Controlling thermal expansion in a nuclear reactor

Abstract

A nuclear reactor system includes at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations. The at least one reactor vessel includes at least one reactor core that includes at least one nuclear fission element. The nuclear reactor system includes a heat exchanger positioned in the borehole proximate the at least one reactor core. The heat exchanger includes a primary loop configured to transport a primary loop liquid between the reactor core and the heat exchanger; and a secondary loop configured to transport a secondary loop liquid through the heat exchanger. The nuclear reactor system includes a canister that at least partially encloses the heat exchanger and includes an open first end and an open second end. The canister is configured to form at least a portion of the secondary loop, the canister including a non-straight surface.

Description

Attorney Docket No.: 57302-0010WO1CONTROLLING THERMAL EXPANSION IN A NUCLEAR REACTORTECHNICAL FIELD

[0001] This disclosure relates to the field of nuclear power and, more particularly, controlling thermal expansion in a nuclear reactor, such as a deep borehole nuclear reactor.BACKGROUND

[0002] In a nuclear reactor, thermal expansion can cause significant mechanical and operational problems if not precisely managed. At the component level, the expansion of fuel pellets and cladding can lead to mechanical interactions that limit fuel lifetime or cause “gap closure,” which complicates heat transfer and increases structural stress. For the reactor vessel and piping, rapid temperature changes can trigger pressurized thermal shock (PTS), where differential expansion between the surface and bulk material induces fatigue, cyclic creep, or the propagation of existing cracks in thick-walled components like the reactor pressure vessel.SUMMARY

[0003] In an example implementation, a nuclear reactor system includes at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations. The at least one reactor vessel includes at least one reactor core that includes at least one nuclear fission element. The nuclear reactor system includes a heat exchanger positioned in the borehole proximate the at least one reactor core. The heat exchanger includes a primary loop configured to transport a primary loop liquid between the reactor core and the heat exchanger; and a secondary loop configured to transport a secondary loop liquid through the heat exchanger. The nuclear reactor system includes a canister that at least partially encloses the heat exchanger and includes an open first end and an open second end. The canister is configured to form at least a portion of the secondary loop, the canister including a non-straight surface.

[0004] In an aspect combinable with the example implementation, the non-straight surface includes an undulating surface.

[0005] In another aspect combinable with one, some, or all of the previous aspects, the undulating surface is formed to approximate a sine wave.

[0006] In another aspect combinable with one, some, or all of the previous aspects, the non-straight surface includes an outer surface of the canister.Attorney Docket No.: 57302-0010WO1

[0007] In another aspect combinable with one, some, or all of the previous aspects, the non-straight surface includes a portion of the wall of the canister.

[0008] In another aspect combinable with one, some, or all of the previous aspects, the non-straight surface is configured to allow expansion or contraction of the canister based on thermal energy generated by the reactor core.

[0009] In another aspect combinable with one, some, or all of the previous aspects, the primary loop includes an upflow pipe portion that includes an inlet in upflow fluid communication with the reactor core; and a downflow pipe portion fluidly coupled to the upflow pipe portion and including an outlet in downflow fluid communication with the reactor core.

[0010] In another aspect combinable with one, some, or all of the previous aspects, the downflow pipe portion includes a first loop portion and a second loop portion.

[0011] In another aspect combinable with one, some, or all of the previous aspects, the downflow pipe portion includes a chirality reversal portion between the first and second loop portions.

[0012] In another aspect combinable with one, some, or all of the previous aspects, a length of the first loop portion and a length of the second loop portion are different.

[0013] In another aspect combinable with one, some, or all of the previous aspects, the downflow pipe portion is configured to allow expansion or contraction of the primary loop based on thermal energy generated by the reactor core.

[0014] Another aspect combinable with one, some, or all of the previous aspects includes insulation applied to the primary loop.

[0015] Another aspect combinable with one, some, or all of the previous aspects includes a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core.

[0016] Another aspect combinable with one, some, or all of the previous aspects includes an annular flowpath between the heat exchanger and the casing.

[0017] In another aspect combinable with one, some, or all of the previous aspects, the annular flowpath is configured to transport a coolant therethrough to adjust a temperature of at least a portion of the casing.

[0018] In another aspect combinable with one, some, or all of the previous aspects, the coolant includes water.7Attorney Docket No.: 57302-0010WO1

[0019] In another aspect combinable with one, some, or all of the previous aspects, the annular flowpath includes an inlet at or near the terranean surface.

[0020] In another aspect combinable with one, some, or all of the previous aspects, the coolant is forcibly pumped through the annular flowpath or is transported through the annular flowpath through natural convection.

[0021] In another aspect combinable with one, some, or all of the previous aspects, the casing includes a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole, the second portion including a downhole end of the casing.

[0022] Another aspect combinable with one, some, or all of the previous aspects includes one or more fasteners configured to secure at least a portion of the casing to a host rock of the one or more subterranean formations.

[0023] In another aspect combinable with one, some, or all of the previous aspects, the casing includes at least two casing portions and a thermal expansion gap between the at least two casing portions in the borehole.

[0024] In another aspect combinable with one, some, or all of the previous aspects, the casing includes at least two casing portions and an expansion joint between the at least two casing portions in the borehole.

[0025] In another aspect combinable with one, some, or all of the previous aspects, the expansion joint includes a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; and a second threaded member threadingly coupled to a second casing portion of the at least two casing portions.

[0026] In another aspect combinable with one, some, or all of the previous aspects, the second threaded member is coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

[0027] In another aspect combinable with one, some, or all of the previous aspects, the secondary loop thermally couples the primary loop with the heat exchanger and is configured to transport the secondary loop liquid between the heat exchanger and a power conversion system.

[0028] In another aspect combinable with one, some, or all of the previous aspects, the secondary loop is configured to transport the secondary loop liquid between the heat exchanger and the terranean surface by natural circulation.Attorney Docket No.: 57302-0010WO1

[0029] Another aspect combinable with one, some, or all of the previous aspects includes means to provide a force for transporting the secondary loop liquid between the heat exchanger and the terranean surface.

[0030] In another aspect combinable with one, some, or all of the previous aspects, the secondary loop liquid includes water.

[0031] In another aspect combinable with one, some, or all of the previous aspects, the primary loop is fluidly isolated from the secondary loop.

[0032] In another aspect combinable with one, some, or all of the previous aspects, the heat exchanger is configured to transfer heat from the primary loop liquid in the primary loop to the secondary loop liquid in the secondary loop.

