Reduced model for deep bed filtration of binary highly heterogeneous colloids

TL;DR

This paper extends the traditional deep bed filtration model to accurately match hyper-exponential retention profiles observed in colloidal transport experiments by introducing a non-linear activity-based suspension function derived from thermodynamic principles.

Contribution

It introduces a novel non-linear suspension function based on Margules' activity model to improve the modeling of colloid retention in porous media, especially for hyper-exponential profiles.

Findings

The new model matches laboratory data well, including hyper-exponential retention profiles.

The suspension function effectively captures complex colloidal interactions with fewer parameters.

Empirical conversions link the new model's parameters to traditional multicomponent colloidal transport parameters.

Abstract

Hyper-exponential retention profiles (HERPs) are often observed during laboratory tests on colloidal and nano-suspension transport in porous media. The aim of this work is an extension of the traditional model for suspended particle transport (deep bed filtration) to match HERPs. Interpreting particle capture in the framework of active mass law for the "chemical reaction" particle-rock, we substitute suspension concentration in the traditional expression for capture rate by non-linear "activity" function, called the suspension function. The non-linear suspension function is derived from Margules' activity model for excess Gibbs free energy. This suspension function is shown to match that derived from multicomponent colloidal transport with good agreement, despite having one less unknown parameter. Empirical formulae are presented to convert between the two unknown parameters of the multicomponent model and the Margules exponent. Comparison between the new model and laboratory coreflooding data shows good agreement, even in cases with distinctly hyper-exponential retention profiles, where the classical model fails to reproduce the laboratory data.