Today's installment will address two of the potential proxies for calculating "true" EROEI (meaning a calculation with no artificial system boundary) for renewable energy sources. Last week's post discussed the price-estimated EROEI theory, and this week I'll discuss two additional potential proxies. Up front, it's important to note that, much like the price-estimated theory, these proxies have significant weaknesses. I don't think either is yet ready for use, but talking through them helps to better define the issues surrounding proxy-calculation of EROEI, and may result in readers figuring out how we CAN make ideas like these work...

The first proxy I'll discuss is--for lack of a better name--the asymptote location model. I'll start by noting that I think this model is still too incomplete to be workable. I include it here because I think it may be fertile ground for someone to develop. Here's the basic concept: under traditional EROEI calculations, there is an artificial system boundary drawn at some point, and the result is an artificially high EROEI (because those energy inputs outside that artificial boundary are not counted). My theory starts with the assumption that, as that system boundary is expanded, the resulting EROEI will approach some theoretical "true" EROEI that lies at an infinite, but uncomputable, system boundary. This is a classic example of an asymptote. If we can plot the degree of system boundary expansion on the Y axis, and the resulting EROEI value on the X axis, then X will approach the true EROEI value as Y approaches infinity (unbounded EROEI calculation). This, in theory, will allow us to fit an equation to a few points (which can be calculated) and deduce the location of the asymptote that represents "true" EROEI without actually needing to perform the impossible calculation of the unbounded EROEI analysis. The problem, of course, is that while it's quite possible to fit that X-value (EROEI) into a meaningful scale, but the same can't quite so easily be said about the Y-value. What does a "5" on the Y-axis (degree of system boundary expansion) mean compared to a "10"? What is the scale? Unless an 8 is double a 4 is double a 2 in some meaningful sense, the equation fit to locate the asymptote will provide a meaningless result. Can we create a meaningful scale for the Y-axis? Maybe. It seems possible to use the number of steps of regression (as in 1=just the energy used at the plant and installation, 2= 1 plus the energy used to create everything in the plant/installation, etc.) as a scale, but this is just speculation. This might be fertile ground for someone looking to develop the field of EROEI analysis, but it's not ready for prime-time at this point. I'm very interested in any ideas readers may have about turning this rough idea into a workable proxy measurement.

Worker-year model:

Neil Howes sent me a a very interesting calculation for wind energy that used the ratio of worker-years involved in the wind industry to total US worker-years as a means to determine what portion of total US energy consumption was required as input to US-produced wind capacity. His EROEI measurement came out at over 100:1, and I think significantly overestimates the true ratio because, like most EROEI calculations, it artificially limited the system boundary quite severely (for example, it based its worker-year number on a DOE study that estimated the number of wind-energy jobs that may be created for a set amount of production--this didn't include all the supporting industry jobs that would be created in mining, transportation, marketing, finance, training, etc.). Additionally, I think that the brute-force methods for calculating EROEI (input/output and process analysis) necessarily represent an upper bound to the "true" EROEI--they accurately count energy output, and are universally low (to an unknown extent) on their accounting for energy input. As a result, any proxy that estimates higher than the brute-force approach must be reconsidered.

The far more significant inaccuracy is that this methodology assumes a uniformity of the very EROEI it attempts to measure. The measurement is only accurate IF every worker-year can act as a proxy for an equal amount of US annual energy consumption--it can't. Instead, some workers (and their associated industrial/commercial processes) represent far more energy than others. This lays bare the problem with this methodology: it would come back with the same energy input for 1000 worker-years on a 50:1 EROEI oil well as for 1000 worker-years on a 3:1 EROEI solar plant, even where the energy generation capacity of each is the same--the energy input is not necessarily the same. I would argue that the energy input could be seen as the same IF we took a boundary-less approach to attributing worker-years, but then we get back to our overarching accounting problem.

I think that these two proxy-methodologies outlined above both present some potential for development, but neither is yet ready for actual use. They both present novel approaches to the proxy-calculation of EROEI, but seem to me unacceptably ill-defined--both when compared to brute-force EROEI calculations and when compared to the price-estimated theory of proxy-EROEI calculation.

Going forward, I'll look at both solar and wind, and I'll present a survey of traditional EROEI calculations as well as proxy calculations based on the price-estimated model. If readers have any thoughts on other proxy-methodologies to use (or how to make the asymptote or worker-year methods work), please let me know.

## 40 comments:

Jeff,

If we are using EROEI to determine how quickly we can replace FF with renewable or nuclear energy, we need not include sunken costs for roads, steel mills etc, just energy used tio maintain or replace this infrastructure. This may allow us to set narrower boundaries using life cycle analysis.

Jeff,

For wind turbines, components are manufactured in many states and imported from other OECD countries. States in the US vary greatly in energy/GDP even allowing for variations in climate and energy intensive industries, so NY and California are about 60% the national average and some SE states(Alabama, Louisiana) 160-200% national average. When comparing with EU most member countries are more in line with the lower US states.

Perhaps it makes more sense in trying to determine a value for labor to ignore the few outlier states and countries ( very high energy/GDP) in calculating a value of kWh/$GDP, and use a value more typical of where turbines are manufactured and assembled.

A value of 7.2MJ/$GDP would be in the middle of many EU countries and US states(CA is 6.2MJ/$GDP).

Whether we include sunken costs or not is of interest when calculating EROEI, but we need to realize that maintaining FF-built infrastructure will not be possible with renewables. This is obvious from the fact that, even though we still have access to FF at what are quite honestly still very low prices (considering the big bang for the buck), infrastructure is crumbling throughout the developed world, and everywhere national and local governments are falling behind on maintenance and replacement.

I'm not saying that calculating EROEI is meaningless -- far from it. We should build as much renewable capacity now while the window of opportunity is still open, and investors will want to know how soon they can expect payback.

Hey Jeff --

I may be jumping the gun, but I keep having the same thought as I read each of these installments... when dealing with EROEI, when do we introduce a variable addressing environmental variations? In other words, most solar and wind installations currently are in areas that have prime conditions... at what point and to what degree does EROEI drop as we scale up and use less prime "real estate"?

Janene

Robert Martini:

If you think Goedel's theorems have no implications outside of number theory, I'd seriously consider to read up on the subject again.

好秘书 我爱皮肤 中国公文网components are manufactured in many states and imported from

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