Kinetics Modeling And Optimization Of L-Glutamic Acid Batch Cooling Crystallization Process

Crystallization engineering is a common operating unit in many industries,including fine chemicals,food and pharmaceuticals.Process manipulations via evaporation,cooling,and addition of solvents etc.result in supersaturated solution,so as to conduct the crystal growth and desired crystal morphology.In this paper,the cooling crystallization process of L-glutamic acid(LGA)is used to study its growth kinetics model,model parameter estimation,and state estimation,for the convenience of control system design and operation optimization.Firstly,based on the population balance model(PBM)of crystal growth process,the temporal and spatial variation of particle number density is analyzed,and meanwhile,the moment modeling method is discussed which is related to the crystal growth size,such that the relationship among the crystal growth rate,crystal size,and solution supersaturation can be effectively described.Taking into account severe nonlinearity of the crystal growth model,an automatic differentiation based sequential quadratic programming(AD-SQP)method is proposed in this paper for estimating the model parameters.By establishing the least-squares type objective function for parameter fitting,accurate and fast estimation is guaranteed by using AD to compute the gradient of the objective function.Compared to the traditional SQP based on the finite difference method,AD-SQP can significantly improve the computation accuracy while largely reducing the computation time.By simulation tests on a kinetics model of LGA cooling crystallization,it is demonstrated that AD-SQP can significantly improve the accuracy of parameter estimation while largely reducing the computation load,compared to the Markov chain Monte Carlo method(MCMC)given in the recent literature.Then,economical experiments was designed for cooling crystallization of ? form LGA.The in-situ attenuated total reflection-Fourier transform infrared(ATR-FTIR)and focused beam reflect measurement(FBRM)were used to measure the solution concentration and particle size,respectively.Using different batch data,a growth kinetic model related to ?-LGA size was established,and the model parameters were estimated by using the AD-SQP method.The experimental results show that the model identified by AD-SQP well predicts the measured data,demonstrating the validity of AD-SQP for estimating the kinetic model parameters.Finally,a comparative study on state estimation of the cooling crystallization process is carried out.The extended Kalman filtering method,unscented Kalman filtering method,and the particle filtering method are used based on a size-dependent crystal growth process model and a size-independent growth-nucleation process model,respectively.The simulation results show that the extended Kalman filtering method based on using AD for derivative computation,named EKF-AD,can give better state estimation owing to that AD computes the Jacobian matrix of such a state model accurately and quickly,and results in the minimum of estimation error bound,compared to the other methods.Hence,EKF-AD is capable of state estimation related to crystal growth and nucleation kinetics for LGA cooling crystallization process.