[0033] In another aspect combinable with one, some, or all of the previous aspects, the power conversion system is located at the terranean surface.

[0034] In another aspect combinable with one, some, or all of the previous aspects, the primary loop liquid includes heavy water.

[0035] In another example implementation, a method of operating a nuclear reactor system includes identifying a nuclear reactor system that includes at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations. The at least one reactor vessel includes at least one reactor core that includes at least one nuclear fission element; a heat exchanger positioned in the borehole proximate the at least one reactor core and including a primary loop and a secondary loop configured to transport a secondary loop liquid through the heat exchanger; and a canister that at least partially encloses the heat exchanger and includes an open first end and an open second end. The canister is configured to form at least a portion of the secondary loop and includes a non-straight surface. The method includes operating the nuclear reactor system by transporting a primary loop liquid between the reactor core and the heat exchanger and transporting a secondary loop liquid through the heat exchanger.

[0036] In an aspect combinable with the example implementation, the non-straight surface includes an undulating surface.

[0037] In another aspect combinable with one, some, or all of the previous aspects, the undulating surface is formed to approximate a sine wave.

[0038] In another aspect combinable with one, some, or all of the previous aspects, the non-straight surface includes an outer surface of the canister.Attorney Docket No.: 57302-0010WO1

[0039] In another aspect combinable with one, some, or all of the previous aspects, the non-straight surface includes a portion of the wall of the canister.

[0040] Another aspect combinable with one, some, or all of the previous aspects includes expanding or contracting the non-straight surface of the canister based on thermal energy generated by the reactor core.

[0041] Another aspect combinable with one, some, or all of the previous aspects includes transporting the primary loop liquid upward to the reactor core in an upflow pipe portion that includes an inlet in fluid communication with the reactor core; and transporting the primary loop liquid downward to the reactor core in a downflow pipe portion fluidly coupled to the upflow pipe portion and including an outlet in fluid communication with the reactor core,

[0042] Another aspect combinable with one, some, or all of the previous aspects includes transporting the primary loop liquid within a first loop portion and a second loop portion of the downflow pipe portion.

[0043] Another aspect combinable with one, some, or all of the previous aspects includes transporting the primary loop liquid within a chirality reversal portion between the first and second loop portions.

[0044] In another aspect combinable with one, some, or all of the previous aspects, a length of the first loop portion and a length of the second loop portion are different.

[0045] Another aspect combinable with one, some, or all of the previous aspects includes expanding or contracting the downflow pipe portion based on thermal energy generated by the reactor core.

[0046] In another aspect combinable with one, some, or all of the previous aspects, the nuclear reactor system includes a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core.

[0047] Another aspect combinable with one, some, or all of the previous aspects includes transporting a coolant in an annular flowpath between the heat exchanger and the casing to adjust a temperature of at least a portion of the casing.

[0048] Another aspect combinable with one, some, or all of the previous aspects includes forcibly pumping the coolant through the annular flowpath; or transporting the coolant through the annular flowpath through natural convection.Attorney Docket No.: 57302-0010WO1

[0049] In another aspect combinable with one, some, or all of the previous aspects, the casing includes a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole.

[0050] In another aspect combinable with one, some, or all of the previous aspects, the second portion includes a downhole end of the casing.

[0051] In another aspect combinable with one, some, or all of the previous aspects, the casing includes at least two casing portions; and a thermal expansion gap between the at least two casing portions in the borehole; or an expansion joint between the at least two casing portions in the borehole.

[0052] In another aspect combinable with one, some, or all of the previous aspects, a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; and a second threaded member threadingly coupled to a second casing portion of the at least two casing portions, the second threaded member coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

[0053] Another aspect combinable with one, some, or all of the previous aspects includes transporting the secondary loop liquid between the heat exchanger and a power conversion system; and transferring heat from the primary loop liquid to the secondary loop liquid in the heat exchanger.

[0054] Another aspect combinable with one, some, or all of the previous aspects includes transporting the secondary loop liquid between the heat exchanger and the terranean surface by at least one of forcible pumping or natural circulation.

[0055] The details of one or more implementations of the subject matter described in this disclosure are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0056] FIG. 1 is a diagram of an example borehole nuclear reactor power plant system according to the present disclosure.

[0057] FIG. 2 is a diagram of an example implementation of a heat exchanger (or steam generator) that can be used in a borehole nuclear reactor according to the present disclosure.Attorney Docket No.: 57302-0010WO1

[0058] FIG. 3 is a diagram of an example implementation of a borehole casing that can be used in a borehole nuclear reactor according to the present disclosure.DETAILED DESCRIPTION

[0059] In example implementations of a deep borehole reactor, nuclear fuel is emplaced in a vertical, slanted, or directional borehole to create an underground fission reactor. A power generation system can be fluidly coupled to remove thermal energy from the borehole to bring useful power to the surface or near surface. The reactor fits in a borehole that is not capable of or designed for or intended for human occupation, formed deep in the ground through one or more subterranean formations. Thus, unlike a reactor designed to fit underground in a mine with human occupants that are capable of working on or attending to the reactor underground, example implementations of a borehole reactor cannot be worked on or attended to by humans within the borehole. Due to the depth at which nuclear fuel is stored in the borehole, the nuclear reactor in a borehole at one kilometer (km) will have a pressure of one hundred atmospheres; at 1.6 km (about 1 mile) the pressure will be one hundred-sixty atmospheres, approximately equal to that in the core of a pressurized water reactor (PWR).

[0060] A diagram of an example reactor system 150 is shown in FIG. 1, and the reactor system 150 can include one or more liquid control rods according to the present disclosure. FIG.1 is an overview of a borehole nuclear reactor system for the embodiment of a vertical borehole. In this example, the vertical borehole (e.g., wellbore) is a deep, human-unoccupiable borehole, i.e., not a borehole formed from a human-occupiable mine. In this embodiment, only one hole is depicted, and it contains only one fuel assembly. In other embodiments, multiple fuel assemblies can be placed in a borehole, either vertically arranged, or spread though branches in the borehole. Further, multiple boreholes can be used to increase the total power delivered to the surface or near surface. In addition, once the fuel in a borehole reactor is depleted, it can be removed, or, in the preferred implementation, left in place, covered with sand or other support, and a second nuclear reactor placed above it. All materials in the reactor system can be designed for low corrosion.

