Mathematics of Geothermal Energy
ebsco.com73 points by srameshc a day ago
73 points by srameshc a day ago
Disclaimer: I work in this field.
This is a very brief, high-level overview. It weirdly dives deep into some less-relevant topics and glosses over a LOT of things.
It is not irrelevant, but not terribly reliable either. The "Mathematics" in the title is self-evidently clickbait.
YMMV.
* It does release CO2, maybe 1/10 the rate of fossil fuels but not negligible
* The well is sealed near the surface. Water is injected down the well and exits thousands of feet below ground level, directly into the hot rocks
* The rock itself is not a perfect heat exchanger; it often needs to be fractured to allow steam to escape quickly. There is a limit to how quickly you can inject water without overcooling the rock
* thermodynamic self-regulation - the temperature of geothermal steam is typically only ~240c, at approximately the point of max enthalpy for saturated steam. Gaseous steam alone does not draw heat from the rocks as efficiently as highly saturated vapor mix, and the hot porous rock acts like a heat pipe to quickly disperse hot spots.
* tyranny of temperature - like all heat engines you want higher temperature inputs for efficiency and to keep the hardware small/simple. 240c is a very low working temperature - so you need complex machinery and/or abundant cooling water to make it work
* modern plants separate the steam from the turbines - which operate on a low boiling point organic compound. they may be entirely air cooled
> It does release CO2, maybe 1/10 the rate of fossil fuels but not negligible
Where from, or is this just lifecycle accounting for the construction works?
> tyranny of temperature - like all heat engines you want higher temperature inputs for efficiency
Yeah. The input heat is ""free"" but the process of turning it into work isn't all that efficient.
Would you be open to do one yourself and share it? (Not sarcastic, just asking)
Honestly, to do anything like justice to this topic would require a publishable academic paper. That is something I simply do not have time for.
There are (at the very least) 2 reasonable places I can think of off the top of my head in which to look around for answers -- both are organizations that run annual meetings on the topic of geothermal energy.
One is the Geothermal Rising professional organization [1]. There is a claim on the website that the papers from the annual meeting (roughly a month back) are available for free download by anybody. I can't find the actual head-link for those papers. A search engine is your friend. (I would not trust an LLM for this particular job.)
A second one is the Stanford Geothermal Workshop [2]. That is also an annual meeting. Again, use a search engine.
Sorry to not be more helpful, but this is a pretty large topic.
[1] https://www.geothermal.org/2026-geothermal-rising-conference... [2] https://geothermal.stanford.edu/events/workshop/past-proceed...
If you want the ACTUAL mathematics of geothermal energy - a good place to start is the open source GEOPHIRES model which is available on github and has a UI
https://github.com/NREL/GEOPHIRES-v2
https://www.nlr.gov/research/software/geophires-v2-0-geother...
I have always been a big proponent of geothermal energy as a reliable renewable resource. Not everywhere is geothermal active (or at least it is very hard to harness in many areas) but in the areas geothermal energy is readily available I don't know why it is not utilized more often, even if it is initially expensive.
In areas like California, or anywhere along an ocean coast that also has geothermal activity, there should be geothermal desalination plants. Solves the issue of desalination being highly energy intensive. One of my favorite college papers I wrote was on using geothermal energy for desalination. After researching it, I could not believe it was not being utilized more.
Wish geothermal energy was being discussed more for a power source for data centers.
Iceland has unlimited geothermal energy and a cold climate. Seems a lot easier than going to space for solar energy
In Michael Lewis book Boomerang [0], there is a chapter about Iceland and he mentions geothermal.
My understanding:
- b/c of geothermal, huge amounts of electricity are available for low cost
- Iceland being an island makes it VERY expensive to build/transport goods back and forth
- The above combo means that aluminum smelting is the only industry where the electricity availability outweighed the costs of transport and being on an island.
> going to space for solar energy (for data centers)
There are other incentives driving this, I suspect more so. Pushback, land acquisition, grid hookup, legal concerns - many circumvented by going to space.
Data centers in space are simply bullshit. I think we should all stop accepting that it is mentioned like something that has to happen only because Elon says so.
there are already Google TPUs in space
We also have a lot of stuff on the Moon. So we've already proven that building a mirror image of NYC on the Moon is a great way to solve the housing problem in NYC.
