|Fig. 1: Estimated U.S. helium uses in 2010, USGS, |
The media tells us we're running out of it, but experts say it's conserved. The United States government has stockpiled vast quantities of it underground, and yet its price continues to rise. If technology is expected to progress and worldwide quality of life is expected to improve, our consumption of it will inexorably increase. No, not energy or oil. I'm talking about helium.
Akin to the constant bombardment of light energy from the sun which overtime found its way into underground deposits of fossil fuels, helium has been continually produced throughout Earth's history, by alpha decay of radioactive metals in the mantle, and also accumulated underground.  Some of the helium escapes into the atmosphere, but because helium is so light, most of it escapes into space, leading to a low, and relatively constant, atmospheric helium concentration.  However, the analogy between the sunlight incident on earth and the helium released by alpha decay should be carried no further. Incident sunlight represents an amount of energy, over an appropriate timescale, which may be a potential long-term solution. The natural production of helium from alpha decay, however, is far too slow.  This would be like relying on the natural production of fossil fuels as an on-demand energy supply. But what about the atmospheric helium? Since the helium concentration has remained relatively constant, surely it is safe to assume that removing helium from the atmosphere and then exhausting it back to the atmosphere will not affect this equilibrium concentration. Well this, too, would be a bad solution.
The concentration of helium in the atmosphere is very low, at 5.2 parts per million (PPM).  By contrast, the highest helium content among natural gas wells is about 7% by volume (70,000 PPM), though the vast majority of helium-producing wells have a much lower concentration. [2,3] Using the concept of chemical availability of a gas mixture, the theoretical minimum work required to separate the helium, as constrained by thermodynamics, can be easily calculated :
In the above equation, W/N is the work per mole required to separate the helium, Δφ is the change in chemical availability, μ is the chemical potential of helium in a mixture, R is the universal gas constant, T0 is the temperature of the surroundings, and y is the helium mole fraction (≈ volume fraction) in a mixture. Separating helium from a 7% mixture to 99.995% (grade A helium) yields a minimum work of roughly 6.6 kJ per mole, assuming an ambient temperature of 298 K (25°C). For a cylinder which contains 390 moles of gas as delivered (approximate size of a "T" cylinder), each cylinder-worth of gas takes approximately 2.6 MJ to separate (at a minimum). On the other hand, converting atmospheric helium (5.2 PPM) to grade A requires 30 kJ per mole, or 11 MJ per T-cylinder. While the increase is indeed large, it is important to put these numbers into perspective. 2.6 and 11 MJ equal 0.72 and 3.05 kilowatt hours (kWh), respectively. The average price of electricity in the United States, in July 2011, was 10.58 cents per kWh.  This would amount to 7.6 vs. 32.3 cents per cylinder. Clearly, simple chemical availability is not the driving force behind the high price of helium.
Calculations of theoretical minimum work, while insightful, do not necessarily speak to ease of separation. The current method for Helium separation from natural gas is a complicated, energy-intensive process called fractional distillation. Among other things, it involves the removal of solid species and heavy gas molecules, cryogenic cooling, and separation from liquid hydrocarbons. However, this process typically occurs anyways, because of the need to "upgrade" the natural gas, increase the heating value by removing inert gas species, and also to liquefy it. Therefore the marginal cost of helium separation is difficult to assess, and not made publicly available. However, some insight can be inferred by tracking the invisible hand of the market.
In 1996, the United States passed the Helium Privatization Act, which, among other things, meant selling of the federal helium reserve to private companies.  Much of the reserve consists of what is referred to as "crude helium," which is a gas mixture that consists of at least 50% helium.  The helium gas mixture that is removed during the fractional distillation of natural gas is also crude helium. This is a valued commodity, and in FY2011, the US Government is selling its crude helium at a price of $75.00 per thousand cubic feet, which amounts to roughly $25.00 per T-cylinder.  Since they have been selling their crude helium, and adjusting its price, for several years, this is therefore roughly the marginal cost of helium separation from natural gas. This is certainly a generalization, but gives us a useful ballpark figure, because otherwise it would not be competitive in the private market. Crude helium is then further refined to Grade A helium in separate systems, usually pressure swing adsorption (PSA) systems.  The government estimates the value of grade A helium at roughly $160 per thousand cubic feet, or $53 per T-cylinder (though retail price is typically much higher), which also sheds light on the marginal cost of this stage of refining - roughly $28.
The ratio of marginal costs for these two stages of refining is roughly 1 to 1. However, the ratio of theoretical minimum work to get from 7% to 60%, and then from 60% to 99.995% (using the previous method) is roughly 5.3 to 1. The reason for this difference is because 'theoretical minimum' calculations often break down when considering practical applications. Cooling gas to cryogenic temperatures is expensive. Liquefying natural gas is profitable because of the gains in storage and transportation costs, but cooling it further until the nitrogen also condenses out of the helium is contrary to the point of upgrading the natural gas. Instead of later cooling the crude helium to cryogenic temperatures, it is instead found more profitable to employ PSA separation. This is why air as a long-term helium source is not economical. It is not the same as 5.2 PPM helium in a gas that you are planning to condense anyways. If the theoretical work required is 5.3 times more to get from rarefied to crude helium than from crude to grade A, and the costs of the PSA refining of crude to grade A helium is approximately $28 per T-sized cylinder, then requiring the first section of refining to be done by a PSA could add an additional $120 to the cost of a T-sized cylinder of helium, and increase its cost by 280%. That is a rough figure which could be an overestimate due to nonlinear capital costs, but is more likely to be an underestimate, because gas separation is strongly nonlinear at low concentrations. In fact, for such low starting concentrations of helium, it will likely be necessary to start by fractional distillation of air. This process is currently in place for creating liquid oxygen nitrogen, but would be far more expensive to produce helium, since unlike natural gas, air contains other noble gases with low boiling points.
This is why it is so important to recycle helium. Both energy and helium can be rendered useless by their application (in both cases, quite literally due to the increase in entropy). However, like energy, it can also be profitable to recover the spent helium. A large fraction of helium usage results in crude helium, at least temporarily - but then is vented to the atmosphere, where it quickly becomes useless. Of the main helium uses, only welding (and sometimes purging) does not exhaust a stream of relatively high helium content that could easily be diverted. And yet in the United States, almost no helium is recovered. The laboratory experiments I personally run exhaust anywhere from 30-50% helium. My colleague in the adjacent laboratory runs experiments that exhaust over 99% helium. Even today, this gas could be compressed back into a T-cylinder worth $25. Gas distributors clearly find it profitable to handle cylinders worth less, because the current retail price for a T-cylinder of nitrogen is less than $20. But looking towards the future, this infrastructure will become ever more profitable, and ever more necessary. Because unlike crude oil, the difference between cheap crude helium and the solution of neglect (ambient air) is night and day.
© Matt Tilghman. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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