(5d) Pi-Criterion Analysis of Non-Steady State Catalytic Oxidation Reactions

Non-steady operation of catalytic reactors can enhance reactant conversions and product selectivities. However, it is challenging to identify the extent of enhancement from kinetic and operating parameters. In this study, we describe two simple methods to establish approximate functional dependencies of isothermal point reaction enhancement on dynamic and kinetic parameters. In low frequency operation, local dynamic rates are approximated as square waves oscillating between two steady states. From this, it is possible to derive analytical functions from global rate expressions relating fractional rate enhancements to concentration wave amplitudes, phase shifts, averages and reaction orders for multiple dynamically-fed reactants. Figs. 1A and B show the rate enhancement mapped in the plane of the dimensionless amplitudes of in-phase modulated reactants A and B. For net concave-up kinetics (n₁+n₂>1) enhancement is achievable for most of the region while the opposite is true for concave-down kinetics (n₁+n₂<1). While the method is confined to local behavior, the approach is effective in determining optimal feed conditions for modular reactors.

Higher frequency concentration modulation provides further complications arising from accumulation effects on catalyst surfaces. Thus, global kinetic descriptions may lack key attributes thereby preventing an accurate quantification of modulation effects. We consider two examples, the oxidation of carbon monoxide (CO) and selective oxidation of butane to maleic anhydride (MAN). Locating regions of dynamic enhancement in such complex parameter spaces is plausible by applying second variation optimization methods to the microkinetic surface balances. Fig. 1C shows the second variation estimate of local rate enhancement for CO oxidation which suggests enhanced performance for large period, out-of-phase operation. The analysis shows good agreement with literature studies [1] without the need for extensive numerical solutions of the governing equations.

[1] Lie, A. B. K., Hoebink, J. & Marin, G. B. Chem. Eng. J. Biochem. Eng. J. 53, 47–54 (1993).