Porous media specific area

Aluminum foam can be used as a porous medium in the model of a heat sink with inner heat generation (Hetsroni et al. 2006a). Open-cell metal foam has a good effective thermal conductivity and a high specific solid-fluid interfacial surface area. 

Increasing the water-wet surface area of a petroleum reservoir is one mechanism by which alkaline floods recover incremental oil(19). Under basic pH conditions, organic acids in acidic crudes produce natural surfactants which can alter the wettability of pore surfaces. Recovery of incremental oil by alkaline flooding is dependent on the pH and salinity of the brine (20), the acidity of the crude and the wettability of the porous medium(1,19,21,22). Thus, alkaline flooding is an oil and reservoir specific recovery process which can not be used in all reservoirs. The usefulness of alkaline flooding is also limited by the large volumes of caustic required to satisfy rock reactions(23). 

Tortuosity is a long-range property of a porous medium, which qualitatively describes the average pore conductivity of the solid. It is usual to define x by electrical conductivity measurements. With knowledge of the specific resistance of the electrolyte and from a measurement of the sample membrane resistance, thickness, area, and porosity, the membrane tortuosity can be calculated from eq 3. 

One approach to quantitatively relate changes in porosity to changes in specific surface area is to assume that the porous medium is composed of spherical grains. The resulting specific surface area per unit volume of rock, J, is related to the porosity, [Pg.236]

The flow rate of water through the porous medium per unit total (bulk) area perpendicular to the direction of flow, the so-called specific discharge q, is related to the effective mean flow velocity in the pores along the x-axis, u, by... 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

The dispersion of metal particles in a nonmetallic porous medium, e.g., kieselguhr or carbon, has been used in practical catalysis for many years. It is a convenient technique to obtain a metallic catalyst with a relatively large specific surface area, yet resistant to sintering during its use or its regeneration. Such classic catalysts contain large amounts of metal, typically between 10 and 50% by weight. 

If e and Kc are known or can be estimated, th and hence A the specific surface area of the porous medium can be determined. According to the well known Kozeny-Carman treatment... 

Dq. The porosity is readily defined as the amount of space unoccupied by the objects and free to be filled with fluid, whereas the average object size is often interpreted as the equivalent spherical diameter Dq = 6js, which is determined in turn from the specific surface area s of the porous medium. If the system is described as a continuum with superficial... 

In many problems of mass transfer in a solid porous medium with a large specific surface area (as with catalysts), with or without a chemical reaction, the solutes are considered to be carried only by diffusion (molecular, superficial or Knudsen diffusion), the molecular barycentric velocity being... 

The specific surface or surface per unit volume, aPy of a porous medium is defined as the ratio of the total open pore surface area to the volume of the solids. The equivalent spherical diameter, dsy is the diameter of an equivalent sphere that has the same surface area per unit volume of the solid material forming the porous medium. 

Permeability for a Rock Formation. For natural consolidated porous medium, however, the definitions of the equivalent spherical diameter and the specific surface area per unit volume are not widely used because of its difficulty in determination and relation to other measurable quantities. Just to serve as a comparison, we give the permeability equation based on the previous passage model with the tortuosity given by equation 61 and assuming that the areal porosity equation 54 still holds. The permeability can then be given by... 

The filter coefficient, X, varies as deposited material changes the morphology of the porous medium and as conditions surrounding the collection sites change. It has been noted that the filtration coefficient increases as fines migrate through a clean filter bed the retained fines increase the specific surface area. This increase in X is short-lived, and the magnitude of the filter coefficient decreases as additional fines are retained. Since Iwasaki published his notes on filtration in 1937, numerous variations of the rate expression have been recorded (72). 

It is common to express the total surface area in terms of an inverse length, termed the specific area S, which is the ratio of the surface area to the volume of the solid s fraction of the porous medium ... 

The Kozeny-Carmen equation for deriving the coefficient of permeability also takes the porosity, n, into account as well as the specific surface area of the porous medium, Sa. that is defined per unit volume of solid... 

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... 

This porous medium is only characterized by its overall porosity and the overall specific area of the solid Sq. Since this neglects local structural details it is termed as being microscopically uniform. Such a model is useful for estimating the expected height of rise and for comparison with the cylindrical capillary model. By comparing equations (7.49) and (7.50), an effective capillary radius for the porous medium can be defined. 

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. 

The geometrical parameters of the porous medium are the grain size d and the number of grains per unit volume p. The geometrical parameters of the network of capillary tubes are the diameter D of the tubes and the number of tubes passing through a unit surface in the Oxy plane. Tortuosity i is a common parameter of the porous medium and the capillary-tube network model. The Kozeny-Carman formula expresses, based on [14.27], the dependence of k on d, t, and e, establishing a link between and D, on the one hand, and between p and d, on the other. These relations are obtained under the hypothesis that the porous medium and the network of capillary tubes have the same porosity e and the same specific area Os... 

Mention was made previously of the electroosmotic flow of water to the cathode encountered in electrophoresis in various stabilizing media. This phenomenon plays a relatively small role in free electrophoresis because of the small surface area in contact with the electrolyte solution in the U tube. However, it is a very familar subject to workers who deal with electrical forces in membranes and porous materials. The well-known streaming potential produced by forcing liquid under pressure through a porous medium is closely related to the electroosmotic flow. The potential of the surface to the liquid (f potential) can be determined by measurements of the volume (V) of liquid transported per second by electroosmosis, through the use of equation (1), where i denotes the current strength, k the specific... 

FIGURE 3.6 A permeameter used to measure hydraulic conductivity in the laboratory. The column, a pipe filled with the porous medium of interest, has cross-sectional area A and length L specific discharge q is therefore equal to total column flow Q divided by A. Hydraulic conductivity K is estimated using Darcy s law K=-q/(Ah/L). In this apparatus, it is assumed that negligible head loss occurs in the hoses connecting the column to the constant-head water reservoirs 1 and 11 and in the screens used to hold the porous medium in place. 

Figure 38 identifies to some extent the possible cell designs in r.b.s. Conventional accumulators are composed of porous electrodes of the second kind [3, 11, 17] (1), but in the case of metal-free cells this is more or less the exception, and solid-state electrodes (A), (B) or (C) are combined, porous or not (2). The theory was developed by Atlung et al. [44-46]. (1) and (2) are based on electrochemical reactions. But electrodes with a high specific surface area, based on active carbon, carbon blacks, or other materials, allow for the special design of an ECDLC (3), where primarily electrochemical reactions are not involved. As indicated in Figure 38, the amount of electrolyte will be medium (i.e. between case (1) and (2)). 

The textural properties of the hybrid materials are also strongly dependent upon the hydrolysis conditions and the nature of the linker. After hydrolysis in a homogeneous medium, nitrogen adsorption and TEM measurements indicate the formation of non-porous solids with BET specific surface areas lower than 7 m except for 2g. Variation of the precursor concentration does not strongly affect these values. In contrast, hydrolysis under microemulsion conditions leads to a significant increase in the specific surface areas, mainly in the case of the flexible alkylene linker (Table 3.2.5). 

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