Modeling non-uniform mixing in shear-thinning polymer flooding

It is customary to assume that the polymer is homogeneously mixed with water in chemical enhanced oil recovery by shear-thinning polymer flooding. This assumption rarely holds during flow in porous media due to factors, such as variable porosity, heterogeneity, adsorption of polymer by the porous matrix, coagulation, polymer solubility, and oil field conditions, like water hardness, salinity, pressure, and temperature. To account for the inhomogeneous mixing of polymers in viscosity calculations, we introduce a mixing parameter which represents complete mixing when it takes a value of 1 and complete segregation when it takes a value of 0. A procedure is developed to calculate the effective dynamic viscosity of the polysolution by incorporating the mixing parameter and shear-thinning effects. The shear-thinning model is dependent on the spatiotemporal shear rate, polymer concentration, and polymer type. This model has been integrated into our in-house surfactant-polymer flooding code, which solves coupled transport and elliptic equations using a hybrid numerical method developed by Daripa and Dutta. Simulations have been performed with two types of mixing parameters: constant and spatially dependent. The first set of simulations with three constant values of the mixing parameter show that enhanced mixing leads to wider fingers, faster front speeds, and lower cumulative oil recovery (COR). A second set of simulations with spatially dependent mixing parameters shows that COR may be skewed toward either completely isolated or completely mixed states. These findings are attributed to complex interplay between mixing and shear-thinning.