Explicit runaway criterion for catalytic reactors with transport limitations

Most existing criteria for predicting parametric sensitivity or runaway in a catalytic reactor are based on a single‐phase model that does not account for interparticle heat and mass transfer resistances and intraparticle diffusion. Accounting for these effects, the simple criterion\documentclass{article}\pagestyle{empty}\begin{document}$$\frac{E}{{RT_f }}\frac{{(- \Delta H)r(T_f,C_f)}}{{T_f }}\left[{\frac{{d_t }}{{4U}} + \frac{{d_p }}{{6h}}} \right] < 0.368f(\phi _0)$$\end{document} defines the boundary of operating conditions, in which a catalytic reactor is insensitive to small perturbations. Here, r(T f ,C f ) is the intrinsic reaction rate at inlet conditions, d t (d p ) and U(h) are the diameter of reactor tube (catalyst particle) and heat transfer coefficient between the fluid and tube wall (catalyst particle), respectively. The function f(ϕ 0 ), where ϕ 0 is the normalized Thiele modulus at inlet conditions, accounts for the effects of intraparticle diffusion. For the common case of equal coolant and feed temperatures, f(ϕ 0 ) = 1 for ϕ 0 < 0.5 and f(ϕ 0 ) = 2 ϕ 0 for ϕ 0 >0.5. The conservatism associated with the above criterion is comparable to the uncertainty involved in determining the parameters of the packed bed.