Ion Exchange Modeling on Mixed Catonite 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 is 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, data on the Einstein diffusion coefficients, which are determined through the ionic conductivities of the corresponding ions, are used. The mass-transfer coefficients are determined using known criterion equations in matrix form. The relationships of the diagonal and non-diagonal elements of the matrix of mass-transfer coefficients are 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 the nonstationary profiles of the concentrations of Ca2+, Н+, Nа+, and HCO $$_{3}^{ - }$$ ions in the aqueous phase and in the ionite phase. The mathematical model contains four parameters, the values of three of which were determined in the previous work, and one of which is identified from experimental data. It is found that due to the 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 gives a significant error. Therefore, it is proposed to use the chemical equilibrium condition to determine the pH of the water at the cartridge outlet. The results of modeling allow us to reveal the peculiarities of ion concentration change at the cartridge outlet, including in the presence of bypass. The modeling results are in satisfactory agreement with the 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.