Nonlinear fixed‐bed sorption when mass transfer and sorption are controlling

Abstract

Separation processes based on adsorption followed by desorption are widely utilized. Sophisticated, yet solvable, models are required for the design of these processes. Considerable progress has been made over the past five decades in the modeling of fixed-bed adsorption and desorption of a single component from a dilute isothermal solution. The typical plots of effluent concentration vs. time have been obtained for a number of systems both for adsorption (i.e., the breakthrough curve) and desorption (i.e., elution curve). The "spreading" of these curves may be due to various mechanisms, including axial dispersion, film and pore diffusion resistances, and finite rates of adsorption and desorption.Analytical solutions have been obtained for each of these mechanisms, operating alone or in combination, for systems marked by a linear equilibrium relationship between sorbate concentration in the fluid and adsorbate concentration on the solid. These solutions are reviewed by Ruthven (1983). However, for many adsorption and desorption processes, the isotherms are nonlinear, resulting in substantial changes in the breakthrough and elution curves (Garg et al., 1974;Arnold et al., 1986a). Analytical solutions are rarely possible for systems with a nonlinear isotherm or with nonlinear sorption kinetics. The only rigorous analytical solution for "Langmuir-type" sorption kinetics (as defined by Eq. 1) was presented by Thomas for fixed-bed adsorption, where sorption is rate-controlling ( Thomas, 1944). Using this result, approximate analytical solutions have been obtained for the breakthrough curves when pore diffusion and film mass transfer are rate-limiting (Hiester et al., 1952).With the exception of the Thomas solution, only numerical solutions have been obtained for adsorption or desorption processes with Langmuir-type sorption kinetics. For example, Zwiebel et al. (1972) computed breakthrough and elution curves where fluid film mass transfer is the rate-controlling step. Various other studies on pore diffusion or solid diffusion haveCorrespondence concerning this paper should be addressed to C. F. Gmchee. also been reported for systems exhibiting nonlinear isotherms (Antonson and Dranoff, 1969; Carter and Hussain, 1972;Garg and Ruthven, 1973;Arve and Liapis, 1987).In this report, a general model is presented for isothermal, single-component adsorption and desorption from a dilute solution in a fixed bed in which both the fluid film mass transfer step and the sorption step are rate-controlling. The sorption kinetics is described by a rate equation which is second order in the forward direction and first order in the reverse direction, and which reduces to the Langmuir isotherm at equilibrium: affinity adsorption (Chase, 1984;Arnold et al., 1986a); ion exchange (Hiester and Vermeulen, 1952); and various other adsorption systems are well represented by such an equation. Breakthrough and elution curves are computed utilizing the method of characteristics. The solutions are presented in terms of dimensionless parameters. Thes...