This is a closed-loop deep borehole heat exchanger (DBHE): working fluid is pumped down an insulated inner pipe, turns around at the bottom of the well, and rises back to the surface through the annulus between that pipe and the well casing — picking up heat purely by conduction from the surrounding rock as it climbs. No formation fluid is ever extracted, which is what makes this different from a permeable reservoir or a hydraulically-fractured EGS well.
Rock temperature follows the local geothermal gradient, and the two counter-flowing streams are solved as a coupled 1-D energy balance along depth z:
T_rock(z) = T_surface + gradient · z
down-flow: ṁcp · dT_down/dz = −U_leak · (T_down − T_up)
up-flow: ṁcp · dT_up/dz = +U_rock · (T_rock − T_up) + U_leak · (T_down − T_up)
turnaround: T_up(L) = T_down(L)
outlet: T_wellhead = T_up(0)
U_rock is the fixed conductive coupling between the annulus and the formation; U_leak is the parasitic coupling between the two internal streams, set by the insulation slider — poor insulation lets the hot returning fluid pre-heat the cold down-going fluid before it ever reaches depth, which lowers the final wellhead temperature.
- Well depth / gradient — set the bottom-hole rock temperature, the ultimate heat source.
- Flow rate — trades exit temperature for total thermal power: faster flow picks up less heat per kilogram but moves more kilograms per second.
- Electrical power is estimated only once the wellhead temperature clears the ~90 °C threshold needed to run an Organic Rankine Cycle (ORC) unit, using a Carnot-limited efficiency scaled by a realistic 35% second-law factor.