Multiphysics methods for species tracking in molten salt reactors

1 Introduction

Recent commercial investment in next-generation nuclear systems has radically shifted the field of nuclear energy over the last decade. A large proportion of this investment is focused on a non-traditional approach to nuclear energy known as Molten Salt Reactors (MSRs). MSRs are characterized by their unique use of uranium fuel that is dissolved within an ionic liquid medium which utilize halogens such as fluorides or chlorides at high liquidus temperatures thereby garnering the name molten salts. MSRs were included within the Generation IV International Forum back in 2002 as one of six reactor technologies deemed worthy of further research and development (U.S. DOE Nuclear Energy Research Advisory Committee and the Generation IV International Forum, 2002).

Thanks to the liquid nature of MSR fuel, these reactors are characterized by their flexibility to accommodate multiple fuel cycles including thorium-uranium and uranium-plutonium cycles and tunable neutron spectrums (e.g., fast, thermal, or hybrid) to achieve various fuel utilization schemes including breeding, burning, and breed and burn designs. This fuel utilization flexibility is cited as an economic and fuel efficiency enhancement over traditional light water reactors (Serp et al., 2014). Additionally, the liquid nature of fuel is thought to provide enhanced safety where the thermal expansion of fuel salt provides a large negative temperature coefficient of reactivity and where the fuel salt can be quickly drained into a non-critical configuration for whatever reason thereby quickly shutting down the reactor and enabling passive cooling (Serp et al., 2014).

The MSR concept was originally developed during the birth of the nuclear era by researchers and the laboratory leadership of Alvin Weinberg at Oak Ridge National Laboratory (ORNL) during the 1950s and 1960s (MacPherson, 1985). Two MSRs were developed and successfully operated at ORNL–the initial Aircraft Reactor Experiment (ARE) and the robust demonstration of molten salt technology in the Molten Salt Reactor Experiment (MSRE) (Rosenthal, 2009). Subsequent work carried out by ORNL envisioned a one of a kind thermal breeder reactor capable of utilizing the thorium-uranium fuel cycle known as the Molten Salt Breeder Reactor (MSBR) which eventually lost support and was canceled–tritium management and complexity of chemical reprocessing needs being some of the reasons that were cited as justification (U.S. Atomic Energy Commission, 1972).

Recent years have seen a resurgence of public and private interest in MSRs. China has recently built the world’s first Thorium Molten Salt Reactor (TMSR) which came online in 2023 (World Nuclear News, 2023). The United States (U.S.) Department of Energy (DOE) has a Molten Salt Reactor Program that funds research which addresses technology challenges to MSRs to support the near-term commercialization of MSR technology (Paviet, 2025). Additionally, there is a plethora of private companies in Europe, Canada, and the United States which are incorporating molten salt technology in some capacity and are working towards bringing MSRs to market. One prominent venture is a partnership between Southern Company and TerraPower to build the world’s first chloride reactor known as the Molten Chloride Reactor Experiment (MCRE) at Idaho National Laboratory (INL) within the next few years (Nuclear News, 2023).

This private-public partnership to push forward MSR technology has identified remaining technical challenges that are currently inhibiting near term commercialization. Along with U.S. DOE Molten Salt Reactor program, the U.S. DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has developed modern computational tools to accelerate the deployment of advanced nuclear reactor systems (Nuclear Energy Advanced Modeling and Simulation, 2025). MSR modeling and simulation needs have been prioritized due to the inherent multiphysics nature of liquid fuel systems where thermal-hydraulics and neutron transport are inexplicable linked due to the circulation of delayed neutron precursors (Shahbazi et al., 2024). These modeling and simulation enhancements have been integrated within the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework (Harbour et al., 2025) for MSR analyses and are showcased on generic open-source models of advanced reactor systems hosted by the National Reactor Innovation Center’s (NRIC) Virtual Test Bed (VTB) (Giudicelli et al., 2023).

The work presented here utilizes and demonstrates these recent developments for modeling and simulation of MSR systems. Specifically, the multiphysics methods required for species tracking within MSR systems are detailed and subsequent analyses necessary for safety, source term, and system design are presented. A summary of the following sections is now presented. Section two defines the unique requirement of species tracking for MSR systems and its importance within MSR analyses. Next, section three describes the multiphysics species tracking framework that couples the primary driving physics in MSR systems. Section four presents and discusses the results of the multiphysics framework applied to the generic Molten Salt Fast Reactor (MSFR) system. Lastly, section five discusses other applications of the framework molten salt system analysis and draws conclusions regarding future work, digital twin development and validation efforts utilizing new experimental data.

2 Importance of species tracking in MSRs

As highlighted in the Introduction, the liquid fuel nature of MSRs give rise to an inherently multiphysics system where the reactor dynamics and subsequent system behavior are intrinsically coupled processes. Species transport is one of these multiphysics driven phenomena in MSRs due to the liquid and chemical nature of the fuel salt where fission products, corrosion products, and actinides subsequently mix within the fuel salt. The resulting fuel salt mixture then is always in a state of change during reactor operation due to ongoing fission and corrosion processes within the MSR core and primary loop or integral system (Walker S. A. et al., 2023).

2.1 Multiphysics driven species transport in MSRs

As identified previously, the physical processes of neutron transport, thermal-hydraulics, and thermochemistry are tightly coupled in MSR systems which drive multiphysics changes within the fuel salt. These multiphysics changes can then have significant downstream consequences on the fuel performance, corrosion of reactor structures, and design of auxiliary reactor support systems. A non-exhaustive list of species transport phenomena include species volatilization, precipitation, leaching, and plating in MSR systems (Walker S. et al., 2023) as illustrated in Figure 1.

Many of these processes are dictated by the chemical activity or redox potential of the base halide in the molten salt (e.g., F or Cl) (Olander, 2002). The changes in the fuel-salt composition due to fuel depletion essentially increases the redox potential of the fuel salt (i.e., increases the chemical potential of the base halide) by depleting cationic charge from the fission of uranium and not sufficiently replacing it through the generation of fission products which are not as thermodynamically stable within the fuel salt (i.e., the production of noble gases and metals like Xe and Mo respectively) (Baes Jr, 1974; Chasanov, 1965; Yoon, et al., 2025). This process has been previously coined as depletion-driven thermochemistry (Walker S. A. et al., 2023) which drives many of the species transport processes observed in Figure 1.

Starting with the far left magnifying glass of Figure 1 the effect of changing thermochemistry has on species volatilization is shown where gaseous species like cesium-iodide volatilize due to depletion-driven oxidation of the fuel salt (Walker S. A. et al., 2023). This effect is critical in understanding source term evolution and off-gas system design as shown in the liquid-gas interface surrounding the pump seen in the top-right magnifying glass.

In addition to fuel salt oxidation through fuel depletion, temperature gradients that arise due to thermal hydraulics from high temperature salt in the core from fission to colder temperature salt through the heat exchanger drives galvanic electrochemical corrosion (Tano et al., 2023; Raiman et al., 2022) of structural materials in contact with the fuel salt as seen in the bottom right magnifying glass of Figure 1. Seen here is the formation of corrosion products Cr²⁺ and Fe²⁺ in the molten salt due to temperature and redox potential gradients in the reactor. Active-chemistry or redox-potential control shown in the top center magnifying glass in Figure 1 is an appropriate mitigation strategy to employe to prevent significant corrosion to occur by reducing the fuel salt with a more thermodynamically favorable metal like beryllium in fluoride salts or zirconium in chloride salts (Zhang et al., 2018).