[0061] The reactor system 150 can be used to provide heat in the form of hot water, steam 126, and / or by using a power conversion system, e.g., generator 122. The generator 122 can be, for example, a turbine or thermocouple stack or other heat-driven generator. The heat can also beAttorney Docket No.: 57302-0010WO1used for commercial purposes (such as heating buildings or for heat-intensive industry) without conversion to electricity.

[0062] FIG. 1 includes a reference arrow 125 defining uphole and downhole directions. FIG. 1 shows a vertical borehole, but the borehole can be directionally drilled into rock 116 at a slanted or near-horizontal or other configuration. The generator 122 is located at a terranean surface 124. A vertical borehole 115 descends to a depth of approximately one-half kilometer (km) or greater (e.g., 1.0 km or greater, 1.5 km or greater, 2.0 km or greater, or other predetermined depth). The borehole 115 includes a casing 108 that can be made to adhere to the borehole wall 135. The borehole 115 can be narrow. The borehole 115 can have a diameter of four to forty-six inches (e.g., four inches or greater, eight inches or greater, twelve inches or greater, eighteen inches or greater, twenty-four inches or greater, thirty-six inches or greater, forty inches or greater).

[0063] At or near the bottom of the borehole 115, nuclear fuel is held in a reactor 130 including one or more fuel rods 120. A height of the reactor 130 is defined between an uphole end 142 and a downhole end 144 of the reactor 130. In other words, for a vertical reactor, the height dimension of the reactor is in the uphole and downhole directions. The reactor 130 is surrounded by a primary coolant, or moderator, 141. In some examples, the moderator 141 is water. The reactor section is isolated from the surface 104 by a heat exchanger (or steam generator) 140. The moderator 141 can flow by natural circulation to the heat exchanger 140 above the reactor 130 through, e.g., a hot water pipe (not shown). The reactor 130 is within a reactor vessel 105.

[0064] An insulated pipe 138 is positioned in the borehole 115. During operation, secondary water 128 flows downward outside of the pipe 138. The secondary water 128 is heated by the primary coolant 141 as the secondary water 128 passes through the heat exchanger 140. The heated water, or steam 126, then flows upward inside the pipe 138. The pipe 138 thus carries heat generated by the reactor 130 to the surface 104.

[0065] The reactor system can include a coolant system that is configured to transport the moderator between the reactor core 130 and the heat exchanger 140 by natural circulation. In some examples, the reactor system includes one or more pumps 123 that provide a force for transporting the moderator between the reactor core 130 and the heat exchanger 140. In some examples, the reactor system 150 includes a second coolant system thermally coupled to the primary coolant system with the heat exchanger 140 and configured to transport a fluid coolant between the heat exchanger 140 and a pow’er conversion system 122. The second coolant systemAttorney Docket No.: 57302-0010WO1can be configured to transport the fluid coolant between the heat exchanger 140 and the terranean surface 124 by natural circulation or by one or more pumps 123. In some examples, the fluid coolant, or moderator, is light water. In some examples, the fluid coolant, or moderator, is heavy water. The primary coolant system and the second coolant system can be isolated from each other. The heat exchanger 140 can be configured to transfer heat from the moderator in the coolant system to the fluid coolant in the second coolant system. The power conversion system 122 can be located at the terranean surface 124.

[0066] A deep borehole reactor according to the present disclosure differs from terranean surface-based light-water reactors. For one, the nuclear fuel of a deep borehole reactor can be approximately one mile underground (e.g., 0.8 miles or more from the surface 104, 1.2 miles or less from the surface 104). Also, the casing 108 (a metal or other tubular installed in the borehole similar to casings installed in hydrocarbon production wells) is filled with liquid (e.g., fresh water or brine), and there is no air to replace the coolant liquid.

[0067] In example implementations of a borehole nuclear reactor, a heat exchanger (i.e., the heat exchanger 140) is positioned in the borehole at a particular depth, such as, for example, 1 mile below a terranean surface. A width of the borehole (which can be cased or uncased) can be about 30 inches. The heat exchanger 140 is placed above (uphole of) the reactor core 130, and the combination of heat exchanger 140 and reactor core 130 (e.g., with nuclear fuel) can be lowered into the borehole 115. When at the particular depth, fission control systems and / or components, such as chemicals and / or control rods can be removed from the reactor core 130. The fission reaction can then go critical to generate, in one example, 50 megawats of heat. This heat is removed by flowing liquid (e.g., water), which also provides a moderator (e.g., a primary loop liquid) for the reactor. In some aspects, the liquid does not boil because it is kept at sufficiently high pressure (e.g., 160 atm) that the hot liquid (e.g., 315°C) will be below its boiling point at that pressure.

[0068] The present disclosure uses the term “heat exchanger” to refer to a component of the borehole nuclear reactor in which heat is transferred from a primary coolant to a secondary coolant. The primary coolant is heated by the fission reaction in the reactor core 130, and heat transferred from the primary coolant to the secondary coolant is subsequently used for electrical power generation (e.g., by power conversion system 122). In example aspects, due to, for example, a pressure of the secondary’ coolant at depth in the borehole nuclear reactor, the secondary coolantAttorney Docket No.: 57302-0010WO1remains a liquid or mixed phase fluid as it is heated in the heat exchanger. Alternatively, if the transfer of energy causes the secondary’ coolant to phase change from liquid to gas (i.e., boil), the heat exchanger can be, and can be referred to as, a steam generator. This term refers to examples where the secondary' coolant is not purely water but can be a liquid that includes or excludes water (and phase changes to a gas phase as it passes through the steam generator).

[0069] Thermal expansion can occur when the reactor becomes critical and generates many megawatts of heat. Prior to reaching criticality, the temperature may be close to the temperature of the host rock formation (through which the borehole is formed), which at a depth of one mile is likely to be about 60°C, When the reactor goes critical, parts of the reactor core 130 and heat exchanger 140 stay at low temperature and other parts become hotter. Mechanical connections between hot and cold components of the reactor core 130 and / or heat exchanger 140 can generate thermal stress, which, without design consideration, could result in buckling or even breaching of containers. Thus, the present disclosure describes systems and methods to accommodate thermal expansion without damage or unacceptable geometric distortion to the components of the borehole nuclear reactor and, particularly, underground components of the borehole nuclear reactor,

[0070] In a deep borehole nuclear reactor, liquid (e.g., water) circulates in a closed loop from the reactor core 130 to the heat exchanger 140 and back in a primary loop. As an example, the liquid can enter the bottom (e.g., downhole end) at the reactor at 275°C, and emerge from the top (e.g., uphole end) at 315°C. The liquid remains, for example, at a pressure of 160 atm, and at this pressure the liquid does not boil at these temperatures. The liquid flows into the heat exchanger 140 located proximately above the reactor core 130 in the borehole 115. The heat exchanger includes a secondary loop of liquid (e.g., water) that is kept in physical isolation (i.e., fluidly decoupled) from the primary loop of water, but is in thermal contact (i.e., thermally coupled) through a thermally-conductive material such as a metal pipe (or pipe made of a thermally conductive material). The liquid in the secondary loop is generally kept at a lower pressure, such as about 80 atm.

