Method for determining a fuel salt composition of a molten salt reactor

Abstract

This description relates to a method (300) for determining, by a computing device, a fuel salt composition of a molten salt nuclear reactor, the method comprising: - the determination of neutron fluxes (ϕ(E)) of several energies and a multiplication factor by a step of solving (302) a neutron transport equation; - the determination, for each of the nuclides, of condensed microscopic cross sections from the neutron fluxes (ϕ(E)); - the determination (303) of the weights of the nuclides on the multiplication factor from the condensed microscopic cross sections; and - the determination (304), from the weights of the nuclides, of a fuel salt inventory including at least one calculation of the evolution of the nuclides, by a step of solving (306) evolution equations, such that the evolution inventory complies with at least one operating condition.

Description

Technical field

[0001] This description relates generally to molten salt reactors, and in particular to the determination of the composition of a fuel salt, or saline composition, of a molten salt reactor.

[0002] This description relates in particular to a method for evaluating the evolution over time of the composition of fuel salt in an operating molten salt reactor.

[0003] This description also relates in particular to a method for determining the composition of the fuel salt to be introduced into the molten salt reactor and / or extracted from the molten salt reactor. Previous technique

[0004] A molten salt reactor (MSR) is a type of nuclear reactor in which the nuclear fuel is in liquid form, dissolved in a molten salt that acts as both fuel and coolant. The reactor may be moderated, for example by graphite, producing thermal neutrons, or it may be designed without a moderator, producing fast neutrons. The molten salt reactor includes a generally metallic vessel designed to contain the molten salt at high temperatures, typically between 450 and 900°C, for example between 600 and 900°C, or between 450 and 700°C, but at ambient pressure.

[0005] There figure 1 illustrates in a simplified way an example of a molten salt nuclear reactor 100.

[0006] The molten salt nuclear reactor 100 comprises a generally metallic vessel 110 in which liquid nuclear fuel in the form of molten salt 10 can be contained at high temperature to undergo fission reactions under the influence of neutrons. The core of the nuclear reactor is located within this vessel 110.

[0007] Thus, molten salt contains the fuel. Molten salt can also be referred to as "molten fuel salt", "fuel salt", or even simply "salt".

[0008] The molten salt 10 comes from a storage unit 130. The storage unit 130 may also include, or be connected to, a molten salt reprocessing unit. The storage unit 130 is connected to the tank 110 by a fluid line 131, which allows the introduction of so-called "new" combustible salt 10a into the tank 110, and by another fluid line 132, which allows the extraction of so-called "spent" combustible salt 10b from the tank 110. The spent combustible salt 10b extracted from the tank 110 can then be processed in the reprocessing unit. The new combustible salt 10a introduced into the tank 110 may be reprocessed combustible salt.

[0009] The tank 110 and the molten salt 10 in the tank can form a first circuit, or fuel circuit, 101 of the nuclear reactor 100.

[0010] One or more first heat exchangers 115 are positioned in the tank 110 to recover the energy produced by the fission reactions. Two first heat exchangers 115 have been shown in the tank 110, only one of which is coupled to an intermediate circuit 120.

[0011] The intermediate circuit 120 is configured for the circulation of a fluid 20 called an intermediate fluid. The intermediate fluid can be a molten salt without fuel or another fluid.

[0012] The intermediate circuit 120 comprises a first portion 121 extending into the first heat exchanger 115 so that the molten salt 10 can transfer all or part of its heat to the intermediate fluid 20, and a second portion 122 extending into a second heat exchanger 125 which allows all or part of the heat from the intermediate fluid 20 to be transferred to a gas to produce heat and drive a turbogenerator, in a circuit known as an energy conversion circuit. The intermediate circuit 120 includes, to connect the first portion 121 and the second portion 122, a third portion 123 for circulating the secondary fluid 20 from the first heat exchanger 115 to the second heat exchanger 125, and a fourth portion 124 for circulating the intermediate fluid 20 from the second heat exchanger 125 to the first heat exchanger 115. The third portion 123 may be equipped with a circulation pump 126.

[0013] Tank 110 is connected to a recovery unit 114 for gaseous fission products 15 that are not soluble in the molten salt 10. These gaseous fission products migrate continuously towards this recovery unit.

[0014] Other fission products, typically metallic or gaseous fission products, insoluble in molten salt 10, can be extracted from molten salt 10 in the reprocessing unit.

[0015] The extraction of the spent fuel salt 10b to the reprocessing unit can be carried out directly, i.e. the reprocessing unit can be directly connected to the tank 110, or indirectly, i.e. the reprocessing unit is not directly connected to the tank 110.

[0016] The introduction of fresh fuel salt 10a can be carried out continuously. This implies also continuously removing a volume of spent fuel salt 10b from the reactor vessel equivalent to the volume of fresh fuel salt introduced. This can be referred to as continuous management. This type of management generally allows for good reactor performance while limiting the amount of reactivity introduced into the vessel and the various reactor units, thus reducing the need for reactivity control. Indeed, continuous feeding generally consists of introducing into the vessel a quantity of fresh fuel salt calculated to counteract a loss of reactivity due to the depletion of the fuel salt. This continuous operation, however, requires not only a fresh fuel salt supply unit coupled to the vessel but also a spent fuel salt reprocessing unit coupled to the vessel.Furthermore, the feeding and extraction operations taking place during reactor operation impose strong constraints from a safety and fuel chemistry management point of view.

[0017] The extraction and introduction (feeding) of molten salt 10 can be carried out in batches. This is referred to as batch management. Batch management is more similar to the method used for managing solid fuels. Batch management of fuel salt involves extracting, generally during a dedicated phase during a production shutdown, a volume of spent fuel salt 10b from the reactor vessel while an equivalent volume of fresh fuel salt 10a is fed into the vessel, before production resumes. This approach eliminates the need to couple the reactor with a reprocessing unit, but can be detrimental to performance, particularly due to the production shutdown. The phase between two production shutdowns for fuel salt extraction / feeding is called the "irradiation cycle."Irradiation cycles also include an initial irradiation cycle at the beginning of reactor life after introduction of an initial fuel salt charge, or initial inventory, without extraction, and a final irradiation cycle at the end of reactor life after a final fuel salt extraction / feed.

[0018] When exposed to neutrons in an operating reactor, the liquid fuel undergoes various reactions, which have significant implications, particularly for the composition of the molten salt (10) in terms of nuclides, i.e., the concentration of nuclides in the molten salt. Knowledge of this composition, and especially its evolution over time, is essential for neutron studies, sizing, management, and / or control of the molten salt reactor. In a solid-fuel reactor, fission products are generally contained within the fuel or the fuel cladding, ensuring their confinement. In a molten salt reactor, insoluble fission products, whether metallic or gaseous, can move within the reactor vessel before being conveyed to one or more recovery units.In a molten salt reactor, it is essential to know the composition of the molten salt and its evolution over time within the reactor vessel. This knowledge is needed, for example, to size a molten salt reactor (pre-operational modeling), to monitor the criticality and / or reactivity of a molten salt reactor (during operation), and to manage the introduction and extraction of the fuel salt, such as determining the quantity and composition of the fuel salt to be introduced / extracted, and / or the frequency of introduction / extraction. It may also be necessary to determine the composition of the molten salt and its evolution over time within the various units through which it circulates, such as the storage, reprocessing, and / or recovery units described above.

[0019] To characterize the molten salt inventory of a reactor at a given time, one challenge is determining how the molten salt's nuclide composition changes. Specifically, a key issue is the ability to account for nuclear reactions and the fluxes of insoluble fission products, while also considering the continuous or batch feeding and extraction of fuel salt from the molten salt reactor. Furthermore, other challenges may include limitations in the accuracy of the composition assessment and / or computation time.

