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.
* 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
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.
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...