Porous media void fraction

The relation between the dusty gas model and the physical structure of a real porous medium is rather obscure. Since the dusty gas model does not even contain any explicit representation of the void fraction, it certainly cannot be adjusted to reflect features of the pore size distributions of different porous media. For example, porous catalysts often show a strongly bimodal pore size distribution, and their flux relations might be expected to reflect this, but the dusty gas model can respond only to changes in the... 

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. 

The term porosity refers to the fraction of the medium that contains the 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 of the media. In a general sense, porous media are classified as either unconsolidated and consolidated and/or as ordered and random. Examples of unconsolidated media are sand, glass beads, catalyst pellets, column packing materials, soil, gravel and packing such as charcoal. 

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). 

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

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. 

The presence of two mobile phases means that each fluid can interact with both the porous medium and the other immiscible fluid. If the porous medium is visualized as a collection of interconnected flow paths, only a fraction of the total flow paths become available to a given fluid, the rest being occupied by the other fluid. This condition necessitates the introduction of fluid saturation as an important parameter. The saturation of a fluid phase is defined as the fraction of total void space occupied by that fluid. For two-phase systems, the sum of the two fluid saturations is equal to unity, because any void space not occupied by one fluid must be occupied by the other fluid. 

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. 

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. 

The void area fraction in (21-76) is based on the fractional area in a plane at constant x that is available for diffusion into catalysts with rectangular symmetry. A rather sophisticated treatment of the effect of g 6) on tortuosity is described by Dullien (1992, pp. 311-312). The tortuosity of a porous medium is a fundamental property of the streamlines or lines of flux within the individual capillaries. Tortuosity measures the deviation of the fluid from the macroscopic flow direction at every point in a porous medium. If all pores have the same constant cross-sectional area, then tortuosity is a symmetric second-rank tensor. For isotropic porous media, the trace of the tortuosity tensor is the important quantity that appears in the expression for the effective intrapellet diffusion coefficient. Consequently, Tor 3 represents this average value (i.e., trace of the tortuosity tensor) for isotropically oriented cylindrical pores with constant cross-sectional area. Hence,... 

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 effective diffusivity in the secondary particle. Deg, can be estimated using the conventional expression for effective diffusivity in porous heterogeneous catalysts, Eq. (42), where is the monomer bulk diffusivity in the reaction medium, and and T are the void fraction and tortuosity of the polymer particle, respectively. The fact that both e and r are likely to vary as a function of the degree of fragmentation and expansion of the secondary particle is certainly one of the difficulties in getting a good estimate for D. ... 

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... 

Recently Desmet and Deridder transformed the effective medium theory (EMT), which applied thermal and electrical conductivity, to determine longitudinal diffusion in chromatography (71). EMT equations can be applied for fully porous, porous shell, spherical, and cylindrical particles. The theory considers the column as a binary medium, which consists of an interstitial void with a volumetric fraction Se and particles with a volumetrical fraction of 1- e. ... 

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