[0020] Some methods are based on the assumption of continuous management of the feeding and removal of fuel salt in the molten salt reactor. These methods are generally based on a prescribed material flow rate (e.g., in grams per second or liters per day), characterizing the fuel salt feeding / removal rate over the reactor's lifetime. This approach is consistent for a continuously managed molten salt reactor, but it is limiting for a batch-managed molten salt reactor. Indeed, a batch-managed reactor generally requires determining a quantity, e.g., a volume, and a composition of fresh fuel salt to be added at the end of an irradiation cycle to ensure the next irradiation cycle, taking into account the nuclear material still available in the molten salt, while respecting the constraints imposed by neutronics and molten salt chemistry.Therefore, determining the molten salt inventory of a batch-managed molten salt reactor using a continuous method can disregard nuclear reactions and the decay of certain nuclides during the irradiation cycle. This can lead to an inaccurate or even incorrect assessment of the amount of fresh fuel salt to be introduced, as well as the composition of the molten salt in the core. Consequently, these methods are not suitable for a batch-managed molten salt reactor.

[0021] Some methods can be adapted to both batch-operated and continuous-operated molten salt reactors, and more generally to any type of nuclear reactor. These methods are based on coupling a neutron calculation code capable of solving the neutron transport equation with a calculation code dedicated to the evolution of the salt composition under irradiation in the molten salt reactor. The calculation code dedicated to this evolution typically implements evolution equations.

[0022] The neutron transport equation, which can be referred to simply as the "transport equation," designates throughout this description any equation resulting from the application of the Boltzmann equation to the distribution of neutrons in a medium containing nuclides. The Boltzmann equation applied to neutron distribution aims to establish a balance of the neutron population in the medium as a function of variables on which the neutron population depends, typically the positions of the neutrons in space, the velocity vectors (or the energy and direction) of these neutrons, and time, taking into account the different types of nuclear reactions capable of creating neutrons in the medium and / or removing neutrons from the medium.

[0023] In the description that follows, a transport equation can be referred to for short as "Boltzmann equation".

[0024] The data needed to solve the Boltzmann equation are typically the nuclear data of the different nuclides present in the medium and the quantities (atomic or mass) of these.

[0025] Solving the Boltzmann equation yields a neutron flux, a quantity characterizing the neutron population. Derived quantities such as reaction rates, obtained for example from the neutron flux and microscopic cross sections, can be deduced from the neutron flux.

[0026] Nuclear reactions not only influence the neutron population, they also change the nuclide population in the medium, which in turn can influence the neutron population.

[0027] An evolution equation refers to any equation that determines the change in the quantity of a nuclide in a medium, taking into account its creation and disappearance through nuclear reactions and radioactive decay. The evolution of all nuclides is governed by the Bateman equation. Therefore, for several nuclides, there are several evolution equations.

[0028] In the description that follows, the evolution equations can be referred to by the shorthand "Bateman equation".

[0029] The data needed to solve the Bateman equation typically include the decay rates of the various nuclides present in the medium and the reaction rates obtained from solving the Boltzmann equation. Other data, known as technological data, include processing rates and migration times of insoluble fission products. A processing rate refers to the number of atoms per second, or atom flow rate, that are introduced into, or removed from, the medium under consideration.

[0030] Solving the Bateman equation provides, among other things, concentrations, or quantities, of the different nuclides present in the medium, which are among the input data for the Boltzmann equation.

[0031] The term "concentration" of a nuclide in a medium generally refers to the quantity of nuclides in that medium, which can be the quantity of atoms of that nuclide per unit volume, usually expressed in atoms / cm³ or at / cm³. In the remainder of this description, the terms quantity and concentration may be used interchangeably.

[0032] Strictly speaking, the Boltzmann and Bateman equations are coupled, because the quantities of nuclides depend on the neutron flux, which itself depends on the quantity of nuclides in the medium. This is why we speak of Boltzmann-Bateman coupling. However, in practice, these equations can be decoupled by solving them separately over successive time intervals short enough to neglect, over each of these intervals, the variations in the concentrations of the nuclides in the Boltzmann equation and the neutron flux in the Bateman equation. This approach is commonly referred to as the "quasi-static approach."

[0033] There figure 2 illustrates in a simplified way an example of method 200 for determining a fuel salt composition of a batch-controlled molten salt reactor.

[0034] Method 200 includes an initialization step 201 (INIT) which defines the nuclides taken into account in the method, as well as the nuclear, nuclear reaction and decay data associated with each of these nuclides and necessary for solving the transport equation and the evolution equations.

[0035] The initialization step 201 further includes the definition of an initial inventory of fuel salt to be introduced into the reactor vessel, this initial inventory having an initial composition, i.e. initial concentrations of nuclides in the fuel salt.

[0036] Method 200 then comprises a step 202 for solving the transport equation, or Boltzmann equation (RESOL TRANSPORT), and a step 203 for solving the evolution equations, or Bateman equation (RESOL EVOLUTION), based on the data defined in the initialization step 201. The Boltzmann and Bateman equations are solved using the quasi-static approach described earlier. The initial concentrations of the different nuclides are used to solve the Boltzmann equation for the first time, before looping back to the Bateman equation using the quasi-static approach. This allows for the determination of the evolution of the nuclide concentrations in the molten salt, that is, the evolution of the molten salt's composition. In particular, molten salt inventories can be determined at different times during reactor operation.

[0037] In a verification step 204 (VERIF), it is determined whether an operating condition, for example a criticality condition, is verified for the molten salt inventories determined by solving the Boltzmann and Bateman equations in steps 202 and 203 starting from the initial inventory.

[0038] If the operating condition is met (YES), we can proceed to the finalization step 207 (FINISH) described below. If the operating condition is not met (NO), we can proceed to an adjustment step 205 (ADJUST) in a loop 206 which then returns to step 202 for solving the transport equation.

[0039] In adjustment step 205, another inventory of fuel salt to be introduced into the reactor vessel, or extracted from the reactor vessel, is defined, this other inventory being defined at least by another composition of the different nuclides, that is to say, other concentrations of the nuclides in the fuel salt.

[0040] We repeat steps 202 and 203 starting from these other concentrations of the different nuclides to solve the Boltzmann and Bateman equations again, and determine other inventories of molten salt during the operation of the reactor, then we go back through the verification step 204 to determine if the operating condition is verified for these other inventories determined by solving the Boltzmann and Bateman equations starting from the other initial inventory.

[0041] If the operating condition is met (YES), we can proceed to the finalization step 207. But as long as the operating condition is not met (NO), we can repeat the loop 206 by going through the adjustment step 205.

[0042] Finalization step 207 records the final composition of the molten salt to be introduced into the reactor. This composition allows the operating condition to be verified during reactor operation, for example, between the beginning and end of an irradiation cycle. Finalization step 207 also records an inventory of the molten salt in the reactor vessel at the end of the cycle, which is essential for determining the concentrations for the next cycle.

[0043] It turns out that the computation times for such a method can be very significant, even prohibitive, and these are mainly due to all the solutions of the transport equation in the quasi-static approach with the evolution equations for each loop. It has been estimated that the solutions of the transport equation can represent approximately 95% of the total computation time.

[0044] A method is sought for determining the composition of a fuel salt in a molten salt nuclear reactor that has a reduced computation time, while maintaining the same accuracy in evaluating the composition, taking into account its evolution over time in the reactor. Summary of the invention

[0045] There is a need for a method for determining the composition of a fuel salt in a molten salt nuclear reactor that at least partially overcomes some of the drawbacks of known methods, in particular one that is suitable for a batch-managed molten salt reactor as well as a continuously managed molten salt reactor, and that allows this salt composition to be tracked over time, over all or part of the reactor's life.

[0046] There is a need for a method to determine the composition of the fuel salt in a molten salt reactor with a reduced computation time.

[0047] It would be advantageous for such a method to allow, for a batch-managed molten salt reactor, to accurately evaluate and with reduced computation time the composition of a batch of new fuel salt feed and / or the composition of a batch of spent fuel salt extraction after an irradiation cycle, while respecting reactor operating constraints.

[0048] One embodiment overcomes all or part of the drawbacks of known methods for determining the composition of a fuel salt in a molten salt reactor.