[0071] In example implementations, the primary loop liquid flows to the top of the heat exchanger 140 and then cools as it descends back to the reactor core 130. The secondary loop liquid temperature rises as it flows upward (toward the terranean surface) and is converted to gas (e.g., steam) near the top of the heat exchanger 140. Both the primary loop liquid and the secondary loop liquid / steam can flow in pipes, or they can flow in larger regions (flowpaths).Attorney Docket No.: 57302-0010WO1

[0072] FIG. 2 shows a portion of a heat exchanger 200 for a borehole nuclear reactor. In some aspects, heat exchanger 200 can be used as the heat exchanger 140 show in FIG. 1. As shown in FIG. 2, a primary loop liquid 205 flow’s to the top of the heat exchanger 200 in a primary pipe loop 202 and then flows downwards in the primary pipe loop 202. A secondary loop (or flowpath) 230 is defined around the primary pipe loop 202 and, in this example, by a canister 218 that surrounds or encloses the primary pipe loop 202. The secondary flowpath 230 fluidly coupled to or is part of, for example, a secondary loop that circulates a secondary fluid (e.g., heated water or steam 126) within the borehole reactor to generate power. In some aspects, the secondary flowpath 230 is fluidly coupled to or part of an annular flowpath in the borehole nuclear reactor that is defined between a subterranean formation (or a casing installed in the subterranean formation), and a pipe (such as pipe 138) that extends from the heat exchanger / reactor core installed in the borehole to a terranean surface.

[0073] In this example, the primary pipe loop 202 is formed of a primary conduit 224 (e.g., for uphole directed flow away from a reactor core) and another, fluidly coupled primary conduit portion 204 (e.g., for downhole directed flow toward the reactor core). In this example, the primary conduit portion 224 is relatively or substantially vertical (from a downhole direction toward uphole), while the primary conduit portion 204 is looped (from the uphole direction toward downhole).

[0074] In this example, the downward, primary conduit portion 224 includes a secondary portion 210 that spirals. In example implementations of the heat exchanger 200, the secondary portion 210 includes two or more secondary loops 226a, b (e.g., looped portions) with opposite chirality. Chirality refers to the direction of spiral; if the downward flow is clockwise as viewed from above, then that is referred to in the engineering literation as right-handed flow. If it rotates counter-clockwise, that is referred to in the engineering literature as left-handed flow. In this example, primary conduit portion 224 has right-handed flow in a first flow region 206, while the primary conduit portion 224 has left-handed flow in a second flow region 208.

[0075] As shown in FIG. 2, the primary conduit portion 224 is fluidly coupled at an uphole end of the heat exchanger 200 to the primary conduit portion 204 to form a single fluid flowpath for the primary loop liquid 205. Thus, as shown, primary loop liquid 205 enters an inlet 212 of the primary conduit portion 224 (and of the single fluid flowpath) as a supply flow 209 and leavesAttorney Docket No.: 57302-0010WO1an outlet 214 of the primary conduit portion 204 (and of the single fluid flowpath) as a return flow 207, which returns to the reactor core (e.g., reactor core 130).

[0076] Supply flow 209 enters the primary loop 202 as a heated liquid from the reactor core, and heat is transferred to a secondary liquid 201 that enters the heat exchanger 200. As heat is transferred from the supply flow 209 to the secondary liquid 201, a heated, mixed phase fluid 203 flows through the secondary flowpath 230. At an uphole end of the heat exchanger 200, the heated, mixed phase fluid 203 can transform into a steam (or heated gas phase) 211 based on an amount of heat transferred from the primary loop liquid 205. The primary loop liquid 205 leaves the outlet 214 as a cooled liquid flow 207 (back to the reactor core).

[0077] In the illustrated implementation, the heat exchanger 200 can be contained in or at least surrounded by the container or canister 218. In this example, the canister 218 includes an open top end 232 and an open bottom end 234.

[0078] In example aspects, the canister 218 is formed with an undulating (or non-straight) surface 210as shown in FIG. 2. This design differs from a standard canister, which has a surface with a varying radius. The undulating pattern 210 can be like or similar to a sine-wave (as shown in FIG. 2) or any other pattern that reduces a force needed to stretch or compress the canister 218 in a vertical direction (uphole or downhole). The canister 218 with an undulating or non-straight surface can require a lower force to stretch or compress it much like a spring requires a lower force to stretch or compress as compared to a straight piece of wire. The undulations 210 can also provide a prescribed buckling that, if the wall of the canister 218 expands in the vertical dimension (uphole and / or downhole), prevents a sudden and larger scale bucking from taking place when the material of the wall undergoes thermal expansion or contraction.

[0079] In a borehole nuclear reactor (such as shown in FIG. 1), the central pipe (or supply pipe) that carries primary loop liquid to the top of the heat exchanger is cool before the reactor becomes critical and becomes hotter when the reactor produces high thermal energy. In FIG. 2, this pipe is show as a straight pipe (primary conduit portion 224 that extends upward through the two or more seconds). In other instances, this pipe (primary conduit portion 224) can be curved or spiral, or have both left-handed and right-handed spirals as shown for the downward part of the loop 202 (primary conduit portion 204). In some aspects, the supply pipe can be covered or enclosed with insulation 236 to prevent heat loss as the liquid (primary loop liquid 205) flows upward. From pre-criticality to full reactor operation, the supply pipe can undergo significantAttorney Docket No.: 57302-0010WO1thermal expansion. For example, for some stainless steels, the thermal expansion coefficient is about 1 x 10-5 per °C. For a vertical pipe of length 4 meters, and a rise in temperature of 315-60 = 255°C, the expansion will be 4 x 255 x 10-5 ~ 0.01 m = 1 cm.

[0080] The canister 218 for the heat exchanger 200, however, is not uniformly heated but is cool near the lower (downhole) section and relatively warmer near the upper (uphole) section. Thus, if the canister 218 did not include an undulating or non-straight surface, a significant force on the canister 218 (e.g., as steel) could cause the upward hot water pipe of the supply pipe (or primary conduit portion 224) to buckle. Thus, the undulating (or non-straight) surface 210 can greatly reduce the force needed to be expanded, and thereby prevent the buckling of the supply pipe 202 (and more specifically, primary conduit portion 224).

