Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

Birri, Anthony; Gallagher, Ryan; Agca, Can; McMurray, Jake W.; Bull Ezell, N. Dianne

doi:10.1016/j.ces.2022.117954

Title: Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

Journal Article · Thu Jul 28 00:00:00 EDT 2022 · Chemical Engineering Science

DOI:https://doi.org/10.1016/j.ces.2022.117954· OSTI ID:1881132

Birri, Anthony ^[1]; Gallagher, Ryan ^[1];

^[1];

^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF₄, LiF-BeF₂-ZrF₄, LiF-BeF₂-ThF₄, NaF-LiF-BeF₂, NaF-KF-BeF₂, NaF-ZrF₄-UF₄, and NaF-BeF₂-UF₄. This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF₄-UF₄ and BeF₂-UF₄, as well as the quantification of ternary interaction in NaF-LiF-ZrF₄, NaF-BeF₂-UF₄, and NaF-ZrF₄-UF₄.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1881132

Journal Information:: Chemical Engineering Science, Vol. 260; ISSN 0009-2509

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (43)

Status of Preconceptual Design of the Advanced High-Temperature Reactor (AHTR) Ingersoll, D. T. https://doi.org/10.2172/861752	report	July 2004
The thermodynamic modeling of multicomponent phase equilibria Kattner, Ursula R. JOM, Vol. 49, Issue 12 https://doi.org/10.1007/s11837-997-0024-5	journal	December 1997
The Density and Surface Tension of Molten Fluorides Mellors, G. W.; Senderoff, S. Journal of The Electrochemical Society, Vol. 111, Issue 12 https://doi.org/10.1149/1.2426003	journal	January 1964
Fluoride-Salt-Cooled High-Temperature Test Reactor Thermal-Hydraulic Licensing and Uncertainty Propagation Analysis Romatoski, R. R.; Hu, L. W. Nuclear Technology, Vol. 205, Issue 11 https://doi.org/10.1080/00295450.2019.1610686	journal	June 2019
Molten-Salt Reactor Chemistry Grimes, W. R. Nuclear Applications and Technology, Vol. 8, Issue 2 https://doi.org/10.13182/NT70-A28621	journal	February 1970
Towards the thorium fuel cycle with molten salt fast reactors Heuer, D.; Merle-Lucotte, E.; Allibert, M. Annals of Nuclear Energy, Vol. 64 https://doi.org/10.1016/j.anucene.2013.08.002	journal	February 2014
Thermodynamic evaluation and optimization of the LiF-NaF-KF-MgF2-CaF2 system using the modified quasi-chemical model Chartrand, Patrice; Pelton, Arthur D. Metallurgical and Materials Transactions A, Vol. 32, Issue 6 https://doi.org/10.1007/s11661-001-0228-1	journal	June 2001
High-temperature XAFS measurement of molten salt systems Okamoto, Y.; Akabori, M.; Motohashi, H. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 487, Issue 3 https://doi.org/10.1016/S0168-9002(01)02202-1	journal	July 2002
A method for the solution of certain non-linear problems in least squares Levenberg, Kenneth Quarterly of Applied Mathematics, Vol. 2, Issue 2 https://doi.org/10.1090/qam/10666	journal	January 1944
Densities, Excess Molar Volumes, and Thermal Expansion Coefficients of Aqueous Aminoethylethanolamine Solutions at Temperatures from 283.15 to 343.15 K Stec, Marcin; Tatarczuk, Adam; Śpiewak, Dariusz Journal of Solution Chemistry, Vol. 43, Issue 5 https://doi.org/10.1007/s10953-014-0175-2	journal	May 2014
Assessment of Molten Eutectic LiF-NaF-KF Density through Experimental Determination and Semiempirical Modeling Gallagher, Ryan C.; Agca, Can; Russell, Nick Journal of Chemical & Engineering Data, Vol. 67, Issue 6 https://doi.org/10.1021/acs.jced.2c00081	journal	June 2022
Empirical methods of predicting and representing thermodynamic properties of ternary solution phases Hillert, Mats Calphad, Vol. 4, Issue 1 https://doi.org/10.1016/0364-5916(80)90016-4	journal	January 1980
Survey and evaluation of equations for thermophysical properties of binary/ternary eutectic salts from NaCl, KCl, MgCl2, CaCl2, ZnCl2 for heat transfer and thermal storage fluids in CSP Li, Yuanyuan; Xu, Xiankun; Wang, Xiaoxin Solar Energy, Vol. 152 https://doi.org/10.1016/j.solener.2017.03.019	journal	August 2017
