Monday, September 18, 2017

A nation-sized battery, revisited

(Note: this is a draft. I will update it if any relevant objections are made).

Introduction

In an excellent blog post, Dr Tom Murphy examined whether it would be possible to power the entire USA using a combination of renewables and lead-acid batteries. He found that it would not be possible, because there is nowhere near enough lead in the earth's crust to make enough lead-acid batteries to compensate for the intermittency of renewables. Renewables occasionally don't produce power for 7 days in a row (during prolonged wind lulls, for example). As a result, it would be necessary to build enough lead acid batteries to power the country for 7 days to prevent the lights going off during those periods. However, the amount of lead in the earth's crust is not sufficient even to power just the USA for 1/3rd that long, to say nothing of the rest of the world. As a result, lead-acid batteries cannot compensate for the intermittency of renewables on a nationwide scale.

However, lead-acid batteries are not the only storage option available. We should investigate whether there are other storage options that have sufficient materials, not just whether lead-acid batteries have sufficient materials.

In this article I’ll investigate some other energy storage options. I'll try to determine if those options would be sufficient to power the entire USA during wind lulls. In all cases, I will assume that society needs 7 days of energy storage (or 336 billion kWh for the USA, as per Dr Murphy’s article) to prevent the lights from going out during occasional prolonged lulls in wind power.


Molten Silicon

First I will examine the possibility of using molten silicon as an energy storage medium. Molten silicon would be stored in insulated tanks, and heated up whenever the wind is blowing. When the wind isn’t blowing, hot air is drawn over the molten silicon and used to drive a turbine. The silicon doesn’t actually change temperature; instead it changes phase from solid to liquid when heat is added, and back from liquid to solid when heat is taken out, so the temperature remains constant at 1414 degrees C. This technology is already being pursued by a startup; see here.

Let’s find out if there is enough silicon in the earth’s crust to provide energy storage for the USA for 7 days. We’ll start by calculating how much silicon metal would be required. Murphy’s article says that we’d need 336 billion kWh to power the entire country for 7 days. Silicon has a latent heat of melting of 1.926 MJ/kg[2], which is equivalent to 0.535 kWh/kg, or 0.278 kWh/kg after subtracting waste heat losses (discussed further below). As a result, we would need 1.2 billion tonnes of silicon (336 billion / 0.278), which is a cube of silicon that’s 0.78 kilometers on a side (at 2.5 g/cm^3 [3]). Silicon is the primary ingredient of dirt, so we could gather a cube of silicon that’s 0.78 kilometers on a side from within a 10 kilometer radius around my house. That would be enough silicon to power the entire USA for 7 days. Furthermore, the silicon is not being “used up” at any rate, but could be re-melted, over and over again, for millions of cycles, with no degradation.

Of course, we’d also need gas turbines, in order to convert the heat back into electricity. However, gas turbines have already been scaled up and already provide much of the electricity generation for the world. Those are natural gas turbines, not hot air turbines, but their construction would be similar. I presume we can continue building gas turbines on a wide scale.

As a result, it is clear that we have vastly more silicon than we need to meet our energy storage requirements for the entire USA for all purposes, and can also build the requisite turbines on a wide scale.


Power-to-methane

Power-to-methane relies upon electrolyzing water to obtain hydrogen gas, then converting that hydrogen gas to methane using the Sabatier process. When the wind is blowing, methane gas is created. When the wind isn't blowing, that gas is converted back into electricity using existing natural gas turbines.

There is enough carbon in the Earth’s atmosphere to create the needed methane gas. We've been burning fossil fuels for more than a century now, so there is obviously enough carbon in the atmosphere to make a 7-day inventory of methane gas. Remember that carbon is not being “used up” during this process of synthesizing gas and burning it. This storage scheme is a closed cycle, in which carbon is taken from the atmosphere (actually, probably absorbed from the atmosphere into the oceans and then taken from there) and then re-released to the atmosphere. As a result, the maximum amount of carbon we would ever need is a 7 day inventory of methane, which obviously is a small fraction of the carbon we have emitted into the atmosphere over the last century.

There is also the question of how we could store 7 days worth of methane gas. However, that gas could be injected into the existing natural gas distribution network, which already is large enough to store months of gas. For example, California (where I live) can store 2 months of gas in the existing gas distribution network.[5]

It is clear that power-to-methane could be scaled up to provide 7 days of storage when the wind isn’t blowing.


Compressed Air Energy Storage

Compressed air energy storage relies upon compressing air when the wind is blowing. The compressed air can be stored in naturally-occurring underground caverns. When the wind stops blowing, the compressed air is released which powers a turbine and generates electricity.

There are enough caverns underground worldwide to hold the compressed air. The world is scattered with underground salt domes, salt caverns, porous rock formations, and aquifers. Here is a map of salt formations in Europe, for example[4].

