Porous hydraulic diameter

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 ... 

Fig. 8. Typical CO concentration and reaction rate profiles in the porous Pt/y-Al203 catalyst reconstructed by particle-packing method. Mean hydraulic diameter of macropores = 300 nm, macroporosity =18.1%. Free space corresponds to macropores, solid gray corresponds to mesoporous y-Al203 with dispersed Pt. Length of the section edge 10 pm. Boundary /.. yco 1%, y0j = 0.5%. (a) T 513 K, (b) T = 533 (Koci et al., 2007a) (see Plate 2 in Color Plate Section at the end of this book).

Of particular interest in porous media is the so-called equivalent hydraulic diameter de = 4Vg/Sg — 4Lg, which is important for permeability scaling (Martys and Garboczi, 1992). 

Only a single channel is considered. The channel has a hydraulic diameter and its wall consists of the porous washcoat with a layer thickness The monolith material, surrounding the washcoat, has a thickness 5, which corresponds to half of the spacing between channels. As a result, cylindrical coordinates can be used. 

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... 

In what follows we derive an empirical relation for the permeability, known as the Kozeny-Carman equation, which supposes the porous medium to be equivalent to a series of channels. The permeability is identified with the square of the characteristic diameter of the channels, which is taken to be a hydraulic diameter or equivalent diameter, d. This diameter is conventionally defined as four times the flow cross-sectional area divided by the wetted perimeter, and measures the ratio of volume to surface of the pore space. In terms of the porous medium characteristics. 

The Taylor-Aris result for the dispersion coefficient (Eq. 4.6.35) has been applied to the empirical correlation of measured and calculated longitudinal dispersion coefficients in flow through packed beds and porous media (see Eidsath et al. 1983). Typically, the velocity in the Peclet number of the Taylor-Aris formula is identified with the superficial velocity, and the capillary diameter with the hydraulic diameter for spherical particles. An alternative velocity suggested by the capillary model is the interstitial velocity, and an alternative length is the square root of the permeability. In an isotropic packing of particles is about one-tenth the particle diameter (Probstein Hicks... 

The present model development is based on a semi-heuristic model of flow through solid matrices using the concept of hydraulic diameter, which is also known as the Carman-Kozeny theory [7]. The theory assumes the porous medium to be equivalent to a series of parallel tortuous tubules. The characteristic diameter of the tubules is taken to be a hydraulic diameter or... 

Tronconi and co-workers (98,116) have validated against experiment a more complex, heterogeneous, transient model, accovmting also for diffusion and reaction of NO and NH3 inside the porous walls of extruded honeycomb SCR catalysts. The model equations are presented in Table 5 x and z are the intraporous and axial coordinate, respectively is the ammonia adsorption capacity of the catalyst 6 is the NH3 surface coverage is the effective intraporous diffiisiv-ity s is the monolith wall half-thickness i is the gas velocity in the monolith channels are gas-solid mass transfer coefficients and dh is the hydraulic diameter of the monolith channels. Notably, a pseudo-steady-state assumption... 

Hagen-Poiseuille s equation is also used for the steady state flow through a porous media. In sueh eases, to define the pore diameter, hydraulic diameter of the pore is considered and calculated on account of non-circularity and irregularity in the pore structure and spacing [58-59], The capillary rise between the time of initial contact and the final equilibrium was obtained by Lukas-Washbum [60-61] ... 

Since the fluid in a porous medium follows a tortuous path through channels of varying size, one method of describing the flow behaviour in the pores is to consider the flow path as a non-circular conduit . This requires an appropriate definition of the hydraulic diameter as shown in Eq. 3.15 ... 

Meniscus-coated composite films of SPPO (lEC value =2.2) on porous polypropylene (MST-110) were tested as a 1 x 3 inch flat sheet in the ROGA unit having a hydraulic diameter of 0.0126 ft, and a flow rate of 2.2 gpm. Tests were performed on secondary sewage from the treatment plant at Selam, NH. 

