Approximations of uptake rate of spherical adsorbent pellets and their application to batch adsorption calculations

Two approximate expressions of sorbate uptake rate of spherical adsorbent pellets (referred to as model I and model II) were derived and applied to batch adsorption calculations. The derivations were made by assuming that the significant part of the concentration profile within a pellet may be represented by a parabolic expression over a spatial domain which expands with time. Both models I and II have expressions similar to that of the linear driving force (LDF) model but give much better accuracy, especially for small time. In particular, the results obtained from using model I were found to be nearly the same as those of the exact solutions.