There is one formation underneath Poland and Germany, for example, that appears to be 1,000 km long and 100 km wide. If it's 2 km deep, then it has a total volume of 200,000 km^3. Compressed air stores approximately 4 kWh/m^3 which is 800,000 billion kWh for the entire formation, whereas we need only 336 billion kWh for the USA according to Murphy's article. Obviously, it wouldn't be possible to convert an entire large underground salt region to a single compressed energy store. Still, if we could use even 0.1% of it, then we'd have more than enough energy storage for that region.

It is also possible to store compressed air in above-ground steel tanks in the regions which do not have suitable geography for underground storage.


Conclusions

There are already many solutions for storing 7 days worth of electricity. Those solutions are fairly low-tech and do not rely upon any technological breakthroughs. Furthermore, they could all be scaled up and do not face any material constraints.

The only objection to the low-tech storage mechanisms listed above is that they have fairly low round-trip energy efficiency. For example, molten silicon storage relies upon heating silicon to 1414 degrees centigrade to power a turbine, which implies a round-trip efficiency of approximately 50%. This means that approximately half the energy placed into storage would be lost as waste heat. Power-to-gas would probably be somewhat less efficient, at 40% or so (60% lost as waste heat). Compressed air could be somewhat higher, at 60-70%. In all cases, however, there would be considerable round-trip energy losses.

However, that drawback is not as important as it would seem. Those energy losses are incurred only part of the time, because most renewable electricity is delivered directly to the grid without ever being placed into storage. As a result, storage losses would constitute only a fairly small fraction of the total electricity generated. For example, if solar panels could provide enough electricity to meet 40% of electricity demand directly, without storage, then only 60% of electricity would need to be drawn from storage. In which case, we would need to overbuild solar panels by only 60% (not 100%) to compensate for storage losses with 50% efficient storage (0.40 electricity delivered directly, 0.60 to storage, and 0.60 to waste heat, which implies 1.60/1.00, which is 60% overbuilding). Waste heat losses would constitute only 37.5% (0.6/1.6) of all energy obtained from solar panels, not 50%.

As a result, the round-trip losses from energy storage would be less important, because those losses are incurred only part of the time. This is quite different from waste heat losses from coal power plants, for example. Coal power plants lose 65% of their energy as waste heat, 100% of the time. On the other hand, the round-trip losses from energy storage from renewables are only occasional, and so would represent a fairly small fraction of all electricity generated.

As a result, it is clearly possible to build a “nation-sized” energy storage mechanism with tolerable energy losses and at reasonable expense. We do not face material constraints on energy storage. No technological breakthroughs are required. We could build an energy storage system that would provide continuous, dispatchable power at all times from renewable sources.

One more thing. There are also newer electricity storage mechanisms being developed. For example there are new flow batteries being developed which use abundant materials (such as the iron flow battery described here, or the organic flow battery described here). Those flow batteries would have higher round-trip efficiency (like 70% or more) and could store large amounts of energy at the same time. If higher round-trip efficiencies could be achieved, then less overbuilding would be required. Overbuilding is unfortunate, and we should try to reduce it. However, even if those new flow battery technologies never reach commercialization, we still have other, lower-tech options which are perfectly workable and which impose modest energy losses relative to all electricity generated.


[1] https://en.wikipedia.org/wiki/Abundance_of_elements_in_Earth%27s_crust.

[2] http://www.engineeringtoolbox.com/fusion-heat-metals-d_1266.html

[3] https://en.wikipedia.org/wiki/Silicon

[4] https://www.researchgate.net/figure/48693439_fig4_Figure-4-2-Salt-structures-and-cavern-storages-in-Europe

[5] https://californiahydrogen.org/sites/default/files/CHBC%20Hydrogen%20Energy%20Storage%20White%20Paper%20FINAL.pdf

*NOTE: I modified this article on Sept 21 and changed the overbuilding example from wind turbines to solar panels. I also re-worded the clumsy opening paragraph.

Thursday, September 14, 2017

Coal will never run out

The United States has 283 years of coal remaining, at present rates of usage, according to the EIA[1]. China, Russia, and Australia have similarly huge amounts.

However, that figure of 283 years remaining is for present rates of usage.  If coal usage declines, then the "hubbert curve" of remaining coal is flattened and pushed further out to the right. For example, if we were using only half the amount of coal per year as we do now, then we would have 566 years of coal remaining, not 283 years. Every reduction in coal usage will extend the amount of time remaining until depletion.

Coal usage has been declining fairly rapidly in the United States, for the last 5 years or so, because renewables and gas are so much cheaper now. Coal plants are being shuttered because coal is relatively more expensive now. In fact, coal usage is down 28% in the United States over the last 5 years, because so many coal plants have been shuttered[2]. As a result, the date of coal depletion is being pushed far out into the future. Since coal usage is down 28% already, the remaining time until coal is depleted has increased from 283 years to 388 years (= 283 / 0.72 - 5). In other words, we have “gained” 105 years of coal during the last 5 years.

