Representative mathematical modeling is essential for
understanding
the batch cooling crystallization processes. Efficient process design
and operation are relevant to achieving high-quality criteria and
minimizing variation between batches. This work first presents the
modeling of batch cooling crystallization based on online dynamic
image analysis. A flow-through microscope was used to track the temporal
evolution of the crystal population. A population balance modeling
(PBM) approach, parameter estimation, and validation were obtained
for the batch cooling crystallization of potassium sulfate in water.
The performed experiments provided new experimental data, giving dynamic
information about the crystal size throughout each run. The kinetic
model parameters for crystal nucleation and growth were estimated
using a hybrid optimization algorithm, followed by the confidence
region construction using a more exploratory particle swarm algorithm.
In the parameter estimation framework, in addition to solute concentration,
the first fourth-order moments computed throughout all experiments
were included in the objective function. A linear size-dependent growth
rate was found to capture well the dynamics of the potassium sulfate
crystal size distribution. The experimental results evidenced that
the crystal shape of potassium sulfate is predominantly constant,
allowing the adequacy of the developed model. The validated PBM was
also employed as a digital twin of the crystallization process to
develop a machine-learning-based control for the process. Then, a
surrogate model based on a recurrent neural network, called an echo
state network (ESN), was applied in a nonlinear model predictive controller
approach (ESN-NMPC). The ESN model could predict the moments of the
population balance model up to five steps (5 min) forward. The ESN-NMPC
achieved the desired control scenarios for the crystal size and its
coefficient of variation. Its performance was comparable to the controller
that uses the PBM as the internal model (PB-NMPC).
Praziquantel (PZQ) is an anthelmintic first-line drug
to treat
schistosomiasis, a neglected tropical disease strongly related to
poverty. PZQ crystalline structures and polymorphs have been studied
mainly via mechanochemical approaches. This work applies a systematic
study to investigate the polymorphism of PZQ using cooling crystallization
experiments under different conditions not yet explored in the literature
for this compound. We accessed all forms previously reported so far
obtained via mechanochemistry and the hydrate found through supercritical
CO2 processing. A novel dimethylacetamide (DMA) solvate
was obtained, and a new form was discovered after desolvation of the
DMA solvate by aging and exposure to water-vapor atmosphere. Toluene
and triethylamine were solvents capable of enabling the formation
of different forms depending on the employed experimental condition.
A new form was discovered using triethylamine as solvent, which differs
from all known polymorphs. The results of this work demonstrate that
solvent selection and variation in the rate of supersaturation generation
can generate forms obtained from more complicated techniques as well
as potentially finding new forms.
Direct contact evaporators are nonisothermal bubble columns where a hot gas, usually obtained by combustion, is used to heat and vaporize the solvent of a given solution that needs to be concentrated. The design of such equipment has been relied on experimental data or on a simplified method that assumes that the gas leaves the evaporator at equilibrium with the liquid phase, giving no information about the necessary bubbling height to attain such equilibrium conditions. Recent advances in the heat and mass transfer processes during the formation and ascension of superheated bubbles together with simple mass and energy balances in the liquid phase and gas distributor system were used to develop a more detailed design procedure. The accuracy of both design procedures are compared to available experimental data in a direct contact evaporator operating in semibatch mode. The new design method agreed well with the experimental data.
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