The density of molten thorium and uranium tetrafluorides Kirshenbaum, A. D.; Cahill, J. A. Journal of Inorganic and Nuclear Chemistry, Vol. 19, Issue 1-2 https://doi.org/10.1016/0022-1902(61)80047-X	journal	September 1961
Densities, Excess Molar Volumes, and Refractive Properties of the Binary Mixtures of the Amino Acid Ionic Liquid [bmim][Gly] with 1-Butanol or Isopropanol at T = (298.15 to 313.15) K Yu, Zhichao; Gao, Haiyan; Wang, Haijun Journal of Chemical & Engineering Data, Vol. 56, Issue 12 https://doi.org/10.1021/je200030k	journal	May 2011
Predictive methods for the estimation of thermophysical properties of ionic liquids Coutinho, João A. P.; Carvalho, Pedro J.; Oliveira, Nuno M. C. RSC Advances, Vol. 2, Issue 19 https://doi.org/10.1039/c2ra20141k	journal	January 2012
Excess Molar Volumes and Viscosities for the Binary Mixtures of n-Octane, n-Decane, n-Dodecane, and n-Tetradecane with Octan-2-ol at 298.15 K Mahajan, Arvind R.; Mirgane, Sunil R. Journal of Thermodynamics, Vol. 2013 https://doi.org/10.1155/2013/571918	journal	June 2013
A simple relation to predict or to correlate the excess functions of multicomponent mixtures Hwang, Chih-An; Holste, James C.; Hall, Kenneth R. Fluid Phase Equilibria, Vol. 62, Issue 3 https://doi.org/10.1016/0378-3812(91)80009-K	journal	January 1991
PHASE EQUILIBRIA IN THE SYSTEMS BeF ₂ -ThF ₄ AND LiF-BeF ₂ -ThF ₄ Thoma, R. E.; Insley, H.; Friedman, H. A. The Journal of Physical Chemistry, Vol. 64, Issue 7 https://doi.org/10.1021/j100836a010	journal	July 1960
The molten salt reactor (MSR) in generation IV: Overview and perspectives Serp, Jérôme; Allibert, Michel; Beneš, Ondřej Progress in Nuclear Energy, Vol. 77 https://doi.org/10.1016/j.pnucene.2014.02.014	journal	November 2014
Density and kinematic viscosity of NaF?ThF4 and KF?ThF4 melts Desyatnik, V. N.; Klimenkov, A. A.; Kurbatov, N. N. Soviet Atomic Energy, Vol. 51, Issue 6 https://doi.org/10.1007/BF01121687	journal	December 1981
Molten salt mixtures. Part 1. Electrical conductivities, activation energies of ionic migration and molar volumes of molten binary halide mixtures Bloom, H.; Knaggs, I. W.; Molloy, J. J. Transactions of the Faraday Society, Vol. 49 https://doi.org/10.1039/tf9534901458	journal	January 1953
Viscosity and Density in Molten BeF ₂ –LiF Solutions Cantor, S.; Ward, W. T.; Moynihan, C. T. The Journal of Chemical Physics, Vol. 50, Issue 7 https://doi.org/10.1063/1.1671478	journal	April 1969
Enthalpies de formation des alliages liquides bismuth-étain-gallium à 723 k. Choix d’une représentation analytique des grandeurs d’excès intégrales et partielles de mélange Muggianu, Yves-Marie; Gambino, Michèle; Bros, Jean-Pierre Journal de Chimie Physique, Vol. 72 https://doi.org/10.1051/jcp/1975720083	journal	January 1975
Temperature-Dependent Properties of Molten Li₂BeF₄ Salt Using Ab Initio Molecular Dynamics Baral, Khagendra; San, Saro; Sakidja, Ridwan ACS Omega, Vol. 6, Issue 30 https://doi.org/10.1021/acsomega.1c02528	journal	July 2021
Thermodynamic assessment of the (LiF+UF3) and (NaF+UF3) systems Beilmann, M.; Beneš, O.; Konings, R. J. M. The Journal of Chemical Thermodynamics, Vol. 57 https://doi.org/10.1016/j.jct.2012.08.001	journal	February 2013
Interpolation and extrapolation with the CALPHAD method Luo, Qun; Zhai, Cong; Sun, Dongke Journal of Materials Science & Technology, Vol. 35, Issue 9 https://doi.org/10.1016/j.jmst.2019.05.016	journal	September 2019
Algebraic Representation of Thermodynamic Properties and the Classification of Solutions Redlich, Otto; Kister, A. T. Industrial & Engineering Chemistry, Vol. 40, Issue 2 https://doi.org/10.1021/ie50458a036	journal	February 1948
