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Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand

Year 2021, Volume: 24 Issue: 1, 9 - 22, 28.02.2021
https://doi.org/10.5541/ijot.790728

Abstract

The studies summarized in this paper aims to predict the steady state operation of a low-enriched uranium fuel ARGUS type aqueous homogeneous reactor for producing 99Mo to meet the domestic demand of Brazil through a coupled multi-physics (Neutronics + Thermal-hydraulics) evaluation. The coupled multi-physics evaluation included aspects related to the neutronic behavior such as fission induced energy deposition profile, medical isotopes production; and the thermal-hydraulic behavior such as temperature, velocities and gas volume fraction profiles. The methodology followed for the multi-physics and multi-scale coupling of the neutronic and thermal-hydraulic codes (MCNP + ANSYS-CFX), discussed in detail in this paper, represent one of the main outcomes of the current study. The methodology was tested for two different operating configurations of the ARGUS reactor, the original high-enriched uranium configuration used since 1981, and the new low-enriched uranium configuration after the conversion process during 2012-2014. The calculations carried out showed that the reactor, in the studied configuration, is able to produce 246.5 six days Curie of 99Mo in operation cycles of five days. Which is equivalent to more than a third of the estimated Brazilian demand for 2025.

Supporting Institution

Conselho Nacional de Desenvolvimento Científico e Tecnológico do Brasil (CNPq)

