This work assesses conservative level set method (LSM) and Cahn–Hilliard phase field method (PFM) in modeling 2D two-phase flow through porous media, based on their ability to capture different phenomena associated with the medium permeability and fluid viscosity contrasts. The assessment includes their accuracy and running time. For this purpose, a robust finite element solver (COMSOL Multiphysics™) is used here to do the computations. To start with, the main parameters of the methods including the interface thickness, mesh size and diffusion coefficient are studied. Rectangular bubble relaxation is simulated to compare the two methods in capturing the physics of the bubble evolution. The comparison is also made for a stratified two-phase flow and flow in different single pore elements. Two models are then constructed to simulate two-phase flow with viscosity contrast through complex porous media, including homogenous medium with obstacle and dual-permeability medium. Both methods are able to capture the basic phenomena; however PFM is more successful in capturing the physical details especially in complicated porous media, compared to LSM. PFM results such as pressure gradients and fluid profiles in the media are more realistic. While LSM is unsuccessful in volume conservation and modeling no-slip boundary conditions. In addition, the running times are considerably less for PFM in simulation of different scenarios.

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