Monday, June 08, 2009

The Renewables Hump 4: EROEI Issues

As discussed in the last post in this series, the energy return on energy invested in renewable sources of energy will be a critical measure of whether it is possible to transition on a large scale from a fossil-fuel powered economy, or whether a global "powerdown" is eventually inevitable.  If EROEI, the net-energy ratio of a renewable energy source, is high--say 40:1--then it should be possible to rapidly transition our fossil-fuel driven economy to a renewable energy base, and to support ongoing economic growth that requires ever more energy.  If this ratio, however, is low--say 4:1--then at a minimum a transition to renewable energy will be extremely challenging, and may be effectively impossible.  As a result, the actual EROEI value of the various renewable energy options available to us is plainly critical.  There are lots of measures, lots of studies, and lots of figures floated about for the EROEI value of solar photovoltaics, wind turbines, etc.  There is not, however, a universally accepted methodology for calculating EROEI.  In fact, I don't think it's a stretch to say that EROEI figures are more likely to be marketing copy intended to secure venture capital than the result of rigorous inquiry.  

In my opinion, understanding the reality of our society's ability to transition to a renewable energy basis for our economy is one of, if not THE most important issue to be resolved.  If this transition is a realistic possibility, then it should be our society's primary and immediate focus.  In addition, improving our understanding of just how realistic such a societal transition is will help us understand the necessary rate of investment in renewables, as well as the nature and degree of the challenges to be accomplished.  If it is not realistic, then we must not waste what little surplus energy we have on a fools errand.  In addition, the present understanding that such a transition is unrealistic will allow us to both develop and focus on those societal options that are realistic.  Given the importance of accurate EROEI calculations, this post will discuss the current methodology issues with EROEI calculation and make recommendations for proceeding.

There are two generally used methods for calculating EROEI:  process-analysis and input-output analysis.  Both basically boil down to a brute-force accounting of energy used in various component processes of producing a renewable energy source, with the key differences being how wide a net is cast in counting energy inputs.  For example, is the diesel fuel required to deliver the turbine blades to the installation site accounted for?  What about the energy required to build the truck, divided by the percentage of that truck's useful life used in that delivery?  What about fraction of the energy required to build the machine tools used in the manufacture of that truck?  

This highlights the problem main problem with current system boundary calculations:  you can regress these energy inputs infinitely far (e.g. what about the energy used to grow the rice eaten by the merchant marine captain who piloted the ship that delivered the metal ores used in manufacturing the bolts that hold together the turbine tower), and it's fundamentally impossible to use a brute-force accounting methodology to account for all energy inputs.  If one hopes to use such a brute force approach (as used in both process-analysis and input-output analysis methods of EROEI calculation), then one must draw an artificial boundary for what is counted, and what is not.  Is it acceptable to artificially constrain the accounted system?  Clearly any artificial system boundary results in an artificially high EROEI, but how artificially high?  Does this long-tail of non-accounted-for system inputs make the resulting EROEI figure 1% too high?  10%?  100%?  10 times too high?  It's easy to dismiss, but how do we know if we are completely ignoring these long-tail energy inputs?  I think there's great cause for concern that our EROEI is significantly over-estimated.  For example, in a paper by Prof. Cutler Cleveland and others, the EROEI of wind-power is assessed by looking at over 100 separate EROEI studies.  These studies are broken down into process-analysis and input-output methodologies.  Prof. Cleveland notes that process-analysis generally draws a tighter system boundary than input-output analysis--that is, it counts fewer inputs.  In that survey, the process-analysis EROEI measurements for wind average 24:1, and the input-output measurements average 12:1.  That's a 100% difference based on where the artificial system boundary is drawn.  In light of that significant difference, how can we be sure that a truly inclusive system boundary wouldn't result in a further 100% (or more) decrease in the measured EROEI?  The take-away here is that we simply can't trust the accuracy of currently available EROEI calculations.  Further, it seems unreasonable to place any credence in any brute-force (e.g process-analysis or input-output analysis) approach to EROEI calculation.

