Cooling for geothermal well drilling

A method for drilling a wellbore in a formation in a subterranean zone, the method comprising:

• inducing, by a contactless drill bit at a downhole end of a drill string, tension to break rock in tension at a rock face ahead of the bit, wherein an inherent temperature of the rock adjacent the rock face ahead of the bit is at least 250 degrees Celsius;
• simultaneously with inducing tension by the contactless drill bit, stressing the rock in tension at the rock face ahead of the bit by flowing a drilling fluid through an interior of the drill string, the drill string having a specified normalized thermal resistance to radial heat transfer across a wall of the drill string between the interior and exterior of the drill string to thereby flow, at the rock adjacent the rock face ahead of the drill bit, the drilling fluid at having a temperature at the rock face at least 100 degrees Celsius less than the inherent temperature of the rock adjacent the rock face ahead of the bit.

A system for forming a geothermal system comprising a wellbore in a geothermal well in a subterranean zone, wherein an inherent temperature of the rock adjacent a rock face at a downhole end of the wellbore is at least 250 degrees Celsius, the system comprising:

• a drill string comprising a contactless drill bit configured to induce tension to break the rock in tension at the rock face;
• a drilling fluid, the system configured such that the drilling fluid flows through an interior of the drill string having a specified normalized thermal resistance to radial heat transfer across a wall of the drill string between the interior and exterior of the drill string to thereby flow, at the rock adjacent the rock face ahead of the drill bit, at a temperature of at least 100 degrees Celsius less than the inherent temperature of the rock adjacent the rock face ahead of the bit, thereby stressing rock in tension simultaneously with the drill bit inducing tension to break the rock at the rock face ahead of the bit.