Lattice Boltzmann Modeling of the Apparent Viscosity of Thinning–Elastic Fluids in Porous Media

Many non-Newtonian fluids, including polymers, exhibit both shear-thinning and viscoelastic rheological properties. A lattice Boltzmann (LB) model is developed for simulation of the flow of thinning–elastic fluids through porous media. This model applies the Oldroyd-B constitutive equation and the Carreau model, respectively, to account for the viscoelastic and shear-thinning behaviors of the thinning–elastic fluid in porous media. Both rheological features are captured well by this model and are verified against analytical solutions. The thinning-then-thickening viscosity curve of the thinning–elastic fluid observed in experiments is reproduced by the present pore-scale simulations. In addition to the traditional extensional theory, we propose other important mechanisms for the increase in apparent viscosity of viscoelastic fluids at higher shear rates. The mechanisms proposed include the reduction in conductivity due to stagnant fluid, the compressed effective flow region, and larger energy dissipations caused by the viscoelastic instability. We find that the viscoelastic thickening effect is more prominent in porous geometries with a large pore–throat ratio. Article Highlights A lattice Boltzmann model is developed to predict the flow behavior of fluids with both viscoelastic and shear-thinning properties The thinning-then-thickening apparent viscosity curve of the thinning-elastic fluid observed experimentally in porous media is predicted in the pore-scale models Pore-scale mechanisms for the thickening behavior of viscoelastic fluids in porous media at higher shear rates are proposed