[0081] The primary loop liquid 201 flowing to the top of the heat exchanger 200 moves, in the instance depicted in FIG. 2, through a straight pipe (the primary conduit portion 224), In other instances, this pipe can be curved or spiral, or have both left-handed and right-handed spirals as shown for the downward part of the loop. This pipe heats, in the instance described, from its initial temperature at the surface (which can be 20°C) to the reactor emission temperature (which can be 315°C). The downward flowing liquid that boils the liquid in the secondary loop cools as it descends, and for that reason, the thermal expansion is not as extensive as for the upflowing liquid. To enable such expansion with a pipe that is rigidly attached to the upflow pipe, and to allow for large surface area to transfer heat to the secondary loop, the downflow pipe (primary conduit portion 204) in FIG. 2 is depicted as a spiral. As with a spring, this spiral allows thermal expansion with a reduced force in the vertical direction (uphole and downhole).

[0082] The spiral of the primary conduit portion 204 can be reversed, one or more times, to reduce torque put on the pipe as it expands with fixed ends. These sections are depicted in FIG.2 as left-handed and right-handed flow regions 208 and 206, respectively. The length of each region can be adjusted to compensate for non-uniform heating that can occur in the downflowing loops. The temperature rise at the top, for example, can be greater than at the bottom. In some aspects, if a two section system is used as shown in FIG. 2, the upper section can be made shorter than the lower section.

[0083] A detailed heat exchanger design has many issues not addressed here, such as the velocity of flow of the liquid, connectors, thickness of the pipe, and other aspects. The upflowing secondary loop liquid can move freely around the downflowing primary loop liquid, or it too canAttorney Docket No.: 57302-0010WO1be confined to tubes. Thus, the features discussed with respect to FIG. 2 can be incorporated into a design that includes components to address the other concerns and design issues of a borehole nuclear reactor heat exchanger.

[0084] As further described herein, a borehole for a deep borehole nuclear reactor can be cased (e.g., with a steel pipe similar to casing in a hydrocarbon well) or uncased. When the casing is lowered into the borehole, it can quickly reach thermal equilibrium w’ith the surrounding rock formation into w’hich the borehole is formed (e.g., drilled). At a depth of 1 mile, the temperature of the casing in a region in which the heat exchanger and reactor core is positioned can be about 60°C, When the casing is cemented into place in the borehole, the cement can also set at a similar temperature,

[0085] When the reactor produces heat, the casing can undergo thermal expansion. Such thermal expansion can cause buckling of the casing, cracking of the cement, both, or other unwanted thermal phenomena. The present disclosure provides for example implementations that can address such thermal expansion, either alone or in combination.

[0086] For example, example aspects of a borehole nuclear reactor can include an annular flowpath for a coolant that extends between the reactor core / heat exchanger and the casing. The coolant can be or include water that is circulated in the annulus flowpath between the reactor core / heat exchanger and the casing. In addition, in some aspects, thermal insulation installed on the outer surfaces of the reactor core and the outer wall of the heat exchanger (e.g., on the undulating surface) can also reduce an amount of heat passed to the liquid in the annular flowpath.

[0087] This flow of liquid (i.e., “casing water”) can be convective, e.g., flowing only when heat is transferred into it, and conveying and dissipating that heat over a large section of the casing. This can prevent any part of the casing from expanding enough to buckle or to break away from the cement (that secures it to the subterranean formation). In some aspects, the casing water can flow convectively (e.g., by pressure difference) or it can be forcibly pumped. For example, a tube can be installed at or near the terranean surface into which the casing water can be circulated into the annular flowpath region near or at the bottom (downhole end) of the reactor core.

[0088] As another example that can be used alone or in combination with the casing water, casing temperature can be controlled with a casing installation in which a lower (downhole) portion of the casing is free from cement between it and the subterranean formation. Thus, a portion of the borehole at or near the downhole end can be cased but a float or shoe can be installedAttorney Docket No.: 57302-0010WO1between the casing and the formation above the downhole end to prevent cement from being provided to that portion (e.g., downhole of the float or show). If the casing water does not cool the casing sufficiently, or is not used, then expansion of the casing may take place primarily at the bottom (downhole end) of the borehole. To accommodate this, the cement in this region can be omitted, and the lower casing joints (one or more joints) of the casing can be hung from the upper joints (which are cemented). Then, when or if the lower casing is heated, it can expand into the borehole space below (downhole).

[0089] As another example that can be used alone or in combination with the casing water, in some aspects at least a portion of casing can be secured into the host rock of the subterranean formation into which the borehole is formed. For example, at the bottom (downhole end) of the borehole, fasteners 318 shown in FIG. 3 (e.g., horizontal bolts) can be extended from the casing into the host rock to keep the casing from moving or thermally expanding or contracting. By locking the casing into the host rock, stress from the heating is conveyed into the rock and casing expansion (due to heat) can be prevented or minimized.

[0090] As another example that can be used alone or in combination with the casing water, one or more expansion gaps can be installed or formed in the casing. Such expansion gaps between casing joints can provide space for thermal expansion of the casing when heated by the reactor core. In some aspects, a thermally reactive material (metal or otherwise) can fill the expansion gaps but still allow expansion of the casing.

[0091] As another example that can be used alone or in combination with the casing water, one or more expansion joints can be placed between casing joints to accommodate thermal expansion. For example, expansion joints can be formed or installed in the casing as bellow-like regions that allow for motion. As another example, expansion joints can be slip joints, which allow casing segments to have sealed gaps between them that prevent formation water (e.g., brine) from mixing with the casing water but allow for casing expansion.

[0092] An example expansion joint is shown in FIG. 3. FIG. 3 shows a cross-section of a portion of casing 300 that incorporates an expansion joint 303 that includes or is formed by a coupling of two (uphole and downhole) members 306 and 308, respectively. The uphole member 306 is connected (e.g., threadingly as a threaded connection 310) to an upper casing joint (or segment) 302. The downhole member 308 is connected (e.g., threadingly as a threaded connection 310) to a lower casing joint (or segment) 304.Attorney Docket No,: 57302-0010WO1

[0093] As shown in FIG. 3, the uphole member 306 connects to the downhole member 308 with a hook connection 305 (e.g., not threaded or rigid connection) to form the expansion joint 303. As shown in FIG. 3, the hook connection 305 defines or includes a slippage length 320 that varies from, e.g., nothing or an insubstantial distance (when the upper and lower members 306 and 308 are in contact due to thermal or other expansion of the casing 300) to a distance equal to a sum of the largest possible distances for gaps 312 and 314 (e.g., when the upper member 306 is in contact with the casing joint 304, and the lower member 308 is in contact with the casing joint 302).

