Development of a Kinetic Model for Metal Biosorption

Aerobic granules are microbial aggregates with a strong and compact structure. Liu et al. (2003a) investigated the biosorption kinetics of heavy metals by aerobic granules. Figure 11.1 shows the adsorption profiles of cadmium by aerobic granules in the course of batch tests (Liu et al., 2003a). It can be seen that the amount of cadmium adsorbed gradually increased as a function of contact time until a stable level. It had been assumed that functional groups or biopolymers on cell surface would

50 100 150 200 250 300

Contact time (min)

Fig. 11.1. Biosorption profiles of Cd2+ at different initial Cd2+ concentrations and initial aerobic granules concentration was fixed at 100 mg/l. The model prediction is shown by a solid curve (Liu et al., 2003a).

50 100 150 200 250 300

Contact time (min)

Fig. 11.1. Biosorption profiles of Cd2+ at different initial Cd2+ concentrations and initial aerobic granules concentration was fixed at 100 mg/l. The model prediction is shown by a solid curve (Liu et al., 2003a).

contribute to the binding of metallic cations by biosorbents, and heavy metal biosorption could be characterized as a physico-chemical process (Guibaud et al., 1999; Jeon et al., 2001; Pethkar et al., 2001) in a way such that where S is the available site for metal binding on aerobic granule surface, M is the free metal ions, and SM represents metal ions bound to the site, while k1 and k2 are the rate constants for the biosorption and desorption processes, respectively.

As shown in Fig. 11.1, the cadmium adsorption on aerobic granules would be subject to a pseudo first-order reversible process kinetics. In fact, a first-order reaction kinetics had been proposed for biosorptions of Ni2+ and Cr6+ by Microcystis as well as Pb2+ by fungal biomass of Aspergillus niger (Singh et al., 2001; Wang et al., 2001). Hence, the overall biosorption rate can be written as:

where C is the concentration of the soluble metal ion at time t, Cb is the apparent concentration of the bound metal ions at time t, i.e. the metal ions adsorbed by aerobic granule per unit volume of the solution. A mass balance on metal ions gives

where C0 is the initial concentration of metal ions. When the biosorption process reaches its equilibrium, equation (11.3) becomes

and equation (11.2) reduces to

Ce k2

where Cbe and Ce is the apparent concentration of the bound metal ions and concentration of free metal ions at biosorption equilibrium, respectively. Combining equations (11.2-11.5) gives dC

Integration of equation (11.6) results in

where k = k1 + k2 is termed the overall biosorption rate of the metal to aerobic granule. Substituting equations (11.3) and (11.4) into equation (11.7) yields ekt - 1

Dividing equation (11.8) by aerobic granule concentration yields a general model that describes the metal biosorption on the surfaces of aerobic granules:

where Q is the amount of metal ions on aerobic granule surface in terms of milligram metal ions per gram granules at time t, and Qe is the biosorption capacity at the equilibrium.

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