Building a model of heating an oil tank under the thermal influence of a spill fire

The object of this study is the process of liquid combustion in a spill, and the subject of research is the distribution of temperature along the wall and roof of a vertical steel tank that is heated under the thermal influence of a spill fire. The heat balance equation for the wall and roof of the tank with oil product was constructed. The assumption of a small thickness of the wall and roof of the tank relative to its linear dimensions makes it possible to move to two-dimensional differential equations of the parabolic type. The equations take into account the radiative heat exchange with the flame, the environment, the internal space of the tank, as well as the convective heat exchange with the surrounding air, the vapor-air mixture, and the liquid inside the tank. Using the methods of similarity theory, estimates of the coefficients of convection heat exchange of the outer surface of the tank with the surrounding air and the inner surface with the vapor-air mixture and liquid in the tank in the conditions of free convection were constructed. The application of the finite difference method for solving the heat balance equations has made it possible to derive the temperature distribution on the surface of the tank at an arbitrary moment in time. It is shown that the value of the coefficient of convection heat exchange of the liquid exceeds the corresponding value for the air-vapor mixture by (1÷2) orders of magnitude. As a result, the part of the wall located below the oil product level is heated to a temperature of (80÷230) °C depending on the viscosity of the liquid. This occurs despite the fact that the value of the mutual radiation coefficient reaches its maximum value at the lower part of the wall. From a practical point of view, this means that the part of the wall above the level of the oil product in the tank can reach dangerous temperature values, and it should be cooled first. The constructed model of tank heating also enables determining the limit time for the start of cooling of the tank.