Fuel Cell Efficiency: A Reality Check
By Dominic Crea
The dream of converting fuels such as coal, alcohol and hydrogen directly and with great efficiency into electricity date back to the middle 1800s-indeed this is no longer a dream as evidenced by the variety of fuel cells now under development-but sadly, reports of efficiency are often times far in excess of both the theoretical and practical realities claimed of this technology. This paper will attempt to clear up some of the common misconceptions that abound in any discussion concerned with fuel cells in general and PEM (proton exchange membrane) fuel cells specifically.
The PEM fuel cell has been the focus of much research and enthusiasm; its intended role as a superior prime mover in automotive applications has been the subject of many popular articles and talk show discussions. It has even been prophesized that “the reign of the internal combustion engine is coming to an end”-but there are good reasons for taking these kinds of statements with a grain of salt. While the perceived advantages of a fuel cell power source seem immense-low or zero pollution, quiet operation, and high efficiency to name a few-it is the last claim that deserves some measure of reassessment.
It has often been said that a fuel cell is a very efficient energy converter, that its efficiency can “approach 83%”. This is actually quite true-in theory. However, when one considers all of the parasitic losses and ancillary subsystems necessary to make a practical fuel cell-powered vehicle, the real world efficiency plummets from 83% to something like 40% or lower-a number that is surprisingly close to the actual efficiency of some Diesels and other high-compression engines! In fact, the 83% theoretical efficiency is not unique to the fuel cell-it is equally applicable to heat engines, thermoelectrics and even human muscles as we shall see later in this paper-and this is a point that is often overlooked by some overzealous proponents of fuel cell technology.
The first step necessary in evaluating the efficiency of any system is to define efficiency explicitly: It is the ratio of the useful work output to the heat energy contained in the fuel being considered. Using hydrogen as our fuel, we find that there are actually two values of heat to be considered: The higher heating value (HHV) and the lower heating value (LHV). Normally, this heat content is given in terms of a quantity called the enthalpy, or heat content as measured in joules per mole of reactants, but it can also be expressed quite nicely in terms of the voltage and electric charge, as would be the case when considering any electrochemical power source. The difference in these two numbers stems from the fact that the HHV represents all the heat that is possible to recover, including the heat that is derived from condensing the water which is an inevitable product of the reaction; the LHV does not include this heat, consequently the two values differ by about 18%.
As it turns out, European engineering practice favors the use of HHV while Americans prefer the LHV when evaluating efficiency and this leads to some interesting consequences, not the least of which is that some devices, like heat exchangers and boilers, can achieve efficiencies exceeding 100% if one chooses to use the LHV instead of HHV-clearly greater than the conservation of energy principle should allow! Moreover, when comparing hydrogen to other fuels like methane and various alcohols that contain a significant fraction of carbon, the difference in the HHV and LHV artificially favors hydrogen (hydrocarbon fuels differ by only about 10% between the HHV and LHV).
The implications of this practice provide for some illuminating revelations: As indicated a moment ago, the heat content, and consequently the efficiency, can be expressed in terms of the voltage-specifically, the ratio of output voltage per cell divided by the theoretical voltage possible for any such combination of fuel and oxidizer.
A typical automotive fuel cell operates in the region of 0.55-0.75 volts per cell; the theoretical values for the HHV and LHV are 1.48 and 1.23 volts respectively. Using the values just given return efficiencies of 37% -51% for the HHV and 44%-61% for the LHV-but this is only the chemical-to-electric conversion efficiency; a car ultimately requires mechanical energy, not electrical, to move it and this is where the highly-touted fuel cell efficiency begins to take a turn for the worse.
As mentioned earlier, there are a number of other systems that must be included in the overall efficiency analysis of a fuel cell-powered vehicle-the electronic inverter, motor, air compressor (fuel cells needs oxygen that must come from the air) and the energy needed to get the hydrogen fuel stored in the tank of the vehicle. These subsystems have their own efficiency conversions that calculate out as follows: Inverter 90%, motor 90%, air compressor 80% and hydrogen storage (compressed gas) at about 85%. Multiplying these efficiencies by the earlier values given for the HHV and LHV efficiencies gives us something like 14%-28% and 24-34% respectively.
