Before revision: In the paper we study miscible injection of liquids with decreasing viscosity in two-dimensional geometry. Polymer flooding of oil fields is our prototype model. Based on several one-dimensional approximate models we give rigorous formulation of the graded viscosity banks (GVB) technology which helps to save polymer by injecting several slugs with gradual decrease of viscosity instead of one slug. Limiting injection curves when number of slugs tends to infinity is calculated .
After revision: The graded viscosity banks technology (tapering) for polymer flooding is studied for several different models of mixing zones behavior. Depending on the viscosity function the limiting polymer injection profile is rigorously derived in case of transverse flow equilibrium assumption, for the Koval model and for the Todd-Longstaff model. The possible gain of the polymer in comparison to finite number of slugs tends to infinity is calculated .