End fitting for reducing hydrogen transfer to rolled joint and pressure tube, and method of using same

Abstract

According to an aspect, there is provided an end fitting for reducing hydrogen transfer to a pressure tube of a nuclear reactor across a rolled joint. The end fitting includes a barrier disposed along at least a portion of an internal diameter of the end fitting configured to contact coolant. According to an aspect, there is provided a method of reducing the transfer of hydrogen to a pressure tube of a nuclear reactor across a rolled joint. The method includes providing an end fitting including a barrier disposed along at least a portion of an internal diameter of the end fitting configured to contact coolant, and burning fuel in a nuclear reactor.

Description

END FITTING FOR REDUCING HYDROGEN TRANSFER TO ROLLED JOINT AND PRESSURE TUBE, AND METHOD OF USING SAMECROSS-REFERENCE

[0001] The present application claims priority to US provisional patent application no. 63 / 660,356, titled “END FITTING FOR REDUCING HYDROGEN TRANSFER TO ROLLED JOINT AND PRESSURE TUBE, AND METHOD OF USING SAME”, filed on 14 June 2024, the contents of which are incorporated herein by reference.FIELD

[0002] The present invention relates to the use of a barrier to reduce ingress and concentration of hydrogen isotopes at the ends of pressure tubes in a nuclear reactor.INTRODUCTION

[0003] Zirconium alloys are commonly used in nuclear reactors because of a combination of desirable mechanical properties, and low thermal neutron capture cross section. At reactor operating temperatures a corrosion reaction between the heat transport water and zirconium produces an oxide and hydrogen isotopes, some of which are absorbed into the metal matrix. Dissolved hydrogen, and its isotopes, may result in hydrogen embrittlement of zirconium when the hydrogen concentration becomes high enough to exceed the solubility limit, and in some situations can result in delayed hydride cracking (DHC), a form of subcritical crack growth. For some reactor components, such as fuel sheathing, hydrogen ingress is not a grave concern as the component life in reactor is short enough that significant amounts of hydrogen are not absorbed into the metal matrix and the fuel is exchanged at intervals much shorter than the life of the reactor. In CANDUTM-type reactors, and other similar pressurized heavy or light water reactors, large permanent components known as pressure tubes made from zirconium alloys (for example, length 6 m, inside diameter 103 mm and thickness 4 mm) are used to contain the fuel and the primary heat transport water. As the reactor ages, concentrations of hydrogen isotopes in pressure tubes can increase to the point where brittle hydrides may form that can initiate DHC and reduce fracture toughness to the extent that fitness for service becomes an issue and can limit the life of the component. A location of particular concern is where the pressure tube is joined to the reactor at a 403 stainless steel end-fitting using a mechanical joint known as a rolled joint.

[0004] Several different zirconium alloys, and manufacturing procedures have been tried and implemented to reduce the rate of hydrogen ingress into pressure tubes with some success, but hydrogen embrittlement is still a potential issue. Several methods to reduce the rate of hydrogen ingress at the connection between the pressure tube and end-fitting and along the body of the tube have been investigated. Shot peening the inside surface of the pressure tube produces a microstructure that has high resistance to corrosion and subsequent hydrogen pick-up could be halved. None of these methods have been implemented because of uncertainty of long term benefit.

[0005] There is therefore a need for an improved method and system for reducing hydrogen ingress into pressure tubes, and the resulting hydrogen embrittlement.SUMMARY

[0006] Described herein are barriers to hydrogen ingress from the end fitting into the pressure tube via the rolled joint. Introduction of a barrier to hydrogen ingress into the end fitting can reduce the amount of hydrogen available to subsequently enter the pressure tube at the rolled joint interface.

[0007] According to an aspect, there is provided an end fitting configured to reduce the transfer of hydrogen to a pressure tube of a nuclear reactor across a rolled joint. The end fitting includes a barrier disposed along at least a portion of an inner surface of the end fitting configured to contact coolant.

[0008] In some embodiments, the barrier includes plating or bonding of a protective material.

[0009] In some embodiments, the barrier extends a distance outboard of the rolled joint, the distance configured to reduce hydrogen ingress to the pressure tube below a threshold.

[0010] In some embodiments, the barrier includes a coating.

[0011] In some embodiments, the coating includes a compound layer.

[0012] In some embodiments, the compound layer is one or more of an oxide and a nitride.

[0013] In some embodiments, the coating includes a plating and / or bonding of a protective material.

[0014] In some embodiments, the coating includes at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

[0015] In some embodiments, the barrier is configured to extend at least 50 mm from an end of the pressure tube when installed.

[0016] In some embodiments, the barrier is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting from an end of the pressure tube when installed.

[0017] In some embodiments, the end fitting further includes a coating or surface treatment along at least a portion of an outer surface of the end fitting.

[0018] In some embodiments, the coating along the at least a portion of the outer diameter of the end fitting comprises at least one of palladium, platinum, ruthenium, and rhodium.

[0019] According to an aspect, there is provided a method of reducing the transfer of hydrogen to a pressure tube of a nuclear reactor across a rolled joint. The method includes providing an end fitting comprising a barrier disposed along at least a portion of an inner surface of the end fitting configured to contact coolant and burning fuel in a nuclear reactor.

[0020] In some embodiments, burning fuel in the nuclear reactor includes generating hydrogen on the inner surface of the end fitting that becomes available for hydrogen ingress into the pressure tube across the rolled joint. The barrier is configured to impede the generation of hydrogen on the inner surface as compared to an end fitting without the barrier.

[0021] In some embodiments, the barrier includes plating or bonding of a protective material.

[0022] In some embodiments, the barrier extends a distance outboard of the rolled joint, the distance configured to reduce hydrogen ingress to the pressure tube below a threshold.

[0023] In some embodiments, the barrier includes a coating.

[0024] In some embodiments, the coating includes a compound layer.

[0025] In some embodiments, the compound layer is one or more of an oxide and a nitride.

[0026] In some embodiments, the coating includes a plating and / or bonding of a protective material.

[0027] In some embodiments, the coating includes at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

[0028] In some embodiments, the barrier is configured to extend at least 50 mm from an end of the pressure tube when installed.

[0029] In some embodiments, the barrier is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting from an end of the pressure tube when installed.

[0030] In some embodiments, the end fitting further includes a coating or surface treatment along at least a portion of an outer diameter of the end fitting.

[0031] In some embodiments, the coating along the at least a portion of the outer diameter of the end fitting comprises at least one of palladium, platinum, ruthenium, and rhodium.DESCRIPTION OF THE FIGURES

[0032] In the figures, embodiments are illustrated by way of example. It is to be expressly understood that the description and figures are only for the purpose of illustration and as an aid to understanding.

[0033] Embodiments will now be described, by way of example only, with reference to the attached figures, wherein in the figures:

[0034] FIG. 1 is a perspective view of a CANDU™-type reactor, according to some embodiments.

[0035] FIG. 2 is a cutaway view of a CANDUTM-type nuclear reactor fuel channel assembly, according to some embodiments.

[0036] FIG. 3 is a finite element mesh of assembly with interface details, according to some embodiments.

[0037] FIG. 4 is a cutaway view of a fuel channel showing pressure tube rolled joint, according to some embodiments.

[0038] FIG. 5 illustrates sources of deuterium ingress to the rolled joint area of the pressure tube, according to some embodiments.

[0039] FIG. 6 is a 1-D example with ingress at left end, fast diffusion to interface at x=0 and chemical potential jump to the slower diffusion region, according to some embodiments.

[0040] FIG. 7 shows the hysteresis in the Terminal Solid Solubility (TSS) of hydrogen equivalent for dissolution and precipitation, according to some embodiments.

[0041] FIG. 8 shows variation with time of concentration (ppm) distribution in end fitting (EF), according to some embodiments.

[0042] FIG. 9 shows final concentration (ppm) distributions in EF and PT for cPT / cEF= 250, according to some embodiments.

[0043] FIG. 10 shows final concentration (ppm) distributions in EF and PT for <T / cF= 500, according to some embodiments.

[0044] FIG. 11 shows a comparison of cases of FIG. 9 and FIG. 10 with pressure tube concentration below TSSD, according to some embodiments.

[0045] FIG. 12 shows final concentration (ppm) distributions in EF and PT for <T / cF= 750, according to some embodiments.

[0046] FIG. 13 shows final concentration (ppm) distributions in EF and PT for <T / cF= 1000, according to some embodiments.

[0047] FIG. 14 shows a comparison of cases of FIG. 12 and FIG. 13 with pressure tube concentration below TSSD, according to some embodiments.

[0048] FIG. 15 shows the temperature and stress change at EF / PT interface, according to some embodiments.

[0049] FIG. 16 shows node points for 1D verification model, according to some embodiments.

[0050] FIG. 17 show results regarding how the concentration distribution can evolve to achieve elevated values in the pressure tube, according to some embodiments.

[0051] FIG. 18 shows case 1 final concentration (ppm), according to some embodiments.

[0052] FIG. 19 shows Case 2 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0053] FIG. 20 shows Case 2 concentration profile at 10800 EFPD, according to some embodiments.

[0054] FIG. 21 shows Case 3 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0055] FIG. 22 shows Case 3 concentration profile at 10800 EFPD, according to some embodiments.

[0056] FIG. 23 shows Case 4 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0057] FIG. 24 shows a comparison of Case 4 and Case 3 concentration profiles at 10800 EFPD, according to some embodiments.

[0058] FIG. 25 shows Case 5 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0059] FIG. 26 shows a comparison of Case 5, Case 4 and Case 3 concentration profiles at 10800 EFPD, according to some embodiments.

[0060] FIG. 27 shows Case 6 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0061] FIG. 28 shows Case 6 concentration profile, according to some embodiments.

[0062] FIG. 29 shows Case 7 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0063] FIG. 30 shows a Comparison of Case 7 and Case 6 concentration profiles, according to some embodiments.

[0064] FIG. 31 shows Case 8 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0065] FIG. 32 shows Case 8 final concentration distributions in EF and PT, according to some embodiments.

[0066] FIG. 33 shows Case 9 final concentration distributions (ppm) in EF and PT, according to some embodiments.

[0067] FIG. 34 shows a Comparison of Case 9 and Case 8 concentration profiles, according to some embodiments.

[0068] FIG. 35 shows Case 8 variation with time of concentration distribution (ppm) in EF, according to some embodiments.

[0069] FIG. 36 shows a process diagram of a method of burning fuel with barriers on the end fitting, according to some embodiments.DETAILED DESCRIPTION

[0070] Before any embodiments are explained in detail, it is to be understood that the disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the accompanying drawings. The disclosure is capable of other embodiments and of being practiced or of being carried out in various ways.

[0071] DEFINITIONS.

[0072] Although terms such as “maximize”, “minimize” and “optimize” may be used in the present disclosure, it should be understood that such term may be used to refer to improvements, tuning and refinements which may not be strictly limited to maximal, minimal or optimal.

[0073] The term “connected” or "coupled to" may include both direct coupling (in which two elements that are coupled to each other and contact each other) and indirect coupling (in which at least one additional element is located between the two elements).

[0074] The term “substantially” as used herein may be applied to modify any quantitative representation which could permissibly vary without resulting in a change in the basic function to which it is related.

[0075] Terms such as "up to", "at least", "greater than", "less than", "more than", "or more", and the like, include the number recited and such terms refer to ranges that can be subsequently broken down into sub-ranges. In the same manner, all ratios recited herein also include all sub-ratios falling within the broader ratio.

