcast in the desert, and there’s no wind in Texas, are fairly rare. Whereas nighttime happens every single day (and would use our efficient storage above), overcast wind lulls happen only a few times per year. Let's assume that 10% of total energy comes from hydrogen storage with a 67% round-trip energy loss. In which case, it would be necessary to overbuild our solar and wind farms by 20% (0.9+0.1*3) to generate enough hydrogen the rest of the time to cover those periods. This compares with coal power plants which use steam turbines and lose 60% of their energy as waste heat all the time, so the coal mines had to be overbuilt by almost triple to keep the coal power plants running.

In conclusion, it appears to be relatively easy to compensate for the intermittency of renewables. The trick is to find an optimal combination of locations and storage technologies. It cannot be done using a simple physics model of a single solution. We must try various things in combination to find something which works. Once this is done, it becomes clear that a renewable future is totally feasible and (in fact) fairly straightforward using currently-available technologies.

Tuesday, July 20, 2021

More on battery-powered tractors

In this article, I intend to continue my prior article and drill down on some of the details regarding battery-powered tractors. I'll fill in some missing details. It will be detailed and boring.

I had a few additional ideas to refine my last article. These ideas would maximize the number of useful recharge cycles and minimize battery size, keeping battery costs down and earning additional money. Also, there are some ideas to minimize the distance driven by the tractor. And there are some other ideas. If all these things are implemented, I believe this idea could be cheaper than operating tractors on diesel, at current prices.

In order to keep battery costs down, it is necessary to use the batteries as many cycles as possible before they expire due to calendar life. Batteries expire after a certain time period (like 10 years). We must maximize the number of useful cycles during that time period, because the upfront purchase price is a sunk cost and we must get as much usage as we can. This would be done in several ways.

1. The same battery trays could be used for the combine harvester also, and for other agricultural machinery. The same algorithm would be used to power the harvester across the field. Different pieces of agricultural machinery are used at different times (for example, the harvester is used in the Fall). As a result, the same batteries could be swapped between different pieces of equipment, using the same forklift.

2. The batteries could fast recharge during the day, while the tractor is operating, and thereby be recharged and used twice in one day. This halves the number of batteries we would need.

3. The area of the field in the diagrams above must be increased by a factor of 21. The tractor will then take 21 days (a typical planting season) to complete the entire field. The tractor would stop at night and the batteries would recharge. The battery swapping idea will still work as long as the tractor returns to the right-hand edge of the field more than once during a single day.

4. The same batteries could feed electricity back into the grid and be used for peak shaving the rest of the year. The recharging station on the farm would need an inverter to feed power back to the grid. This could cycle the batteries even more and earn the farmer additional money, thereby paying for the batteries.

Electricity peaks are much higher during the hot months of June, July, and August. However, the planting and harvesting seasons are in Spring and Fall. Thus, they do not overlap. This would allow the batteries to be used for planting during April or May, peak shaving in June, July, and August, and harvesting later, for example.

As a result, each battery would recharge twice per day for 21 days each of planting, fertilizing, and harvesting. I'll assume the batteries are used to shave peaks 40 times during the summer and are discharged almost completely during those 40 times. Thus, each battery would undergo 1,660 recharge cycles over 10 years. If we assume a battery cost of $100/kwh, then the price of batteries per kwh delivered is 6 cents (100/1660). That price is way below the cost of peak generators, and that price plus the price of electricity is below the price of diesel. As a result, this idea is cost effective and would be modestly cheaper than what is done now.

The price of the battery trays would be on the order of $150,000 every 10 years. This compares with a total price for tractor, harvesters, and so on of $600,000 or so, which also last about 10 years (the engines run continuously near the top rated horsepower for 4000 hours). Thus, the batteries would add 25% more cost than just buying a tractor and harvester. However, that additional cost would be offset by the farmer being paid for peak shaving, and also savings on fuel costs.

Overall, this idea could be slightly cheaper than using diesel at current prices.

A few additional ideas

Instead of the forklift going back and forth to the recharge station every swap, the forklift could bring 4 battery trays at once to the general area where 4 swaps would take place. There could be a covered raised shed for swaps so the batteries don't need to be left on the ground. Each shed could have a stack for fresh battery trays and another for depleted. This would minimize forklift driving. For example, there could be 8 sheds along the right side of the field in diagram above, and the forklift removes 4 spent batteries from the shed when necessary, takes them all at once to the recharging station, and then takes 4 fresh batteries from the recharging station to the next shed. The individual swaps then involve only driving to the nearby shed and back. The farmer would drive 4 fresh batteries to a shed, operate the tractor, stop periodically on the right hand side of the diagram, remove the depleted tray, place it in the nearest shed, take a fresh battery from that shed back to the tractor, and so on. When the shed has nothing but depleted batteries, the farmer drives all 4 trays back to the recharging station and drives 4 fresh trays from the recharging station to the NEXT shed.

