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1.
The objective of this article is to make use of the phenomenological approach to construct models for the transport of extensive
quantities, such as mass of a fluid phase, mass of a component of a fluid phase, momentum of a phase and energy, in porous
medium domains. Special attention is devoted to express the fluxes of these extensive quantities, especially the non-advective
ones, as functions of their relevant driving forces, obeying the principle of minimum entropy production. It is shown that
for each extensive quantity, we have a linear diffusive flux term, a non-linear diffusive term, and a dispersive flux term.
The latter is shown to be proportional to the velocity squared. In each case, the number of moduli that describe fluid and
porous matrix properties is determined. The momentum balance equation for a porous medium domain, which is the “motion equation,”
is analyzed and simplified for special cases, leading to Darcy’s law and to Brinkman’s equation. 相似文献
2.
Arieh Pistiner 《Transport in Porous Media》2007,70(3):293-304
The saturation distribution—within an anisotropic aquifer—of a pollutant discharging from an underground source is modeled
by a two-dimensional, nonlinear diffusion–convection equation. A closed form self-similar solution is obtained for the steady
saturation distribution in the immiscible zone. The results may be used to rationalize field data collected for predicting
locations of underground leakage sources in aquifers and to understand the influence of the anisotropic permeability’s parameters
on the oil distribution in the porous medium.
An erratum to this article can be found at 相似文献
3.
This paper presents the analytic solution for flow of a magnetohydrodynamic (MHD) Sisko fluid through a porous medium. The
non-linear flow problem in a porous medium is formulated by introducing the modified Darcy’s law for Sisko fluid to discuss
the flow in a porous medium. The analytic solutions are obtained using homotopy analysis method (HAM). The obtained analytic
solutions are explicitly expressed by the recurrence relations and can give results for all the appropriate values of material
parameters of the examined fluid. Moreover, the well-known solutions for a Newtonian fluid in non-porous and porous medium
are the limiting cases of our solutions. 相似文献
4.
Fluid flow at the interface of a porous medium and an open channel is the governing phenomenon in a number of processes of
industrial importance. Traditionally, this has been modeled by applying the Brinkman’s modification of Darcy’s law to obtain
the velocity profile in terms of an additional parameter known as the “apparent viscosity” or the “slip coefficient”. To test
this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close
vicinity of the permeable boundary of a porous medium. The porous medium used in the experiments consisted of a network of
continuous glass strands woven together in a random fashion.
A Hele–Shaw cell was partially filled with a fibrous preform such that an open channel flow is coupled with the Darcy flow
inside the preform through the permeable interface of the preform. The open channel portion of the Hele–Shaw cell also acts
as an ideal porous medium of known in-plane permeability which is much higher than the permeability of the fibrous porous
medium. A viscous fluid is injected at a constant flow rate through the above arrangement and a saturated and steady flow
is established through the cell. Using LDA, steady state velocity profiles are accurately measured by traversing across the
cell in the direction perpendicular to the flow. A series of experiments were conducted in which fluid viscosity, flow rate,
solid volume fraction of the porous medium and depth of the Hele–Shaw cell were varied. For each and every case in which the
conditions for Hele–Shaw approximation were valid, the depth of the boundary layer zone or the screening length inside the
fibrous preform was found to be of the order of the channel depth. This is much larger as compared to the Brinkman’s prediction
of the screening length which is of the order of √K, where K is the permeability of the fibrous porous medium. Based on this finding, we modified the boundary condition in the Brinkman’s
solution and found that the velocity profile results compared well with the experimental data for the planar geometry and
the fibrous preforms for volume fractions of 7%, 14% and 21% for Hele–Shaw cell depths of 1.6 and 3.175 mm. For a cell depth
of 4.8 cm, in which the Hele–Shaw approximation was not valid, the boundary layer thickness or the screening length was found
to be less than the mold or channel depth but was still much larger than the Brinkman’s prediction.
Received: 10 May 1996 / Accepted: 26 August 1996 相似文献
5.