[0094] Expansion gaps 312 and 314 are formed between the members (306 and 308) and the casing joints (302 and 304) to allow movement of the expansion joint members (upper and lower members 306 and 308) due to, e.g., thermal stress. Optionally, slip covers 316 can be installed over the gaps 312 and 314. In this example, the casing joints 302 and 304 can be standard (e.g,, hydrocarbon well) casing joints with the expansion joint 303 formed therebetween,

[0095] In some aspects, the previously described concepts need not be applied, nor is the casing water concept applied, in example implementations of a borehole nuclear reactor. For example, casing joints of sufficient wall thickness so that it will not buckle if put under thermal compression can be used. While adjacent cement may break, that would be a local effect in a very deep location that has no impact on human safety. Such an option (no expansion joints or gaps, no omitted cement, no casing water) can be implemented in a deep borehole nuclear reactor without catastrophically affecting the nuclear fission reaction and power generation of the reactor.

[0096] In example implementations of a deep borehole nuclear reactor, the casing can be, e.g., a mile long, although the casing can be segregated into stages with, e.g., different diameters and different length. If, in some aspects, insulation is installed on the reactor core / heat exchanger, leakage of reactor heat into the casing water, for the entire length of the casing, can be kept below 1 MWth (megawatt thermal). This heat can be removed from the casing water by conduction and convection to the length of the casing.

[0097] The cooling can be augmented by active pumping of the casing water to the surface followed by return to the annular flowpath (if necessary). For example, the casing water can heat to 1°C above a temperature of the local host rock at every level of depth. For a casing with an inner diameter of 28 inches and length of 1 mile, the area of the casing is about 3,600 m2. If the casing is 1-inch thick and has thermal conductivity (typical for carbon steel) of 50 W / m2 / C, thenAttorney Docket No.: 57302-0010WO1the power flow out will be 7 MWth. With a thinner casing, the flow will be even greater. (The cement and water outside the casing is being ignored in these calculations.) This is a much higher flow out from the casing water than is flowing in from the steam pipe. Based on this rough estimate, there is no expectation of the temperature rise of the casing to be more than 1°C when the reactor becomes operational. Such temperature changes are similar to or lower than those experienced in the hydrocarbon industry when production of deep (warm) oil and gas begins, and the cemented casings are designed to tolerate such temperature rises as a matter of course. Thus, in some aspects, warming of the 1-mile long casing may not create thermal expansion problems in the casing.

[0098] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what can be claimed, but rather as descriptions of features specific to particular implementations of particular inventions. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features can be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination can be directed to a subcombination or variation of a subcombination.

[0099] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations.

[0100] This disclosure describes a number of example embodiments. In a first example embodiment, a nuclear reactor system (and method for operating) includes at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations. The at least one reactor vessel includes at least one reactor core that includes at least one nuclear fission element. The system includes a heat exchanger positioned in the borehole proximate the at least one reactor core. The heat exchanger includes a primary loopAttorney Docket No.: 57302-0010WO1configured to transport a primary loop liquid between the reactor core and the heat exchanger; and a secondary loop configured to transport a secondary loop liquid through the heat exchanger. The system includes a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core; and an annular flowpath between the heat exchanger and the casing, the annular flowpath configured to transport a coolant therethrough to adjust a temperature of at least a portion of the casing.

[0101] In an aspect combinable with the first example embodiment, the coolant includes water.

[0102] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the annular flowpath includes an inlet at or near the terranean surface,

[0103] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the coolant is forcibly pumped through the annular flowpath or is transported through the annular flowpath through natural convection,

[0104] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the casing includes a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole, the second portion including a downhole end of the casing.

[0105] Another aspect combinable with one, some, or all of the previous aspects of the first example embodiment includes one or more fasteners configured to secure at least a portion of the casing to a host rock of the one or more subterranean formations.

[0106] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the casing includes at least two casing portions and a thermal expansion gap between the at least two casing portions in the borehole.

[0107] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the casing includes at least two casing portions and an expansion joint between the at least two casing portions in the borehole.

[0108] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the expansion joint includes a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; and a second threaded member threadingly coupled to a second casing portion of the at least two casing portions.Attorney Docket No.: 57302-0010WO1

[0109] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the second threaded member is coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

[0110] Another aspect combinable with one, some, or all of the previous aspects of the first example embodiment includes a canister that at least partially encloses the heat exchanger and includes an open first end and an open second end, the canister configured to form at least a portion of the secondary loop, the canister including a non-straight surface,

[0111] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the non-straight surface includes an undulating surface,

[0112] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the undulating surface is formed to approximate a sine wave.

[0113] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the non-straight surface includes an outer surface of the canister.

[0114] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the non-straight surface includes a portion of the wall of the canister.

[0115] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the non-straight surface is configured to allow expansion or contraction of the canister based on thermal energy generated by the reactor core.

[0116] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the primary loop includes an upflow pipe portion that includes an inlet in upflow fluid communication with the reactor core; and a downflow pipe portion fluidly coupled to the upflow pipe portion and including an outlet in downflow fluid communication with the reactor core.

[0117] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the downflow pipe portion includes a first loop portion and a second loop portion.

[0118] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the downflow pipe portion includes a chirality reversal portion between the first and second loop portions.Attorney Docket No.: 57302-0010WO1

[0119] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, a length of the first loop portion and a length of the second loop portion are different.

[0120] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the downflow pipe portion is configured to allow expansion or contraction of the primary loop based on thermal energy generated by the reactor core.

[0121] Another aspect combinable with one, some, or all of the previous aspects of the first example embodiment includes insulation applied to the primary loop.

[0122] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the secondary loop thermally couples the primary loop with the heat exchanger and is configured to transport the secondary loop liquid between the heat exchanger and a power conversion system.

[0123] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the secondary loop is configured to transport the secondary loop liquid between the heat exchanger and the terranean surface by natural circulation.

[0124] Another aspect combinable with one, some, or all of the previous aspects of the first example embodiment includes means to provide a force for transporting the secondary loop liquid between the heat exchanger and the terranean surface.

[0125] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the secondary loop liquid includes water.