[0049] One embodiment provides a method for determining, by means of a calculation device, the composition of the fuel salt in a molten salt nuclear reactor during the operation of said nuclear reactor, the method comprising: the determination of neutron fluxes) of several energies and a multiplication factor by a step of solving a neutron transport equation, from an initial fuel salt inventory, having initial atomic quantities of nuclides, in the nuclear reactor; the determination, for each of the nuclides, of condensed microscopic cross sections from the neutron fluxes; the determination of the weights of the nuclides over the multiplication factor, from the condensed microscopic cross sections; the determination, from the weights of the nuclides, of a fuel salt feed inventory, having atomic quantities of feed of the nuclides, to be added to the initial inventory and / or of an extraction inventory, having atomic quantities of extraction of the nuclides, to be extracted from the initial inventory; the determination of the feed inventory and / or the extraction inventory including at least one calculation of the evolution of the nuclides, by a step of solving evolution equations, starting, for each nuclide, from the initial atomic quantity to which is added a value of the atomic quantity of feed of this nuclide and / or is subtracted a value of the atomic quantity of extraction of this nuclide, so as to evaluate at least one evolution inventory of the fuel salt during the operation of the nuclear reactor; the feed inventory and / or the extraction inventory being determined in such a way that the evolution inventory meets at least one operating condition.

[0050] According to one embodiment, the computing device is capable of controlling a feed unit to supply the reactor with the feed inventory and / or an extraction unit to extract the extraction inventory from the nuclear reactor.

[0051] According to one embodiment, the supply inventory and / or the extraction inventory are beginning inventories of an nth irradiation cycle, where n is a natural number greater than or equal to 2, and the evolution inventory is an end inventory of the nth irradiation cycle.

[0052] According to one embodiment, the starting inventory is a starting inventory of the (n-1)th irradiation cycle, for example an inventory of a first load of fuel salt intended for the first irradiation cycle of the nuclear reactor.

[0053] According to one embodiment, the determination of the supply inventory and / or the extraction inventory includes: the determination of a first value of the feed inventory having first atomic quantities of feed of the nuclides and / or of a first value of the extraction inventory having first atomic quantities of extraction of the nuclides; a first calculation of the evolution of the nuclides in the nuclear reactor in operation, by the step of solving the evolution equations, starting, for each nuclide, from the initial atomic quantity to which is added the first atomic quantity of feed of this nuclide and / or is subtracted the first atomic quantity of extraction of this nuclide, so as to calculate a first value of the evolution inventory of the fuel salt during the operation of the nuclear reactor; a first verification, in a verification step, whether at least one operating condition of the molten salt nuclear reactor is respected for the first value of the evolution inventory.

[0054] According to one embodiment, the first value of the feed inventory and / or the first value of the extraction inventory are determined from a calculation of weight loss of the starting inventory during the operation of the nuclear reactor, for example during an irradiation cycle.

[0055] According to one embodiment, the calculation of weight loss from the beginning inventory includes: the calculation of a starting weight for the (n-1)th irradiation cycle, corresponding to the starting inventory weight, based on the starting atomic quantities and the weights of the nuclides; the calculation of a finishing weight for the (n-1)th irradiation cycle, based on a calculation of the evolution of the starting inventory during the (n-1)th irradiation cycle; and The first value of the feed inventory and / or the first value of the extraction inventory are determined from the difference between the starting weight of the (n-1)th cycle and the ending weight of the (n-1)th cycle.

[0056] According to one embodiment, the first value of the feed inventory is determined from a feed weight and / or the first value of the extraction inventory is determined from an extraction weight, the feed and / or extraction weights being deduced from the difference between the starting weight of the (n-1)th cycle and the ending weight of the (n-1)th cycle.

[0057] According to one embodiment, the method includes, as long as at least one operating condition is not met: a p-th adjustment step so as to determine a (p+1)-th feed inventory value having (p+1)-th atomic feed quantities of nuclides and / or a (p+1)-th extract inventory value (R1(p).yk) having (p+1)th atomic quantities of nuclide extraction; a (p+1)th calculation of the evolution of the fuel salt in the operating nuclear reactor, by the step of solving evolution equations, starting, for each of the nuclides, from the initial atomic quantity to which is added the (p+1)th atomic quantity of nuclide feed and / or is subtracted the (p+1)th atomic quantity of nuclide extraction, so as to calculate a (p+1)th value of the inventory of evolution of the fuel salt during the operation of the nuclear reactor; a (p+1)th verification, in the verification step, whether at least one operating condition of the molten salt nuclear reactor is met for the (p+1)th value of the inventory of evolution; . where p is a natural number greater than or equal to 1; and the fitting step preferably includes an optimization method, for example a Newton method or an interior points method.

[0058] According to one embodiment, the method further includes an initialization step for: define the nuclides taken into account in said method; and define nuclear data and nuclear reaction data, associated with each of the defined nuclides, necessary for solving the transport equation and the evolution equations; and define the starting inventory of fuel salt.

[0059] According to one embodiment, the condensed microscopic cross section of each nuclide is determined by the following equation: σ k s = ∫ 0 ∞ σ k s E ϕ E dE ∫ 0 ∞ ϕ E dE where ϕ(E) is the neutron flux of energy E, and σ k s E is the microscopic cross section of the nuclide k given for the energy E, for a reaction s, where s is a fission reaction or an absorption reaction.

[0060] According to one embodiment, the determination of the weight of each nuclide includes a calculation according to the following equation: σ + k = ν ¯ k σ k f − σ k a Or vk is an average number of neutrons emitted as a result of fission induced on the nuclide k by a neutron, σ k f is the condensed microscopic fission cross section of the k nuclide, and σ k a is the condensed microscopic absorption cross section of the nuclide k.

[0061] According to one embodiment, the average number of neutrons is determined by the following equation: ν ¯ k = ∫ 0 ∞ ν k E ϕ E dE ∫ 0 ∞ ϕ E dE where ϕ(E) is the neutron flux of energy E, and vk(E) is the microscopic cross section of the nuclide k given for energy E.

[0062] According to one embodiment, at least one operating condition includes at least one of the following: a criticality or reactivity condition, a solubility condition of the nuclides in the fuel salt, and / or a maximum feed volume condition.

[0063] According to one embodiment, the method further includes the implementation of a predictor-corrector model to evaluate the evolution of the weights of the nuclides over time.

[0064] Another embodiment provides for a computing device configured to implement the above method.

[0065] Another embodiment involves a molten salt nuclear reactor comprising: the above computing device; a fuel salt supply unit in the nuclear reactor; and a fuel salt extraction unit out of the nuclear reactor; the computing device being connected to the power supply unit and the extraction unit.

[0066] Another embodiment provides a computer program comprising instructions for implementing the above method when the program is executed by a computing device. Brief description of the designs

[0067] These features and advantages, as well as others, will be described in detail in the following description of particular embodiments, given by way of non-limiting example, in relation to the attached figures, among which: there figure 1 illustrates in a simplified way an example of a molten salt nuclear reactor; the figure 2 illustrates in a simplified way an example of a method for determining the composition of fuel salt in a molten salt reactor; the figure 3illustrates in a simplified manner an example of a method for determining the composition of fuel salt in a molten salt reactor according to one embodiment; the figure 4 illustrates in a simplified way a calculation device according to a particular embodiment; and the figure 5 illustrates in a simplified manner a molten salt nuclear reactor according to one embodiment. Description of the modes of realization

[0068] The same elements have been designated by the same reference numerals in the different figures. In particular, structural and / or functional elements common to the different embodiments may have the same reference numerals and may have identical structural, dimensional and material properties.

[0069] For the sake of clarity, only the steps and elements useful for understanding the implementation methods described have been represented and are detailed.

[0070] Unless otherwise specified, when referring to two connected elements, this means directly connected without any intermediate elements other than connectors or conductors, and when referring to two coupled elements, this means that these two elements can be connected or linked through one or more other elements.

[0071] In the description that follows, when referring to absolute positional qualifiers, such as the terms "front", "back", "top", "bottom", "left", "right", etc., or relative positional qualifiers, such as the terms "above", "below", "superior", "inferior", etc., or to orientational qualifiers, such as the terms "horizontal", "vertical", etc., unless otherwise specified, it refers to the orientation of the figures.

[0072] Unless otherwise specified, the expressions "approximately", "roughly", "approximately", and "on the order of" mean to within 10% or 10°, preferably to within 5% or 5°.

[0073] In the description that follows, when referring to a flux, unless otherwise specified, it refers to a neutron flux, or neutron flux.

[0074] In the description that follows, when a reactor or nuclear reactor is referred to, unless otherwise specified, a molten salt nuclear reactor is being referred to.

[0075] There figure 3 illustrates in a simplified way an example of method 300 for determining a fuel salt composition of a molten salt reactor according to an embodiment.