How can we get around the accounting difficulties and arrive at an accurate EROEI calculation--a calculation that can do more than just provide a comparison between renewables, and can actually provide a self-contained assessment of whether a given technology can facilitate a societal energy-transition?  Odum has proposed what he calls an "Emergy" measurement that intends to account for a true EROEI measurement.  However, while Odum recognizes the importance of an inclusive calculation, Odum's methodology does nothing to address these accounting issues, and the end result is still a brute-force estimate that suffers from the same methodological failings as traditional EROEI calculations (even if it tends to arrive at lower EROEI figures).  

Rather than a brute-force approach that literally attempts to count all the energy inputs, I think it will be necessary to use a proxy to calculate "true" EROEI.  One methodology that I've proposed for this task is to use price as a proxy for EROEI.  I'll discuss briefly the theory of how this would work, as well as the clear problems with this approach.

It always struck me as fishy that various EROEI claims (especially for wind) result in an energy payback time of less than a year.  In other words, these figures suggest that it would only take a few months to pay back all the energy required to build a wind turbine, and then that wind turbine would go on generating electricity for decades more.  Why, then, didn't we already transition the vast majority of our energy base to wind if it's so efficient?  The answer is that the financial payback isn't nearly so rosy.  What accounts for the difference between the rapid energy payback (only months) and the much longer financial payback (often an order of magnitude or more longer)?  Intuitively, it seems that at least part of the answer is that the EROEI wasn't accounting for many inputs that were counted in the financial analysis.  For example, the financial analysis accounted for the high salaries--derivatives of the long years of training--that must be paid to the engineers, the financiers, the technicians, the managers, the materials scientists, etc. that are involved in the production of a wind turbine.  These long years of education certainly represent an energy input, but aren't accounted for in either process-analysis or input-output analysis EROEI calculations.  Similarly, the cost of raw materials represents, at least in theory, the full spectrum of energy, machinery, personnel, and support systems needed to extract, refine, transport, and market it--a great deal of which lies outside the traditional artificial system boundaries drawn in traditional EROEI calculations.  It seemed to me that the financial cost of a renewable was a better proxy for the energy inputs to that renewable than were any of the accepted EROEI calculation methodologies.  This is the core of what I've called "price-estimated EROEI," which uses financial cost as a proxy for energy cost.  The basic calculation assumes that the entire cost of a renewable is made up--eventually, if one regresses far enough--by energy, so divides that cost by an average energy cost to arrive at the energy input, and then compares that as a ratio to the amount of energy the renewable will produce over its lifetime.  Not surprisingly, this form of calculation tends to produce a far lower EROEI than any of the accepted EROEI methodologies.

Of course, there are acknowledged flaws with this price-estimated EROEI methodology.  Just to name a few, it's difficult to account for the differing values of the various types of input energies and the resulting output energy; there are market distortions, tax-incentive distortions, geopolitical distortions, etc.  That said, I think this type of proxy calculation at least directly addresses the need to calculate a truly inclusive EROEI, and may well be much closer to the "truth" of the required energy inputs than any traditional methodology.

In the next two post I'll address two other potential methods for measuring "true" EROEI:  asymptote location and worker-year calculation (as suggested by Neil Howes).  Then, I'll look at the EROEI of wind power and solar power from both traditional and proxy methods of calculation.


rks said...

I agree that price-estimated EROEI is the best starting point. Two points: (1) In a declining economy with wages dropping in real terms then EROEI improves, and so working out the proportion of wages in the cost becomes a crucial question;

(2) I suggest we look at the input to the economy as energy and expertise-weighted workers. In our fossil fuel world there is a shortage of workers and energy costs are driven into the ground. When we are short of energy then it is wages that will be driven into the ground. This will make the price-estimated mechanism exactly right.

Robert Martini said...
This comment has been removed by the author.
Robert Martini said...


As a college student, I will be doing some price based EROI analysis like that which you speak of during the next year. I think you make a good point of the financial cost accounting for much wider boundary energy inputs. Which I believe is one of the best bets for making a more realistic EROEI analysis, because the accounting system in already recorded and in place, the trick is just to figure out how to properly relate the financial input into units of energy.

