MATHEMATICAL MODELING AND EXPERIMENTAL STUDIES OF MEMBRANE CONCENTRATION IN APPARATUSES WITH THE WITHDRAWAL OF THE POLARIZATION LAYER

A mathematical model of membrane concentration using the Automation Control theory is proposed . The model can be used for describing membrane processes in different kinds of apparatuses that withdraw polarization layer. The model considers technical, constructive and conditional parameters of the membrane apparatus itself and those of the withdraw device. The information scheme of the described model is presented, consisting of two conventional elements - the membrane module and the withdrawal device, which is a basic representation of apparatuses that withdraw polarization layer. Also, the information schema contains information relations. In addition, to connect the membrane module and the withdrawal device, the scheme has been modified with intermediate parameters which are output for the membrane module and input for the withdrawal device. A technique for calculating the transfer function of a system is described. Comparative evaluation of the values obtained using the given model and the experimental values of the industrial pilot membrane apparatus have been done. The difference between experimental data and observational studies with different parameters of the process does not exceed 10%. Based on the evaluation results, it has been concluded that the proposed mathematical model describes the modeling object adequately and has sufficient predictive power to be used in the calculation of industrial installations. Based on the results of experimental studies of the industrial pilot plant, theregression equation has been obtained. The regression equation connects the concentration of the withdrawn polarization layer with technological parameters, whose rational values have been obtained.