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Open AccessArticle

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

1
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
2
School of Engineering, University of Tasmania, Hobart, Tasmania 7001, Australia
3
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(3), 364; https://doi.org/10.3390/sym12030364
Received: 5 February 2020 / Revised: 22 February 2020 / Accepted: 28 February 2020 / Published: 2 March 2020
(This article belongs to the Special Issue Symmetry in Newtonian and Non-Newtonian Fluids)
Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs. View Full-Text
Keywords: threshold pressure gradient; non-Darcy flow; fractal theory; residual water saturation threshold pressure gradient; non-Darcy flow; fractal theory; residual water saturation
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Wang, H.; Wang, J.; Wang, X.; Chan, A. Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media. Symmetry 2020, 12, 364.

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