A numerical investigation into the influence of the surfactant injection technique on the foam flow in heterogeneous porous media

We propose a sequential algorithm to investigate the influence of surfactant injection on foam-induced mobility reduction in two-phase liquid-gas flows in highly heterogeneous porous media. A foam model in local equilibrium is adopted in this context, assuming non-Newtonian foam behavior. A fractional flow formulation based on global pressure that includes the surfactant in the liquid phase is adopted, resulting in a system that couples elliptic and hyperbolic equations. These equations are split into two sub-systems that group equations of the same kind and are solved employing a sequential numerical algorithm that combines a locally conservative hybrid finite element method to approximate the hydrodynamics of the system with a central-upwind finite volume method for the transport equations. The resulting spatial discretized system is approximated in time by applying a multi-step, implicit finite difference method. The hydrodynamics and hyperbolic problems are solved using a staggered algorithm in different time scales. Through comparison with experimental data and classical numerical methods, we validated the proposed methodology and demonstrated its ability to produce stable approximations with reduced numerical dissipation and computational cost. Then, we apply the sequential algorithm to compare the co-injection of the water-gas-surfactant with the Surfactant Alternating Gas (SAG) technique in two-dimensional flows in highly heterogeneous media. The numerical results suggest a better sweep efficiency using the SAG injection technique when compared with the co-injection approach for the equivalent amount of injected surfactant.