2.2 Species tracking requirement in MSRs

Adequately accounting for these integral effects through modeling and simulation enables researchers and reactor designers to develop successful corrosion mitigation strategies, source term minimization, safety analyses, and safeguards considerations (Walker S. A. et al., 2023; Kovacic et al., 2018). The multiphysics driven phenomena then require a species-tracking framework capable of coupling the various physics that drive species volatilization, precipitation, leaching, and plating in MSR systems (Walker S. et al., 2023). The resulting species tracking framework should then be able to accurately predict these phenomena for both MSR system design via simulation and for experimentalists to inform the measurement and control requirements of auxiliary system instrumentation. The work detailed here is a crucial step forward in resolving this issue through the development and application of multiphysics modeling of species tracking in MSRs.

As previously highlighted, managing and monitoring radionuclide species in MSR systems is crucial (Walker S. et al., 2023). Tracking these species ensures reactor safety, improves performance, and supports long-term operation. This process involves identifying, measuring, and analyzing the amounts and locations of different isotopes, like fission products, actinides, and other transmutation products in the reactor and auxiliary systems. The following sections explain how species tracking is important for containment, heat removal, reactivity, corrosion, and safeguards, all of which are essential for the safe and efficient operation of MSRs.

2.2.1 Radionuclide containment and source term

Tracking radioactive species is crucial for preventing their release from nuclear reactors (Thomas and Jerden, 2020). “Source term” refers to the amount and types of radioactive materials that could be released during normal operations or accidents (Shahbazi, et al., 2023). Accurate species tracking helps understand the behavior of radionuclides under different conditions, which is essential for containment strategies. In advanced reactors like MSRs, understanding the movement and accumulation of radioactive isotopes in liquid and gas phases in varying redox potential and temperature gradients is vital (Haubenreich and Engel, 1970). This knowledge helps model their mobility, interactions with materials, and potential release pathways, ensuring effective containment. Source term analysis also guides the design of safety features and emergency response measures.

2.2.2 Decay heat and passive cooling

A second application of species tracking is to design efficient heat removal systems in MSRs (Tano et al., 2025a). Heat removal in MSRs is influenced by how radioactive fission product species behave in the coolant. As the coolant moves through the reactor, radioactive fission products can deposit on surfaces like heat exchangers, pipes, and other structural components. This deposition can reduce heat transfer efficiency, create hot spots, and potentially damage the cooling system. Species tracking helps monitor where and how fast insoluble fission products like noble metals (e.g., Mo) are depositing within the reactor (Walker and Ji, 2021). By knowing where isotopes accumulate, operators can improve the design and upkeep of the cooling system to avoid the buildup of radioactive deposits (Yang et al., 2025). Multiphysics informed species tracking models predict fission product behavior under different reactor conditions, leading to better management of the reactor’s heat removal.

2.2.3 Delayed neutron fraction and reactor dynamics

Additionally, the volatility of fission product species in MSRs may play an important role in reactor dynamics under certain conditions. Specifically, species transport of delayed neutron precursors can significantly alter the effective delayed neutron fraction, β e f f, which is vital for reactor control (Krepel et al., 2008). Reactivity control is central to nuclear reactor operation, and the distribution of delayed neutron emitters is crucial in determining β e f f. This parameter impacts the reactor’s response to reactivity changes, affecting its safety and control. Tracking species provides the necessary data to monitor and model the behavior of these neutron precursors. In liquid-fueled reactors, where fuel and fission products move freely, the migration of these precursors within the core and coolant loop greatly influences β e f f (Lee et al., 2024). Accurate species tracking allows for the creation of detailed reactivity feedback models that consider the spatial and temporal changes in precursor distribution. These models are essential for predicting the reactor’s behavior during transient conditions, such as power demand changes or operational disturbances. By understanding the movement, concentration, and volatility of neutron precursors, operators can better manage reactivity and keep the reactor within safe operating limits.

2.2.4 Corrosion mitigation and redox control

Species tracking is crucial for predicting corrosion in nuclear reactors, especially those using molten salts or other harsh coolants (Sridharan and Allen, 2013). Corrosion can accelerate when fission products interact with structural materials, potentially damaging key components and containment barriers (Tano et al., 2025b). By identifying which fission products contribute most to corrosion and where they accumulate, reactor designers can choose more resistant materials. This data also helps develop protective coatings or treatments to extend the life of these materials in contact with the fuel salt. In MSRs where everything is exposed to high-temperature molten salts, maintaining the integrity of containment and structural materials is essential. Accurate species tracking helps predict material lifespan and plan maintenance to avoid failures. Understanding the evolving redox potential due to depletion and temperature gradients is critical for predicting galvanic corrosion rates and how to effectively control these processes through active or passive redox control (Walker S. A. et al., 2023; Zhang et al., 2018).

2.2.5 Nuclear safeguards

Finally, species tracking facilitates the implementation of advanced monitoring technologies to support the International Atomic Energy Agency (IAEA) for advanced reactor safeguards (Walker et al., 2025). Due to the intrinsically multiphysics behavior of MSRs, species tracking can look at subsequent changes in fuel salt chemistry and off-gas system performance due to material diversion or reactor misuse. Its application can be utilized to analyze various in situ sensors and thermochemistry measurements which could provide real-time data on the distribution and concentration of fissile material in the MSR. The resulting methodology and technologies further enhance the ability of inspectors to detect and respond to any system anomalies that may indicate unauthorized diversion of nuclear materials.

3 Computational methods and multiphysics framework

This section will detail the modeling methodology implemented and the resulting multiphysics framework for species tracking within MSR systems. The following subsections introduce these multiphysics methods and discuss how the species tracking framework is coupled within the MOOSE framework to simulate various MSR phenomena.

3.1 General framework for species tracking

As previously stated, the general framework for species tracking in MSRs was developed using NEAMS codes all coupled and integrated via the MOOSE framework. The general NEAMS codes and coupling scheme are shown in Figure 2 (Walker S. et al., 2023). Here, the primary physics driving species transport phenomena in MSRs is incorporated and coupled for various modeling and simulation applications.

Neutron transport and fuel salt depletion (shown in blue in in Figure 2) typically drives incremental changes in the multiphysics behavior of chemical species within an MSR (Walker S. A. et al., 2023). Thermal-hydraulics listed in the yellow square can be solved at various levels of spatial-fidelity, and individual radionuclides or element concentrations can be transported and tracked in media including molten salts and two-phase flow regimes (Tano et al., 2024a). Finally, thermochemistry (shown in green), is incorporated to simulate how elemental and temperature changes in the MSR alter the thermochemical equilibrium of the ionic liquid utilizing thermodynamic databases and kinetic parameters (Tano et al., 2024b). The following subsections will briefly introduce the individual physics equations that are solved and detail the individual codes within the framework.