This trend looks set to continue. New turbines are being developed ("supercritical CO2 turbines") to replace the old steam turbines in coal power plants. Those new turbines are 50% efficient instead of 33%, which pushes back the date of depletion another 262 years ( =393 * (0.5/0.33) ).  Any further encroachment of renewables would push back the date of depletion even further, and could easily result in millennia of coal before it runs out. For example, if coal plants are gradually replaced by wind turbines during the next few decades, until coal is used only for steelmaking and also during the time when the wind isn't blowing, then coal usage could decline by more than 50%, which would result in 1,190 years total until the coal runs out (= 595/0.5). That figure is without any electricity storage technology at all for when the wind isn't blowing. Coal could still be used for electricity generation when the wind isn't blowing, but we'd still have enough coal for 1,190 years.

Of course, there are several trends happening in the opposite direction also, which could push toward increased use of coal. First, the United States looks like it will phase out nuclear power over the next several decades, and some of that lost generation may be replaced by coal. Second, south Asia is growing quickly and will increase its usage of coal. However, both of those trends are temporary. Coal usage may bounce up and down, but in the long run, it is probably headed way downwards, which implies that remaining reserves will last far longer than reserve figures suggest.

Of course, it is possible that further technological developments will occur during the next few centuries, in which case the date of depletion for coal will be pushed even further outward. If flow batteries are commercialized, for example, then coal may not be needed for electricity generation at all. If new steel-making technologies continue to progress, then coal wouldn't be needed for that purpose either.

Our civilization has at least centuries to develop technologies such as flow batteries and alternative steel-making technologies. If those technologies are developed and commercialized in the next few centuries, then the remaining coal would be left in the ground as useless.

Technology is rapidly outpacing depletion. This time to depletion for coal keeps getting further and further away, and fairly rapidly. If this trend continues for long, then coal will never run out.


[1] https://www.eia.gov/energyexplained/index.cfm?page=coal_reserves

[2] https://www.eia.gov/coal/production/quarterly/pdf/t1p01p1.pdf

*NOTE: This post was revised several times during the 24 hours after its initial publication. I also updated this article on Sept 21 to use a more realistic example of how much electricity could be generated from renewables without storage.

Sunday, March 5, 2017

Dr Charles Hall is still totally wrong about EROI

Recently I saw an article on energyskeptic.com and found that Dr Charles Hall is still making the same incorrect claims. Once again, Dr Hall is claiming that civilization requires an EROI higher than a certain amount to feed its population and support advanced activities. Apparently, if EROI drops below a certain level, then civilization will revert to a primitive state. It could even result in mass starvation if EROI drops too low.

The following remarks are taken from the article:

[Summarizing his research] Pretty soon it looked like we needed an EROI of at least 10:1 to take care of the minimum requirements of society, and maybe 15:1 (numbers are very approximate) for a modern civilization.

Similar ideas are expressed in his earlier papers, such as Hall's "energy pyramid"[1] in Lambert & Hall[2].

Apparently, we require an EROI of at least 5:1 just to grow enough food to survive, whereas we require an EROI of at least 15:1 to have a modern, industrialized society, according to Dr. Hall and associates.

However, those numbers are clearly wrong. A decline in EROI from 15 to 5 implies a decline in net energy of only ~14%, and this can be shown using arithmetic ( (1-1/5)/(1-1/15) = ~86%). As a more extreme example, a decline in EROI from 1 billion down to 5 implies a decline in net energy of less than 20% (19.999...). Such declines in EROI imply only modest losses of net energy, and do not imply the collapse of civilization, mass starvation, or a return to a medieval mode of life. Above a very low level, EROI makes practically no difference; for example, a decrease in EROI from 1 trillion down to 10 implies a loss of less than 10% of net energy.

Presumably, the error here is to infer that modern civilization must have a proportionally higher EROI than primitive civilization, in order to gain more net energy to support more advanced activities. Dr Hall observes that the kung (a hunter-gatherer tribe) has an EROI of approximately 10. Presumably, Dr Hall infers that modern civilization must have a higher EROI to obtain more net energy.

From the article:
Lee's assessment of the traditional kung hunter gatherer life style implies an EROI of 10:1 and lots of leisure (except during droughts–which is the bottleneck).

However, Hall's inference is incorrect. Modern civilization doesn't just have a higher EROI than primitive societies; it also has a greater AMOUNT of gross energy which it can obtain. Primitive societies have too little energy they obtain, regardless of EROI. Even if the kung increased their EROI from 10 to 1 billion, it would result in less than 10% additional net energy, which presumably would make little difference. The problem is amount, not EROI. It is not possible to know how much net energy will be obtained from EROI alone.

