Optimal polymer slugs injection curves

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.