The study is dedicated to the numerical modeling of boiling (evaporation) processes for cryogenic liquids, such as liquefied natural gas and liquid nitrogen, during spills onto various surfaces. A mathematical model based on a heat-conductivity differential equation system that accounts for the film and bubble boiling modes of cryogenic liquids has been proposed.
The developed numerical model has been verified using experimental data on liquid nitrogen boiling on sand and steel sheet, as well as liquefied natural gas boiling on concrete and sandy soil. A significant improvement in convergence between the proposed model and experimental data has been demonstrated due to accounting for the transition from film to bubble boiling mode, particularly for boiling modeling on metals. Considering boiling in film mode is specifically crucial when describing the initial stage of the process, when the transition to the vapor phase is particularly intense, and it is necessary to avoid excessive evaporation rates. According to calculations, neglecting the film boiling stage and considering only the bubble boiling stage results in significantly overestimated intensities.
The difficulties of modeling boiling processes during spills on surfaces with porous, permeable structures, such as loose sand, are specifically noted. In this case, the roughness and permeability of the surface layer increase the surface area of contact between the cold liquid and the heated solid phases and, consequently, the intensity of heat exchange and evaporation. Therefore, the experiments show a more intense boiling, compared to smooth and impermeable underlying surfaces. Boiling intensity increase was registered, in this case, by introducing a correction factor considering the increase in contact surface of various phases. The developed model can be further improved by including a filtration factor.
Safonov V.S. Problems of ensuring the safety of liquefied natural gas facilities. Part II. Modern approaches to modeling of emergency processes and their consequences at the facilities of production, storage and transportation of liquefied natural gas. Moscow: ZAO NTTs PB, 2020. 478 p. (In Russ.).
2. Fernandez M.I., Harper M., Mahgerefteh H., Witlox H.W.M. An integral model for pool spreading, vaporisation and dissolution of hydrocarbon mixtures. Available at: https://discovery.ucl.ac.uk/id/eprint/10114235/1/xxiii-paper-61.pdf (accessed: October 27, 2025).
3. Болодьян И.А., Молчанов В.П., Дешевых Ю.И. Пожаровзрывобезопасность объектов хранения сжиженного природного газа. Анализ состояния проблемы // Пожарная безопасность. 2000. № 2. С. 86–96.
Bolodyan I.A., Molchanov V.P., Deshevykh Yu.I. Explosion and fire safety of liquefied natural gas storage facilities. Problem status analysis. Pozharnaya bezopasnost = Fire Safety. 2000. № 2. рр. 86–96. (In Russ).
4. Старовойтова Е.В., Галеев А.Д., Поникаров С.И. Экспериментальное исследование интенсивности парообразования сжиженного газа // Вестник Казанского технологического университета. 2012. Т. 15. № 4. С. 70–71.
Starovoytova E.V., Galeev A.D., Ponikarov S.I. Experimental investigation of the intensity of liquefied gas evaporation. Vestnik Kazanskogo tekhnologicheskogo universiteta = Bulletin of the Technological University. 2012. Vol. 15. № 4. pp. 70–71. (In Russ.).
5. Старовойтова Е.В., Галеев А.Д., Поникаров С.И. Моделирование парообразования с поверхности аварийного пролива сжиженного газа // Вестник Казанского технологического университета. 2012. Т. 15. № 4. С. 110–112.
Starovoytova E.V., Galeev A.D., Ponikarov S.I. Modeling evaporation from the surface of an accidental liquefied gas spill. Vestnik Kazanskogo tekhnologicheskogo universiteta = Bulletin of the Technological University. 2012. Vol. 15. № 4. pp. 110–112. (In Russ.).
6. Van den Bosch C.J.H, Weterings R.A.P.M. Methods for the calculation of physical effects due to releases of hazardous materials (liquids and gases). Available at: https://content.publicatiereeksgevaarlijkestoffen.nl/documents/PGS2/PGS2-1997-v0.1-physical-effects.pdf (accessed: October 27, 2025).
7. Сравнение результатов моделирования аварийных выбросов опасных веществ с фактами аварий / С.И. Сумской, К.В. Ефремов, М.В. Лисанов, А.С. Софьин // Безопасность труда в промышленности. 2008. № 10. С. 42–50.
Sumskoy S.I., Efremov K.V., Lisanov M.V., Sofin A.S. Comparing results of modeling of hazardous substance accidental spills with facts of accidents. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2008. № 10. рр. 42–50. (In Russ.).
8. Верификация методик оценки последствий аварийных выбросов газа от источников продолжительного действия / С.И. Сумской, А.В. Пчельников, М.В. Лисанов и др. // Безопасность труда в промышленности. 2005. № 8. С. 28–35.
Sumskoy S.I., Pchelnikov A.V., Lisanov M.V., Pecherkin A.S., Shargatov V.A. Verification of assessment methodologies for consequences of gas accidental emissions from long-acting sources. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2005. № 8. рр. 28–35. (In Russ.).
9. Верификация методик для оценки последствий химических аварий / С.А. Губин, С.М. Лыков, И.В. Маклашова и др. // Химическая промышленность. 1999. № 10. С. 58–66.
Gubin S.A., Lykov S.M., Maklashova I.V., Pecherkin A.S., Sidorov V.I., Sumskoy S.I. Verification of methodologies to assess consequences of chemical accidents. Khimicheskaya promyshlennost = Chemical Industry Developments. 1999. № 10. рр. 58–66. (In Russ.).
10. Сверчков А.М., Сумской С.И. Верификация программного средства TOXI+Гидроудар для моделирования нестационарных процессов в трубопроводах // Безопасность труда в промышленности. 2017. № 10. С. 5–10.
Sverchkov A.M., Sumskoy S.I. Verification of TOXI+Water-Hammer Software for Modelling of Non-Stationary Processes in the Pipelines. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2017. № 10. рр. 5–10. (In Russ.).
11. Болодьян И.А., Вогман Л.П. Экспериментальные исследования проливов криогенных жидкостей (топлив) // Безопасность труда в промышленности. 2022. № 8. С. 13–18. DOI: 10.24000/0409-2961-2022-8-13-18
Bolodyan I.A., Vogman L.P. Experimental Studies of Cryogenic Liquids (Fuels) Spills. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2022. № 8. рр. 13–18. (In Russ.). DOI: 10.24000/0409-2961-2022-8-13-18
12. Успехи теплопередачи / под. ред. Н.Н. Анфимова. М.: Мир, 1971. 576 c.
Anfimov N.N. Heat transfer success. Мoscow: Мir, 1971. 576 p. (In Russ.).