Sunday, March 5, 2017

Dr Charles Hall is still totally wrong about EROI

Recently I saw an article on 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.




[3] . 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.


  1. I've been frustrated by the low quality of Hall's work for quite some time. One big example: he still uses data for wind and solar EROEI from 20 years ago. The wind turbines used in the studies he includes are much smaller than today's turbines. His charts show a very strong correlation between turbine size and EROEI, so there's an obvious need to update his meta-analysis.

    As you note, the problems you've identified are obvious, and don't need peer review or field data: they're just basic, logical problems.

    1. Hi Nick G,

      One problem is the severe cherry-picking which occurs inside the energy decline movement. Inside that movement, they treat the works of Charles Hall and a few others as scientific and essentially factual. However, there are many researchers who've looked in to net energy. The others haven't been warning about the imminent collapse of civilization repeatedly since the 1970s/1980s.

      Another important point which you mentioned: "there's an obvious need to update his meta-analysis". The EROI of renewables has been improving. For those who remember, Richard Heinberg warned back in the 2000s (using data which was already outdated then) that solar PV had an EROI of only 1, so presumably would be useless. A lot has changed since then.

      The EROI of renewables CONTINUES to improve. I read in a paper recently (sorry for the missing reference) that the payback time for solar PV will drop to 6 months if trends continue. That implies an EROI of ~60, which is higher than any fossil fuels have ever been for generating electricity.

      -Tom S

    2. > the payback time for solar PV will drop to 6 months if trends continue. That implies an EROI of ~60, which is higher than any fossil fuels have ever been for generating electricity.

      ...Then why isn't any country solar-powered?

    3. Hitssquad:

      Presumably because of intermittentcy. Solar panels are far, far cheaper than batteries.

      Electricity from pv costs less than $0.05/kwh in some desert areas. However, if you put that electricity in a battery and then take it back out, the price increases by about 5x to be $0.25/kwh, which is not competitive. The problem is price of storage, not EROI.

    4. Tom:

      Okay. Thanks. Are you sure EROI doesn't drop below 1 when sufficient storage is added to make it baseload at a single constant level year-round (say, 10 gigawatts for a single solar power plant),, and when it's never allowed to rise above its minimum output level? The reverberating knock-on effects of running every country on the planet on battery-backed single-constant-output solar might prove to be unsustainable. In other words, the inability to maintain and regenerate the power plants themselves, and a price per kWh approaching infinity.

      We might imagine that additional industries would become seasonal. Aluminum production, for example, might shut down at any given factory for 6 months every year, and switch between factories in the northern hemisphere and factories in the southern hemisphere.

      My theory, of course, is that any modern society would collapse if it tried to run on wind/solar, and that the definite reason would be diffuseness of the fuel. According to my theory, intermittency could be dealt with if the fuel were dense enough.

  2. Thanks for your article, Tom,

    I think this post illustrates some important points. Have you read any of Ugo Bardi’s writing (he has a blog called "Cassandra's legacy")? I think you should make your work known to him.

    I still think that your “cost of net energy” observation is a good one, and captures some elements that EROI fails to capture. However, it in turn has its limits.

    For example, I think in a prior post, you mentioned that it doesn’t matter if a device has an EROI of 1.1, as long as it is cheap to manufacture (because we can then make millions/billions of them). This is true in an academic sense, but not true in others. The reason is that the cost of net energy of a particular device will change as more of them are made.

    The first solar mono-crystalline PV panel was incredibly expensive to make. The 1000000th is cheaper, because our manufacturing process becomes better with economy of scale. However, at some point we will start running out of the resources we need to make them and they will start to become more expensive again. At some point, additional units will become unavailable at any price, because all the needed resources are already contained in PV panels.

    Clearly, that’s simplistic, because chemistries and ingredients can change, but the point remains that eventually we’ll start to run out of the needed raw materials. I think that your “cost of net energy” argument fails to consider this. Interestingly, EROI somewhat captures this, because as required resources become harder to get, the EROI goes down.

    So, while EROI doesn’t capture all of the complexity, neither does yours. They both capture elements of reality that the other fails to capture. Neither are perfect, and both are useful (since they allow us to think about different aspects of the economic-energy system).

