Donnan Dialysis (DD) utilizes ion exchange membranes that allow a selective transport of target ions from a feed solution to a concentrated receiver solution. This technology is attractive for its significant advantages of low energy consumption and simple operation. The overall rate of DD mass transfer is determined by the sum of two resistances: a resistance related to the ion diffusion through the membrane and a resistance related to the mass transfer between the bulk solution and the membrane interface. The kinetics of the system can be divided into three transport mechanisms: pure boundary layer diffusion (BLD), pure diffusional membrane transport (MD) and a mixed regime where both mechanisms are effective.

The objective of the research was to develop an automated computational model that can predict nitrate, bicarbonate and sulfate concentration profile and transport mechanism in DD processes. Experiments were conducted in a batch dialyzer in sole- and multi-component feed solutions. NaCl receiver solutions (100 and 1000 mM) were used. Various operating parameters were applied including: initial concentration of the target ions (0.5-250 mM), Reynolds number (288-7475), and feed to receiver volume ratio (1.0-6.3).

The kinetics of the DD mass transfer was described by the Nernst-Planck formulation of diffusive fluxes as well as the mass balance and electro-neutrality governing the overall driving force of the process. The kinetics equations were algorithmized in MATLAB^? 2021a (MathWorks Inc) computing platform.

Initially, the BLD and MD coefficients were numerically extracted from the experimental data obtained in this research along with data obtained in the Rabin Desalination Laboratory since 2014. The relationship between the experimental conditions and the kinetic coefficients were statistically analyzed. It was found that the BLD coefficients were influenced by the Reynolds number while the MD coefficients were significantly impacted by the initial concentration of the target ions. Both the BLD and MD coefficients were found to depend on the molar ratio of bicarbonate to total target ions. Analytical correlations between the statistically significant parameters and the kinetic coefficients, under different transport mechanisms, for both sole- and multi-component feed solutions were developed. Mapping of the ratio between the boundary layer resistance and the membrane resistance, the transport mechanism, and the target ions concentrations was created. These steps are referred to as model training.

Prolonged experiments (30 h) were conducted under pure membrane diffusion conditions. Nitrate and bicarbonate concentration profiles were accurately predicted using a single MD coefficient whereas, sulfate prediction required two MD coefficients reflecting short (6 h) and long terms (6-30 h) DD transport.

The predictive model, which included the kinetic equations, the analytical correlations, and the mapping of the transport mechanism was algorithmized in MATLAB^? with the input being the experimental conditions and the output being the predicted concentration profiles and transport mechanism. The model was verified by experimental data used for the model training and validated by independent datasets. Overall, very good fits between the predicted and experimental datasets were obtained and the ability to determine the transport mechanism, without carrying out experiments, was demonstrated.