Equilibrium, kinetic and dynamic modelling of biosorption processes

This chapter presents an overview of the different modelling approaches used to represent the equilibrium data of heavy metal biosorption, the kinetics in batch reactors and the dynamics in continuous-flow configurations. For each category the attention was focused on the model architecture as a function of the degree of complexity adopted for the representation of the mechanisms involved. Equilibrium distribution of metals between solid biophase and aqueous phase strictly depends on the operating conditions of the system (mainly pH, ionic strength and solution composition), which influence the state of dissociation of the active sites, the intensity of electrostatic effects, the speciation of metals in solution and their competition. Biosorption isotherms can be represented by empirical and mechanistic models. The first are simple mathematical relations (such as Langmuir and Freundlich isotherms and their extensions) able to represent experimental trends but without any interpretative or predictive intent. The latter are theoretically derived assuming a set of reactions between biosorbent active sites and ionic species in solution: these models can not only represent but also interpret and predict the effect of the most influencing factors on equilibrium metal distribution. Mechanistic models can also include electrostatic effects due to the electric double layer at the interface, heterogeneity of biosorbent sites and non ideal competition among metals. Time profiles of metals in both batch and continuous configurations can be determined by different limiting rate steps depending on the nature of the metal-biosorbent system and the specific operating conditions adopted during the tests. Metal biosorption generally occurred by the following steps: bulk transport; film diffusion through the hydrodynamic boundary layer around the biosorbent surface; intraparticle diffusion through the biophase; chemical reaction of binding with the active sites. Kinetic data in batch reactors are generally represented by empirical models neglecting mass transfer effects (pseudo-first and pseudo-second-order models), while phenomenological models including the description of mass transport steps limiting the global rate of sorption are less diffuse. Continuous applications of heavy metal biosorption are generally performed in fixed-bed reactors: mechanisms operating in these systems are axial dispersion in the direction of the liquid flow, film diffusion resistance, intraparticle diffusion resistance, and sorption kinetic at the adsorbent surface. Rigorous models taking in consideration all these mechanisms present mathematic and numerical difficulties (especially due to the non linearity associated to equilibrium models) and require independent experiments and/or reliable engineering correlations to estimate the numerous equilibrium, transport and kinetic parameters to avoid the loose of the physical significance of the mechanistic parameters. For these reasons approximate modelling approaches have been widely used (such as Thomas, and Adams-Bohart models), which allow to model breakthrough behaviour without the need of numerical solution and with immediate practical benefits in process development and design.