Mathematical Modeling of Evaporation Consequences of Toxic Substance Emergency Spillage at Railway Transport

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.