An analytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit

TL;DR

This paper presents a comprehensive mathematical model for solute transport and sorption in porous media, incorporating intra-particle diffusion and adsorption kinetics, validated with experimental data for mercury and CO2 removal.

Contribution

The work introduces a novel coupled PDE model including intra-particle diffusion and a new characteristic time scale, advancing understanding of adsorption processes in dual-porosity systems.

Findings

Model accurately predicts contaminant breakthrough curves.

Intra-particle diffusion significantly affects adsorption dynamics.

Analytical solutions via traveling wave approach are feasible under certain conditions.

Abstract

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damk\"ohler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against available experimental data for the removal of Mercury(II) and CO$_\text{2}$. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions.