Dynamic Modeling and Optimization of Batch Crystallization of Sugar Cane under Uncertainty

Fed-Batch Sucrose Crystallization Model for the B Massecuite Vacuum Pan, Solution by Deterministic and Heuristic Methods

Fed-batch crystallization is a crucial step for sugar production. In order to relate parameters that are difficult to measure (average diameter of the crystals and total mass formed) to other easier to measure parameters (volume, temperature, and concentration), a model was developed for a B massecuite vacuum pan composed of mass and energy balances together with empirical relations that describe the crystal development inside equipment. The generated system of ordinary differential equations (ODE) had eight parameters which were adjusted through minimization of relative differences between the model results and experimental data. It was solved through the function fmincon, available in MATLABTM, which is a deterministic and gradient-based optimization method. The objective of this paper is to improve the model obtained and, for this purpose, two metaheuristic functions were used: genetic algorithm and particle swarm. To compare the results, the convergence time of each algorithm was used as well as the resulting quadratic deviation. The particle swarm method was the best option among the three used, presenting a shorter execution time and lower quadratic relative deviation.

Constructing regions of attainable sizes and achieving target size distribution in a batch cooling sonocrystallization process

The application of ultrasound to a crystallization process has several interesting benefits. The temperature of the crystallizer increases during ultrasonication and this makes it difficult for the temperature controller of the crystallizer to track a set temperature trajectory precisely. It is thus necessary to model this temperature rise and the temperature-trajectory tracking ability of the crystallizer controller to perform model-based dynamic optimization for a given cooling sonocrystallization set-up. In our previous study, we reported a mathematical model based on population balance framework for a batch cooling sonocrystallization of l-asparagine monohydrate (LAM). Here we extend the previous model by including energy balance equations and a Generic Model Control algorithm to simulate the temperature controller of the crystallizer that tracks a cooling profile during crystallization. The improved model yields very good closed-loop prediction and is conveniently used for studies related to particle engineering by optimization. First, the model is used to determine the regions of attainable particle sizes for LAM batch cooling sonocrystallization process by solving appropriate dynamic optimization problems. Then the model is used to determine optimal operating conditions for achieving a target crystal size distribution. The experimental evidence clearly demonstrates the efficiency of the particle engineering approach by optimization.

Particle engineering by optimization for the unseeded batch cooling crystallization of l-asparagine monohydrate

A model-based optimization approach is proposed to obtain temperature profiles to achieve the target CSD in a batch cooling crystallization process.