Model order reduction of an ion exchange process for ammonium removal in groundwater

This work introduces a formal framework for model order reduction of an ion exchange process commonly used in water treatment for human consumption. The objective is to retrieve a finite dimension model to describe the advection-diffusion-reaction-equation governing the ion exchange process in a packed bed reactor. A state-space model is derived using a finite-difference scheme to explain the ion exchange process for ammonium removal. Further, a model order reduction step is incorporated to streamline the computational complexity while preserving the essential dynamics of the system. Three model order reduction criteria are established based on the breakthrough curve retrieved by numerical simulations. The results quantitatively demonstrate the influence of the reduction criteria on the behavior of the breakthrough curves. This proposal aims to serve as a reference framework for designing experiments in ion exchange processes for ammonium removal and further optimizing these processes using estimation and control strategies.