I will would argue that the sociopolitical "distortions" you speak of are not to be worried about. For instance, in nature, life itself is an EROI process with a positive value. A wolfpack expends a certain amount of energy chasing reindeer and such, and gain a certain amount of energy from that consumption. However, you might find that a wolf pack uses more energy than would be expected from finding and taking down some game. Some amount of their excess energy would go to reproduction and defending their territory and recent kills from other wolves and predators. The cost of defending their territory and kills from other predators is not a distortion and should not be ignored, because without that energy, the wolf pack could not survive or perpetuate themselves.
Similarly, the political distortion of a financial subside for a wind turbine should simply be included as another energy input. because some positive EROEI energy process out there is producing a surplus in order to make that subside available for wind power.

The interesting thing about EROI is, IMO, that averages should be avoided as much as possible. because the EROI is such a process/system dependent figure. This means that if you were not to include the wind turbine subside, the entire process would change through various feedback loops. For example, the lack of subside might force the wind turbine producer to switch to heavier more inexpensive materials which impact the energy return or they may go out of business all-together. If the ladder case is true, then it would be unwise to imagine the process without the subside and write off the political whim of a subside as a some sort of natural distortion. Because, that distortion not only affects the process's energy inputs but also the outputs and therefore is viability.

The other thing I see, that might also be hard to do, is to make predictions about such a complex chaotic system over time. There are a lot of things that are not constant and subject to systemic shocks, like the value of the dollar for instance. The butterfly effect is in full swing, with the more complex processes added the more "possible butterflies" you have, which I imagine would make the predictive abilities of this type of analysis, probably similar to trying to find a farm in a country, to find a haystack, so that you can find the needle you want.

Great post Jeff! And don't regard my comments as criticism, I am the first to admit I am probably overlooking or misconstruing something. just some thoughts to add to the discussion.

Garrai Eoin said...

Looking forward to it.

Why no EROEI analysis of nuclear energy?

I just got back from Europe and they've got their act together w/ no-incident nuclear. And, so does our U.S. Navy. Just a thought.

TH in SoC said...

It seems to me that using price as a proxy measure of EROEI also lends greater weight to the conclusion that the world has passed the geologic peak of oil production. Sooner or later, given the exhaustion of oil reservoirs, the price of extracting the marginal barrel must exceed the revenues generated by that marginal barrel. Whether it was caused by the collapse in consumers' ability to pay for expensive petroleum or the collapse of credit to oil producers, it seems that we have passed the point where EROEI goes negative for many of the most exotic sources of oil.

Kal said...

It really makes little difference whether the true ratio is 12:1 or 24:1. What mattes is consistency of application across compared options.

However, I believe the price-esitmated basis is the worst possible. Inevitably the result of the calculation will be compared with oil and nuclear, neither of which is priced to account for all, or even most, of the costs.

For example, how do you figure in the price of our two wars in Iraq? Clearly much of the cost of these should have been "paid for at the pump", but of course we know that they were not.

With nuclear the obvious example is the long tail of storage and dicomissioning.

But given the way we do financial accounting, wind pays quite a lot of these costs.

Rice Farmer said...

This approach seems to make more sense than the others. Just the examples of various costs you have listed is quite striking, all the more so because they are paid for with fossil fuels. Obviously the low density of real-time solar energy would be unable to cover all those costs. Which again leads us back to the need for fossil fuels.

I look forward to the next installment.

Quesalid said...

this one could be helpful

jagged ben said...

Jeff, thanks for the seriousness with which you're interrogating this issue.

I agree that price-as-proxy-for-energy can serve as a useful reality check against ERoEI calculations. For example, if renewables didn't have ANY financial payback, over any period, that should be highly worrisome for those who say it has positive energy payback; it would suggest they must have done some calculations wrong. But beyond that, it's clear that the price-as-proxy method runs into categorical problems when comes to being quantitatively accurate.

For example, just look at the price of oil in the past year (let alone farther into the past). What price of oil is one supposed to use as a proxy for the energy it contains? It is clear that price is very contingent. Not only that, but it is contingent on a whole variety of factors that are not thermodynamically based; markets, politics, warfare, and social change, to name the most pertinent.

