The study on non-Darcy seepage equation of low velocity flow

Wang, Rui; Zhou, Hongwei; Zhong, J.C.; Yi, HaiYang; Chen, ChaoFan; Zhao, Yang

doi:10.1360/sspma2016-00366

Cited by 15 publications

(11 citation statements)

References 10 publications

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“…As suggested by decades of literature, the Swartzendruber equation can well describe the non-Darcian flow in tight porous media with low permeability [13,14]. Based on the Swartzendruber equation, the following equation can be written as:…”

Section: Conformable Derivative Approach To Swartzendruber Equationmentioning

confidence: 99%

“…As the linear operator does not inherit all the operational behaviors from the typical first derivative, the Swartzendruber equation fails to capture the full range of non-Darcy flow behavior in porous media [13][14][15]. Fortunately, as a well-behaved and efficient method, conformable derivative approach with real order can be applied to address this problem.…”

Section: Conformable Derivative Approach To Swartzendruber Equationmentioning

confidence: 99%

“…Until now, appropriate non-linear model for fluid flow through tight porous media remains unclear, though some more formulas have been established to describe the non-linear flow, such as power function model [9], exponential function model [10], incomplete Gamma function model [11,12] and fractional derivative approach [13][14][15]. As stated in the literature, in some extent, these models above are suitable for the description of non-linear flow in porous media with lower permeability [9][10][11][12][13][14]. Most recently, Yang [14] and Zhou [15] also suggested that the conformable derivative approach is suitable for the describing non-linear flow in low-permeability porous media.…”

Section: Introductionmentioning

confidence: 99%

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A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

et al. 2018

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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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Section: Conformable Derivative Approach To Swartzendruber Equationmentioning

confidence: 99%

Section: Conformable Derivative Approach To Swartzendruber Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

et al. 2018

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“…Liu et al [18] proposed two modified alternate directions method for solving the non-continuous seepage problems with fractional derivatives in 2-D homogeneous media. Wang et al [19] used the Laplace transform of a fractional derivative sense Swartzendruber motion equation and an analytical expression of the experimental data fitting of an unsaturated seepage analysis of the fractional Swartzendruber precision. The classical Forchheimer formula plays an important role in the study of non-linear seepage properties, but it needs to be improved in terms of an accurate description of the non-linear seepage properties of the broken rock.…”

Section: Introductionmentioning

confidence: 99%

Coupling effects of porosity and particle size on seepage properties of broken sandstone based on fractional flow equation

Qiu

Chen

et al. 2019

THERM SCI

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Studying the seepage properties of broken rock is important for understanding the behavior of engineering projects and preventing seepage disasters from occurring. Therefore, a test system was developed to test the seepage properties of broken rock under different porosities and particle sizes. A non-linear seepage equation of broken rock was developed based on the Forchheimer equation and the theories of fraction calculus. The influence of the coupling mechanism of the porosity and particle size on the seepage properties of broken rock was analyzed. The results show that the non-linear seepage equation can describe the non-linear seepage properties of broken rock well. The relations between the permeability and the porosity and particles size can all be represented through an exponential function. It is thought that watercourses are developed in broken rock with high porosity and large particle size, which shows a stronger hydraulic conductivity capability. However, the inertial potential energy of a non-Darcy flow is relatively small.

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“…Considering the memory effectiveness induced by solid-liquid interaction and time-dependent deformation of rocks (Yang et al 2019), and referring to the fractional-order modeling ideas of non-Darcy flow (Zhou et al 2018b(Zhou et al , 2019(Zhou et al , 2021Yang et al 2019;Wang et al 2017). Eq.…”

mentioning

confidence: 99%

Estimation and verification of fractional derivative-based permeability of coals considering mining-induced stresses

Zhou

Xie

Jia

et al. 2021

Preprint

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To overcome the inaccuracy of the traditional transient pulse test, a new fractional derivative-based permeability estimation formula based on the transient pulse test is proposed to describe the pressure difference decay of a coal body subjected to mining-induced stresses. The permeability of coal specimens under mining disturbance conditions is measured using the MTS815 rock mechanics test system. The experimental results show that the transient pulse test based on the fractional derivative model provides a much better estimation of the coal specimen’s permeability than the conventional exponential decay model. Analyzing the evolution of the coal’s permeability shows that the permeability tends to decrease in the pre-peak compaction stage, following which it gradually increases in the plastic phase, and then increases sharply in the post-peak phase. The significance of the fractional derivative order γ is discussed, and its analysis shows that the solid-liquid interaction inside the specimen becomes complicated when the stress within the coal specimen changes.

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The study on non-Darcy seepage equation of low velocity flow

Cited by 15 publications

References 10 publications

A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

Coupling effects of porosity and particle size on seepage properties of broken sandstone based on fractional flow equation

Estimation and verification of fractional derivative-based permeability of coals considering mining-induced stresses

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