(131c) Stochastic Optimal Control of Batch Crystallization Applying Ito Process

Batch crystallization is one of the most important industrial separation and purification processes. Being a particulate process, crystallization is modeled in terms of population balance equations which include kinetics of nucleation, growth, aggregation and breakage.  Analytical solutions to PBE’s are available only for simplified kinetics and known initial size distribution and hence development of numerical methods for solving complex process kinetics was a major area of interest. It mainly consisted of estimation of kinetic parameters for efficient process operation using earlier experimental data. However, the uncertainties associated with these parameters were given little importance. Minimization of operation costs and the enhancement in product quality have been a major concern for all industrial processes. Predetermined operating conditions can help in achieving the goals for efficient production. These conditions can be determined using an optimal control analysis of the batch crystallization process. Optimal control problems are characterized by determination of time varying profiles for process parameters. Batch crystallization is associated with parameters like temperature, supersaturation and agitation. Some process parameters are functions of fundamental properties of the system into consideration like solubility, crystal lattice. Thus, the process parameters can have various physical and engineering sources of uncertainties associated which in turn would prevent the real process operation to be optimal. These uncertainties result in dynamic uncertainties due to the unsteady state nature of the process.   This paper presents a novel approach to optimal control problems in batch crystallization.  The uncertainties and variabilities are modeled by stochastic processes called Ito processes.  The resulting stochastic optimal control problem is solved using Ito’s Lemma, stochastic calculus, and stochastic maximum principle.