MATHEMATICAL MODELING OF EVAPORATION CONSEQUENCES OF TOXIC SUBSTANCE EMERGENCY SPILLAGE AT RAILWAY TRANSPORT

Y. O. Skob, M. L. Ugryumov

Abstract


Purpose. The main purpose of the article is calculation of spatial distribution fields of the conditional probability of lethal damage to the railway station personnel, caused by the inhalation of toxic gas, which is dissipated in the surface layer of the atmosphere under the conditions of a given wind situation, for a numerical assessment of the safety level of the technogenic object. Methodology. The authors developed a three-dimensional mathematical model of the evaporation processes of toxic chemical substance from the surface of the spillage stain as a result of emergency destruction of the storage or transportation capacity of liquefied gas and further dispersion of the gaseous admixture in the ground layer of the atmosphere, taking into account the cluttering of space by buildings. Also it was developed a calculation technology for determining the conditional probability of human injury by toxic gas on the basis of probit-analysis of the impact degree of damaging factor (inhalation toxodose) on human body. To automate the calculation process, the tabular dependence «probit-function-injury probability» is replaced by a generalized piecewise cubic spline. Findings. Based on the developed model we obtained the results of calculations of the space-time fields of the conditional probability of lethal injury to the railway station personnel who underwent inhalation exposure of a cloud of hydrogen cyanide gas. We also determined that the presence of buildings on the way of the toxic cloud dispersion increases the concentration area and the time of cloud passage along the calculated area, which, accordingly, increases the exposure time of station personnel to harmful impact. Originality. The developed mathematical model takes into account: the flow compressibility, the complex terrain (cluttering of the calculation space by the buildings of technogenic object), the three-dimensional nature of dispersion process of the gaseous admixture, the evaporation of a toxic substance with a variable intensity depending on the wind conditions, physical characteristics of admixture and the roughness grade of atmosphere surface layer. The mathematical model makes it possible to obtain spatio-time distributions of a dangerous parameter – the relative mass concentration of toxic gas and the damaging factor – inhalation toxodose, which are necessary to determine the nonstationary three-dimensional fields of the conditional probability of injury to the technogenic object  personnel on the basis of the probit-analysis apparatus. Practical value. The developed calculation technology allows the expert at the decision-making stage to perform automated numerical analysis and forecast in time and space of the conditional probability of lethal injury to service personnel exposed to the inhalation effect of toxic gas as an integral part of the safety index of a technogenic object - individual risk.


Keywords


gas mixtures; numerical methods; partial differential equations; exposure to harmful substances; pollution

References


Belyaev, N. N., & Koptilaya, O. V. (2002). Kompyuternoe modelirovanie zagryazneniya okruzhayushchey sredy pri razlive ammiaka. Ekolohiia i pryrodokorystuvannia, 2, 158-162. (in Russian)

Biliaiev, M. M., Kalashnikov, I. V., & Kozachyna, V. A. (2018). Territorial Risk Assessment after Terrorist Act: Express Model. Science and Transport Progress, 1(73), 7-14. doi: 10.15802/stp2018/123474 (in Russian)

Matsak, V. G., & Khotsyanov, L. K. (1956). Gigienicheskoe znachenie skorosti ispareniya i davleniya para toksicheskikh veshchestv, primenyaemykh v proizvodstve. Moscow: Medgiz. (in Russian)

RD-03-26-2007 Metodicheskie ukazaniya po otsenke posledstviy avariynykh vybrosov opasnykh veshchestv. (2008). Moscow: NTTs Promyshlennaya bezopasnost. (in Russian)

Skob, Y. A. (2017). Matematicheskoe modelirovanie struynogo istecheniya gazovozdushnoy smesi s razlichnoy kontsentratsiey primesi v atmosferu. Aerospace Technic and Technology, 4, 83-92. (in Russian)

Stoetsky, V. F., Golinko, V. I., & Dranishnikov, L. V. (2014). Risk assessment in man-caused accidents. Scientific Bulletin of National Mining University, 3, 117-124. (in Russian)

Chernyshev, Y. K. (2000). Vypuklye vektornye splayny v primenenii k profilirovaniyu lopatok GTD. Aerospace Technic and Technology, 21, 16-18. (in Russian)

