Porous media void volume

Now suppose e(a) denotes the total void volume associated with pores of radii < a, per unit volume of the porous medium. This includes the contributions of any dead-end pores. Chough these are not taken into account in the distribution function f(a,ri). Then we shall write... 

We may begin by describing any porous medium as a solid matter containing many holes or pores, which collectively constitute an array of tortuous passages. Refer to Figure 1 for an example. The number of holes or pores is sufficiently great that a volume average is needed to estimate pertinent properties. Pores that occupy a definite fraction of the bulk volume constitute a complex network of voids. The maimer in which holes or pores are embedded, the extent of their interconnection, and their location, size and shape characterize the porous medium. 

If the organic liquid saturation is measured as the volume of organic liquid per unit void volume, measured over a representative volume of the porous medium, then S, the fraction of pore space occupied by the organic liquid is... 

R = retardation factor. The retardation factor is the ratio of the solution velocity to the radioelement velocity in a system of solution flow through a porous medium. The retardation factor R = 1 + Kd (p/) where p is bulk density of Hanford sediment (=1.65 g/cm3) and is the fraction of void volume in the sediment (=0.38). 

Hence, on the pore level, e can be seen as the ratio of two length scales the characteristic pore scale length rneasrneas(1V ) and the problem related scale L. The balance (10) is quite natural for a porous medium, where meas(Tc) denotes the total surface of the porous skeleton and meas(fl) the total void volume. Assuming the medium being periodic with periodicity e it... 

Porosity. The fraction of total volume occupied by the voids is called the porosity of the porous medium. A distinction can be made between the pores that are interconnected and the pores that are totally isolated. The absolute or total porosity is the fraction of bulk volume occupied by all voids, connected or not. The effective porosity is the fraction of bulk volume occupied by interconnected pores. 

Porosity The ratio of the volume of all void spaces to total volume in a porous medium. 

A porous medium is simply a solid material (i.e., solid phase) through which a significant void volume extends. Typically, the term is used when the void size in the... 

The term pore-scale implies behavior or analysis performed at a resolution where the void phase and solid phase can be distinguished. At this scale, the void phase is conceptually divided into pores (the larger voids, which provide its volume) and pore throats (constrictions that connect the pores), though the distinction is rarely black and white. In contrast, the continuum-scale approach is usually adopted in engineering practice. Continuum techniques treat the bulk porous medium as a single phase, which in turn requires spatially averaged parameters to be introduced that are intended to capture relevant characteristics of the pore-scale structure. 

Porosity is one of the most important continuum-scale parameters. It is defined as the fraction of the total volume that comprises void space e = Woid/ ktotai-Equivalently, the solid volume fraction ((f) = 1 - e) is generally used for fibrous materials or other open structures. The term microporosity implies that the particles in a porous medium are themselves porous, usually at a much smaller scale. A common example is porous catalyst in a packed-bed reactor. 

The general approach is to define the traditional hydraulic radius, but for a more complex cross section for flow. For a porous medium, it is equivalent to the ratio of void volume to surface area, which is known for certain geometries, such as a packing of spheres ... 

Four different three-dimensional numerical infiltration experiments were carried out in a simulated porous medium with a central parallel crack as shown in Fig. 4-2. The lattice size is 10 by 100 by 150 sites in the x, y and z directions, respectively. Solid sites are represented in red. A probabilistic algorithm generated at random the solid distribution of the microporous matrix. The mean microporosity and macroporosity are 0.52, and 0.192, respectively, of the total volume of the medium. A gravity force was simulated as described in Di Pietro et al. (1994), oriented parallel to the crack in the z-downward direction. Void sites (white color in Fig. 4-2) are initially f ss are expressed in arbitrary lat-... 

These macroscopic measurements of gas trapping are confirmed by visual observations in transparent etched-glass micromodels and bead packs (24—26, 41). Trapped foam severely reduces the effective permeability of gas moving through a porous medium by blocking all but the least resistive flow paths. Hence, trapped gas reduces the void volume of the porous medium available for flow. Thus, higher flow resistances are measured, and lower permeabilities to gas are computed. This trapped gas accounts for some, but not all, increased resistance to flow. 

Porosity. The fraction of total (bulk) volume occupied by the voids is defined as the porosity of the porous medium. A porous medium can be classified according to the type of porosity involved. In sandstone and unconsolidated sand, the voids are between sand grains, and this type of porosity is known as intergranular. Carbonate rocks are more complex and may contain more than one type of porosity. The small voids between the crystals of calcite or dolomite constitute intercrystalline porosity (47). Often carbonate rocks are naturally fractured. The void volume formed by fractures constitutes the fracture porosity. Carbonate rocks sometimes contain vugs, and these carbonate rocks constitute the vugular porosity. Still some carbonate formations may contain very large channels and cavities, which constitute the cavernous porosity. 