[0076] In the description of the figure 3 , we define: a cycle time as the time T during which the fuel is irradiated during an irradiation cycle; a cycle number n as a number assigned to the irradiation cycle starting from 1; and the time denoted t.

[0077] At the beginning of the first cycle (n=1), which we denote as being at t=0, i.e., at the beginning of the reactor's life, we have an initial charge INV1 (commonly called the initial inventory), which includes initial atomic quantities N1 < k of nuclides k (with a total of K nuclides) that can be represented as a composition vector N 1< ( t = 0) with: N → 1 t = 0 = N 1 1 t = 0 N 2 1 t = 0 ⋮ N K 1 t = 0

[0078] Method 300 includes an initialization step 301 (INIT) which defines the nuclides taken into account in Method 300, and nuclear data and nuclear reaction data (absorption / diffusion, fission, decay) associated with each of these nuclides and necessary for solving the transport equation and the evolution equations described below.

[0079] Nuclear data include microscopic cross sections σ(E) (which are functions of the neutron energy E), fission data (spectrum and multiplicity of neutrons emitted by fission, fission yields, etc.), radioactive decay data of nuclides, branching ratio data, etc. This data is generally available, in a way known to the person skilled in the art, in a nuclear database, or nuclear data library, for example one of the JEFF (Joint Evaluated Fission and Fusion file) databases, one of the ENDF / B (Evaluated Nuclear Data File) databases, or one of the JENDL (Japanese Evaluated Nuclear Data Library) databases.

[0080] The functions / definitions of this data are known to those skilled in the art. However, it is worth recalling that a microscopic cross section σ(E) is an equivalent interaction area that characterizes the probability of a specific type of interaction occurring between an incident particle, in this case a neutron, and a target particle, in this case a nuclide. It allows us to estimate the number of interactions between a particle flux, in this case neutrons, and a system of target particles, in this case nuclides. Cross sections are generally expressed in barns (1 barn = 10⁻²⁴ cm²). In neutronics, we primarily distinguish between neutron-induced reactions: fission, capture, and scattering (elastic and inelastic). An absorption reaction corresponds to either fission or neutron capture. Therefore, the majority of reactions involve absorption and scattering.Each of these reactions, for each nuclide, corresponds to a microscopic cross section. Furthermore, these microscopic cross sections are functions of the neutron energies.

[0081] The 301 initialization step may further include the definition of reactor technology data, such as geometry, molten salt nuclear reactor reflector material, and irradiation cycle characteristics (cycle duration and reactor power).

[0082] The initialization step 301 further includes the definition, as a basis for the following calculations, of a starting inventory (INV0) of fuel salt in the core, or vessel, of the reactor, this starting inventory being defined by a starting composition, that is to say the starting concentrations, or quantities N 0< k of the different nuclides k taken into account.

[0083] The starting inventory INV0 can be the initial inventory INV1 defined above, in which case the starting quantities N0 < k of the nuclides can be equal to the initial quantities N1 < k of the nuclides in the initial inventory INV1 defined above. In this case, there is no differentiation between INV0 and INV1. In the following calculations, we use this definition of the starting inventory, which corresponds to considering that we are starting from the beginning of the first cycle, knowing that it could more generally be an inventory of combustible salt at the beginning, during, or at the end of a cycle n, which is not necessarily the first cycle. Thus, we could start from the beginning of a cycle n, or the end of a cycle n-1, and from a time T0, which is not necessarily equal to 0.

[0084] It is recalled that the term "concentration" of a nuclide generally corresponds to a quantity of nuclides, which can be a quantity of atoms of this nuclide per unit volume, generally expressed in atoms / cm³, or at / cm³.

[0085] Method 300 then includes a step 302 of solving the transport equation (TRANSPORT), or Boltzmann equation, from the data defined in the initialization step 301, in particular the starting inventory, and the nuclear and technological data.

[0086] An example of the Boltzmann equation applied as the neutron transport equation in a system, in a quasi-static form, without an external neutron source, is given below: Ω → ⋅ ∇ ψ r → Ω → E t + ∑ k N k r → t σ k E ψ r → Ω → E t = ∑ k ∫ 0 ∞ ∫ 4 π N k r → t σ s , k Ω ′ → → Ω → , E ′ → E ψ r → , Ω ′ → , E ′ , t d Ω ′ → dE ′ + 1 k eff t ∑ k ∫ 0 ∞ ∫ 4 π ν k E N k r → t σ f , k E χ r → E t ψ r → Ω → E t d Ω → dE Or : ψ ( r , Ω , E, t ) represents the in-phase neutron flux, or angular neutron flux, at a time t at a point r(or volume, or position) of the system, of neutrons of energy E having an angular direction Ω ; Ω·∇ψ( r ,Ω, E , t ) translates the leakage of neutrons out of the system in a time t; s k ( E ) is the total microscopic cross section of the nuclide k for an incident neutron of energy E; N k ( r, t ) is the concentration of the target nuclide k of the neutrons at the point r and at time t; Σ kNk ( r, t)σ k ( E ) ψ ( r ,Ω, E , t ) represents the disappearance of neutrons from the system over time t by reaction (diffusion, absorption) with all the nuclides k present in the system: absorptions cause the neutrons to disappear and diffusions cause them to change energy levels and / or send them in another direction; σ s,k (Ω' → Oh , E ' → E) is the microscopic scattering cross section that causes the neutron to move from energy E' to energy E and from direction Ω' to direction Ω during scattering on a nuclide k; ψ (r,Ω', E' , t ) represents the angular neutron flux at time t and at point r of neutrons of energy E' having an angular direction Ω'; ∑ k ∫ 0 ∞ ∫ 4 π N k r → t σ s , k Ω ′ → → Ω → , E ′ → E ψ r → , Ω ′ → , E ′ , t d Ω ′ → dE ′ translates the arrival of neutrons in the system at time t resulting from scattering: these are the neutrons which, before the collision with the nuclides, were at an energy E' and moving in another direction Ω', and which exit the collision at energy E and in the direction Ω; k eff ( t ) represents the multiplication factor, that is, the ratio, for a given time interval t, of the number of neutrons produced by fission to the number of neutrons that disappeared; vk ( E) represents the average number of neutrons emitted following a fission induced on the nuclide k by an incident neutron of energy E; σ f,k ( E ) is the microscopic fission cross section of the nuclide k, for an incident neutron of energy E; x ( r, E, t ) represents the energy spectrum of neutrons emitted following fission induced on a nucleus by an incident neutron of energy E; and 1 k eff t ∑ k ∫ 0 ∞ ∫ 4 π ν k E N k r → t σ f , k E χ r → E t ψ r → Ω → E t d Ω → dE translates the creation in time t of neutrons emitted by fission of nuclides in the system.

[0087] Total microscopic, diffusion and fission cross sections are available in the nuclear databases described above.

[0088] Other forms of Boltzmann equation can be considered, in a way known to a person skilled in the art.

[0089] There are several ways to solve a Boltzmann equation, such as the neutron transport equation, including the deterministic approach (analytical solution of the transport equation) and the stochastic approach (probabilistic modeling of the transport equation). The details of solving the Boltzmann equation will not be described here, as this can be achieved using various computational codes, in a manner familiar to those skilled in the art. For example, many transport equation solving codes use a Monte Carlo method; for instance, the SERPENT or TRIPOLI-4 codes for the probabilistic approach, or the APOLLO3 or ERANOS codes for the deterministic approach.

[0090] In this step 302 of solving the transport equation, we take as the concentration N k of each nuclide, the starting concentration N 0< k defined in the initialization step 301.

[0091] Solving the neutron transport equation yields neutron observables as output data, specifically neutron fluxes, and in particular scalar neutron fluxes ϕ(E), or scalar fluxes, for several neutron energies E and a multiplication factor keff at a given time (t). A scalar neutron flux ϕ is derived from the integral over all directions of the angular neutron flux ψ. In the following description, when we refer to flux, we are referring to a scalar neutron flux, or scalar flux.

[0092] Starting from the concentrations of the nuclides in the initial charge INV1 at t=0, solving the transport equation allows us to evaluate the neutron fluxes ϕ( r , E , t =0) as a function of the energy E, of the position r in the system considered at t=0, as well as a multiplication coefficient k eff (t=0) at t=0.

