Dynamic modelling and optimal control of sugar crystallisation in a multi-compartment continuous vacuum pan.
Love, David John.
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The objective of this work was to determine the operating conditions which would maximise the crystallisation performance of continuous vacuum pans used in the sugar industry. The specific application investigated in detail is crystallisation of high grade product sugar (A-sugar) in a South African raw cane sugar factory. The optimisation studies are based on a detailed dynamic mathematical model of a continuous pan. Whilst this model is based on the published work of others, the selection of variables and the formulation of the equations have been structured to produce a modular model of an individual compartment with the minimum number of independent variables. The independent variables have also been selected to meet the requirements of both a state-space control formulation and those necessary for the dynamic programming technique of optimisation. The modular compartment models are linked together to model a multi-compartment pan and the steady state model is derived as a special case of the dynamic model. For the model to simulate the conditions in South African sugar factories adequately requires appropriate descriptions of sucrose solubility and growth kinetics. Given the limited applicability of published data, experiments were undertaken to determine these parameters. Sucrose solubility in impure solutions was determined in laboratory tests designed to approach equilibrium by dissolution at conditions approximating those during pan boiling. The dependence of crystal growth rate on the concentration of impurity present in the mother liquor was investigated in both laboratory scale and pilot scale batch pan boiling experiments. The primary dependence of crystal growth rate on the super-saturation driving force was determined by fitting the steady state model to results of tests on an industrial scale continuous pan. The dynamic programming technique was used in conjunction with the mathematical model to determine the operating conditions which maximise steady state crystallisation performance. Using the crystallisation parameters determined for South African conditions, this approach has shown that the conventional wisdom of running with high crystal contents in all compartments of continuous pans boiling A-massecuite is not optimum. Pans should operate at lower crystal contents in earlier compartments, only increasing to higher crystal contents towards the final compartment. The specific values depend on seed conditions, pan design and the solubility and growth kinetics. To reap the benefits of being able to determine the optimum steady state operating condition for a continuous pan, it is necessary to be able to achieve effective steady state operation under industrial conditions. This requires both a steady loading on the pan and effective control of the crystallisation conditions within the pan. To stabilise loading, a strategy has been developed which uses buffer tanks in an optimal way to damp out flow fluctuations. This strategy accommodates multiple buffer tanks in series without the amplification of disturbances that occurs with some of the simpler published techniques. The dynamic behaviour of absolute pressure control and compartment feed control were investigated in an industrial scale pan. This work has demonstrated the importance of high quality absolute pressure control and developed techniques for effective automatic tuning of pan feed controls. As part of this research, computer control systems were developed as tools to provide the appropriate monitoring and control of the experiments undertaken.