The GDE for hydrochloric acid electrolysis is characterised by micro-scale hydraulic problems connected with the competition between the gas phase (oxygen), which has to diffuse towards the catalyst, and the liquid phase (water), which must be released. This competition is managed basically by a flow-through structure provided with hydrophobic channels of relatively large diameter. These are formed from PTFE (the binder of the structure) and catalyst particles and account for regulating the gas phase. Hydrophilic channels with smaller diameters (one order of magnitude smaller), which are located in the micro-porous carbon particles of the catalyst support (e.g. Vulcan XC-72), act as water absorbers. A consequence of the electrolysis process is that the catalyst itself is partially covered by liquid. This reduces its effectiveness and accounts for extra voltage. 

Following this analysis Q depends on two eapillary structure parameters - the mean hydraulic pore diameter and the inner diameter of the porous wick. To find the Qmax we need equation (3.9) analyze for the extreme function finding. Due to the temperature dependenee of the thermo-physical properties of the working fluid the maximum heat flow Q ,ax will be different for different saturated vapor temperatures Tsat in the heat pipe transport zone. Figure 8. For different angles of heat pipe inelination to the horizon we need to determine Qmax at the worst situation with the point of view of the heat transfer, when the heat pipe evaporator is above the heat pipe eondenser, vertieal (inverted) heat pipe disposition. 

The properties of gas flow in porous media depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collisions. The Knudsen number Kn is a characteristic parameter defining different regions of this ratio. Its value is defined by Kn = Xl dp with X being the average free path length of the gas molecules and dp the characteristic pore diameter (sometimes the hydraulic pore radius is taken). 

The structure of a tissue influences its resistance to the diffusional spread of molecules, as discussed previously (see Figure 4.18). Similarly, the structure of a tissue will influence its resistance to the flow of fluid. If Darcy s law is assumed, then the hydraulic conductivity, k, depends on tissue structure. Models of porous media are available in the simplest model, the medium is modeled as a network of cylindrical pores of constant length, but variable diameter. This model produces a relationship between conductivity and geometry ... 

The permeation experiments were carried out on 2 cm thick clay specimens placed into an aluminium cylinder of 5.38 cm diameter. The testing equipment allows the generation of a constant flow rate using a piston moving at a constant velocity. The chamber of the piston is connected to the fluid chamber in the permeameter cell located above the clay specimen, which is toped by a porous stone. A pressure transducer is connected to the hydraulic circuit. The fluid outlet in the lower aluminium plate is kept at atmospheric pressure. An external vertical load is applied to the specimen by means of a spring-loaded cap prior to permeation. Vertical settlements are monitored using a dial gauge and a settlement rod mounted on top of the specimen. 

The velocity U is defined as the ratio of the liquid s volume flow rate to the net cross section of all spacings between particles in the given layer of porous medium. It is obvious that U < Ug, since also includes the volume flow rate of liquid through the pores of particles. The constant k is known as permeability (its dimensionality is m ). In order to determine k, we must choose a certain model of porous medium. A low-permeable porous medium can be conceptualized as a medium consisting of a set of microchannels of diameter de (it is called hydraulic, or equivalent, diameter). This diameter is usually defined as... 

However, there is a limitation in increasing the diameter of monolith m brane elements. The upper limit is when the hydraulic resistance of the porous walls becomes higher than the hydraulic resistance of the membrane top layer developing... 

S is the ratio of the surface area of the medium to its pore volume and stands for equivalent diameter of the pores. The hydraulic (mean) radius m is defined as the ratio of the average pore cross-sectional area to the average wet perimeter, in line with the concept of the equivalent loads (as explained in Section III). All the geometrical parameters from Eq. (19) can be estimated for particulars of the porous media. For example, in the case of aligned fibers, hydraulic radius and equivalent diameter can be expressed by ... 

Example 3.4.4 The utility of equation (3.4.86) for the determination of the solvent flux through a porous membrane will be briefly illustrated with an example worked out by Cheryan (1987). For an XMIOOA ultrafQtration (UF) membrane, the mean pore diameter (= 2 x hydraulic mean pore radius) = 17.5 nm the number of pores/cm of the top membrane surface area (skin) = 3 x 10 = membrane... 

Techniques d and e do not allow a determination of the pore size distribution. Mean hydraulic pore diameters can be estimated from permeability measurements using the flow of an inert gas through the porous structure. The total porosity given by Eq. 4... 

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