A Regression Model for Estimating Sugar Crystal Size in a Fed-batch Vacuum Evaporative Crystalliser

Abstract

Crystallisation occurs in a large group of biotechnological, food, pharmaceutical and chemical processes. These processes are usually carried out in a batch or fed-batch mode. Traditionally, in sugar industry, the crystals quality is examined at the end of the process. Consequently, lack of real time measurement of sugar crystal size in a fed-batch vacuum evaporative crystalliser hinders the feedback control and optimisation of the crystallisation process. A mathematical model can be used for online estimation of the sugar crystal size. Unfortunately, the existing sugar crystallisation models are not in the form suitable for online implementation. Therefore, based on these existing models and seven process variables namely temperature (T), vacuum pressure (Pvac), feed flowrate (Ff), steam flowrate (Fs), crystallisation time (t), initial super-saturation (S0) and initial crystal size (L0), 128 data sets which were obtained from a 2-level factorial experimental design using MINITAB 14 were used to obtain a simple but online-implementable 6-input regression model for estimating crystal size. The initial crystal size (L0) was found to play no significant role within the range of the studied process conditions. The performance of the model was evaluated. The coefficient of determination, R2 was obtained as 0.994 and the maximum absolute relative error (MARE) was obtained as 4.6%. The high R2 (~1.0) and the reasonably low MARE values are an indication that the proposed model can be used online for accurate estimation of sugar crystal size in a fed-batch vacuum evaporative crystalliser.