Mathematical modeling and optimal control strategy development for an adipic acid crystallization process

The aim of this work is to propose ways to improve crystallization processes performance, choosing the batch crystallization of adipic acid as a case study. In this process, representative of many industrial systems, the supersaturation necessary for the crystals to appear and grow is generated by the cooling of the solution. The proposed approach involves the process modeling and its further optimization in a real-time fashion. The modeling of the crystallization process is presented and it takes into account the contribution of agglomeration. The influence of the process variables on the final crystal size distribution (CSD) and on the quantity of solids is analyzed. This analysis is fundamental because it gives evidence of the role and magnitude of each variable as well as their interaction in the process performance. The optimization of the process is then considered, and it can be focused on finding the optimal cooling trajectory through optimal control theory. A study of the best way to postulate the problem is considered, taking into account the constraints and which is the best performance criterion to be used. The problem is postulated as a non-linear programming problem, which is solved through sequential quadratic programming (SQP). The non-linearity feature of the problem is strongly increased by the agglomeration contribution. The results have shown that the developed mathematical model is a good representation of the process, able to reproduce results from the literature. The optimization problem has shown to be strongly non-linear and difficult to postulate. Nevertheless, the solutions obtained through the optimization study, though the global optimum may not be guaranteed, lead to a substantial improvement of the end product quality, expressed in terms of the mean size and the variation coefficient.