# Evaluation of a Volume-Averaged Species Transport Model with Micro–Macro Coupling for Breakthrough Curve Prediction

## TL;DR

This paper evaluates a new model for predicting contaminant transport in water filters, comparing it with simulations and experiments to identify its limitations.

## Contribution

The study introduces a micro–macro coupling model based on volume-averaged transport equations and identifies time constraint violations as a key issue.

## Key findings

- The volume-averaged model's predictions disagree with direct simulations and experiments.
- Time constraint violations are identified as the main cause of model failure.
- Alternative closure formulations are needed for accurate predictions.

## Abstract

In porous water filters, the transport and entrapment of contaminants can be modeled as a classic mass transport problem, which employs the conventional convection–dispersion equation to predict the transport of species existing in trace amounts. Using the volume-averaging method (VAM), the upscaling has revealed two possible macroscopic equations for predicting contaminant concentrations in the filters. The first equation is the classical convection–dispersion equation, which incorporates a total dispersion tensor. The second equation involves an additional transport coefficient, identified as the adsorption-induced vector. In this study, the aforementioned equations were solved in 1D for column tests using 3D unit cells. The simulated breakthrough curves (BTCs), using the proposed micro–macro-coupling-based VAM model, are compared with the direct numerical simulation (DNS) results based on BCC-type unit cells arranged one-after-another in a daisy chain manner, as well as with three previously reported experimental works, in which the functionalized zeolite and zero-valent iron fillings were used as an adsorbent to remove phosphorous and arsenic from water, respectively. The disagreement of VAM BTC predictions with DNS and experimental results reveals the need for an alternative closure formulation in VAM. Detailed investigations reveal time constraint violations in all the three cases, suggesting this as the main cause of VAM’s failure.