3.2 Griffin depletion

Griffin is a NEAMS tool used for multifidelity neutronics and fuel depletion. Recent efforts in FY-22 incorporated nuclide removal and multi-region microscopic depletion capability for modeling off-gas and other waste streams in MSR systems during burnup (Walker et al., 2022).

The depletion equation solved by Griffin, also known as the Bateman equations, track the nuclide number density of the fuel and resulting fission products, and incorporates fission, neutron transmutation, and radioactive decay as seen in Equation 1:where

d N Z A ′ t d t = ∑ Z ′ , A ′ = 1 M ( γ Z A ′ ∑ g = 1 G σ f Z ′ , A ′ , g t ϕ g t + ∑ g = 1 G σ Z ′ , A ′ → Z , A ′ , g t ϕ g t + r Z ′ , A ′ → Z , A ′ λ Z ′ A ′ ) N Z ′ A ′ t − λ Z A ′ N Z A ′ t − ∑ g = 1 G σ a Z , A , g t ϕ g t N Z A ′ t − f c h e m , Z A ′ t − f s t r e a m , Z A ′ t (1)

• N Z ′ A ′ t = the number density of other nuclides with atomic number Z ′ and mass number A ′, which produce nuclide N Z A ′ t,
• γ Z A ′ = the fission yield of nuclide N Z A ′ from N Z ′ A ′ t,
• σ f Z ′ , A ′ , g t = the groupwise microscopic fission cross section of N Z ′ A ′ t,
• ϕ g t = the groupwise scalar neutron flux,
• σ Z ′ , A ′ → Z , A ′ , g t = the groupwise microscopic transmutation cross section of N Z ′ A ′ t that produces N Z A ′ t,
• r Z ′ , A ′ → Z , A ′ = the branching ratio for radioactive decay,
• λ Z ′ A ′ = the radioactive decay constant for N Z ′ A ′ t,
• λ Z A ′ = the radioactive decay constant for N Z A ′ t,
• σ a Z , A ′ , g t = the groupwise absorption cross section for N Z A ′ t,
• f c h e m , Z A ′ t = a chemical reaction source at interfaces,
• f s t r e a m , Z A ′ t = a mass transfer removal source term for feed and waste streams.

Equation 1 has additional terms not traditionally seen in the Bateman equations, which represent sources and sinks from removal waste streams and from chemical reactions at interfaces. One application of this code focuses on using the term f s t r e a m , Z A ′ t, where nuclides will be withdrawn or added to the reactor system. This alters the ongoing depletion of the fuel and nuclide inventory. Altering the f s t r e a m , Z A ′ t term, changes the chemical composition, and this will drive any observed thermochemical-equilibrium changes in the fuel salt. The form that f s t r e a m , Z A ′ t takes is defined in Equation 2:where

f s t r e a m , Z A t = L N Z A t (2)

L = the effective removal or addition rate (1/s).

L is a type of effective removal rate that depends on the existing amount of the nuclide in the fuel salt and a feed rate L, where L can be positive or negative for material additions or subtractions from the system.

3.3 Thermochimica chemical equilibrium

The thermochemistry library Thermochimica (Poschmann et al., 2021) was developed to couple with multiphysics codes, and it was recently integrated into the Chemical Reactions Module (CRM) of MOOSE (Tano et al., 2025b). Using the Gibbs energy-minimization method, Thermochimica can calculate the stable-phase assemblage of a system given its temperature, pressure, and composition. It can also provide various material properties and boundary conditions, such as element potentials. In MSR simulations, Thermochimica can help in mass accountancy because the dissolved fissile material flows in the entire loop and interacts with several components. Furthermore, the addition and removal of fission products alters the salt chemistry and can be of safety concern due to corrosion, off gassing, etc. Thermochimica minimizes the integral Gibbs energy of the system, which is given as Equation 3:where

G = ∑ ϕ = 1 Φ n ϕ ∑ i = 1 N ϕ x i μ i , (3)

• G = the Gibbs energy of the system,
• n ϕ = the number of moles of phase ϕ in the system,
• x i = the mole fraction of species i of phase ϕ,
• μ i = the chemical potential of species i of phase ϕ.

The above equation results in a non-linear, non-convex Gibbs-energy function, and Thermochimica aims to identify a unique combination of the molar amounts of phases and the mole fractions of the species such that the Gibbs energy of the system is at a global minimum. This is subject to the mass-balance constraint, which is given as Equation 4:where

b j = ∑ ϕ = 1 Φ n ϕ ∑ i = 1 N ϕ x i ν i j , (4)

• b j = the molar amount of element j in the system,
• ν i j = the stoichiometry of element j in species i.

Also, the Gibbs phase rule must be respected. It imposes a constraint on the degree of freedom of the system as follows in Equation 5:where

F = C − Φ , (5)

• F = the degree of freedom of the system where F ≥ 0,
• C = the number of elements in the system,
• Φ = denotes the number of phases in the system.

For most phases, the Gibbs energy is composed of a reference, an ideal mixing term, and an excess mixing contribution. For molten salts, the modified quasichemical model in Quadruplet Approximation (Pelton et al., 2001) is often used, and Thermochimica has the mixing models required for such systems. A thermodynamic database is required by Thermochimica and, while it supports any database in the ChemSage format, the Molten Salt Thermodynamic Database: Thermochemical (MSTDB-TC), V3.1 (Ard et al., 2022) was used because it has many validated and quality-controlled thermodynamic treatments.

3.4 Navier Stokes–Nernst-Planck species transport

Recent development of the Navier Stokes (NS) module within the MOOSE framework includes both incompressible and weakly compressible formulations of the NS equations which are discretized utilizing the finite volume method (Lindsay et al., 2023). These thermal-hydraulic methods can then be directly coupled with neutronics for multiphysics analysis of MSR systems within the MOOSE framework (Jaradat et al., 2024). More recently, a drift flux mixture model for two-phase flow simulations has been implemented to account for gaseous species and bubble transport in MSRs (Li et al., 2025). For a detailed description of the NS module, the reader is directed to the references listed above. This present work focuses primarily on modeling thermochemically driven processes (i.e., dissolution and precipitation of species) in MSRs and future work will extend these analyses to model gaseous and solid particulate flows in greater detail to determine how these processes may alter flow fields.

Implemented within the NS module of MOOSE lies the Nernst-Planck species transport model. Solving species transport is by its nature an extension of thermal-hydraulic calculations capturing the diffusion and advection of soluble and insoluble species concentrations within the molten salt media. As most species within the molten salt are in fact soluble ionic species, the incorporation of leaching and plating within the Nernst-Planck transport equation follows intuitively and is now described.

Here, leaching is defined as a process in which structural materials, such as metals and alloys, will dissolve into the molten salt in direct contact with the material to achieve thermochemical equilibrium between the metal and the salt. This phenomenon can lead to material degradation and corrosion in high-temperature applications. Modeling this process requires both simulating the transport mechanism of soluble and insoluble materials and the thermochemical driving force and electrochemical reactions that occur at the interface between the structural material and the bulk molten salt.

