Porous media definition

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 expressions for the hydraulic diameter and the superficial velocity can be incorporated into the definition of the friction factor to give an equivalent expression for the porous medium friction factor ... 

Most references use Eq. (13-10) without the numerical factor of 3 as the definition of the porous medium friction factor, i.e.,... 

Our definition of the phases is mechanically motivated. A kinematical criterion on the other hand would sort species according to their velocities. Cartilage is viewed as a three-phase, multi-species, porous medium ... 

By definition, with the area-averaged velocity defined as above, the continuity equation for flow in a porous medium w ill have the same form as that for the flow of a pure fluid, i.e., the continuity equation for flow through a porous medium is, if density variations are negligible ... 

As discussed in Chapters 2 and 3, in the integral method it is assumed that the boundary layer has a definite thickness and the overall or integrated momentum and thermal energy balances across the boundary layer are considered. In the case of flow over a body in a porous medium, if the Darcy assumptions are used, there is, as discussed before, no velocity boundary layer, the velocity parallel to the surface near the surface being essentially equal to the surface velocity given by the potential flow solution. For flow over a body in a porous medium, therefore, only the energy integral equation need be considered. This equation was shown in Chapter 2 to be ... 

Capillary Number in Oil Mobilization. The capillary number is a dimensionless ratio of viscous to capillary forces it provides a measure of how strongly trapped residual oil is within a given porous medium (5). Various definitions have been used for capillary number, but the following equation is common ... 

Snow is a porous medium formed of air, ice crystals and small amounts of chemical impurities. Because ice has a high vapor pressure (165 Pa at -15°C, 610 Pa at 0°C), the vertical temperature gradient that is almost always present within the snowpack generates sublimation and condensation of water vapor that change the size and shape of snow crystals. This results in changes in physical variables such as density, albedo, heat conductivity, permeability and hardness. These physical changes have formed the basis for the definition of snow metamorphism. ... 

From a topologiccil point of view an open porous medium has only one very complicated surface. Here we mean by outer or inner surface tiie geometrical surfaces on a macroscade of the outside and inside of single or multihole tubes, respectively. The definition of these surfaces on a microscale is arbitrary to some extent and depends on the yardstick used. 

The inversion temperature of a confined gas becomes lower the more severely confined is the gas. This follows from Eq. (5.184) and the definition of Op () in Eq. (4.24) which turns out to become smaller the smaller is. Sz (i.e., the smaller is ). This implies that a gas that might be cooled during an isenthalpic expansion in a wider porous medium ( 11 < 0) may get heated in a narrower porous medium instead ((5 > 0). At the mean-field level, the magnitude of the associated confinement-induced shift of the inversion temperature is given quantitath ely by the term in brackets in Eq. (4.24). 

The presence of liquid crystalline phases, their intermolecular structure and especially their state of dispersion definitely can affect interfacial tensions and interfacial tension transients (10), and may also influence other factors such as viscosity and the retention of surfactant during flow through a porous medium. 

FIGURE 441 Definition sketch for vertical plate (a), long horizontal strip (b), long horizontal circular cylinder (c), and short vertical cylinder with insulated ends ([Pg.273]

Areal Porosity and Tortuosity. Areal porosity or areosity, Ap, is defined as the effective areal ratio of the open pore cross-section to the bulk space. A more strict definition of areosity was introduced by Ruth and Suman (56). However, the areosity as defined by them is not a property of the porous medium only but a property of both the porous medium and the transport strength of the fluid such as the flow strength and electric current strength. The areal porosity is undoubtedly a very useful quantity for a bundled or ensemble passage model because it represents the ratio of the total passage cross-sectional area to the total cross-sectional area of the porous medium at a given planar section. 

The areal porosity has been invariably considered to be equivalent to the porosity, e, of the medium (I, 31, 33). This is by and large due to the success and popularity of the straight bundle passage models and nonconnecting constricted passage models, in which the ratio of the total open pore area to the total cross-sectional area for the direction under consideration has to be equivalent to the (volume) porosity of the porous medium. However, as it is expected from the difference in the definitions, it is no surprise that Dullien and Mahta (57) found their measured (areal) porosity is significantly different from the measured (volume) porosity with a different technique for the same porous medium sample. 

The tortuosity, r, of a porous medium is defined as the ratio of the distance between two fixed points and the tortuous passage followed by a fluid element of a single fluid saturated in the porous medium when traversing the two points. It may be viewed as a line porosity because, by definition, tortuosity is a one-dimensional property of the porous medium. It can be related to the formation factor, or formation conductivity factor, Ft by... 

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 tortuosity describes the ratio of the (average) incremental distance that an ion/molecule must travel to cover the direct distance in the direction of diffusion (Berner, 1980) and is thus the factor, which describes the increase in travel distance in the porous medium. Since the definitions of tortuosity in literature indicate small however substantial differences (an excellent overview of different procedures, equations and definitions is given by Boudreau (1997)), the definition used here is described briefly. The diffusion coefficient is corrected by the squared tortuosity. The square of the tortuosity is called tortuosity factor (Carman, 1937). This factor represents the... 

In porous media, by definition, the capillary pressure is positive when water is the more wetting phase and, accordingly, the capillary pressure is negative when oil is the more wetting phase. Capillary pressure becomes zero at the oil-water interface, also called the free fluid level that would exist outside of the porous medium. 

Will depend on the internal geometry of the porous medium. fWe present definition for principal directions of the anisotropy. 

The UK and American literature on porous medium flows often calls permeability the quantity we know as hydraulic conductivity. The quantity k/p (units m s/kg) is also found introduced with the name of permeability. We advise the reader being careful with these different definitions. It is quite easy passing from one definition to another, as the definition of permeability is readily identified by examining the units. 

One of the widely used, although rather rough, models of a porous medium is the ideal ground, or the Kozeny-Carman model [36]. In this model, the porous medium is represented as a buneh of eylindrical capillaries of different radii. The capillaries may be tortuous, but their radii remain invariable along their extent. This excludes hysteresis related to different locations of the menisci in the same capillary (cf Fig. 1). Meanwhile, the absence of the network structure excludes the effects caused by the interaction of different capillaries. It may be shown that in the ideal ground, all of the capillaries with radii below a certain value are saturated by a wetting phase (for definiteness, by liquid). The rest of the capillaries are filled by gas [22]. The value of r. is determined as... 

As we have seen in Section 6.3.1.4 on the removal of particles from air by a fibrous bed via the mechanism of inertial deposition, if one can locate the limiting trajectory (dimension b in Figure 6.3.9A), the particle capture efficiency can be determined (e.g. definition (6.3.42a)). Determination of the limiting trajectory is achieved via particle trajectory analysis in the porous medium, i.e. the granular filter medium. The governing equation for particle motion in the inter-particle space is equation (6.2.45) ... 

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