scholarly journals Modeling Transport and Adsorption of Arsenic Ions in Iron-Oxide Laden Porous Media. Part I: Theoretical Developments

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 779
Author(s):  
Krishna Pillai ◽  
Aman Raizada
Keyword(s):  
Porous Media ◽  
Transport Coefficient ◽  
Solid Phase ◽  
Arsenic Species ◽  
Volume Averaging ◽  
Diffusion Problem ◽  
Passive Diffusion ◽  
Dispersion Tensor ◽  
Modeling Transport ◽  
Water Filters

The process of transport and trapping of arsenic ions in porous water filters is treated as a classic mass transport problem which, at the pore scale, is modeled using the traditional convection-diffusion equation, representing the migration of species present in very small (tracer) amounts in water. The upscaling, conducted using the volume averaging method, reveals the presence of two possible forms of the macroscopic equations for predicting arsenic concentrations in the filters. One is the classic convection-dispersion equation with the total dispersion tensor as its main transport coefficient, and which is obtained from a closure formulation similar to that of the passive diffusion problem. The other equation form includes an additional transport coefficient, hitherto ignored in the literature and identified here as the adsorption-induced vector. These two coefficients in the latter form are determined from a system of two closure problems that include the effects of both the passive diffusion as well as the adsorption of arsenic by the solid phase of the filter. This theoretical effort represents the first serious effort to introduce a detailed micro–macro coupling while modeling the transport of arsenic species in water filters representing homogeneous porous media.

Thermal Analysis of Multijet Impingement Through Porous Media to Design a Confined Heat Management System

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Carlos Zing ◽  
Shadi Mahjoob
Keyword(s):  
Porous Media ◽  
High Efficiency ◽  
Solid Phase ◽  
Electronics Cooling ◽  
Jet Impingement ◽  
Fluid Phase ◽  
Volume Averaging ◽  
High Heat Flux ◽  
Base Temperature ◽  
Heat Management

Thermal management has a key role in the development of advanced electronic devices to keep the device temperature below a maximum operating temperature. Jet impingement and high conductive porous inserts can provide a high efficiency cooling and temperature control for a variety of applications including electronics cooling. In this work, advanced heat management devices are designed and numerically studied employing single and multijet impingement through porous-filled channels with inclined walls. The base of these porous-filled nonuniform heat exchanging channels will be in contact with the devices to be cooled; as such the base is subject to a high heat flux leaving the devices. The coolant enters the heat exchanging device through single or multijet impingement normal to the base, moves through the porous field and leaves through horizontal exit channels. For numerical modeling, local thermal nonequilibrium model in porous media is employed in which volume averaging over each of the solid and fluid phase results in two energy equations, one for solid phase and one for fluid phase. The cooling performance of more than 30 single and multijet impingement designs are analyzed and compared to achieve advantageous designs with low or uniform base temperature profiles and high thermal effectiveness. The effects of porosity value and employment of 5% titanium dioxide (TiO2) in water in multijet impingement cases are also investigated.

Comments on “Lamb's problem for fluid-saturated porous media”

1992 ◽  
Vol 82 (5) ◽  
pp. 2263-2273
Author(s):  
M. D. Sharma
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Elastic Solid ◽  
Porous Solid ◽  
Surface Boundary ◽  
Vertical Force ◽  
Saturated Porous Media ◽  
Concentrated Load ◽  
Lamb’S Problem

Abstract Philippacopoulos (1988) discusses axisymmetric wave propagation in a fluid-saturated porous solid half-space. The disturbance is considered to be produced by the concentrated load P0exp(iωt) acting vertically at the surface. Boundary conditions chosen imply that a vertical force acting on the surface of fluid-saturated porous solid exerts no pressure on the interstitial liquid. These boundary conditions do not seem appropriate. In the present study, the boundary conditions have been changed in order to satisfy the concept of porosity. These are also in accordance with those discussed by Deresiewicz and Skalak (1963) for the special case of interface between liquid and liquid-saturated porous media. Analytic expressions have been derived for the displacements at the surface. The limiting case of a dry elastic solid is also deduced. Effects of intergranular energy losses due to solid phase and of dissipation due to flow of pore fluid are exhibited on the displacements at the surface. Contrary to Philippacopoulos (1988), the displacements in saturated poroelastic solids are found to be larger than those in a dry elastic solid with same Lamb's moduli.

Fundamentals of Transport Equation Formulation for Two-Phase Flow in Homogeneous and Heterogeneous Porous Media

1999 ◽  
Author(s):  
Michel Quintard ◽  
Stephen Whitaker
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Practical Importance ◽  
Volume Averaging ◽  
Heterogeneous Porous Media ◽  
Homogenization Theory ◽  
Length Scale ◽  
Two Phase ◽  
The Hierarchical Structure ◽  
Method Of Volume Averaging

Most porous media of practical importance are hierarchical in nature; that is, they are characterized by more than one length-scale. When these length-scales are disparate, the hierarchical structure can be analyzed by the method of volume averaging (Anderson and Jackson, 1967; Marie, 1967; Slattery, 1967; Whitaker, 1967). In this approach, macroscopic quantities at a given length-scale are defined in terms of a boundary value problem that describes the phenomena at a smaller length-scale, and information is filtered from one scale to another by a series of volume and area integrals. Other methods, such as ensemble averaging (Matheron, 1965; Dagan, 1989) or homogenization theory (Bensoussan et al, 1978; Sanchez-Palencia, 1980), have been used to study hierarchical systems, and developments specific to the problems under consideration in this chapter can be found in Bourgeat (1984), Auriault (1987), Amaziane and Bourgeat (1988), and Sáez et al. (1989). The transformation from the Darcy scale to the large scale is a recurrent problem in reservoir and aquifer engineering. A detailed description of reservoir properties is available through geostatistical analysis (Journel, 1996) on a fine grid with a length-scale much smaller than the scale of the blocks in the reservoir simulator. “Effective” or “pseudo” properties are assigned to the coarse grid blocks, while the forms of the large-scale equations are required to be the same as those used at the Darcy scale (Coats et al., 1967; Hearn, 1971; Jacks et al., 1972; Kyte and Berry, 1975; Dake, 1978; Killough and Foster, 1979; Yokoyama and Lake, 1981; Kortekaas, 1983; Thomas, 1983; Kossack et al., 1990). A detailed discussion of the comparison between the several approaches is beyond the scope of this chapter; however, one can read Bourgeat et al. (1988) for an introductory comparison between the method of volume averaging and the homogenization theory, and Ahmadi et al. (1993) for a discussion of the various classes of pseudofunction theories.

scholarly journals Measurement and simulation of the nonlocal dispersion tensor in porous media

2007 ◽  
Vol 25 (4) ◽  
pp. 563
Author(s):  
M.W. Hunter ◽  
A.N. Jackson ◽  
P.T. Callaghan
Keyword(s):  
Porous Media ◽  
Dispersion Tensor ◽  
Nonlocal Dispersion
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