Project Number

141270/2016-0

References

  • [1] IAEA, “Homogeneous Aqueous Solution Nuclear Reactors for the Production of Mo-99 and other Short Lived Radioistotopes,” Vienna, 2008.
  • [2] J. A. Lane, “AQUEOUS HOMOGENEOUS REACTORS,” in Fluid Fuel Reactors, Oak Ridge, 1962, p. 30.
  • [3] IAEA, “Research Reactor Database (RRDB),” 2020. [Online]. Available: https://nucleus.iaea.org/RRDB/RR/ReactorSearch.aspx?filter=0. [Accessed: 28-May-2020].
  • [4] IAEA, “IAEA Coordinated Research Project (CRP) Feasibility Evaluation of the Use of Low Enriched Uranium Fuelled Homogeneous Aqueous Solution Nuclear Reactors for the Production of Short Lived Fission Product Isotopes,” Vienna, 2010.
  • [5] NEA, “The Supply of Medical Radioisotopes Results from the Third Self-assessment of the Global Mo-99/Tc-99m Supply Chain,” Paris, 2017.
  • [6] NEA, “The Supply of Medical Radioisotopes 2018 Medical Isotope Demand and Capacity Projection for the 2018-2023 Period,” Paris, 2018.
  • [7] NEA, “The Supply of Medical Radioisotopes. 2019 Medical Isotope Demand and Capacity Projection for the 2019-2024 Period,” 2019.
  • [8] A. G. Buchan et al., “Simulated transient dynamics and heat transfer characteristics of the water boiler nuclear reactor – SUPO – with cooling coil heat extraction,” Ann. Nucl. Energy, vol. 48, pp. 68–83, Oct. 2012.
  • [9] A. G. Buchan et al., “The immersed body supermeshing method for modelling reactor physics problems with complex internal structures,” Ann. Nucl. Energy, vol. 63, pp. 399–408, Jan. 2014.
  • [10] A. J. Youker, S. D. Chemerisov, M. Kalensky, P. Tkac, D. L. Bowers, and G. F. Vandegrift, “A Solution-Based Approach for Mo-99 Production: Considerations for Nitrate versus Sulfate Media,” Sci. Technol. Nucl. Install., vol. 2013, pp. 1–10, 2013.
  • [11] A. J. Youker, D. C. Stepinski, L. Ling, and G. F. Vandegrift, “Mo Recovery Updates and Physical Properties of Uranyl Sulfate Solutions,” Argonne, 2014.
  • [12] C. M. Cooling, M. M. R. Williams, E. T. Nygaard, and M. D. Eaton, “The application of polynomial chaos methods to a point kinetics model of MIPR: An Aqueous Homogeneous Reactor,” Nucl. Eng. Des., vol. 262, pp. 126–152, Sep. 2013.
  • [13] C. M. Cooling, M. M. R. Williams, E. T. Nygaard, and M. D. Eaton, “An extension of the point kinetics model of MIPR to include the effects of pressure and a varying surface height,” Ann. Nucl. Energy, vol. 72, pp. 507–537, Oct. 2014.
  • [14] P. H. Liem, H. N. Tran, and T. M. Sembiring, “Design optimization of a new homogeneous reactor for medical radioisotope Mo-99/Tc-99m production,” Prog. Nucl. Energy, vol. 82, pp. 191–196, Jul. 2015.
  • [15] Z. Gholamzadeh, S. A. H. Feghhi, S. M. Mirvakili, A. Joze-Vaziri, and M. Alizadeh, “Computational investigation of 99Mo, 89Sr, and 131I production rates in a subcritical UO2(NO3)2 aqueous solution reactor driven by a 30-MeV proton accelerator,” Nucl. Eng. Technol., vol. 47, no. 7, pp. 875–883, Dec. 2015.
  • [16] S. M. Mirvakili, Z. Gholamzadeh, and A. Davari, “Neutronic and thermo hydraulic analysis of a modeled subcritical uranyl nitrate aqueous reactor driven by 30-MeV protons,” Ann. Nucl. Energy, vol. 97, pp. 171–178, Nov. 2016.
  • [17] D. M. Pérez et al., “Thermal-Hydraulics Study of a 75 kWth Aqueous Homogeneous Reactor for 99 Mo Production,” J. Thermodyn., vol. 2015, pp. 1–11, 2015.
  • [18] D. M. Pérez, D. E. M. Lorenzo, C. A. B. De Oliveira Lira, C. R. G. Hernández, M. C. Rodríguez, and L. P. R. Garcia, “Effects of some calculation parameters on the computational modelling of temperature, velocity and gas volume fraction during steady-state operation of an aqueous homogeneous reactor,” Int. J. Nucl. Energy Sci. Technol., vol. 11, no. 1, p. 1, 2017.
  • [19] D. M. Pérez, D. E. M. Lorenzo, C. A. B. de Oliveira Lira, and L. P. R. Garcia, “Neutronic evaluation of the steady-state operation of a 20 kWth Aqueous Homogeneous Reactor for Mo-99 production,” Ann. Nucl. Energy, vol. 128, 2019.