[0076] The singular forms "a," "an," and "the" include the plural reference unless the context clearly dictates otherwise. The term "and / or" means any one of the items, any combination of the items, or all of the items with which this term is associated.

[0077] The term "about" can refer to a variation of± 5%, ± 10%, ± 20%, or± 25% of the value specified. For example, "about 50" percent can in some embodiments carry a variation from 45 to 55 percent. For integer ranges, the term "about" can include one or two integers greater than and / or less than a recited integer at each end of the range. Unless indicated otherwise herein, the term "about" is intended to include values and ranges proximate to the recited range that are equivalent in terms of the functionality of the composition, or the embodiment.

[0078] GENERAL REACTOR DESIGN DETAILS.

[0079] FIG. 1 is a perspective of a reactor core of a CANDUTM-type reactor 6, according to some embodiments. The reactor core is typically contained within a vault that is sealed with an air lock for radiation control and shielding. Although aspects are described with particular reference to the CANDUTM-type reactor 6 for convenience, the disclosure is not limited to CANDUTM-type reactors and may be useful outside this particular field as well. A generally cylindrical vessel, known as the calandria vessel 10 of the CANDUTM-type reactor 6, contains a heavy-water moderator. The calandria vessel 10 has an annular shell 14 and a tube sheet 18 at a first end 22 and a second end 24. The tube sheets 18 include a plurality of apertures (referred to herein as bores 19) that each accept a fuel channel assembly 28. As shown in FIG. 1, a number of fuel channel assemblies 28 pass through the tube sheets 18 of calandria vessel 10 from the first end 22 to the second end 24.

[0080] As in the illustrated embodiment of FIG. 1 and FIG. 2, in some embodiments the reactor core is provided with two walls at each end 22, 24 of the reactor core: an inner wall defined by the tube sheet 18 at each end 22, 24 of the reactor core, and an outer wall 64 (often referred to as a “end shield”) located a distance outboard from the tube sheet 18 at each end 22, 24 of the reactor core. A lattice tube 65 spans the distance between the tube sheet 18 andthe end shield 64 at each pair of bores 19 (i.e., in the tube sheet 18 and the end shield 64, respectively).

[0081] FIG. 2 is a cutaway view of one fuel channel assembly 28 of the reactor core illustrated in FIG. 1, according to some embodiments. As illustrated in FIG. 2, each fuel channel assembly 28 includes a calandria tube (“CT”) 32 surrounding other components of the fuel channel assembly 28. The CTs 32 each span the distance between the tube sheets 18. Also, the opposite ends of each CT 32 are received within and sealed to respective bores 19 in the tube sheets 18. In some embodiments, a rolled joint insert, for example calandria tube insert 34, is used to secure the CT 32 to the tube sheet 18 within the bores 19. A pressure tube (“PT”) 36 forms an inner wall of the fuel channel assembly 28. The PT 36 provides a conduit for reactor coolant and fuel bundles or assemblies 40. The PT 36, for example, generally holds two or more fuel assemblies 40, and acts as a conduit for reactor coolant that passes through each fuel assembly 40. An annulus space 44 is defined by a gap between each PT 36 and its corresponding CT 32. The annulus space 44 is normally filled with a circulating gas, such as dry carbon dioxide, helium, nitrogen, air, or mixtures thereof. One or more annulus spacers or garter springs 48 are disposed between the CT 32 and PT 36. The annulus spacers 48 maintain the gap between the PT 36 and the corresponding CT 32, while allowing passage of annulus gas through and around the annulus spacers 48.

[0082] As also shown in FIG. 2, each end of each fuel channel assembly 28 is provided with an end fitting assembly 50 located outside of the corresponding tube sheet 18. Each end fitting assembly 50 includes an end fitting body 57 and an end fitting liner 58. At the terminal end of each end fitting assembly 50 is a closure plug 52. Each end fitting assembly 50 also includes a feeder assembly 54. The feeder assemblies 54 feed reactor coolant into or remove reactor coolant from the PTs 36 via feeder tubes 59 (FIG. 1). In particular, for a single fuel channel assembly 28, the feeder assembly 54 on one end of the fuel channel assembly 28 acts as an inlet feeder, and the feeder assembly 54 on the opposite end of the fuel channel assembly 28 acts as an outlet feeder. As shown in FIG. 2, the feeder assemblies 54 can be attached to the end fitting assemblies 50 using a coupling assembly 56 including a number of screws, washers, seals, and / or other types of connectors. The lattice tube 65 (described above) encases the connection between the end fitting assembly 50 and the PT 36 containing the fuel assemblies 40. Shielding ball bearings 66 and cooling water surround the exterior of the lattice tubes 65, which provides additional radiation shielding.

[0083] A positioning hardware assembly 60 and bellows 62 are also coupled to each end fitting assembly 50. The bellows 62 allows the fuel channel assemblies 28 to move axially - a capability that can be important where fuel channel assemblies 28 experience changes in length over time, which is common in many reactors. The positioning hardware assemblies 60 can be used to set an end of a fuel channel assembly 28 in either a locked configuration that fixes the axial position, or an unlocked configuration. The positioning hardware assemblies 60 are also coupled to the end shield 64. The illustrated positioning hardware assemblies 60 each include a rod having an end that is received in a bore of the respective end shield 64. In some embodiments, the rod end and the bore in the end shield 64 are threaded. Again, it should be understood that although a CANDUTM-type reactor is illustrated in FIG. 1 and FIG. 2, the invention may also apply to other types of reactors, including reactors having components that are similar to those illustrated in FIG. 1 and FIG. 2.

[0084] END FITTING BARRIERS.

[0085] As described above, the fuel channel assemblies 28 can include at each end an end fitting 50 that can act as an inlet or outlet for coolant. The pressure tube 36 spans the length of the reactor core between opposite end fittings 50. The end fitting 50, not being in the core, can be made of materials without substantial regard for its impact on neutron capture. Accordingly, the end fittings 50 can be made of materials such as stainless steel. The pressure tube 36 does span the length of the core and is thus made from materials which are less capable of capturing neutrons and impeding the neutron flux within the reactor (e.g. zirconium-based alloys). While this may be a beneficial property for the nuclear reactions occurring within the core, it can leave the pressure tubes 36 susceptible to corrosion processes.

[0086] The end fitting 50 and the pressure tube 36 can be coupled together using a rolled joint 102. The rolled joint 102 enables the end fitting 50 to provide the coolant (e.g., high pressure deuterated water) to the pressure tube 36 or receive the coolant from the pressure tube 36 at the opposite end. Accordingly, the end fitting 50 and the pressure tube 36 are coupled together to carryout their functions of carrying coolant through the reactor core (to be heated by the core).

[0087] Hydrogen can be generated from corrosion processes occurring on the surface of metals in contact with the coolant. Zirconium-based alloys (such as those of the pressure tubes 36) have a high affinity for hydrogen. The build-up of hydrogen within the pressure tubes 36 canlead to Delayed Hydride Cracking (DHC). Stainless steel (such as that used in the end fitting 50) can likewise absorb hydrogen, but because of its lower affinity for hydrogen, hydrogen is not a significant problem for the end fitting 50 over the lifetime of that component. Accordingly, measures have generally been taken to protect the pressure tubes 36 from DHC, but not the end fittings 50.

[0088] The pressure tube 36 itself can be protected using an oxide layer which can be effective to prevent the generation of hydrogen on the surface of the pressure tube 36, however this oxide layer (or any protective coating) may be disrupted at the location of the rolled joint 102 making the rolled joint susceptible to hydrogen ingress. While there is no coolant that comes in contact with the pressure tube 36 where the rolled joint 102 is made, hydrogen can still migrate across the rolled joint 102 from the end fitting 50. Described herein are techniques that provide a barrier to the generation of hydrogen on the end fitting proximate the rolled joint 102. While the end fitting 50 itself does not significantly suffer from the effects of DHC, reducing the amount of hydrogen generated on the end fitting 50 proximate the location of the rolled joint 102 (e.g., with a barrier 100) can reduce the amount of hydrogen available for hydrogen ingress across the rolled joint 102 and protect the pressure tube 36 from DHC. Furthermore, because the end fitting 50 itself is not as susceptible to DHC, the barrier 100 need not protect the complete inner surface of the end fitting 50 which can make the manufacturing of end fittings 50 with such a barrier 100 more straightforward. The barrier 100 on the end fitting 50 is implemented not to protect the end fitting 50 per se, but because it can provide a protective factor for components of the system ‘downstream’ the hydrogen transport (e.g., the pressure tube 36). Such a barrier 100 protects the pressure tube 36 to an extent that is unexpected because it addresses an indirect pathway of hydrogen ingress (e.g., through the rolled joint 102) as opposed to the direct pathway of hydrogen ingress (e.g., hydrogen generation on the pressure tube 36).

[0089] Described herein are barriers 100 to hydrogen ingress to reduce hydrogen ingress from the end fitting 50 into the pressure tube 36 via the rolled joint. Introduction of a barrier 100 as described herein to hydrogen ingress into the end fitting 50 can reduce the amount of hydrogen available to subsequently enter the pressure tube 36 at the rolled joint 102 interface.

[0090] Other approaches have relied on the composition of the end fitting 50 material (e.g., stainless steel) to mitigate corrosion processes on the end fitting 50. While these may have been suitable to mitigate the corrosion on the end fitting 50 itself (to the extent that the corrosion was not an issue for the end fitting 50 itself), described herein are additional methods to mitigatethe corrosion processes occurring on the end fitting 50 to reduce the downstream effects of those corrosion processes (namely the effects of generation of hydrogen on the end fitting and ingress of the hydrogen on the pressure tube 36).

[0091] The barriers 100 described herein can mitigate the generation of hydrogen isotopes such that deleterious effects of hydrogen isotopes can be avoided or minimized. The primary application is for CANDUTM-type nuclear reactor fuel channels where sustained hydrogen isotope ingress into the pressure tubes 36 can be a limiting mechanism for the pressure tube 36 operating life, however the concepts described herein may be applicable to other nuclear reactor designs as well. Stopping, or slowing, the ingress of hydrogen isotopes into the pressure tube 36 can result in safer and longer operation for the pressure tubes 36.

[0092] The barrier 100 may be disposed on the internal diameter (ID) of the end fitting 50 to prevent the formation of hydrogen through corrosion processes. The barrier 100 may cover a portion of the end fitting 50 that is outboard of the rolled joint 102. This barrier 100 may act to reduce or eliminate the hydrogen that would otherwise be produced along the surface of the end fitting 50 and it may act to prevent the ingress of hydrogen at the barrier 100. The barrier 100 may reduce the amount of hydrogen available in the end fitting 50 to migrate towards the pressure tube 36 and ingress into the pressure tube 36 (e.g., across the rolled joint 102 where any oxide layer on the pressure tube 36 may be disrupted and offer little impedance to hydrogen ingress).

[0093] The barrier 100 may block the flow of hydrogen to the pressure tube 36 by blocking a major source of its production. This major source may be from the corrosion of the bore of the end fitting 50 metal in contact with the pressurized coolant flowing through the fuel channel (e.g., outboard of the rolled joint 102). Hydrogen released during the corrosion process can enter the end fitting 50 metal and travel via diffusion to the pressure tube 36 at the rolled joint 102 interface. Hydrogen reaching the interface can be drawn into the pressure tube 36 material due to a strong difference in electro-chemical potential between the stainless steel end fitting 50 material and the zirconium alloy pressure tube 36. Reducing the amount of hydrogen available in the end fitting 50 may result in a corresponding reduction in the amount of hydrogen entering the pressure tube 36 at the rolled joint 102 interface.

