ION EXCHANGE MODELING ON MIXED CATIONITE H+, NA+ IN WATERPROOF PROCESSES

A mathematical model of multicomponent ion exchange on mixed cationite (H+, Na+) in cartridges produced by the Russian company “AquaBrite” has been developed. The purpose of this process is to maintain the total and carbonate hardness, as well as the pH value of water within the norms of its use in various systems. The model uses the author's method of describing the matrix of multicomponent diffusion coefficients for ion exchange in the aqueous phase. To calculate the matrix of multicomponent diffusion coefficients, the data on Einstein diffusion coefficients, which are determined through ionic conductivities of corresponding ions, are used. Mass transfer coefficients were determined using known criterion equations in matrix form. The relations of diagonal and non-diagonal elements of the matrix of mass transfer coefficients were analyzed. The possibility to neglect non-diagonal elements under certain conditions is shown.The solution of the system of equations of the mathematical model is nonstationary profiles of concentrations of Ca2+, H+, Nа+ , HCO 3 - ions in the aqueous phase and in the ionite phase. The mathematical model contains 4 parameters, the values of 3 of which were determined in the previous work, and one was identified from experimental data. It was found that due to extremely low concentrations of hydrogen compared to the concentration of other ions for the pH fixed in the experiment, the numerical solution of the system of equations of the mathematical model gave a significant error. Therefore, it is proposed to use the chemical equilibrium condition to determine the pH of water at the cartridge outlet. The results of modeling allowed to reveal the peculiarities of ion concentration change at the cartridge outlet, including in the presence of bypass. Modeling results are in satisfactory agreement with experimental data, which gives grounds to recommend the model for use in solving design and verification problems in the field of ion-exchange processes and apparatuses for water softening.