# Euler-Euler simulations to describe colloidal transport for groundwater remediation

Nassim Cheikh, Emmanuel Le Trong, Cyprien Soulaine

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Nassim Cheikh, Emmanuel Le Trong, Cyprien Soulaine. Euler-Euler simulations to describe colloidal transport for groundwater remediation. 8th French/Belgian OpenFOAM® users conference, Apr 2025, Bruxelles, Belgium., 2025. insu-05052528

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Submitted on 30 Apr 2025

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# Euler-Euler Simulations To Describe Colloidal Transport For Groundwater Remediation

Nassim Cheikhª, Emmanuel Le Trongª, Cyprien Soulaineª

ªInstitut des Sciences de la Terre d'Orléans, Orléans, France

Non-aqueous liquids (NAPLs) are water-immiscible pollutants that can disperse and release significant amounts of toxic compounds into underground water resources. Numerous methods have been developed to remove these pollutants from aquifers, but NAPL droplets remain trapped by capillary forces in the porous matrix even after depollution. The aim of our research is to explore the potential of colloids (e.g. nanoparticles, bacteria) to remobilize immiscible pollutant droplets. Our final objective is to develop a multiphase model that includes colloidal interactions with the solid phase, the aqueous phase, and the NAPL. Euler-Lagrange models allow us an accurate description of colloidal particle interactions (e.g. transport and retention) but remains very time- and resource-intensive. In this work, we are developing Euler-Euler approaches based on OpenFOAM's multiphaseEuler module to represent particles as a dispersed phase in water. The use of this model in the context of the remediation of polluted porous media is currently under development. Our model includes new viscosity models and plastic behavior, as well as the poromechanic properties. We present preliminary results such as: i) comparisons with Euler-Lagrange simulations for very diluted suspension, and ii) response to fluid stresses and its compressibility.
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erc

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# Euler-Euler simulations to describe colloidal transport for groundwater remediation

Nassim Cheikh¹, Emmanuel Le Trong¹, Cyprien Soulaine¹

¹Institut des Sciences de la Terre d'Orléans, Orléans, France

## INTRODUCTION

Non-aqueous phase liquids (NAPLs) are water-immiscible pollutants that can contaminate groundwater by releasing toxic compounds. Despite various remediation methods, NAPL droplets often remain trapped in porous media due to capillary forces. Our research investigates the potential of colloids—such as nanoparticles or bacteria—to mobilize these trapped pollutants. While Euler-Lagrange models offer detailed insight into colloid transport and retention, they are computationally demanding. To address this, we are developing a more efficient Euler-Euler approach using OpenFOAM®'s multiphaseEuler module, treating colloids as a dispersed phase in water. This model incorporates new viscosity formulations, plastic behavior, and poromechanical effects relevant to porous media. The continuity and momentum equations are solved for each phase.

$$ \frac{\partial(\phi_i \rho_i)}{\partial t} + \nabla \cdot (\phi_i \rho_i \hat{u}_i) = 0 $$

$$ \frac{\partial (\phi_i \rho_i \hat{u}_i)}{\partial t} + \nabla \cdot (\phi_i \rho_i \hat{u}_i \hat{u}_i) = \phi_i \nabla \hat{p}_i + \phi_i \nabla \cdot \hat{\tau}_i + \hat{F}_i $$

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(Ford et al., 2014)

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## PERMEABILITY

The test initializes a solid phase column at the inlet to the porous medium. A solid volume fraction of 0.2 is used for the simulation. This solid phase is displaced as the liquid phase is injected into the domain. With the flow of the solid phase out of the domain, the permeability of the medium increases. In the future, we intend to introduce aggregation forces for the solid phase, to observe pore clogging under certain conditions.

## COMPRESSIBILITY TEST

A compressibility test was carried out on a column half-filled with a solid phase having a volume fraction of 0.5. Water was injected through the upper limit, compressing the solid phase. The liquid phase can pass through the lower boundary condition, but not the solid phase. With this test, we observe a compression of the solid phase up to a limit of around 0.65 volume fraction.

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"Solid column no longer
compresses beyond a certain
limit"

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## REFERENCES

Depiction of the Distribution of Contaminant(s) within the Pore Space of the Unsaturated and Saturated Zones of an

Unconsolidated Aquifer (Ford et al., 2014)

Micro-Continuum Modeling: An Hybrid-Scale Approach for Solving Coupled Processes in Porous Media (Soulaine, 2024)