Wednesday, December 7, 2011

The Efficiency Fallacy

One of the most common arguments that I hear against different types of alternative energy is that the respective technologies are inefficient. Solar and wind power are two of the most common subjects to receive this treatment. The argument implies that the low efficiency of many renewable energy processes when compared with fossil fuel processes are an indication of a correspondingly low technical maturity, or still worse, of outright impracticality.

That asinine arguments like this gain traction is a result of efficiency numbers being taken out of context and used to, in effect, compare apples to oranges in more ways than one. Efficiency measures can only be used as a basis for judging technology in the narrowest of cases. Unfortunately, I have yet to find a single case where efficiency is correctly cited in a debate about renewable energy, whether for or against.

This uniform lack of understanding and the sheer ubiquity of the efficiency fallacy makes it one of the most dangerous red herrings in arguments on renewable energy.

The definition of a generic "efficiency" term is simple. It is the energy output from an energy input. However, what is critical in any discussion of efficiency is what the efficiency is comparing. In any measure of efficiency of a process, there is a significant amount of information lost by simply giving the percentage. In no particular order, these include:

  • The part of the process being measured
  • The type of energy input and the type of energy output
  • The quality and gradient of the resource inputs and outputs
  • Any information about the sub-processes within the overall process being measured.
The removal of an efficiency figure from its context amounts to destroying enough information as to render the measurement meaningless. Let us take the example of a hydroelectric dam. If I told you that a hydroelectric dam was 90% efficient, then there are several assumptions we have to make. First, we have to assume (safely, in this case) that the input energy is provided by gravitional potential. Second, we have to assume that this efficiency encompasses the entire machine, including the spillway, turbine, and alternator, and possibly the transmission line. Third, we have to assume the output is electricity.

Given this efficiency number, what does it tell us? If we do not know the quality of the resource, we can't say much. Are we talking about the hundreds of feet of hydraulic head gotten from Hoover dam, or the few feet of head gotten from a three-foot run-of-river system? One of these yields water of much higher energy than the other and consequently allows machines to harvest energy from it more efficiently in a manner unrelated to the mechanical design of the system.

The overall efficiency tells us nothing about the technical sophistication of the system. A dam with a primitive spillway, crude turbine but 300 feet of potential difference to work with would still have higher efficiency than some of the most modern turbines that work with 10 to 15 feet of head. The dam might have a clogged spillway or a bad turbine, or a middling one of both. We can't tell from a single number.

Given these facts, it should be obvious that any decent comparison of efficiency can only be done by varying one of the factors I listed above. To compare the technical maturity of one dam system to another (assuming, of course, that you are designing for greater efficiency alone), you would have to give them the exact same potential energy to work with, measure over the entire system, and make sure that both dams are generating electricity, rather than shaft work.

Imagine extending this comparison to a gasoline engine. A gasoline engine is a heat engine that burns fuel to produce hot gases and outputs work. Obviously, this is a completely different type of machine with a different input and output, so immediately we should know that efficiency can only be properly compared between two machines of the same type with the same heat inputs. Why would it make sense for me to tout the superior efficiency of my space heater compared to your car engine, for example?

Even barring these observations, we should be intuitively suspicious of any claims of superior efficiency, for example, because work is easier to produce from heat than electricity is. In order to generate electricity from heat (barring thermoelectric materials, which are rare and nowhere near prime-time), one needs to use a heat engine to convert the heat into work, and then a generator to convert the work into electricity. On the other hand, a dam needs only capture the work and use that work to drive the generator. Heat as an energy source is fundamentally disadvantaged compared to work.
Similarly, if we hooked up our engine to a generator to produce electricity, it still would be meaningless to say the engine-generator is more or less efficient than a hydroelectric plant, since the amount of energy that can be extracted and the ease of its conversion into electricity are fundamentally different. I could be extracting my energy from a wood fire, burning at a toasty 500 degrees F, or I could be extracting it from natural gas, burning at 4200 degrees F. Natural gas would provide greater theoretical extractable energy - that is, exergy - simply by virtue of being hotter, even if the absolute amount of energy released by a wood fire piled high with logs and a few cubic feet of natural gas are the same.

It should be obvious in light of these facts how spurious claims of "low efficiency" are as an argument against renewable energy. Simply put, efficiency numbers provide a context only for systems of the same type and inputs.

Admittedly, for renewable energy, this can be harder to see. However, look closely and the distinctions become obvious. One favorite target is geothermal energy, whose low-efficiency processes are often criticized. The favored comparison of those with this rhetorical strategy is often between geothermal electricity (efficiencies of around 15% for electricity) and modern combined cycle coal plants, which will give you around 45%. On the face of it, we are talking about something similar - that is, heat converted into electricity - but in fact, the technologies are completely different and the efficiencies reflect fundamental differences in the inputs.

A geothermal well is never going to output steam at more than around 300 degrees C. If we are rejecting heat to the atmosphere at room temperature (call it around 25 degrees C), then the iron laws of thermodynamics dictate that an absolutely perfect theoretical heat engine will at most get out 48% of the work from a temperature gradient of that magnitude (using the Kelvin or Rankine temperature scales, [T_hot-T_cold]/[T_hot]). After that, the work still needs to be translated into electricity, incurring further losses due to generator efficiency.

Compare this to a pulverized coal blast furnace. Since I'm too lazy to open up my textbooks, Wikipedia tells me that you will get temperatures of 900 to 1300 degrees C in one of those. Applying the same theoretical heat engine efficiency calculation, we find that this produces a startling 74.6 - 81% efficiency. Additional efficiency discrepancies between the two systems can be easily explained by the highly nonlinear behavior of steam used to translate heat into work and the scale of the turbines involved.

Ask yourself a question: Given the previous facts, can you honestly say that the lower efficiency figure for geothermal electricity when compared to a coal plant reflects the inferiority or immaturity of the technology? The answer is most definitely no. But it did take a higher level of understanding to expose this fallacy, and that is why I fear it so.


For reference, another law of thermodynamics and physics that frequently applies to renewable energy is the Betz limit, which states that the maximum efficiency of harvesting work for a wave or wind turbine (essentially, any flow machine) is 16/27, or about 59.2% - and that this still needs to be converted to electricity.

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