Prediction And Optimization Of Crystal Size Distribution In Crystallization Processes Based On Population Balance Model

In recent years the crystallization process plays an important role in industries such as pharmaceutical,microelectronics,and food industries,besides it has a prominent impact on the control of product quality(particle size distribution).The main difficulty in crystallization process is to produce a uniform and reproducible desired particle size distribution.In order to solve the related problems,this paper adopts the model-based crystallization process control method oriented with optimization problem,in which the optimal temperature control profile that has guiding significance for crystallization process can be calculated,to achieve the improvement of product quality.The population balance model is used to model the crystallization process to dynamically track the evolution of the crystal size distribution.The population balance model involves the solution of the nonlinear integral differential equation.In the size-dependent growth model,the crystal size distribution of the final product is directly solved by the method of characteristic.When the model is simplified,there could be analytical solutions.In order to extract the predicted crystal size distribution at each discrete time,the finite volume high resolution algorithm is used to solve the population balance model.Three groups of crystallization experiments under different operating conditions were designed to estimate the parameters of the size-dependent growth model,and the parameters were estimated in two different approaches.One parameter estimation method based on optimization problem is introduced.The accuracy of parameter estimation is improved in an iterative way according to each experimental data.The other method based on Markov chain Monte Carlo sampling method solve the problem that parameter expectation is difficult to solve within the integral and can get the parameter uncertainty at the same time.In the crystallization process of ? form L-glutamic acid,the optimal temperature control curve was calculated by optimizing the supersaturation of the crystallization process in order to achieve the desired crystal size distribution.Consequently,the crystal growth process optimization control based on constant supersaturation was implemented.The optimized constant supersaturation value can keep the crystal grow steadily in the metastable zone to avoid nucleation.The crystal size distribution of the experimental products,obtained by the controlled solution temperature curve to keep the constant supersaturation,were analyzed by the image processing system.On this account,the effectiveness of the control process based on the optimal constant supersaturation crystal growth process was proved.A large number of small crystals would often accumulate in simple cooling crystallization experiments,so the growth-dissolution of the crystal size distribution control strategy is proposed.In order to achieve the desired crystal size distribution in the each stage of the crystallization processes,the weights of the small crystals are increased to suppress the formation of small crystals,and the rising temperature is introduced into the process.Hence the optimal temperature curve is calculated to ensure the desired distribution of product and suppression of the fine crystals.The validity of the strategy is verified by comparing the experimental results.