Determining external film mass transfer coefficients for adsorption columns

Abstract

Radcliffe et al. (1982), while presenting a method for determining the external film mass transfer coefficient k, by the analysis of initial breakthrough concentrations, stated that external film mass transfer dominates mass transfer behavior during the early portion of breakthrough curves obtained from fixed-bed adsorbers. It is important, however, to define the conditions under which their assumptions and their method are valid, as will be discussed in this note. DevelopmentThe solute continuity equation for a fixed-bed adsorber, with provision for axial dispersion, is for "dilute" systems (i.e., systems for which u is essentially constant). Assuming that only external film mass transfer is of importance during the early part of the breakthrough curve, Radcliffe et al. employed the rate law ( c -c,) at where c, is the interfacial fluid-phase solute concentration. They stated that "initially the fluid-phase concentration at the particle surface is zero." Hence, setting c,= 0, substituting Eq. 2 into Eq. 1, and letting (ac/at), be zero based on the physical argument that it is small (this assumption is valid if the solute distribution ratio, qo/co, is large), we get The analogous solution for D,=O (which is often the case, especially when the fluid phase is a liquid) is:Again, a plot of c/co vs. 0, extrapolated back to d = 1, allows one to determine k,, if E , a, L , and u are known. I Frequently, "a" is unknown and hence is lumped together with k,, and the combined quantity k g is determined. This procedure is acceptable because the product k,a, and not either one alone, is what really matters in determining the fixed-bed behavior).The question arises as to whether the assumption that c, = 0 at O= 1 is indeed correct, thereby validating this method. Consideration of the simple limiting case where the solid phase has no adsorption capacity whatsoever is sufficient t o prove that c, > 0 can easily exist near O = 1 . When fluid containing solute first contacts the solid phase, diffusion starts to occur across the fluid boundary layer. After a relatively short time (on the

Étude cinétique de l’adsorption du rouge de Congo sur une bentonite

“…Plusieurs chercheurs ont étudié le problème du transport externe afin de définir les conditions dans lesquelles les hypothèses de ce type de transfert et, par la suite, la méthode du calcul du coefficient dans le film externe, k f , sont valides (COONEY, 1991;GORDON et al, 1980;CHOY et al, 2004;MATHEWS et WEBER, 1976;RADCLFFE et THOMAS, 1982). Dans toutes ces méthodes de calcul de k f , la résistance dans le film externe est l'étape limitante au début d'adsorption.…”

Characterization of adsorption uptake curves for both intraparticle diffusion and liquid film mass transfer controlling systems

“…Many techniques to determine the effective intraparticle diffusivity (D S ) and liquid film mass transfer coefficient (k F ) have been proposed [1][2][3][4][5], such as fixed bed breakthrough curves [1,4,6], Completely Mixed Batch Reactor (CMBR) method [2,3,5,7] and shallow bed technique [5,8]. One of the most commonly used techniques is the Mass Transfer Zone (MTZ) method [6].…”

Uptake of phenol from aqueous solutions by adsorption in a Pinus pinaster bark packed bed

“…Assuming that only external film mass transfer is of importance during the early part of the breakthrough curve, solving for C as a function of z with the corresponding boundary conditions and evaluating the resulting equation at the end of the bed (z = L) results [20]:…”