In a porous material, both the pressure drop across a bubble and its speed are nonlinear functions of the fluid velocity. Nonlinear dynamics of bubbles in turn affect the macroscopic hydraulic conductivity, and thus the fluid velocity. We treat a porous medium as a network of tubes and combine critical path analysis with pore-scale results to predict the effects of bubble dynamics on the macroscopic hydraulic conductivity and bubble density. Critical path analysis uses percolation theory to find the dominant (approximately) one-dimensional flow paths. We find that in steady state, along percolating pathways, bubble density decreases with increasing fluid velocity, and bubble density is thus smallest in the smallest (critical) tubes. We find that the hydraulic conductivity increases monotonically with increasing capillary number up to Ca 10–2, but may decrease for larger capillary numbers due to the relative decrease of bubble density in the critical pores. We also identify processes that can provide a positive feedback between bubble density and fluid flow along the critical paths. The feedback amplifies statistical fluctuations in the density of bubbles, producing fluctuations in the hydraulic conductivity. 相似文献
6.
In this paper steady flow of a third grade fluid through porous space is considered. Modified Darcy’s law for third grade
fluid in a porous space has been introduced. The governing non-linear equation is first modelled and then solved using homotopy
analysis method (HAM). The convergence of the obtained series solution is discussed. The effects of the emerging parameters
on the velocity field are seen. It is noted that meaningful solution exists only in the case of suction. 相似文献
7.
A thin film of a power–law fluid flowing down a porous inclined plane is considered. It is assumed that the flow through the porous medium is governed by the modified Darcy’s law together with Beavers–Joseph boundary condition for a general power–law fluid. Under the assumption of small permeability relative to the thickness of the overlying fluid layer, the flow is decoupled from the filtration flow through the porous medium and a slip condition at the bottom is used to incorporate the effects of the permeability of the porous substrate. Applying the long-wave theory, a nonlinear evolution equation for the thickness of the film is obtained. A linear stability analysis of the base flow is performed and the critical condition for the onset of instability is obtained. The results show that the substrate porosity in general destabilizes the film flow system and the shear-thinning rheology enhances this destabilizing effect. A weakly nonlinear stability analysis reveals the existence of supercritical stable and subcritical unstable regions in the wave number versus Reynolds number parameter space. The numerical solution of the nonlinear evolution equation in a periodic domain shows that the fully developed nonlinear solutions are either time-dependent modes that oscillate slightly in the amplitude or time independent stable two-dimensional nonlinear waves with large amplitude referred to as ‘permanent waves’. The results show that the shape and the amplitude of the nonlinear waves are strongly influenced by the permeability of the porous medium and the shear-thinning rheology. 相似文献
8.
Effects of porous medium have been investigated on the steady flow of a third grade fluid between two stationary porous plates. The continuity and momentum equations along with modified Darcy??s law are used for the development of mathematical problem. The governing nonlinear problem is solved by a homotopy analysis method. The dimensionless velocity and shear stresses at the plates are analyzed. 相似文献
9.
Accepted theory for anisotropic flow in porous media establishes that the properties of a particular flow may depend upon
the flow orientation, but generally assumes that flow properties are invariant for a reversal of the flow direction. By simulating
simple two-dimensional and three-dimensional flows from the pore-scale, we demonstrate that while this assumption holds true
when flow is slow such that the approximations supporting Darcy’s law apply, reversal of the flow direction can have a significant
impact on nonlinear corrections to Darcy’s law that become important at higher flow rates. In this study, we consider flow
through simple periodic porous media consisting of oriented, asymmetrical grains for Reynolds numbers <150. Analysis of the
pore-scale flow structure demonstrates that direction-dependent effects can be linked with asymmetry. We present a nonlinear
correction to Darcy’s law that accounts for this extended anisotropy and propose a macroscopic morphological measure to quantify
asymmetry of the solid phase. 相似文献
10.
11.
