Role of viscoelastic fluid rheology in miscible viscous fingering

Abstract

Classical viscous fingering patterns in flow displacement can be modulated by incorporating polymers into either of the two fluids. The polymeric solutions are viscoelastic fluids exhibiting both shear-thinning as well as elastic behavior. The present numerical study examines the dynamics of viscous fingering in miscible flow displacement with either displacing or displaced fluid being treated as polymeric fluid. The nonlinear rheology of the polymeric fluid is described using the White–Metzner model. The role of fluid rheology in the transient evolution of concentration field and fingering patterns defined using quantities such as mixing length, relative contact area, finger width, and the number of fingers, is investigated by performing numerical simulations. The correlation between fingering structure and rheological properties is established. The study shows that incorporation of polymer into the fluid alters the viscous fingering attributed to the three main factors: viscosity modification, shear-thinning behavior, and fluid elasticity. Primarily, incorporating polymers into the displaced (displacing) fluid leads to suppressed (enhanced) fingering patterns, attributed to modification of the viscosity contrast between two fluids, the governing parameter for viscous fingering. Interestingly, when the viscosity contrast at a gap-averaged shear-rate is held fixed, the shear-thinning behavior promotes the longitudinal growth of fingers irrespective of the fluid to which polymers are added. Moreover, the fluid elasticity ends to inhibit the growth of fingers leading to a more efficient flow displacement regardless of the flow arrangement. Thus, the study suggests that in addition to the viscosity at the gap-averaged shear-rate, the nature of the entire flow curve representing nonlinear rheology plays an important role in fingering dynamics. The mechanism for the destabilization due to shear-thinning behavior is explained by analyzing the vorticity structures, local shear-rate, and local viscosity distribution in the flow domain. The normal stress distribution is analyzed to comprehend the stabilization attributed to the fluid elasticity. Overall, the interplay between the viscosity contrast and the complete rheological description of the fluid governs the fingering dynamics.