3.4.1 Nernst-Planck species transport

The leaching process begins with the oxidation of metal atoms from the structural material in Equation 6:where

M → M z + + z e − (6)

• M = the metal atom in the solid structure,
• M z + = the metal ion in the salt with valence z,
• e − = the electron.

This oxidation reaction releases metal atoms into the molten salt due to an electrochemical potential difference between the molten salt and the metal. Once formed, the metal ions (i.e., soluble corrosion products) are transported into the molten salt through various transport processes including diffusion, electromigration, and convection.

The flux of metal ions is described by the Nernst-Planck equation shown in Equation 7:where

J M 2 + = − D M 2 + ∇ c M 2 + − D M 2 + z e k B T c M 2 + ∇ ϕ + c M 2 + v (7)

• J M 2 + = the flux vector of metal ions [mol/(m² ·s)],
• D M 2 + = the diffusion coefficient of the metal ion (m²/s),
• c M 2 + = the concentration of metal ions (mol/m³),
• k B = the Boltzmann’s constant (1.381 · 10^–23 J/K),
• T = the temperature (K),
• ϕ = the electrostatic potential (V),
• v = the velocity vector of fluid flow (m/s).

The time evolution of the soluble metal ion concentration is shown in the continuity equation in Equation 8:where

∂ c M 2 + ∂ t = − ∇ · J M 2 + + R M 2 + (8)

R M 2 + = the reaction rate source [mol/(m³ ·s)].

It should be noted that the weakly compressible formulation of the NS equations are utilized to provide the impact of the changing temperature field on the fuel-salt’s density and viscosity and resulting fuel-salt velocity. These effects are then incorporated into the species transport in the advection and thermoelectric diffusion terms (i.e., final and penultimate terms respectively) on the right-hand side of Equation 7.

3.4.2 Butler-Volmer redox kinetics

Here, the reaction rate source can come from electrochemical redox kinetics occurring at the solid-liquid interface where plating and leaching are occurring simultaneously through an exchange current density (Tano et al., 2024b). The current density i associated with the oxidation reaction is given by the anodic subcomponent term of the Butler-Volmer equation which is equivalent to the Anodic Tafel Equation seen in Equation 9:where

i = i 0 ⁡ exp α a z F η R T (9)

• i = the reaction rate current density (A/m²),
• i 0 = the exchange current density (A/m²),
• α a = the anodic electron transfer coefficient,
• F = the Faraday’s constant (96,485 C/mol),
• R = the universal gas constant [8.314 J/(mol · K)],
• η = the overpotential (i.e., ϕ m e t a l − ϕ m o l t e n s a l t − E E q).

It should be noted that the exchange current density i 0 is an experimentally measured value and is represented by Equation 10 (Yang et al., 2021):where

i 0 = z F k 0 C e q , b (10)

• k 0 = the standard rate constant (m/s),
• C e q , b = the equilibrium concentration of ionic species in the bulk (mol/m³).

The temperature dependent standard rate constant k 0 for specific redox reaction kinetics (i.e., Cr²⁺/Cr) can then be experimentally determined independent of bulk and can be used for simulating electrochemical cells and galvanic corrosion experiments (Yang et al., 2021). Additionally, the overpotential η which drives the redox current is essentially the difference between the acting potential (ϕ m e t a l − ϕ m o l t e n s a l t), whether it be an applied or galvanic potential, and the equilibrium electrochemical potential in the bulk E E q (Yang et al., 2021; Tano et al., 2024b).

Similarly, the plating process involves the reduction of metal ions from the molten salt onto a structural surface as seen in Equation 11:

M z + + z e − → M . (11)

Here again, the current density i associated with the reduction reaction is given by the cathodic subcomponent term of the Butler-Volmer equation which is equivalent to the Cathodic Tafel Equation seen in Equation 12:where

i = − i 0 ⁡ exp − α c z F η R T (12)

α c = the cathodic electron transfer coefficient.

For both plating and leaching processes, the flux of metal ions can be related to the current density by Faraday’s law, shown in Equation 13:where

J M 2 + · n = − i z F (13)

n = the unit normal vector pointing from the metal surface into the molten salt.

3.4.3 Poisson-Nernst-Planck coupled formulation

Last, the Poisson equation can be solved to determine the electrostatic potential due to ion transport within the molten salt in Equation 14:where

− ϵ ∇ 2 ϕ = ∑ i z i e c i (14)

• ϵ = the permittivity of the molten salt,
• c i = the sum of all ionic species in the salt.

In conjunction, Equations 1–8 are known as the Poisson-Nernst-Planck (PNP) equations with Butler-Volmer kinetics and can be coupled and solve numerically within the MOOSE framework (Tano et al., 2024b). Ongoing efforts under the NEAMS-Thermochemistry workscope are currently enhancing this component of the CRM within MOOSE for modeling corrosion and subsequent electrorefining applications.

3.5 Utilization of thermochemical equilibrium calculations for species tracking

Another similar approach to solving the PNP equations is to utilize Gibbs Energy Minimization (GEM) calculations through the open-source tool Thermochimica for MSR systems (Poschmann et al., 2021). Thermochimica then utilizes the most up-to-date version of the Molten Salt Thermodynamic Database–Thermochemical (Ard et al., 2022) to predict leaching and plating concentrations of structural components in thermochemical equilibrium that exists between the fuel salt and structural material. This reduced order pseudo-equilibrium calculation allows for the same leaching and plating processes to be modeled by coupling thermochemical equilibrium calculations with the Nernst-Planck species transport equations detailed in the previous subsection.

3.5.1 Thermochemical equilibrium modeling of leaching and plating

As previously discussed, Thermochimica outputs thermochemical equilibrium values of a given salt composition at pressure and temperature. These values can be directly used by the Butler-Volmer redox kinetics to inform the correct galvanic or applied overpotentials (i.e., Thermochimica calculates a fluorine chemical potential which can be readily converted to an electrochemical equilibrium potential E E q for various redox reactions). Additionally, if the standard rate constant k 0 is known, the exchange current density i 0 can be directly calculated from Equation 10 through the use of the equilibrium concentration of ionic species in the bulk C e q , b.

Next, we apply a boundary condition for the − ∇ · J M 2 + term in Equation 8 at salt-structure interfaces by incorporating the resulting redox current from Equation 13 to arrive at Equation 15:

− D M 2 + ∇ c M 2 + = i z F . (15)

The leaching process then occurs whenever there is a concentration gradient between the soluble metallic ion concentration predicted by Thermochimica and the amount transported within the Nernst-Planck species transport equation at the liquid-structure interface giving rise to a chemical overpotential η in Equation 9 driving dissolution. If, at some point, the concentration of the ionic species from the species transport equation becomes larger than what is predicted by Thermochimica at thermochemical equilibrium, then the reverse process of reduction to metallic species occurs at the interface driven by a negative chemical overpotential η driving plating. This coupling then allows for a rapid and robust calculation of galvanic corrosion to be modeled within large engineering-scale MSR systems.

