Mathematical Modeling of the Membrane Concentration of Whey by the State Space Method

Abstract

In this paper, the development of a mathematical model for the membrane concentration process and the methods for determining the design parameters of the pilot membrane (ultra-filtration) device based on tubular membrane filters are studied. The state space method has been used to compile the state and control matrices, including coefficients that have been obtained taking into account the structure of transfer functions. The experimental studies have allowed carrying out a parametric identification of the mathematical model of the membrane concentration process of whey in the membrane (ultra-filtration) device with tubular membranes. The authors have developed a set of interrelated mathematical models that make it possible to evaluate the dynamics of the membrane concentration process of whey, taking into account its technological parameters and the design peculiarities of the membrane device. The authors have carried out software implementation of the set of models and have developed methods for calculating the rational values of the design parameters of a pilot device. The main parameters of the mathematical models include high prediction accuracy (the discrepancy between experimental values and values obtained using the model does not exceed 7.8%) and simplicity of implementation in most modern software products. The effectiveness of the methods for calculating the design parameters of the membrane device is determined by their versatility in the design of pilot membrane plants based on tubular membrane filters.