What quantity of basalt would power NYC with power for a day?

Question

Some companies are refitting steam power stations to hot basalt, where many tons of rocks are heated to 750°C by wind power and the thermal energy is used to generate steam in power stations.

How much basalt can supply 11,000 megawatt-hours, enough to power New York City for a day, given a total process efficiency rate of 55%?

What's the specific heat capacity of basalt? Then you can work it out. — , Jun 05 '21 at 12:05
"... given a total process efficiency rate of 75%?" Where does this number come from? As far as I know 45% would be considered good for a steam plant on its own, never mind the additional losses with hot rock. — , Jun 05 '21 at 12:16
http://endmemo.com/chem/specificheatsearch.php?q=Basalt%20Rock and "The average density of basalt is 2.9 g/cm3" from wikipedia. — , Jun 05 '21 at 12:57
Reason you can't find a spec has to do with there being a fairly wide variety in composition. To make it more annoying, you probably shouldn't just consider composition by mass since there are vesicles which can be air pockets of varying sizes (probably part of why you're considering it in the first place - insulation built in) — , Jun 05 '21 at 13:14
I remember, ~35 years ago, we used "heat accumulating space heater" - in essence, a block of heat-resistant bricks, heated by electricity at night (3x cheaper) and slowly releasing the heat by the day. It was quite a pleasure to get rid of it, back then. Now I am starting to think I made a mistake trashing it. — , Jun 05 '21 at 20:34
Do you have a reference giving an example of what is supposed to be happening? I'm tending to think that heating basalt via wind power is an inefficient process & a waste of effort. Instead of heating basalt & then using it to generate steam I would have thought it more efficient to get the wind generators to directly store the electricity they generate in batteries which can then be utilized when required. — Fred, Jun 07 '21 at 05:10

score 5 · Accepted Answer · edited Jun 08 '21 at 12:24

5

Engineering Toolbox gives the specific heat capacity of rock as 0.84 kJ/kg.K.

Let's work with 40 TJ = 4 × 10¹³ J = 4 × 10¹⁰ kJ.

Let's say we could operate with rock starting at 600°C and ending at 200°C so a ΔT of 400°C through the heat extraction cycle.

From the SHC we can calculate

At 3 T/m³ that gives a volume of

That's a cube of 34 m side.

edited Jun 08 '21 at 12:24

Harper - Reinstate Monica

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answered Jun 05 '21 at 13:18

