The place I saw this most clearly described was in Standard Thermal's concept, which will store the heat in huge piles of dirt heated to 600 C. The thermal time constant of such piles can be many years.
If we assume the delta of 550 degrees (600 down to 50), you'll need: 7.913×10^10 J / (550K * 1000Jkg^-1K^-1) = 143,872,727 kg of material in your pile. This is a ridiculously stupid number. And I don't see any obvious mistakes?
I use units(1), which also helps me avoid dimensional errors (dividing when I should have multiplied, etc.):
You have: 7.913e10 J / 550K / (1J/g/K)
You want: kg
* 143872.73
/ 6.9505876e-06
maxerickson says, "Still big number," and 144 tonnes would typically be an unwieldy quantity of material if you had to buy it. But Standard Thermal's intention is not to buy dirt, just pile up already-on-site dirt with a bulldozer or excavator. If we assume 1.3 tonnes/m³, that's 110m³, or, in medieval units, 144 cubic yards. https://www.eaglepowerandequipment.com/blog/2022/03/how-much... tells us:
> An excavator could be used to dig anywhere from 350 to 1,000 cubic yards per day, depending on a number of factors including bucket capacity, type of ground, operator skill and efficiency level, and more. (...)
> One of the biggest factors that impact how much an excavator can dig in one day is the unit’s bucket size, which typically ranges from 0.5 to 1.5 cubic yards of bucket capacity. Most common regular-size excavators have a 1 cubic yard bucket capacity, and mini excavators are closer to the 0.5 cubic yard capacity.
So, with this number, we're talking about a few hours of work for a "mini excavator". https://www.bigrentz.com/rental-locations/pennsylvania/pitts... tells us that a "4,000 lb. mini excavator" rents for US$197 per day. So the expense of moving the dirt is not really significant, compared to other household projects such as replacing the roof, insulating the walls, or repainting the exterior.
Standard Thermal mentions that they are in effect firing the clay in the ground, that they've had significant trouble with resistance-heater reliability, and that their objective is to power steam-turbine power stations with the stored heat. These three facts lead me to believe that they're targeting a temperature closer to 1000° than to 600°.
600 C is about what a coal fired power plant would use. And 600 C is around the maximum that you want if you're using cheap steel for the pipes. Much beyond that and creep becomes a problem. So I don't think 1000 C is their target.
Hmm! Interesting! I would have thought that 600° would be close to the minimum for producing supercritical steam, so any energy stored up to 600° would be "overhead" that couldn't be effectively recovered—only the heating above that. And I assumed they would have to use cheap ceramic for the pipes, because oxidation is usually a problem for cheap steel even below 600°.
Oh, apparently because of "dramatic improvements in power plant performance":
> Starting with the
traditional 2400 psi / 1000 F (165 bar / 538 C)
single-reheat cycle, dramatic improvements in
power plant performance can be achieved by
raising inlet steam conditions to levels up to
4500 psi/310 bar and temperatures to levels in
excess of 1112 F/600 C. It has become industry
practice to refer to such steam conditions, and
in fact any supercritical conditions where the
throttle and/or reheat steam temperatures
exceed 1050 F/566 C, as “ultrasupercritical”.
Anyway, those are the plants that Standard Thermal wants to sell their product/service to. And once the hot dirt falls below 600°, it can no longer heat the water to 600°. So I think they have to be aiming far above that temperature, which is also why heating element reliability is a challenge and why the clays in the soil are firing (a phenomenon which only happens at 600° for the lowest-firing terra-cotta clays, more typically requiring 1000°–1400°).
Here's an article giving the state of such plants in the US in 2011. Since then I imagine some of the smaller/older plants have been retired. There is no new coal capacity coming online in the US.
Sounds like it was 80% subcritical at the time. I hadn't realized. It sounds like even "regular supercritical steam" is at like 580°, though. Maybe dirt at only 600° could still provide a substantial fraction of its stored energy to subcritical steam circuits, if they're much colder than that?
I think "storage at 600 C" could provide most of its heat output at close to 600 C. It's not like the entire thermal store is tapped at the same time.
Imagine a pile with long pipes through it. Cool fluid is introduced at one end; the steam is gradually heated as it travels down the pipes, emerging as hot steam at the end. If needed, gang two of these together with the second pile acting to top off the temperature from the first one (or more than two).
So, during discharge, a wave of cold sweeps down the pile(s), while the pile near the outlet end stays pretty hot. Only when most of the piles are discharged does the temperature decline.
The Standard Thermal approach is described as heating the piles with embedded resistive heaters, but it could also use an external heater that sends in steam in the opposite direction from when it discharges. This would turn the system into a giant counterflow heat exchanger. Counterflow heat exchangers are known for their high performance, enabling almost all the delta-T between two fluid streams to be interchanged.
Hmm, you're right that a counterflow heat exchanger could indeed provide 600° output by cooling a hot dirt pile most of which is well below 600°. I hadn't thought of that, even though I knew it in other contexts. I mistakenly thought that only the heat over the output temperature would be available.
The only drawback is that, when you're heating the pile, most of the time you are only heating part of it (the cold part), so your heating elements need to have a significantly higher power capacity, assuming you're heating the pile with embedded resistors as described, rather than with a heat transfer fluid as you suggest.
I don't think you want the heat transfer fluid in the dirt pile to be steam; that would involve making the pipes through the hot dirt resistant to both pressure and steam corrosion, which would make them expensive. It also means you'd have a high-pressure steam leak deep inside the dirt pile when they did fail, which would probably cause damage to other pipes and to resistors and a significant uncontrolled heat transfer from the zone of the leak to other parts of the dirt pile. I think you want a more relaxing atmospheric-pressure heat transfer fluid that allows you to use cheap pipes, or even no pipes. Air, for example. Solar salt can reach those temperatures, and it has a much larger heat capacity, but it's fairly corrosive.
For a seasonal thermal store, also, we're talking about astoundingly low power densities, so low-density heat transfer fluids like air should be fine. If we're cooling the hot dirt from 600° down to 100° over a 3-month low-sun season, and the dirt is 1J/g/K, we're only extracting 63 watts per tonne, which at 1.3 tonnes of dirt per cubic meter is 80 watts per cubic meter. My human body is largely air-cooled and generates about 800 watts per tonne in normal operation, even without forced air.
I don't think it's necessary for the pipes in the piles to be operating at the pressure of the steam in the turbines. There could be an intermediate heat exchanger to transfer heat from the low density steam (or air) in the pipes to the high pressure steam in the turbine loop.
Yes, that is what I meant to propose, but when you have that additional heat exchanger, why would you use steam rather than air (or some other fluid like helium or argon) in the low-pressure pipes?
An expensive gas would present the problem of leakage. If that could be cheaply addressed, great, otherwise go with something where making up small leaks is not expensive. That probably means steam or air.
I think steam would have better heat transfer properties than air, maybe?
I do wonder how much we should worry about oxidation of the pipes. Stainless is certainly fine at 600 C in an oxidizing atmosphere, but what about cheaper steel?
The surface will always be only slightly hot. Heat will be stored inside, insulated by overlying dirt. Dirt isn't the best insulator by thickness, but it's a very good insulator by $.
https://www.orcasciences.com/articles/standard-thermal-copy
https://austinvernon.substack.com/p/building-ultra-cheap-ene...
https://news.ycombinator.com/item?id=45012942