This paper develops a new simulation
model for crystal size distribution
dynamics in industrial batch crystallization. The work is motivated
by the necessity of accurate prediction models for online monitoring
purposes. The proposed numerical scheme is able to handle growth,
nucleation, and agglomeration kinetics by means of the population
balance equation and the method of characteristics. The former offers
a detailed description of the solid phase evolution, while the latter
provides an accurate and efficient numerical solution. In particular,
the accuracy of the prediction of the agglomeration kinetics, which
cannot be ignored in industrial crystallization, has been assessed
by comparing it with solutions in the literature. The efficiency of
the solution has been tested on a simulation of a seeded flash cooling
batch process. Since the proposed numerical scheme can accurately
simulate the system behavior more than hundred times faster than the
batch duration, it is suitable for online applications such as process
monitoring tools based on state estimators.
This
work investigates the design of alternative monitoring tools
based on state estimators for industrial crystallization systems with
nucleation, growth, and agglomeration kinetics. The estimation problem
is regarded as a structure design problem where the estimation model
and the set of innovated states have to be chosen; the estimator is
driven by the available measurements of secondary variables. On the
basis of Robust Exponential estimability arguments, it is found that
the concentration is distinguishable with temperature and solid fraction
measurements while the crystal size distribution (CSD) is not. Accordingly,
a state estimator structure is selected such that (i) the concentration
(and other distinguishable states) are innovated by means of the secondary
measurements processed with the geometric estimator (GE), and (ii)
the CSD is estimated by means of a rigorous model in open loop mode.
The proposed estimator has been tested through simulations showing
good performance in the case of mismatch in the initial conditions,
parametric plant-model mismatch, and noisy measurements.
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