Dynamic modelling optimisation and control of lactose crystallisations: Comparison of process alternatives

A general technique is derived to formulate and solve the dynamic optimisation problems for crystallisation, in order to re-evaluate the growth rate correlations and search for the optimal cooling and heating strategies (evaporative mode only). The dynamic model of a process making α-lactose monohydrate is first revised for these operations using seed crystals: batch cooling, semi-batch cooling and heating, and continuous cooling. Experiments are conducted in 2 and 20 L crystallisers under various seeding, cooling and heating strategies to evaluate the constants in the power law function, which correlates the growth rate of the particles with supersaturation. Using a nonlinear least square method, the best curve fitting of experimental data to the model yields G = 0.007T(100(xα/xw) − solα)2.7. The value of n = 2.7, which is applicable to all operations investigated in the study. The value of k however, must be estimated for selected seeding and cooling strategies, and most importantly for the type of syrup fed to the crystalliser. Using k = 0.007 in simulations and experiments of jet-milled seeds at 1.5% seeding ratio, the experimental results agreed well with predictions before the growth became slow. A semi-batch is slightly faster than a batch process and evaporative semi-batch is much faster than cooling operation but is more difficult to control. The performance of a cooling and seeding run in continuous mode is simulated. The system reached steady state after seven residence times but the predicted particle size could only be stabilised after 100 h. The developed methodology can be applied to the crystallisation of many other substances but is not limited to the food or dairy industries.