It’s hard to come up with any idea that is not easier than going to space for solar energy.
It's easier to dump all the excess heat in Iceland than in space.
I read it as 'it's easier to dump the execs in Iceland than in space` :-D
Which might be true, though the second thing sounds promising as well...
Lots of hamsters in wheels driving tiny generators?
I’m not going to bother to check the math but Gemini estimated $20billion/y to generate 1gw with hamsters on wheels so honestly that could be competitive.
Don't worry, data centers are not going to space.
Exactly. Racks are going to space.
For compute jobs that can be efficiently farmed out to individual racks, this is a nice way to stretch your PV manufacturing capacity to serve more chips (as long as launch costs aren't too high).
For LLM training and other jobs that need an entire datacenter of racks working in parallel, that wouldn't be feasible to do in space with today's technology.
The general shape of geothermal, where you're up here where it's cool, and you push a fluid down there where it's hot, and you bring the heat back up here to do work... Would a good enough insulator make it thermodynamically feasible to do it from an airship in the Venusian atmosphere?
Like, clearly Earth's crust supports temperature gradients which are steep enough to make the juice worth the squeeze. Presumably you're not going to find gradients so steep in the case of a runaway greenhouse effect, but whatever gradients you do find, are there fundamental limits preventing them from being steep enough?
The "airships riding on clouds of Venus" is a scifi genre that we need way more of.
To be at 1 atm you need to be way up near 50km, but you'd probably want to be up closer to 55km to get temperatures down, filling it with higher concentration O2 to make it breathable. Making the envelope durable would be pretty crazy in H2SO4, but maybe Ti would self passivate?
Arguably, more dangerous and harder to navigate than vacuum.
You guys are imaginative, I'll give you that.
But there are so many more fundamental problems with the high altitude Venusian colony idea that you would never get to the "temperature gradients > power" pipeline implementation in any case.
I mean right off the bat, imagine building or navigating anything in hurricane Katrina. Then, since we're talking 50km, imagine winds that would make the forces you're dealing with an order of magnitude more problematic.
Yeah, in terms of knowledge and technology, mankind is just not there yet to be perfectly frank.
I still think the temperature and corrosive atmosphere are a lot worse. Two proposed missions come to mind that don't seem concerned with wind or turbulence:
https://www.morningstarmissions.space/samplereturnmission
https://science.nasa.gov/mission/davinci/
Of course anything could happen with funding in the next 5 years that would derail these.
Wind speed could be fairly irrelevant to the balloon-city; it will never touch "ground". If you can steer away from vortexes (assuming them to be rare), they simply don't matter as a safety issue. (Staying in a desirable temperature zone could create a need for resisting the wind, but that's not a safety issue.)
OTOH, because wind velocity is highly tied to altitude on Venus, wind farming could be an important source of energy generation (along with chemical generation for emergency demand). Drag a fan at a hotter, lower, higher-pressure altitude, and harvest the electricity. In fact, storing an excess of wind-farm energy as chemical energy could power the occasional need to steer away from vortexes.
If the problem of a chemically-inert package can be solved, floating inhabited stations could be feasible.
I hadn't considered the drag-a-fan approach. It brings to mind an interesting kind of sailing where you've got multiple wind directions to solve for. Never mind that an atmospheric colony wouldn't really have a lot of destinations besides itself. Might as well just be one big flotilla.
I expect that a more boring approach would prevail: solar panels. No need for impossibly tall airships to resist wind shear just so they could get at both sides of the hot/cold setup for operating a sterling engine.
Engineering sense aside, I still wanna know if nature would allow the geothermal approach. Something about the idea that a column of air at rest would settle down into such a disequilibrium that it could be harvested of energy in this way feels wrong to me, but I've been unable to muster the thermodynamics chops to align my head with my gut.
The problem is the reflective sulphuric acid clouds of Venus extend quite high up... and of course those eat most anything unprotected. If the wind sheer wasn't so bad, you could try and build tall chimneys with fans in them.. but probably easier to just drag fans.
I think i just saw Fervo delivered their 100MW facility a day ahead of schedule in 23 months.
Related, there are people thinking about how we might mitigate super volcano risk and generate electricity at the same time.
https://microgridmedia.com/dangerous-volcano-in-oregon-could...
