Why don't we drill to whatever is the termal limit, make a big cavity there, install radiators there and just heat the watter to that temperature and take it out to surface where we can heat homes.
I know this is done in Bucharest for a water park (to much lesser depths because apparently we have hot springs near Bucharest).
Do we need to reach magma?
You need a thermal gradient to move heat from the surrounding rock to the water your pumping in. The higher the initial temperature the larger the difference and therefore faster you can extract heat. Aka even if the working fluid is at a constant temperature you can simply pump it faster.
Also, Carnot efficiency limits means you want the hottest steam you can handle. Further, you have various inefficiencies such as losing heat as water moves back up a borehole.
And the temperature to destroy steel under the immense mechanical stress of a drill string is surprisingly modest. Jet fuel can’t melt steel beams, but softening them is enough.
This is why wooden sauna seats work well, aluminum seats in the sauna would not go over so well.
Lots to consider when solving thermal problems, it's not just about turning up the dial to be able to withstand more heat. Sometimes it's about the nuance of moving the heat efficiently and putting it where it's wanted, and not where it isnt.
My general rule is that everything is 1 J/g/K except water, which is 4.2. It's obviously not true, but almost always within a factor of 2, and 1 is an especially easy number to multiply and divide by.
Reading your second paragraph, I see you're familiar with the principle, and added a good heuristic to my stockpile, thank you.
ISWYDT.
Nooo --- don't dig the Well to Hell!
Nope. Over the last ~20 years the drilling industry has gotten good at: angle drilling (not slant drilling but turning the drill angle at the bottom) and fracking, or pumping fluid through rock to break it up. This means conventional methods can dig far down, turn the drill and make a reserve with fracking. The heat is much less but it's conventional technology.
https://www.ted.com/talks/jamie_c_beard_the_untapped_energy_...