Nonlinear Dynamics of Displacement Fronts in Two-Phase Flows Propagating Through Porous Media

A generalized mathematical model is constructed to describe the isothermal two-phase flow of a three-component system and to investigate light non-aqueous phase liquid (LNAPL) displacement during surfactant-enhanced remediation in vertical porous media. The model integrates the dominant physical mechanisms governing immiscible fluid redistribution, including gravitational and capillary forces under different wettability conditions. The hyperbolic part of the system is analyzed within the framework of a Riemann problem, allowing for the characterization of shock and rarefaction wave formation in saturation and concentration profiles. Numerical simulations performed using a first-order upwind (FOU) scheme reveal pronounced artificial dissipation, as confirmed by von Neumann stability analysis. To overcome this limitation, a high-order non-oscillatory scheme based on nonlinear flux limiters and polynomial reconstruction is developed, enabling accurate resolution of sharp displacement fronts. A comparative analysis of limiter functions reveals that their suitability depends on the degree of nonlinearity in relative phase permeabilities, highlighting the necessity for careful selection in multiphase flow modeling. Parametric investigations quantify the effects of gravity, capillary parameters, Peclet number, and wettability alteration on displacement efficiency in homogeneous porous media. The proposed framework is validated against experimental MRI data, demonstrating its reliability for describing two-phase displacement in porous media. Overall, the developed numerical model provides a predictive framework for resolving nonlinear front dynamics and optimizing surfactant-enhanced remediation strategies in contaminated subsurface reservoirs.