Porosity packed bed

Before the bed can become fluidized, however, the particles must dislodge from their packed state, which expands the bed. Thus, the porosity (s) in Eqs (14-5) and (14-9) is not the initial packed bed porosity but the expanded bed porosity at the point of minimum fluidization ( ml ), i.e., the minimum bed voidage in the bed just prior to fluidization. Actually, the values of C and C2 in Eq. (14-8) that give the best results for fluidized beds of uniform spherical particles have been found from empirical observations to be ... 

The equivalent packed body diameter, d, is related to the bed holdup, e, and specific packed surface, s, as well as via the relationship d = 4e/a. For the packed bed from spherical bodies (e = 0.44 and ct = 6/dp), the equivalent packed body diameter depends only on the sphere diameter. The mean internal packed bed fluid velocity represents the ratio between the fictive velocity and the packed bed porosity (e). According to these data, we can write ... 

Density, adsorbent porosity, packed bed porosity Solid density (true density, skeleton density)... 

Heat Transfer between a Fluid and Particles of a Packed Bed For the heat transfer between a fluid and spheres of a packed bed (porosity e w 0.4) we have (Schluender, 1986 VDI, 2002) ... 

Fig. 22. Performance cut diameter predictions for typical dry packed bed particle collectors as a function of bed height or depth, packing diameter and packing porosity (void area) S. Bed irrigation increases collection efficiency or decreases cut diameter (271). SoHd lines, = 25 mm dashed lines,...

Glaser and Thodos [Am. Jn.st. Chem. Eng. J., 4, 63 (1958)] give a correlation involving individual particle shape and bed porosity. Kunii and Suzuki [Jnt. ]. Heat Mass Tran.sfer, 10, 845 (1967)] discuss heat and mass transfer in packed beds of fine particles. 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

Sintered metal fibers with filaments of uniform size (2-40 (tm), made of SS, Inconel, or Fecralloy , are fabricated in the form of panels. Gauzes based on thicker wires (100-250 tm) are made from SS, nickel, or copper. They have a low surface area of about 10 m g. Several procedures are used to increase the surface area, for example, leaching procedures, analogous to the production of Ra-Nickel, and electrophoretic deposition of particles or colloid suspensions. The porosity of structures formed from metal fibers range from 70 to 90%. The heat transfer coefficients are high, up to 2 times larger than for random packed beds [67]. 

J. Gotz, K. Zick, C. Heinen, T. Konig 2002, (Visualisation of flow processes in packed beds with NMR imaging Determination of the local porosity, velocity vector and local dispersion coefficients), Chem. Eng. Process. 41 (7), 611-630. 

A packed bed is composed of crushed rock with a density of 175 lbm/ft3 of such a size and shape that the average ratio of surface area to volume for the particles is 50 in.2/in.3. The bed is 6 ft deep, has a porosity of 0.3, and is covered by a 2 ft deep layer of water that drains by gravity through the bed. Calculate the flow rate of water through the bed in gpm/ft2, assuming it exits at 1 atm pressure. 

In a packed bed of unit volume, the volumes occupied by the voids and the solid particles are e and (1 — e) respectively where e is the voidage fraction or porosity of the bed. Let S0 be the surface area per unit volume of the solid material in the bed. Thus the total surface area in a packed bed of unit volume is (1 — e)S0. 

The theoretical value of the minimum fluidising velocity may be calculated from the equations given in Chapter 4 for the relation between pressure drop and velocity in a fixed packed bed, with the pressure drop through the bed put equal to the apparent weight of particles per unit area, and the porosity set at the maximum value that can be attained in the fixed bed. 

Intraparticle porosity refers to the fraction of the particle volume which is occupied by internal pores most manufactured food particles are porous. However, it is important to distinguish this quantity from bed voidage. The interparticle voidage e is the fraction of the packed bed occupied by the void spaces between particles and is defined as... 

Other correlations for flow through packed beds involve the porosity, e, e.g. 

One example of this type of reactor is in the synthesis of catalyst powders and pellets by growing porous soHd oxides from supersaturated solution. Here the growth conditions control the porosity and pore diameter and tortuosity, factors that we have seen are crucial in designing optimal catalysts for packed bed, fluidized bed, or slurry reactors. 

In addition to the packed bed acting as an ultrafilter, the porous frits used at both ends of the column may act as very effective filtering devices. Thus a 2-vim porosity frit would have an average pore radius of 1 lun. Because of the tortuosity and relatively wide pore-size distribution present in frits, it would be safe to assume that it contains much smaller crevices which can entrap macromolecules. 

Al-Dahhan and Dudukovic, 1996 Dudukovic et al., 1999). This way, more solid-liquid contact points over which the liquid flows are created and the bed porosity is reduced, especially near the reactor wall. Following a proper procedure for packing a trickle bed with catalyst particles and fines decouples the apparent kinetics from hydrodynamics, which is highly desirable. The addition of lines is not the same as reducing the particle size of the catalyst, as in the latter case the particle effectiveness factor is smaller. 

If we express the free cross-section of the column bed by the interparticle porosity (knowing total porosity of packed beds with porous particles is larger because of intraparticle space), we can obtain the true average fluid velocity, v,... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

To consolidate the experimental screening data quantitatively it is desirable to obtain information on the fluid mechanics of the reactant flow in the reactor. Experimental data are difficult to evaluate if the experimental conditions and, especially, the fluid dynamic behavior of the reactants flow are not known. This is, for example, the case in a typical tubular reactor filled with a packed bed of porous beads. The porosity of the beads in combination with the unknown flow of the reactants around the beads makes it difficult to describe the flow close to the catalyst surface. A way to achieve a well-described flow in the reactor is to reduce its dimensions. This reduces the Reynolds number to a region of laminar flow conditions, which can be described analytically. 

---