3.5.2 Thermochemical equilibrium modeling of metallic particulate precipitation

Additionally, a bulk reaction rate source can also be formulated for disproportionation reactions between ionic species in the salt, as illustrated in Equation 16:where

M i 2 + + 2 M j 3 + ↔ M i s + 2 M j 4 + (16)

• M j 3 + = a metallic ion j within the bulk salt that is oxidized from 3⁺ to 4⁺,
• M i s = a reduced solid metal atom product forming a colloidal particulate in the bulk salt.

Here, precipitation of metallic species due to thermochemical changes in the fuel salt within the bulk salt can also be modeled and predicted utilizing MSTDB-TC with Thermochimica coupled with the species transport capability within the engineering framework. An example of such a reaction shown in Equation 16 would be the reduction of Cr²⁺ to Cr(s) through the oxidation of U³⁺ to U⁴⁺ due to temperature or fuel salt composition changes (Shaffer, 1971).

A reaction rate source R M s B within the bulk can be defined for these metallic particle precipitation reactions as shown in Equation 17:where

R M c B = − k 0 a i c M c − c M c * (17)

• a i = the interfacial area concentration (1/m) of metallic particulates or colloidal flocculants within the bulk salt,
• c M c = the metallic particle precipitant concentration (mol/m³) calculated by species transport,
• c M c * = the metallic particle precipitant concentration predicted by thermochemical equilibrium calculation (mol/m³).

It should be noted that a closure model for interfacial area transport to determine a i is required. In this work we assumed a constant 1e⁻² m⁻¹ value for the interfacial area concentration. Future work will implement a colloid flocculation model for more accurately resolved interfacial area tracking. Additionally, this method utilizes the same experimentally measured standard rate constant k 0 for a given redox reaction which is independent of concentration and only dependent on temperature.

3.6 Coupled species transport and thermochemical equilibrium calculation formulation

Coupling the Nernst-Planck Equation 8 with the reduced order thermochemically informed interface and bulk reaction rate terms in Equations 15, 17 arrive at a system of Equations 18–20 for metallic leaching, plating, and precipitation in MSR systems: where

∂ c M 2 + ∂ t + ∇ · c M 2 + v − ∇ · D M 2 + ∇ c M 2 + = i z F + k 0 a i c M c − c M c * (18)

∂ c M c ∂ t + ∇ · c M c v − ∇ · D M c ∇ c M c = − k 0 a i c M c − c M c * ) − ∇ · c M c k c − s (19)

∂ c M s ∂ t = − i z F + ∇ · c M c k c − s (20)

• k c − s = the mass transfer coefficient of metal particulates depositing on solid structures from the bulk salt (m/s),
• c M s = the concentration of solid metal within the structure or material alloy (mol/m³).

Here the terms on the right-hand sides of Equations 18–20 represent the boundary conditions of redox kinetics at interfaces and the volumetric source term for thermochemically driven precipitation and solvation (i.e., volumetric reduction or oxidation of metallic particulates).

Essentially then, the metallic species are tracked within their appropriate medium (i.e., salt or structure) and within their appropriate phase (i.e., metallic ion within the salt–Equation 18, metallic colloid precipitant within the salt–Equation 19, or metallic structural solid–Equation 20). The source terms on the right-hand side of Equations 19, 20 represent the thermochemical driving functions that push the system toward thermochemical equilibrium at salt-structure interfaces (i.e., leaching and plating) and within the fuel salt as various redox reactions occur within the bulk salt (i.e., particle precipitation and dissolution).

Lastly, it should be noted that the mass transfer coefficient k c − s can be defined by several mass transfer correlations. In this case, the mass-transfer equivalent of the Dittus-Boelter heat-transfer correlation (Kedl, 1972) was utilized to model the flux of metal particulates c M c from the bulk to the boundary layer as a boundary condition at the edge of the domain shown in the final terms of Equations 19, 20. This is discussed in further detail in Section 4.3.

This self-consistent formulation then allows for rapid galvanic corrosion modeling over large timesteps to be performed on MSR systems at an engineering scale driven by temperature and elemental composition changes within the fuel salt as predicted by MSTDB-TC-informed thermochemical equilibrium calculations. A schematic of the processes occurring as described by Equations 19, 20 is illustrated in Figure 3.

Shown in Figure 3, the fuel salt in an MSR proceeds from a hot temperature regime with a hot wall to a cold temperature regime with a relatively colder wall (i.e., salt transport from hot core to cold region after heat exchanger). At the hot salt-structure interface, structural components like Fe(s) are oxidized to Fe²⁺ as seen in Equation 16 (Shaffer, 1971). As these soluble corrosion products travel throughout the system, they may experience changes in redox potential and/or temperature gradients, which will force these corrosion products to precipitate as metallic particulates or plate out at cold wall interfaces. The resulting engineering framework can then simulate galvanic corrosion with leaching and plating, metallic particle precipitation and dissolution, noble metal deposition, and various redox reactions at interfaces including redox control applications.

The authors want to highlight here the current limitations of this coupled model. Firstly, diffusion-controlled species transport within the solid-alloy structure is not currently included within this study. Ongoing work is currently building this capability within the MOOSE framework by coupling phase-field analysis of alloys to accurately simulate dealloying effects of chromium transport along grain boundaries (Bhave et al., 2023). Future studies will highlight the fully coupled phase-field to engineering scale method for modeling multi-scale corrosion of material alloys in MSRs. Secondly, the incorporation of thermochemical data from the existing database is representative of pure metallic components immersed in the salt (i.e., pure nickel, pure chromium, pure iron) and there is no existing alloy model that is being thermochemically modeled in equilibrium with the molten salt. Consequentially, the findings of this study are illustrative rather than definitive. Further development of the framework to incorporate both structural alloy models coupled with salt thermochemistry and phase-field analysis of species transport in the alloy are important and logical next steps.

4 Results: multiphysics species tracking in the Molten Salt Fast Reactor

With this fundamental understanding of the modeling framework developed for material leaching, plating, and precipitation in MSR systems, various applications of the framework will now be demonstrated. For simplicity, the demonstrations will utilize an existing MSR model from the National Reactor Innovation Center’s (NRIC) Virtual Test Bed (VTB) repository of advanced reactor concepts (Giudicelli, et al., 2023). Specifically, the Molten Salt Fast Reactor (MSFR) design based on work carried out under the Euratom Evaluation and Viability of Liquid Fuel Fast Reactor Systems (EVOL) and ROSATOM Minor Actinides Recycling in Molten Salt (MARS) projects (Brovchenko, et al., 2019) was chosen as it is an engineering-scale power reactor design with existing NEAMS code models previously developed (Abou-Jaoude, et al., 2021). Additionally, Table 1 highlights some of the MSFR design parameters including thermal power, reactor size, fuel salt composition, total salt inventory, and structural alloy composition.

TABLE 1. Description of MSFR design parameters.

4.1 Temperature driven material leaching and plating in MSFR

The first demonstration case will essentially be the temperature driven process shown in Figure 3, but applied to an entire engineering-scale MSR system. This analysis will utilize the species transport coupled with thermochemical equilibrium calculations to simulate hot and cold leg leaching and plating in the MSFR system. Here, the MSTDB-TC V3.1 for fluoride salts is used with Thermochimica within the CRM of MOOSE to perform the tightly coupled leaching, plating, and metallic particulate precipitation analysis. The two most important physics fields that dictate the multiphysics-informed galvanic corrosion in the MSFR are the temperature and velocity profiles calculated at reactor steady state as seen in Figure 4.

