Dynamic coupling of flow and surfactant adsorption at interfaces in a heterogeneous pore network

Soil and rock formations experience variation in saturation and chemical composition over time that may alter relative saturation of one phase or the other due to change in interfacial tension (IFT) at the pore structure. We can physically describe this process within a porous network hosting two phases where one initially invades the other and then surfactants are introduced to the invading phase and alter the IFT of the interfaces, thus leading to further invasion. This study explores the dynamic interplay between fluid flow and surfactant adsorption in porous media, focusing on the spatio-temporal evolution of invasion patterns in heterogeneous pore networks. We develop a time-dependent pore network model (PNM) to simulate the effects of surfactant-induced IFT reduction on two-phase flow under constant driving pressure. The initial invasion follows invasion percolation theory, and pressure drops across the network are calculated using a random resistor network and mass conservation equations. Node-specific flux and velocity are derived via the Hagen-Poiseuille law. Surfactant adsorption is modeled using Langmuir kinetics, capturing its impact on fluid-fluid and solid-fluid interfaces within the invaded path. Over time, reduced IFT and contact angle alterations trigger secondary invasions, reshaping the invasion patterns. The model investigates how pore-scale heterogeneity and reaction timescales influence this evolution. Results indicate that invasion patterns evolve with surfactant mass transfer and network heterogeneity, scaling with the cumulative Gaussian distribution used for pore allocation. These dynamic patterns align with Kosugi’s quasi-static model of water retention versus capillary pressure, emphasizing the significance of IFT alterations. This work provides theoretical insights into surfactant-driven invasion dynamics in porous media and their dependence on physical and chemical parameters.