Thermal runaway criterion for chemical reaction systems: A modified divergence method

The chemical reaction in certain range of operating conditions may exhibit parametric sensitivity where small changes in one or more of the input parameters lead to changes in the output variables (eg. reaction temperature). The sharp rise of the reaction temperature is a critical behavior that may lead to runaway conditions. Thus, it is of vital importance to determine the critical operating parameters consisting of the parametric sensitivity region under the consideration of intrinsic safety. In this paper, a modified divergence criterion is proposed based on the trace of Jacobian matrix at the maximum temperature. The nonlinear differential equations describing the dynamic behavior of the chemical reaction is linearized locally in the vicinity of the equilibrium point by the small perturbation analysis. The relationship between the perturbation equation and parametric sensitivity of the reaction system is investigated. The critical values computed by the modified divergence criterion are compared with Morbidelli and Varma criterion (MV criterion), Adler and Enig criterion (AE criterion) and divergence criterion (Div criterion). The comparison demonstrates the validity of the new criterion. In addition, the critical explosion pressures of two kinds of hazardous chemicals are computed by the various critical criteria and compared with published experimental data. The results show that the modified divergence criterion could give smaller computational error compared with the previous criteria.