The amount of net energy can be calculated using the following formula:

net = gross - gross/eroi

You will notice that it's not possible to solve the simple equation above using EROI alone. As a result, any remarks along the lines of "we require an EROI of at least x to have modern civilization" are incorrect. Without knowing how much GROSS energy is obtained, we cannot calculate how much NET energy will be obtained. Modern civilization runs on net energy, not a high EROI, so an EROI number by itself (without any indication of gross energy) provides no important information, unless the EROI ratio is lower than 1.

At present, the United States uses 6916 kg of oil equivalent capita, per year. Even if the average EROI ratio for the entire country dropped down to 3, the US would still have more net energy per capita than France[3]. The French are obviously capable of growing food, having education, and so on.

Dr. Hall then claims that we require an EROI of at least 3 to support modern transportation:

We found you needed to extract 3 liters at the well head to use 1 liter in the gas tank to drive the truck, i.e. an EROI of 3:1 was needed... But even this did not include the energy to put something in the truck (say grow some grain)

That claim is incorrect. Hall's paper in question[4] includes depreciation of all vehicles as an energy cost. It also includes all road construction. However, most vehicle depreciation occurs in personal vehicles which are used for discretionary trips. As a result, an EROI of 3 is not the minimum which civilization must have to deliver food in trucks, because civilization could curtail personal vehicles while retaining food delivery in trucks. Furthermore, the replacement rate of personal vehicles would decline proportionally as the rate of net energy to drive them declined. In other words, vehicle depreciation is not constant. As a result, the minimum EROI needed for modern transportation would be far lower than 3 because most of that energy investment could be curtailed without (thereby reducing the minimum EROI figure) without sacrificing anything essential.

It's not necessary for civilization to construct the entire first world edifice of cars and freeways before commencing any other activities. As a result, Hall's energy pyramid is incorrect, because the numbers contained in it would change as EROI declined, and also because those activities are not stacked on top of each other in the way implied by that diagram.

Dr. Hall then turns his attention to the idea of chaining energy sources. You could "chain" power plants (or "stack" them) and thereby achieve a higher aggregate EROI (This is discussed further on this blog, here). For example, if you had solar PV plant with an EROI of 2, you could use the output of that plant to build twice as many new ones, which would yield 4 units of energy for an initial investment of 1. Alternatively you could use the output from the initial plant to build 1.5 times as many new ones (which would yield 3 units of energy for an initial investment of 1) and then return the remaining net energy to society.

Dr. Hall addresses that issue in the same thread, as follows:

The problem with the "stacked" idea is that if you do that you do not deliver energy to society with the first (or second or third) investment — it all has to go to the "food chain" with only the final delivering energy to society.  So stack two EROI 2:1 technologies and you get 4:2, or the same ratio when you are done.

That is clearly incorrect. It is not necessary to devote the entire amount of gross energy obtained to building more solar panels. It would be possible to invest more than is required to replace existing solar panels, but less than the entire amount. This would still lead to exponential growth in net energy obtained (with any EROI higher than 1) while also providing energy for other purposes in the mean time. Exponential growth in energy supply would obviously allow us to obtain any amount until some limit (other than EROI) is reached. As a result, EROI is not proportional to net energy obtained by society.

Dr Hall also claims that solar PV with an EROI of 8 may not actually provide any net energy to society after including more factors as energy investments:

If the EROI [of solar] is 8:1 ... then it seems like you could make your society work. But let’s look closer. If you add in security systems, roads, and financial services and the EROI drops to 3:1 then it seems more problematic. But if you add in labor (i.e. the energy it takes to make the food, housing etc that labor buys with its salaries, calculated from national mean energy intensities times salaries for all necessary workers) it might drop to 1:1. Now what this means is that the energy from the PV system will support all the purchases of the workers that are building/maintaining the PV system, let’s say 10% will be taken care of, BUT THERE WILL BE NO PRODUCTION OF GOODS AND SERVICES for the rest of the population.

Of course, that implies that 7/8ths of the output of a modern power plant is devoted to the employees who work there and miscellaneous expenses like security cameras, roads to the plant, and so on. On its face, that number is highly implausible.  A modern solar PV power plant often has more than 250 MW nameplate capacity, which is equivalent to 47.5 MW continuously at a capacity factor of 0.19. Even if there were 2,000 employees who worked at the plant continuously for 30 years (which is false; solar plants have only a handful of employees), that would still imply more than 23.75 kw continuously per employee which is vastly higher than the total energy usage per capita of any industrialized country. That figure of energy usage includes the employees' discretionary consumption (such as taking plane trips to the Bahamas for vacation) which is not an energy investment.