[0094] The pressure tube 36 can be prepared with an oxide on the inner and outer surfaces that keep hydrogen ingress to a low rate. When the pressure tube 36 is joined to the end fitting50 with a rolled joint 102, the oxide layer can be disrupted by the rolling process. This may allow for a higher ingress rate through the rolled joint 102 interface, but ingress may not be by a corrosion process occurring at the rolled joint 102 since the interface may not be exposed to flowing water. Rather ingress may be by a process of direct flow of hydrogen from one side (the end fitting 50) of the interface to the other (the pressure tube 36). The situation is illustrated in FIG. 3 showing a fuel channel cross-section where flow of hydrogen into the pressure tube 36 may only be through the rolled joint 102 interface. The amount of hydrogen in the end fitting 50 that reaches the rolled joint 102 interface may depend on the ingress rate into the end fitting 50 bore due to corrosion and the egress rate from the outer surface exposed to an annulus gas flow (at the annulus gas system 104).

[0095] The barriers 100 described herein can involve introducing a coating on the bore of the end fitting 50 outboard (to the left in FIG. 3) of the rolled joint 102. This can leave the mechanical design of the rolled joint 102 unchanged which may avoid risks and costs associated with redesigning the rolled joint 102. In some embodiments, the entire interior of the end fitting 50 can be coated to reduce or eliminate the formation of hydrogen. However, in some embodiments, it may be technically difficult to manufacture an end fitting 50 with full coating. Accordingly, in some embodiments, the barrier 100 may coat a surface of the end fitting 50 outboard of the rolled joint 102 (e.g., where the end fitting 50 metal is in contact with the pressurized coolant flowing through the fuel channel). In some embodiments, the axial barrier 100 length may be selected to reduce hydrogen ingress below a threshold during a predefined period (e.g., the expected lifetime of the pressure tube 36). This predefined threshold may achieve a significant (e.g., 30-50%) reduction in hydrogen ingress as compared to a full barrier applied to the internal diameter of the end fitting with a short barrier 100 length.

[0096] Diffusion modelling (as is described in greater detain in the following sections) may show that blocking hydrogen ingress can substantially reduce the amount of hydrogen available to pass through the rolled joint 102 interface. Therefore, this approach can achieve the desired improvement as long as the barrier 100 is effective (e.g., blocks a significant fraction of ingress). Effective barriers 100 may be coatings such as a compound layer (oxide, nitride, etc.) or else plating / bonding of some other protective material. In either case, the corrosion process to release hydrogen may be impeded.

[0097] In some embodiments, other components of the fuel channel which produce hydrogen may also be coated to reduce the amount of hydrogen available for hydrogen ingress to thepressure tube 36. In some embodiments, the end fitting liner 58 may have the barrier 100 applied thereon. The end fitting liner 58 can corrode and that may be a source of hydrogen. Additional interfaces between the end fitting liner 58 and the pressure tube 36 may make this an unlikely source.

[0098] In some embodiments, the barrier 100 material may be inert with respect to the environment of the pressurized water flow. There may be no detrimental effects on the water chemistry, and there may be no potential mechanical effects such as flaking / spalling of loose material into the flowing water. The barrier 100 may also be capable of lasting as an effective barrier for the intended life of the fuel channel. Such barrier 100 materials (or strategies) would enable implementation of the barrier 100 without modifying other aspects of the physical and chemical properties of the heat exchange system.

[0099] In some embodiments, the barrier 100 may include a different composition (e.g., plating and oxide / nitride) of the coating and the placement (e.g., how far outboard to extend) of the coating.

[0100] In some embodiments, different strategies may be implemented in addition to or instead of the barrier 100. For example, in some embodiments, there may be a treatment applied to the outer diameter of the end fitting 50. Such an outer diameter treatment may include a coating such as a palladium coating or a roughening to provide greater surface area on the external surface of the end fitting 50. There is a steady state concentration in the end fitting 50 material brought about by the equilibrium between the reactions that introduce hydrogen into the end fitting 50, namely corrosion on the internal diameter surface, and reactions that remove hydrogen, namely recombination and desorption from the outer diameter surface and ingress across the rolled joint 102. This equilibrium hydrogen concentration provides the driving force for ingress into the pressure tube 36. Increasing the recombination and desorption rates, while maintaining the same corrosion rate, can lower the steady state hydrogen concentration, which can reduce the ingress of hydrogen into the pressure tube 36. The purpose of a treatment (e.g., a coating or a surface treatment) on the outside surface of the end fitting 50 is to ensure that recombination of hydrogen diffusing through the thickness of the end fitting 50 occurs readily and the permeation of most of the hydrogen through the wall of the end fitting 50 into the AGS 104 (as opposed to diffusing axially into the PT 36). The presence of an oxide on the outer surface of the end fitting 50 may create a rate limiting step for the permeation of hydrogen, increasing the concentration of hydrogen in the end fitting. Accordingly,it may be beneficial to treat the outside of the end fitting 50 with a treatment that renders it more reactive with the hydrogen (e.g., a coating with a composition with a high hydrogen affinity or a surface treatment to render the hydrogen recombination reaction more prevalent).

[0101] In some embodiments, another strategy which may be implemented in addition to or instead of the barrier 100 is that the end fitting 50 may be configured to promote the passthrough of the hydrogen generated on the inner diameter through the end fitting 50 out of the annulus gas system 104. By promoting the transport of hydrogen through the end fitting 50 and out the AGS 104, hydrogen transport to the AGS 104 can compete with hydrogen transport to the pressure tube 36 through the rolled joint 102. As described above such a treatment could include applying or providing a coating or surface treatment (e.g., roughening) on the outside surface of the end fitting 50 to increase the hydrogen affinity of that surface to have a higher proportion of the hydrogen generated exit through the outside surface as opposed to migrating through the rolled joint 102.

[0102] According to an aspect, there is provided an end fitting 50 configured to reduce the transfer of hydrogen to a pressure tube 36 of a nuclear reactor 6 across a rolled joint 102. The end fitting 50 includes a barrier 100 disposed along at least a portion of an inner surface of the end fitting 50 configured to contact coolant. The inner surface may alternatively be referred to as the inner or internal diameter of the end fitting 50. The inner surface may generally correspond to the surface defining an interior channel for coolant within the end fitting 50 and the barrier 100 may be configured to extend from the rolled joint 102 to an outboard distance and around the whole circumference of the interior channel.

[0103] In some embodiments, the barrier 100 includes plating or bonding of a protective material.

[0104] In some embodiments, the barrier 100 extends a distance outboard of the rolled joint 102, the distance configured to reduce hydrogen ingress to the pressure tube 36 below a threshold.

[0105] In some embodiments, the barrier 100 includes a coating.

[0106] In some embodiments, the coating includes a compound layer.

[0107] In some embodiments, the compound layer is one or more of an oxide and a nitride.

[0108] In some embodiments, the coating includes a plating and / or bonding of a protective material.

[0109] In some embodiments, the coating includes at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

[0110] In some embodiments, the barrier 100 is configured to extend at least 50 mm from an end of the pressure tube 36 when installed. In some embodiments, the barrier 100 is configured to extend at least 60 mm from an end of the pressure tube 36 when installed. In some embodiments, the barrier 100 is configured to extend at least 120 mm from an end of the pressure tube 36 when installed.

[0111] In some embodiments, the barrier 100 is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting 50 from an end of the pressure tube 36 when installed.

[0112] In some embodiments, the end fitting 50 further includes a coating or surface treatment along at least a portion of an outer surface of the end fitting 50. The outer surface may alternatively be referred to as the outer diameter of the end fitting 50. The outer surface may generally correspond to the surface defining the exterior of the end fitting 50 and may be in contact with the annulus gas system 104. In some embodiments, the coating or surface treatment may be configured to cover substantially all of the exterior surface in contact with the annulus gas system 104. In some embodiments, the coating or surface treatment may be configured to cover a portion of the exterior surface in contact with the annulus gas system 104 that is proximate the rolled joint 102.

[0113] In some embodiments, the coating along the at least a portion of the outer diameter of the end fitting 50 comprises at least one of palladium, platinum, ruthenium, and rhodium.

[0114] FIG. 36 shows a process diagram of a method 3600 of burning fuel with barriers 100 on the end fitting 50, according to some embodiments.

[0115] According to an aspect, there is provided a method 3600 of reducing the transfer of hydrogen to a pressure tube 36 of a nuclear reactor across a rolled joint 102. The method includes providing an end fitting 50 comprising a barrier 100 disposed along at least a portion of an inner surface of the end fitting 50 configured to contact coolant (block 3602) and burning fuel in a nuclear reactor (block 3604). The inner surface may alternatively be referred to as the inneror internal diameter of the end fitting 50. The inner surface may generally correspond to the surface defining an interior channel for coolant within the end fitting 50 and the barrier 100 may be configured to extend from the rolled joint 102 to an outboard distance along the whole circumference of the interior channel.

[0116] In some embodiments, burning fuel in the nuclear reactor (block 3604) includes generating hydrogen on the inner surface of the end fitting 50 that becomes available for hydrogen ingress into the pressure tube 36 across the rolled joint 102. The barrier 100 is configured to impede the generation of hydrogen on the inner surface as compared to an end fitting 50 without the barrier 100.

[0117] In some embodiments, the barrier 100 includes plating or bonding of a protective material.

[0118] In some embodiments, the barrier 100 extends a distance outboard of the rolled joint 102, the distance configured to reduce hydrogen ingress to the pressure tube 36 below a threshold.

[0119] In some embodiments, the barrier 100 includes a coating.

[0120] In some embodiments, the coating includes a compound layer.

[0121] In some embodiments, the compound layer is one or more of an oxide and a nitride.

[0122] In some embodiments, the coating includes a plating and / or bonding of a protective material.

[0123] In some embodiments, the coating includes at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

[0124] In some embodiments, the barrier 100 is configured to extend at least 50 mm from an end of the pressure tube 36 when installed. In some embodiments, the barrier 100 is configured to extend at least 60 mm from an end of the pressure tube 36 when installed. In some embodiments, the barrier is configured to extend at least 120 mm from an end of the pressure tube 36 when installed.

[0125] In some embodiments, the barrier 100 is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting 50 from an end of the pressure tube 36 when installed.

[0126] In some embodiments, the end fitting 50 further includes a coating or surface treatment along at least a portion of an outer diameter of the end fitting 50. The outer surface may alternatively be referred to as the outer diameter of the end fitting 50. The outer surface may generally correspond to the surface defining the exterior of the end fitting 50 and may be in contact with the annulus gas system 104. In some embodiments, the coating or surface treatment may be configured to cover substantially all of the exterior surface in contact with the annulus gas system 104. In some embodiments, the coating or surface treatment may be configured to cover a portion of the exterior surface in contact with the annulus gas system 104 that is proximate the rolled joint 102.

[0127] In some embodiments, the coating along the at least a portion of the outer diameter of the end fitting 50 comprises at least one of palladium, platinum, ruthenium, and rhodium.

[0128] 1. HYDROGEN INGRESS MODELLING 1 - DIFFUSION MODELS.