Transistor

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Just one gold mine can dig >150 m cube of rocks though. the total value of the gold is $7.5 trillion, and the same volume of basalt is priced at a competitive $4 million. I think it's amazing that it would take only 4 million's worth of basalt battery to keep NYC running every day for a year. perhaps its'the future? https://www.google.com/search?q=gold+mine – Jun 05 '21 at 13:51
@Transistor It's possible they are making that limited comparison. That's not really how I read their comments. However, my view on it may be a bit biased by having seen a quite substantial number of people who jump to the misconception I described as they get enthusiastic about what the numbers look like for such energy storage mechanisms when you ignore that you still have to have a source of the energy. – Makyen Jun 06 '21 at 18:53
@Makyen, I think s/he's just saying that the total amount of basalt required to make enough thermal storage for the whole world small relative to other mining exercises. The practicality of the whole thermal storage idea is a different matter. – Jun 06 '21 at 18:45
@Transistor No, I didn't miss that. The question is reasonable. The comments here are what I'm talking about. The comments they've placed on this answer make direct comparisons of basalt to coal, as if you can just mine basalt and use it as an energy source, without the need to get the energy you're storing from somewhere else. Such comparisons just don't make sense and indicate that the OP has fallen into a fairly common misconception about what such an energy storage mechanism is and can do. It's that misconception I'm trying to address. – Makyen Jun 06 '21 at 18:41
@Makyen, DeltaEnfieldWaid is the OP. S/he said, "... where many tons of rocks are heated to 750°C by wind power ...". Did you miss that? – Jun 06 '21 at 18:33
@DeltaEnfieldWaid Your comments here appear to be assuming that the basalt is actually a source of energy. It's not. It's merely a way to store energy as a thermal differential. The energy still has to be generated somehow. In the example mentioned in the question, the energy is generated from wind power. Overall, comparisons of the basalt to the use of coal don't make a lot of sense, because we, humans, don't use coal as a way to store energy which we collect from elsewhere (coal is, ultimately, an energy storage mechanism, but it's not something we use/conceive of in the same way). – Makyen Jun 06 '21 at 18:30
@transisor, 25m3 of gold are mined per year, vs 8 cubic kilometers of coal (1m3 for every human)... 10,000 times more coal is mined per year than than basalt that would be necessary for the planet – Jun 05 '21 at 21:29
@fraxinus Indeed i thought that gold isn't a fair indicator of basalt cost.. coal is on-topic, 2000 tons of gold per year vs 8 billion tonnes of coal that are mined per year... basalt sounds cheaper than coal and 1/9th of nuclear. – Jun 05 '21 at 21:23
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@DeltaEnfieldWaid be aware that the basalt will be nowhere the most expensive part of such an operation. It may as well go into "others" category in the Big Table Of Expenses. – Jun 05 '21 at 20:25
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Ask Iceland if they have any going cheap. They can supply you a load already pre-heated. – Jun 05 '21 at 13:53
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Just for comparison, the total amount of gold mined in human history is about a 19 m cube. – Jun 05 '21 at 13:25
That confidence is what i required!!! cheers! compare that to fossil fuels it's a lot less quantity through the year. – Jun 05 '21 at 13:21
All your formulas appear to be broken. They didn't survive the migration from ee.se I think. @Transistor – Harper - Reinstate Monica Jun 06 '21 at 20:51
Where do you account for the 55% efficiency of the system, as stated in the question? Wouldn't this mean the size of the basalt cube would be 62 m (34/0.55)? – Fred Jun 07 '21 at 05:17

score 1 · Answer 2 · edited Jun 07 '21 at 04:59

I'll try to figure it out:

11,000 MWh = 39,600,000,000 kJ

Basalt specific heat: 0.84 kJ/kg kelvin

if we were using 1 kelvin of the basalt we would need 39,000,000,000 kg / 0.84 = ~47,000,000,000 kg of basalt

Using 600° C of usable thermal storage: 47,000,000,000/600 = ~ 78,000,000 kg of basalt, 78 thousand tonnes,

basalt is about 3 tonnes per m³, NYC needs 26,000 m³ of basalt

say 50,000 m³ of basalt given an efficiency of 50%, that's cube of 36m L-w-h

A giant shipping container is 78m³, it's only 649 shipping containers, it's about 5% the capacity of the biggest shipping container boat in the world.

5% of this boat:

I'd say there are more than 200 containers visible above deck on the first row of that ship. — , Jun 05 '21 at 13:23

score 1 · Answer 3 · edited Jun 14 '21 at 01:45

A few hints...

Basalt has a specific heat capacity of 603 joules per kg per °C. This means that to warm 1 kg basalt up by 750°C you need to imbibe it with 603 x 750 joules of heat energy. That's 0.452 MJ. It's the same story when extracting heat from the warmed-up basalt but, you only want to cool it a small fraction of what it has been "charged" to so that the conversion to steam process is not compromised. Bear this in mind.

Also note that 11,000 MWh in joules is 11,000 MJ x 3600 = 39,600 GJ.

The next part calls for a judgement to be made on how much energy you can take from the Basalt without cooling it too much. You don't want to cool it too much else the steam process is going to sag a little. But, maybe you can allow it to cool by 100°C with a bit of hand-waving.

So now, you have to work out how much mass of Basalt will cool by 100°C when 39,600 GJ is taken from it.

Hey Andy, I tried to figure it out using 600'C of usable temperature, i.e. from 150 to 750'C. Perhaps the range is 750'C, from 200'C to 950? — , Jun 05 '21 at 13:19

What quantity of basalt would power NYC with power for a day?

3 Answers3