"Geothermal also has two key advantages over nuclear generation. Nuclear power plants are dependent upon a finite resource (uranium), and nuclear waste disposal is both controversial and costly. In contrast, geothermal generation depends on a virtually infinite source (heat generated in Earth’s interior), and there are no long-term waste issues."
1) Scientific consensus is that the Earth is also finite.
2) Also, the heat generated in the Earth's interior is...nuclear power.
3) Nuclear waste disposal is a political problem, not a technical one; it is "controversial" and "costly" precisely because it's used for these sorts of unserious comparisons.
I love the idea of geothermal, but this sort of nonsense has to be called out and shamed.
Wow, that comment is extremely misleading and exaggerated.
1) Everything in the universe, including the sun's solar radiation, is finite. It's just a matter of scale. The heat in the earth's core is practically infinite for humanity's current and near-term needs.
2) The heat generated in the earth's core is a combination of fission decay and residual heat from the earth's initial formation. The fission reaction is locked away 5000 KM deep (as in 5 million meters), deep-enough that it poses no threat even if you drill down thousands of meters to tap into that. That is very much not true of man-made nuclear fission.
3) There is still no long term storage mechanism that is guaranteed to keep nuclear waste for the several million years it would take to decay to safe levels, considering possible things that could happen over that time scale.
> Wow, that comment is extremely misleading and exaggerated.
Wow, quite the oversell there! Modern nuclear reactors are widely recognized as safe by nonpartisan sources. And why do we need to solve for millions of years of storage? In a couple centuries at most, we'll be able to blast the stuff into space if that's what makes us comfortable.
This is getting very off topic, but this "let's dispose of nuclear waste by shooting it into space" is such an insane idea. In which universe is the risk associated with a frickin space launch lower than a deep underground geological repository?
Also wasting valuable mass... of heavy elements. Transfuse it and possibly even use it as an energy source, or bury it, and let's be done.
So you are 100% confident that a few centuries from now there will be no safe way to dispose of nuclear waste by shooting it into space? Well, maybe you have a time machine, but I don't, so I still think it's a fine idea that we can determine the practicality of later. The point remains that we don't need to solve for millions of years.
Of course, I can't predict the future. So sure, if we in the future have some magical Star Trek technology that would make space travel entirely safe and ordinary, sure. Won't happen with anything like chemical fuels though, thanks to the tyranny of the rocket equation. And if we have such magical Star Trek technology, surely we'd also have the technology to transmute the waste into safer elements that don't present a long-term radiological hazard (that we in principle know how to do already today, it's just prohibitively expensive for little benefit)?
In the meantime, while waiting for the magical Star Trek future to arrive, I'd much prefer if we'd store the waste we have and continue to generate in a safe and responsible manner. Which, whether we do reprocessing or not, would involve deep geological disposal. If we later come up with a significantly better idea and for some reason have a motivation for doing something, sure, then we can dig it up again and shoot it into space, transmute it, or whatever the idea at that time is.
What I'm saying is that with anything like current day rocket technology, disposing of nuclear waste by shooting it into space is just a laughably insane idea.
Even getting it from storage pools in reactors to storage facilities overland has risk.
Massively larger than the risk getting it from the storage pools to the space launch facility, to the extent it cancels out the definitely non-zero risk of the rocket launch failing?
1) With proven technology, nuclear is "practically infinite" in the same sense (available fuel will out-last the sun, even at 10x current energy usage).
2) The "residual heat" is long gone, and my whole point here was that saying nuclear was limited when geothermal is a form of nuclear was disingenuous/misleading. Trying to turn that into a scare / safety issue is exactly the sort of nonsense I was objecting to.
3) There are lots of viable long-term storage options, including grinding it up, mixing it with the tailings and putting it back into the same hole we dug it out of. Or dropping it into a subduction zone, and letting it fuel future geothermal plants. But we won't do any of those, because it's far too valuable. If you are worried about things being "misleading and exaggerated" you probably shouldn't be bringing up the nuclear waste "problem".
4) Thorium nuclear waste disposal would be orders of magnitude easier than for U/Po.
I was interested until I saw the picture for labor month was a clearly generated picture with protest signs saying “Workers Unit” instead of “Workers Unite”.
Does that mean everything in the site is bogus or low-effort? No, but it means I don’t want to potentially waste my time or be misled.