[0126] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the primary loop is fluidly isolated from the secondary loop.

[0127] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the heat exchanger is configured to transfer heat from the primary loop liquid in the primary loop to the secondary loop liquid in the secondary loop.

[0128] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the power conversion system is located at the terranean surface.

[0129] In another aspect combinable with one, some, or all of the previous aspects of the first example embodiment, the primary loop liquid includes heavy water.

[0130] In a second example embodiment, a nuclear reactor system (and method for operating) includes at least one reactor vessel positioned in a borehole that extends from aAttorney Docket No.: 57302-0010WO1terranean surface through one or more subterranean formations. The at least one reactor vessel includes at least one reactor core that includes at least one nuclear fission element; and a heat exchanger positioned in the borehole proximate the at least one reactor core. The heat exchanger includes a primary loop configured to transport a primary loop liquid between the reactor core and the heat exchanger; and a secondary' loop configured to transport a secondary’ loop liquid through the heat exchanger. The primary loop includes a first loop portion, a second loop portion, and a chirality reversal portion between the first and second loop portions.

[0131] In an aspect combinable with the second example embodiment, the primary loop includes an upflow pipe portion that includes an inlet in upflow fluid communication with the reactor core; and a downflow pipe portion fluidly coupled to the upflow pipe portion and including an outlet in downflow fluid communication with the reactor core,

[0132] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the downflow pipe portion includes the first loop portion and the second loop portion.

[0133] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the downflow pipe portion is configured to allow expansion or contraction of the primary loop based on thermal energy generated by the reactor core.

[0134] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, a length of the first loop portion and a length of the second loop portion are different.

[0135] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, insulation applied to the primary loop.

[0136] Another aspect combinable with one, some, or all of the previous aspects of the second example embodiment includes a canister that at least partially encloses the heat exchanger and includes an open first end and an open second end, the canister configured to form at least a portion of the secondary loop, the canister including a non-straight surface.

[0137] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the non-straight surface includes an undulating surface.

[0138] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the undulating surface is formed to approximate a sine wave.Attorney Docket No.: 57302-0010WO1

[0139] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the non-straight surface includes an outer surface of the canister.

[0140] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the non-straight surface includes a portion of the wall of the canister.

[0141] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the non-straight surface is configured to allow expansion or contraction of the canister based on thermal energy generated by the reactor core.

[0142] Another aspect combinable with one, some, or all of the previous aspects of the second example embodiment includes a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core.

[0143] Another aspect combinable with one, some, or all of the previous aspects of the second example embodiment includes an annular flowpath between the heat exchanger and the casing, the annular flowpath configured to transport a coolant therethrough to adjust a temperature of at least a portion of the casing.

[0144] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the coolant includes water.

[0145] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the annular flowpath includes an inlet at or near the terranean surface.

[0146] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the coolant is forcibly pumped through the annular flowpath or is transported through the annular flowpath through natural convection.

[0147] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the casing includes a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole, the second portion including a downhole end of the casing.

[0148] Another aspect combinable with one, some, or all of the previous aspects of the second example embodiment includes one or more fasteners configured to secure at least a portion of the casing to a host rock of the one or more subterranean formations.Attorney Docket No.: 57302-0010WO1

[0149] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the casing includes at least two casing portions and a thermal expansion gap between the at least two casing portions in the borehole.

[0150] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the casing includes at least two casing portions and an expansion joint between the at least two casing portions in the borehole.

[0151] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the expansion joint includes a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; and a second threaded member threadingly coupled to a second casing portion of the at least two casing portions.

[0152] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the second threaded member is coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

[0153] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the secondary loop thermally couples the primary loop with the heat exchanger and is configured to transport the secondary loop liquid between the heat exchanger and a power conversion system.

[0154] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the secondary loop is configured to transport the secondary loop liquid between the heat exchanger and the terranean surface by natural circulation.

[0155] Another aspect combinable with one, some, or all of the previous aspects of the second example embodiment includes means to provide a force for transporting the secondary loop liquid between the heat exchanger and the terranean surface.

[0156] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the secondary loop liquid includes water.

[0157] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the primary loop is fluidly isolated from the secondary loop.

[0158] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the heat exchanger is configured to transfer heat from the primary loop liquid in the primary loop to the secondary loop liquid in the secondary loop.Attorney Docket No.: 57302-0010WO1

[0159] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the power conversion system is located at the terranean surface.

[0160] In another aspect combinable with one, some, or all of the previous aspects of the second example embodiment, the primary loop liquid includes heavy water.

[0161] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. For example, example operations, methods, or processes described herein may include more steps or fewer steps than those described. Further, the steps in such example operations, methods, or processes may be performed in different successions than that described or illustrated in the figures. Accordingly, other implementations are within the scope of the following claims.

Claims

Attorney Docket No.: 57302-0010WO1WHAT IS CLAIMED IS:

1. A nuclear reactor system, comprising:at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations, the at least one reactor vessel comprising at least one reactor core that comprises at least one nuclear fission element;a heat exchanger positioned in the borehole proximate the at least one reactor core, the heat exchanger comprising:a primary’ loop configured to transport a primary loop liquid between the reactor core and the heat exchanger; anda secondary loop configured to transport a secondary loop liquid through the heat exchanger; anda canister that at least partially encloses the heat exchanger and comprises an open first end and an open second end, the canister configured to form at least a portion of the secondary loop, the canister comprising a non-straight surface.

2. The nuclear reactor system of claim 1, wherein the non-straight surface comprises an undulating surface.

3. The nuclear reactor system of claim 2, wherein the undulating surface is formed to approximate a sine wave.

4. The nuclear reactor system of claim 1, wherein the non-straight surface comprises an outer surface of the canister.

5. The nuclear reactor system of claim 1, wherein the non-straight surface comprises a portion of the wall of the canister.

6. The nuclear reactor system of claim 1, wherein the non-straight surface is configured to allow expansion or contraction of the canister based on thermal energy generated by the reactor core.Attorney Docket No.: 57302-0010WO17. The nuclear reactor system of claim 1, wherein the primary loop comprises: an upflow pipe portion that comprises an inlet in upflow fluid communication with the reactor core; anda downflow pipe portion fluidly coupled to the upflow pipe portion and comprising an outlet in downflow fluid communication with the reactor core.

8. The nuclear reactor system of claim 7, wherein the downflow pipe portion comprises a first loop portion and a second loop portion.

9. The nuclear reactor system of claim 8, wherein the downflow pipe portion comprises a chirality reversal portion between the first and second loop portions.

