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  • Articles  (12)
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  • Darcy's law  (12)
  • Springer  (12)
  • 1995-1999  (12)
  • 1955-1959
  • Technology  (12)
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  • Articles  (12)
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  • Springer  (12)
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  • 1
    Electronic Resource
    Electronic Resource
    A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media (1997)
    Springer
    Transport in porous media 27 (1997), S. 243-264 
    Details
    ISSN: 1573-1634
    Keywords: permeability ; Darcy's law ; unsaturated flow ; dual scale ; resin transfer molding ; liquid injection molding.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006544107324
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  • 2
    Electronic Resource
    Electronic Resource
    Mathematical Treatment of Point Sources in a Flow Through Porous Media Governed by Darcy's Law (1997)
    Springer
    Transport in porous media 28 (1997), S. 51-67 
    Details
    ISSN: 1573-1634
    Keywords: point sources ; Darcy's law ; jumping conductivity ; discrete maximum principle ; gas flow ; wells
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We consider stationary air flow in a porous medium caused by extraction wells and governed by Darcy's law. Point sinks are described by Dirac functions. We distinguish two different situations: locally continuous and discontinuous conductivity near the wells. In both cases, well-posedness is proved. We propose a finite-element scheme in the general case and show the convergence of the approximated solution to the exact one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006598701763
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  • 3
    Electronic Resource
    Electronic Resource
    A Continuum Approach to Two-Phase Porous Media (1999)
    Springer
    Transport in porous media 35 (1999), S. 15-36 
    Details
    ISSN: 1573-1634
    Keywords: axioms of continuum ; resistance force ; relative flux density ; number D ; hydraulic conductivity ; Darcy's law ; Darcian mechanics.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An axiomatic method is used to derive governing equations of isothermal mechanics of two-phase porous media. The first and second axioms of continuum are formulated in order to define the continuum approach to the problem. A dimensionless number is introduced to simplify the general equations and to obtain the equations of Darcian mechanics. Several aspects of the method and the results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006508810941
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  • 4
    Electronic Resource
    Electronic Resource
    The Forchheimer equation: A theoretical development (1996)
    Springer
    Transport in porous media 25 (1996), S. 27-61 
    Details
    ISSN: 1573-1634
    Keywords: Forchheimer equation ; Darcy's law ; volume averaging ; closure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper we illustrate how the method of volume averaging can be used to derive Darcy's law with the Forchheimer correction for homogeneous porous media. Beginning with the Navier-Stokes equations, we find the volume averaged momentum equation to be given by $$\langle v_\beta \rangle = - \frac{K}{{\mu _\beta }} \cdot (\nabla \langle p_\beta \rangle ^\beta - \rho _\beta g) - F\cdot \langle v_\beta \rangle .$$ The Darcy's law permeability tensor, K, and the Forchheimer correction tensor, F, are determined by closure problems that must be solved using a spatially periodic model of a porous medium. When the Reynolds number is small compared to one, the closure problem can be used to prove that F is a linear function of the velocity, and order of magnitude analysis suggests that this linear dependence may persist for a wide range of Reynolds numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00141261
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  • 5
    Electronic Resource
    Electronic Resource
    Flow of Maxwell fluids in porous media (1996)
    Springer
    Transport in porous media 25 (1996), S. 167-192 
    Details
    ISSN: 1573-1634
    Keywords: elastic fluid ; volume averaging ; closure ; Darcy's law ; dynamic permeability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper we analyze the flow of a Maxwell fluid in a rigid porous medium using the method of volume averaging. We first present the local volume averaged momentum equation which contains Darcy-scale elastic effects and undetermined integrals of the spatial deviations of the pressure and velocity. A closure problem is developed in order to determine the spatial deviations and thus obtain a closed form of the momentum equation that contains a time-dependent permeability tensor. To gain some insight into the effects of elasticity on the dynamics of flow in porous media, the entire problem is transformed to the frequency domain through a temporal Fourier transform. This leads to a dynamic generalization of Darcy's law. Analytical results are provided for the case in which the porous medium is modeled as a bundle of capillary tubes, and a scheme is presented to solve the transformed closure problem for a general microstructure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00135854
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  • 6
    Electronic Resource
    Electronic Resource
    Permeability Tensor for Heterogeneous Porous Medium of Fibre Type (1998)
    Springer
    Transport in porous media 32 (1998), S. 1-19 
    Details
    ISSN: 1573-1634
    Keywords: anisotropic porous media ; permeability tensor ; cell model ; bundle of parallel fibres ; Darcy's law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A theoretical model which allows us to determine the permeability of a fibrous porous medium is proposed. Fibres are assumed to be parallel and nonuniform in space and material with a low volume fraction of fibres is considered. The model includes two geometric parameters: the diameter of fibres and the diameter of caverns or fissures inside the bundle of fibres. The tensor of permeability of the porous medium is determined based upon a generalized cell model. The components of permeability tensor depend on two parameters which are determined using experimental data and least-squares approximation. The influence of the geometric parameters on components of permeability tensor is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006548025449