Assael, M. J., & Kakosimos, K. E. (2010). Fires, Explosions, and Toxic Gas Dispersions: Effects Calculation and Risk Analysis. New York: CRC Press Publisher. doi: 10.1201/9781439826768 (in English)

Biliaiev, M. M., & Muntian, L. Y. (2016). Numerical simulation of toxic chemical dispersion after accident at railway. Science and Transport Progress, 2(62), 7-15. doi: 10.15802/stp2016/67279 (in English)

Brauer, R. L. (2016). Safety and Health for Engineers. New Jersey: Wiley Publisher. (in English)

Andersson, B., Andersson, R., Hakansson, L., Mortensen, M., Sudiyo, R., & Frontmatter, B. W. (2012). Computational Fluid Dynamics for Engineers. Cambridge: Cambridge University Press Publisher. (in English)

Engeln-Müllges, G., Niederdrenk, K., & Wodicka, R. (2010). Numerik-Algorithmen: Verfahren, Beispiele, Anwendungen. Berlin: Xpert.press Publisher. (in Germany)

Hughes, P., & Ferrett, E. (2011). Introduction to Health and Safety at Work: The Handbook for the NEBOSH National General Certificate. Kidlington: Oxford, Butterworth-Heinemann. (in English)

Knott, G. D. (2012). Interpolating Cubic Splines. Boston: Birkhäuser Publisher. (in English)

Nolan, Dennis P. (2011). Handbook of Fire and Explosion Protection Engineering Principles: for Oil, Gas, Chemical and Related Facilities. Burlington: Gulf Professional Publishing, Elsevier. (in English)

Dadashzadeh, M., Kashkarov, S., Makarov, D., & Molkov, V. (2018). Risk assessment methodology for onboard hydrogen storage. International Journal of Hydrogen Energy, 43(12), 6462-6475. doi: 10.1016/j.ijhydene.2018.01.195 (in English)

Nakayama, J., Misono, H., Sakamoto, J., Kasai, N., Shibutani, T., & Miyake, A. (2017). Simulation-based safety investigation of a hydrogen fueling station with an on-site hydrogen production system involving methylcyclohexane. International Journal of Hydrogen Energy, 42(15), 10636-10644. doi: 10.1016/j.ijhydene.2016.11.072 (in English)

Skob, Y. A., Granovskiy, E. A., & Ugryumov, M. L. (2017). Mathematical modeling of hydrogen explosion consequences at fueling station. Proceedings of 7-th International Conference on Hydrogen Safety, 1-12. Retrieved from https://www.hysafe.info/wp-content/uploads/2017_papers/159.pdf (in English)

Tashvigh, A. A., & Nasernejad, B. (2017) Soft computing method for modeling and optimization of air andwater gap membrane distillation – a genetic programming approach. Desalination and Water Treatment, 76, 30-39. doi: 10.5004/dwt.2017.20696 (in English)

Toro, E. F. (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Berlin: Springer Publisher. (in English)