10. The nuclear reactor system of claim 8, wherein a length of the first loop portion and a length of the second loop portion are different.

11. The nuclear reactor system of claim 7, wherein the downflow pipe portion is configured to allow expansion or contraction of the primary loop based on thermal energy generated by the reactor core.

12. The nuclear reactor system of claim 7, comprising insulation applied to the primary loop.

13. The nuclear reactor system of claim 1, comprising a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core.

14. The nuclear reactor system of claim 13, comprising an annular flowpath between the heat exchanger and the casing, the annular flowpath configured to transport a coolant therethrough to adjust a temperature of at least a portion of the casing.

15. The nuclear reactor system of claim 14, wherein the coolant comprises water.

16. The nuclear reactor system of claim 14, wherein the annular flowpath comprises an inlet at or near the terranean surface.Attorney Docket No.: 57302-0010WO117. The nuclear reactor system of claim 14, wherein the coolant is forcibly pumped through the annular flowpath or is transported through the annular flowpath through natural convection.

18. The nuclear reactor system of claim 13, wherein the casing comprises a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole, the second portion comprising a downhole end of the casing.

19. The nuclear reactor system of claim 13, comprising one or more fasteners configured to secure at least a portion of the casing to a host rock of the one or more subterranean formations.

20. The nuclear reactor system of claim 13, wherein the casing comprises at least two casing portions and a thermal expansion gap between the at least two casing portions in the borehole.

21. The nuclear reactor system of claim 13, wherein the casing comprises at least two casing portions and an expansion joint between the at least two casing portions in the borehole.

22. The nuclear reactor system of claim 21, wherein the expansion joint comprises: a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; anda second threaded member threadingly coupled to a second casing portion of the at least two casing portions, the second threaded member coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

23. The nuclear reactor system of claim 1, wherein the secondary loop thermally couples the primary loop with the heat exchanger and is configured to transport the secondary loop liquid between the heat exchanger and a power conversion system.

24. The nuclear reactor system of claim 23, wherein the secondary loop is configured to transport the secondary loop liquid between the heat exchanger and the terranean surface by natural circulation.Attorney Docket No.: 57302-0010WO125. The nuclear reactor system of claim 23, comprising means to provide a force for transporting the secondary loop liquid between the heat exchanger and the terranean surface.

26. The nuclear reactor system of claim 23, wherein the secondary loop liquid comprises water.

27. The nuclear reactor system of claim 23, wherein the primary loop is fluidly isolated from the secondary loop.

28. The nuclear reactor system of claim 23, wherein the heat exchanger is configured to transfer heat from the primary loop liquid in the primary loop to the secondary loop liquid in the secondary loop.

29. The nuclear reactor system of claim 23, wherein the power conversion system is located at the terranean surface.

30. The nuclear reactor system of claim 1, wherein the primary loop liquid comprises heavy water.

31. A method of operating a nuclear reactor system, comprising:identifying a nuclear reactor system that comprises at least one reactor vessel positioned in a borehole that extends from a terranean surface through one or more subterranean formations, the at least one reactor vessel comprising:at least one reactor core that comprises at least one nuclear fission element; a heat exchanger positioned in the borehole proximate the at least one reactor core, the heat exchanger comprising a primary loop and a secondary loop configured to transport a secondary loop liquid through the heat exchanger; anda canister that at least partially encloses the heat exchanger and comprises an open first end and an open second end, the canister configured to form at least a portion of the secondary loop, the canister comprising a non-straight surface; andoperating the nuclear reactor system by transporting a primary loop liquid between the reactor core and the heat exchanger and transporting a secondary loop liquid through the heat exchanger.Attorney Docket No.: 57302-0010WO132. The method of claim 31, wherein the non-straight surface comprises an undulating surface.

33. The method of claim 32, wherein the undulating surface is formed to approximate a sine wave.

34. The method of claim 31, wherein the non-straight surface comprises an outer surface of the canister.

35. The method of claim 31, wherein the non-straight surface comprises a portion of the wall of the canister.

36. The method of claim 31, comprising expanding or contracting the non-straight surface of the canister based on thermal energy generated by the reactor core.

37. The method of claim 31, comprising:transporting the primary loop liquid upward to the reactor core in an upflow pipe portion that comprises an inlet in fluid communication with the reactor core; andtransporting the primary loop liquid downward to the reactor core in a downflow pipe portion fluidly coupled to the upflow pipe portion and comprising an outlet in fluid communication with the reactor core.

38. The method of claim 37, comprising transporting the primary loop liquid within a first loop portion and a second loop portion of the downflow pipe portion.

39. The method of claim 38, comprising transporting the primary loop liquid within a chirality reversal portion between the first and second loop portions.

40. The method of claim 38, wherein a length of the first loop portion and a length of the second loop portion are different.

41. The method of claim 37, comprising expanding or contracting the downflow pipe portion based on thermal energy generated by the reactor core.Attorney Docket No.: 57302-0010WO142. The method of claim 31, wherein the nuclear reactor system comprises a casing installed in at least a portion of the borehole from the terranean surface toward the reactor core.

43. The method of claim 42, comprising transporting a coolant in an annular flowpath between the heat exchanger and the casing to adjust a temperature of at least a portion of the casing.

44. The method of claim 43, comprising:forcibly pumping the coolant through the annular flowpath; ortransporting the coolant through the annular flowpath through natural convection.

45. The method of claim 42, wherein the casing comprises a first portion cemented in a first portion of the borehole and a second portion uncemented in a second portion of the borehole downhole of the first portion of the borehole, the second portion comprising a downhole end of the casing.

46. The method of claim 42, wherein the casing comprises at least two casing portions; and:a thermal expansion gap between the at least two casing portions in the borehole; or an expansion joint between the at least two casing portions in the borehole.

47. The method of claim 46, wherein the expansion joint comprises:a first threaded member threadingly coupled to a first casing portion of the at least two casing portions; anda second threaded member threadingly coupled to a second casing portion of the at least two casing portions, the second threaded member coupled to the first threaded member with a hook connection to form thermal expansion gaps between the first and second casing portions.

48. The method of claim 31, comprising:transporting the secondary loop liquid between the heat exchanger and a power conversion system; andtransferring heat from the primary loop liquid to the secondary loop liquid in the heat exchanger.Attorney Docket No.: 57302-0010WO149. The method of claim 48, comprising transporting the secondary loop liquid between the heat exchanger and the terranean surface by at least one of forcible pumping or natural circulation.

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