If the ambient temperature is already close to 500°C (at a depth of around 13 km), I cannot see how you want to work with a liquid—and there is (NOT YET) no drill at all working and generating additional heat! And your great diamond drill bit will be worn out in no time at such a temperature. The idea with the bucket will certainly work up to several hundred meters—if the drill and rods have been removed from the borehole beforehand—I am curious to see what the client says about a drilling system where the entire string has to be pulled back every 10 minutes to clear the drilling debris.
Incidentally, cooling and blowing out is NOT carried out with air but with inert gas—e.g. liquid CO2.
Since several cross connections between the two vertical deep boreholes have to be created for the “closed loop system” and provided with pressure-tight walls, it would be interesting to know how you would clear a horizontal, 0.5-1km long borehole at a depth of 15km with a bucket! And for several 100 MW, you need—a whole bundle - such cross pipes as heat exchangers—which also have to be tight for the 300 bar pressure of the supercritical water! Approx. 900 l/s (0.9688 kWh/kg ) for 1GW output power of the generators - - - which needs 3 MW of power for the approx. 15 high pressure pumps—to produce that stream!
e.g. https://de.starpumpalliance.com/pumpen/verdraengerpumpen/plungerpumpen/
In this context, the most important advantage of supercritical water is that it contains nearly SIX times as much energy per ton—e.g. at 300 bar and 600°C—than in 160 bar 300°C superheated steam.
As a result, almost 5 times less water has to be driven through the heat exchanger system at depth—whereby—due to the higher pressure—the pump load is about three times lower—and about five times the output is possible with the same borehole diameter. Stone is a poor conductor of heat. So after the initial heat loss to heat up the wall of the riser borehole, only a small part of the 600°C depth temperature at 15-16 km depth is lost, so that about 500°C reaches the turbines. Then the 300 liters per second are enough for about 1 GW production—with a pump output of about 0.1%