An analytical solution for non-Darcian flow in a confined aquifer using the power law function

Wen, Zhang; Huang, Guanhua; Li, Mingguang

doi:10.1016/j.advwatres.2007.06.002

Cited by 71 publications

(125 citation statements)

References 30 publications

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“…On the other hand, power law functions such as the Izbash equations are more appropriate to model post-linear nonDarcian flows that might be caused predominately by turbulent effects (Wen et al, 2008).…”

Section: Cherubini Et Al: Bench Scale Laboratory Tests To Analyzementioning

confidence: 99%

Bench scale laboratory tests to analyze non-linear flow in fractured media

Cherubini

Giasi

Pastore

2012

Hydrol. Earth Syst. Sci.

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Abstract. The knowledge of flow phenomena in fractured rocks is very important for groundwater resources management in hydrogeological engineering.A critical emerging issue for fractured aquifers is the validity of the Darcian-type "local cubic law", which assumes a linear relationship between flow rate and pressure gradient to accurately describe flow patterns.Experimental data obtained under controlled conditions such as in a laboratory increase our understanding of the fundamental physics of fracture flow and allow us to investigate the presence of non-linear flow inside fractures that generates a substantial deviation from Darcy's law.In this study the presence of non-linear flow in a fractured rock formation has been analyzed at bench scale in laboratory tests. The effects of non-linearity in flow have been investigated by analyzing hydraulic tests on an artificially created fractured rock sample of parallelepiped (0.60 × 0.40 × 0.8 m) shape.The volumes of water passing through different paths across the fractured sample for various hydraulic head differences have been measured, and the results of the experiments have been reported as specific flow rate vs. head gradient. The experimental results closely match the Forchheimer equation and describe a strong inertial regime. The results of the test have been interpreted by means of numerical simulations. For each pair of ports, several steady-state simulations have been carried out varying the hydraulic head difference between the inlet and outlet ports. The estimated linear and non-linear Forchheimer coefficients have been correlated to each other and respectively to the tortuosity of the flow paths.A correlation among the linear and non-linear Forchheimer coefficients is evident. Moreover, a tortuosity factor that influences flow dynamics has been determined.

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Section: Cherubini Et Al: Bench Scale Laboratory Tests To Analyzementioning

confidence: 99%

Bench scale laboratory tests to analyze non-linear flow in fractured media

Cherubini

Giasi

Pastore

2012

Hydrol. Earth Syst. Sci.

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“…The Izbash equation has been applied frequently (e.g. Şen 1989;Wen et al 2006Wen et al , 2008aWen et al , b, 2009Sedghi-Asl et al 2014). For many applications, both the Forchheimer and Izbash equations are equally well suited to describe non-Darcian flow (Bordier and Zimmer 2000;Moutsopoulos et al 2009;Qian et al 2011;Tzelepis et al 2015).…”

Section: Flow Laws For Linear Laminar (Darcy) Flowmentioning

confidence: 97%

述评:水井水力学—水流定律和几何学的影响

Houben

2015

Hydrogeol J

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Water wells are an indispensable tool for groundwater extraction. The analytical and empirical approaches available to describe the flow of groundwater towards a well are summarized. Such flow involves a strong velocity increase, especially close to the well. The linear laminar Darcy approach is, therefore, not fully applicable in well hydraulics, as inertial and turbulent flow components occur close to and inside the well, respectively. For common well set-ups and hydraulic parameters, flow in the aquifer is linear laminar, non-linear laminar in the gravel pack, and turbulent in the screen and the well interior. The most commonly used parameter of well design is the entrance velocity. There is, however, considerable debate about which value from the literature should be used. The easiest way to control entrance velocity involves the well geometry. The influence of the diameter of the screen and borehole is smaller than that of the screen length. Minimizing partial penetration can help to curb head losses.

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“…Sen (2000) also derived a transient drawdown solution for Izbash flow toward a fully penetrating well of infinitesimal radius in a confined aquifer by using Boltzmann transform as well. Recently, Wen et al (2008aWen et al ( , 2008b have done much work on Izbash nonDarcian flow to a fully penetrating pumping well in different aquifer systems and some approximate solutions have been obtained by using the Laplace transform associated with a linearization approximation. It has been proven that the linearization procedure can lead to an underestimation of the drawdown at early times, but works quite well at late times (Wen et al 2008a, b).…”

Section: Introductionmentioning

confidence: 99%

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Feng

Wen

2016

Hydrogeol J

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Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed nonDarcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K r2 ), and the specific storage of the formation zone (S s2 ) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness (r s ).

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An analytical solution for non-Darcian flow in a confined aquifer using the power law function

Cited by 71 publications

References 30 publications

Bench scale laboratory tests to analyze non-linear flow in fractured media

Bench scale laboratory tests to analyze non-linear flow in fractured media

述评:水井水力学—水流定律和几何学的影响

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

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