Advances in modeling completely mixed flow reactors for ion exchange

This work advances the mathematical modeling of ion exchange treatment in completely mixed flow reactors in which there is recycle and regeneration of the ion exchange resin. The most common application of this process is magnetic ion exchange resin to remove dissolved organic carbon from raw drinking water. The motivation for this work was the complex distribution of resin particle ages and sizes that result from the recycle and regeneration processes. The newly developed model uses a single "age-averaged" diffusion equation to represent resin particle age as compared with the previous Monte Carlo model that uses a large number of diffusion equations to represent various resin particle ages. Advantages of the age-averaged model over the Monte Carlo model include a closed-form analytical solution for the steady-state case of the model, advanced numerical techniques used for the nonsteady-state case of the model, and model simulations require much less computational time and yield more accurate results. The age-averaged model is a robust numerical tool that can be used to evaluate a range of treatment scenarios as a result of these advancements.