Non-Darcian flow in a single confined vertical fracture toward a well

Wen, Zhang; Li, Mingguang

doi:10.1016/j.jhydrol.2006.05.001

Cited by 80 publications

(44 citation statements)

References 33 publications

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“…Darcy's law and the cubic law are only valid when the inertial force is negligible, compared with the magnitude of the viscous force, and this condition is anticipated only when is low. Nonlinear flow occurs when, with an incremental increase in Re, increases more than a proportional incremental amount [26,[32][33][34][35]]. Forchheimer's law [8,[36][37][38] has been most widely used to describe the nonlinear flow in fractures and porous media, especially in strong inertial regimes:…”

Section: Non-darcy Flowmentioning

confidence: 99%

Effects of Hydraulic Gradient, Intersecting Angle, Aperture, and Fracture Length on the Nonlinearity of Fluid Flow in Smooth Intersecting Fractures: An Experimental Investigation

Fan

Zhao

2018

Geofluids

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This study experimentally investigated the nonlinearity of fluid flow in smooth intersecting fractures with a high Reynolds number and high hydraulic gradient. A series of fluid flow tests were conducted on one-inlet-two-outlet fracture patterns with a single intersection. During the experimental tests, the syringe pressure gradient was controlled and varied within the range of 0.20-1.80 MPa/m. Since the syringe pump used in the tests provided a stable flow rate for each hydraulic gradient, the effects of hydraulic gradient, intersecting angle, aperture, and fracture length on the nonlinearities of fluid flow have been analysed for both effluent fractures. The results showed that as the hydraulic gradient or aperture increases, the nonlinearities of fluid flow in both the effluent fractures and the influent fracture increase. However, the nonlinearity of fluid flow in one effluent fracture decreased with increasing intersecting angle or increasing fracture length, as the nonlinearity of fluid flow in the other effluent fracture simultaneously increased. In addition, the nonlinearities of fluid flow in each of the effluent fractures exceed that of the influent fracture.

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Section: Non-darcy Flowmentioning

confidence: 99%

Effects of Hydraulic Gradient, Intersecting Angle, Aperture, and Fracture Length on the Nonlinearity of Fluid Flow in Smooth Intersecting Fractures: An Experimental Investigation

Fan

Zhao

2018

Geofluids

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“…Lomize, 1951;Louis, 1969;Qian et al, 2005Qian et al, , 2007Qian et al, , 2011Wen et al, 2006). Tortuosity, which usually characterizes the ratio of the effective path length connecting two locations in porous media to the geometric distance (Tenchine and Gouze, 2005), has been found to significantly affect fluid flow in fractured media under certain conditions (Tsang, 1984;Wang and Narasimhan, 1985).…”

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

confidence: 99%

“…Experimental evidence has shown that both the Forchheimer and the Izbash equations are equally possible, depending on field-specific conditions (Wen et al, 2006).…”

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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“…Wu (2002b) found that the quasi-steady flow assumption in Warren & Root's model provides a good approximation for non-Darcian flow cases, as long as the double-porosity concept applies. Wen et al (2006) presented the non-Darcian flow towards a well which fully penetrates a single vertical fracture on the basis of the Izbash equation.…”

Section: Introductionmentioning

confidence: 99%

“…In the continuous models, fractured media are often treated either as equivalent homo-geneous porous media, or as media with multi-porosity/multi-permeability, to reflect various hydrological properties of the fractures and solid matrixes (Barenblatt, et al, 1960;Huyakorn & Pinder, 1983;Bai, et al, 1993). In the discrete models, geometrical properties of the fractures, such as aperture, orientation, and inter-connection and distribution of the fracture networks, are taken into consideration (Ge, 1997;Cornaton & Perrochet, 2002;Wen et al, 2006). Although it is difficult to describe the exact nature of flow in complex fractures, for example, Ge (1997) derived a general governing equation for fluid flow in fractures bounded by rough surfaces, considering the true aperture and tortuosity variations.…”

Section: Introductionmentioning

confidence: 99%

A double-porosity model for a fractured aquifer with non-Darcian flow in fractures

Altinörs¹,

Önder

2008

Hydrological Sciences Journal

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Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture-block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model. Mots clefs double porosité; aquifère fracturé; équation de Forcheimer; écoulement non-Darcien

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Non-Darcian flow in a single confined vertical fracture toward a well

Cited by 80 publications

References 33 publications

Effects of Hydraulic Gradient, Intersecting Angle, Aperture, and Fracture Length on the Nonlinearity of Fluid Flow in Smooth Intersecting Fractures: An Experimental Investigation

Effects of Hydraulic Gradient, Intersecting Angle, Aperture, and Fracture Length on the Nonlinearity of Fluid Flow in Smooth Intersecting Fractures: An Experimental Investigation

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

A double-porosity model for a fractured aquifer with non-Darcian flow in fractures

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