An Approximate Algebraic Model for Conversion and Light-off Curves by First-order Reactions in Monolith Converters Operated in the Graetz Regime

Abstract The interaction of mass transfer with irreversible first order heterogeneous-homogeneous chemical reactions in an isothermal circular channel with laminar Poiseuille velocity profile is investigated theoretically. Starting from a novel approximate solution for the reactant mass balance valid in the Graetz regime with fully developed concentration field, a one-term exponential model for conversion is derived which depends on three dimensionless groups: the normalized transversal diffusion time scale ( $$\\alpha$$ ) and the Damköhler numbers of the heterogeneous ( $${Da}_{\\text{w}}>0$$ ) and homogeneous ( $${Da}_{\\text{b}}\\ge\\:0$$ ) reactions. The model requires the determination of the root of a polynomial of the Damköhler numbers, which entails only minimal numerical effort. The accuracy of the model is tested for the case of a heterogeneous reaction ( $${Da}_{\\text{b}}=0$$ ), showing good agreement with numerical solutions and formal analytical limits provided $$\\alpha\\le1$$ . The proposed single channel conversion model is used to determine observed and intrinsic rate constants, as well as kinetic parameters (pre-exponential factor and activation energy), based on literature data regarding NO conversion via selective catalytic reduction in monolith reactors. In combination with temperature dependent rate constant and diffusion coefficient, the model allows studying effects of parameter variations on the light-off curve in monolith reactors within seconds. The proposed model may therefore be a useful tool for engineering design and optimization of monolith converters.