The Porous Media

A porous medium may be described as a solid coutainii many holes and tortuous passages. The number of holes or pores is sufficiently great that a volume average is needed to estimate pertinent properties. Pores that occupy a definite fiuction of the bulk volume consdmte a complex network of voids. The manner in which holes or pores are embedded, the extent of their interconnection, and dieir location, size and shape characterize the porous medium. The term porosity refers to the fraction of the medium that contains voids. When a fluid is passed over the medium, the fraction of the medium (i.e., the pores) that contributes to the flow is referred to as the effective porosity. 

Porous media can be further categorized in terms of geometrical or structural properties as they relate to the matrix that affects flow and in terms of (he flow properties that describe the matrix from the standpoint of the contained fluid. Geometrical or structural properties are best represented by average properties, from which these average structural properties are related to flow properties. 

A microscopic description characterizes (he strucmre of the pores. The objective of pore-strucmre analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are porosity, permeability, tortuosity and connectivity. In studying different stunples of (he same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical capillaries. The diameters of the model capillaries are defined on die basis of a convenient distribution function. 

Pore structure for unconsolidated media is inferred from a particle size distribution, the geometry of the particles and flie packii arrangement of particles. The theory of packing is well established for symmetrical geometries such as spheres. Information on particle size, geometry and the theory of packii allows relationships between pore size distributions and particle size distributions to be established. 

A macroscopic description is based on average or bulk properties at sizes much larger than a single pore. In characterizing a porous medium macroscopically, one must deal with the scale of description. The scale used depends on the manner and size in which we wish to model the porous medium. A simplified, but sometimes accurate, approach is to assume the medium to be ideal meaning homogaieous, uniform and isotropic. 

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D Arcy s work was published in a book with the unlikely title "Les fontanes publiques de la ville de Dijon." The porous media in question were filter beds through which the water for the fountains circulated. 

Due to difficulties and uncertainties in the experimental separation of the porous media [93], and the inevitability of approximations in the analytical treatment [87,89], the nature of the chain movement in a random environment is still far from being well understood, and theoretical predictions are controversial [87,89]. Thus, on the ground of replica calculations within a variational approach, one predicts three regimes [87] in which the chain gyration radius Rg scales with the number of repeatable units N as rI (X for low, R x N for medium, and R x for high... 

Figure 16.22 shows SEM micrographs for the porous media of ceramic support at different magnifications. The non-uniformity resulted from the synthetic foam used as a base to absorb the ceramic solution before vaporising any water from the inorganic mixture. Uniform porous media as a solid support for the membrane was obtained. 

One approach to extend such theories to more complex media is network theory. This approach utihzes solutions for transport in single pores, usually in one dimension, and couples these solutions through a network of nodes to mimic the general structure of the porous media [341], The complete set of equations for aU pores and nodes is then solved to determine overall transport behavior. Such models are computationally intense and are somewhat heuristic in nature. 

Fig. 5.1.9 (a) MR measured propagators and es the velocity distribution narrows due to the (b) corresponding calculated RTDs for flow in a dispersion mechanisms of the porous media model packed bed reactor composed of 241- this effect is observed in the RTDs as a pm monodisperse beads in a 5-mm id circular narrowing of the time window during which column for observation times A ranging from spins will reside relative to the mean residence 20 to 300 ms. As the observation time increas- time as the conduit length is increased. 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

The design of a cross-flow filter system employs an inertial filter principle that allows the permeate or filtrate to flow radially through the porous media at a relatively low face velocity compared to that of the mainstream slurry flow in the axial direction, as shown schematically in Figure 15.1.9 Particles entrained in the high-velocity axial flow field are prevented from entering the porous media by the ballistic effect of particle inertia. It has been suggested that submicron particles penetrate the filter medium and form a dynamic membrane or submicron layer, as shown in... 

The hydraulic conductivity, K, is a parameter that includes the behavior of both the porous media and the fluid. It is often desirable to know the behavior of just the porous media or its intrinsic permeability, k, which is theoretically independent of the fluid. The relationship between the two parameters is given by... 

Thermally enhanced extraction is another experimental approach for DNAPL source removal. Commonly know as steam injection, this technique for the recovery of fluids from porous media is not new in that it has been used for enhanced oil recovery in the petroleum industry for decades, but its use in aquifer restoration goes back to the early 1980s. Steam injection heats the solid-phase porous media and causes displacement of the pore water below the water table. As a result of pore water displacement, DNAPL and aqueous-phase chlorinated solvent compounds are dissolved and volatilized. The heat front developed during steam injection is controlled by temperature gradients and heat capacity of the porous media. Pressure gradients and permeability play a less important role. 

The solubility of contaminants in subsurface water is controlled by (1) the molecular properties of the contaminant, (2) the porous media solid phase composition, and (3) the chemistry of the aqueous solution. The presence of potential cosolvents or other chemicals in water also affects contaminant solubility. A number of relevant examples selected from the literature are presented here to illustrate various solubility and dissolution processes. 

As mentioned previously, the retention of contaminants on geosorbents may occur by surface adsorption on or into the coUoid fraction of the solid phase and by physical retention as hquid ganglia or as precipitates into the porous media. The type of retention is defined by the properties of the solid phase and the contaminants as well as by the composition of the subsurface water solution and the ambient temperature. 

We simulate these systems using standard finite element techniques (e.g.. Baker 1983) for solutions to the porous media conservation equations of mass, momentum, and energy on a rectilinear mesh using a code called BasinLab (Manning etal. 1987). 

The thickness (t), location L/D), and pore size (p) of the porous media were all shown to affect NO, emissions. The NOj, emissions decreased with increasing thickness up to t 2.5 cm and with smaller pore sizes. The lowest NO, emissions were found when L/D = 1.1-1.5. 

Moreover, if one assumes that the (Ur) changes very slowly on the length scale of the porous media, (i.e., ), then the viscous stress term in the Brinkman equation can be neglected and this equation reduces to ... 

L. A. Peletier, The Porous Media Equation in Application of Nonlinear Analysis in the Physical Sciences, H. Amann, N. Baxley, and K. Kirchgassner, eds., Pitman, Boston, 1981, pp. 229-241. 

Until now, we have tacitly assumed that the diffusing compound does not interact chemically with the solid matrix of the porous media. Yet, in a porous medium the solid-to-fluid ratio is several orders of magnitude larger than in the open water. 

The total flux of the chemical per unit bulk area across the porous media is approximated by the flux in the fluid phase. The latter follows from the first Fickian law (see Eq. 18-56) ... 

Note that once the front has crossed the layer and both the fluid and sorbed concentrations have reached steady-state, the flux becomes independent of f. If the initial concentration in the porous media is different from zero, it takes less time to load the media to steady-state, and thus the breakthrough time is smaller. 

Simplicity requires choice to choose wisely, the options should be known among which the choice is possible. The following characteristics make the porous media special ... 

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