The best objective function for seeded batch crystallization

Abstract

in Wiley Online Library (wileyonlinelibrary.com).Although many researchers have optimized the operation of seeded batch crystallization, there remains little understanding of the effect of the choice of objective function on the optimization and no consensus on which objective function is best. In this work, different objective functions for seeded batch crystallization are compared by calculating the supersaturation trajectory that minimizes each objective function and then comparing the results of each trajectory. We show that some objective functions lead to trajectories that cause excessive nucleated mass and should be avoided. We conclude that the best objective function in most cases is to minimize the nucleated mass. This also corresponds to maximizing the growth of seeds, and leads to a product with a large volume mean size. We also show that the width of the product crystal size distribution can be controlled much more effectively by manipulating seed properties than by adjusting the supersaturation trajectory.

Ensemble local kernel learning for online prediction of distributed product outputs in chemical processes

“…This is because the CSD output of batch crystallization processes is important in the production of high quality products and for determining the efficiency of downstream operations (Braatz, 2002;Chung et al, 1999;Hsu and Ward, 2013). The simulated models are based on the comprehensive moment equations.…”

“…However, even if an accurate model has been developed, its estimation performance is likely to deteriorate when the process characteristics or the operating conditions change. Moreover, the training samples with distributed product outputs often show uneven distributions (e.g., bimodal distribution) in different operating conditions of a chemical process (Braatz, 2002;Hsu and Ward, 2013;Zeaiter et al, 2006). Especially for those distributed product processes with batch operations, batch-to-batch variations may further introduce more uncertainties.…”

“…For example, as shown in Fig. 1, the molecular weight distribution (MWD) in polymerization processes (Clarke-Pringle and MacGregor, 1998;Crowley and Choi, 1998;Kiparissides, 2006;Richards and Congalidis, 2006;Takamatsu et al, 1988;Vicente et al, 2003), the crystal size distribution (CSD) in crystallization processes (Braatz, 2002;Chung et al, 1999;Fiordalis and Georgakis, 2013;Hsu and Ward, 2013), the particle size distribution (PSD) in powder industries (Crowley et al, 2000;Flores-Cerrillo and MacGregor, 2002;Immanuel and Doyle III, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces 2002; Ko and Shang, 2011;Shi et al, 2006;Zeaiter et al, 2006), and the pulp fiber length distribution in paper industries (Smook, 2002;Wang, 2000) are all distributed outputs (Wang, 2000). In polymerization processes, the MWD directly affects many end-use properties, such as thermal properties, stress-strain properties, impact resistance, strength, and hardness (Kiparissides, 2006;Richards and Congalidis, 2006).…”

“…For these complex processes with distributed outputs, it is generally difficult to develop a comprehensive first-principle model, although great efforts have been made by many researchers (Braatz, 2002;Hsu and Ward, 2013;Kiparissides, 2006;Richards and Congalidis, 2006). Moreover, a set of partial differential equations for the distributed outputs are only valid to white noise inputs.…”

Seed Recipe Design for Batch Cooling Crystallization with Application to l-Glutamic Acid

“…The operating conditions for seed recipe optimization are the same with the above model simulation as shown in Table 3. In view of that the constrained optimization in (16) and (17) is a constrained nonlinear programming problem, the sequential quadratic programming (SQP) approach in the MATLAB optimization toolbox is adopted to solve the optimal seed recipe. The main steps for seed recipe optimization are summarized as follows.…”