Modeling shear thinning polymer flooding using a dynamic viscosity model

Abstract

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 shear thinning effect through 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 empirical coefficients that depend on a spatio-temporally evolving variable, namely, concentration of polymer. Since viscosity calculation is performed in space and time, the results obey correct physics and are more accurate than what exists in the 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 and Dutta [“DFEM-MMOC based EOR code in MATLAB” (2020); P. Daripa and S. Dutta, “Modeling and simulation of surfactant–polymer flooding using a new hybrid method,” J. Comput. Phys. 335, 249–282 (2017); and P. Daripa and S. Dutta, “On the convergence analysis of a hybrid numerical method for multicomponent transport in porous media,” Appl. Numer. Math. 146, 199–220 (2019)]. The above method solves a system of coupled elliptic and transport equations modeling 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 optimize cumulative oil recovery; (iii) permeability affects the choice of polymer; (iv) dynamically evolving traveling viscosity waves; and (v) shallow mixing regions of small scale viscous fingers in homogeneous porous media. The overall goal of this study is to develop an effective yet easy approach to make design choices of polymers in any given flooding condition, which has been shown here.