Dynamic Multi-Objective Optimization of Batch Chromatographic Separation Processes

This contribution presents a novel offline dynamic multi-objective optimization framework for high-pressure liquid chromatographic (HPLC) processes in batch elution mode. The framework allows for optimization of general elution trajectories parametrized with piecewise constant control signals. It is based on a simultaneous method where both the control and state variables are fully discretized in the temporal domain, using orthogonal collocations on finite elements, and the state variables are discretized in the spatial domain, using a finite volume weighted essentially non-oscillatory (WENO) scheme. The resulting finite dimensional nonlinear program (NLP) is solved using a primal-dual interior point method and automatic differentiation techniques. The advantages of this open-loop optimal control methodology are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography (HIC) system. For a bi-objective optimization of the target component productivity and yield, subject to a purity constraint, the set of Pareto solutions generated with general elution trajectories showed considerable improvement in the productivity objective when compared to the Pareto set obtained using conventional linear elution trajectories