Heat exchanger in a borehole receives heat through a rock formation from another borehole which includes a nuclear reactor

A method of constructing a nuclear reactor system, comprising:

• forming a first drillhole from a terranean surface through one or more subterranean formation;
• forming a second drillhole from the terranean surface through the one or more subterranean formation and separated from the first drillhole by a portion of a rock formation of the one or more subterranean formations;
• moving at least one nuclear fuel element into a reactor core positioned in the first drillhole;
• positioning the at least one nuclear fuel element at a first depth of the first drillhole, wherein one or more void collectors are each attached to a cladding of the at least one nuclear fuel element, the one or more void collectors each comprising an inverted cup;
• moving a heat exchanger into the second drillhole;
• positioning the heat exchanger in thermal communication with the portion of the rock formation;
• installing a primary coolant system in thermal communication with the portion of the rock formation and configured to transport a primary fluid coolant through the reactor core, wherein the one or more void collectors are positioned in the primary coolant system and within a flowpath of the primary fluid coolant;
• and
• installing a secondary coolant system in thermal communication with the heat exchanger and configured to transport a secondary fluid coolant between the heat exchanger and the terranean surface.

A method, comprising:

• transporting a primary fluid coolant in a primary coolant system through a reactor core of a nuclear reactor system that comprises:
• a first drillhole that extends from a terranean surface through one or more subterranean formations;
• the reactor core positioned in the first drillhole and comprising at least one nuclear fuel element;
• one or more void collectors each comprising an inverted cup positioned in the primary coolant system and within a flowpath of the primary fluid coolant, wherein each of the one or more void collectors is attached to a cladding of the at least one nuclear fuel element;
• a second drillhole that extends from the terranean surface through the one or more subterranean formations and is separated from the first drillhole by a portion of a rock formation of the one or more subterranean formations;
• the primary coolant system in thermal communication with the portion of the rock formation;
• a heat exchanger positioned in the second drillhole and in thermal communication with the portion of the rock formation;
• and
• a secondary coolant system thermally coupled to the heat exchanger and configured to transport a secondary fluid coolant between the heat exchanger and the terranean surface;
• transporting a secondary fluid coolant in the secondary coolant system between the heat exchanger and the terranean surface, wherein the secondary fluid coolant is heated in the heat exchanger by the portion of the rock formation;
• and
• generating power with the heated secondary fluid coolant.