The electrodes to recharge the battery trays can be way up some round holes in the bottom of the trays. The batteries are recharged using poles which stick up the holes on the bottoms of the trays and have electrodes on the ends. The holes close automatically using spring loaded plastic doors. In that manner, the electrodes are not exposed to rain or debris.

Of course it would be possible to optimize the size of the batteries, the number of battery trays, the number of swaps, the number of sheds, and so on.

Similar battery swapping ideas could be used for mining dump trucks, which also return to the same location over and over again. Similar ideas could also be used for ferries, shuttle buses, and so on.

Minor update 2023-01-18: Of course it would be possible to have only two small batteries, and to swap back and forth between them. This might be the most economical thing. If the farmer needs to run an electrical line to his field anyway, it would cost very little extra to run a higher voltage line. This implies that the tractor couldn't recharge overnight.

Tuesday, July 13, 2021

Tractors can easily run on batteries

Recently I saw a new book released by the Post Carbon Institute, entitled The Future is Rural. In that book, the author claims that everyone must relocate to the countryside because Peak Oil is near, and the tractors will stop running. According to the book, tractors cannot possibly run on anything other than liquid fossil fuels, so they will stop running fairly soon. We need to go back to farming by hand. Here is a quote from the book:

Farm equipment tends to operate near its horsepower capacity, whereas a car might only work near capacity when accelerating into traffic now and then. Hydrocarbon liquid fuels are the only known substances with enough energy density that can be carried easily onboard a tractor under typical working conditions and enable work to be performed continuously for many hours (pp 12).

Similar sentiments are echoed repeatedly within the energy decline movement. One of the core beliefs of that movement is that industrial agriculture will soon end, because of peak oil, and we'll need to revert to farming by hand.

It’s worth pointing out, right away, that tractors could easily run on alternative fuels like methane, ammonia, or hydrogen. One tractor manufacturer (New Holland) has already been preparing for several years to manufacture methane-powered tractors, and is releasing a methane-powered model for regular purchase later this year. Methane can easily be produced using renewable electricity and the Sabatier process, which has been in widespread use for more than a century. Ammonia and hydrogen are other chemical fuels which can be produced using renewable electricity and can be used to power tractors. A hydrogen-powered tractor is already in use (although it’s a prototype). The notion that tractors can only run on liquid fossil fuels is therefore clearly wrong.

However, decline theorists also argue that tractors cannot possibly run on batteries, either. The batteries would weigh too much for the tractor to carry. Tractors run all day continuously, and they run near the top rated horsepower for the entire time. As a result, they have enormous fuel consumption. Batteries do not have sufficient energy density to power tractors. The batteries needed to power a tractor all day (and near the top rated horsepower) would be too large and heavy to fit on the tractor. Most of the energy would be spent carrying the batteries themselves.

For example, I looked up a typical tractor here, and found it has a fuel tank of 135 gallons. Diesel weighs about 7 pounds per gallon, so the weight of the fuel is 945 pounds. A lithium-ion battery weighs about 100x more than diesel for the same energy (see here and here), however batteries are about 3x as efficient as small diesel engines, so the battery needed to replace 135 gallons of diesel fuel in that tractor would weigh 31,185 pounds (135*7*100/3). That is more than the weight of the tractor! As a result, tractors cannot run on batteries.

However, in this article, I will demonstrate that tractors can easily run on batteries. It can easily be accomplished using battery-swapping.

The convenient thing about tractors is they don’t travel in a straight line. Instead, they zig-zag across an agricultural field, like this:


(Apologies for the ASCII art).

You will notice that the tractor repeatedly returns almost to the same location, over and over again throughout the day. This allows us to use much smaller batteries on the tractor and swap the batteries on occasion. If this were done, then the energy density of batteries is more than sufficient to power a tractor all day.

I am proposing a new idea of battery swapping for tractors. I suggest that the battery for a tractor be divided into 32 smaller batteries. This is easy to do, because the batteries for EVs consist of many individually-packaged 2860 cells. So the battery for a tractor could be divided in to 32 smaller batteries which are packaged in removable battery trays. Those trays could be swapped using a forklift. The batteries would all recharge overnight. The forklift is also battery-powered. When the battery in the tractor is running fairly low and the tractor approaches the right-hand side of the diagram above, the forklift takes a new battery tray to the tractor and swaps out the old battery tray. The forklift ends up traveling only a fairly short distance throughout the day, because the tractor returns to the right-hand edge of the field repeatedly anyway, and the forklift meets it there.

Here is another ASCII art diagram:

               | #
<---<---<---<--- |
|                |
--->--->--->---> |
               | *
<---<---<---<--- |
|                |
--->--->--->---> |
               | #

The tractor follows the zig-zag pattern on the left, but the forklift only travels up and down the vertical bar on the right. The forklift meets the tractor at the hash marks. The batteries are stored in a small shed at the asterisk, which has a 480 volt recharger.

During each swap, the forklift will carry the depleted battery from the last swap (which had been left on the ground temporarily) to the recharging station, obtain a new battery, drive back to the tractor, remove the old battery from the tractor and set it on the ground, then install the new battery.