[0129] The following represents an exemplary description of a model used to predict the hydrogen migration within the fuel channel 28. In particular, the following exemplary description describes the migration of hydrogen across the end fitting 50 and pressure tube 36 and the models for the transfer of hydrogen between said components. It is intended for exemplary purposes only and is not intended to limit the scope of the application.

[0130] Hydrogen isotopes may be present in CANDUTM-type reactor pressure tubes 36 as initial protium from manufacturing and through ingress during operation. Ingress may be more prominent at the rolled joint 102 connection at each end of the pressure tube 36 such that concentration gradients cause inboard diffusion of the hydrogen.

[0131] Ingress and diffusion modelling can be applied to demonstrate that hydrogen equivalent concentration, [Heq], remains within safe limits to ensure pressure tube 36 integrity over the reactor operating interval. Other modelling may apply ingress as a source due to corrosion with heavy water at the pressure tube 36 inner surface plus an empirically determined source at the rolled joint 102. The empirical ingress source may be unsuitable for evaluation of potential fuel channel design changes made to mitigate ingress.

[0132] Described herein, the rolled joint 102 ingress model can be extended to explicitly include the end fitting 50 and pressure tube 36 assembly. The flow of hydrogen into the pressure tube 36 at the rolled joint can be determined by diffusion in both components and the interface condition where they are connected by the rolled joint 102. A more comprehensive depiction of the ingress and diffusion processes can be modelled.

[0133] 1.1. Introduction

[0134] In CANDUTM-type nuclear reactor pressure tubes 36, evaluating the effect of hydrogen isotopes on Delayed Hydride Cracking (DHC) and fracture toughness may require determination of the hydrogen concentration distribution along the pressure tube 36. From manufacturing, an initial concentration of protium (P) can be assumed to be uniformly distributed along the pressure tubes 36. During reactor operation, deuterium (D) may continuously be picked up due to corrosion in the heavy water system.

[0135] The presence of hydrogen isotopes (e.g., protium and deuterium) either in solution or as precipitates may affect the pressure tube 36 properties, and in combination with other degradation mechanisms can assist pressure tube 36 failure mechanisms where stresses are tensile. When the terminal solid solubility dissolution (TSSD) is exceeded, zirconium hydrides may form and preferentially accumulate at sites of stress concentration (such as pressure tube 36 flaw tips) or local temperature depression (such as contact between the pressure tube 36 and calandria tube 32). The presence of hydride can result in DHC initiation and eventually pressure tube rupture. Furthermore, at high levels of [Heq] in Zr 2.5Nb, hydrides can lead to a reduction in the fracture toughness. For the purpose of evaluating hydride formation, the equivalent measure of concentration [Heq]=[P]+1 / 2 [D] may be used in applicable models and codes and is applied in the CSA standards (e.g., CSA N285.4 and CSA N285.8, both of which are incorporated herein by reference). The equivalent hydrogen concentration is applied and assumed in any discussion when “hydrogen” is stated without further qualification within this section (Hydrogen Ingress Modelling 1- Diffusion Models).

[0136] FIG. 4 is a cutaway view of a fuel channel showing pressure tube 36 rolled joint 102, according to some embodiments.

[0137] FIG. 5 illustrates sources of deuterium ingress to the rolled joint 102 area of the pressure tube 36, according to some embodiments.

[0138] Accumulation of hydrogen has long been observed at the rolled joint 102 connection between the pressure tube 36 and end fitting 50 shown in FIG. 4. Other assessments and predictions of the accumulation of hydrogen in the pressure tube 36 near the rolled joint 102 consider hydrogen ingress in terms of sources applied directly to the pressure tube 36 surfaces as indicated in FIG. 5. The rolled joint 102 ingress from the end fitting 50 may, however, be the dominant source over direct ingress from the pressure tube 36. Representing rolled joint 102 ingress from the end fitting 50 as a source on the pressure tube 36 surface may forgo the details of hydrogen transport upstream of the rolled joint 102 interface between the end fitting 50 and pressure tube 36.

[0139] 1.2. Sources of Hydrogen Isotopes in the Fuel Channel Assembly 28

[0140] Both the pressure tube 36 and end fitting 50 may have some content of protium from the production process. Aside from the initial content, hydrogen isotopes can enter or leave the fuel channel assembly 28 by different process and at different locations.

[0141] The inner walls of the pressure tube 36 and end fitting 50 can be exposed to the pressurized heavy water used to transport heat from the nuclear reaction. Corrosion reactions at the metal surfaces can dissociate deuterium from the water molecules and a portion of the dissociated deuterium atoms enter the metal.

[0142] 1.2.1 Sources Directly into Pressure Tube 36

[0143] An oxide layer on the inner and outer surfaces of the pressure tube 36 can be used as a barrier to minimize the amount of hydrogen entering the pressure tube 36 metal. Due to the high affinity of zirconium to hydrogen, any hydrogen entering the pressure tube 36 may remain. Hydrogen entering due to corrosion on the inner surface may not leave from the outer surface to the annulus gas (e.g., through the annulus gas system 104). Rather, there is a possibility of ingress from the annulus gas, but this may be negligible with the combination of the oxide barrier and a low concentration of gaseous hydrogen in the annulus gas.

[0144] Since ingress into the body of the pressure tube 36 can be relatively uniform, hydrogen measurements may directly indicate ingress rate without the need to account for redistribution by diffusion. Quantification of the net ingress rate into the body of the pressure tube 36 can be based on direct measurements of hydrogen isotope concentration. The model for body of tube ingress rate can be empirically based on hydrogen measurements.Consequently, this boundary condition for the pressure tube 36 can be applied without further development. Note that this ingress rate may apply to the body of tube and may not consider the hydrogen entering at the rolled joint 102.

[0145] 1.2.2 Sources Directly into End Fitting 50

[0146] The end fitting 50 material can be a type of martensitic stainless steel, AISI 403, that has a moderate amount of chromium (-12%) and thus may only be corrosion resistant in mild environments. It can be more susceptible to corrosion in comparison with austenitic stainless steels which have higher nickel and chromium content. Material similar to the end fitting 50 material (e.g., AISI 410 martensitic stainless steel end fitting liner) may experience significant corrosion. The end fitting 50 is in principle like the pressure tube 36 in the sense that hydrogen ingress may occur at the inner surface via corrosion with heavy water. However, due to the lower affinity of the end fitting 50 metal to hydrogen, there may be egress of hydrogen through the outer surface to the annulus gas (e.g., through the annulus gas system 104). In this situation, measurements of hydrogen in the end fitting 50 material may not be in direct proportion to the ingress rate from corrosion.

[0147] If there is egress of hydrogen to the annulus gas, the rate may be a function of the concentration in the metal at the outer surface and the partial pressure of hydrogen in the annulus gas. This can be suitably quantified by Sievert’s law:

[0148] c = Kp2(1)

[0149] such that the concentration in the metal may be proportional to the square root of the gas pressure p, (K is Sieverts’ law constant). In combination with ingress at the inner surface and diffusion through the wall, a steady state concentration profile can be achieved, and this can be a useful condition to apply in the model. This model can be applicable for the diffusion limited permeation of hydrogen which may exist at sufficiently high pressures and corrosion rates. In the absence of direct measurement of hydrogen concentrations in the end fitting 50, quantitative representation of the ingress and egress conditions are required.

[0150] 1.2.3 Interface Condition at Rolled Joint 102

[0151] Since the pressure tube 36 and end fitting 50 are in direct contact at the rolled joint 102, hydrogen may flow from one component to the other. Transfer of hydrogen across therolled joint 102 interface may depend on the chemical potentials associated with the different metals. Chemical potential can be a function of concentration as per:

[0152] n = i0+ RT \n c (2)

[0153] where / J.Ois a reference chemical potential, R is the gas constant and T is absolute temperature. At an ideal interface (with no resistance to flow), the chemical potential at an infinitesimal distance from either side of the interface can be assumed to be equal (i.e., equilibrium):

[0155] This representation of the interface can be rearranged to:

[0157] which shows that there can be a step change concentration across the interface.

[0158] The physical details (such as discontinuity of metal-to-metal contact) of the interface layer at a microscopic scale can introduce some resistance to the flow. It is anticipated that this may be small in comparison with the resistance associated with diffusion over distances of the scale of the component dimensions. In this case, an arbitrary small value can be assumed in a numerical model.

[0159] FIG. 6 is a 1-D example with ingress at left end, fast diffusion to interface at x=0 and chemical potential jump to the slower diffusion region, according to some embodiments.

[0160] A simple one-dimensional model can be used to verify numerical implementation. In FIG. 6, an independently programmed model (limited to one dimension) is compared to the corresponding model solved with the general-purpose finite element code (H3DMAP), according to some embodiments. The interface with chemical potential jump is at the position x=0 with “end fitting” 50 elements to the left of the interface (negative x) and “pressure tube” 36 elements to the right (positive x). The initial concentration can be zero everywhere and ingress at a constant rate can be applied to the left-most node. The length scale of this model is deliberately small in comparison with actual reactor components so that the concentration distribution can develop throughout the entire model in a short time.

[0161] Diffusivity of the pressure tube 36 may be per the model for a temperature of 300 °C. The diffusivity of the end fitting 50 can be assumed to be 20 times higher than the pressure tube 36 diffusivity. The results plotted in FIG. 6, show how the concentration distribution can evolve to form a shallow gradient toward the interface, where a concentration jump can be seen to approach the equilibrium value of cPT / cEF=50 applied in the model. The open circles indicate the positions of the nodes in the model which are deliberately not uniformly spaced. The results may be in agreement to the 7 significant digits of the numerical output and can confirm that the finite element code can correctly represent the chemical potential jump condition with non- uniform mesh and different diffusivity properties. The results may also foreshadow that concentration in the end fitting can be low in comparison with concentration in the pressure tube.

[0162] 1.3. Overview of Fuel Channel Assembly Model

[0163] The finite element model of the fuel channel assembly 28 is shown in FIG. 3 as a two- dimensional representation of the cross-section of the pressure tube 36 and end fitting 50 components. For proof of concept, this model can apply truncated portions of the pressure tube 36 and end fitting 50. The body-of-tube ingress into the pressure tube 36 can be ignored since the primary concern is the supply of hydrogen through the rolled joint 102 interface. Ingress at the end fitting 50 bore can be applied as a distributed source boundary condition applied to be a uniform surface flux. Since the end fitting 50 thickness may vary along its length, the uniform flux can result in nonuniform concentration, but this is physically realistic.

[0164] Egress to the annulus gas at the end fitting 50 outer surface may not be applied as a simple boundary condition since the driving force for egress rate depends on the concentration of hydrogen in the metal and annulus gas. Therefore, the annulus gas system 104 can be represented with elements to accumulate hydrogen as it leaves the metal. Interface elements can connect the end fitting 50 elements to the annulus gas elements; the conductivity of these interface elements can be arbitrarily set but may preferentially correspond to the physical processes as per Sievert’s law or surface limited processes like recombination.

[0165] The pressure tube 36 and end fitting 50 can be connected by interface elements at the rolled joint 102. The flow of hydrogen through these elements may account for the concentration step of equation (4). This can be done by applying the appropriate (positive) offset to chemicalpotential in the end fitting 50 elements. Arbitrary values can be considered for the chemical potential step.

