Adsorption 5, 373–380 (1999) c  1999 Kluwer Academic Publishers. Manufactured in The Netherlands. New Approximate Model for Nonlinear Adsorption and Concentration Dependent Surface Diffusion in a Single Particle GERARDINE G. BOTTE, RUYU ZHANG AND JAMES A. RITTER Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208, USA ritter@engr.sc.edu Received November 3, 1998; Revised December 22, 1998; Accepted January 12, 1999 Abstract. A new approximate model for nonlinear adsorption (Langmuir model) and concentration dependent surface diffusion (HIO model) in a single particle was derived, based on a parabolic concentration profile assumption for the summation of the gas and adsorbed phases. The surface diffusivity was approximated with the adsorbed phase concentration evaluated at the surface of the particle, as the average of the adsorbed phase concentration, and as the average of the first two approximations. Overall, the approximate model based on the average of the first two approximations compared the best with the exact solution for a wide variety of systems and conditions. Keywords: langmuir isotherm, parabolic profile, pore diffusion, concentration dependent surface diffusion, HIO Introduction Surface diffusion is the transport of a substance within the adsorbed phase, and it occurs simultaneously with gas phase or pore diffusion. Moreover, although the mobility of molecules in the adsorbed phase is smaller than in the gas phase, the adsorbed phase concentration is usually much higher; thus, significant surface fluxes are possible. In fact, under certain conditions, surface diffusion can contribute significantly to the overall in- traparticle mass transport (Kapoor and Yang, 1990), es- pecially in microporous adsorbents (like activated car- bon) which necessarily promote large adsorbed phase concentrations. This point has been raised by Doong and Yang (1986), where they found that surface dif- fusion contributed as much as 50% to the total flux in the pores of activated carbon during the pressure swing separation of CO 2 ,H 2 and CH 4 . Moreover, it has been shown that the surface diffu- sivity increases rather significantly with an increase in the adsorbed phase concentration (Kapoor et al., 1989). Several models have been suggested in the liter- ature to describe concentration dependent surface dif- fusion. These models have been thoroughly reviewed by Kapoor et al. (1989). Among them, the HIO model developed by Hihashi et al. (1963) has been widely used to account for concentration-dependent surface diffusion in spherical adsorbent particles (Doong and Yang, 1986; Sun and Meunier, 1987; and Kapoor and Yang, 1991). Many approximate expressions have also been developed to simplify the mathematical complex- ities associated with an exact description of intraparti- cle diffusion in spherical adsorbent particles (Liaw et al., 1979; Wakao and Kaguei, 1982; Do and Rice, 1986; Hills, 1986; Do and Mayfield, 1987; Tomida and McCoy, 1987; Do and Nguyen, 1988; Buzanowski and Yang, 1989; Kim, 1989; Goto et al., 1990; Lai and Tan, 1991; Goto and Hirose, 1993; Xiu and Wakao, 1993; Yao and Tien, 1993; Zhang and Ritter, 1997; Carta and Cincotti, 1998; Botte et al., 1998). However, none of these approximate models have accounted for concen- tration dependent surface diffusion. In this paper, a new approximate model based on a concentration-dependent surface diffusivity (HIO),