Does Rheology of Bingham Fluid Influence Upscaling of Flow through Tight Porous Media?

Non-Newtonian fluids may cause nonlinear seepage even for a single-phase flow. Through digital rock technologies, the upscaling of this non-Darcy flow can be studied; however, the requirements for scanning resolution and sample size need to be clarified very carefully. This work focuses on Bingham fluid flow in tight porous media by a pore-scale simulation on CT-scanned microstructures of tight sandstones. A bi-viscous model is used to depict the Bingham fluid. The results show that when the Bingham fluid flows through a rock sample, the flowrate increases at a parabolic rate when the pressure gradient is small and then increases linearly with the pressure gradient. As a result, an effective permeability and a start-up pressure gradient can be used to characterize this flow behavior. By conducting flow simulations at varying sample sizes, we obtain the representative element volume (REV) for effective permeability and start-up pressure gradient. It is found that the REV size for the effective permeability is almost the same as that for the absolute permeability of Newtonian fluid. The interesting result is that the REV size for the start-up pressure gradient is much smaller than that for the effective permeability. The results imply that the sample size, which is large enough to reach the REV size for Newtonian fluids, can be used to investigate the Bingham fluids flow through porous media as well.