GOST Style Citations


  1. Беляев, Н. Н. Компьютерное моделирование загрязнения окружающей среды при разливе аммиака / Н. Н. Беляев, О. В. Коптилая // Екологія і природокористування : зб. наук. пр. – Дніпропетровськ, 2002. – Вип. 2. – С. 158–162.
  2. Беляев, Н. Н. Расчет территориального риска при теракте: экспресс модель / Н. Н. Беляев, И. В. Калашников, В. А. Козачина // Наука та прогрес транспорту. – 2018. – № 1 (73). – С. 7–14. doi: 10.15802/stp2018/123474
  3. Мацак, В. Г. Гигиеническое значение скорости испарения и давления пара токсических веществ, применяемых в производстве / В. Г. Мацак, Л. К. Хоцянов. – Москва : Медгиз, 1959. – 231 с.
  4. РД-03-26-2007. Методические указания по оценке последствий аварийных выбросов опасных веществ. – Введ. 2008–01–25. – Москва : НТЦ Промышленная безопасность, 2008. – 122 с.
  5. Скоб, Ю. А. Математическое моделирование струйного истечения газовоздушной смеси с различной концентрацией примеси в атмосферу / Ю. А. Скоб // Авиационно-космическая техника и технология. – 2017. – № 4. – С. 83–92.
  6. Стоецкий, В. Ф. Оценка риска при авариях техногенного характера / В. Ф. Стоецкий, В. И. Голинько, Л. В. Дранишников // Наук. вісн. НГУ. – 2014. – № 3. – С. 117–124.
  7. Чернышев, Ю. К. Выпуклые векторные сплайны в применении к профилированию лопаток ГТД / Ю. К. Чернышев // Авиационно-космическая техника и технология. – 2000. – № 21. – С. 16–18.
  8. Assael, M. J. Fires, Explosions, and Toxic Gas Dispersions: Effects Calculation and Risk Analysis / Marc J. Assael, Konstantinos E. Kakosimos. –New York: CRC Press, 2010. – 349 p. doi: 10.1201/9781439826768
  9. Biliaiev, M. M. Numerical simulation of toxic chemical dispersion after accident at railway / M. M. Biliaiev, L. Ya. Muntian // Наука та прогрес транспорту. – 2016. – № 2 (62). – С. 7–15. doi: 10.15802/stp2016/67279
  10. Brauer, R. L. Safety and Health for Engineers / R. L. Brauer. –New Jersey: Wiley, 2016. – 608 p.
  11. Computational Fluid Dynamics for Engineers / B. Andersson, R. Andersson, L. Hakansson [et al.]. –Cambridge:CambridgeUniversityPress, 2012. – 212 p.
  12. Engeln-Müllges, G. Numerik-Algorithmen: Verfahren, Beispiele, Anwendungen / G. Engeln-Müllges, K. Niederdrenk, R. Wodicka. –Berlin: Xpert.press, 2010. – 756 p.
  13. Hughes, P. Introduction to Health and Safety at Work: The Handbook for the NEBOSH National General Certificate / P. Hughes, E. Ferrett. – Kidlington,Oxford: Butterworth-Heinemann, 2011. – 608 p.
  14. Knott, G. D. Interpolating Cubic Splines / G. D. Knott. –Boston: Birkhäuser, 2012. – 254 p.
  15. Nolan, Dennis P. Handbook of Fire and Explosion Protection Engineering Principles: for Oil, Gas, Chemical and Related Facilities / Dennis P. Nolan. –Burlington: Gulf Professional Publishing, Elsevier, 2011. – 351 p.
  16. Risk assessment methodology for onboard hydrogen storage / M. Dadashzadeh,S. Kashkarov, D. Makarov , V. Molkov // Intern. Journal of Hydrogen Energy. – 2018. – Vol. 43. – Іss. 12 – Р. 6462–6475. doi: 10.1016/j.ijhydene.2018.01.195
  17. Simulation-based safety investigation of a hydrogen fueling station with an on-site hydrogen production system involving methylcyclohexane / Jo Nakayama, Hitoshi Misono, Junji Sakamoto, Naoya Kasai, Tadahiro Shibutani, Atsumi Miyake // International Journal of Hydrogen Energy. – 2017. – Vol. 42. – Іss. 15. – Р. 10636–10644. doi: 10.1016/j.ijhydene.2016.11.072
  18. Skob, Y. A. Mathematical modeling of hydrogen explosion consequences at fueling station [Электронный ресурс] / Y. A. Skob, E. A. Granovskiy, M. L. Ugryumov // 7th Intern. Conference on Hydrogen Safety. –Hamburg(Germany), 2017. – P. 1–12. – Режим доступа: https://www.hysafe.info/wp-content/uploads/2017_papers/159.pdf – Загл. с экрана. – Проверено : 28.05.2018.
  19. Tashvigh, A. A. Soft computing method for modeling and optimization of air and water gap membranedistillation – a genetic programming approach / Akbar Asadi Tashvigh, Bahram Nasernejad // Desalinationand Water Treatment. – 2017. – Vol. 76. – Р. 30–39. doi: 10.5004/dwt.2017.20696
  20. Toro, E. F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction / E. F. Toro. –Berlin: Springer, 2009. – 724 p.


DOI: https://doi.org/10.15802/stp2018/133637

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