[0093] From these neutron fluxes ϕ(E) and the microscopic cross sections σ(E) defined in step 301, we determine for each of the nuclides k, weighted microscopic cross sections σ k s by these neutron fluxes. We speak of condensed microscopic cross sections. These condensed microscopic cross sections reflect the probabilities of the nuclides to participate in the reaction s with the neutrons for the system considered, where s can be a fission f or an absorption a.

[0094] A condensed microscopic cross section is defined as a weighting of the microscopic cross section by the energy distribution of the neutron flux.

[0095] For example, condensed microscopic cross sections σ k s r → t (for reaction s and nuclide k), per unit time t (taking t=0) and volume in r , can be calculated according to the following equation: σ k s r → , t = 0 = ∫ 0 ∞ σ k s E ϕ r → , E , t = 0 dE ∫ 0 ∞ ϕ r → , E , t = 0 dE = ∫ 0 ∞ σ k s E ϕ r → , E , t = 0 dE ϕ r → , t = 0 Where each σ k s E represents the microscopic cross section of the nuclide k with a neutron of energy E for a reaction s, and is data available in nuclear databases.

[0096] Thus, for K nuclides, it is possible to determine: the condensed fission cross section, denoted σ k f r → , t = 0 ; the condensed absorption cross-section, denoted σ k a r → , t = 0 .

[0097] Similarly, the number of neutrons emitted n k (E) by fission is a function of the energy in the nuclear data. From the neutron fluxes ϕ(E), one can determine, for each nuclide k, an average number of neutrons emitted n k ( t ) by fission in the system considered, per unit of time t (taking t=0) and volume in r , according to the following equation: ν ¯ k t = 0 = ∫ 0 ∞ ν k E ϕ r → , E , t = 0 dE ∫ 0 ∞ ϕ r → , E , t = 0 dE

[0098] Neutron observables also allow the calculation of reaction rates. A reaction rate τs,k represents the number of reactions s between neutrons and a nuclide k per second at a given time and position. For example, one can calculate a reaction rate τ s,k ( r ,E,t) per unit of time t and volume in r , and for a neutron energy E, by the following equation: τ s , k r → E t = N k r → t σ k s E ϕ r → E t Or : σ k s E represents the microscopic cross section of the nuclide k for the reaction s; N k ( r,t ) is the concentration of the nuclide k at the point r and at time t; and ϕ ( r,E,t ) represents the scalar flux at time t and at point r in neutrons of energy E.

[0099] In the following steps, the evolution equations, or Bateman equation, are used in a 306 evolution equations solution step (EVOLUTION) to determine the evolution of the nuclide concentrations. The evolution equations can be used at various points during the method, as described later.

[0100] A simplified example of an equation of evolution over time t at a point is given below. r of the system for each nuclide k, based on the Bateman equation applied to a molten salt reactor: ∂ N k r → t ∂ t = ∑ j ∈ K j ≠ k ∑ s γ s , j , k σ j s r → t ϕ r → t + b j , k λ j + τ j N j r → t − ∑ s σ k s r → t ϕ r → t + λ k + τ k N k r → t

[0101] Or : j is another nuclide from the set K of nuclides and different from the nuclide k; c s,j,k represents the branching ratio, for reaction s, of nuclide j towards nuclide k; ϕ ( r,t ) corresponds to the energy integral of the scalar flux ϕ ( r,E,t), calculated in the denominator of equation [Math. 3]; σ j s r → t is the condensed microscopic cross section for the reaction s and the nuclide j, from equation [Math. 3]; bj,k represents the branching ratio, by decay, of the nuclide j towards the nuclide k; l j represents the decay time constant of the nuclide j; t j represents a processing rate, in this case a feed rate of nuclide k from nuclide j in the system; N j ( r, t ) represents the concentration of the nuclide j; σ k s r → t is the condensed microscopic cross section for the reaction s and the nuclide k, from equation [Math. 3]; λ k represents the decay time constant of the nuclide k; t k represents a processing rate, in this case an extraction rate of the nuclide k from the system; and N k ( r,t ) represents the concentration of the nuclide k.

[0102] The decay data λ and branching ratio γ, b are available in the nuclear databases described later. The processing rates τj, τk are, for example, defined in initialization step 301.

[0103] Several methods can be implemented to solve this equation, for example Runge-Kutta, TTA or CRAM methods, in a way known to the person in the trade.

[0104] Solving the Bateman equation allows us to determine the concentrations of the nuclides in the system at any given time, that is, the evolution over time of the composition of the fuel salt in the system. It also allows us to monitor the insoluble fission products in the different units of the reactor (treatment unit, fission gas management unit, etc.).

[0105] Method 300 includes a step 303 for evaluating the equivalence weight of nuclides (POIDS).

[0106] This step allows us to assess the impact, or weight, which can be called the "equivalence weight," of each of the nuclides present in the molten salt on the multiplication factor k eff. It also allows us to calculate equivalence weights of mixtures of several nuclides in a combustible salt inventory, or saline composition.

[0107] The weights σ +< k of the nuclides k are determined from the condensed microscopic cross sections of fission and absorption determined in step 302 of solving the transport equation, and in particular equations [Math 3] and [Math 4].

[0108] As an example, the weights σk of the nuclides k can be calculated using the following equation: σ k + n t = ν ¯ k t σ k f t − σ k a t

[0109] Or : σ k + n t represents the weight of the nuclide k for the cycle n at time t; n k ( t) represents the average number of neutrons emitted as a result of a fission induced on the nuclide k by a neutron; σ k f t represents the condensed microscopic fission cross-section for the nuclide k; and σ k a t represents the condensed microscopic absorption cross section for the nuclide k.

[0110] At the beginning of the first cycle, we take t=0 and n=1, and we obtain the weights σ k + 1 t = 0 k nuclides at the beginning of the first cycle.

[0111] This definition of the equivalence weight comes from perturbation theory applied to the transport equation. The principle of perturbation theory is to apply a perturbation, or modification, to each nuclide k, for example, changing its concentration Nk, and to determine the impact of this perturbation on keff. There are many ways to apply the perturbation method to the transport equation, and these methods can vary depending on the computational code used to solve the equation. These perturbation methods are familiar to those skilled in the art. Examples include the Iterated Fission Power method adapted to a Monte Carlo (probabilistic) method for solving the transport equation, and analytical methods for solving the adjoint transport equation.

[0112] A positive equivalence weight corresponds to a nuclide that produces more neutrons than it consumes, such as a fissile nucleus. A negative equivalence weight corresponds to a nuclide that absorbs more neutrons than it produces, typically an absorbing nuclide, which will tend to decrease the reactor's reactivity.

[0113] We can then evaluate the weight W c (t) of a saline composition in the core during a cycle n, at a given time t, by the equation: W c t = ∑ k = 1 K N k n t σ k + n t

[0114] Where K is the number of nuclides in the salt composition, N k n t is the concentration of each nuclide k in the saline composition and σ k + n is the weight of the nuclide k.

[0115] In particular, the total weight of the fuel salt in the core at the beginning of the first cycle (n=1 and t=0) can be calculated from the weights σ k + 1 t = 0 and concentrations N k 1 t = 0 κ nuclides at the beginning of the first cycle: W c t = 0 = ∑ k = 1 K N k 1 t = 0 σ k + 1 t = 0

[0116] At the beginning of the first cycle, there is no loading / unloading data from the end of the previous cycle. However, the evolution equations can be solved up to the end of the first cycle (n=1) over the cycle duration T. For the first cycle, this can correspond to step 306, solving the evolution equations without performing the selection step 305 described later, and by selecting YES for the verification step 307 described later, so as to go directly to the finalization step 309 described later. Solving the evolution equations allows us to determine the concentrations of the nuclides (in other words, an inventory of fuel salt) at the end of the first cycle at t=T, which can be represented as the following vector: N → 1 t = T = N 1 1 t = T N 2 1 t = T ⋮ N K 1 t = T

[0117] In the same way as at the beginning of the cycle, we can then determine the total weight of the fuel salt in the core at the end of the cycle, from the weights of the nuclides evaluated at the beginning of the cycle: W c t = T = ∑ k = 1 K N k 1 t = T σ k + 1 t = 0

[0118] From the total weight at the beginning of the cycle and the total weight at the end of the cycle, we can obtain an equivalent weight of reactivity loss ΔW n< on the first cycle (n=1): Δ W 1 = W c t = 0 − W c t = T

[0119] Thanks to the use of equivalence weights, it is possible to evaluate the impact, on the reactivity of the reactor, of a saline composition, for example of one or more concentrations of nuclides in the fuel salt, without having to solve the transport equation several times with the evolution equations, as indicated later.

