Dynamic Optimization of a Batch Cooling Crystallization Process

Abstract

Dynamic optimization techniques are applied for the optimization of crystallization processes. These obtain promising results, especially for difficult industrial applications with significant heat effects, concentrated slurries, and state constraints. Here we introduce some concepts that focus not only on the optimization strategy but also on the practical implementation. As a case study, we consider a batch crystallization process, which has been studied in the field. The dynamic model includes not only moment equations but also thermodynamic equations to make the model closer to practical operating characteristics. Significant differences between this research and previous work are that we incorporate the heat-transfer components and control directly into the model. After demonstrating in plant that the dynamic model is valid in both model formulation and parameter identification, we optimize this model. The objective is to maximize the final crystal size in order to obtain the highest purity of the desired product. Here, we use the package DynoPC, which includes recently developed dynamic optimization strategies. The dynamic model, consisting of differential and algebraic equations, is discretized using collocation on finite elements. The resulting nonlinear programming problem is solved with a reduced successive quadratic programming algorithm. The results are then compared with those obtained using a maximum principle for minimum operation time and with previous plant operation profiles. The optimal results show important improvements as the mean size of the crystals is 50% larger than the ones obtained under original operating conditions.

Control of batch cooling crystallization processes based on orbital flatness

“…Jones (1974) applied Pontryagin's maximum principle to obtain an optimal cooling policy. Dynamic optimization was applied, for example, in Miller and Rawlings (1994) and Lang et al (1999). This approach handles path constraints and final time constraints.…”

Random Sampling-Based Automatic Parameter Tuning for Nonlinear Programming Solvers

“…In addition to generic moment equations, a nucleation rate equation is included for the batch crystallization process. 19 In order to maximize crystal length, a dynamic Table 9. 20 In this work, the simultaneous approach is applied to the crystallization problem and the generated NLP is solved with IPOPT.…”

A study on the effect of the polymeric additive HPMC on morphology and polymorphism of ortho-aminobenzoic acid crystals

“…Tailor-made and structurally related additives can promote nucleation of certain polymorphs because of structural similarities between them [22] [23]. Additives can be absorbed on surfaces (templates) and induce heterogeneous nucleation of the target polymorph without the risk of incorporation in the crystal structure [24] [29]. They can also delay nucleation [30] and promote the formation of very small crystals [31], sometimes in an amorphous form [14].…”