On the occurrence of thermal explosion in a reacting gas: the effects of natural convection and consumption of reactant

Whether or not a chemical reaction in a fluid leads to an explosion is shown to depend on four timescales: that for the chemical reaction to heat up the fluid containing the reactants and products, for heat conduction out of the reactor, for natural convection in the fluid, and finally for chemical reaction. This approach is developed for an irreversible, n-th order chemical reaction, A → B occurring exothermically in a closed spherical vessel, whose wall is held at a fixed temperature. These four timescales are expressed in terms of the physical and chemical parameters of the system. A new three-dimensional regime diagram is proposed, in which the three effects inhibiting explosion, viz. the consumption of reactant, and heat removal both by thermal conduction and by natural convection, appear separately. Numerical simulations are performed for laminar natural convection occurring, so that the development of temperature, composition and velocity throughout a reacting gas is computed for increasing times. The results are compared with previous experimental measurements in the gas phase for the decomposition of azomethane. The criterion for an explosion is considered in some detail; it appears that these systems explode if and when the maximum dimensionless rise in temperature exceeds a value close to 5.