Laminar, single-phase, finite-volume solutions to the Navier–Stokes equations of fluid flow through a fracture within permeable
media have been obtained. The fracture geometry was acquired from computed tomography scans of a fracture in Berea sandstone,
capturing the small-scale roughness of these natural fluid conduits. First, the roughness of the two-dimensional fracture
profiles was analyzed and shown to be similar to Brownian fractal structures. The permeability and tortuosity of each fracture
profile was determined from simulations of fluid flow through these geometries with impermeable fracture walls. A surrounding
permeable medium, assumed to obey Darcy’s Law with permeabilities from 0.2 to 2,000 millidarcies, was then included in the
analysis. A series of simulations for flows in fractured permeable rocks was performed, and the results were used to develop
a relationship between the flow rate and pressure loss for fractures in porous rocks. The resulting friction-factor, which
accounts for the fracture geometric properties, is similar to the cubic law; it has the potential to be of use in discrete
fracture reservoir-scale simulations of fluid flow through highly fractured geologic formations with appreciable matrix permeability.
The observed fluid flow from the surrounding permeable medium to the fracture was significant when the resistance within the
fracture and the medium were of the same order. An increase in the volumetric flow rate within the fracture profile increased
by more than 5% was observed for flows within high permeability-fractured porous media. 相似文献
12.
The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix
is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space.
The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques
from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration.
At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate
boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties
are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach
is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation
employing finite elements or analogous numerical procedures. 相似文献
13.
This study concentrates on the unsteady magnetohydrodynamics (MHD) rotating flow of an incompressible generalized Burgers’s
fluid past a suddenly moved plate through a porous medium. Modified Darcy’s law for generalized Burgers’s fluid in a rotating
frame has been used to model the governing flow problem. The closed form solution of the governing flow problem has been obtained
by employing Laplace transform technique. The integral appearing in the inverse Laplace transform has been evaluated numerically.
The influence of various parameters on the velocity profile has been delineated through several graphs and discussed in detail.
It was found that the fluid is decelerated with increasing Hartmann number M and porosity parameter K. However, for large Hall parameter m, the real part of velocity decreases and the imaginary part of velocity increases. 相似文献
14.
A. K. Ghosh A. D. Williams J. M. Zucker J. L. Mathews N. Spinhirne 《Experimental Mechanics》2008,48(2):139-152
In nature, shape and structure evolve from the struggle for better performance. Often, biological structures combine multiple
beneficial properties, making research into mimicking them very complex. Presented here is a summary of observations from
a series of experiments performed on a material that closely resembles the human skull bone’s cancellous structure under acoustic
loads. Transmission loss through flat and curved open-cell polyurethane foam samples is observed using air and water as the
two interstitial fluids. Reduction in strength and stiffness caused by porosity can be recovered partially by filling the
interstitial pores with a fluid. The test findings demonstrate the influence of the interstitial fluid on the mechanical characteristics
of a porous structure in a quantitative manner. It is also demonstrated that the transmission loss does not depend only on
the mass per unit area of the structure as predicted by acoustic mass law. Current tests also demonstrate that the transmission
loss is more sensitive to the interstitial fluid than the shape and support conditions of the structures. Test observations
thus support the concepts of “moisture-sensitivity of biological design” and the “law of hierarchy in natural design”. 相似文献
15.
Permeability of the Fluid-Filled Inclusions in Porous Media 总被引:1,自引:0,他引:1
In this article, we propose an approach to obtain the equivalent permeability of the fluid-filled inclusions embedded into
a porous host in which a fluid flow obeys Darcy’s law. The approach consists in the comparison of the solutions for one-particle
problem describing the flow inside the inclusion, firstly, by the Stokes equations and then by using Darcy’s law. The results
obtained for spheres (3D) and circles (2D) demonstrate that the inclusion equivalent permeability is a function of its radius
and, additionally, depends on the host permeability. Based on this definition of inclusion permeability and using effective
medium method, we have calculated the effective permeability of the double-porosity medium composed of the permeable matrix
(with small scale pores) and large scale secondary spherical pores. 相似文献
16.
