Porosity of porous medium

Where D is the invasion depth and 0m is the porosity of porous medium. 

In the formula xeff = x + xt xt- Turbulent viscosity coefficient x- Coefficient of kinematic viscosity n- Porosity of porous medium. 

S, thickness of porous medium 4>, porosity of porous medium ... 

Perturbation parameter in Enskog expansion Porosity of porous medium (—)... 

Migration of fluids in a porous matrix with solid-liquid fractionation results in a process much similar to the chromatographic separation of elements (DeVault, 1943 Korzhinskii, 1970, Hofmann, 1972). This mechanism has recently been revived in the context of mantle metasomatism by Navon and Stolper (1987), Bodinier et al. (1990), Vasseur et al. (1991), in the context of hydrothermal systems by Lichtner (1985) and, for stable isotopes, by Baumgartner and Rumble (1988). Only a simplified account of this model will be given here. Let

solid matrix and melt, respectively, and vHq the fluid velocity relative... 

The quantity of water that can be retrieved from a medium is related to size and shape of the connected pore spaces within that medium. The quantity of water that can be freely drained from a unit volume of porous medium is referred to as the specific yield. The volume of water retained in the medium by capillary and surface active forces is called the specific retention. The sum of specific retention and specific yield is equal to the effective porosity (see Table 3.4). Neither term has a time value attached. Drainage can occur over long periods (i.e., weeks or months). 

To calculate the reduction in the concentration of surfactant in the fluid by adsorption it is necessary to have an estimation of the inner surface area of the reservoir. This parameter is related to the porosity of the medium and to its permeability. Attempts have been made to correlate these two quantities but the results have been unsuccessful, because there are parameters characteristic of each particular porous medium involved in the description of the problem (14). For our analysis we adopted the approach of Kozeny and Carman (15). These authors defined a parameter called the "equivalent hydraulic radius of the porous medium" which represents the surface area exposed to the fluid per unit volume of rock. They obtained the following relationship between the permeability, k, and the porosity, 0 ... 

Consider a solid sphere of radius a, which is surrounded by another concentric spherical liquid envelope of radius yS, whose thickness is adjusted so that the porosity of the medium is equal to that of the model. The governing equation for the steady state mass transport in the fluid phase within the porous medium can be written in spherical coordinates as... 

Materials of more or less broad utility, reported in the literature, include the following filter paper [93], asbestos [51, 94, 95], cellophane [96], nylon cloth [52], and porous plastic [97] other potential candidates are listed in Chapter 31. The porosity of the medium may be decreased by partially filling the voids with another material, such as agaragar, silica gel [9], or magnesium hydroxide. 

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. 

Mass flow through a porous medium is influenced by the porosity of the medium in much the same way as diffusion is influenced by porosity. Thus, mass flow proceeds faster in a high-porosity sand than in a low-porosity clay. In addition, many of the physical properties of atmospheric air influence the aeration of soil and porous overburden by mass flow. Baver et al. (1972) estimate their contributions (Table l-III). 

X10 seconds. In this example, the critical concentration of solid is 0.67 mole/dm of porous medium. In the variable porosity case the solid concentration rises asymptotically toward the critical value, again as a result of decreasing influxes of reactants at the boundary caused by decreasing porosity there. 

Much of the recent research in combustion in porous media has focused on developing a porous burner as a radiant heater [7-13]. This is an attractive application because the porous solid is an efficient radiator while still permitting the use of a clean fuel such as methane. One design that has shown promise is a burner consisting of two sections of porous medium with different characteristics [2, 9, 10]. This design is based on the idea that the effective flame speed within the matrix is determined by the porous medium properties such as solid conductivity, porosity, and pore diameter. The interface between the two sections of porous media acts as a flame holder preventing flashback. 

The computational domain is shown in Fig. 14.1. The domain was discretized into 300 grid points with a cluster located in regions of high-temperature gradient. The burner consists of two sections of porous media. For the reference case, the burner consisted of an upstream section of porous medium with 25.6 ppc and a downstream section with 3.9 ppc. The upstream and downstream porosities were 0.84 and 0.87, respectively. The upstream and downstream pore diameters were 0.029 and 0.152 cm, respectively. Methane and air. with an equivalence ratio of 0.65, a temperature of 298 K, and a specified velocity, flow into the domain. Hot products exit at the downstream end of the domain. Both downstream and upstream boundaries radiate to a black body at 298 K. 

In structured disperse systems, where particles of the dispersed phase form united spacial networks, as well as in porous media with open porosity, the existence of double layers at interfacial boundaries results in some peculiarities in the processes of substance transfer and electric current transport. We will devote most of our attention to the discussion of transfer phenomena in an individual capillary, which is the simplest element of any structured disperse system, and then only qualitatively address the peculiarities related to complex structure of porous medium. 

Equation 71 is the basic equation that relates permeability of a porous medium to its other properties. However, equation 71 contains the hydraulic diameter of the passage (pore), tortuosity, and areal porosity of the medium, which may not be easily accessible. For example, sandstones or rock formations have irregular pore structure and often have inconsistent pore size measurement values (see previous section). It is rather difficult to measure the average hydraulic pore diameter. On the other... 

The parameter b denotes the Biot s coefficient of porous medium and S the water saturation degree, and < i the porosity occupied by gas... 

Offset constant of the applied magnetic field Ferrofluid/solid interface inside V Gravitational amplification factor of a-phase Goeffrcient in the Muller porosity model Porous medium porosity Bed holdup of a-phase Vortex viscosity Dynamic viscosity... 

When dealing with a porous medium, the viscous flux is usually expressed in terms of the total cross sectional area. Thus if the porosity of the medium is 8, the desired flux expression is ... 

Filtration and Adhesion. In the cleanup of dust-containing process gases or air, the particles suspended in the gas stream pass through a porous filter medium and stick to the surfaces of this material. The dust precipitate thus accumulated becomes, in turn, the filter medium for the subsequent particles. As the deposit builds up, the porosity of the medium decreases, hindering the free flow of gas. At some point this deposit must be removed. 

Conclusive parameters of the problem, as it has been stated, are four nondimensional values the Mach number of incident shock wave Mj, the thickness of the specimen d, the density of porous medium p porosity ttQ. 

Some relief may be formd by adjusting diffusivity upward. Chapter 3 provides an expression for the rough estimate of diffusivity in porous media, given by D = D e/l. D represents the free-space diffusivity, of the order 10 m /s for gases, and e is the porosity of the medium. If we assume a highly porous soil with e = 0.4, D is reduced by two orders of magnitude and the lifetime of the benzene deposit drops to 0.074 years = 27 days. For the less volatile substances, it remains unacceptably high, at 669 years. 

The fluid velocity distribution given by Eqs. (93)-(96) are only valid for an isolated particle. However, there are a number of practically important situations, like the deep-bed filtration process, when the flow past an assembly of spheres (forming a porous mediiun) takes place. In this case, the flow field around a single sphere is influenced by the presence of other spheres. Various models that describe the flow field in the packed bed consisting of spheres are available. The sphere in cell models [81-83] assume that each sphere in the packed bed is surrounded by the spherical cavity filled with fluid. The size of the cavity is determined by the overall average porosity of the medium. The general solution of the Navier-Stokes equation for the stream function inside the cavity may be written as [7]... 

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. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

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