[0120] Method 300 then includes a determination phase 304 of a feed inventory INV2 of fuel salt to be added to the initial inventory INV0, taken here to be equal to INV1, in the reactor core, for example to compensate for the loss of reactivity. An extraction inventory EXTR2 to be extracted from the reactor core can also be determined during this phase 304.

[0121] This feed / extraction inventory is for the cycle following the starting cycle defined in step 301, which, in the example described, is the first cycle, so the following cycle is the second cycle. This can be generalized to determining a feed / extraction inventory for an nth cycle determined at the end of an (n-1)th cycle, where n is greater than or equal to 2.

[0122] A feed / extraction inventory can be a batch of fuel salt being fed or extracted in the case of a batch-controlled molten salt reactor. For a continuously controlled reactor, the feed / extraction inventory can correspond, for example, to a selection, or a modification, of a continuously fed / extracted fuel salt inventory.

[0123] We start with an initial assessment of the reactivity loss ΔW2 during the second cycle, considered equivalent to the reactivity loss ΔW1 during the first cycle. In other words, we assume that: Δ W 2 = Δ W 1 = W c t = 0 − W c t = T

[0124] We seek to supply the reactor core with a quantity of fuel equivalent to a weight equal to ΔW 1< to compensate for the loss of reactivity.

[0125] The INV2 feed inventory is a mixture of L nuclides l whose composition is represented in the form of a feed vector An< , where n=1 for a feed at the end of the first cycle (t=T) in preparation for the second cycle.

[0126] The food vector A 1< can be expressed as follows: A → 1 t = T = A 1 t = T x 1 t = T x 2 t = T ⋮ x L t = T

[0127] Where A1 is the total atomic quantity of the feed inventory, and x1 (l ranging from 1 to L) are the atomic proportions of the nuclides in this feed inventory. The proportions x1 are organized as a feed proportions vector. x .

[0128] One objective of the following steps may be to evaluate the total atomic quantity A 1< , assuming the proportions xl defined, this atomic quantity corresponding to the quantity with which to reload the reactor after the first cycle to compensate for the anticipated loss of reactivity ΔW 2< in the second cycle.

[0129] We seek to determine the weight in reactivity of the diet, denoted Wa, in the same way as for the heart, that is to say: W a t = T = A 1 ∑ l = 0 L x l t = T × σ l + 1 t = 0

[0130] The EXTR2 extraction inventory is a mixture of J nuclides j whose composition is represented as an extraction vector R n< , where n=1 for an extraction at the end of the first cycle (t=T) in preparation for the second cycle.

[0131] The extraction vector R 1< can be expressed as follows: R → 1 t = T = R 1 t = T y 1 t = T y 2 t = T ⋮ y J t = T

[0132] Where R1 is the total atomic quantity of the extraction inventory and yj (j ranging from 1 to J) are the atomic proportions of the nuclides in this extraction inventory. The proportions yj are organized into an extraction proportions vector. y .

[0133] Another objective of the following steps may also be to evaluate the atomic quantity R 1< , assuming the proportions yj defined, this atomic quantity corresponding to the quantity with which to discharge the reactor after the first cycle.

[0134] We can try to determine the reactivity weight of the extraction, denoted W r, in the same way as for the feed, that is: W r t = T = R 1 ∑ l = 0 J y j t = T × σ j + 1 t = 0

[0135] To determine the total atomic quantity A 1< , and possibly the total atomic quantity R 1< , an iterative process is preferably used.

[0136] The determination phase 304 of the feed / extraction inventory includes a selection step 305 (SELECT), in which a first value for the total atomic quantity, denoted A1<(0), is defined to compensate for the loss of reactivity. More broadly, a first evaluation can be defined. An< (0) of the feed inventory, with n=1 for a feed at the end of the first cycle in view of the second cycle, if we want to play on the proportions xl.

[0137] In a non-limiting example, we can assume in a first evaluation that there is no extraction, that is to say that R 0 1 is equal to 0.

[0138] We can then determine A1 (0) using the following equations: W a t = T = Δ W 2 = Δ W 1 = W c t = 0 − W c t = T

[0139] Using equation [Math 15], this amounts to determining the atomic quantity A 1< (0) which allows us to solve the equation: A 0 1 ∑ l = 0 L x l t = T × σ k + 1 t = 0 = W c t = 0 − W c t = T

[0140] From A 1< (0) , insofar as we know the feeding proportions vector x , we can obtain a first assessment of the feed inventory, and we then obtain a first assessment of the initial composition of the second cycle (n=2) as being: N → 0 2 t = T = N → 1 t = T + A → 0 1 t = T

[0141] A person skilled in the art will be able to adapt the following calculations for a value of R 0 1 different from 0. In particular, we would then determine the reactivity weight of the extraction Wr and the reactivity loss ΔW1 would then be equal to Wa - Wr, then to determine the initial cycle composition of the second cycle, we would subtract the extraction vector from equation [Math 20] R → 0 1 t = T .

[0142] The equivalence weights σk are assumed constant in these calculations. However, it is possible to perform a new solution of the transport equation to update the weights σ k + 2 t = T Nuclides at the end of the first cycle, or at the beginning of the second cycle, i.e., at t=T. This allows us to adjust the reactivity weight of the feed Wa(t=T) in equation [Math 15], or even of the extraction Wr(t=T) in equation [Math 17]. Alternatively, a predictor-corrector model can be used to estimate the evolution of these equivalence weights σk over time.

[0143] The determination phase 304 of the supply / extraction inventory then includes a step of solving the evolution equations 306, for example the Bateman equation [Math 6] given earlier, without there necessarily being a loop with the transport equation.

[0144] This solution of the evolution equations is performed over time T of the second irradiation cycle, starting from the first evaluation of the initial cycle composition of the second cycle. N (0) 2< ( t = T), and in particular allows for an initial assessment of the final composition of the second cycle N (0) 2< ( t = 2 T ) (end-of-cycle inventory).

[0145] In a verification step 307 (VERIF) of the feed / extraction inventory determination phase 304, it is determined whether all the operating conditions of the molten salt reactor are met for the first evaluation of the end-of-second-cycle composition. N (0) 2< ( t = 2 T ) determined in step 306 of the evolution equations.

[0146] An operating condition could be, for example: a criticality (or reactivity) limit or value; a solubility limit or value for the nuclides in the fuel salt; a fuel salt volume limit or value; a technological constraint, for example a maximum feed volume...

[0147] If each operating condition is verified (YES), we can proceed to the finalization step 309 (FINAL) described below.

[0148] If at least one operating condition is not met (NO), we can proceed to an adjustment step 308 (ADJUST) which then returns after the selection step 305, to the input of the resolution step 306 of the evolution equations.

[0149] The adjustment step 308 is included in the determination phase 304 of the supply / extraction inventory. This adjustment step 308 performs an iteration that therefore does not return to the transport equation resolution step 302, thanks in particular to the use of equivalence weights. Each iteration includes a repetition of the evolution equation resolution step 306 and the verification step 307, as well as the adjustment step 308 if the result of the verification step 307 is NO.

[0150] The use of equivalence weights thus avoids, in most cases, having to recalculate the transport equation to update the neutron fluxes and condensed microscopic cross sections as a function of the fuel salt supply, particularly during iterations. The time savings can be considerable, for example, by a factor of 10, compared to known methods that loop back to the transport equation at each iteration, because evaluating the weights of the nuclides is very fast compared to calculating the neutron flux by solving the transport equation.

[0151] The adjustment step 308 preferably includes an optimization method, for example a Newton method, an interior point method, or any other method allowing the end-of-cycle fuel salt inventory to remain within a prescribed operating range, with the operating condition(s).