Ab-initio molecular dynamics study on thermal property of NaCl–CaCl2 molten salt for high-temperature heat transfer and storage Rong, Zhenzhou; Pan, Gechuanqi; Lu, Jianfeng Renewable Energy, Vol. 163 https://doi.org/10.1016/j.renene.2020.08.152	journal	January 2021
Thermal and physical properties of molten fluorides for nuclear applications van der Meer, J. P. M.; Konings, R. J. M. Journal of Nuclear Materials, Vol. 360, Issue 1 https://doi.org/10.1016/j.jnucmat.2006.08.010	journal	January 2007
Roadmap for thermal property measurements of Molten Salt Reactor systems Mcmurray, Jake; Johnson, Kaitlin; Agca, Can https://doi.org/10.2172/1778081	report	March 2021
Molten fluorides for nuclear applications Delpech, Sylvie.; Cabet, Céline; Slim, Cyrine Materials Today, Vol. 13, Issue 12 https://doi.org/10.1016/S1369-7021(10)70222-4	journal	December 2010
Computational methods to simulate molten salt thermophysical properties Porter, Talmage; Vaka, Michael M.; Steenblik, Parker Communications Chemistry, Vol. 5, Issue 1 https://doi.org/10.1038/s42004-022-00684-6	journal	June 2022
Phase Equilibria in the Systems NaF–ZrF₄, UF₄–ZrF₄ and NaF–ZrF₄–UF₄ Barton, C. J.; Grimes, W. R.; Insley, H. The Journal of Physical Chemistry, Vol. 62, Issue 6 https://doi.org/10.1021/j150564a008	journal	June 1958
The study of partial and excess molar volumes for binary mixtures of nitrobenzene and benzaldehyde with xylene isomers from T = (298.15 to 318.15) K and P = 0.087 MPa Rafiee, Hamid R.; Frouzesh, Farshid Journal of Advanced Research, Vol. 7, Issue 5 https://doi.org/10.1016/j.jare.2015.11.003	journal	September 2016
A Density Model for Multicomponent Liquids Based on the Modified Quasichemical Model: Application to the NaCl-KCl-MgCl2-CaCl2 System Robelin, Christian; Chartrand, Patrice; Eriksson, Gunnar Metallurgical and Materials Transactions B, Vol. 38, Issue 6 https://doi.org/10.1007/s11663-007-9090-x	journal	October 2007
Molten Salts: Volume 4, Part 1, Fluorides and Mixtures Electrical Conductance, Density, Viscosity, and Surface Tension Data Janz, G. J.; Gardner, G. L.; Krebs, Ursula Journal of Physical and Chemical Reference Data, Vol. 3, Issue 1 https://doi.org/10.1063/1.3253134	journal	January 1974
Empirical estimation of densities in NaCl-KCl-UCl3 and NaCl-KCl-YCl3 molten salts using Redlich-Kister expansion Agca, Can; McMurray, Jake W. Chemical Engineering Science, Vol. 247 https://doi.org/10.1016/j.ces.2021.117086	journal	January 2022
Molar volumes in the LiFThF4 system Hill, D. G.; Cantor, S.; Ward, W. T. Journal of Inorganic and Nuclear Chemistry, Vol. 29, Issue 1 https://doi.org/10.1016/0022-1902(67)80163-5	journal	January 1967
Using the Quasi-chemical formalism beyond the phase Diagram: Density and viscosity models for molten salt fuel systems Ocádiz Flores, J. A.; Konings, R. J. M.; Smith, A. L. Journal of Nuclear Materials, Vol. 561 https://doi.org/10.1016/j.jnucmat.2022.153536	journal	April 2022
The thorium molten salt reactor: Moving on from the MSBR Mathieu, L.; Heuer, D.; Brissot, R. Progress in Nuclear Energy, Vol. 48, Issue 7 https://doi.org/10.1016/j.pnucene.2006.07.005	journal	September 2006
Physical Properties of Molten Reactor Fuels and Coolants Powers, W. D.; Cohen, S. I.; Greene, N. D. Nuclear Science and Engineering, Vol. 17, Issue 2 https://doi.org/10.13182/NSE63-5	journal	October 1963
Density and surface tension of melts of zirconium and hafnium fluorides with lithium fluoride Katyshev, S. F.; Artemov, V. V.; Desyatnik, V. N. Soviet Atomic Energy, Vol. 63, Issue 6 https://doi.org/10.1007/BF01126108	journal	December 1987

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Title: Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

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