Attachment and detachment rate distributions in deep-bed filtration

TL;DR

This paper introduces a mean-field model with a spectrum of attachment and detachment rates to analyze colloid transport and deposition in porous media, providing analytical solutions and experimental protocols.

Contribution

It presents a novel mean-field model with a continuous spectrum of rate constants, offering analytical insights into filtration dynamics and front propagation.

Findings

Analytical solutions for long-time behavior and deposition profiles.

Characterization of filtering front structure, stability, and velocity.

Proposed experimental protocol for parameter determination.

Abstract

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long-time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability, and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.