Paul Birch

Geothermal pre-heat.

Why? Our policy should be to withdraw from them.

I don't understand what these figures are supposed to refer to, but from the critical point up to 1000 bar at constant volume yields a top temperature ~2940K (a bit hot, but never mind) or temperature difference of ~2300K, so the enthalpy difference can't be less than ~3900 kJ/kg (assuming a Cv for steam of 1.7 kJ/kg, which is probably on the low side for such densities). And, of course, a cycle doesn't have to stay above the critical point all the way round.

The simplest proof is an ordinary hydrogen-oxygen rocket; a steam engine that yields up to 10MJ/kg at overall efficiencies >~90%. Now, as a thought experiment, put the rocket motor on a sled on rails, circling at 4.6km/s, with dynamos on the wheels. Electric power at an efficiency approaching ~90%. QED.

Start off with plain water and a nuclear rocket (such as a NERVA design, specific impulse up to ~10km/s) and you've got a nuclear power station at an even higher efficiency.

Hudson

Great. We could use the Tipton-Darlington fault line to access that, or the famous hot water springs of West Bromwich.
Seriously though, geothermal energy is not to be sniffed at where it's readily available. Extracting it is a question of cost-benefit analysis.

Fair comment. America had enough sense not to get involved.

Next bit:
My figures come from a bog standard T-s chart and on site measurements of Rugeley B power station, generator no. 6, taken December 2nd 2004. My chart shows T (supercritical at 1000 bar) as 763K. Where does your 2940K come from?

In theory, yes. In theory, theory and practice are the same thing. In practice they seldom are. Can you specify a material for the pipes, boilers etc that can happily withstand 1000 bar and 2940K with sufficient safety factor to avoid fatigue and thermal creep while maintaining public confidence without costing the same as a space program to implement and requiring an installation the size of Canada?

I'd rather a specific proof for a power station application. BTW where does this hydrogen and oxygen come from? Had we better get the molecular resonance electrolysis warmed up?

NERVA? :shock: Is this power station still going to be built on Earth? I'll let you announce that one on Newsnight.

Paul Birch

The advantage of geothermal pre-heat is that it can be used (and should be cost-effective) almost anywhere you can drill a deep hole. It doesn't need the sort of high temperatures you'd need for a fully geothermal power plant.

Please don't misunderstand me, though. I fully agree with you on the advantages of CHP (whether for nuclear or conventional power stations). Indeed, I think it could be even more useful than you suggest, especially in conjunction with new developments and improved infrastructure (such as separate sewers and storm drains, roads constructed on the cut and cover principle with a service tunnel below, etc.). Even in the countryside, the heat could be valuable for intensive large-scale hydroponic greenhouses (as could the CO2 from fossil fuel stations).

That's only 116K above the critical point, so no wonder the enthalpy figures are close. To get an efficient cycle you need the widest temperature range you can manage.

From your arbitrary pressure of 1000 bar, going from the critical point by heating at constant volume. 647K x 1000bar/220bar = 2940K. That won't be completely accurate, since at those densities it's obviously not a perfect gas, but it won't be far out.

I could, certainly (fused or vapour deposited aluminium oxide). But I wasn't suggesting that those specific values should actually be used (I pointed out myself that it was a bit hot); I was merely calculating on the basis of the 1000 bar you specified.

You should be able to adapt that cycle yourself for use in a fixed power station. I've given you a simple existence proof, which should suffice. I'm not going to try to do more than that on a text-based medium - I'd want to be sketching diagrams and scribbling equations, which isn't very practicable.

The LOX from air, the hydrogen usually from producer gas. If we were using it as a real sea-level power plant we'd use a hydrocarbon fuel instead. The specific energy is then a little less.

It was a thought experiment. Not that there's any rational objection to using NERVA-type rockets on Earth. Only the prevailing ignorance and superstition.

Hudson

I suspect (but have no definitive proof) that the energy saving from geothermal pre-heat would be negated by the cost in extracting it. Unless we used the famous hot water springs etc. it'd be cheaper to burn the extra ton of coal. Obviously worth investigating further though.

Aluminium oxide? Why not reaction bonded silicon nitride or zirconia, or a silica/aluminium borosilicate fibre composite? Good luck making pressure vessels out of that lot! Size of Canada and the cost of a space program.

I agree about infrastructure. CHP needs including in the planning stage (which is why we don't just cobble it on, of course). I reckon we could move away from the few, giant power stations to smaller, local units thus allowing infrastructure to be upgraded gradually.

Hydrogen is all very well providing you can get enough of it and, more importantly, extract it without expending more energy than the subsequent combustion will release. Doing both at once is the tricky part.

Feel free to write up those proofs as a word.doc and email them to me, I'd be very interested. As they say in poker, I'll see you.

Paul Birch

I seem to recall that the figures were quite favourable. Let's do a very rough calculation. For a temperature rise of ~100K and ~400MJ/tonne we drill down ~10km. Assume a 1 sq.m bore, and a flow rate of 1m/s, yielding ~400MW of geothermal pre-heat energy, a reasonable magnitude. We need to extract 20,000 cubic metres of rock. As an upper limit, assume that we have to vaporise all that rock to remove it; total heat required ~160TJ, which we get back in just over four days. We could usefully go down deeper and get even more heat out at a higher temperature; the ratio stays the same. Now fluid dynamic frictional drag costs us ~2x0.5 J/tonne per 100m of depth (assuming Cd~0.003), or 100J/tonne in all, a tiny fraction of the energy extracted.

There's a slight snag. Either we need a network of total length ~400km at the bottom of the shaft to couple the heat from the rocks INTO phpbb_the water, or we need to reduce the flow rate by a factor of ~40 (which would still reach energy pay-back in 160 days); or we could reduce the bore to about 20cm diameter, and use 40 double shafts suitably spaced.

Because aluminium oxide (sapphire) would be the simplest and cheapest solution, with a developed technology already employed on a small scale (at a cost ~£100/kg). It can happily take pressures in excess of 50GN/m/m.

If you want to hire me to design a power station, I'll do it. In a handwritten format only. Getting it INTO phpbb_a computer format would cost thousands of pounds more and call for the services of experienced professional typesetters.

Hudson

Aluminium oxide is sapphire is it?
So the graphite in my pencil must be diamond?

Thanks for the chat.

Paul Birch

Technically this would be corundum. Sapphire is the gemstone variety, coloured blue by cobalt impurities; however, the term sapphire is conventionally also applied to man-made or reformed corundum, as used for example in the electronics industry, which may be colourless or doped with various impurities.

lkelly

I am very happy with this excellent discussion. It is great that people are considering the environment, or policies which would benefit it, anyway.

However, I will always want to retain England's 'nuclear option'. I will always want enough of the right kind of power stations that will enable us to retain it, therefore.

gareth2

I think you 2 should play nice. The discussion was, as ikelly said, interesting. Not that i understood it all, and that is unusual for me.

I cant summon the courage to contradict you, so ill ask you both; Is what you describe realistic for our countries energy source? What do you feel about nuvlear? (im all in favour)

Cheers!

Gareth.