  • [20] S. V Myasnikov, A. K. Pavlov, N. V Petrunin, and V. A. Pavshook, “Conversion of the ARGUS Solution Reactor to LEU Fuel : Results of Feasibility Studies and Schedule,” in RERTR 2012 - 34th International Meeting on Reduced Enrichment for Research and Test reactors, 2012, p. 8.
  • [21] P. P. Boldyrev, V. S. Golubev, S. V. Myasnikov, A. K. Pavlov, N. V. Petrunin, and V. A. Pavshook, “The Russian ARGUS Solution Reactor HEU-LEU Conversion: LEU Fuel Preparation, Loading and First Criticality,” in RERTR 2014 - 35th International Meeting on Reduced Enrichment for Research and Test reactors, 2014, p. 8.
  • [22] A. Vakulenko, “ROSATOM’s vision of Russia’s role in global molybdenum-99 supply,” Vienna, 2017.
  • [23] CNEN, “RELATÓRIO DE GESTÃO DO EXERCÍCIO DE 2017,” RIO DE JANEIRO, 2018.
  • [24] CNEN, “RELATÓRIO DE GESTÃO DO EXERCÍCIO DE 2015,” Rio de Janeiro, 2016.
  • [25] IAEA, “ARCAL Perfil Estratégico Regional para América Latina y el Caribe (PER) 2016 –2021,” Vienna, 2015.
  • [26] D. M. Pérez, “Diseño conceptual de un AHR de 75 kWt que utiliza combustible LEU para la producción de isótopos médicos,” Instituto Superior de Tecnologías y Ciencias Aplicadas, La Habana, 2015.
  • [27] D. M. Pérez, D. E. M. Lorenzo, C. A. Brayner, D. O. Lira, and L. P. R. Garcia, “NEUTRONIC AND THERMAL-HYDRAULIC STUDIES OF AQUEOUS HOMOGENEOUS REACTOR FOR MEDICAL ISOTOPES PRODUCTION,” in International Nuclear Atlantic Conference - INAC 2017, 2017, vol. 99, p. 22.
  • [28] E. S. Glouchkov and V. E. Khvostionov, “Graphite-reflected uranyl sulphate (20.9% 235U) solutions,” Moscow, 1997.
  • [29] Y. Li et al., “FMSR: A code system for in-core fuel management calculation of aqueous homogeneous solution reactor,” Nucl. Eng. Des., vol. 240, no. 4, pp. 763–770, 2010.
  • [30] C. C. Pain, C. R. E. De Oliveira, A. J. H. Goddard, and A. P. Umpleby, “Non-linear space-dependent kinetics for the criticality assessment of fissile solutions,” Prog. Nucl. Energy, vol. 39, no. 1, pp. 53–114, 2001.
  • [31] F. Barbry, “French solution reactor experience and contribution to the Feasibility of the Use of LEU Fuelled Homogenous Aqueous Solution Nuclear Reactors for the Production of Short Lived Fission Product Isotopes,” Vienna, 2010.
  • [32] F. J. Souto, R. H. Kimpland, and A. S. Heger, “Analysis of the Effects of Radiolytic-Gas Bubbles on the Operation of Solution Reactors for the Production of Medical Isotopes,” Nucl. Sci. Eng., vol. 150, no. 3, pp. 322–335, 2005.
  • [33] A. J. Wass, “Supo Thermal Model Development II,” Los Alamos, 2017.
  • [34] L. D. P. King, “Design and Description of Water Boiler Reactors,” in International Conference Peaceful Uses Atomic Energy, 1955, vol. 5, no. 32, pp. 372–391.
  • [35] M. E. Bunker, “Status Report on the Water Boiler Reactor,” Los Alamos, 1963.
  • [36] S. Chemerisov et al., “Experimental Results for Direct Electron Irradiation of a Uranyl Sulfate Solution: Bubble Formation and Thermal Hydraulics Studies,” Argonne, 2015.
  • [37] C. M. Cooling, “Development of a Point Kinetics Model with Thermal Hydraulic Feedback of an Aqueous Homogeneous Reactor for Medical Isotope Production,” Imperial College London, London, 2014.
  • [38] F. J. Souto and A. S. Heger, “A Model to Estimate Volume Change due to Radiolytic Gas Bubbles and Thermal Expansion in Solution Reactors,” Los Alamos, 1996.
  • [39] F. J. Souto and R. H. Kimpland, “Reactivity analysis of solution reactors for medical-radioisotope production,” Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms, vol. 213, no. 3, pp. 369–372, 2004.
  • [40] Los Alamos National Laboratory, “MCNP6.1/MCNP5/MCNPX User Manual.” Los Alamos National Laboratory, Los Alamos, p. 1001, 2013.
  • [41] ANSYS Team, “ANSYS CFD 19.0 Documentation, User’s Guide manual,” 2019. [Online]. Available: http://www.ansys.com. [Accessed: 01-Jul-2019].
Year 2021, Volume: 24 Issue: 1, 9 - 22, 28.02.2021
https://doi.org/10.5541/ijot.790728