There is another serious problem with Dr. Hall's ideas on this matter. Over and over again, Dr. Hall treats energy returns as energy investments. In doing so, he places terms in the denominator of the EROI fraction which belong in the numerator. For example, in his paper What is the minimum EROI that society must have?[4], he treats all personal vehicle depreciation as an energy investment. However, most personal vehicle travel is for discretionary trips and not for activities such as (say) gathering coal. As a result, such vehicle travel represents an energy return, not an investment. As another example, Hall repeatedly treats first world salaries for certain workers as energy investments; for example, in the remarks above, or in his book Spain's Photovoltaic Revolution[8], he treats salaries of power plant employees as energy investments.

If we treat things like first world salaries, discretionary car travel, vacations, etc as energy investments, then it would be possible to increase EROI greatly, by simply curtailing discretionary first-world activities somewhat for power plant employees. As a result, the EROI of those sources of energy would increase greatly as salaries declined, in which case, Hall's EROI figures would no longer hold. This implies that Hall's warnings about the decline of industrial civilization wouldn't hold either, because any decline in the first world incomes of power plant employees would cause a concomitant large increase in the EROI of power plants.

In conclusion. Dr. Hall's ideas and papers contain serious mathematical and logical errors which invalidate his analysis. He assumes that modern civilization must have a proportionally higher EROI than primitive civilization in order to obtain more net energy to support advanced activities. However, that assumption is clearly wrong, because modern civilization also has more gross energy than primitive civilization, and so would obtain vastly more net energy even with far lower EROI ratios. Furthermore, Dr Hall is throwing around numbers which are clearly implausible and which are refuted using straightforward arithmetic. What's more, Dr. Hall's criticism of the "stacked" energy source idea is incorrect, insofar as he wrongly assumes that society must devote either all of leftover energy, or none, to obtaining more energy. Finally, Dr. Hall repeatedly treats energy returns as investments, and in so doing, invalidates his other conclusions.

There is one more thing I should point out. These ideas are not new. Dr. Hall and his mentor (HT Odum) have issued warnings about declining net energy and imminent grim consequences to civilization, over and over again, since the early 1970s. Odum first warned in the early 1970s that all sources of energy then had perilously low and declining EROI (called "energy yield ratio" back then) [5]. Odum claimed repeatedly during the 1970s that nuclear reactors probably would not yield more energy over their lifetimes than was required to construct them and refine the Uranium. Odum also claimed at that time that the EROI of coal fired electricity was extremely low and declining. Dr Hall started warning in the early 1980s (during the oil crisis) that the EROI of oil was disastrously low and could decline to just above 1 fairly soon thereafter[6].  Dr Hall warned again, in 2009, that the EROI of oil and gas was perilously declining: "The fact that the EROI for global oil and gas extraction declined by nearly half from 1999 to 2006 is cause for concern."[7] Both Hall and Odum devoted much of their professional careers to issuing such warnings about almost all sources of energy, over many decades. These most recent warnings about the EROI of renewables are simply repetitions of earlier, failed predictions and warnings, applied to other sources of energy back then. Dr. Hall needs to explain why these ideas and methods have failed so badly in their predictions in the past, when applied to fossil fuels, but are still correct now when applied to renewables.

I have pointed out repeatedly, for several years, that Dr Hall's analysis contains mathematical errors. Dr Hall responds to this by being petulant and insulting:

First I would like to say that the bountiful energy blog post is embarrassingly poor science and totally unacceptable. As one point the author does not back his (often erroneous) statements with references. The importance of peer review is obvious from this non peer-reviewed post.

However, that simply does not address the mathematical errors I have pointed out.

If Dr Hall offers no relevant response to these objections, then his ideas are refuted.

---

[1] https://i1.wp.com/energyskeptic.com/wp-content/uploads/2014/07/societys-hierarchy-of-energetic-needs-eroi-12-14.jpg

[2] http://energyskeptic.com/2016/lambert-hall-energy-eroi-and-quality-of-life/

[3] http://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE . The USA has an energy use per capita of 6916 kg of oil equivalent, which is 4613 net energy per capita with an EROI of 3. France has an energy use per capita of 3840 kg of oil per capita, which implies lower net energy per capita regardless of the EROI of France.

[4] What is the minimum EROI that society must have?, pp 42, table 2. Charles A. S. Hall, Stephen Balogh and David J. R. Murphy. Energies 2009, 2, 25-47.

[5] Energy Basis for Man and Nature. Howard T Odum and Elisabeth C Odum. MacGraw Hill, 1974.

[6] Petroleum Drilling and Production in the United States: Yield per Effort and Net Energy Analysis. Charles A.S. Hall, Cutler Cleveland. Science, 211, 4482, 576-579.

[7] A Preliminary Investigation of Energy Return on Energy Investment for Global Oil and Gas Production. Nathan Gagnon, Charles A.S. Hall, and Lysle Brinker

[8] Spain's Photovoltaic Revolution. Pedro A. Prieto and Charles A.S. Hall. Springer, 2013.

