The Ergosphere
Wednesday, October 01, 2008

On the hazards of ignorance of thermodynamics

Wherein the author continues a discussion as an essay

Over at The Oil Drum, a discussion subthread about gas turbines as energy converters ended with this late-arriving statement by Cyril R.:

Non-combustion gas turbines are not proven. They're mostly in pilot/research stages. You say that the conditions in non-combustion lower temp operation are more reasonable than in higher temp combustion gas turbines, but the fact that they are not commercially competing with Rankine steam cycles, even in the higher temperature regimes, should caution us not to trivialize the engineering/commercial issues.

The one-week period for comment on the post ended before I could write a response.

What's missing from this analysis?  Let me lay it out in easy pieces:

  1. One can already purchase simple-cycle combustion turbines achieving 46% thermal efficiency.
  2. These are internal-combustion units running on open cycles, requiring neither hot-side nor cold-side heat exchangers.
  3. A turbine using inert gas as a working fluid is not internal combustion, by definition.  The source of heat must be something outside the fluid.  If the heat source is combustion, this requires a hot-side heat exchanger.  This is an unnecessary capital expense.
  4. Preserving the inert working fluid against loss requires a cold-side heat exchanger.  This is another unnecessary capital expense for a combustion system.
  5. Reducing the operating temperature from ~1100°C to ~800°C would also reduce the thermal efficiency.  If the heat source is combustion, this increases fuel costs.

We can see from a relatively simple analysis that today's absence of inert-gas turbine generators has nothing to do with technical feasibility.  It is soley a matter of economics.

How does a nuclear heat source change the economics?  Comparing to the points above:

  1. One cannot buy a steam turbine operating at 650°C and higher temperatures.  The most feasible option for taking advantage of the high temperature of molten-salt and pebble-bed reactors is gas turbines.
  2. The hot-side heat exchanger is either implicit (in a gas-cooled reactor) or required to separate the nuclear materials and the working fluid (molten-salt reactor).
  3. Nuclear plants do not chemically modify the working fluid of their heat engines, so are the equivalent of "external combustion".
  4. The cold-side heat exchanger is required (like the condenser in a steam turbine).
  5. The reduced operating temperature is a given, set by the nuclear heat source.
  6. Since the gas turbine can operate at a higher source temperature than a steam turbine and can thus achieve greater thermal efficiency, it improves the return on the capital investment in the rest of the plant.  This reduces costs relative to revenue.

The thermodynamic properties of inert gases are well-understood.  Designing a fractional gigawatt gas turbine to run on e.g. helium would require design changes such as gas bearings (to eliminate petroleum lubricants or water which would cause corrosion or coking in the hot side), but these have already been proven in other applications.  The only reason we aren't running helium turbines today is that it would increase both capital and operating expenses.  If the heat source was a high-temperature nuclear reactor, the helium turbine would generate more revenue than a steam turbine for the same capital expense in the reactor.  This is why we can expect to see inert-gas turbines as part and parcel of any PBMR or MSR powerplant.

It's a good thing I didn't ignore thermodynamics then, but made a completely different point about a technology that is not operating today, with commercial aspects and practical learning by doing completely unknown and absent. You know I can't deal with everything in those text boxes, and I regret to admit I'm short on time.

Next post: 'on the hazards of misinterpreting other peoples comments'.

No hard feelings mate.
Also, you're comparing non combustion braytons with combustion braytons, when really you have to compare non combustion braytons with ultracritical steam cycles. Ultracritical cycles do exist up to about 600 degrees celsius in real systems (IIRC China has GWs of it in ultracritical coal plants). Since slightly lower temperature operation in the reactor has economic advantages, 650 degrees celsius may not be the most cost-effective operating temperature. Efficiency is similar or better (the gas turbine diverts a big portion of it's energy to the compressor).
I've just done some calcs. Real world, proven ultracritical steam turbines get higher efficiency with lower temperatures (say 550 degrees C) than even an ideal helium Brayton gets (at 650 degrees C). Going higher on temperature makes the nuclear island more challenging (as that would then have to operate under a higher temperature regime as well)

I remembered what's wrong - the amount of power diverted to the compressor in the Brayton cycle is just really big. The ultracritical Rankine doesn't suffer such large parasitics.

Ergo, an ultracritical Rankine gets more revenue, with less technological risk (eg no helium bearings creeping problems) while making the nuclear island a bit cheaper and prolonging the life of the moderator (if graphite, which is one of the more likely candidates).
I did some searching for ultracritical steam system efficiencies.  One of Sulzer's documents claims a potential efficiency of 48% for ultracritical Rankine, which I admit is outstanding compared to historical practice.  However, the document doesn't reference turbine considerations, so I'm still in the dark about time between turbine rebuilds under such extreme conditions.

If a reactor is built to supply heat for thermochemical hydrogen production as well as electric generation, the minimum temperature appears to be in the region of 850°C.  It would be possible to use a secondary coolant loop with recirculation of cold coolant to drop the temperature for an ultracritical boiler, but it would be simpler to just use a heat engine capable of 850°C.  An open-cycle gas turbine running on air would be effective and cheap (and amenable to combined-cycle operation) but inert gas has possibilties too.

This comment will be continued as a post, because damn Blogspot won't allow lists, subscripts or blockquotes in comments.
You may be right about the thermochemical hydrogen production. The capital costs of such hydrogen plants are supposed to be low, if that turns out real it may be interesting to make electricity during peak electric demand, while producing hydrogen during trougs in electric demand. Load following problem solved without wasting energy or turning off the reactor, and at very reasonable cost.

Of course, the GEN IV aren't expected before 2030 on the GW commercial scale. Do you think this date can be pushed back, perhaps with an LFTR?
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