To put it another way, it seems perfectly possible that the value of renewables could increase in the future while the costs do not keep pace (because, let's say, the factories to make turbines and panels were built in financially better times). This would decrease the payback period for renewables, even while the physics of the technology remains unchanged. Or, the opposite could happen. Either way, the price-as-proxy method now suggests a different ERoEI, even though the technology will not have physically changed. That's pretty silly.

It seems to me that the whole reason for talking about ERoEI is to make predictions about the future economic viability of a technology. However, if you take as your data the current or past economic viability of a technology, you are begging the question. That's why I think the brute force calculations are the better starting point, despite their limitations. (At least the limitations can be rather precisely agreed upon.) Without these thermodynamically based calculations, the ERoEI concept doesn't actually add anything practical to our knowledge, and one is simply left following the market herd. ERoEI will either prove to be a useful predictor of economics, or it won't. But in order to be potentially predictive and not circular, it has to begin with data that isn't economic.

Jeff Vail said...

OK, back from a bit of vacation, I'll try to respond to comments in order:


Wages definitely are a sticking point for the price-estimated EROEI methodology. Also, can we say that the lower wages in developing nations are completely the result of the lower energy intensity of living in those nations? Probably not. (As I'll discuss more belwo), I don't think the price-estimate theory can serve as a perfect mechanism to measure EROEI (in part due to issues like wage parity), but I do agree that it is a good starting point, and probably best serves a role as a reality check...

Jeff Vail said...


I agree that socio-political distortions are omnipresent, but I do worry that it is possible that one form of energy (e.g. oil which is very unevenly distributed and has very exposed supply lines) is systematically more exposed to such distortions than, say, passive solar design (as perhaps the least socio-politically vulnerable "source" of energy).

I also agree that issues such as subsidies create problems, but that we can't easily remove them because of the feedback loops they generate. I don't have any solutions to this problem that can be realistically applied (my only idea is the desert island thought-experiment, but that 1) only vaidates that EROEI is greater than or less than 1:1, and isn't exactly easy to implement in the real world...)

rks said...

Perfection will only apply in a theoretical future where wages are driven to the floor (as they were before fossil fuels). During the fossil fuel era, including now, it is energy prices that have been driven to the floor, but still price is a better starting point for discussion than back of the envelope calculations.

Jeff Vail said...


I do hope to get to an EROEI analysis of nuclear energy to accompany my analysis of solar and wind (also hope to approach geothermal and tidal). However, I'm pressing forward with the series just looking at wind and solar first so I can get through it, and leaving those elements that will require more initial research to later.

Also, I don't see nuclear as a true renewable--more of a late-peaking, low-carbon fossil fuel source. There's been some good analysis of peak-uranium on The Oil Drum, and the peak date for Uranium may actually be quite soon (2025-ish) if we rapidly scale up our nuclear fuel use. Additionally, as pointed out by a comment above, EROEI is less accurate the more it involves unaccoutned-for externalities. Nuclear has (arguably) the greatest of these, since we really have no idea 1) what the actual carbon footprint is, or 2) how to dispose of the waste in perpetuity. All that said, it still requires analysis...

Jeff Vail said...


I think we'll see the viability of renewables in general gradually decline in the coming years as we mover further past peak oil. In part, I think it's as you point out--as societal EROEI as a whole declines, the cost of the marginal BOe increases, and the cost (both energy and financial) of operating the whole system (e.g. the unaccounted for energy inputs in renewables that get missed by using artificial system boundaries for EROEI calculations) goes up. More specifically, we're still using largely legacy equipment (mines, machinery, infrastructure, skilled personnel, etc.) that were "produced" in an era of cheap, high-EROEI energy. As a result, the energy and financial cost of these inputs to current renewables production is relatively low. Increasingly, though, we'll need to replace these with substitutes that were produced in the current era of much more expensive (energy and financially) energy. As a result, the EROEI for the exact same process will actually increase over time...

Jeff Vail said...