    Cheers, Angus

  3. Hi Angus,

    "However, at some point we will start running out of the resources we need to make them and they will start to become more expensive again."

    I'm not disputing that. I wasn't implying that the EROI of all solar panels has to be the same.

    "At some point, additional units will become unavailable at any price, because all the needed resources are already contained in PV panels."

    I think the limiting factor would be running out of prime desert land to put solar panels. Solar panels can be made out of only silicon, aluminum, and trace amounts of a dopant. There is enough of those materials in the earth's crust to cover the entire terrestrial landmass many times over before running out of materials or coming anywhere close to it.

    "I think that your "cost of net energy" argument fails to consider this."

    The cost of net energy would include that.

    "They both capture elements of reality that the other fails to capture."

    The problems I identified in Hall's papers are mathematical or logical errors. It's not just a matter of leaving things out; all models do that. The problem was mathematical error. A correct analysis would yield VERY different answers.

    -Tom S

    1. Also:

      "Neither are perfect, and both are useful"

      Hall's (and Odum's) model implied declining net energy and a gradual reversion to a semi-medieval mode of life, starting in the late 1970s and early 1980s. What happened was the exact opposite. There was a huge INCREASE in net energy during that time. The reason their models failed was because of mathematical and logical errors.

      Hall's and Odum's ideas on these matters are not useful. Their models contain mathematical and logical errors which completely invalidate their conclusions.
      It would be one thing if their models simply omitted some minor factors. It's okay if models leave things out, or contain simplifications of various kinds. However, if models contain mistakes, and they predict the exact OPPOSITE of what happens, then it's a serious problem. In that case, the model is not even good as an estimate.

      Perhaps Hall and Odum raised some interested concerns which inspired ideas. Perhaps Odum pointed the way toward doing net energy analysis, which was useful. His specific analysis, however, was just incorrect.

      -Tom S

    2. Hi Tom,

      I'm not defending Hall/Odum -- I've heard of them but am not familiar with their work. I'm discussing the idea of EROI and cost-net-energy in general. (As I've said to you recently, I like your idea of the cost of net energy, but have always felt there is something it fails to capture)

      I understand and agree that the cost of net energy would increase as required resources become scarce. The problem, is that you are trying to use it as some sort of indicator tool and are saying that since the cost of net energy for PV is low, we can therefore rely on PV into the future as a substitute for fossil energy.

      Conversely, (whether it is accurate or not, or is even possible to estimate) EROI at least tries to reconcile observed supplies to an underlying physical reality (the total amount of recoverable material). That is why I make the point that both metrics are useful, but they tell different things.

      A couple of thoughts about your replies:
      "Solar panels can be made out of only silicon, aluminum, and trace amounts of a dopant."
      I think more is required than just silicon and aluminium. Your example produces no power at night.

      Cheers, Angus

  4. Hi Angus,

    "Conversely, (whether it is accurate or not, or is even possible to estimate) EROI at least tries to reconcile observed supplies to an underlying physical reality (the total amount of recoverable material)."

    I don't think EROI does that. The EROI estimates I've read do not address how much recoverable material there is for building the power plants.

    If we include how much recoverable material there is, then the EROI for solar PV would be vastly higher than the EROI for any fossil fuel.

    "I think more is required than just silicon and aluminium. Your example produces no power at night."

    Sure, but I was talking about the materials needed to make the solar panels. If we're talking about batteries/storage also, then there are extremely abundant materials for that too. For example, there is a company called "1414 degrees" that uses silicon as a storage medium by heating it up to 1414 C then using the latent heat of melting to drive a turbine. I'm using silicon as an example (again) because it's the most abundant element in the earth's crust by a wide margin except oxygen.

    -Tom S

  5. California Valley Solar Ranch is rated at 250 MW, and only produces an average of 37 MW (15%) in December. That's before factoring in storage inefficiencies.

  6. Great post,
    I did some Excel simulation on EROEI that proves that it is not a limitating factor.

    So the problem behind "gross" energy is essentially scalability of our thechnology: how much "energy extractors" can me make and how much can we extract with them.

    We know that, unless technology improves (and it does, but it does not implies that it improves in energy extraction) ressources are limited.