The temperature profile is what drives the galvanic corrosion where there is a greater solubility of corrosion products Cr²⁺, Cr³⁺, Fe²⁺, and Ni²⁺ within the fuel salt at high temperature where the thermochemical equilibrium of fuel salt is pushed hard to the left-hand side of Equation 16, forming corrosion products and the reduced form of the UF₃ fuel form rather than the oxidized UF₄ fuel form. The fuel salt heats up significantly in the center of and the top of the core where the velocity is also slowest, as seen in Figure 4, and then rapidly cools through the heat exchanger in the integral loop to form a cold leg at the bottom of the core inlet. Therefore, the place where galvanic corrosion will occur most is at the very top of the hot zone in the core where corrosion products will leach into the fuel salt and be transported throughout the reactor by the velocity field.

As the corrosion products build up in the salt and cycle several times throughout the reactor core, they will eventually reach a precipitation point where the soluble amount generated in the hot core will precipitate due to disproportionation reactions in the cold leg after the heat exchanger, where thermochemical equilibrium is shifted far to the right-hand side of Equation 16. Therefore, it is expected that metallic particulate precipitation will occur here subsequently plate out in this cold region at the entrance to the reactor core. Since there is an effective source for corrosion products in the hot core and an effective sink in the cold leg at the inlet, a steady-state corrosion product concentration in the fuel salt is achieved where the sources reach equilibrium. Material degradation through corrosion and subsequent plating continues like a galvanic cell; however, it should be noted that there would be a limiting rate effect wherein corrosion product diffusion along grain boundaries in the structure would prevent a steady-state corrosion rate from forming. Future work will incorporate higher fidelity phase-field models of corrosion to inform the reduced order engineering-scale methods presented here.

Now that the anticipated behavior of material leaching and plating in the MSFR have been described, various results are presented that illustrate the thermochemically informed species-tracking framework for hot and cold leg corrosion in the MSFR. First, chromium leaching is illustrated in Figure 5.

The left-hand side of Figure 5 shows that c C r s is depleted from the wall structure at the top of the core due to galvanic corrosion. This is driven by the thermochemical equilibrium calculation source concentration c C r z + *, which is shown in the right-hand side of the figure, where the formation of ∼120 mol/m³ is predicted in the salt boundary layer in thermochemical equilibrium with the wall structure at the temperature prescribed in Figure 4. Contrarily, a meager thermochemical equilibrium corrosion product concentration of ∼12 mols/m³ is expected in the cold leg, thereby generating the hot leg leaching to cold leg deposition phenomena.

Next, the chromium ion corrosion species concentration c C r z + in the liquid salt and chromium metallic particulate concentration c C r c is shown in Figure 6. The impact of the temperature and velocity fields shown in Figure 4 can be seen clearly in the c C r z + field in the right-hand side of Figure 6 where recirculation zones in the integral loop result in an accumulation of chromium corrosion products. Additionally, the impact of temperature is seen reflected in c C r z + and c C r c in the center pane of Figure 6 where material plating, and eventually metallic particulate precipitation, occur in the cold leg at the core inlet. Finally, the thermochemical equilibrium c C r c * is shown in the right-hand side of Figure 6 showing the impact of both the concentration and temperature fields on metallic particulate formation within the bulk salt.

The leaching of iron ionic species c F e 2 + and precipitation of c F e c is shown in Figure 7. Here, the downstream impact of temperature gradients that form corrosion products and alter the UF₄ to UF₃ ratio in the fuel salt can be seen in the fluoride (F⁻) chemical potential, which is shown on the right-hand side of Figure 7. The redox potential is reduced in the high fuel salt temperature region within the core where UF₃ and corrosion products dominate, as seen on the left-hand side of Equation 16. In the cold salt region at the core inlet, the redox potential is increased due to a higher ratio of UF₄ to UF₃ and where corrosion products are forced to precipitate as seen on the right-hand side of Equation 16.

Finally, the relative formation of iron to chromium corrosion products can be seen by contrasting Figures 6, 7. The equilibrium concentration of chromium ionic species in the salt is orders of magnitude larger than the iron ionic species due to the differences in their Gibbs energy of formation within fluoride salts as characterized in the MSTDB-TC. As anticipated, the effects of temperature gradients in MSR systems can be appropriately and readily simulated using the new leaching and plating formulation within the species-tracking framework.

4.2 Redox potential driven material leaching and plating in MSFR

This next application looks at material leaching and plating between structures in contact with fuel salt due to changes in the fuel salt redox potential. The same temperature profile from the previous subsection is present, driving galvanic corrosion as previously described. This application, however, looks at altering the redox potential and the effect it would have on enhancing or mitigating the galvanic corrosion simulated in the previous subsection. Here the equilibrium redox potential E E q contributes to the overpotential which drives redox reactions at salt-structure interfaces as seen in Equation 12. This thermochemical potential value calculated by Thermochimica is then forced to be more reducing or oxidizing by slightly altering the beryllium concentration in the fuel salt which then alters redox kinetics at the salt-structure interface. Additionally, through fuel-salt depletion, the uranium concentration decreases which has a cumulative effect of raising the equilibrium electrochemical potential.

As shown in Figure 8, increasing or decreasing the redox potential of the fuel salt through composition changes has effects on the corrosion of chromium in the MSFR. Here, the total moles of chromium ionic corrosion products within the fuel salt in the entire 18 m³ salt volume is illustrated throughout the entire operational period of the MSFR (i.e., approximately 17 years when taking the exponent of the natural log days plotted). As seen in the graph, modulating the average redox potential in the fuel salt corresponds to an increase or decrease in the fuel salt capacity to accommodate ionic corrosion species from structural leaching processes. Here the total moles of Cr^z+ in the MSFR converted to parts-per-million (ppm) at their highest concentration in the fuel salt corresponds to 11.6 ppm (green line), 2.89 ppm (red line), and 0.96 ppm (blue line) respectively. The graph shows that if the redox potential can be controlled through fuel salt reduction strategies (i.e., reducing the salt with more thermodynamically stable metals like uranium, beryllium, or lithium additions) corrosion processes can be sufficiently mitigated (Zhang et al., 2018).

By decreasing the fuel salt capacity for corrosion products by controlling the redox potential, the overall rate of hot leg leaching and cold leg plating can be significantly slowed to prevent significant material degradation. Therefore, knowing the initial fuel salt composition and purity is an important and perhaps challenging task in large MSR power reactors with significant fuel salt inventories. Even with the presence of significant impurities, subsequent redox control strategies should prove sufficient to control corrosion.

However, the redox potential is also anticipated to shift throughout reactor operation as illustrated in Figure 9 and reported in literature (Walker S. A. et al., 2023; Yoon et al., 2025). The depletion of uranium metal due to fission and the subsequent generation of fission products creates a slow cationic deficiency in the fuel salt thereby increasing the fluorine chemical potential over time. Due to the formation of noble gas and noble metal fission products, the cationic charge of the fuel form (i.e., primarily U⁴⁺ with some U³⁺) is not sufficiently replaced by fission products, which allows structural metals to leach into the fuel salt to replace the lost uranium.