Abstract

Project Number

141270/2016-0

References

  • [1] IAEA, “Homogeneous Aqueous Solution Nuclear Reactors for the Production of Mo-99 and other Short Lived Radioistotopes,” Vienna, 2008.
  • [2] J. A. Lane, “AQUEOUS HOMOGENEOUS REACTORS,” in Fluid Fuel Reactors, Oak Ridge, 1962, p. 30.
  • [3] IAEA, “Research Reactor Database (RRDB),” 2020. [Online]. Available: https://nucleus.iaea.org/RRDB/RR/ReactorSearch.aspx?filter=0. [Accessed: 28-May-2020].
  • [4] IAEA, “IAEA Coordinated Research Project (CRP) Feasibility Evaluation of the Use of Low Enriched Uranium Fuelled Homogeneous Aqueous Solution Nuclear Reactors for the Production of Short Lived Fission Product Isotopes,” Vienna, 2010.
  • [5] NEA, “The Supply of Medical Radioisotopes Results from the Third Self-assessment of the Global Mo-99/Tc-99m Supply Chain,” Paris, 2017.
  • [6] NEA, “The Supply of Medical Radioisotopes 2018 Medical Isotope Demand and Capacity Projection for the 2018-2023 Period,” Paris, 2018.
  • [7] NEA, “The Supply of Medical Radioisotopes. 2019 Medical Isotope Demand and Capacity Projection for the 2019-2024 Period,” 2019.
  • [8] A. G. Buchan et al., “Simulated transient dynamics and heat transfer characteristics of the water boiler nuclear reactor – SUPO – with cooling coil heat extraction,” Ann. Nucl. Energy, vol. 48, pp. 68–83, Oct. 2012.
  • [9] A. G. Buchan et al., “The immersed body supermeshing method for modelling reactor physics problems with complex internal structures,” Ann. Nucl. Energy, vol. 63, pp. 399–408, Jan. 2014.
  • [10] A. J. Youker, S. D. Chemerisov, M. Kalensky, P. Tkac, D. L. Bowers, and G. F. Vandegrift, “A Solution-Based Approach for Mo-99 Production: Considerations for Nitrate versus Sulfate Media,” Sci. Technol. Nucl. Install., vol. 2013, pp. 1–10, 2013.
  • [11] A. J. Youker, D. C. Stepinski, L. Ling, and G. F. Vandegrift, “Mo Recovery Updates and Physical Properties of Uranyl Sulfate Solutions,” Argonne, 2014.
  • [12] C. M. Cooling, M. M. R. Williams, E. T. Nygaard, and M. D. Eaton, “The application of polynomial chaos methods to a point kinetics model of MIPR: An Aqueous Homogeneous Reactor,” Nucl. Eng. Des., vol. 262, pp. 126–152, Sep. 2013.
  • [13] C. M. Cooling, M. M. R. Williams, E. T. Nygaard, and M. D. Eaton, “An extension of the point kinetics model of MIPR to include the effects of pressure and a varying surface height,” Ann. Nucl. Energy, vol. 72, pp. 507–537, Oct. 2014.
  • [14] P. H. Liem, H. N. Tran, and T. M. Sembiring, “Design optimization of a new homogeneous reactor for medical radioisotope Mo-99/Tc-99m production,” Prog. Nucl. Energy, vol. 82, pp. 191–196, Jul. 2015.
  • [15] Z. Gholamzadeh, S. A. H. Feghhi, S. M. Mirvakili, A. Joze-Vaziri, and M. Alizadeh, “Computational investigation of 99Mo, 89Sr, and 131I production rates in a subcritical UO2(NO3)2 aqueous solution reactor driven by a 30-MeV proton accelerator,” Nucl. Eng. Technol., vol. 47, no. 7, pp. 875–883, Dec. 2015.
  • [16] S. M. Mirvakili, Z. Gholamzadeh, and A. Davari, “Neutronic and thermo hydraulic analysis of a modeled subcritical uranyl nitrate aqueous reactor driven by 30-MeV protons,” Ann. Nucl. Energy, vol. 97, pp. 171–178, Nov. 2016.
  • [17] D. M. Pérez et al., “Thermal-Hydraulics Study of a 75 kWth Aqueous Homogeneous Reactor for 99 Mo Production,” J. Thermodyn., vol. 2015, pp. 1–11, 2015.
  • [18] D. M. Pérez, D. E. M. Lorenzo, C. A. B. De Oliveira Lira, C. R. G. Hernández, M. C. Rodríguez, and L. P. R. Garcia, “Effects of some calculation parameters on the computational modelling of temperature, velocity and gas volume fraction during steady-state operation of an aqueous homogeneous reactor,” Int. J. Nucl. Energy Sci. Technol., vol. 11, no. 1, p. 1, 2017.
  • [19] D. M. Pérez, D. E. M. Lorenzo, C. A. B. de Oliveira Lira, and L. P. R. Garcia, “Neutronic evaluation of the steady-state operation of a 20 kWth Aqueous Homogeneous Reactor for Mo-99 production,” Ann. Nucl. Energy, vol. 128, 2019.
