Fed-batch sucrose crystallization model for the B massecuite vacuum pan, solution by deterministic and heuristic methods

Abstract

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.