THE MODELING OF COMPETITIVE SORPTION EQUILIBRIA USING STATISTICAL THERMODYNAMICS

In most cases adsorption onto activated carbon is modelled with no con sideration of competing or contaminant species. A recent awareness abo ut this problem of fouling of adsorbents has led to new modelling effo rts, such as the formulation of empirical expressions for multi-compon ent isotherms. All these so-called empirical models suffer from the di sadvantage that their parameters cannot be used to extrapolate beyond the range of measured data. A brief review of existing methods is prov ided, so as to indicate the enormous lack of knowledge in this field. The principles of statistical thermodynamics are used to simulate adso rption onto heterogeneous surfaces in terms of a distribution of energ ies for the active sites, interactions between adsorbed species, the s ize of adsorbates, the reversibility of adsorption and the selectivity of adsorption. Any adsorption process at equilibrium is described mat hematically in terms of the probabilities of collision of a species wi th the surface, the availability of a site, and the exchange of an ads orbed species with an adsorbing species. In this way the energy distri bution and the interaction between species can be determined. These pa rameters bear a fundamental relevance, and can then be used to predict competitive adsorption for complex systems where available data are i nadequate. The competitive adsorption of metal cyanides onto activated carbon is considered as a case study. It is shown that these calculat ions are complex in view of the numerous statistical calculations invo lved. However response surface modelling techniques such as neural net works can be used to approximate the surface predicted by the rigorous calculations, which can then be incorporated in the dynamic model sim ulators. These very powerful theoretical techniques are relatively new in process engineering, but hold much promise for the complex systems encountered in minerals processing.