Spatio-temporal dynamics of surfactant driven secondary invasion in Gaussian pore networks

TL;DR

This paper develops a pore-network model to study how surfactants influence secondary invasion in porous media, revealing that surfactant kinetics and heterogeneity control invasion timing and pathways.

Contribution

It introduces a coupled IP and transport-adsorption framework that captures surfactant effects on capillary thresholds and invasion dynamics in heterogeneous porous networks.

Findings

Invasion trajectories follow sigmoidal patterns consistent with Gaussian statistics.

Surfactant kinetics and heterogeneity primarily rescale invasion timescales.

The model links interfacial changes to post-breakthrough invasion behavior.

Abstract

Capillarity-dominated two-phase displacement in porous media often continues beyond the initial invasion-percolation (IP) breakthrough, as surfactants alter interfacial properties and reopen pathways once sealed by capillary forces. This study examines such secondary invasion, where adsorption-driven reductions in interfacial tension and contact-angle shifts lower entry thresholds in yet uninvaded throats, enabling further displacement at a fixed inlet pressure. To capture this process, we employ a time-dependent pore-network framework that couples IP with a reduced-order transport-adsorption module. Local fluxes are governed by Poiseuille flow, interfacial adsorption follows a Langmuir isotherm, and wettability evolution is modeled through a calibrated phenomenological relation. Heterogeneity is prescribed by Gaussian throat-size distributions whose variance controls structural disorder. The resulting invasion trajectories are sigmoidal, consistent with Gaussian cumulative statistics, indicating that surfactant mass-transfer kinetics and network variance primarily rescale invasion timescales while preserving the overall functional form. The framework thus connects interfacial conditioning to time-varying capillary thresholds and reveals how surfactant-mediated processes govern post-breakthrough dynamics in heterogeneous porous systems.