[0152] For example, optimization method 308 can define an objective function f to be optimized, for example minimized, with a set of constraints g and h, such that: min f N → σ + avec g N → ≥ 0 et h N → = 0

[0153] Or N is the composition vector of the cycle considered and σ +< represents the weights of the nuclides.

[0154] In this adjustment step 308, as long as the optimization has not converged, the feed is adjusted and the extraction can also be adjusted. This allows for p iterations, where p varies between 1 and P.

[0155] We can cite, among many others, two examples of adjustment.

[0156] In the first example, we assume that the feed volume (quantity of atoms A1) is fixed: if there are not enough actinides in the reactor core to ensure the criticality condition or the salt's melting temperature, then we can feed with a salt higher in actinides. This amounts to adjusting the feed proportions vector. x Thus : x 1 ′ t = T x 2 ′ t = T ⋮ x L ′ t = T

[0157] With A 1 1 equal to A 0 1

[0158] In a second example, we assume that the feed volume (quantity of atoms A1) is variable: if there are not enough actinides in the reactor core to ensure the criticality condition and / or the salt melting temperature, we can choose to extract a fraction of fuel salt with a low actinide content and increase the fuel salt feed with a fraction highly charged with actinides. This can be equivalent to reusing the same feed proportions vector and increasing the feed and extraction volumes (quantities of atoms A1 and R1), i.e.: A 1 1 > A 0 1 et R 1 1 > 0

[0159] More generally, the adjustment can play on one or more parameters among: the total atomic quantity of feed A 1< , the total atomic quantity of extraction R 1< , the feed proportions vector and / or the extraction proportions vector.

[0160] We can determine as many new evaluations of the initial composition of the second cycle (n=2, t=T) as there are iterations, or loops, in this example P evaluations: N → p 2 t = T = N → 1 t = T + A → p 1 t = T − R → p 1 t = T

[0161] Each new solution of the evolution equations is performed over time T of the second irradiation cycle from the p-th composition evaluation. N ( p ) 2< (t = T) de beginning of the second cycle and it allows in particular to obtain a p-th evaluation of the composition N ( p ) 2< ( t = 2 T ) of the end of the second cycle.

[0162] The adjustment steps 308, as well as the selection step 305, correspond to a heuristic method based on the weights of the nuclides, which can play on several parameters: the quantity of atoms of the fuel salt to be fed / extracted, the atomic fraction of each of the nuclides in this fuel salt, which can be positive or negative depending on whether it is a feeding or an extraction of this nuclide.

[0163] Finalization step 309 (FIN) records the final composition of the fuel salt to be introduced, ensuring that each operating condition of the molten salt reactor is verified during reactor operation, for example, between the start and end of an irradiation cycle. Finalization step 309 also records an inventory of fuel salt at the end of the cycle, which is essential for defining the next cycle, particularly the fuel salt supply and / or extraction inventory for the following cycle.

[0164] Thus, once the optimization is complete, after P iterations, we obtain: The final composition at the beginning of the second cycle (n=2): N 2< ( t = T ) = N ( P ) 2< ( t = T )

[0165] The final composition at the end of the second cycle (n=2): N 2< ( t = 2 T ) = N ( P ) 2< (t = 2 T ) via the resolution of evolution equations.

[0166] If necessary, the transport calculation can be recalculated to update the nuclide weights. σ k + 2 t = 2 T at the end of the second cycle, and determine the weight of the heart at the end of the cycle W c (t=2T) thus giving more precise access to the loss of reactivity ΔW 2< at the end of the second cycle.

[0167] The process has been described starting from the first irradiation cycle to define a supply / extraction inventory for the second cycle (n=2). A person skilled in the art will be able to adapt the described steps starting from the nth cycle to define a supply / extraction inventory for the nth cycle, where n is greater than or equal to 3, and in this case, t=T0. In the preceding equations, cycle 2 can be replaced by cycle n and cycle 1 by cycle n-1.

[0168] For example, we repeat as many as necessary the whole set of steps described for the second cycle for the following cycles, starting each time from the concentrations of the nuclides in the core at the end of the previous cycle.

[0169] Thanks to the use of equivalence weights, the 300 determination method described above implements an iteration that loops back to the 306 step of solving the evolution equations without having to repeat the 302 step of solving the transport equation, which is a very computationally expensive step. Thus, the 300 determination method eliminates the need for transport equation calculations in the iterative phases, significantly reducing computation time.

[0170] Method 300 is implemented in a computing device, such as computing device 400 of the figure 4described below, or the 510 calculation device of the figure 5 described later. For example, the computing device is capable of controlling a feed unit to supply the reactor with the feed inventory and / or an extraction unit to extract the extraction inventory from the nuclear reactor.

[0171] There figure 4 illustrates in a simplified way a calculation device 400 according to one embodiment.

[0172] In this example, the 400 computing device is based on a P processor. The P processor is adapted to execute a computer program comprising instructions for implementing the determination method described below.

[0173] The computing device 400 also includes, connected to the processor P: an instruction memory (INSTR_MEMORY) containing the computer program instructions; an input / output interface (I / O INTERFACE) allowing, in particular, the retrieval of the necessary nuclear data; a user interface (USER INTERFACE), which allows, for example, the computing device to interface with a user, for example, a molten salt nuclear reactor operator; and a data storage (DATA_MEMORY), allowing, for example, the storage of data measured by the computing device, for example, neutron fluxes, nuclide concentrations, condensed microscopic cross sections, average number of neutrons emitted per fission, equivalence weights....

[0174] This example is not exhaustive, and a person skilled in the art may consider other computing devices. For example, it could be a hardware-based computing device, such as an application-specific integrated circuit (ASIC), or a field-programmable gate array (FPGA).

[0175] There figure 5 illustrates in a simplified manner a 500 molten salt nuclear reactor according to one embodiment.

[0176] The molten salt 500 nuclear reactor illustrated in the figure 5 is similar to the molten salt nuclear reactor 100 illustrated in the figure 1Some common elements are not illustrated and are described again here. In nuclear reactor 500, the storage unit 530 is separated into a feed unit 531 for fresh fuel salt 10a and an extraction unit 532 for spent fuel salt 10b. The extraction unit 532 can be connected to an inlet of a reprocessing unit. The feed unit 531 can be connected to an outlet of a reprocessing unit. The feed unit 531 is connected to the reactor vessel 110 by the fluidic line 131, which introduces fresh fuel salt 10a into the vessel 110. The extraction unit 532 is connected to the reactor vessel 110 by the fluidic line 132, which extracts the spent fuel salt 10b from the vessel 110.

[0177] The molten salt 500 nuclear reactor illustrated in the figure 5 further includes a calculating device 510 which is connected to the power supply unit 531, and which may be the calculating device 400 of the figure 4The computing device 510 can also be connected to the extraction unit 532. For example, the computing device 510 is adapted to control the feed unit 531 so that the feed unit 531 supplies the nuclear reactor 500 with the feed inventory. For example, the computing device 510 is adapted to control the extraction unit 532 so that the extraction unit 532 extracts the extraction inventory from the nuclear reactor 500.

[0178] The computing device 510 can be linked to a nuclear database 520.

[0179] One advantage of using an evolution calculation, based on evolution equations, is that this calculation is relatively fast, on the order of a second, a factor of 100-1000 compared to a Monte Carlo transport calculation, which justifies calls to the evolution module in the iterative phase.

[0180] Various embodiments and variations have been described. Those skilled in the art will understand that certain features of these various embodiments and variations could be combined, and other variations will become apparent to them. In particular, embodiments have been described for a batch-controlled molten salt reactor, bearing in mind that the described method can be applied to any type of molten salt reactor, whether batch-controlled or continuous-control. In a continuously controlled reactor, an irradiation cycle then corresponds to a virtual, or digital, cycle, since the reactor is not shut down for fuel salt feeding / extraction: a digital cycle corresponds, for example, to a period in the reactor's life at the beginning and / or end of which it is verified that the operating conditions are met for the inventory determined by the evolution equations.

[0181] Finally, the practical implementation of the described methods and variants is within the reach of the person in the trade, based on the functional indications given above.

