Mathematical modeling of the kinetics of gibbsite extraction and kaolinite dissolution/desilication in the Bayer process

An unsteady-state mathematical model incorporating the rates of external mass transfer, intraparticle diffusion and chemical reaction has been developed to describe the extraction of gibbsite from bauxite particles allowing for the competitive reactions - gibbsite and free caustic, and kaolinite and free caustic accompanied by the reprecipitation of the dissolved silica (as sodalite). The governing partial differential equations have been reduced to ordinary differential equations by the method of orthogonal collocation and solved using a standard variable step integration algorithm in terms of two parameters characteristic of the nature of the bauxite. The usefulness of the model is demonstrated by providing examples of cases where it has been applied to elucidate process performance under conditions that are envisaged for the future, or to gain ar insight into reasons for certain apparently anomalous trends in process stream quality in terms of silica concentrations.