On the use of different parabolic concentration profiles for nonlinear adsorption and diffusion in a single particle

Abstract

Different parabolic concentration profile assumptions have been used in simplifying pore and/or surface diffusion models that describe mass transport inside a single adsorbent particle. A parabolic concentration pofile assumption for the adsorbed phase has been used to describe solid diffusion (Liaw et al., 1979), and also surface diffusion (Yao and Tien, 1993) inside adsorbent particles. A parabolic concentration profile assumption for the gas phase has also been used to account for pore diffusion within adsorbent particles (Yang and Doong, 1985; Do and Rice, 1986; Yao and Tien, 1993; Lai and Tan, 1991) and more recently Zhang and Ritter (1997) used a parabolic concentration profile assumption for the summation of the gas and adsorbed phases to describe pore and/or surface diffusion inside adsorbent particles. These three different parabolic concentration profile assumptions are the same, only for a linear adsorption isotherm, When the adsorption isotherm is nonlinear, the approximate models of the pore-surface diffusion model obtained by using the parabolic concentration profile assumptions of the gas, adsorbed, or summation of the gas and adsorbed phases inside the adsorbent particle are totally different. Nevertheless, the parabolic concentration profile assumptions for the gas and adsorbed phases have been used with essentially no regard for the validity of such an assumption for a given system. Therefore, the objective of this communication is to present three simplified models of the general adsorption and diffusion equation, each based on one of the parabolic distribution concentration profile assumptions. The utility of these models is demonstrated, along with some rules of thumb that a priori indicate which parabolic concentration profile assumption is more appropriate for a given system.