Porous media examples

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... 

One of Che earliest examples of a properly conceived experimental investigation of the flux relations for a porous medium is provided by the work of Gunn and King [53] on the dusty gas model equations, and the following discussion is based largely on their work. Since all their experiments were performed on binary mixtures, the appropriate flux relations are (5.26) and (5,27). Writing... 

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. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

The >eff across the porous medium for this example is linearly related to the porosity of the path, which is in turn simply the ratio of the open cross-sectional area to the total cross-sectional area. There are no constriction or tortuosity effects in this example i.e., t = 1 and... 

The material balance is consistent with the results obtained by OSA (S2+S4 in g/100 g). For oil A, the coke zone is very narrow and the coke content is very low (Table III). On the contrary, for all the other oils, the coke content reaches higher values such as 4.3 g/ 100 g (oil B), 2.3 g/ioo g (oil C), 2.5 g/ioo g (oil D), 2.4/100 g (oil E). These organic residues have been studied by infrared spectroscopy and elemental analysis to compare their compositions. The areas of the bands characteristic of C-H bands (3000-2720 cm-1), C=C bands (1820-1500 cm j have been measured. Examples of results are given in Fig. 4 and 5 for oils A and B. An increase of the temperature in the porous medium induces a decrease in the atomic H/C ratio, which is always lower than 1.1, whatever the oil (Table III). Similar values have been obtained in pyrolysis studies (4) Simultaneously to the H/C ratio decrease, the bands characteristics of CH and CH- groups progressively disappear. The absorbance of the aromatic C-n bands also decreases. This reflects the transformation by pyrolysis of the heavy residue into an aromatic product which becomes more and more condensed. Depending on the oxygen consumption at the combustion front, the atomic 0/C ratio may be comprised between 0.1 and 0.3 ... 

By making use of these analogies, electrical analog models can be constructed that can be used to determine the pressure and flow distribution in a porous medium from measurements of voltage and current distribution in a conducting medium, for example. The process becomes more complex, however, when the local permeability varies with position within the medium, which is often the case. 

In many cases the medium in which the molecules move is not homogeneous and the diffusion motion of the molecules is influenced by the structure of the medium. Examples are the diffusion of water and oil in porous rock or in water-oil emulsions. Many publications have shown that the NMR diffusion results can be used to quantitatively study the porous structure, like the determination of pore and droplet sizes, pore connectivity and pore hopping or of the surface to volume ratio of the pores. 

Nonadsorptive retention of contaminants can also be beneficial. For example, oil droplets in the subsurface are effective in developing a reactive layer or decreasing the permeability of a sandy porous medium. Coulibaly and Borden (2004) describe laboratory and field studies where edible oils were successfully injected into the subsurface, as part of an in-situ permeable reactive barrier. The oil used in the experiment was injected in the subsurface either as a nonaqueous phase liquid (NAPL) or as an oil-in-water emulsion. The oil-in-water emulsion can be distributed through sands without excessive pressure buildup, contrary to NAPL injection, which requires introduction to the subsurface by high pressure. 

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

Although such studies are in their early stages, this example clearly demonstrates that we have the measurement tools to investigate the complex interaction of hydrodynamics and chemical kinetics in the complex porous medium represented by a fixed bed. Looking to the future, we may expect experiments of this nature to demonstrate how a catalyst with intrinsic high selectivity can produce a far wider product distribution when operated in a fixed-bed environment as a result of the spatial heterogeneity in hydrodynamics and hence, for example, mass transfer characteristics between the inter-pellet space within the bed and the internal pore space of the catalyst. 

Abstract A general theoretical and finite element model (FEM) for soft tissue structures is described including arbitrary constitutive laws based upon a continuum view of the material as a mixture or porous medium saturated by an incompressible fluid and containing charged mobile species. Example problems demonstrate coupled electro-mechano-chemical transport and deformations in FEMs of layered materials subjected to mechanical, electrical and chemical loading while undergoing small or large strains. 

In the last section, convection in a two-dimensional porous medium is presented as a physical problem. Porous media is important in environmental heat transfer studies, transpiration cooling, and fuel cells, as some examples. Using the slug flow assumption, the energy equation is solved using an alternating implicit method to show its effectiveness. 

An example of heat transfer through a porous medium is heat transfer through a layer of granular insulating material. This material will be saturated with air, i.e., the space between the granules of insulating material is entirely filled with air, and this air will flow through the insulation material as a result of the temperature difference imposed on the material, i.e., there will be a free convective flow in the porous material. Even when a fibrous insulation is used, the flow in the insulation can be... 

Another example of heat transfer involving a porous medium is heat transfer from a pipe or cable buried in soil or in a bed of crushed stones which is saturated with around water which is flowing through the soil or stones. This is illustrated in Fig. 10.3. 

The present chapter gives no more than a brief introduction to convective heat transfer in a porous medium. It is an area of considerable practical importance and there is a large body of literature on the topic to which the reader is referred for more detail, for example see [1] to [12]. 

As a last example of the use of the integral equation method consider again two-dimensional flow about an isothermal cylinder in a porous medium. The situation considered is shown in Fig. 10.22. 

One of the important transformation processes in the porous media is the deposition of solid material in pores and the subsequent clogging of the fluid flow through the porous medium. Typical examples are filtration and clogging of well walls in oil fields due to the particles present in the injected fluid. Another example is the deposition of clusters of active catalyst species in porous supports. 

In the fractal porous medium, the diffusion is anomalous because the molecules are considerably hindered in their movements, cf. e.g., Andrade et al., 1997. For example, Knudsen diffusion depends on the size of the molecule and on the adsorption fractal dimension of the catalyst surface. One way to study the anomalous diffusion is the random walk approach (Coppens and Malek, 2003). The mean square displacement of the random walker (R2) is not proportional to the diffusion time t, but rather scales in an anomalous way ... 

We are not going to deal with all these examples of application of percolation theory to catalysis in this paper. Although the physics of these problems are different the basic numerical and mathematical techniques are very similar. For the deactivation problem discussed here, for example, one starts with a three-dimensional network representation of the catalyst porous structure. Systematic procedures of how to map any disordered porous medium onto an equivalent random network of pore bodies and throats have been developed and detailed accounts can be found in a number of publications ( 8). For the purposes of this discussion it suffices to say that the success of the mapping techniques strongly depends on the availability of quality structural data, such as mercury porosimetry, BET and direct microscopic observations. Of equal importance, however, is the correct interpretation of this data. It serves no purpose to perform careful mercury porosimetry and BET experiments and then use the wrong model (like the bundle of pores) for data analysis and interpretation. 

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