(595b) Multipoint Pade Method for Cyclic Adsorptions with Reactions in Slab, Cylinder and Sphere Catalysts

An accurate mathematical description for the dynamic mass transfer in a particle is the pore diffusion model represented by a parabolic partial differential equation. Practical separation processes such as packed bed adsorbers involve mass balance equations of the bulk flow through the adsorber in addition to this pore diffusion model equation. These coupled partial differential equations are rather complicate and the pore diffusion model equation need be approximated for a reduced computational load. The linear driving force (LDF) model is the simplest approximation. In pressure swing adsorption (PSA) for gas separation, the adsorbent particles in the bed are subject to a periodic concentration change. The LDF approximation has been used to simplify modeling and to reduce computation time in simulations of cyclic operations. As the frequency of the cyclic operation increases, it has been shown that the LDF approximation becomes invalid.

   For fast cyclic operations, approximations derived for general concentration forcing should be modified. The LDF whose coefficients are varied as a function of the frequency has been suggested by several researchers. Kim (Chem. Eng. Sci. 1996, 51, 4137-4144) proposed the first order model for which exact response is obtained for sinusoidal wave of the given frequency. For the cyclic operations, the first order model can also be obtained by dividing the particle into active and inactive zones and applying the one-point collocation method to the active zone. High-order approximations for general periodic concentration changes are available (Lee, J.; Kim, D. H., Chem. Eng. Sci., 1998, 53, 1209-1221).

   Here the multipoint Pade method based on the continued fraction expansion is applied to obtain high order models for a fast cyclic operation of diffusion, adsorption and a first-order reaction in a slab, cylinder and sphere catalyst. Model parameters can be calculated easily. Trends of responses as the operation period decreases are obtained.