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
defines the boundary of operating conditions, in which a catalytic reactor is insensitive to small perturbations. Here, r(Tf,Cf) is the intrinsic reaction rate at inlet conditions, dt(dp) 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(ϕ0), where ϕ0 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(ϕ0) = 1 for ϕ0 < 0.5 and f(ϕ0) = 2 ϕ0 for ϕ0>0.5. The conservatism associated with the above criterion is comparable to the uncertainty involved in determining the parameters of the packed bed.
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