Porosity The ratio of the volume of all void spaces to total volume in a porous medium. In geology primary porosity refers to initial, or unweathered, media, and secondary porosity refers to that associated with weathered media. 

Repulsive potential energy between two identical spheres of same charge Volume of voids in porous medium Dimensionless applied voltage,... 

Powdered metal is a porous medium. The physical characteristics, chemical composition, structure, porosity, strength, ductility, shape and size can be varied to meet special requirements. The porosity ranges up to 50% void by volume, tensile strength up to 10,000 psi, varying inversely with porosity, and ductility of 3-5% in tension, and higher in compression. 

The effective, apparent or net porosity is a measure of the effective void volume of a porous medium and is determined as the excess of bulk volume over grain volume and occluded pore volume. It may be regarded as the pore space from which water can be removed. Groundwater does not drain from occluded pores. 

Porosity, volume of voids per unit volume of filter cake (or porous medium)... 

A fundamental characteristic of a porous medium is its specific surface area E (expressed in m per kilogram of material). Qualitatively, we have E = ps d), where ps is the density of the compacted solid devoid of pores (typically, ps I g/cm ), and d is the diameter of the capillary. For a pore diameter d = 10 jim, E is of the order of 100 m /kg. Another important parameter of the porous medium is its void fractional volume Therefore, its average density is ps l — ). The surface area Ev per unit volume is... 

The total porosity , is defined as the ratio of the void volume in a porous medium to the total volume... 

The specific area (Os) is defined as the ratio of the area between sohd and void to the total volume of the sample. Its unit is m . The smaller the size of the grains or pores is, the larger the specific area is. The specific area is important for evaluating a transfer capacity between the solid of the porous medium and the fluid. The larger the specific area is, the easier the transfers will be. 

In the development of an expression for Et, a more detailed model of the porous medium is needed. Of the three types of models of a granular filter as a porous medium, the capillaric model is not preferred. For the sake of simplicity, we will consider one of the other two, namely the spherical collector model. In this model, the filter grain is assumed to be a sphere. There are a number of alternative approaches based on a spherical collector. We will illustrate the approach by Happel (1958). In Happel s model, the granular porous medium is assumed to consist of a large collection of identical cells, where each cell consists of a spherical particle of radius ((dgr)/2) (i.e. half of the average grain diameter) surrounded by a liquid envelope of radius b, such that the void volume of this cell is identical to the void volume of the porous medium ... 

Indeed, one recognizes a common feature to all these examples. All are described as solids with holes, i.e., presenting connected void spaces, distributed—randomly or quite homogeneously—within a solid matrix. Fluid flows can occur within the porous medium, so that we add one essential feature this void space consists of a complex tridimensional network of interconnected small empty volumes called pores with several continuous paths linking up the porous matrix spatial extension, to enable flow across the sample. 

Diffusion coefficients for porous media are generally referred to as effective diffusivities, since the actual molecular diffusion process occurs in the fluid phase and interactions with the porous medium inhibits the chemical movement. There are both physical and chemical factors that go into estimating effective diffusivities. The physical effects are twofold. First, some fraction of the porous media is solid, limiting the volume through which fluid phase diffusion can occur. This is quantified by the porosity, which is defined as the ratio of the volume of void space to the total volume. Second, the connectivity between pore spaces in soil and sediment grain packs (as well as other porous media) are circuitous and lengthen the distance a molecule must travel to traverse the material. This lengthening of the diffusion path is quantified... 

The objective of this smdy is to be able to estimate the effective transport resistance of a porous medium by characterizing its void morphology by mercury porosimetry. A series of porous catalyst solids were obtained differing only in void morphology, overall porosity and pore sizes. We cahnilated the tortuosity by a dynamic experiment employing solid-gas chromato phy, SGC. Tortuosities of aU solids were very si ar, in the range of 5-25. Transport resistance is more easily related to overall volume porosity rather than specific network architectu features observable by porosimetry. 

Characterization of the morphology of a porous medium is not an unambiguous problem. It generally involves some assumption regarding the architecture of the media before any data may be analyzed. For catalysts made firom random agglomeration and fusion of non rous microparticles, a useful and sufficiently general structure is the pore-throat model. In this visualization, it is assumed that internal void volume is distributed within channels which connect pores. Channels provide the connecting paths between pores and ultimately between transport boundaries. The properties that are sufficient to define this type of medium are ... 

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