Building a model of choosing water supply rate to cool a tank in the case of a fire

The object of this study is the process of liquid burning in a spill, and the subject of the study is the temperature distribution along the wall of a vertical steel tank when it is heated under the thermal influence of a fire and cooled by water. The conventional approach to cooling vertical steel tanks with petroleum products with water during a fire is based on cooling the wall along the entire half-perimeter from the fire side. Instead, it is proposed to cool only that part of the tank wall that is heated above a certain limit value. In this case, the intensity of water supply for cooling is chosen so that the temperature of the tank wall does not exceed this value. The proposed approach is based on a system of equations consisting of a heat balance equation for the tank wall, heat and mass balance equations for the water film flowing down the tank wall. These equations take into account heat exchange by radiation and convection with the fire and the environment. An optimization problem has been constructed, the criterion of which is the minimum water consumption, and the restriction is not exceeding the wall temperature of the specified limit value. An algorithm for determining the optimal intensity of water supply for cooling the tank wall has been developed. At the first stage, a reasonable intensity of water supply is determined, which ensures that the wall temperature does not exceed the limit value. At the second stage, the dichotomy method is used to determine the minimum possible intensity at which the specified condition remains fulfilled. The example of a diesel fuel spill shows that the application of the proposed approach makes it possible to reduce water consumption for cooling the tank by almost 3.5 times. This, in turn, means reducing the number of equipment and personnel involved for localization and elimination of the fire