This paper generalizes the analysis of four magnetohydrodynamic (MHD) flow problems of an Oldroyd-B fluid discussed by Asghar
et al. [Int. J. Non-linear Mech. 40, 589–601 (2005)] into three directions: (i) to discuss the problems in a porous medium using modified Darcy’s law (ii) to
see the influence of Hall current (iii) to determine the effect of rheological parameter of Burgers’ fluid. Analytical solutions
of velocity distribution valid at large and small times are given in each problem. Comparison has been provided for Oldroyd-B
and Burgers’ fluids through graphs. The physical interpretation is also included. 相似文献
17.
Smoothed Particle Hydrodynamics Modeling of Transverse Flow in Randomly Aligned Fibrous Porous Media
The Lagrangian smoothed particle hydrodynamics (SPH) method is employed to obtain a meso-/micro-scopic pore-scale insight
into the transverse flow across the randomly aligned fibrous porous media in a 2D domain. Fluid is driven by an external body
force, and a square domain with periodic boundary conditions imposed at both the streamwise and transverse flow direction
is assumed. The porous matrix is established by randomly embedding a certain number of fibers in the square domain. Fibers
are represented by position-fixed SPH particles, which exert viscous forces upon, and contribute to the density variations
of, the nearby fluid particles. An additional repulsive force, similar in form to the 12-6 Lennard-Jones potential between
atoms, is introduced to consider the no-penetrating restraint prescribed by the solid pore structure. This force is initiated
from the fixed solid material particle and may act on its neighboring moving fluid particles. Fluid flow is visualized by
plotting the local velocity vector field; the meandering fluid flow around the porous microstructures always follow the paths
of least resistance. The simulated steady-state flow field is further used to calculate the macroscopic permeability. The
dimensionless permeability (normalized by the squared characteristic dimension of the fiber cross section) exhibits an exponential
dependence on the porosity within the intermediate porosity range, and the derived dimensionless permeability—porosity relation
is found to have only minor dependence on either the relative arrangement condition among fibers or the fiber cross section
(shape or area). 相似文献
18.
Consider an incompressible fluid, filtrating through a saturated cylindrical porous layer with rectangular cross-section. A steady pressure gradient, parallel to the axis of the layer, drives a one-directional stationary non recirculating flow when the Darcy law has to include inertial and viscous corrections. This is the case, for instance, when the porosity of the medium or the seeping flow rate are not very small. The resulting nonlinear problem belongs to a class of equations which was proved to have positive solutions. It also satisfies a comparison principle from which approximations from above and from below are derived for the steady flow. The estimate from above is the flat profile which solves the Darcy-Forchheimer equation, which does not take account of viscous effects, and the approximation is excellent when the modified Darcy number is small, under the additional condition that the Forchheimer coefficient be small also. The flow still solves the problem when gradient forces, orthogonal to the axis of the layer, are also present. 相似文献
19.
This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments. 相似文献
20.
The classic constitutive equation relating fluid flux to a gradient in potential (pressure head plus gravitational energy)
through a porous medium was discovered by Darcy in the mid 1800s. This law states that the flux is proportional to the pressure
gradient. However, the passage of the fluid through the porous matrix may cause a local variation of the permeability. For
example, the flow may perturb the porous formation by causing particle migration resulting in pore clogging or chemically
reacting with the medium to enlarge the pores or diminish the size of the pores. In order to adequately represent these phenomena,
we modify the constitutive equations by introducing a memory formalism operating on both the pressure gradient–flux and the
pressure–density variations. The memory formalism is then represented with fractional order derivatives. We perform a number
of laboratory experiments in uniformly packed columns where a constant pressure is applied on the lower boundary. Both homogeneous
and heterogeneous media of different characteristic particle size dimension were employed. The low value assumed by the memory
parameters, and in particular by the fractional order, demonstrates that memory is largely influencing the experiments. The
data and theory show how mechanical compaction can decrease permeability, and consequently flux. 相似文献