Notice that even the overly-optimistic LHV efficiency falls short of some state-of-the art Diesels, natural gas and high-compression alcohol engines (40% LHV); this is a point that is often glossed over when hydrogen automotive fuel cells are discussed: Proponents like to use the highest chemical-to-electric conversion efficiencies (when the loads are smallest) of the fuel cell and compare them to the average brake thermal efficiency (chemical-to-motive power) of a conventional automobile engine. This sort of analysis is really misleading since it uses the most ideal operating characteristics of a fuel cell (and the most unrealistic in everyday driving) and compares them to a vehicle that is not optimized for maximum efficiency. In fact, when an internal combustion engine is designed to use a high-compression fuel like methane or alcohol in a hybrid configuration, the perceived differences in overall efficiency begin to blur. And this leads us to the final point alluded to earlier in this paper: Just what is the maximum theoretical efficiency of any prime mover using hydrogen and oxygen as an energy source?
Contrary to what most papers on the subject suggest, the “Carnot” Equation (for some reason, many pseudo-scientists think this equation is responsible for the rather poor efficiency of current internal combustion engines) places a theoretical limit on heat engines that actually is higher than a fuel cell-approaching 100% ! As long as we allow for an arbitrarily high temperature reservoir (or conversely, a lower temperature of absolute zero), the theoretical efficiency of a Carnot engine can be arbitrarily close to 100%.
Now, in fact, because we are using a chemical fuel to operate an engine, we find that some of the energy content of the fuel must be expended as heat-this is a consequence of the Second Law of Thermodynamics-which, by the way, applies with equal validity to a fuel cell (some hydrogen enthusiasts have misunderstood this point and claim that a fuel cell is not subject to the same thermodynamic limits as a heat engine-in fact, it is subject to exactly the same limits.).
When an ideal heat engine and fuel cell are operating on a chemical fuel, the actual maximum possible energy recovered as work is dictated by the Gibbs/Helmholtz equation: ÄG = ÄH - T ÄS; where “ÄG” represents the maximum energy that is available for work; “ÄH” is the heat content, or enthalpy, of the reactants in question; “T” is the temperature in degrees Kelvin at which the reaction takes place and ÄS is the entropy associated with the reaction. It turns out that we can react this combination electrochemically or convert it directly into heat, both methods ultimately converting into mechanical work. But in either case, the energy that is released is actually electrical in origin-believe it or not. The point is this: If we take a theoretically ideal fuel cell or heat engine, exhaust the products of the reaction at the same lower temperature (say, 25 degrees Centigrade), then the actual efficiencies will be identical for both systems!
Practically we see this fact being born out in the case of some vehicles that use Diesel or high-compression alcohols: The Toyota ES3 diesel-electric hybrid concept vehicle achieves a fuel economy of 103 MPG; the Honda FCX hybrid squeezes out roughly 61 MPG. Clearly, the ES3 is a different car -- lighter in weight, more aerodynamic and uses a fuel of higher energy content per gallon-but even when we make allowances for these facts, it becomes very clear that fuel cells may not be all that much better overall-perhaps worse in terms of efficiency. Certainly, the claim that “fuel cells are at least 2-3 times more efficient than a heat engine” needs to be looked upon with serious skepticism.
Currently, the average efficiency of the only production fuel cell now in use to any significant measure (UTC Fuel Cells PC 25) has achieved an average of only 35% chemical-to-electric; a natural gas, combined cycle generating facility (a compound heat engine system and one that is currently quite standard practice) pushes the envelope at 55% chemical-to-electric conversion efficiency.
Hopefully, this paper will instill a sense of caution about the claims being loosely thrown about these days-claims that need to be investigated quantitatively rather than qualitatively. The premise that a “fuel cell is 2-3 times more efficient than a heat engine” forms the basis for a series of “hydrogen hard sells” that are misleading the public into complacency and inaction. There are better ways to achieve energy independence; ways that are proven and yet, have been overshadowed by the glitz and sex-appeal of fuel cells and the hydrogen economy.
While fuel cells will doubtless continue to improve, it must be remembered that internal combustion engines will do the same-indeed they are as evidenced by efficiency numbers that are approaching 40% and beyond. It might be well to postpone writing the obituaries for the internal combustion engine at this time; it has survived for good reasons and its demise is far from certain.
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