Modelling and kinetics estimation in gibbsite precipitation from caustic aluminate solutions
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Precipitation of gibbsite from supersaturated caustic aluminate solutions has been investigated extensively due to its central role in the commercial Bayer plant, for extracting the alumina compound from bauxite. The primary focus of Bayer process simulation and optimisation is to help maximise the product recovery and the production of a product crystal size distribution (CSD) that meets the product specification and improves downstream process performance. The product CSD is essentially determined by the nucleation, growth and agglomeration kinetics, which occur simultaneously during the precipitation process. These processes are still poorly understood, owing to the high complexity of their mechanisms and of the structure of the caustic aluminate solutions. This research focuses on the modelling and kinetics estimation aspects of simulating gibbsite precipitation. Population balance theory was used to derive different laboratory gibbsite precipitator models, and the discretised population balance models of Hounslow, Ryall & Marshall (1988) and Litster, Smit & Hounslow (1995) were employed to solve the resulting partial integro-differential equations. Gibbsite kinetics rates were determined from literature correlation models and also estimated from the CSD data using the, so-called, differential method. Modelling of nonstationary gibbsite precipitation systems showed that error propagated with the precipitation time scale. The main contribution to the observed error was found to be from the uncertainties in the kinetic parameter estimates, which are estimated from experimental data and used in the simulation. This result showed that care is required when simulating the CSD of non-stationary precipitators over longer time scales, and methods that produce precise estimates of the kinetics rates from the experimental data need to be used.Kinetics estimation study from repeated batch gibbsite precipitation data showed that the uncertainty in the experimental data coupled with the error incurred from the kinetic parameter estimation procedure used, resulted in large uncertainties in the kinetics estimates. The influences of the experimental design and the kinetics estimation technique on the accuracy and precision of estimates of the nucleation, growth and agglomeration kinetics for the gibbsite precipitation system were investigated. It was found that the operating conditions have a greater impact on the uncertainties in the estimated kinetics than does the precipitator configuration. The kinetics estimates from the integral method, i.e. non-linear parameter optimisation method, describe the gibbsite precipitation data better than those obtained by the differential method. However, both kinetics estimation techniques incurred significant uncertainties in the kinetics estimates, particularly toward the end of the precipitation runs where the kinetics rates are slow. The uncertainties in the kinetics estimates are strongly correlated to the magnitude of kinetics values and are dependent on the change in total crystal numbers and total crystal volume. Batch gibbsite precipitation data from an inhomogeneously-mixed precipitator were compared to a well-mixed precipitation system operated under the same operating conditions, i.e. supersaturation, seed charge, seed type, mean shear rate and temperature.It was found that the gibbsite agglomeration kinetic estimates were significantly different, and hence, the product CSD, but the gibbsite growth rates were similar. It was also found that a compartmental model approach cannot fully account for the differences in suspension hydrodynamics, and resulted in unsatisfactorily CSD predictions of the inhomogeneously-mixed precipitator. This is attributed to the coupled effects of local energy dissipation rate and solids phase mixing on agglomeration process.
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