Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 1: Modeling with Method of Characteristics

Abstract

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.

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 2: Structure Design for State Estimation with Secondary Measurements

“…The model with parameters of Case 1 in Table 1 ( 29 ) are considered for scenarios i, ii, and iii. Estimation performances with Case 1’s and Case 2’s parameters are tested for scenario iv.…”

“… The birth rate by agglomeration can be evaluated by means of the approximation of the integral A detailed analysis of the performance of this algorithm can be found in the paper by Porru and Özkan. 29 …”

“…In particular, a subset of the distinguishable states is chosen as innovated states, and the evolution of the CSD, which is not distinguishable, is evaluated by means of the PBE in open loop mode. The PBE accounts for crystal growth, nucleation, and agglomeration, and it is numerically solved with the method of characteristics (MOC), 29 which guarantees accuracy and acceptable resolution time. The measurements are processed with the Geometric Estimator (GE) 28 which offers simple tuning guidelines and implementation, in the understanding that the performance mostly depends on the estimation structure rather than the algorithm.…”

Dynamic Density Estimation in Heterogeneous Cell Populations

“…Note that the actual measurement noise acts on single cell measurements and not directly onto the density function n y . Therefore, (7) does not give an exact representation of the measurement noise. A classical particle filter can now be implemented for the obtained discretized system.…”

Modeling of Nucleation, Growth, Dissolution, and Disappearance of Paracetamol in Ethanol Solution for Unseeded Batch Cooling Crystallization with Temperature-Cycling Strategy

“…3,19,20 Most PBMs cannot be solved analytically except for very simple cases. Therefore, various techniques have been employed to solve the PBM numerically, which include method of moments, [21][22][23] method of characteristics, 24,25 finite-element method (FEM), 26 finite-volume method (FVM), [27][28][29] and the conservation element/solution element (CE/SE). 17,30 Qamar et al 31 compares various numerical methods to solve the PBM, and the CE/SE scheme demonstrated "much better performance" among tested approaches.…”