On the derivation of the Forchheimer equation by means of the averaging theorem

Ruth, Douglas; Ma, H.

doi:10.1007/bf01063962

Cited by 260 publications

(137 citation statements)

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“…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. Inertial effects dominate over viscous effects at the critical Forchheimer number (Fo > 1) (Ruth and Ma, 1992). The Reynolds number is instead a dimensionless number that indicates when microscopic inertial effects become important.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, a high microscopic Reynolds number does not necessarily imply non-Darcian flow. Instead, Fo indicates precisely the onset of non-Darcian flow (Ruth and Ma, 1992); it accounts for both velocity (v) and structure of the medium because β is structure dependent. The term β inherently contains information on the tortuosity of the flow paths that leads to changes in the microscopic inertial terms.…”

Section: Discussionmentioning

confidence: 99%

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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%

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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“…From the permeability measurements we can obtain some insight into the onset of inertial effects inside magmatic foams during outgassing. The Forchheimer number (Fo), which is essentially a Reynolds number at the scale of the porous medium, provides an easy way to quantify this (Ruth and Ma, 1992). It is obtained from the quantities defined in Eq.…”

Section: Insights Into Inertial Effects In Vesicular Magmasmentioning

confidence: 99%

“…3 and 4 was estimated tõ 2% from multiple measurements of the same sample. To take into account energy loss due to both viscous and inertial effects, the onedimensional form of the Forchheimer equation (Ruth and Ma, 1992;Rust and Cashman, 2004) was fit to our experimental data to obtain the viscous (Darcian) k 1 and inertial (non-Darcian) k 2 permeabilities:…”

Section: Permeability Measurementsmentioning

confidence: 99%

Permeability measurements of Campi Flegrei pyroclastic products: An example from the Campanian Ignimbrite and Monte Nuovo eruptions

Polacci

Maisonneuve

Giordano

et al. 2014

Journal of Volcanology and Geothermal Research

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In order to understand outgassing during volcanic eruptions, we performed permeability measurements on trachy-phonolitic pyroclastic products from the Campanian Ignimbrite and Monte Nuovo, two explosive eruptions from the active Campi Flegrei caldera, Southern Italy. Viscous (Darcian) permeability spans a wide range between 1.22 × 10 −14 and 9.31 × 10 −11 m 2 . Inertial (non-Darcian) permeability follows the same trend as viscous permeability: it increases as viscous permeability increases, highlighting the strong direct correlation between these two parameters. We observe that vesicularity does not exert a first order control on permeability: the Monte Nuovo scoria clasts are the most permeable samples but not the most vesicular; pumice clasts from the Campanian Ignimbrite proximal facies, whose vesicularity is comparable with that of Monte Nuovo scoriae, are instead the least permeable. In addition, we find that sample geometry exhibits permeability anisotropy as samples oriented parallel to vesicle elongation are more permeable than those oriented perpendicular. We compare our results with permeability values of volcanic products from effusive and explosive activity, and discuss the role of melt viscosity and crystallinity on magma permeability.

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“…(1.7), |u| represents the 2-norm of u, and the term − µ K u − ∇p + ρg is the Darcy term. For very high velocities in porous media, inertial effects can also become significant, so the inertial term ρF √ K |u|u, which is also called the Forchheimer term [24], is included in (1.7).…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Mixed finite element-based fully conservative methods for simulating wormhole propagation

Kou

Sun

2016

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. MIXED FINITE ELEMENT-BASED FULLY CONSERVATIVE METHODS FOR SIMULATING WORMHOLE PROPAGATION *JISHENG KOU † , SHUYU SUN ‡ , AND YUANQING WU § Abstract. Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy-Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy-Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

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On the derivation of the Forchheimer equation by means of the averaging theorem

Cited by 260 publications

References 5 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

Permeability measurements of Campi Flegrei pyroclastic products: An example from the Campanian Ignimbrite and Monte Nuovo eruptions

Mixed finite element-based fully conservative methods for simulating wormhole propagation

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