Nonlinear controller for batch crystallization: Development and experimental demonstration

Abstract

Particle-size control in crystallization is important for product quality control, as well as plant productivity. Since rapid crystallization traps impurities within the crystal, it is desirable to manipulate solution desupersaturation rates so as to maintain quality. However, the crystal-size distribution (CSD) is influenced by supersaturation levels through complex nucleation and growth kinetics as well as through particulate phenomena such as agglomeration and attrition. Plant productivity is severely hindered when excessive fines are produced since the solid-liquid separation system must be slowed to compensate.Significant advances have been made toward the development of dynamic CSD measurements, however, these sensors are not as yet widely accepted by industry. As a result, the conventional practice involving the control of seeding or desupersaturation profiles rather than CSD continues. The preferred CSD measurement is obtained from laser light scattering instruments, since these avoid the plugging problems associated with Coulter counters, require little calibration and are easily automated (Rawlings et al., 1993). However, combining the process and light scattering measurement model into a form suitable for model-based control is difficult.Consider a crystallization and measurement process:where for the process model The full identification of a crystallization process according to model Eqs. 1 and 2 is restricted by structural and parametric plant/model mismatch, mathematical conditioning problems and mixing pattern uncertainties. Structural mismatch is introduced in Eq. 1 by the size-axis discretation scheme used to reduce the population balance to an ODE and into Eq. 2 since the measurement itself is a subset of the process states. Parametric and structural mismatch occurs in Eq. 1 due to the difficulty in modeling, as well as identifying time-varying rate mechanisms representing nucleation, growth, agglomeration, breakage, and so on (Farrell and Tsai, 1994). Finally, the computations associated with reducing the Laser measurement to CSD are not only mathematically ill-conditioned, but also dependent on hydrodynamics, particle shape, spatial distribution of the suspended particles around the sensor and the focal plane of the laser beam (Rawlings et al., 1993;Boxman, 1992).To avoid some of the conditioning problems associated with developing a model identification and control scheme based upon Eqs. 1 and 2, Witkowski et al. (1990) proposed using the bulk crystallizer transmittance measurement in place of Eq. 2 as a CSD related secondary measurement. Transmittance can be shown to have a one-to-one relationship to the projected crystal area (second moment). Using dynamic transmittance data together with concentration measurements, Rawlings et al. (1993) discuss the successful kinetic model identification of a batch KN0,-H,O crystallizer. Using the potassium nitrate model, Miller and Rawlings (1994) formulated a model-based approach to the open-loop computation of the cooling profiles that maximizes final...

Estimating Average Particle Size by Focused Beam Reflectance Measurement (FBRM)

“…For many applications this distinction is not important because the relevant process variable can be correlated with some aspect of the chord data, and accurate particle sizing is not specifically required. The instrument×s rapid in-line analysis make it attractive to workers modelling the kinetics of flocculation [29,35] or crystallisation [13,18,20] by population balance. However, in dynamic modelling, both accurate sizing and counting of particles are desirable for the estimation of model parameters, and the raw chord length data may not be suited to this.…”

Modeling and Experimental Analysis of PSD Measurements through FBRM

“…Several research groups have used the method to monitor crystal size distributions on-line [16±18]. Attempts to exploit the measurement for control purposes have already been reported [19,20]. In industrial applications, FBRM has proven its reliability in tracking qualitative trends in particle population [21].…”

In-line FBRM Monitoring of Particle Size in Dilute Agitated Suspensions

“…Overall, the FBRM probe is ideal for industrial utilisation as a quality and process control device, providing rapid and accurate data accumulation, with the collected information requiring minimal attention from the plant operators [6,7]. Work published to date on the FBRM system has attempted to either directly relate the measured chord length data to the particle size data [3,4] or, more successfully, to simply correlate it to properties dependent on particle size [5,7,8]. Others have investigated some of the relevant operating issues associated with its use [9,10].…”