New insights on steady, non-linear flow in porous media

Prediction of the non-linear flow in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on non-linear flow in porous media are not yet definitive. The principal aim of this paper is to develop a meaningful and reasonable quantitative model that manifests the most important fundamental controls on low velocity non-linear flow. By coupling a new derivative with fractional order, referred to conformable derivative, Swartzendruber equation and modified Hertzian contact theory as well as fractal geometry theory, a flow velocity model for porous media is proposed to improve the modeling of Non-linear flow in porous media. Predictions using the proposed model agree well with available experimental data. Salient results presented here include (1) the flow velocity decreases as effective stress increases; (2) rock types of “softer” mechanical properties may exhibit lower flow velocity; (3) flow velocity increases with the rougher pore surfaces and rock elastic modulus. In general, the proposed model illustrates mechanisms that affect non-linear flow behavior in porous media.

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A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 1: Model development

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1650140104 ◽

1992 ◽

Vol 14 (1) ◽

pp. 25-45 ◽

Cited By ~ 5

Author(s):

Amir Gamliel ◽

Linda M. Abriola

Keyword(s):

Porous Media ◽

Multiphase Flow ◽

Linear Equations ◽

Model Development ◽

Flow In Porous Media ◽

Moving Grid ◽

One Dimensional ◽

Non Linear ◽

Grid Solution ◽

Non Linear Equations

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

Symmetry ◽

10.3390/sym12030364 ◽

2020 ◽

Vol 12 (3) ◽

pp. 364 ◽

Cited By ~ 1

Author(s):

Huimin Wang ◽

Jianguo Wang ◽

Xiaolin Wang ◽

Andrew Chan

Keyword(s):

Porous Media ◽

Pressure Gradient ◽

Water Saturation ◽

Flow Behavior ◽

Low Permeability ◽

Threshold Pressure ◽

Threshold Pressure Gradient ◽

Linear Flow ◽

Multi Scale ◽

Non Linear

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.

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