Bifurcation-Aware Optimal Control of Nonlinear Reactive Crystallization Systems for Enhanced Productivity and Dynamic Stability

Abstract

Lakshmi. N. Sridhar

Reactive crystallization systems are widely used in pharmaceutical manufacturing, specialty chemicals production, and advanced materials processing, where crystal quality, process stability, and productivity are critically important. However, the strong nonlinear coupling between nucleation, crystal growth, and thermal feedback can generate complex dynamic behavior, including steady-state multiplicity, oscillatory instability, and limit cycle oscillations, which significantly affect industrial operability and product consistency. In this work, a nonlinear reactive crystallization model incorporating Arrhenius-type thermal effects, nonlinear nucleation kinetics, and reduced-order crystal surface area closure is investigated using bifurcation analysis and dynamic optimal control.

Bifurcation analysis was performed using MATCONT with the Damköhler number as the continuation parameter. The analysis identified a limit point and two supercritical Hopf bifurcation points, indicating the existence of stable oscillatory operating regimes. An optimal control framework was subsequently developed in Pyomo, where the Damköhler number was treated as a time-dependent control variable and the cumulative crystal mass production was maximized over a finite operating horizon.

To improve reactor operability, a Hopf-bifurcation-avoidance constraint was incorporated into the optimization problem. The bifurcation-aware strategy produced higher overall productivity compared to unconstrained operation by preventing inefficient oscillatory behavior. The results demonstrate that integrating nonlinear dynamics with optimal control can significantly enhance process stability, crystal production, and operational efficiency in industrial reactive crystallization systems.

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