Figure 10 depicts the effect the increasing redox potential (due to depletion) has on total chromium corrosion driven into the fuel salt within the MSFR. Note that the chromium c C r z + peaks later in Figure 10 than in Figure 8 due to the gradual shift in the redox potential over time, where the capacity of c C r z + in the fuel salt continues to rise. Here the concentration of c C r z + in the fuel salt reaches a magnitude of 11.86 ppm before volumetric precipitation occurs in the cold leg.

Additionally, both Figures 9, 10 detail the effect fuel depletion has in enhancing galvanic corrosion without redox potential control strategies. Here the fluoride (F⁻) chemical potential in Figure 9 and c C r z + in Figure 10 only peak because the reactor power is shut down prematurely, stopping depletion and allowing the system to approach a new thermochemical equilibrium steady-state. In continuous operation, the redox potential and corrosion product concentrations would continue to increase until material degradation occurs or until an active redox control strategy is implemented.

On the contrary, what is illustrated in these figures is the participation of chromium in controlling the redox potential of the fuel salt. Chromium is the next-most thermodynamically stable element available to the fuel salt when uranium has been depleted. Once uranium depletion has stopped, the system shifts to a new thermodynamic equilibrium where eventual production of c C r z + in the hot core prevents the fluoride chemical potential from increasing any more. This is also evidenced by the production of c C r c in the cold leg. The precipitation of metallic particulates would never occur unless the redox potential plateaus or is reduced. This effect can be visualized in the final three data points in both Figures 9, 10 where the redox potential is reduced due to reaching c C r z + capacity in the fuel salt and subsequent c C r c formation occurs due to the temperature gradient. These demonstration results showcase how the effect of redox potential changes in MSR systems driven by depletion or redox potential control strategies can be readily simulated using the new salt-structure interaction models within the species-tracking framework.

4.3 Noble metal deposition and decay heat in MSFR

The importance of noble metal species tracking and deposition will be briefly discussed and initial results showcased in this final demonstration of the new species-tracking framework. As previously noted, noble metal fission products form within the fuel salt but are not soluble as ions within the reduced redox potential of the system. Therefore, their behavior during the MSRE was to form insoluble metallic particulates and would flocculate within the salt and subsequently deposit on salt-structure interfaces (Compere et al., 1975). Future MSR systems are similarly anticipated to be reduced particulates due to the redox control strategies envisioned to mitigate galvanic corrosion.

With these considerations, noble metals in this demonstration problem are treated as completely insoluble and are condensed into a single pseudo-element that can be tracked throughout the MSFR core as it deposits on structures through advection and mass transfer processes. Here Equations 19, 20 simplify to Equations 21, 22 for noble metal species tracking. where

∂ c N M c ∂ t + ∇ · c N M c v − ∇ · D N M c ∇ c N M c = γ eff Σ f ϕ − λ e f f c N M c − ∇ · c N M c k c − s (21)

∂ c N M s ∂ t = ∇ · c N M c k c − s − λ e f f c N M s (22)

• γ eff = the effective one-group condensed fission yield for noble metals,
• Σ f = the macro fission cross section in the fuel salt (1/m),
• ϕ = the one-group scalar neutron flux in the fuel salt [n/(m² · s)],
• λ e f f = the effective one-group condensed decay constant for noble metals (1/s).

Additional source and sink terms are included due to production of noble metals from fission and their radioactive decay. Production from fission occurs only in the metal particulate concentration c N M c within the salt, whereas radioactive decay occurs in both concentrations including noble metal species deposited on structural surfaces c N M s. This radioactive decay process can then be explicitly tracked within the MSFR to provide greater spatial resolution for subsequent heat generation, including decay heat emanating from structures due to noble metal deposition.

Additionally, various mass transfer coefficients k c − s can be prescribed depending on the flow regime and geometries detailed in experimentally derived mass transfer correlations or informed by higher fidelity computational fluid dynamics (CFD) calculations. For modeling noble metal transport and deposition in the MSRE, the mass transfer variant of the Dittus-Boelter correlation (Kedl, 1972) was utilized, as seen in Equation 23:where

S h = k c − s L D N M c = 0.023 R e 0.8 S c 0.4 = 0.023 ρ v L μ 0.8 μ ρ D N M c 0.4 (23)

• S h = the dimensionless Sherwood number for mass transfer,
• L = the characteristic length of the geometry (m),
• R e = the dimensionless Reynolds number representing the ratio of inertial forces to viscous forces,
• S c = the dimensionless Schmidt number representing the ratio of viscous diffusion to mass diffusion,
• ρ = the fuel salt density (kg/m³),
• μ = the fuel salt viscosity (Pa · s).

Other mass transfer correlations could also be utilized within the framework depending on the specific application and processes that are modeled (Wu, et al., 2024; Peebles, 1968). Finally, the spatially resolved decay heat from the noble metals is included within the energy conservation in the fuel salt shown in Equation 24.where

∇ · T v − ∇ · ν t Pr t ∇ T − 1 ρ c p Q q = 0 (24)

• ν t = the turbulent kinematic viscosity (m²/s),
• Pr t = the turbulent dimensionless Prandtl number for heat transfer,
• c p = the heat capacity of the fuel salt (J/K),
• Q q = the volumetric heat generation rate due to fission, radioactive decay, and heat loss to heat exchanger (W/m³).

Here the decay heat contribution to the volumetric heat source term Q q is shown in Equation 25:where

Q q = ϵ eff · λ e f f · c N M c · N a (25)

• ϵ eff = the effective one-group condensed decay energy of the noble metals (MeV),
• N a = Avogadro’s number (6.022 · 10²³ atoms/mol).

These modeling considerations are incorporated within the engineering framework for species transport, so various transients can now be simulated to look at the effect that noble metal decay heat has on the reactor system. During full power operation the spatial distribution of decay heat from noble metal deposition may not have a large impact beside the larger fission heat contribution. However, during reactor shut down, the effect of noble metal decay heat from surfaces in the reactor core becomes a dominant heat source that should be properly modeled. Therefore, the following demonstration is a reactor shutdown transient where the system’s control rods are inserted and the pump is shut off. The fuel salt heat is still extracted from the primary heat exchanger in the integral loop after shutdown, but natural circulation of the fuel salt forms within the reactor and primary loop aided by the noble metal decay heat source.

First, as shown on the left-hand side of Figure 11, the noble metal particulate concentration in the MSFR is influenced by growth from fission in the core and rapid radioactive decay, and is driven around the loop by convection. The corresponding concentration of noble metals deposited on the wall structures through mass transfer is shown on the right-hand side of Figure 11, where a large concentration is deposited immediately after being formed at the top of the reactor core and into the top of the integral loop.

Seen next in Figure 12 are the resulting temperature profiles both prior to shutdown and 100 s after shutdown. A considerable amount of heat has been extracted from the MSFR through the primary heat exchanger in the integral loop during the shutdown transient. However, there is a relative hot region forming at the top of the reactor outlet due to the large deposition of noble metals along the top of the core as seen above in Figure 11. Due to natural circulation and buoyancy effects, this hot region forms above the heat exchanger and is not actively cooled.

