Non-equilibrium effects on fast reactions in a heterogeneous batch reactor

Abstract

Recent studies by the authors of the heterogeneous catalysis of fast binary reactions have taken a dynamical systems approach, assuming that fast enough reactions are confined to a manifold upon which surface equilibrium holds. This approximation makes substantial simplification possible, for instance in the case of a batch reactor, it allows a naturally sixth order system to be approximated by a two dimensional manifold for the dynamics of two modified Thiele moduli. Nevertheless, a proper assessment of how much faster must the velocity of surface reaction be than the velocity of mass transfer to the catalytic surface before the quasi-equilibrium on the surface holds should be made. In this paper, a theory for the systematic correction to infinitely fast reactions is made for large but finite velocity reactions. It is compared to full numerical solutions to the model equations. Recommendations about the regime of applicability of the quasi-equilibrium approximation are made. In general, the predictions of the quasi-equilibrium theory hold for ratios of mass transfer coefficients to reaction velocity ξ of less than 1 / 1000 , with qualitative agreement in regimes of less than 1 / 100 . The general trend, however, is that the stronger the kinetic asymmetry between the mass transfer coefficients of the reactants, the slower the reaction rate can be and still have the quasi-equilibrium theory hold. A perturbation analysis demonstrates that the quasi-equilibrium theory is a regular limit of the fast non-equilibrium theory. In the irreversible case, a matched asymptotic analysis gives the same prediction for the switch time from effective surface depletion of one reagent to the other as the quasi-equilibrium theory. Furthermore, it gives an estimate of the smoothing out of the transition zone with a temporal width of ξ 1 / 2 . It should be noted that the continual drive for improved catalyst activities inevitably leads to mass transfer limited reactions, and thus this regime is not uncommon.