An improved linear formula for cyclic adsorption, diffusion and reaction in a catalyst

Abstract

Simple linear models including the linear driving force (LDF) model for approximating unsteady-state diffusion, adsorption in an adsorbent under cyclic operating environments have been proposed to reduce the computational load of the exact partial differential equations. The models are in the form of a first-order ordinary differential equation and consist of a term with the external concentration surrounding the adsorbent particle and another term with the average adsorbate concentration in the adsorbent. Although very simple to use, the approximation models are first-order approximations of the pore diffusion model, and hence their accuracy is not high enough to compute fine details of fast responses. By incorporating the time derivative of the external concentration into the approximation, an improved linear formula for cyclic adsorption is developed in this study. As the time derivative is usually computed simultaneously with the external concentration, the improved formula has little additional complexity over the previous approximations in its applications, and yet it is considerably more accurate than the previous first-order approximations for cyclic adsorption.