The concentration profile of decaying noble metal particulates within the MSFR is visualized on the left-hand side of Figure 13. This multiphysics-informed concentration profile of noble metals subsequently drives the heat generation profile after reactor shutdown, as observed in Figure 12, and in the natural circulation velocity profile on the right-hand side of Figure 13. As illustrated in the results, the reduced order method shown here demonstrates the importance of noble metal species tracking during reactor operations.

4.4 Depletion driven volatilization of gaseous species

Turning towards chemical species volatilization, Figure 14 showcases the oxidizing effect that depletion has on increasing the vapor pressures of CsI(g) in the MSFR. Here the vapor pressure of CsI(g) increases from ∼9.9e-07 to ∼7.9e-05 [atm] due to depletion. This is a spatially resolved analogous result to (Walker S. A. et al., 2023) which reported that vapor pressure of I greatly increases due to the oxidizing change in redox potential.

This effect is even more pronounced in the increasing vapor pressure of I_2(g) shown in Figure 15. Here the vapor pressure of I_2(g) increases, approximately from 3.3e-11 to 1.3e-02 atm, due to depletion-driven changes in the redox potential of the fuel salt.

A few items to note from this analysis are that I_2(g) forms more readily in regions with the highest redox potential. This can be visualized by comparing Figure 15 to the right-hand side of Figure 7. Additionally, it is important to understand that vapor-pressure distribution calculations like these are only useful when stable liquid/gas interfaces are present. This would imply that a liquid/gas boundary to an off-gas system should be used at a specific location in the core or integral loop or some homogenized surface area from noble-gas bubbles present in the MSFR bulk fuel salt.

4.5 Effect of active-chemistry control

The final example that will be simulated with the multiphysics species tracking framework is active-chemistry control. As detailed in previously, leaching and plating of species due to thermal convection loops and oxidizing fuel salt redox potential from depletion has a dramatic effect on predicting corrosion in MSRs. The corrosion process can be heavily mitigated by controlling the redox potential of the fuel salt via reducing metal additions as seen in Equation 16.

To prevent natural redox control through galvanic corrosion via chromium and iron dissolution into the fuel salt, more thermodynamically favorable metals like lithium, beryllium, or additional uranium can be introduced. In the following analysis, a small amount of beryllium is added to the fuel salt as a fuel salt reducing agent. The species tracking framework calculates BeF₂ at an interface where extra beryllium is being introduced to actively control the chemistry of the fuel-salt system. It then tracks this new BeF₂ concentration as it mixes in the MSFR. The introduction of beryllium into the MSFR can be seen in Figure 16. Here the inlet boundary is set at the bottom of the MSFR lower plenum.

As seen in Figure 16, the beryllium inlet at the boundary is advected into the MSFR system, mixing and diffusing towards a new thermochemical and thermal-hydraulic steady state. The reductive effect of introducing beryllium on the redox potential of the fuel-salt can be seen in Figure 17, which captures the changing fluorine potential due to the beryllium addition. Here the fluoride (F⁻) potential steadily decreases from ∼ − 460,000 to ∼ − 465,000 J/mol, corresponding to a final fluorine (F₂) potential of ∼ − 930,000 J/mol as the additional BeF₂ circulates throughout the MSFR system.

5 Discussion and conclusion

In conclusion, this work highlights the multiphysics challenge of species tracking in MSR systems. The importance of species tracking in MSR systems for reactor design, safety analyses, source term quantification, component degradation, corrosion and redox control modeling, and safeguards applications is identified. New multiphysics methods and NEAMS code coupling within MOOSE was performed to derive a multiphysics species tracking framework capable of simulating various applications. The resulting engineering framework coupling depletion, thermochemical equilibrium, and species transport is now capable of analyzing material leaching and plating, localized decay heat, volatilization of gaseous species, and active redox chemistry control. These capabilities were applied to the MSFR as a demonstration analysis showcasing the utility of the new framework in solving pertinent issues related to derisking MSR technologies for near-term advanced reactor deployment.

5.1 Primary outcomes

In terms of MSR design, operation, and analysis, the following key points can be derived from this work:

• New material leaching, plating, and precipitation modeling capability developed utilizing thermochemical equilibrium calculations in Thermochimica coupled with the Nernst-Planck species transport equation in the Navier Stokes module within MOOSE.
• New species tracking framework capability for modeling temperature and redox potential driven galvanic corrosion at engineering scale for MSR systems.
• Effect of fuel depletion on enhancing corrosion rates in MSR systems demonstrated through MSFR example simulation.
• Effect of noble metal mass transfer, plating, and decay heat modeling coupled with multiphysics framework for MSR system design and safety analyses.
• Volatilization of gaseous species is a non-homogenous process within the reactor core and integral loop and should be resolved for accurate source term calculations and off-gas system design.
• Active redox control simulation for redox control system design and subsequent analysis for MSR fuel cycle, pyro-processing, and tritium breeding in molten salt fusion blankets (Walker et al., 2025).

Cumulatively, this work advances wholistic, multiphysics design of molten salt systems. These analyses show that thermochemically driven processes are an essential consideration in fission MSRs where the fuel salt chemistry is changing due to the consumption of uranium and the generation of noble gas and noble metal fission products.

Correspondingly, these same analyses can be directly extended to molten salt tritium breeding blankets designed for various fusion energy systems that are under rapid development. For example, in a FLiBe molten salt blanket designed for tritium breeding, fast neutrons from the deuterium-tritium fusion reaction are captured in the liquid salt blanket to generate heat and form tritium from lithium-6 neutron capture. Here the consumption of lithium in the FLiBe salt directly makes the salt redox potential more oxidizing thereby driving the same enhanced corrosion observed in Section 4.2. Additionally, the changing thermochemical equilibrium concentration of diatomic hydrogen to hydrogen-fluoride in the salt should be predicted and controlled via redox control methods to design robust tritium extraction techniques from the fluoride molten salt.

5.2 Future work

Finally, future work regarding the further development of the species tracking framework and its open-sourced publication for use within the MSR community is as follows:

• Further development of species-tracking framework to incorporate validation exercises against existing and ongoing experimental efforts detailing species transport, thermochemical measurements, corrosion, and redox control within static and dynamic fluoride and chloride thermal convection salt loops.
• Utilization of multiphysics species tracking framework for simulating electrorefining processes used in waste recovery and subsequent validation and refining of models through new and existing pyro-processing data.
• Utilization of engineering framework to support generation of a generic MSR evaluation design to accelerate MSR system design and provide an up-to-date reference model for both academia and industry.
• Publication of a one-stop-shop fully integrated open-source framework for MSR modeling along with example simulations, and validation exercises against existing MSRE, separate, and integrated effects salt loop data for the MSR community.

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Footnotes

Edited by: Gert Van den Eynde, Belgian Nuclear Research Centre (SCK CEN), Belgium

Reviewed by: Suneela Sardar, University of Lincoln, United Kingdom

Kieran Dolan, Kairos Power LLC, United States