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

Tong Liu,Shiming Zhang,Moran Wang

doi:10.3390/en14030680

Abstract

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.

Highlights

Flow in porous media is ubiquitous in nature and industrial application [1,2,3]
Experiments and simulations have been conducted to study the relation between flowrate and pressure gradient when a Bingham fluid flows through porous media
Digital rock analysis provides a powerful tool to investigate the transport of complex fluids in porous media while the critical size of representative element volume (REV) and scanning resolution should be satisfied to guarantee representativeness and accuracy

Summary

Introduction

Flow in porous media is ubiquitous in nature and industrial application [1,2,3]. Darcy’s law is the basic formula to depict the single-phase flow in porous media. The Bingham fluid through porous media can lead to a “start-up pressure gradient” [17,18,19,20] caused by the yield stress. Experiments and simulations have been conducted to study the relation between flowrate and pressure gradient when a Bingham fluid flows through porous media. George et al [21] and Bauer et al [20] did measure the flow of yield-stress fluids through packed beads and found the power-law relation at the high-velocity flow regime. Talon and Bauer [22] performed numerical simulations of Bingham fluids through stochastically reconstructed porous media and found a parabolic transition flow regime and the linear flow regime when the pressure gradient increased. Chevalier et al [23] performed lattice Boltzmann simulations on 2D statistically reconstructed structures to study the statistical properties of Bingham fluid flows

Methods

Discussion

Conclusion