Phenomenological based Semi-Physical Model for the Milk Evaporation Process

The aim of this study was present a Phenomenological Based Semi-physical Model (PBSM) for the milk evaporation process. The evaporation is the elimination of solvent in form of water steam from a solution. In the dairy industry, the evaporation is a pretreatment for the powder milk processes that reduce the cost of the drying process, storage and transport. Thus, an appropriated mathematical model is necessary in order to get a good control and optimized process of milk evaporation, which allows obtaining a high-quality product. Previous studies have presented mathematical models for the evaporation process. However, the majority of these models are based on maintaining constant values such as the thermal properties of fluids, latent heat of vaporization and global coefficient of heat transfer, among others and this means that there will be high errors of predictions. The aim of this model was to predict the temperature, concentration and milk level in the evaporator. The model obtained was solved using the Runge-Kutta method with the software ＂LABVIEW 2011＂ and it was quantitatively validated with experimental data from a real process using the absolute mean error. The experimental data of temperature, concentration and milk level in the evaporator were obtained applying step-like disturbances in the process variables: vacuum pressure in the evaporation chamber, steam flow and milk feeding flow. The quantitative validation showed that the obtained model can predict satisfactorily the dynamic behavior of the target variables of the milk evaporation process because the error was less than 5%.