Coupled two-phase flow and surfactant/PFAS transport in porous media with angular pores: From pore-scale physics to Darcy-scale modeling

TL;DR

This work addresses the challenge of predicting coupled two-phase flow and surfactant/PFAS transport in porous media with angular pores, where the traditional Leverett $J$-function fails to capture pore geometry and tension–wettability coupling. It introduces a four-step upscaling workflow based on a bundle-of-capillary-tubes model to derive explicit and closed-form expressions for capillary pressure, relative permeability, and fluid–fluid interfacial area as functions of saturation, pore geometry, and interfacial properties, and then couples these properties into a transient Darcy-scale flow–transport framework. The study demonstrates nonlinear and geometry-dependent behavior of $P^c$–$S_w$, $k_r$–$S_w$, and $A_{wn}$–$S_w$, validates the scaling functions against experimental data, and applies the model to PFOS transport in unsaturated soils, revealing that pore angularity strongly controls water flow, interfacial area, and PFAS retention while surfactant-induced flow is typically modest under typical conditions. The framework provides a physically grounded, generalizable tool for predicting multiphase flow and contaminant transport in angular porous media, with implications for PFAS remediation, oil recovery, and CO$_2$/H$_2$ storage in heterogeneous rocks and soils.

Abstract

Two-phase surfactant-laden flow and transport in porous media are central to many natural and engineering applications. Surfactants alter two-phase flow by modifying interfacial tension and wettability, while two-phase flow controls surfactant transport pathways and interfacial adsorption. These coupled processes are commonly modeled using Darcy-type two-phase flow equations combined with advection--dispersion--adsorption transport equations, with capillary pressure--saturation relationships scaled by the Leverett $J$-function. However, the Leverett $J$-function idealizes porous media as bundles of cylindrical tubes and decouples interfacial tension and wettability, limiting its ability to represent angular pore geometries and interfacial tension--wettability coupling effects. We present a modeling framework that explicitly incorporates pore angularity and interfacial tension--wettability coupling into Darcy-scale surfactant-laden flow and transport models. Two-phase flow properties are derived for angular pores, upscaled across pore size distributions, and formulated as explicit and closed-form expressions. These upscaled relationships are integrated into a coupled flow--transport model to simulate transient two-phase flow and surfactant transport. Results reveal a nonlinear and nonmonotonic dependence of two-phase flow properties on pore angularity, pore size distribution, and interfacial tension. Example simulations of water flow and PFAS migration in unsaturated soils indicate that surfactant-induced flow effects on PFAS leaching are generally minor under typical conditions, whereas pore angularity strongly controls water flow, interfacial area, and PFAS retention. Overall, the proposed framework provides a more physically grounded approach for modeling two-phase surfactant-laden flow and transport in porous media.

Figures (15)

• Figure 1: (a) Schematic of soil contamination by surfactant-like chemicals, such as per- and polyfluoroalkyl substances (PFAS). (b) Accumulation and adsorption of PFAS at the air--water interfaces in unsaturated soil pores. (c) Surface tension and contact angle of PFAS-laden water compared with PFAS-free water. Panels (a) and (b) are revised from chen2023pore with permission of the authors and Wiley.
• Figure 1: Pore size distributions of porous media with (a) a mean pore size of 100$\mu$m and normalized standard deviation of 0.3, and (b) a mean pore size of 100$\mu$m and normalized standard deviation of 0.5.
• Figure 2: A upscaling workflow to bridge pore-scale physics of coupled two-phase flow and surfactant/PFAS transport into a Darcy-scale modeling framework. The workflow consists of four steps: (a) Compute the configuration of the wetting and nonwetting fluids in an angular corner for a given capillary pressure with or without the presence of surfactant/PFAS in the fluids. Equilateral triangular tubes are used as examples. (b) Compute the configuration of the wetting and nonwetting fluids in a bundle of capillary tubes for a given capillary pressure. (c) Apply the bundle-of-capillary-tubes model to derive two-phase flow properties (e.g., capillary pressure, relative permeability, and fluid--fluid interfacial area vs. fluid saturation curves) for a porous medium. The capillary pressure vs. wetting-phase fluid saturation curve is used as an example. (d) Couple the new two-phase flow properties into Darcy-scale transient two-phase flow and surfactant/PFAS transport models. Note that a nanometer-scale thin wetting-phase fluid film (referred to as "precursor film") may form on partially-wet surfaces, while a macroscopic thin wetting-phase fluid film (thicker than precursor film) will form on completely-wet surfaces. Due to the small film thickness, the thin films are not shown in Panels (a) and (b).
• Figure 2: Impact of interfacial tension ($\gamma_{wn}$) on the relative permeability and fluid--fluid interfacial area as functions of saturation in porous media with cylindrical pores. A near neutral-wet condition (e.g., an intrinsic contact angle $\theta_0$ of $80^{\circ}$) is used as an illustrative example.We present the curves for the $\gamma_{nw}$ range where the contact angles become 0 and remain constant. Note that $\gamma_{wn}$ is a proxy of the surfactant effect, i.e., a smaller $\gamma_{wn}$ corresponds to a more interfacially active surfactant and/or a higher surfactant concentration.
• Figure 3: Impact of interfacial tension ($\gamma_{wn}$) on the (a--b) capillary pressure--saturation curves, (c) relative permeability--saturation curves, (d) fluid--fluid interfacial area--saturation curves in a porous medium with cylindrical pores. A near neutral-wet condition (e.g., an intrinsic contact angle $\theta_0$ of $80^{\circ}$) is used as an illustrative example. Two $\gamma_{wn}$ ranges are modeled: (1) A range within which the contact angles ($\theta$) are greater than or near 0, and (2) A range within which $\theta \equiv 0$. Because the relative permeability--saturation curves are the same in all cases, we only show those for contact angles greater than 0. In the figure, $\gamma_{wn,0}$ refers to the interfacial tension for surfactant-free fluids. Note that $\gamma_{wn}$ is a proxy of the surfactant effect, i.e., a smaller $\gamma_{wn}$ corresponds to a more interfacially active surfactant and/or a higher surfactant concentration.