Control of Batch Crystallizers

Batch crystallizers are used extensively for crystallization procedures that are of small capacity and have a high added value, and often when multipurpose reactors are used for the crystallization process. Therefore the control of a batch process differs considerably from that of a continuous process. In addition, although a batch crystallizer can be described by a similar model to the continuously operated crystal-lizer, because of the inherently nonstationary process conditions and the strong dominant role of the start-

Figure 8 Input-output structure for a multivariable controller (Eek, 1995).

Figure 9 (A) Temperature profiles for a batch cooling KNO3-H2O crystallizer and (B) the resulting supersaturation in the crystallizer for different cooling policies (Miller and Rawlings, 1994).

Figure 8 Input-output structure for a multivariable controller (Eek, 1995).

Figure 9 (A) Temperature profiles for a batch cooling KNO3-H2O crystallizer and (B) the resulting supersaturation in the crystallizer for different cooling policies (Miller and Rawlings, 1994).

up phase on the product quality process conditions, a completely different control strategy must be followed.

Literature references to the control of batch crystallization processes are mainly directed towards finding cooling or supersaturation profiles (a supersaturation versus time trajectory) that optimizes the product quality of the crystals profile.

Cooling profiles have been determined directly from MSMPR crystallization models with some additional simplifications. Other studies use simulation to calculate a cooling profile that maintains a constant supersaturation or an optimal control theory in combination with an objective function for the final product. The problem with these studies is that they all are limited to strict crystallizer configuration (MSMPR, no fines removal), and simple kinetic models. In addition they are unable to incorporate constraints in the process variables.

An alternative approach is to solve the general multivariable optimal control problem as a nonlinear programming problem.

Using this approach an optimal cooling programme can be calculated. An example is shown in Figure 9, in which a natural, a linear and an optimal cooling profile are given together with the resulting supersaturation profile for a KNO3-H2O system crystallized in a 3 L cooling crystallizer. The curves were determined using a first principle model in which four parameters were estimated using experimental data, maximizing the terminal seed size. Constraints were imposed on the crystallizer temperature and on the production yield. Experimental verification of the optimal cooling profile gave a 9% increase in the terminal seed size over that with linear cooling, and an 18% increase over that with natural cooling.

The determination of optimal cooling profiles is, however, not sufficient for an optimal operation of a batch crystallizer. Uncertainties in the start-up phase and in the crystallization model make the need for on-line measurements and a feedback control relevant. Depending on the reproducibility of the startup phase, on line optimization procedures might be desirable for optimization of the process.

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