This research aims to develop a three-dimensional, shear-thinning, non-Newtonian flow model to simulate field scale polymer flooding as a tertiary oil recovery mechanism. The viscosities are calculated based upon direction dependent shear-rates. This provides an accurate representation of the non-Newtonian flow behavior in a three dimensional porous medium. The model considers a full-tensor permeability (3 x 3 matrix with non-zero off diagonal values) as a measure of resistance (or shearing) to flow. The shear-rate is then calculated as a function of the directional permeability and polymer phase velocity. Consequently, the shear-rate dependent fluid viscosity varies with direction resulting in an accurate physical description of shear thinning flow behavior in a three dimensional porous medium. The form of the velocity dependent permeability tensor, or in other words the coefficient in front of the gradient of pressure, is guided by a pore-scale non-Newtonian, Navier-Stokes flow solution on an assumed representative element volume (REV).
The model developments are being implemented and tested approach in IPARS (Integrated Parallel Accurate Reservoir Simulator). A multi-point-flux mixed finite element (MFMFE) scheme is further used for spatial discretization of the associated partial differential equations. This scheme provides accurate fluid velocities at the faces of each element, which further improves viscosity calculations. A retardation factor, for polymer concentration, is further used to study the effect of polymer adsorption on recovery predictions. Additionally, we also consider viscosity variation due to changes in polymer concentration. Preliminary results show significant differences in sweep efficiencies due to changes in polymer front behavior, when compared to conventional models. The shear-thinning polymer viscosity is shown to decrease in a direction of low permeability and high pressure gradient (high shear rates) resulting in better sweep efficiencies. The results also show that the velocity dependent dispersion of polymer concentration is better represented due to accurate fluid velocities at the grid element faces.
This development is a joint effort being carried out at the Center for Subsurface Modeling in collaboration with Kundan Kumar (Associate Professor, University of Bergen, Norway). We also acknowledge Thomas Wick (Research Scientist, Austrian Academy of Sciences) for his deal.II fluid structure interaction toolset for solving non-Newtonian Navier Stokes flow in the REV.