  • [20] S. V Myasnikov, A. K. Pavlov, N. V Petrunin, and V. A. Pavshook, “Conversion of the ARGUS Solution Reactor to LEU Fuel : Results of Feasibility Studies and Schedule,” in RERTR 2012 - 34th International Meeting on Reduced Enrichment for Research and Test reactors, 2012, p. 8.
  • [21] P. P. Boldyrev, V. S. Golubev, S. V. Myasnikov, A. K. Pavlov, N. V. Petrunin, and V. A. Pavshook, “The Russian ARGUS Solution Reactor HEU-LEU Conversion: LEU Fuel Preparation, Loading and First Criticality,” in RERTR 2014 - 35th International Meeting on Reduced Enrichment for Research and Test reactors, 2014, p. 8.
  • [22] A. Vakulenko, “ROSATOM’s vision of Russia’s role in global molybdenum-99 supply,” Vienna, 2017.
  • [23] CNEN, “RELATÓRIO DE GESTÃO DO EXERCÍCIO DE 2017,” RIO DE JANEIRO, 2018.
  • [24] CNEN, “RELATÓRIO DE GESTÃO DO EXERCÍCIO DE 2015,” Rio de Janeiro, 2016.
  • [25] IAEA, “ARCAL Perfil Estratégico Regional para América Latina y el Caribe (PER) 2016 –2021,” Vienna, 2015.
  • [26] D. M. Pérez, “Diseño conceptual de un AHR de 75 kWt que utiliza combustible LEU para la producción de isótopos médicos,” Instituto Superior de Tecnologías y Ciencias Aplicadas, La Habana, 2015.
  • [27] D. M. Pérez, D. E. M. Lorenzo, C. A. Brayner, D. O. Lira, and L. P. R. Garcia, “NEUTRONIC AND THERMAL-HYDRAULIC STUDIES OF AQUEOUS HOMOGENEOUS REACTOR FOR MEDICAL ISOTOPES PRODUCTION,” in International Nuclear Atlantic Conference - INAC 2017, 2017, vol. 99, p. 22.
  • [28] E. S. Glouchkov and V. E. Khvostionov, “Graphite-reflected uranyl sulphate (20.9% 235U) solutions,” Moscow, 1997.
  • [29] Y. Li et al., “FMSR: A code system for in-core fuel management calculation of aqueous homogeneous solution reactor,” Nucl. Eng. Des., vol. 240, no. 4, pp. 763–770, 2010.
  • [30] C. C. Pain, C. R. E. De Oliveira, A. J. H. Goddard, and A. P. Umpleby, “Non-linear space-dependent kinetics for the criticality assessment of fissile solutions,” Prog. Nucl. Energy, vol. 39, no. 1, pp. 53–114, 2001.
  • [31] F. Barbry, “French solution reactor experience and contribution to the Feasibility of the Use of LEU Fuelled Homogenous Aqueous Solution Nuclear Reactors for the Production of Short Lived Fission Product Isotopes,” Vienna, 2010.
  • [32] F. J. Souto, R. H. Kimpland, and A. S. Heger, “Analysis of the Effects of Radiolytic-Gas Bubbles on the Operation of Solution Reactors for the Production of Medical Isotopes,” Nucl. Sci. Eng., vol. 150, no. 3, pp. 322–335, 2005.
  • [33] A. J. Wass, “Supo Thermal Model Development II,” Los Alamos, 2017.
  • [34] L. D. P. King, “Design and Description of Water Boiler Reactors,” in International Conference Peaceful Uses Atomic Energy, 1955, vol. 5, no. 32, pp. 372–391.
  • [35] M. E. Bunker, “Status Report on the Water Boiler Reactor,” Los Alamos, 1963.
  • [36] S. Chemerisov et al., “Experimental Results for Direct Electron Irradiation of a Uranyl Sulfate Solution: Bubble Formation and Thermal Hydraulics Studies,” Argonne, 2015.
  • [37] C. M. Cooling, “Development of a Point Kinetics Model with Thermal Hydraulic Feedback of an Aqueous Homogeneous Reactor for Medical Isotope Production,” Imperial College London, London, 2014.
  • [38] F. J. Souto and A. S. Heger, “A Model to Estimate Volume Change due to Radiolytic Gas Bubbles and Thermal Expansion in Solution Reactors,” Los Alamos, 1996.
  • [39] F. J. Souto and R. H. Kimpland, “Reactivity analysis of solution reactors for medical-radioisotope production,” Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms, vol. 213, no. 3, pp. 369–372, 2004.
  • [40] Los Alamos National Laboratory, “MCNP6.1/MCNP5/MCNPX User Manual.” Los Alamos National Laboratory, Los Alamos, p. 1001, 2013.
  • [41] ANSYS Team, “ANSYS CFD 19.0 Documentation, User’s Guide manual,” 2019. [Online]. Available: http://www.ansys.com. [Accessed: 01-Jul-2019].
There are 41 citations in total.

