A numerical study on the effects of viscoelastic properties of upper convected Maxwell fluid on immiscible Saffman-Taylor instability

In this paper, Saffman-Taylor instability of an immiscible displacement in a Hell-Shaw cell is studied numerically for the first time. The VOF method is used for two phases flow simulation. Viscoelastic fluid with less viscosity is considered as the displacing fluid and Newtonian fluid with high viscosity is used as the displaced fluid. The upper convected Maxwell constitutive equation is applied to simulate the viscoelastic fluid. In this research, the effects of dimensionless parameters consisting of the mobility ratio, elasticity number and capillary number are studied and the sweep efficiency diagram is depicted. The results show that, increasing the elasticity number and capillary number, and decreasing the mobility ratio can stabilize the flow. It is also found that, changing these parameters has a significant effect on the phase contours and mechanisms of viscous fingering patterns. The results of this numerical study could be helpful for enhanced oil recovery process, especially in polymer flooding technique. As a main consequence, it is concluded that, the elastic properties of displacing viscoelastic fluid in the presence of capillary forces has a stabilizing effect on the flow instability.