Multi-scale modelling of Gibbsite calcination in a fluidized bed reactor

Abstract

The alumina industry provides the feedstock for aluminium metal production and contributes to around A$6 billion of Australian exports annually. One of the most energy-intensive parts of alumina production, with a strong effect on final product quality, is calcination or thermal decomposition, in which gibbsite powder is converted into alumina. Industrially, gibbsite calcination is conducted in bubbling or circulating fluidized beds. Better modelling of fluid bed calciners is needed to improve process design, control and operations. Multi-scale models, which account for phenomena interacting across different length and time scales, are increasingly being used to describe complex, multidisciplinary, nonlinear, non-equilibrium processes, including fluidized bed reactors. In order to attain more insight into the gibbsite calciner, from a multi-scale viewpoint, this investigation has been conducted in five steps as follows.Firstly, the possibilities for developing a multi-scale model for the fluidized bed calcination of gibbsite are investigated, followed by recommendations on promising directions. The key elements of the multi-scale approach that is considered were: (i) identification of the relevant scales of interest for bubbling and circulating fluidized bed reactors; (ii) characterisation of the dominant phenomena, modelling approaches and available data at each scale; (iii) an integrated communication framework to link the scales of interest, and briefly (iv) experiment design and model validation for multi-scale models. A conceptual model having three scales (particle, volume element / cluster, and vessel) was proposed and the information flows between the scales were outlined. There are several possibilities for the sub-models used at each scale, and these have been noted.Secondly, as a part of the particle scale modelling efforts, a 1-D mathematical model describing the calcination of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially-distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation was developed by closely iimatching experimental data reported previously in the literature. Estimated values of the transformation kinetic parameters are reported.The reaction order with respect to water vapour concentration was negative, meaning that the water vapour that is produced impedes further gibbsite calcination, which is in agreement with previous kinetic studies. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction is shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.Thirdly, a new variation on the unreacted shrinking core model has been developed for calcination and similar non-catalytic thermal solid-to-gas decomposition reactions in which there is no gaseous reactant involved and the reaction rate decreases with increasing product gas concentration. The numerical solution of the developed model has been verified against an analytical solution for the isothermal case. The model parameters have been tuned using literature data for the calcination of gibbsite to alumina over a wide range of temperatures. The model results for gibbsite conversion are found to agree well with the published experimental data. Predictions of the non-isothermal unreacted shrinking core model compare well with the more complex, distributed model developed in the previous step.Fourthly, a multi-stage, multi-reaction, shrinking core model is proposed for the simulation of solid-to-gas reactions with self-inhibiting behaviour and in which the build-up of internal pressure caused by the product gas may alter the reaction pathway in a way that favours one pathway over others. This model emphasises the role of the produced gas, not only in mass transfer, but also in the reaction kinetics. It includes parallel and series reactions, allowing for the formation of an intermediate species. The model has been applied to the conversion of gibbsite to alumina, including the formation of intermediate boehmite. Modelling results for gibbsite conversion, boehmite formation and its subsequent consumption, as well as alumina formation, agree well with literature data; the corresponding kinetic parameters are estimated for all reactions. Significantly, the experimentally-observed plateaux in the particle’s temperature history are predicted by the model. The role of heating rate and particle size on boehmite formation is also evaluated using the model, and is in agreement with observation.Fifthly, a simplified version of the multi-scale model proposed in the first step has been developed. Particle scale models are valuable for analysing kinetics, understanding behaviour and some experimental design of gas-solid reactions. However, engineers are always interested in practical, equipment-scale models that can predict the performance of operating units in different scenarios. In this part of the research, some fluid bed reactor phenomena are described along with their modelling methodologies, and then a two-scale model combining one of the particle scale models with a simple reactor scale model is described. The simple reactor model consists of a collection of ideal mixed volumes connected in series. In each volume element, the reaction rate from the particle scale is linked into material and energy balances at the reactor scale. The number of volume elements is variable and thus able to simulate reactor behaviour from an ideal CSTR to a near-ideal PFR, and also for flow regimes in between them. In spite of the simplicity, the solid residence time distribution and gas flow rate variation are accounted for at the reactor scale. Even though a general discussion of fluid bed reactors is presented, gibbsite calcination is again considered for the case study, the same as for the other steps in the project. The developed two-scale model predicts the gas and solid temperature profiles, trends in overall gas flow rate and water vapour pressure, and alumina and gibbsite concentration profiles through the reactor. Sensitivity analyses are conducted into the number of volume elements and the solid throughput rate.Finally, potential research opportunities for multi-scale modelling of fluidized bed reactors are outlined.