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

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.

A Novel Threshold Pressure Gradient Model and Its Influence on Production Simulation for Shale Oil Reservoirs

“…16,28,29 In addition, experimental researches require significant instrumentation requirements, consume time and labor, so pore-scale numerical methods (e.g., molecular dynamics models, finite volume methods, and pore-network models) are widely accepted to study TPGrelated issues in the development of low permeability reservoirs. 30,31 Although pore-scale numerical methods can complement experimental research, their calculation accuracy is affected by algorithm accuracy and discretization error. Compared with experimental and numerical methods, analytical methods can obtain accurate results effectively.…”

“…Until now, experiments, numerical methods, and analytical methods have been used to study TPG in low-permeability reservoirs. In general, experimental methods obtain TPG of low permeability porous medium by fitting the experimental results and take TPG as an empirical function of permeability. ,,,,− Although the phenomenon of TPG in porous medium has been measured by many scholars since it was reported in 1963 by Miller and Low, the influence mechanisms of different factors on TPG are difficult to be fully revealed by experiments. ,, In addition, experimental researches require significant instrumentation requirements, consume time and labor, so pore-scale numerical methods (e.g., molecular dynamics models, finite volume methods, and pore-network models) are widely accepted to study TPG-related issues in the development of low permeability reservoirs. , Although pore-scale numerical methods can complement experimental research, their calculation accuracy is affected by algorithm accuracy and discretization error.…”

Macroscopic model for unsteady generalized Newtonian fluid flow in homogeneous porous media

“…Nowadays, the study of porous media systems can be carried out by performing pore-scale simulations in detailed reconstructions of the porous matrix topology [16] or by developing upscaled models that capture the essential information from the microscale and carry it to the macroscale. In this regard, there are many upscaling techniques available as reviewed in [17].…”