INVESTIGATION OF VISCOUS FINGERING INSTABILITY IN HETEROGENEOUS POROUS MEDIA

Viscous fingering instability in porous media has various applications and models in industry, processes, and natural issues. Several studies on the stability in porous media have been done by researchers in recent years. In this paper, a solution is introduced to stabilize the viscous fingering instability, which is described as channeling. In this solution, narrow channels were placed next to the walls, and an exponential function was used to represent it. In linear stability analysis the governing equations are transferred to Fourier space. By introducing a novel numerical method, the transferred equations are analyzed. The results show that when the ratio of maximum to minimum permeability is approximately equal to one, the channeling has no significant effect. By increasing the permeability ratio, the channeling effect increases, more fluid flows near the walls, and the system becomes more stable at the center and unstable along the walls. Also increasing the mobility ratio increases the system instability. In nonlinear simulation, by using stream function and vortices, new equations have been rewritten and because of no slip boundary condition, the direct solution method is conducted and concentration contours are presented. Similar results for nonlinear simulation are found, which are in good agreement with linear stability analysis.