"Non­linearities and upscaling in porous media"

This paper focuses on the fractional flow formulation for two-phase flow in porous media and its applications. The IMPES (IMplicit-PressureExplicit-Saturation) concept is introduced for the fractional flow formulation using a finite volume element (FVE) method. Based on the differences between the fractional flow (FF) and fully coupled (FC) formulation, more adaptive possibilities are proposed for the FF system. Numerical results and CPU times for both formulations are given and compared to prove that the FF formulation is more efficient for the solution of advection-dominated two-phase flow problems, and the numerical simulation for one of the adaptive possibilities is also shown to investigate its feasibility. Furthermore, the FF formulation is combined with time-of-flight (TOF) calculation using a discontinuous Galerkin (dG) method which gives another application of the FF formulation. Numerical simulations for two real-life flow problems (single-phase models) are presented.