Modeling shear thinning polymer flooding using a dynamic viscosity model

Two distinct effects that polymers exhibit are shear thinning and viscoelasticity. The shear thinning effect is important as the polymers used in chemical enhanced oil recovery usually have this property. We propose a novel approach to incorporate this shear thinning effect through an effective dynamic viscosity of the shear thinning polysolution. The procedure of viscosity calculation of the polysolution, although based on a very basic power law model, is based on empiric coefficients which depends on a spatio-temporally evolving variable namely concentration of polymer. Since viscosity calculation is done pointwise, the accuracy of the model is higher than what exists in literature. This method has been integrated with an existing method for a Newtonian physics based model of porous media flows. The solver uses a hybrid numerical method developed by Daripa \& Dutta~\cite{DFEMcode,daripa2017modeling,daripa2019convergence}. The above method solves a system of coupled elliptic and transport equations modelling Darcy's law based polymer flooding process using a discontinuous finite element method and a modified method of characteristics. Simulations show (i) competing effects of shear thinning and mobility ratio; (ii) injection conditions such as injection rate and injected polymer concentration influence the choice of polymers to optimise cumulative oil recovery; (iii) permeability affects the choice of polymer; (iii) dynamically evolving travelling viscosity waves; and (v) shallow mixing regions of small scale viscous fingers in homogeneous porous media. This work shows an effective yet easy approach to make design choices of polymers in any given flooding condition.