Pergamon Chemical Enoineerin~l Science, Vol. 52, No. 18, pp. 3161 3172. 1997 i 1997 Elsevier Science ltd. All rights reserved Printed in Great Britain PII: S0009-2509(97)00124-3 0009 2509/97 $17.00 + 0.00 New approximate model for nonlinear adsorption and diffusion in a single particle Ruyu Zhang and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208, U.S.A. (Received 4 December 1996; in revised form 12 March 1997; accepted 17 March 1997) Abstract--A new approximate model of the general adsorption and diffusion model is derived that describes gas and adsorbed phase dependent diffusion in a single spherical sorbent particle governed by a nonlinear adsorption isotherm. This new approximate model compares very well with the exact (numerical) solution of the general adsorption and diffusion model over a wide range of (Langmuir) isotherm nonlinearity, and pore and surface diffusivities. Thus, it provides a significant advantage in terms of computation compared to the exact (numerical) model. This new model is simple to use and far superior to the popular linear driving force model, which severely underpredicts the uptake curve (compared to the new model) unless the adsorption isotherm is very favorable and the bulk concentration is low, approaching the Henry's law region of the isotherm. ~ 1997 Elsevier Science Ltd Keywords: Pore diffusion; surface diffusion; linear driving force; parabolic profile; Langmuir isotherm. INTRODUCTION Diffusion generally plays an important role in adsorp- tion processes. Hence, modeling of fixed-bed and pres- sure swing adsorption (PSA) processes often requires a description of intraparticle diffusion rates (Yang, 1987). Because of the mathematical complexities asso- ciated with an exact description of intraparticle diffu- sion in a spherical sorbent particle, approximate expressions of different mechanistic models have been sought (Liaw et al., 1979; Wakao and Kaguei, 1982; Do and Rice, 1986; Hills, 1986; Do and Mayfield, 1987; Tomida and McCoy, 1987; Do and Naguyen, 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). The models of interest to this work are the solid diffusion (Liaw et al., 1979) and pore diffusion (Do and Rice, 1986; Lai and Tan, 1991) models. For the solid (surface) diffusion model, the first and most widely used approximation is the linear driving force (LDF) (Glueckauf, 1955). Liaw et al. (1979) as- sumed the adsorbed phase concentration profile in- side a sorbent particle to be parabolic, and obtained an ordinary differential equation for the rate of change of the volume-averaged concentration. This equation was identical to the LDF expression given by Glueckauf (1955) and thus independent of the Corresponding author. Tel.: (803) 777-3590;fax: (803) 777- 8265; e-mail: ritter@sun.che.sc.edu. adsorption isotherm. The LDF expression has been widely used in modeling fixed-bed and cyclic adsorp- tion processes. However, it has inherent weaknesses as pointed out by numerous investigators (Nakao and Suzuki, 1983; Do and Mayfield, 1987; Do and Nguyen, 1988; Buzanowski and Yang, 1989; Goto and Hirose, 1993; Yao and Tien, 1993), and as shown in this study. The pore diffusion model necessarily includes a gas phase; thus, diffusion depends on the adsorption iso- therm. Approximate solutions to the pore diffusion model have been reported for both linear (Do and Rice, 1986) and nonlinear (Lai and Tan, 1991) adsorp- tion isotherms. Do and Rice (1986) assumed a para- bolic gas-phase concentration profile inside the sorbent, and also derived an ordinary differential equation similar in form to the LDF model, but with a different time constant. Lai and Tan (1991) assumed a combined gas and adsorbed-phase concentration profile inside the sorbent, and also derived an ordi- nary differential equation similar in form to the LDF model, but with a time constant that depends on the slope of the adsorption isotherm at the external sur- face of the sorbent. Results from these approximate pore diffusion models agreed well with the exact nu- merical solution under conditions where the assump- tions of the models were valid. However, no approximate solutions, at least that are similar in form to the LDF model, have been reported for the pore-surface (parallel) diffusion model, for which a paucity of work has been done (Kapoor and Yang, 1991). 3161