I disagree that it makes little difference whether the EROEI is 12:1 or 24:1. While I agree that consistency of application is key when creating a comparative metric (not the point of this series, though certainly important in its own right), the "true" EROEI is critical in evaluating whether or not a given plan to transition our society to a renewable energy base is realistic or not. For example, a "true" EROEI of 4:1 vs. 20:1 makes a huge difference in whether it is fundamentally possible to meet the target I laid out in my previous post and mitigate peak oil...

I agree that there are serious problems in the price-estimated EROEI methodology posed by unaccounted for externalities, as you point out. I think that, to a large extent, these can be addressed by comparing coal-generated electricity to wind/solar-generated electricity. These two sources are quite similar in geopolitical and infrastructure (grid) requirements. The key difference, of course, is that coal-fired electricity doesn't account for its carbon-externality whereas wind and solar (arguably) do. However, for the purpose of comparing energy inputs, in an envronment where this externality doesn't yet create a financial difference (at least in the US, due to lack of any carbon tax/cap), the result should still be valuable as an EROEI measure. There are still unequal subsidy issues to be worked out, but I think these are far less thorny than the accounting-impossibility of a boundary-less input/output accounting.

Also worth pointing out that there are interesting global-warming implications of a near-term scale-up of renewable energy. Take either wind or solar: the vast majority of the energy used to produce this generating capacity will still come from fossil fuels. The result will actually be a near-term spike in demand for fossil fuels. There's been very little study (to my knowledege) about the importance of this timing aspect of carbon output: is it better to spike carbon output now in order to achive a long-term decline, or to achieve immedaite, if smaller overall, cuts in output?

Jeff Vail said...


I think Hall's take on the minimum EROEI for society (of a given energy source) is very illuminating--particularly in why he reaches 3:1 instead of the (superficially obvious) 1:1.

First, as Hall points out, the 3:1 is actually "that to deliver one barrel of fuel to the
final consumer and to use it requires about three barrels to be extracted from the ground, with two
being used indirectly." That's actually quite different than his title, which is the minimum EROEI for a sustainable society. Additionally, he's only counting the "10%" of US society that's actively involved in producing energy in this accounting--as I've mentioned elsewhere, it's very difficult to separate any part of our society as unnecessary to the production of energy (see Lenin & Lohan).

Logically, if we accept zero boundaries and a non-growing economy (as measured by energy consumption), the EROEI seems fundamentally fixed at 1:1. The 3:1 measure seems to me to present a more pressing advantage: it pays itself off faster. If you take a 1:1 EROEI energy resource that lasts 10 years, then you'd need to invest X amount of energy, and you'd never get it back, because it would take the full useful lifespan of 10 years to build the replacement necessary to maintain stability of energy production--it would be a self-licking ice cream cone. So EROEI must be some level greater than 1:1 make sense on any level. Perhaps 3:1 is the right measure? This question alone seems like something that deserves a post...

Jeff Vail said...

Jagged Ben:

Good points on the difficulty of including economic indicators in the equation. I think, as you point out, the price-estimated theory is best as a reality-check. Can it provide an accurate measure of "true" EROEI? I don't know. However, I think it can tell us if a given renewable technology is better-than or worse-than the current (largely fossil fuel) societal average. That's probably a good go/no-go indicator.

I agree as well with your concerns about the use of oil--low elasticity fo supply, highly vulnerable to geopolitical disruptions--as a comparison for price-estimated EROEI. Especially when it comes to evaluating electricity-producing renewables like wind and solar, using coal as a comparable is probably much better. I think it could lead to quite accurate comparsions. Additionally, some of the problems introduced by using economic, as opposed to thermodynamic data, can be controlled by using projects from the same historical dates. For example, comparing the cost per KWh of a coal-plant brought online in 2007 and a wind farm brough online in 2007 will control for many (though not all) of the economic oscillations... the biggest economic factor remaining is the significant difference between the value of base-load power and peaking power production--something that will only be accentuated as renewables like wind and solar produce an increasing proportion of our power supply...

Rice Farmer said...

Jeff, your comment on legacy equipment was of great interest to me, as it gets close to the heart of my own position on the future viability of renewables. So I hope you'll go into this matter in a future post.

