A local equilibrium between the concentration of adsorbate in the bulk fluid and surface phases is often assumed in the description of adsorption processes. This assumption leads to a considerable simplification in the problem by allowing an equilibrium treatment of the relationship between adsorbate concentration and surface coverage. The assumption indicates that the fractional coverage of the adsorbent by an adsorbate at any point in the process is in dynamic equilibrium with the adsorbate concentration in solution. Simple criteria developed here determine conditions under which such an assumption is justified.The local equilibrium assumption has been used in an equilibrium theory of parametric pumping (Pigford et al., 1969) to develop a theory for multicomponent chromatography (Rhee et al., 1970), to analyze multicomponent ion exchange adsorption separations in packed beds (Helfferich, 1967), and to model the concentration profiles during impregnation of porous catalysts (Vincent and Merrill, 1974). The assumption is almost invariably invoked in temperature-and pressure-swing adsorption separation modeling (Yang, 1987). Often this takes the form of a Langmuir isotherm or a linear version of the isotherm.Many of the empirical guidelines used in adsorption process engineering, such as that mass transfer is the rate-limiting step rather than adsorption kinetics, were developed from experience with processes involving adsorption of simple gas-phase molecules, strong adsorbents, and so on. Adsorption processing's scope has expanded considerably over the years, and adsorption separations have a significant foothold in the environmental and biochemical fields today. Engineers must deal with novel systems more often than in the past. Guidelines for good judgments are of great value in such an environment. In view of the importance of the above separation processes, as well as the significant role that adsorption plays in catalyst preparation (such as, Komiyama et al., 1980), an investigation of the conditions, under which such an assumption can be justified, is long overdue.
Adsorption ProblemConsider the competitive adsorption of n species from a Correspondence concerning this work should be addressed to H. H. Lee fluid onto a solid adsorbent in a packed bed. Species' concentrations evolve based on the response times associated with various resistances, such as dispersion in the bulk fluid, mass transfer to the surface, convection, diffusion in porous adsorbents, and kinetics. To establish a direct absolute criteria between adsorption kinetic rate effects and bulk fluid convection effects, assume that all effects of mass transfer are negligible. The ultimately derived criteria will consequently state only when adsorption kinetics cannot be considered in equilibrium relative to bulk fluid change rates. The relative importance of mass transfer rate effects to either bulk convection or adsorption kinetic rate effects will not be established by what follows. These assumptions yield the following solute mass balances: wh...