Upscaling non-Newtonian rheological fluid properties from pore-scale to Darcy’s scale

Abstract

Continuity and momentum equations govern the pore-scale flow properties of the fluid in the porous media, whereas Darcy’s law governs Darcy scale properties of the fluid transport in porous media. The empirical shift factor relates the steady shear-dependent viscosity of non-Newtonian fluids to the Darcy viscosity in porous media. The reported values of the empirical shift factor cover three orders of magnitude depending on the considered fluid-medium configurations. This creates a challenge to upscale non-Newtonian rheology from pore-scale to Darcy’s scale. We upscale Darcy viscosity based on pore-scale shear viscosity of Meter model fluid and viscoelastic linear Phan-Thien-Tanner fluid. We propose a Bundle-of-Capillaries model modified with pore-correction coefficient and fluid-correction coefficient. We numerically simulate the flow of polyacrylamide fluid, modelled using Meter model and linear Phan-Thien-Tanner model, through 3D symmetric micro-channel, 2D porous medium and 3D Mt Simon sandstone. Pore-scale direct numerical simulation using linear Phan-Thien-Tanner model showed viscoelastic instability in heterogeneous Mt Simon sandstone at low Reynolds number flow. Direct numerical simulations overestimate Darcy viscosity due to the presence of stagnant zones without active flow.