[0166] 1.3.1 Diffusion Model

[0167] The redistribution of the hydrogen by diffusion can be considered to take place at uniform temperature and over a long period of time as per reactor operation. In some embodiments, stress gradients can be ignored. Thus, the diffusion follows the basic Fick’s law except for the presence of the chemical potential jump.

[0168] Diffusivity of hydrogen in pressure tube 36 material may follow an Arrhenius form of temperature dependence. This may also be the case for metals in general, but the end fitting 50 material can have a much higher diffusivity (~an order of magnitude higher). The appropriate diffusivity may respectively be assigned to the pressure tube elements, and end fitting 50 elements can use a diffusivity that is 20x higher. While hydrogen trapping effects may be a major consideration for the diffusion of hydrogen in steels, trapping effects may be small in the temperature range of operation in CANDUTM-type reactors which is higher than 250°C.

[0169] FIG. 7 shows the hysteresis in the Terminal Solid Solubility (TSS) of hydrogen equivalent for dissolution and precipitation, according to some embodiments.

[0170] In the pressure tube 36 material, hydrogen concentration in solution may be limited by TSS and any excess concentration takes the form of immobile zirconium hydride. As shown in FIG. 7, the solubility may be temperature dependent and exhibit hysteresis relating to how dissolution and precipitation solvi are approached. The TSS response can be important when temperature changes take place. Reactor startup and shutdown cycles can therefore be applied when simulating ingress and diffusion at rolled joints. Upon heating to the uniform operating temperature, the concentration in solution can be limited to Terminal Solid Solubility of Hydrogen Isotopes for Dissolution (TSSD) but subsequent ingress or transfer across the rolled joint 102 interface can increase the concentration in solution above TSSD and up to Terminal Solid Solubility of Hydrogen Isotopes for Precipitation (TSSP).

[0171] All of the required diffusion and TSS capabilities can be implemented into a 3-D general finite element analysis code called H3DMAP. This code can include the effects of temperature and stress gradients on diffusion, but these may not be present in the conditions being modelled here.

[0172] For the model to be representative of reactor operation, the occurrence of thermal cycles as per startup and shutdown events of reactor operation can be considered. Thermal cycles can be simplified to occur at equal intervals of one year and are applied by rapidly lowering the temperature such that TSSP will precipitate virtually all of the hydrogen present. Then the temperature can be rapidly increased to dissolve hydrogen up to TSSD. In effect, all diffusion can occur at the operating temperature, but the sequence of cooling and heating may be important with respect to the TSS behavior.

[0173] 1.4. Example Simulations

[0174] Demonstration of the model can be done for some combinations of inputs to realize certain modes of response: 1) Concentration in pressure tube 36 remains below TSSD; and 2) Concentration in pressure tube 36 exceeds TSSD for at least several operating cycles.

[0175] To achieve mode 2) response may depend mainly on the combination of concentration achieved in the end fitting 50 and the magnitude of chemical potential jump at the rolled joint 102 interface.

[0176] The chemical potential jump may be arbitrarily applied over a range to ensure response above and below TSSD can be observed. For the concentration achieved in the end fitting 50, the specific cases correspond to <T / cF= 250, 500, 750 and 1000. If boundary conditions for the end fitting 50 were to achieve higher concentration in the end fitting 50, TSSD in the pressure tube 36 can be exceeded with correspondingly lower values for the chemical potential jump.

[0177] The operating temperature can be arbitrarily chosen to be 300 °C, which may be representative of outlet rolled joints 102. The model can equally be applicable to inlet rolled joints 102 with lower temperature, but diffusion will be slower. Therefore, initial study with the model may begin with a higher temperature case.

[0178] Initial hydrogen can be set to zero in all elements as focus is on the transfer of hydrogen from the end fitting 50 to the pressure tube 36. Also, ingress on the inside surface of the pressure tube 36 may not be applied. This may make clear that any hydrogen in the pressure tube 36 originated from the end fitting 50. In practical applications, initial hydrogen concentration and ingress from corrosion of the pressure tube 36 may be included.

[0179] FIG. 8 shows variation with time of concentration (ppm) distribution in end fitting 50 (EF), according to some embodiments.

[0180] The concentration achieved in the end fitting 50 can be determined by the net flow of hydrogen at the inside and outside surfaces. A constant ingress rate can be applied at the inside surface and the rate of outflow to the anulus gas system (AGS) 104 can be determined by the boundary condition applied at the AGS 104 interface. Presently, this can be modelled as a resistance such that the flow can be proportional to the concentration difference at the outer wall and in the AGS 104. The concentration of gaseous hydrogen in the AGS 104 may remain low if recombination of hydrogen with oxygen can take place which is the case in the AGS 104, which also has frequent purging of the system to maintain low levels of moisture and hydrogen. In this case, the AGS 104 boundary condition may behave analogously to a convection heat transfer boundary condition. In combination with the constant ingress rate on the inside and radial diffusion, the through-wall concentration gradient can become steady with time to establish the nominal concentration in the end fitting. For the cases below, the same boundary conditions at the inside and outside surface can be applied such that the same average concentration can be achieved in the end fitting 50 away from the rolled joint 102. The contours plotted in FIG. 8 show that the average concentration may roughly be 0.5 ppm and can be achieved early in the timeframe of reactor life.

[0181] 1.4.1 Pressure Tube 36 Concentration Remaining Below TSSD

[0182] FIG. 9 shows final concentration (ppm) distributions in EF and PT for <T / cF= 250, according to some embodiments.

[0183] FIG. 10 shows final concentration (ppm) distributions in EF and PT for <T / cF= 500, according to some embodiments.

[0184] FIG. 11 shows a comparison of cases of FIG. 9 and FIG. 10 with pressure tube 36 concentration below TSSD, according to some embodiments.

[0185] Applying a chemical potential jump such that <fT / cF= 250 and 500 can result in significant transfer of hydrogen from the end fitting 50 to the pressure tube 36, but the maximum concentration remains below TSSD. The results plotted in FIG. 9 and FIG. 10 show that the EF 50 concentration can be similarly low like in FIG. 8 and may not be sensitive to the value of <T / cF. The results described herein show a sharp peak at the end of the pressure tube 36which may be a consequence of the interface condition being applied uniformly over the length of the rolled connection. Interface resistance may be expected to be locally lower at groove edges in the joint and such details can be incorporated into the model in much the same way that spatial profiles of ingress have been applied directly to the pressure tube 36 in other models.

[0186] 1.4.2 Pressure Tube 36 Concentration Exceeding TSSD

[0187] A higher chemical potential jump at the rolled joint 102 interface can result in sufficient transfer of hydrogen from the end fitting 50 to the pressure tube 36 to exceed TSSD at some point during reactor life. When cPT / cEF= 750, TSSD may be exceeded after 11 years of operation, and when cPT / cEF= 1000, TSSD may be exceeded after just 5 years. Consequently, the peak concentration for the highest chemical potential jump may be enhanced by more ratchetting cycles, each with a stronger action.

[0188] FIG. 12 shows final concentration (ppm) distributions in EF and PT for <T / cF= 750, according to some embodiments.

[0189] FIG. 13 shows final concentration (ppm) distributions in EF and PT for <T / c^F= 1000, according to some embodiments.

[0190] FIG. 14 shows a comparison of cases of FIG. 12 and FIG. 13 with pressure tube 36 concentration below TSSD, according to some embodiments.

[0191] The concentration contours plotted in FIG. 12 and FIG. 13 may show that the concentration distribution in the end fitting 50 is barely affected by the magnitude of chemical potential jump. The peak concentration in the pressure tube 36 may still occur at the very end of the pressure tube 36 and the profiles in FIG. 14 may show that the region above TSSD is evolving inboard much in the same way as models that directly apply ingress to the pressure tube.

[0192] 1.5. Discussion

[0193] The results described herein may demonstrate that hydrogen ingress at the rolled joint 102 can be modelled more comprehensively in terms of an upstream supply from the end fitting 50.

[0194] It may also be shown that very low concentration in the end fitting 50 can feed significant ingress into the pressure tube 36 with a sufficient chemical potential jump. In case the range of chemical potential jump is too high to be consistent with physical properties of the materials, lower chemical potential jump can be sufficient in combination with boundary conditions leading to higher hydrogen content in the end fitting 50. In this respect, engineering application may require empirical or theoretical quantification of boundary and interface conditions. For some of these inputs, practical means may be available.

[0195] The response of the end fitting 50 remote from the rolled joint 102 indicates that the ingress on the inside surface may flow mainly radially through to the AGS 104. The pressure tube 36 may thus compete with the AGS 104 for hydrogen so a strong driving force to the AGS 104 may mitigate transfer to the pressure tube 36. A weak driving force to the AGS 104 may imply a lower ingress rate at the inside of the end fitting 50 to prevent buildup of high concentration in the end fitting 50, or the presence of an oxide layer at the outside of the end fitting 50 facing the AGS 104. In this case the permeation of hydrogen radially through the end fitting 50 may be limited by recombination on the outside diameter requiring the use of slightly different model than described above. This situation may produce quite different results from the those shown here.

[0196] Details of the interface at the rolled joint 102 may require more elaboration for a practical model. In particular, the spatial distribution of the interface resistance may be accounted for. Sectioned rolled joints 102 may show local deformation at grooves where the oxide barrier may offer little resistance, so there should be a basis for refining the interface condition. Also, the chemical potential jump should be determined from more fundamental properties to avoid the need to approach this input parametrically. In some embodiments, may be higher than assumed in the present cases but if limited to local regions at grooves the net flow could be restricted. Also, resistance effects due to oxide and surface topography may combine to affect the net flow.

[0197] The ingress at the inside of the end fitting 50 may be understood to be due to a corrosion process that could be modelled to quantify the ingress rate. This may require experimental data in the range of temperature and pressure of reactor operation.

[0198] 1.6. Conclusions

[0199] A model of the fuel channel assembly 28 is described which may address the transfer of hydrogen from the end fitting 50 to the pressure tube 36 at the rolled joint 102. The model may introduce many new boundary conditions and interface conditions that are not considered in previous rolled joint 102 ingress modelling. Results demonstrate how the low chemical potential of hydrogen in zirconium can result in significant transfer of hydrogen to the pressure tube 36 even from low concentrations in the end fitting 50. The model may provide understanding regarding exacerbating or mitigating factors affecting rolled joint 102 ingress and support assessment of hydrogen ingress and redistribution.

[0200] 2. HYDROGEN INGRESS MODELLING 2 - END FITTING BARRIER.

[0201] The following represents an exemplary description of a model used to predict the hydrogen migration within the fuel channel 28 with and without a barrier 100 on the end fitting 50. In particular, the following exemplary description describes the migration of hydrogen across the end fitting 50 and pressure tube 36 and the models for the transfer of hydrogen between said components when implementing various possible mitigation strategies such as a barrier 100 outboard of the rolled joint 102 or an enhanced hydrogen sink in the AGS 104. It is intended for exemplary purposes only and is not intended to limit the scope of the application.

[0202] 2.1. Introduction

[0203] Ingress of hydrogen isotopes into CANDUTM-type reactor pressure tubes 36 can occur due to corrosion of the primary heat transport heavy water on the Internal Diameter (ID) of the pressure tube 36. An additional source of ingress can come through the Outer Diameter (OD) of the pressure tube 36 in the rolled joint 102 region. The rolled joint 102 ingress may be quantified directly by a time dependent distribution of hydrogen isotope flux to the pressure tube 36 volume outboard of the burnish mark of the rolled joint 102. This approach can allow for modelling and prediction of hydrogen ingress and redistribution for fuel channel 28 fitness-for- service assessments. However, the rolled joint 102 ingress model may not address the mechanics of the hydrogen source upstream of the joint interface.

