A Criterion for Non-Darcy Flow in Porous Media

Zeng, Zhengwen; Grigg, Reid B.

doi:10.1007/s11242-005-2720-3

Cited by 540 publications

(301 citation statements)

References 28 publications

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“…According to Zeng and Grigg (2006), the Forchheimer number is recommended as a criterion for identifying non-Darcy flow because it has the advantage of clear meaning. It equals the ratio of pressure drop caused by liquid-solid interactions to that by viscous resistance, and it is directly related to the non-Darcy effect.…”

Section: Discussionmentioning

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: Discussionmentioning

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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“…Extensive discussion of the limits of applicability of Darcy flow in porous media and references to further studies are given by Zeng & Grigg (2006). The two criteria-the Reynolds number and the Forchheimer number-are in general used for assessing limits to the applicability of Darcy flow.…”

Section: (C) Test Procedures and Resultsmentioning

confidence: 99%

Surface permeability tests: experiments and modelling for estimating effective permeability

Selvadurai

2010

Proc. R. Soc. A.

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This paper presents a technique for determining the near surface permeability of geomaterials and involves the application of a uniform flow rate to an open central region of a sealed annular patch on an otherwise unsealed flat surface. Darcy's flow is established during attainment of a steady pressure at a constant flow rate. This paper describes the experimental configuration and its theoretical analysis via mathematical and computational techniques. The methods are applied to investigate the surface permeability characteristics of a cuboidal block of Indiana limestone measuring 508 mm. An inverse analysis procedure is used to estimate the permeability characteristics at the interior of the Indiana limestone block. The resulting spatial distribution of permeability is used to estimate the effective permeability of the tested block.

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“…Determination of the vertically integrated volume fluxes Volume fluxes, in the context of simulating CO 2 storage problems, are generally calculated using Darcy's law. However, owing to the lower dynamic viscosity of CO 2 at the relevant pressures of concern, it is pertinent to consider non-Darcy losses using the Forchheimer equation (Zeng & Grigg 2006). Therefore, the fluxes q i are defined by the Forchheimer equation …”

Section: Mass Conservationmentioning

confidence: 99%

Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs

2014

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In this article, a two-layer vertical equilibrium model for the injection of carbon dioxide into a low-pressure porous reservoir containing methane and water is developed. The dependent variables solved for include pressure, temperature and CO 2 -CH 4 interface height. In contrast to previous two-layer vertical equilibrium models in this context, the compressibility of all material components is fully accounted for. Non-Darcy effects are also considered using the Forchheimer equation. The results show that, for a given injection scenario, as the initial pressure in the reservoir decreases, both the pressure buildup and temperature change increase. A comparison was conducted between a fully coupled non-isothermal numerical model and a simplified model where fluid properties are held constant with temperature. This simplified model was found to provide an excellent approximation when using the injection fluid temperature for calculating fluid properties, even when the injection fluid was as much as ±15 • C of the initial reservoir temperature. The implications are that isothermal models can be expected to provide useful estimates of pressure buildup in this context. Despite the low viscosity of CO 2 at the low pressures studied, non-Darcy effects were found to be of negligible concern throughout the sensitivity analysis undertaken. This is because the CO 2 density is also low in this context. Based on these findings, simplified analytic solutions are derived, which accurately calculate both the pressure buildup and temperature decline during the injection period.

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A Criterion for Non-Darcy Flow in Porous Media

Cited by 540 publications

References 28 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

Surface permeability tests: experiments and modelling for estimating effective permeability

Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs

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