Al Eggen said...

An interesting approach though I'm not convinced that you can find realistic and consistent ways to go between $ and energy. How do you arrive at an energy price when converting the cost of a renewable back into energy? I assume the lifetime O&M costs also would have to be loaded into a renewable's cost. One problem with any of these calculations is that not all forms of energy are created equal. You have 2nd law effects (eg electrical vs chemical) and use effects (eg motor fuel vs lighting). If you throw nuclear into the mix how do you account for (subsidized) insurance costs?

I think you previously made the point that a critical test is how rapidly you pay back the energy invested and that's not necessarily tied to the EROEI. eg PV has a very long life, with very modest main maintenance requirements, so the payback period will be very long compared to shorter life systems with the same EROEI. Another limiting factor on renewables is materials availability. For example, a lot of technologies depend on rare earth metals which are not exactly in unlimited supply. Theoretically, you could include it in the investment by projecting price increases as supply dwindles – but really, why bother. Just use material limitations as a separate test of what's possible.

Actually, I think it's gut obvious that an extension of business as usual into the future by shifting to renewable energy is not possible for many reasons. For example, the interrelationships of energy with food, water, etc, etc, and especially population pressures (something I've started to talk about in my blog). However, I do believe that in any case realistic EROEI numbers (and getting people to pay attention to them) are needed for evaluating programs and proposals – especially some of the wildly optimistic stuff out there. Certainly the whole corn ethanol debacle could have been avoided even if just the optimistic EROEIs had been take seriously.

Roger Brown said...

Here is a calculation concerning the energy cost of transitioning to renewables. I define the following variables:

C0 : Current yearly net energy supply from depleting resources

L : Length of time in years over which C0 linearly descends to zero. Yes I know this is probably not a realistic assumption. So sue me.

f×C0 : Target yearly net energy supply at the end of L years. If f<1 then we are undergoing energy descent.

P : Average energy payback time in years of new renewable installations.

µ: Energy utilization rate of renewable generators. µ is the fraction of the life time energy produced by a renewble generator which is left over after the energy used in manufacturing and installation is subtracted out. If the generator produces constant energy for LR years then µ=(LR-P)/LR. In case anyone is interested µ=(EROEI-1)/EROEI.

In order to produce f×C0 units of net energy per year an over capacity will be required since in long term equilibrium we must replace worn out generators on an ongoing basis. The total capacity that needs to be installed to produce f×C0 units of net energy per year is f×C0/µ.

I will assume that this capacity is installed at a uniform rate over the L years of depletion of the conventional resources. That is we install (f×C0)/(µ×L) units of new renewable generation each year. The energy cost of this installation is (P×f×C0)/(µ×L). If we divide this number by C0 we get the energy cost as a fraction of the intial yearly supply of net energy from depleting resources:

Fractional Energy Cost = (P×f)/(µ×L)

To give a specific example suppose P=4 years, f=1, L=30 years and µ=26/30=0.867 (This value of µ corresponds to constant energy output over a lifetime of 30 years.) Plugging in the numbers we find:

Fractional Energy Cost = 4/26=0.154

Dave Kimble said...

I have written an article called "The energy dynamics of energy production" that deals with this very subject.

It is not so wordy and descriptive as your article, but gets down to the calculations more quickly (contrast the lawyer with the mathematician :-)

The key is to use a spreadsheet to lay out the history of a single year's worth of production - its EIUF (Energy Input Up Front) and the following ER, and then to repeat that for each year with a growth factor representing the increase in production. These histories can then be totalled for each year, and the results plotted in a chart.

The results will be counter-intuitive for some, but you are right that the green vision of PV, which I once championed myself, is a myth. We will get half way there and then the remaining fossil fuels willbe too precious to spend on anything other than keeping the lights on.

Obviously there is a different history for each technology, and PV is simple because all the EI is EIUF, whereas with nuclear, a lot of EI is spent on making fuel rods and in the decommissioning phase.

Anyway, have a look at it, and I look forward to you getting on to the serious calculations.

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