Sunday, July 17, 2016

The Energy Trap

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

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

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

If I run my simulation with those parameters, what results do I get? Here are the results in tabular format:
yeargross_ffgross_pvgross_totalnet_totalinvest_pvinvest_fffraction_original_net
01.00000.00001.00000.90000.00000.10001.0000
20.99780.00000.99780.89780.00000.10000.9975
40.99120.00000.99120.89120.00000.10000.9902
60.98020.00000.98020.88020.00000.10000.9780
80.96510.01670.98170.84490.05000.08690.9388
100.94600.05000.99600.86080.05000.08510.9565
120.92310.08331.00640.87340.05000.08310.9704
140.89680.11671.01350.88280.05000.08070.9809
160.86740.15001.01740.88940.05000.07810.9882
180.83530.18331.01860.89340.05000.07520.9927
200.80070.21671.01740.89530.05000.07210.9948
220.76420.25001.01420.89540.05000.06880.9949
240.72610.28331.00950.89410.05000.06540.9935
260.68690.31671.00360.89180.05000.06180.9908
280.64690.35000.99690.88870.05000.05820.9874
300.60650.40001.00650.85190.10000.05460.9466
320.56620.46671.03280.88190.10000.05100.9799
340.52610.53331.05950.91210.10000.04741.0134
360.48680.60001.08680.94290.10000.04381.0477
380.44830.65001.09830.95800.10000.04031.0644
(Note: All values are fractions of the original gross amount of energy from fossil fuels; so an invest_pv column of 0.05 means that 5% of the original gross amount of energy is invested in PV panels)

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

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

Tom Murphy has this to say about it:

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

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

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

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

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

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

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

Sunday, June 19, 2016

ERoEI is unimportant and is being used incorrectly

In this article I will show that ERoEI is unimportant by itself. It usually does not matter if ERoEI is increasing or decreasing. ERoEI provides no guidance about which sources of energy we should pursue, nor does it offer any guidance about how much net energy will be available to us in the future. By itself, ERoEI is a useless figure, unless it is lower than 1, which it almost never is. Although different sources of energy (such as coal or solar PV) have different ERoEI ratios, this means nothing important.

What is important to civilization (and to us) is the amount of net energy obtained from a source of energy. It is an amount of net energy (not a high ERoEI) which allows us to drive cars, fly airplanes, and so on. If we obtain 1 GWh of NET energy, then it does not matter if it came from a high-ERoEI source, or from a low one. What matters is the amount of net energy.

In turn, the amount of net energy depends upon two things: ERoEI AND the amount of gross energy. BOTH of those figures are required to determine the amount of net energy obtained. ERoEI by itself tells us almost nothing.

Let me provide an example, to demonstrate this point. Suppose you have a solar PV panel with an ERoEI of 3, which returns 1KW on average continuously for 30 years. In that case, the net energy provided by that solar panel is 175.2 MWh ((1*24*365*30)*(1-1/3)) over its lifetime. If, however you have ten such solar panels, then the net energy returned is ten times higher (1752 MWh), despite no change in ERoEI.

For the most part, the amount of NET energy we can obtain is determined by the amount of GROSS energy we can obtain, not by ERoEI. Usually, ERoEI is only a minor factor. This is because the difference in the amount of gross energy between sources of energy is so large that it completely overshadows any minor influence that ERoEI would have.

For example, suppose we had single 1KW solar panel, and the panel had a very low ERoEI of 4 (which is certainly an underestimate [1]). Even if you increased the ERoEI from the very low value of 4, all the way up to to infinity, so that no energy was required to replace that solar panel, it would make little difference--it would increase the amount of NET energy obtained by only 25%. On the other hand, if you could build 3 such solar panels, instead of 1, then you would triple the net energy obtained. In this case, building two more solar panels had 12x greater effect than increasing the ERoEI to infinity.

For the most part, the net energy obtained from solar power would be determined by the number of solar panels built, not by their ERoEI. In turn, the number of solar panels which can be built, is determined by non-energy factors like capital and labor, because those are the scarce factors which prevent the construction of more solar panels. Energy for investment is not scarce, because this planet is bombarded with 23,000 terawatt-years/year of solar radiation, which is vastly more than we will ever use. It is the scarce factors which determine how many solar panels we can build, and therefore, for the most part, how much net energy we will obtain. This point is complicated and requires further elaboration, so I will discuss it in a subsequent article. Suffice it to say, that the net energy of solar power is determined by non-energy factors such as capital and labor, and has almost no relation to ERoEI, because capital and labor (not energy) are the scarce factors which prevent the construction of more solar panels.

Generally speaking, the amount of net energy goes up as ERoEI declines, although it’s a weak correlation. This is because the amount of gross energy is vastly higher at lower ERoEI ratios, and the greater amount of gross energy more than compensates for any decline in ERoEI.