[0204] A prospective mechanism for rolled joint 102 ingress may be the direct transfer of hydrogen in the end fitting 50 material to the pressure tube 36 material at the rolled joint 102 interface. This can be modelled by explicitly including the end fitting 50 and pressure tube 36 components with appropriate interface properties.

[0205] 2.2. Multi-Body Diffusion Model

[0206] 2.2.1 Overview of Finite Element Method

[0207] Hydrogen diffusion capabilities can be programmed into the H3DMAP finite element code to allow for simulations using arbitrary and complex geometry. The redistribution of hydrogen can be driven by gradients in concentration as well as gradients in hydrostatic stress and temperature. Temperature dependent solubility constraints are included through TSS models and hydrogen mobility can be restricted to the solute portion of concentration. Temperature distribution and ingress boundary conditions may be varied with time to be representative of reactor operating history.

[0208] The governing equation for diffusion is:

[0210] In which csis the concentration in solution, D is the diffusion tensor, vsrepresents the fraction of material not occupied by hydride, Q* is the heat of transport, VH is the molar volume of hydrogen in the material and oHis the hydrostatic stress. For computational convenience, a change of variable:Q*+VH °H

[0211] s = c e (6)

[0212] is applied to the concentration such that the governing equation becomes:

[0214] The form of equation (7) can be exploited in numerically rendering the interface of dissimilar metals.

[0215] 2.2.2 Demonstration Model for End Fitting 50 and Pressure Tube 36 Assembly

[0216] A source of rolled joint 102 ingress to the pressure tube 36 can be from hydrogen isotopes entering the end fitting 50 via corrosion at the bore surface. Hydrogen in the end fitting 50 can be drawn into the pressure tube 36 due to the much lower chemical potential of hydrogen in solid solution in the zirconium metal. Hydrogen in the end fitting 50 can also bedesorbed into the annulus gas system 104. The hydrogen entering the inner surface of the end fitting 50 can move by diffusion to the outer surface and to the rolled joint 102 interface.

[0217] Finite element modelling of the ingress and diffusion process may require that elements corresponding to the end fitting 50 and pressure tube 36 are assigned their respective physical properties. The diffusion modelling function in H3DMAP may be fixed to allow only one material, but temperature and stress dependence of properties are accounted for. The diffusion model applies pressure tube 36 properties for all elements (EF 50 and PT 36), but temperature and stress distributions can be set to render the necessary differences in properties.

[0218] 2.2.2.1 Details of Setting Diffusion Properties

[0219] The EF / PT application primarily concerns ingress and diffusion at nominally uniform temperature that may be steady with time except for intermittent cooling / heating associated with shutdown and startup events. Therefore, the temperature history for the PT 36 elements can be assigned in the usual way with physical temperatures. The temperature history for the EF 50 elements may use an artificially higher temperature chosen to result in the higher diffusivity of the EF 50 material. This approach of using temperature variation to distinguish between materials can preserve the physical properties of the PT 36 including TSS behaviour. The artificially higher temperature to the EF 50 may also result in higher TSS values for the EF 50 material such that all hydrogen may be in solution in the EF 50 at operating conditions; in effect, no solubility limit may be applied to the EF 50. The temperature corresponds to the physical temperature of the system and the EF 50 side is set to an artificially higher temperature, T+AT, to achieve the appropriately higher diffusivity.

[0220] Diffusivity of the Zr-Nb pressure tube material can be:

[0222] Diffusivity of the end fitting material can be:

[0224] Combining the two equations and rearranging can give:

[0227] to define the artificially higher temperature necessary to achieve the higher diffusivity of the end fitting.

[0228] FIG. 15 shows the temperature and stress change at EF / PT interface, according to some embodiments.

[0229] On the EF 50 side of the interface, the diffusion may proceed with uniform properties at the artificially higher temperature but no gradients in stress and temperature may exist. On the PT 36 side the diffusion may proceed with uniform properties at the lower temperature. This configuration is illustrated in FIG. 15 in which nodes 1 and 2 are on the EF 50 and PT 36 sides of the interface respectively.

[0230] 2.2.2.2 Details of Setting PT / EF Interface Properties

[0231] Transfer of hydrogen across the PT / EF interface may depend on the chemical potentials associated with the different metals. Chemical potential can be a function of concentration as per:

[0232] n = ii0+ RTin c (12)

[0233] At an ideal interface, the chemical potential at an infinitesimal distance from either side of the interface is assumed to be equal (i.e., equilibrium):

[0237] In the FE model, the concentrations in the above equation can be applied at separate nodes connected with an arbitrarily thin element such that the jump in concentration occurs overthe element. This can be achieved numerically by imposing appropriate stress values for the EF50 and PT 36 such that:

[0239] The interface layer can introduce some resistance to the flow due to the thickness of the element connecting the nodes, but this resistance can be made arbitrarily small to avoid biasing the response. The diffusivity of the interface elements can be based on the average properties, and the net resistance is proportional to the thickness.

[0240] 2.2.2.3 Correction for Applied Temperature Difference

[0241] The strategy to apply the interface condition may be straightforward if temperature is uniform, but temperature may be numerically manipulated to adjust diffusivity. In H3DMAP, the effect of temperature and stress gradients can be applied by transforming with equation (9) the nodal concentrations according to the corresponding nodal temperature and stress quantities.

[0243] With temperature uniform in both the PT 36 and EF 50, there may be no thermal gradient effect on the diffusion. However, the presence of the artificial temperature difference between the EF 50 and PT 36 can be felt as a temperature gradient over the thickness of the interface element. This unintended consequence of the applied temperature distribution may be eliminated by setting Q*=0. At equilibrium, sEF= sPTso that equations (13) provide

[0245] The step in chemical potential can be achieved by arbitrarily setting= 0 and combining with the above equation to solve for VHa^F

[0246] gj) (18)

[0247] Equation (18) can simply scale the stress term to account for the fact that the temperatures are numerically different on either side of the interface due to the manipulation to adjust the end fitting 50 diffusivity even though the temperatures are physically the same.

[0248] 2.2.3 Verification of Modelling Approach

[0249] 2.2.3.1 1D Model Description

[0250] FIG. 16 shows node points for 1D verification model, according to some embodiments.

[0251] FE modelling with H3DMAP can be verified with a simple 1-D model computed in Excel. The end fitting 50 and pressure tube 36 can each be modelled with 3 elements with an interface element connecting the two regions as shown in FIG. 16 (the x-coordinate of nodes are indicated below respective nodes). The initial condition may have a hydrogen concentration of zero at all nodes and the boundaries are insulated except for one node on the end fitting 50 that has ingress (at the left-most node in FIG. 16). The cross-section of all elements can be the same.

[0252] The model can be devised to demonstrate that as time passes, hydrogen entering the end fitting 50 (at x = -8 ) flows toward the interface and is drawn into the pressure tube 36. Input values listed in Table 1 may be arbitrarily selected such that the response can be easily observed but are otherwise intended to be approximately consistent with properties that are expected for more detailed applications. These inputs may be adequate for the purpose of verifying the numerical aspects of the model.

[0253] Table 1: General input values for model

[0254] 2.2.3.2 Interface Element Details

[0255] A jump in chemical potential can occur at the interface element since the end fitting 50 side has compressive stress and the pressure tube 36 side has no stress. Diffusivity can be higher in the end fitting 50 but may otherwise uniform in the respective elements for the end fitting 50 and pressure tube 36 sections of the model.

[0256] The interface stiffness can be determined as an average of conductance in series as per the method applied in H3DMAP. The approach may correspond to the harmonic mean of properties at the two nodes and follows on treating the interface element as two conductors in series. Each conductor can represent the material between its respective node and the midpoint of the element. Each conductance can be determined in accordance with conditions (i.e., temperature and stress) at the related node. H3DMAP can apply this approach at all elements but the averaging may be of no consequence where properties are uniform. In some embodiments, it will only apply at the interface elements.

[0257] The interface element can introduce resistance to the flow of hydrogen to the PT 36 and in H3DMAP; this resistance can automatically determined from the geometry and properties. The resistance can be made arbitrarily large or small by manipulating either the distance between the nodes, or by defining a cross-sectional area that is different from the rest of the model. In addition to resistance, the interface element can have an associated volume. This can also be made arbitrarily large or small by manipulating the nodal distance and cross- sectional area; increasing resistance by reducing cross-sectional area can also decrease the volume while increasing resistance by increasing nodal distance will increase the volume. It may be sufficient for verification purposes that the model of FIG. 16 applies the nodal separation as shown and does not apply any modification to the cross-sectional area.

[0258] 2.2.3.3 1D Model Results

[0259] Three versions of the model may be prepared (for exemplary purposes):

[0260] Excel 1: All nodes / elements are at the same temperature such that the chemical potential jump is calculated with AT=0. Higher diffusivity in the end fitting 50 is directly set(which cannot be done in the current H3DMAP code). This case avoids any issues that may arise with temperature gradients present in the H3DMAP model; thus, a baseline case can be achieved with the most simplification.

[0261] Excel 2: The end fitting 50 nodes are set to higher temperature so that the calculated diffusivity will be higher (as will be the case in H3DAMP). The chemical potential jump is calculated with the necessary value of AT. This case involves a significant temperature jump at the interface which if not handled correctly may cause error.

[0262] H3DMAP: The same mesh, temperature and stress inputs of Excel 2 are applied in an input file for H3DMAP.

[0263] The results plotted in FIG. 17 show how the concentration distribution can evolve to achieve elevated values in the pressure tube 36. All three cases are in agreement to the 7 significant digits of the numerical output. This may demonstrate the validity of approach of manipulating temperature and stress in H3DMAP to define suitable end fitting 50 properties and potential jump.

[0264] In addition to comparing the outputs of the three models, conservation of mass may be checked by performing a numerical integration of the concentration distribution over the volume of the model. The diffusion model in general conserves mass, but the unorthodox use of stress and temperature to render properties and the interface condition warranted checking that the conservative property is not compromised.

[0265] 2.2.42D Finite Element Model Description

[0266] The PT / EF assembly model can reasonably be represented with two dimensions (radial and axial). Geometry can be dictated by the layout and dimensions of the components. Ingress of hydrogen can be represented as nodal source boundary conditions at the inner surface (in contact with heavy water). Ingress at the inner surface of the PT 36 is ignored at this time since it corresponds to body-of-tube pickup which may be of secondary importance to the rolled joint ingress. The hydrogen can be picked up solely by the EF 50 to then accumulate and diffuse throughout the end fitting, but may also migrate into the AGS 104 and PT 36. The migration into the PT 36 can be treated the same way as the interface in the 1 D model with stress and temperature difference causing the necessary driving force. A similar approach can be used to interface with the AGS 104. The configuration of the 2D model is shown in FIG. 3.

[0267] 2.2.4.1 Modelling Ingress to End Fitting 50

[0268] Ingress can be applied as concentrated nodal sources in H3DMAP. The numerical implementation can involve applying increments of concentration at each time step to the nodes on the affected surface. The physical amount of ingress into a node may depend on the concentration increment (or rate) and the volume associated with the node. Typically, units of mass ratio (ppm) can be used for hydrogen concentration so that the mass rate of ingress is the product of the source term, nodal volume and the density of the material. Since the model applies zirconium properties to all elements, the mass rate is related to the numerical ingress rate by the nodal volume and the atomic masses of hydrogen and zirconium.

