Modeling and simulation of the dynamic behavior of monoliths. Effects of pore structure from pore network model analysis and comparison with columns packed with porous spherical particles

A mathematical model is presented that could be used to describe the dynamic behavior, scale-up, and design of monoliths involving the adsorption of a solute of interest. The value of the pore diffusivity of the solute in the pores of the skeletons of the monolith is determined in an a priori manner by employing the pore network modeling theory of Meyers and Liapis [J. Chromatogr. A, 827 (1998) 197 and 852 (1999) 3]. The results clearly show that the pore diffusion coefficient, D-mp, of the solute depends on both the pore size distribution and the pore connectivity, it,, of the pores in the skeletons. It is shown that, for a given type of monolith, the film mass transfer coefficient, K-f, of the solute in the monolith could be determined from experiments based on Eq. (3) which was derived by Liapis [Math. Modelling Sci. Comput., 1 (1993) 397] from the fundamental physics. The mathematical model presented in this work is numerically solved in order to study the dynamic behavior of the adsorption of bovine serum albumin (BSA) in a monolith having skeletons of radius r(o)=0.7510(-6) m and through-pores having diameters of 1.510(-6)-1.8.10(-6) m [H. Minakuchi et al., J. Chromatogr. A, 762 (1997) 135]. The breakthrough curves of the BSA obtained from the monolith were steeper than those from columns packed with porous spherical particles whose radii ranged from 2.50.10(-6) m to 15.00.10(-6) m. Furthermore, and most importantly, the dynamic adsorptive capacity of the monolith was always greater than that of the packed beds for all values of the superficial fluid velocity, V-tp. The results of this work indicate that since in monoliths the size of through-pores could be controlled independently from the size of the skeletons, then if one could construct monolith structures having (a) relatively large through-pores with high through-pore connectivity that can provide high flow-rates at low pressure drops and (b) small-sized skeletons with mesopores having an appropriate pore size distribution (mesopores having diameters that are relatively large when compared with the diameter of the diffusing solute) and high pore connectivity, n(T), the following positive results, which are necessary for obtaining efficient separations, could be realized: (i) the value of the pore diffusion coefficient, D-mp, of the solute would be large, (ii) the diffusion path length in the skeletons would be short, (iii) the diffusion velocity, v(D), would be high, and (iv) the diffusional response time, t(drt), would be small. Monoliths with such pore structures could provide more efficient separations with respect to (a) dynamic adsorptive capacity and (b) required pressure drop for a given flow-rate, than columns packed with porous particles. (C) 1999 Elsevier Science BN. All rights reserved.