Details

Primary Language English
Journal Section Regular Original Research Article
Authors

Daniel Milian Pérez

Daylen Milian Pérez 0000-0001-7266-9019

Liván Hernández Pardo 0000-0002-6173-0854

Daniel Milian Lorenzo This is me 0000-0003-1643-2337

Carlos Brayner De Oliveira Lira This is me 0000-0002-8287-4822

Project Number 141270/2016-0
Publication Date February 28, 2021
Published in Issue Year 2021 Volume: 24 Issue: 1

Cite

APA Milian Pérez, D., Milian Pérez, D., Hernández Pardo, L., Milian Lorenzo, D., et al. (2021). Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand. International Journal of Thermodynamics, 24(1), 9-22. https://doi.org/10.5541/ijot.790728
AMA Milian Pérez D, Milian Pérez D, Hernández Pardo L, Milian Lorenzo D, Brayner De Oliveira Lira C. Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand. International Journal of Thermodynamics. February 2021;24(1):9-22. doi:10.5541/ijot.790728
Chicago Milian Pérez, Daniel, Daylen Milian Pérez, Liván Hernández Pardo, Daniel Milian Lorenzo, and Carlos Brayner De Oliveira Lira. “Multi-Physics Evaluation of the Steady-State Operation of an Aqueous Homogeneous Reactor for Producing Mo-99 for the Brazilian Demand”. International Journal of Thermodynamics 24, no. 1 (February 2021): 9-22. https://doi.org/10.5541/ijot.790728.
EndNote Milian Pérez D, Milian Pérez D, Hernández Pardo L, Milian Lorenzo D, Brayner De Oliveira Lira C (February 1, 2021) Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand. International Journal of Thermodynamics 24 1 9–22.
IEEE D. Milian Pérez, D. Milian Pérez, L. Hernández Pardo, D. Milian Lorenzo, and C. Brayner De Oliveira Lira, “Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand”, International Journal of Thermodynamics, vol. 24, no. 1, pp. 9–22, 2021, doi: 10.5541/ijot.790728.
ISNAD Milian Pérez, Daniel et al. “Multi-Physics Evaluation of the Steady-State Operation of an Aqueous Homogeneous Reactor for Producing Mo-99 for the Brazilian Demand”. International Journal of Thermodynamics 24/1 (February 2021), 9-22. https://doi.org/10.5541/ijot.790728.
JAMA Milian Pérez D, Milian Pérez D, Hernández Pardo L, Milian Lorenzo D, Brayner De Oliveira Lira C. Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand. International Journal of Thermodynamics. 2021;24:9–22.
MLA Milian Pérez, Daniel et al. “Multi-Physics Evaluation of the Steady-State Operation of an Aqueous Homogeneous Reactor for Producing Mo-99 for the Brazilian Demand”. International Journal of Thermodynamics, vol. 24, no. 1, 2021, pp. 9-22, doi:10.5541/ijot.790728.
Vancouver Milian Pérez D, Milian Pérez D, Hernández Pardo L, Milian Lorenzo D, Brayner De Oliveira Lira C. Multi-physics evaluation of the steady-state operation of an Aqueous Homogeneous Reactor for producing Mo-99 for the Brazilian demand. International Journal of Thermodynamics. 2021;24(1):9-22.