Claims

1. Method (300) for determining, by a computing device (400; 510), the fuel salt composition of a molten salt nuclear reactor (500) during the operation of said nuclear reactor, the method comprising: - the determination of neutron fluxes (ϕ(E)) of several energies (E) and a multiplication factor (k eff ) by a step of solving (302) a neutron transport equation, from an inventory (INV0) of starting fuel salt, having starting atomic quantities (N0 k ) of nuclides (k), in the nuclear reactor; - the determination, for each of the nuclides, of condensed microscopic cross sections ( σ k s ) from the neutron fluxes (ϕ(E)); - the determination (303) of weights (σ + k ) of the nuclides (k) on the multiplication factor (k eff ), from the condensed microscopic cross sections ( σ k s ) ; - the determination (304), from the weights (σ + k ) of nuclides (k), from a fuel salt supply inventory (INV2), having atomic quantities of supply (A 1 .x k ) of nuclides, to be added to the starting inventory (INV0) and / or an extraction inventory (EXTR2), having extraction atomic quantities (R 1 .y k ) of the nuclides to be extracted from the starting inventory (INV0); the determination (304) of the feed inventory (INV2) and / or the extraction inventory (EXTR2) including at least one calculation of the evolution of the nuclides, by a step of solving evolution equations (306), starting, for each nuclide (k), from the starting atomic quantity (N 0 k ) to which is added a value of the atomic quantity of feed (A 1 .x k ) of this nuclide and / or a value of the atomic extraction quantity (R) is subtracted 1 .yk ) of this nuclide, so as to evaluate at least one inventory of evolution of the fuel salt during the operation of the nuclear reactor; the supply inventory and / or the extraction inventory being determined so that the evolution inventory meets at least one operating condition.

2. Method (300) according to claim 1, wherein the computing device (400; 510) is capable of controlling a feed unit (531) to supply the reactor with the feed inventory and / or an extraction unit (531) to extract the extraction inventory from the nuclear reactor.

3. Method (300) according to claim 1 or 2, wherein the supply inventory (INV2) and / or the extraction inventory (EXTR2) are beginning inventories of an nth irradiation cycle, where n is a natural number greater than or equal to 2, and the evolution inventory is an end inventory of the nth irradiation cycle.

4. Method (300) according to claim 3, wherein the starting inventory (INV0) is a starting inventory of the (n-1)th irradiation cycle, for example an inventory of a first loading (INV1) of fuel salt intended for the first irradiation cycle of the nuclear reactor.

5. Method (300) according to any one of claims 1 to 4, wherein the determination (304) of the supply inventory (INV2) and / or the extraction inventory (EXTR2) comprises: - the determination of a first value (A 1 (0) ) of the food inventory having initial atomic quantities of food (A 1 (0) .x k ) of the nuclides and / or of a first value (R 1 (0) ) of the extraction inventory having first atomic quantities of extraction (R 1 (0) .x k) of nuclides; - a first calculation of the evolution of nuclides in the operating nuclear reactor, by the step of solving (306) the evolution equations, starting, for each nuclide (k), from the initial atomic quantity (N 0 k ) to which is added the first atomic quantity of feed (A 1 (0) .x k ) of this nuclide and / or the first atomic extraction quantity (R) is subtracted 1 (0) .y k ) of this nuclide, so as to calculate a first value of the inventory of evolution of the fuel salt during the operation of the nuclear reactor; - a first verification, in a verification step (307), if at least one operating condition of the molten salt nuclear reactor is met for the first value of the inventory of evolution.

6. Method (300) according to claim 5, wherein the first value (A 1 (0)) of the food inventory and / or the first value (R 1 (0) ) of the extraction inventory are determined from a weight loss calculation of the starting inventory (INV0) during the operation of the nuclear reactor, for example during an irradiation cycle.

7. Method (300) according to claim 6 in its dependence on claim 3 or 4, wherein the calculation of the weight loss of the starting inventory (INV0) comprises: - the calculation of a starting weight of the (n-1)th irradiation cycle, corresponding to the weight of the starting inventory (INV0), from the starting atomic quantities (N 0 k ) and weights (σ + k ) of the nuclides (k); - the calculation of a final weight of the (n-1)th irradiation cycle, based on a calculation of the evolution of the initial inventory (INV0) during the (n-1)th irradiation cycle; and the first value (A 1 (0)) of the food inventory and / or the first value (R 1 (0) ) of the extraction inventory are determined from the difference between the starting weight of the (n-1)th cycle and the ending weight of the (n-1)th cycle; for example, the first value (A 1 (0) ) of the food inventory being determined from a food weight (W a ) and / or the first value (R 1 (0) ) of the extraction inventory being determined from an extraction weight (W r ), the feeding and / or extraction weights being deduced from the difference between the starting weight of the (n-1)th cycle and the ending weight of the (n-1)th cycle.

8. A method (300) according to any one of claims 5 to 7, comprising, as long as at least one operating condition is not met: - a p-th adjustment step (308) so as to determine a (p+1)-th value of the feed inventory having (p+1)-th atomic quantities of feed of the nuclides (A 1 (p) .x k ) and / or a (p+1)th value of the extraction inventory (R 1 (p) .y k ) having (p+1)-th atomic quantities of nuclide extraction (R 1 (0) .y k ) ; - a (p+1)th calculation of the evolution of the fuel salt in the operating nuclear reactor, by the step of solving (306) evolution equations, starting, for each of the nuclides (k), from the initial atomic quantity (N 0 k ) to which is added the (p+1)-th atomic quantity of nuclide feed (A 1 (p) .x k) and / or the (p+1)-th atomic quantity of nuclide extraction (R is subtracted 1 (p) .x k ), so as to calculate a (p+1)-th value of the inventory of evolution of the fuel salt during the operation of the nuclear reactor; - a (p+1)-th check, in the check step (307), whether at least one operating condition of the molten salt nuclear reactor is met for the (p+1)-th value of the inventory of evolution; where p is a natural number greater than or equal to 1; and the adjustment step (308) preferably includes an optimization method, for example a Newton method or an interior points method.

9. Method (300) according to any one of claims 1 to 8, further comprising an initialization step (301) for: - defining the nuclides (k) taken into account in said method; and - defining nuclear data and nuclear reaction data, associated with each of the defined nuclides, necessary for solving the transport equation and the evolution equations; and - defining the starting inventory (INV0) of fuel salt.

10. Method (300) according to any one of claims 1 to 9, wherein the condensed microscopic cross section ( σ k s The coefficient of each nuclide (k) is determined by the following equation: σ k s = ∫ 0 ∞ σ k s E ϕ E dE ∫ 0 ∞ ϕ E dE where ϕ(E) is the neutron flux of energy E, and σ k s E is the microscopic cross section of the nuclide k given for the energy E, for a reaction s, where s is a fission reaction or an absorption reaction.

11. Method (300) according to any one of claims 1 to 10, wherein the determination (303) of the weight (σ + k ) of each nuclide includes a calculation according to the following equation: σ + k = ν ¯ k σ k f − σ k a Or v k is an average number of neutrons emitted as a result of fission induced on the nuclide k by a neutron, σ k f is the condensed microscopic fission cross section of the k nuclide, and σ k a is the condensed microscopic absorption cross-section of the nuclide k; for example, the average number of neutrons ( v k ) being determined by the following equation: ν ¯ k = ∫ 0 ∞ ν k E ϕ E dE ∫ 0 ∞ ϕ E dE where ϕ(E) is the neutron flux of energy E, and v k (E) is the microscopic cross section of the nuclide k given for the energy E.

12. Method according to any one of claims 1 to 11, wherein at least one operating condition comprises at least one of: a criticality or reactivity condition, a solubility condition of the nuclides in the fuel salt, and / or a maximum feed volume condition.

13. A method according to any one of claims 1 to 12, further comprising the implementation of a predictor-corrector model to evaluate the evolution of the weights (σ + k ) of nuclides over time.

14. Calculation device (400; 510) configured to implement the method according to any one of claims 1 to 13.

15. Molten salt nuclear reactor (500) comprising: - the calculation device (400; 510) according to claim 14; - a fuel salt feeding unit (531) into the nuclear reactor (500); and - a fuel salt extraction unit (532) out of the nuclear reactor; the calculation device being connected to the feeding unit to control said feeding unit and to the extraction unit to control said extraction unit.

16. Computer program comprising instructions for implementing the method according to any one of claims 1 to 13, when the program is executed by a computing device (400; 510).

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