[0269] Concentrated nodal sources corresponding to ingress are shown in FIG. 16. The mass rate of hydrogen ingress may be proportional to the area of nodal volume that is exposed to the source. For the same mass ingress rate per unit area, nodes attached to longer elements may require a higher numerical value of ingress than nodes attached to shorter elements. To this end, each node with ingress may have its own factor to be applied to the physical mass rate such that a consistent flux is results over the entire exposed area.

[0270] At this stage of model development, the physical ingress rate may be arbitrarily selected to be in a range that will accumulate sufficient concentration such that distributions and transfer to the PT 36 can be observed and evaluated. More rigorously quantified ingress rates may be applied without further numerical complication.

[0271] 2.2.4.2 Modelling Desorption to the AGS 104

[0272] The end fitting 50 and pressure tube 36 may be in contact with the AGS 104 atmosphere such that atomic hydrogen may flow from the metal to recombine into gas in the AGS 104. The AGS 104 may in principle also act as a source for the hydrogen to enter the pressure tube 36, but the protective oxide seems to prevent this. Extensive OPEX for typical hydrogen ingress along the body of the pressure tube 36 supports that the AGS 104 may not be a source of hydrogen for ingress. However, the possibility of the AGS 104 acting as a sink for hydrogen requires consideration in modelling.

[0273] One means of numerically rendering a hydrogen sink for the AGS 104 is to apply fixed (low) concentration boundary condition at the end fitting 50 nodes exposed to the AGS 104. This approach may have some limitations in defining the strength of the sink and may also beless convenient for accounting for the inventory of hydrogen lost to the AGS 104. Therefore, an alternative approach can be used where the AGS 104 is explicitly represented in the finite element model with a row of 2-D elements which can act as a reservoir for hydrogen leaving the end fitting 50. The size of the reservoir can be adjusted by varying the element thickness (normal to the plane). Setting a large thickness can cause the elements to constitute a reservoir of sufficient size to receive considerable hydrogen from the end fitting 50 while keeping the concentration in the AGS 104 elements low.

[0274] Having explicit elements for the AGS 104 can also provide more flexibility in numerically defining the extent to which the AGS 104 draws hydrogen from the end fitting 50. Flow from the end fitting 50 to the AGS 104 can be through interface elements for which resistance to flow can be set as required to represent the physics of transfer and recombination. Since the process takes place over a long time and at a constant temperature, a single resistance should apply over the entire surface. Time dependence of the resistance can be set in the model if known quantitatively. The overall mesh along with details of the interface elements is shown in FIG. 3.

[0275] 2.2.4.3 Additional Modelling Considerations for Fuel Channels 28

[0276] The model shown in FIG. 3 shows the three parts of the assembly (EF 50, PT 36 and AGS 104). Due to the present limitations of H3DMAP, all three of these items may be represented by a single material; it may be impractical to use anything but zirconium properties since these include TSS parameters which are essential for zirconium. For the end fitting 50, TSS may not be applicable (not a hydride forming material) and the presence of zirconium TSS constraints may have no effect due to the much lower concentrations in the end fitting. As described above, the higher diffusivity in the end fitting material can be achieved by applying an artificially higher temperature.

[0277] For the AGS 104, the single row of elements may represent a reservoir as opposed to resolving details in redistribution. However, the diffusivity can be altered through temperature as per the end fitting and an additional (Sievert) driving force can be approximated by imposing a difference in hydrostatic stress across the interface. These in combination with defining the resistance through the interface can allow for considerable numerical control over the interface behaviour. Simple conditions can be applied until a technical basis warrants more detailed inputs.

[0278] 2.3. Test Cases for 2D Model

[0279] The 2D model may cover the range of reactor operating conditions, so input parameters that are not present in the 1 D model must be included; these parameters are listed in Table 2. All other parameters are the same as those listed in Table 1 unless a change is explicitly stated.

[0280] Several test cases with different input conditions can be used to establish how the model performs. The variation of inputs is chosen to demonstrate different regimes of response that may be encountered in reactor applications. These cases are listed in Table 3 along with brief descriptions of their relevance.

[0281] Table 2: Additional input values required for 2D model

[0282] Table 3: EF-PT assembly simulation cases

[0283] 2.3.1 Case 1: Short Term Steady Ingress at Isothermal Conditions

[0284] Case 1 has the simplest inputs and simulates ingress and diffusion of a short time to expediently verify numerical implementation to be correctly represented by the input file. This case mainly establishes the overall mesh and boundary condition framework common to all cases considered herein. The results are presented to provide a reference for comparison of the other cases to follow with more complex transient conditions.

[0285] FIG. 18 shows case 1 final concentration (ppm), according to some embodiments.

[0286] 2.3.2 Case 2: Nominal Reactor Cycles

[0287] The input file for Case 1 can be modified to include the temperature history with shutdown and start-up cycles for a nominal 30-year reactor life. The results plotted in FIG. 19 show the development of a concentration profile in the PT 36. The combination of hydrogen ingress rate into the EF 50, absorption into the AGS 104 and transfer to the PT 36 is such that the maximum concentration in the PT 36 may not exceed TSSD as shown in FIG. 20. At each axial position in FIG. 20, the nodal concentration values at the three corresponding radial positions can be coincident to within graphical accuracy and depict a profile shape that is roughly consistent with observations when concentration is below TSSD. Since TSSD has not been reached, the thermal cycles may have no influence on the response and the results can be effectively a continuation of Case 1 for a longer simulation time.

[0288] Concentration contours are displayed in FIG. 19 for case 2 show that the concentrations may be less that 1 ppm in the end fitting while reaching nearly 30 ppm in thepressure tube 36. The ratio of peak concentration in the pressure tube 36 to the adjacent concentration in the end fitting 50 is 48.23 which may approach the value of 50 used to define the jump in chemical potential.

[0289] Observation: in order for the concentration in the pressure tube 36 to exceed TSSD, the concentration ratio relating to the potential difference step may need to be sufficient to amplify the concentration in the end fitting 50. For a factor of 50, the end fitting concentration may need exceed 1; otherwise the potential difference step can never increase the concentration beyond 50 ppm (which is less than TSSD).

[0290] FIG. 19 shows Case 2 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0291] FIG. 20 shows Case 2 concentration profile at 10800 EFPD, according to some embodiments.

[0292] 2.3.3 Case 3: Nominal Reactor Cycles with Higher Ingress Rate

[0293] Increasing the ingress rate of Case 2 by a factor of 4 can ensure that the concentration in the PT 36 will exceed TSSD before the end of the simulation. The thermal cycles can then cause a ratcheting effect on the redistribution of hydrogen such that hydrides will be present close to the end of the PT 36. The contour plots in FIG. 21 show the distribution of total concentration as well as the distribution of hydride present at operating conditions, according to some embodiments. FIG. 22 shows the concentration profile in the pressure tube 36 in relation to TSSD, according to some embodiments. In comparison with Case 2, this may illustrate the dependence on ingress rate into the EF 50. Near the end of the PT 36, the concentration at the OD nodes may be significantly higher than the adjacent midpoint and ID nodes.

[0294] The concentration distribution in the EF 50 may demonstrate that the AGS 104 is absorbing a considerable portion of the hydrogen that enters the EF 50. Consequently, the concentration in the AGS 104 elements may increase to reduce the radial concentration gradient in the EF 50. This effect can reduce the amount of hydrogen that the AGS 104 absorbs such that the EF 50 retains a higher concentration of hydrogen.

[0295] FIG. 21 shows Case 3 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0296] FIG. 22 shows Case 3 concentration profile at 10800 EFPD, according to some embodiments.

[0297] 2.3.4 Case 4: Reduced Ingress 60mm from Rolled Joint 102

[0298] The effect of a barrier 100 to ingress on the EF 50 bore may be explored by adjusting the Case 3 input file to eliminate the ingress for about 60 mm from the end of the pressure tube 36. FIG. 23 shows the resulting concentration distributions along with the indication of where the ingress has been blocked, according to some embodiments. FIG. 24 compares the concentration profiles of Case 4 and Case 3 to illustrate the effect of an ingress barrier 100 on the reduction in hydrogen transfer to the PT 36, according to some embodiments.

[0299] FIG. 23 shows Case 4 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0300] FIG. 24 shows a comparison of Case 4 and Case 3 concentration profiles at 10800 EFPD, according to some embodiments.

[0301] 2.3.5 Case 5: Reduced Ingress 120mm from Rolled Joint 102

[0302] The effect of a barrier 100 to ingress on the EF 50 bore may be further explored by adjusting the Case 4 input file to extend the ingress-free zone to about 120 mm from the end of the pressure tube 36. FIG. 25 shows the resulting concentration distributions along with the indication of where the ingress has been blocked, according to some embodiments. FIG. 26 compares the concentration profiles of Case 5, Case 4 and Case 3 to illustrate the trend of effect of ingress barrier on the reduction in hydrogen transfer to the PT 36, according to some embodiments.

[0303] FIG. 25 shows Case 5 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0304] FIG. 26 shows a comparison of Case 5, Case 4 and Case 3 concentration profiles at 10800 EFPD, according to some embodiments.

[0305] 2.3.6 Case 6: 120mm Ingress Barrier 100 and Increased Absorption to AGS 104

[0306] The influence of absorption to the AGS 104 may further be investigated by increasing the volume of the AGS 104 to the extent that the AGS 104 elements remain at lowconcentration. This can be achieved numerically by scaling the thickness of the AGS 104 elements. The boundary conditions for ingress rate to the EF 50 and absorption of hydrogen to the AGS 104 are the same for Case 3 through Case 5 and results in EF 50 concentrations of ~2 ppm.

[0307] Case 6 may correspond to the modification of Case 5 with the AGS 104 volume increased by a factor of 100,000x the thickness of the EF 50 and PT 36 elements is applied, which is 100x greater than the factor used in Case 3, Case 4 and Case 5. FIG. 27 and FIG. 28 show that the AGS 104 may now absorb more hydrogen to keep the net concentration in the EF 50 lower, according to some embodiments. Consequently, the transfer to the PT 36 may be lower to the extent that the amplification factor is insufficient to elevate the concentration in the PT 36 to exceed TSSD. At the end of the simulation, the AGS 104 concentration may still be very low in accordance with a condition of constant radial flux through the wall of the EF 50.

[0308] FIG. 27 shows Case 6 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0309] FIG. 28 shows Case 6 concentration profile, according to some embodiments.

[0310] 2.3.7 Case 7: No Ingress Barrier and Increased Absorption to AGS 104

[0311] Case 7 corresponds to Case 6 with the ingress modified to apply to the entire bore of the EF 50. The results plotted in FIG. 29 show that the EF 50 concentration may be similarly low like the Case 6 result, but now reaches closer to the PT 36 such that more hydrogen is transferred to the PT 36. FIG. 30 shows the comparison of concentration profiles in the pressure tube 36 for Case 6 and Case 7, according to some embodiments.

[0312] FIG. 29 shows Case 7 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0313] FIG. 30 shows a Comparison of Case 7 and Case 6 concentration profiles, according to some embodiments.

