Evolution of invasion patterns due to surfactant adsorption in non-Gaussian pore distribution: Role of mass transfer and Laplace pressure

Immiscible two-phase flow in porous media occurs in many processes, such as enhanced oil recovery (EOR), as well as oil spill and soil remediation. These processes involve a fluid displacing another immiscible fluid within the confines of a heterogeneous porous structure. The invasion pattern generally remains the same under constant conditions but can also evolve over time in the presence of surfactants, which alter the interfacial tension (IFT) and surface wettability. The dynamics under such conditions extend beyond the usual way in which such immiscible displacement is modeled. Here, we develop a time-dependent pore network model (PNM) to simulate the effects of surfactant-induced IFT reduction on immiscible displacement driven by constant inlet pressure, with pressure drops across the network calculated using a random resistor network and mass conservation equations. Node-specific flux and velocity are derived using the Hagen-Poiseuille equation, and surfactant adsorption is modeled using the Langmuir isotherm, capturing its impact on fluid-fluid and solid-fluid interfaces within the invaded path. Since the evolution of the invasion pattern comprises the cooperative mechanisms of surfactant mass transfer to the interfaces and the resulting changes in capillary and Laplace pressures, we employ two strategies to quantify this complex feedback behavior: mass transfer based, introducing a mass transfer timescale, and Laplace pressure based, scaling with the inlet pressure. Results reveal that heavy-tailed pore throat distribution accelerates the onset of secondary invasions, which enhances the dominance of Laplace pressure. As the distribution becomes more symmetric or Gaussian, mass transfer becomes the dominant mechanism. This interplay highlights the intricate balance between mass transfer and capillary effects in governing the spatiotemporal evolution of immiscible fluid invasion.