For example, solar PV could provide far more net energy than coal, regardless of its lower ERoEI. This is because solar radiation is so much more abundant that its lower ERoEI would be completely overshadowed by its greater amount. As a demonstration, suppose we could convert only 1% of solar radiation striking this planet into electricity using solar panels. In that case, we would obtain 40,000 times more electricity from solar power than we currently obtain from burning coal [2]. That figure does not take into account ERoEI, but it would make little difference. Even if solar PV had an extremely low ERoEI of 4 (certainly an underestimate), and coal had an ERoEI of infinity, it still would only reduce the maximum net energy of solar power by 25% relative to coal [3]. Since solar power is 40,000 times more abundant than coal, an ERoEI adjustment of 25% is not important. It would mean only that we could obtain 30,000 times more energy from solar power than from coal, rather than 40,000 times more [4].

Of course, if the ERoEI of some energy source were extremely low (like less than 2), then ERoEI would become an important factor. In that case, ERoEI would actually make a substantial difference, because it would cause a 50% or greater net energy loss. However, all common sources of generating electricity have ERoEI ratios far higher than that. With an ERoEI higher than 8 (which all sources of generating electricity have), the amount of energy spent obtaining more energy is only 12.5%, which is completely overshadowed by differences in gross amount between energy sources.

Again: net energy available is a function of BOTH EROEI AND AMOUNT. Either one of them by itself cannot be used to calculate net energy. If we wish to use a “rule of thumb”, then we should assume that MORE net energy is available at lower ERoEI ratios, but the correlation is so weak that it can’t be relied upon. In any case, ERoEI is not generally an important factor.

Unfortunately, ERoEI theorists do not realize any of this. Over and over again, they wrongly assume that ERoEI is somehow proportional to net energy. They assume that a higher ERoEI somehow implies more net energy obtained. This is a severe mathematical error, but it’s repeated endlessly throughout the ERoEI literature, across decades.

Let me provide some examples which I read just a few days ago:

“Look [at a] Cheetah… That beautiful and ultra efficient machine, needs an EROI of about 3:1... That’s a metabolic minimum EROI for mammals.Being the minimum EROI for any live being (mammals in particular) 2-3:1 in average, to be kept alive as species and for the couple to successfully breed their offspring (minimum of 2-3 per couple), probably Charles Hall is very right to state that a minimum EROI of 5:1 is required to have a minimum (very primitive and elemental) of civilization, beyond us living as naked apes.”
No, because that wrongly assumes that greater amounts of net energy are obtained at higher ERoEI. That is a basic mathematical error. Frequently, using a lower ERoEI source of energy will obtain more net energy than a higher ERoEI one.

The Cheetah example is also mistaken in other ways. The Cheetah doesn’t just have a low ERoEI; it also has TOO FEW prey which it can catch. If the Cheetah could eat prey every 5 minutes, then it would have a vast excess of energy even at an ERoEI of 1.5. The problem is that many animals eat only once per day and some animals (such as crocodiles) eat only once per week or so. The problem is amount, not ERoEI. If they eat only 10,000 kilocalories per week, then increasing the ERoEI wouldn’t matter much (even increasing ERoEI to infinity in this case would only gain the animal another 3,300 kilocalories). What would help is to catch MORE prey.

Here is another example of the same mistake:
We can take our ERoEI 20 FF and invest them in ERoEI 50 sources and make a huge energy profit. Or we can invest them in <5 and make a loss. Our policy makers have lost their heads electing to promote loss making activities.”

No, because that is confusing ERoEI with an AMOUNT of net energy. If an ERoEI were an amount, then spending fossil fuels with ERoEI 20 on solar panels with ERoEI 5, would imply a loss of 15. However, you cannot subtract the ERoEIs of different sources of energy, because they are not AMOUNTS which can subtracted. The correct mathematical operation is to multiply those two numbers, not subtract them.

If you take ERoEI 20 fossil fuels, and invest them in ERoEI 5 solar PV, then the aggregate ERoEI is 100 (invest 1 unit of fossil fuels initially, obtain 20 units of fossil fuels with ERoEI of 20 thereby, invest each of those 20 units in solar panels with ERoEI 5, then obtain 100 units at the end of it for an initial investment of 1).

Here is another example:
IMO, the only thing that could delay the bad impacts of declining high ERoEI FF is to introduce to the global energy mix an energy source that has higher ERoEI than the fuels they have to replace. Introducing low ERoEI energy sources simply makes things worse.”

No, because (again) that is confusing ERoEI with an AMOUNT of net energy. The “bad impacts” are caused by TOO LITTLE net energy, not a low ERoEI. Adding any source of energy with an ERoEI higher than 1 increases the total amount of net energy available. Only an ERoEI lower than 1 would make things worse. If the source of energy is cheaper per unit of net energy (as solar power actually is) then it is easier to obtain more net energy that way, regardless of its ERoEI.

