APPROXIMATION OF INTRAPARTICLE MASS-TRANSFER IN ADSORPTION PROCESSES .1. LINEAR-SYSTEMS

Approximate expressions of adsorbate uptake rate by spherical pellets were derived from the solutions of the intraparticle diffusion equation by the methods of weighted residuals. For systems with linear adsorption isotherms, the classic linear driving force (LDF) expression was shown to be equivalent to the solution of the intraparticle diffusion equation using the orthogonal collocation method with one collocation point. Alternatively, it can be shown that the LDF expression gives the best approximation (in the least-square sense) if a parabolic adsorbate concentration profile within the pellet is assumed. The use of higher-order polynomials for approximating the adsorbate concentration profile is equivalent to the use of a correspondingly larger number of collocation points in the solution of the intraparticle diffusion equation.