[0314] This case may illustrate how the absorption to the AGS 104 is tied to the ingress rate to determine the local concentration available at the rolled joint 102 for transfer to the PT 36. With the increased absorption by the AGS 104, the peak concentration in the PT 36 may remain well below TSSD so that no ratcheting occurs.

[0315] 2.3.8 Case 8: Increased PT 36 Affinity for Hydrogen

[0316] Transfer of hydrogen to the PT 36 can be increased by using a higher value for the concentration jump at the EF / PT interface with other inputs the same as Case 7. As an extreme condition, the factor can be increased from 50 to 1000 such that the PT 36 will more aggressively take hydrogen from the EF 50.

[0317] The results for Case 8 plotted in FIG. 31 and FIG. 32 show that the concentration in the PT 36 may significantly exceed TSSD and by the end results in very high concentration localized at the very end (first 10 mm) of the pressure tube 36.

[0318] FIG. 31 shows Case 8 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0319] FIG. 32 shows Case 8 final concentration distributions in EF 50 and PT 36, according to some embodiments.

[0320] 2.3.9 Case 9: Increased PT 36 Affinity for Hydrogen and Ingress Barrier 100

[0321] Case 9 may be a modification of Case 8 such that no ingress occurs for about 60 mm from the PT 36. The contours in the top image of FIG. 33 show that in the region where there is no ingress, the concentration remains very low such that ingress to the PT 36 results in relatively low concentration in the PT 36 (bottom image of FIG. 33), according to some embodiments. The profiles plotted in FIG. 34 show that for the combination of ingress rate, AGS 104 absorption and PT 36 affinity for hydrogen, the ingress barrier 100 may be very effective in mitigating transfer of hydrogen to the PT 36.

[0322] FIG. 33 shows Case 9 final concentration distributions (ppm) in EF 50 and PT 36, according to some embodiments.

[0323] FIG. 34 shows a Comparison of Case 9 and Case 8 concentration profiles, according to some embodiments.

[0324] 2.4. Discussion of simulation results

[0325] Collectively, the results of Case 2 through Case 9 may demonstrate that the model can cover a wide range or response depending on the input conditions. Also, the results givesome indication of the sensitivity to the key inputs of ingress rate, absorption to the AGS 104 and the chemical potential jump at the EF / PT interface.

[0326] 2.4.1 Final Concentration Distributions

[0327] Accumulation of hydrogen in the pressure tube 36 can be predicted in a distribution that is qualitatively consistent with observed concentration distributions. Quantitively reasonable predictions may depend on the input conditions resulting in sufficient net flow of hydrogen into the PT 36. This can be understood to be mainly achieved by having both high enough EF 50 concentration at the rolled joint 102 and high enough step in chemical potential at the interface. A lower EF 50 concentration can be overcome by a higher chemical potential step as can be seen by comparing the results of Case 3 to Case 8. In this respect, similar results in the PT 36 may be obtainable with very different input values.

[0328] The concentration in the EF 50 may depend mainly on the ingress rate to the EF 50 bore and absorption rate into the AGS 104. A high ingress rate can be countered by high absorption rate such that similar concentration in the EF 50 can be obtained with very different input values.

[0329] 2.4.2 Transient Response in EF 50

[0330] According to the cases described herein, the concentration distribution in the EF 50 has a radial (through-thickness) gradient that is effectively linear. This may be consistent with predominantly one-dimensional steady-state diffusion from the point of ingress on the EF 50 ID to the corresponding point on the OD. The diffusivity of the EF 50 may be sufficiently high that the steady-state condition may be largely achieved with respect to the axial direction as well. This can be seen in FIG. 35 where the concentration in the EF 50 may change only slightly after one year such that the EF 50 may act as a sustained source of hydrogen from early in the reactor life. In order for the concentration in the EF 50 to increase steadily with time, the ingress rate may need to be very low and absorption into the AGS 104 would need to be even lower.

[0331] FIG. 35 shows Case 8 variation with time of concentration distribution (ppm) in EF 50, according to some embodiments.

[0332] 2.4.3 Effect of Ingress Barrier 100

[0333] The results shown in the previous section demonstrate that hydrogen ingress at the rolled joint 102 can be modelled more comprehensively in terms of an upstream supply from the end fitting 50.

[0334] It is shown that very low concentration in the end fitting 50 can feed significant ingress into the pressure tube with a sufficient chemical potential jump. In case the range of chemical potential jump is too high to be consistent with physical properties of the materials, lower chemical potential jump can be sufficient in combination with boundary conditions leading to higher hydrogen content in the end fitting 50.

[0335] The ingress at the inside of the end fitting 50 may be understood to be due to a corrosion process that can be modelled to quantify the ingress rate.

[0336] In some embodiments, the spatial distribution of the interface resistance may be accounted for. Sectioned rolled joints 102 show local deformation at grooves where the oxide barrier may offer little resistance, so there may be a basis for refining the interface condition. Also, the chemical potential jump may be determined from more fundamental properties to avoid the need to approach this input parametrically. It may be higher than assumed in the present cases but if limited to local regions at grooves the net flow could be restricted. Also, resistance effects due to oxide and surface topography might combine to affect the net flow.

[0337] The response of the end fitting 50 remote from the rolled joint 102 indicates that the ingress on the inside surface may flow mainly radially through to the AGS 104. The pressure tube 36 may thus compete with the AGS 104 for hydrogen so a strong driving force to the AGS 104 could mitigate transfer to the pressure tube 36. A weak driving force to the AGS 104 may imply a lower ingress rate at the inside of the end fitting 50 to prevent buildup of high concentration in the end fitting 50, or the presence of an oxide layer at the outside of the end fitting 50 facing the AGS 104. In this case the permeation of hydrogen radially through the end fitting 50 may be limited by recombination on the outside diameter requiring the use of slightly different model. This situation can produce quite different results from the those shown here.

[0338] Comparison of FIG. 24 with FIG. 34 shows that the mitigating effect of a barrier 100 to ingress may generally achieved. It appears that the mitigating effect may be stronger in FIG. 34 which corresponds to cases where the EF 50 concentration is low. Other results may also be obtainable. The AGS 104 may have a high affinity to compete with the affinity of the pressuretube 36. Lower ingress and egress rates resulting in similar end fitting 50 concentration may respond differently to barrier 100 length.

[0339] 2.4.4 Physical Input Determination

[0340] Ultimately, there may be an appropriate combination of inputs such that the net mass of hydrogen transferred to the PT 36 may be in the range of observed rolled joint 102 ingress. In this respect, the inputs may be such that the ratchetting should occur in the latter part of the simulation.

[0341] Table 4 summarizes the inputs with comments to indicate how they might be determined.

[0342] Table 4: Overview of input parameters requiring quantification

[0343] 2.5. Conclusions

[0344] A model of the fuel channel assembly 28 is described herein to address the transfer of hydrogen from the end fitting 50 to the pressure tube 36 at the rolled joint 102. The modelintroduces many new boundary conditions and interface conditions that have not been considered in previous rolled joint 102 ingress modelling. Results may demonstrate how the low chemical potential of hydrogen in zirconium can result in significant transfer of hydrogen to the pressure tube 36 even with low concentrations in the end fitting 50.

[0345] The model has been applied with some reasonable but arbitrary inputs, but the framework is herein provided to apply any inputs as determined with physical basis. Preliminary results may demonstrate that a barrier 100 to ingress on the end fitting 50 bore can substantially reduce the transfer of hydrogen to the pressure tube 36. This may be an important result that can support the evaluation of modifications to the end fitting 50 and to predict the outcome of such design changes over the life of reactor operation.

[0346] The model may be capable of simulating the rolled joint 102 ingress process in much more detail than has been done before. The model can become a comprehensive predictive tool upon determining end fitting 50 boundary conditions with improved technical basis.

[0347] IMPLEMENTATION DETAILS.

[0348] Applicant notes that the described embodiments and examples are illustrative and non-limiting. Practical implementation of the features may incorporate a combination of some or all of the aspects, and features described herein should not be taken as indications of future or existing product plans. Applicant partakes in both foundational and applied research, and in some cases, the features described are developed on an exploratory basis.

[0349] Although the embodiments have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the scope. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification.

[0350] As one of ordinary skill in the art will readily appreciate from the disclosure, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.

[0351] As can be understood, the examples described above and illustrated are intended to be exemplary only.

Claims

WHAT IS CLAIMED IS:

1. An end fitting for reducing hydrogen transfer to a pressure tube of a nuclear reactor across a rolled joint, the end fitting comprising: a barrier disposed along at least a portion of an inner surface of the end fitting configured to contact coolant.

2. The end fitting of claim 1, wherein the barrier comprises plating or bonding of a protective material.

3. The end fitting of claim 1 , wherein the barrier extends a distance outboard of the rolled joint, the distance configured to reduce hydrogen ingress to the pressure tube below a threshold.

4. The end fitting of claim 1, wherein the barrier comprises a coating.

5. The end fitting of claim 4, wherein the coating comprises a compound layer.

6. The end fitting of claim 5, wherein the compound layer is one or more of an oxide and a nitride.

7. The end fitting of claim 4, wherein the coating comprises a plating and / or bonding of a protective material.

8. The end fitting of claim 4, wherein the coating comprises at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

9. The end fitting of claim 1 , wherein the barrier is configured to extend at least 50 mm from an end of the pressure tube when installed.

10. The end fitting of claim 1, wherein the barrier is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting from an end of the pressure tube when installed.

11. The end fitting of claim 1, further comprising a coating or surface treatment along at least a portion of an outer surface of the end fitting.

12. The end fitting of claim 1, wherein the coating along the at least a portion of the outer surface of the end fitting comprises at least one of palladium, platinum, ruthenium, and rhodium.

13. A method of reducing the transfer of hydrogen to a pressure tube of a nuclear reactor across a rolled joint, the method comprising: providing an end fitting comprising a barrier disposed along at least a portion of an inner surface of the end fitting configured to contact coolant; and burning fuel in a nuclear reactor.

14. The method of claim 13, wherein burning fuel in the nuclear reactor comprises: generating hydrogen on the inner surface of the end fitting that becomes available for hydrogen ingress into the pressure tube across the rolled joint, wherein the barrier is configured to impede the generation of hydrogen on the inner surface as compared to an end fitting without the barrier.

15. The method of claim 13, wherein the barrier comprises plating or bonding of a protective material.

16. The method of claim 13, wherein the barrier extends a distance outboard of the rolled joint, the distance configured to reduce hydrogen ingress to the pressure tube below a threshold.

17. The method of claim 13, wherein the barrier comprises a coating.

18. The method of claim 17, wherein the coating comprises a compound layer.

19. The method of claim 18, wherein the compound layer is one or more of an oxide and a nitride.

20. The method of claim 17, wherein the coating comprises a plating and / or bonding of a protective material.

21. The method of claim 17, wherein the coating comprises at least one of zirconium nitrite (ZrN), titanium nitride (TiN), nickel, chromium.

22. The method of claim 13, wherein the barrier is configured to extend at least 50 mm from an end of the pressure tube when installed.

23. The method of claim 13, wherein the barrier is configured to extend a distance equal to about 5 to about 10 thicknesses of a wall of the end fitting from an end of the pressure tube when installed.

24. The method of claim 13, wherein the end fitting further comprises a coating or surface treatment along at least a portion of an outer surface of the end fitting.

25. The method of claim 13, wherein the coating along the at least a portion of the outer surface of the end fitting comprises at least one of palladium, platinum, ruthenium, and rhodium.

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