…All three of the above quotations are taken from leading figures in the ERoEI literature, all published within the last few weeks. Granted, the ERoEI movement is a tiny fringe movement, but these people are among the leading figures of it. Over and over again, they wrongly assume that ERoEI and net energy are somehow proportional, and that higher ERoEI implies more net energy. That is a basic mathematical error. Frequently, the opposite is the case.


What matters is the AMOUNT of NET energy available to civilization, and that amount is far higher for renewables than for any other source, regardless of ERoEI.

* NOTE: In this article, I am using the term "ERoEI" to by synonymous with "EROI" and other spellings. I am referring to the amount of energy obtained for an investment of energy. If ERoEI for some energy source were extremely low (like lower than 3) then ERoEI would start to become more important, since we'd need to build significantly more power plants to generate the same net energy. Since all common sources of generating electricity have an ERoEI much higher than that, ERoEI is not important in any real-world scenario.

I revised this article on August 18, two months after its initial publication, to improve the flow of the text.

Wednesday, June 17, 2015

There are many alternatives to oil

One of the main ideas of the peak oil doom movement is that there are no possible alternatives to oil. Oil is apparently some magical irreplaceable substance with no known alternatives, and no way to find alternatives. For example, here is a recent post from a prominent peak oiler on peakoil.com:

...It is highly unlikely we will discover a viable alternative to oil... We can't invent a new energy source to oil since that would violate the laws of thermodynamics. You can't make something out of thin air just by imagining it.

As usual, that idea is factually totally wrong.

There have always been many alternatives to oil, since the beginning of the oil age. For example, cars can use electricity from batteries (most major car companies have released, or are releasing, battery-electric cars). Trains and buses can use electricity from overhead wires; more than half of rail traffic worldwide now uses this. Ships can use steam turbines which can use anything that will burn as fuel, such as coal, peat, wood chips, oil shale, torrefied biomass, etc. Internal combustion engines can use natural gas--even gas from fracking or methane hydrates. For the few uses which really require a liquid combustible fuel, there are many synthetic liquid fuels such as anhydrous ammonia, dimethyl ether, and many others. Those synthetic liquid fuels can be manufactured using electricity from renewable sources and abundant elements. All of the aforementioned alternatives have been available for many decades, and everyone in the relevant industries knows about them.

The only reason we don't use those alternatives already is price. For example, battery-electric cars and synthetic fuels are only competitive when oil costs $120/bbl or so.

When oil production enters its gradual terminal decline, the price of oil will shoot up and stay there. The economy will then gradually transition to now-cheaper alternatives. There is vastly more time than is required for the economy to transition to those alternatives (we have at least a century), and the economy has already begun transitioning to them, far earlier than required (car companies started designing plug-in vehicles at least a decade before any declines in oil production).

This kind of transition is something the economy does all the time. Companies are always evaluating alternatives and switching between them. Take ships as an example: the shipbuilding industry started off using sail, then switched to reciprocating steam engines burning coal, then switched to steam turbines burning coal, then switch to steam turbines burning oil, then switched to diesel engines burning oil. There have already been four major transitions in ship propulsion. There are many, many alternatives for the fifth transition. As another example, electricity production switched from hydroelectric, to oil, to coal, to nuclear and back, and now is switching from coal to gas in the US, because gas is now cheaper.

This notion that "there are no alternatives to oil" is just factually totally wrong.

It is also possible to use oil far more efficiently. When oil begins its very gradual decline and prices shoot up, people can buy cars such as Priuses which get twice the mileage. Shipping companies are already ordering ships that are more than twice as fuel-efficient. Cargo traffic can be switched from truck to rail which is 4x more efficient. Those things by themselves would compensate for declines in oil production for many decades.

Don't expect anything exciting or dramatic to happen to transportation networks. Granted, the price of oil may swing around wildly (because of inelasticity of demand), and there are recessions caused by many things. However, the actual supply of oil changes gradually over decades. Oil production won't enter a sustained decline for at least another decade, and the decline will be very gradual thereafter. There is a lot of time, and there are many alternatives.

Thursday, May 21, 2015

Energy decline theory is pseudoscience

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

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

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

If you guys want to start doing science, then you need to respond to criticism without badly misreading it, modify your theories in light of failed predictions, and make falsifiable, risky predictions which are confirmed by subsequent evidence. Those things would be the first steps toward actual science, but those things are just not happening here.
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Here is another post from the same thread:
George, you said:
"I'm talking about net free energy per capita, not raw energy produced... The numbers you quote do not take into account the amount of that energy it took to obtain that amount...So with slowing net energy increase and increasing total population the amount of usable energy for the economy per individual is in decline."

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

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

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

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

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

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

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

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

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Here is another post from the same thread:

Hi Harry,

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

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

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

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

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


The original conversation is here.