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  • 7
    Electronic Resource
    Electronic Resource
    Flow pattern analysis for a well defined by point sinks (1995)
    Springer
    Transport in porous media 21 (1995), S. 209-223 
    Details
    ISSN: 1573-1634
    Keywords: well ; Darcy's law ; perfect layering ; point sinks ; Hankel transform ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper deals with the analytical description of single-phase flow caused by abstraction wells and governed by Darcy's law. Since we are mainly interested in the velocity field upon which an analysis of transport phenomena can be based, we may assume that the flow is quasi steady. A well may be composed of a number of point sinks, therefore the main problem is to determine the flow field caused by one point sink. For a perfectly layered subsurface the solution can be found by an approximation of the Hankel Transform using a Fast Fourier Transform. The final result is an algorithm that can be used to determine velocities and flow paths on any spatial scale, as will be shown by some examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00617406
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  • 8
    Electronic Resource
    Electronic Resource
    Generalized Forchheimer Equation for Two-Phase Flow Based on Hybrid Mixture Theory (1997)
    Springer
    Transport in porous media 26 (1997), S. 261-275 
    Details
    ISSN: 1573-1634
    Keywords: swelling porous media ; high velocity flow ; non-Darcy flow ; two-phase flow ; multi-phase flow ; mixture theory ; Forchheimer equation ; unsaturated flow ; Darcy's law ; non-linear flow ; hybrid mixture theory ; isotropic function theory.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper, we derive a Forchheimer-type equation for two-phase flow through an isotropic porous medium using hybrid mixture theory. Hybrid mixture theory consists of classical mixture theory applied to a multiphase system with volume averaged equations. It applies to media in which the characteristic length of each phase is ‘small’ relative to the extent of the mixture. The derivation of a Forchheimer equation for single phase flow has been obtained elsewhere. These results are extended to include multiphase swelling materials which have nonnegligible interfacial thermodynamic properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006536424162
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  • 9
    Electronic Resource
    Electronic Resource
    Effective Radius and Underpressure of an Air Extraction Well in a Heterogeneous Porous Medium (1997)
    Springer
    Transport in porous media 29 (1997), S. 323-340 
    Details
    ISSN: 1573-1634
    Keywords: Soil venting ; effective radius ; Darcy's law ; mixed nonconforming method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We consider the compressible steady state air flow in a porous medium caused by an extraction well and governed by Darcy's law. For a homogeneous soil matrix we have derived formulas (in 2-D and 3-D) to determine the effective radius of a single well depending on the well position and the depth of the domain. For inhomogeneous case (in 2-D) the influence of the heterogeneity, well position and the depth of the water table on the effective radius and on the pressure at the well is studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006598132143
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  • 10
    Electronic Resource
    Electronic Resource
    Inertial and Second Grade Effects on Macroscopic Equations for the Flow of a Fluid in a Porous Medium (1998)
    Springer
    Transport in porous media 33 (1998), S. 205-226 
    Details
    ISSN: 1573-1634
    Keywords: Darcy's law ; Forchheimer's equation ; homogenization ; linear stability analysis of interface ; non‐Newtonian fluids of grade two ; porous media.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Homogenization techniques are used to upscale from pore to laboratory or field scale viscous and second grade non‐Newtonian flow in a porous medium. Nonlinear forms of Darcy's law are obtained and analysed under a series of symmetry properties. The general case of displacement of one of these fluids by another with different properties is considered and a linear stability analysis is performed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006520326273
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  • 11
    Electronic Resource
    Electronic Resource
    Optimal fluid injection strategies for in situ mineral leaching in two-dimensions (1999)
    Springer
    Journal of engineering mathematics 36 (1999), S. 185-206 
    Details
    ISSN: 1573-2703
    Keywords: mineral leaching ; Darcy's law ; boundary-integral approach ; injection strategy ; withdrawal flows.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004406311441
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  • 12
    Electronic Resource
    Electronic Resource
    Onset of bouyancy-driven convection in superposed reacting fluid and porous layers (1998)
    Springer
    Journal of engineering mathematics 33 (1998), S. 31-47 
    Details
    ISSN: 1573-2703
    Keywords: linear stability ; Darcy's law ; zero-order exothermic reaction ; collocation method.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A linear stability analysis is applied to the onset of bouyancy-driven convection in a horizontal layer of reacting fluid overlying a porous region saturated with the same fluid. The fluid is assumed to be undergoing zero-order exothermic reactions in both regions. At the interface between fluid and porous layers the boundary conditions proposed by Nield [1] are employed; these include the empirical slip condition suggested by Beavers and Joseph [2]. Predictions for the onset of convection and critical wavenumbers are obtained from the analysis by the collocation method and solution of the resulting generalized eigenvalue problem. The effect of variable fluid/porous layer depth ratio, Frank–Kamenetskii number or thermal boundary conditions on the onset of fluid motions is studied, and ignition values of the Frank–Kamenetskii number for the system are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004238905710
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