ali pak - Professor, Sharif University of Technology, Tehran, Iran
bahman sheikh - M.Sc. student, Sharif University of Technology, Tehran, Iran

Flow of two immiscible fluids in porous media has numerous applications in engineering. Numerical simulation of this phenomenon has become increasingly important. Complexities involved in determination of the advancing front of one fluid into another can well be simulated using Lattice Boltzmann (LB) Method. In this study, multicomponent LB model is developed to study the flow of two immiscible fluids with different viscosities in a channel and also in porous media. A multiple relaxation time (MRT) approximation is employed in the simulator, which leads to a viscosity independent velocity field. In this paper, the effects of capillary number on the shape and speed of advancement of the finger are investigated. The results of the study show that with the increase of the capillary number, the finger width, the slip distance of the contact lines and the breakthrough time decrease, while the finger length and areal sweep efficiency increase

Two phase flow, Capillary, Relative permeability, Lattice Boltzmann method