Of course, this does add a small additional energy expenditure. The forklift needs to travel back and forth along the right-hand edge of the diagram above, in order to accomplish the battery swapping.

Let’s calculate how far the forklift needs to travel, and how much energy is consumed by doing so. We’ll assume a hypothetical farm which has a square plot of land. The tractor must zig-zag throughout the entire plot of land during a single day. If it takes more than one day, then the tractor could recharge overnight, so we’ll assume that one day is the maximum energy expenditure between recharging. We’ll assume that the width of the agricultural machinery dragged by the tractor is 1/200th the width of the plot of land (this number is realistic), so the tractor must zig-zag 200 times in a day to cover the entire plot of land. As a result, the maximum distance travelled by a tractor in a single day is 201 times the width of the land (going back and forth 200 times, and also going all the way down the length of the land once). In contrast, the forklift must travel 16 times the width of the land in a day. The forklift travels only along the edge, and only 32 times, because 32 is the number of battery swaps. Furthermore, the average distance travelled by the forklift for each battery swap is only half the width of the land (sometimes, the tractor happens to be right near the middle of the field anyway, near the recharging station, where the fresh batteries already were). As a result, the distance travelled by the forklift is 8% of the distance travelled by the tractor (16/201 = 0.08). It is also worth noting that the forklift could weigh less than 10% of what the tractor weighs. If we assume that energy consumption is proportional to weight, then the forklift will use 0.8% of the total energy that the tractor uses. This is still a massive overestimate, because most of the energy used by the tractor is spent on dragging plows through the Earth, not just carrying the weight of its battery, whereas the forklift needs only to carry the weight of the tractor’s battery. Suffice it to say that the energy consumed by the forklift would be far less than 0.8% of the energy used by the tractor. As a result, the battery-swapping scheme imposes negligible additional energy costs.

Now that we have divided the battery into 32 sub-batteries, we can calculate the weight of those sub-batteries and see how much they would affect the weight of the tractor. Lithium ion batteries weigh about 100x more than diesel for the same amount of energy (as described above). However, I will assume (as a rough estimate) that batteries have 3x the energy efficiency of a small diesel engine (this is realistic; small internal combustion engines waste more than 70% of their energy as waste heat). Furthermore, we have divided the battery into 32 smaller batteries so we can swap them. Conveniently, the weight of each swappable battery works out to be approximately the same as the diesel fuel it replaces (1*100/3/32 = 1). Thus, our battery swapping scheme would not increase the weight of the tractor at all. In fact, it would slightly reduce the weight of the tractor, because the diesel engine and transmission could be removed, and electric motors are lighter.

As a result, we can easily power tractors with batteries. Energy decline theorists assumed it could never be done, but they wrongly assumed that a single large battery must be used. If we divide the battery, and use battery swapping, then it becomes entirely feasible to use batteries for tractors.

Of course, it’s worth pointing out that small diesel engines in tractors lose more than 70% of their energy as waste heat, whereas batteries and electric motors lose only about 15% as waste heat. Thus, the battery-swapping scheme I described above is actually far more energy-efficient than the diesel tractors we use now. Although battery swapping imposes a 0.8% energy loss due to forklift usage, diesel engines impose a 70% energy loss.


Originally, I intended to write this post only as a hypothetical example. I wanted to show that there are many alternatives to diesel for tractors, and even batteries would work. I certainly don't expect that this will be used in practice. I admit to knowing very little about farming.

However, after considering the idea further, I think it’s actually plausible and could be used in practice. In fact, this idea might be preferable to alternative fuels. Alternative fuels (such as hydrogen, ammonia, and synthetic methane) would impose large efficiency losses and are much more expensive than diesel fuel. Battery swapping, however, could be slightly cheaper than diesel fuel, even including the cost of replacing worn-out batteries after 12 years.

The big drawback of this idea is that it requires additional labor. The person who operates the tractor would need to stop every 5 or so passes across his field, get out, walk to where the forklift was last parked (the last battery swap, which would be about 50 feet away), pick up the last depleted battery from the ground, drive the forklift to the recharging station at the center of the right edge of the field, drop off the last depleted battery tray, fetch a new battery tray, drive back to the tractor, remove the recently depleted battery tray from the tractor and leave it on the ground, install the fresh battery, get back in the tractor, and keep driving. Since he would have to do this 32 times per day, I would guess it would add at least two hours of labor. He would end up driving a forklift for 6 miles if we assume a plot of land that’s 2000 feet on a side, so just driving the forklift that distance in a day would take more than half an hour. However, it would save at least $350 each day for an additional two hours of labor, compared to using synthetic fuels (I assume synthetic fuels would cost $6/gallon which is $2 more than diesel, and a typical tractor uses 175 gallons in a day). My labor is worth less than $350 for two hours. Of course, the farmer would have to buy a small forklift too, which looks like it would cost about $4,000. However, that cost would be recovered in less than 12 days of usage (4000/350 = ~12). As a result, this looks like it could actually be the best alternative to diesel fuel for tractors.

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.