    How can we evaluate depletion ? reserves and ressources are notoriously hard to evaluate.
    Price volatility ? price elasticity ?
    Anything else ?


    1. Hi Yoananda,

      I'm glad somebody else reached the same result using an excel spreadsheet. It's certainly always possible I am missing something.

      I don't think there are any resource constraints which would limit our deployment of solar cells. It is possible to make pv cells out of only silicon, aluminum, and a dopant such as boron, which are practically inexhaustible.

      Solar pv is scalable as far as we want to scale it. That's one reason I called this blog "bountiful energy". We have vastly more energy available to us than we use now, and will have as the world lasts.

  7. "It is possible to make pv cells out of only silicon, aluminum, and a dopant such as boron..."

    This is manifestly untrue, as it requires enormous quantities of diesel fuel and heavy machinery to extract and process these materials. It requires good asphalt roads upon which to transport them. It requires sophisticated precision manufacturing structures which are not made out of sticks or cob but concrete, an extremely energy-intensive material.

    And so forth and so on.

    Your facile reductionism isn't limited to just obtain the materials you regard as necessary.. "Bountiful energy" also means bountiful pollution, especially in the form of waste heat, and we are already at or beyond planetary limits for the absorption of the waste of industrial civilization. In none of the cornucopian energy proposals I have come across is this failing addressed (because it cannot be).

    The Limits to Growth folks were systems thinkers.

    1. Hi Cynthia,

      "This is manifestly untrue, as it requires enormous quantities of diesel fuel and heavy machinery to extract and process these materials. It requires good asphalt roads upon which to transport them."

      You're misinterpreting what you read. In that sentence, I was referring to the materials which solar PV modules are made out of.

      Furthermore, your point is incorrect. Silicon PV modules are overwhelmingly made from ELECTRICITY since that is by far the largest energy input. Although some diesel fuel is required, in order to transport the panels to the installation site, the amount of energy required from diesel fuel is negligible (not "enormous") compared to the energy returned from the solar panels. Diesel fuel used for installation represents less than 1% of the energy returned from the panels over their lifetime.

      It is quite feasible to manufacture that small amount of hydrocarbon fuel using renewable electricity. The process to do so is chemically very simple, and has been known since the early 20th century, and requires only water, air, and renewable electricity.

      It is extremely straightforward and obvious to install the first generation of solar panels using diesel from the ground, then to manufacture hydrocarbons using those solar panels. That is a very basic asset-allocation problem, of a kind which is routinely carried out, all the time, in market economies.

      "Bountiful energy also means bountiful pollution, especially in the form of waste heat"

      Sure, but you're changing the topic. Pollution is certainly a problem, but we're still never running out of energy or materials, and this "energy decline" theory and movement is still totally wrong.

      Furthermore, solar cells and windmills emit no pollution during their operation. The materials used to make them can easily be recycled. Although the devices which use the renewable electricity do emit waste heat, that heat is negligible compared to global warming from CO2:

      "[From] The contribution of waste heat to the global climate is 0.028 W/m2. In contrast, the contribution from human greenhouse gases is 2.9 W/m2. Greenhouse warming is adding about 100 times more heat to our climate than waste heat."

      As a result, waste heat is minor compared to global warming from CO2.

      "The Limits to Growth folks were systems thinkers."

      Limits to growth was a mess which was refuted decades ago.

      -Tom S

  8. >Limits to growth was a mess which was refuted decades ago.

    Could you go into this in a bit of detail, perhaps on a blog post?

    1. Hi jimofwales,

      I'd like to go into that in more detail. At present, however, I have a backlog of things which I wish to write. I don't post to this blog too often, so I have a backlog already. I may eventually post something about Limits to Growth, but not in the imminent future.

      -Tom S

  9. Tom your comparisons of EROI showing a purported 14% difference aren't correct. You are not comparing the net energy of one unit of input energy at 15:1 EROI to the net energy of one unit of input energy at 5:1 EROI, you are comparing 1/5 of a unit of input energy to 1/15 of a unit of input energy...

    Net Energy is Gross (15) - Input (1) = 14 units net energy for the EROI 15:1 example, vs Gross (5) - Input (1) = 4 units net energy for the EROI 5:1. So the ratio of net energy in that example is 3.5 times the other, 350% different.

    Best stick to economics