Packed beds particle shape

In industrial packed beds, particle shapes vary widely. Irregular shapes are often used to minimize frictional... 

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. 

The absorption of reactants (or desorption of products) in trickle-bed operation is a process step identical to that occurring in a packed-bed absorption process unaccompanied by chemical reaction in the liquid phase. The information on mass-transfer rates in such systems that is available in standard texts (N2, S6) is applicable to calculations regarding trickle beds. This information will not be reviewed in this paper, but it should be noted that it has been obtained almost exclusively for the more efficient types of packing material usually employed in absorption columns, such as rings, saddles, and spirals, and that there is an apparent lack of similar information for the particles of the shapes normally used in gas-liquid-particle operations, such as spheres and cylinders. 

Further work regarding the axial dispersion of gas in irrigated packed beds seems needed, and it may be noted, with particular regard to gas-liquid-particle processes, that no results have been reported for beds of cylindrically or spherically shaped packing materials. 

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. 

The shape of a particle may be one of many that can be formed by extrusion or tabletting. As in Chapter 8, we restrict attention to three shapes (solid) cylinder, sphere, and flat plate. The size for use in a packed bed is relatively small usually about a few mm. 

The form of the above equations suggests that the only properties of the bed on which the pressure gradient depends are its specific surface S (or particle size d) and its voidage e. However, the structure of the bed depends additionally on the particle size distribution, the particle shape and the way in which the bed has been formed in addition both the walls of the container and the nature of the bed support can considerably affect the way the particles pack. It would be expected, therefore, that experimentally determined values of pressure gradient would show a considerable scatter relative to the values predicted by the equations. The importance of some of these factors is discussed in the next section. 

The necessity of forming zeolite powders into larger particles or other structures stems from a combination of pressure drop, reactor/adsorber design and mass transfer considerahons. For an adsorption or catalytic process to be productive, the molecules of interest need to diffuse to adsorption/catalytic sites as quickly as possible, while some trade-off may be necessary in cases of shape- or size-selective reactions. A schematic diagram of the principal resistances to mass transfer in a packed-bed zeolite adsorbent or catalyst system is shown in Figure 3.1 [69]. 

The objective of AxelTs [11] experimental study is twofold (1) to develop methods to study the combustion process of a packed-bed of biomass (2) to study the effect of mass flow of air on the combustion process in different conditions with respect to fuel particle size, density, and shape. The results are planned to be applied to computer simulations of packed-bed combustion of wood fuels as well as design data for construction of PBC systems. 

Flow through granular and packed beds occurs in reactors with solid catalysts, adsorbers, ion exchangers, filters, and mass transfer equipment. The particles may be more or less rounded or may be shaped into rings, saddles, or other structures that provide a desirable ratio of surface and void volume. 

Example 18. Shape Factors for Particles in Packed Bed Exchange... 

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

The generalized relation for the pressure drop for flows through a packed bed was formulated by Ergun (1952). The pressure loss was considered to be caused by simultaneous kinetic and viscous energy losses. In Ergun s formulation, four factors contribute to the pressure drop. They are (1) fluid flow rate, (2) properties of the fluid (such as viscosity and density), (3) closeness (such as porosity) and orientation of packing, and (4) size, shape, and surface of the solid particles. 

The simplest kind of a fixed catalyst bed is a random packing of catalyst particles in a tube. Different particle shapes are in use like spheres, cylinders, rings, flat disc pellets or crushed material of a certain sieve fraction. Mean particle diameters range from 2 to 10 mm, the minimum diameter is limited primarily by pressure drop considerations, the maximum diameter by the specific outer surface area for mass and heat transfer. 

Density When a powder is poured into a container, the volume that it occupies depends on a number of factors, such as particle size, particle shape, and surface properties. In normal circumstances, it will consist of solid particles and interparti-clulate air spaces (voids or pores). The particles themselves may also contain enclosed or intraparticulate pores. If the powder bed is subjected to vibration or pressure, the particles will move relative to one another to improve their packing arrangement. Ultimately, a condition is reached where further densilication is not possible without particle deformation. The density of a powder is therefore dependent on the handling conditions to which it has been subjected, and there are several definitions that can be applied either to the powder as a whole or to individual particles. 

The first three types (pellets, extrudates and granules) are primarily used in packed bed operations. Usually two factors (the diffusion resistance within the porous structure and the pressure drop over the bed) determine the size and shape of the particles. In packed bed reactors, cooled or heated through the tube wall, radial heat transfer and heat transfer from the wall to the bed becomes important too. For rapid, highly exothermic and endothermic reactions (oxidation and hydrogenation reactions, such as the ox-... 

The problem of the optimal particle shape and size is crucial for packed bed reactor design. Generally, the larger the particle diameter, the cheaper the catalyst. This is not usually a significant factor in process design - more important are the internal and external diffusion effects, the pressure drop, the heat transfer to the reactor walls and a uniform fluid flow. 

Hie most commonly found shape of catalyst particle today is the hollow cylinder. One reason is the convenience of manufacture. In addition there are often a number of distinct process advantages in the use of ring-shaped particles, the most important being enhancement of the chemical reaction under conditions of diffusion control, the larger transverse mixing in packed bed reactors, and the possible significant reduction in pressure drop. It is remarkable (as discussed later) that the last advantage may even take the form of reduced pressure losses and an increased chemical reaction rate per unit reactor volume [11]. 

With this definition, for spheres, the use of Equation 8.39 gives just the diameter of sphere. Expressions of equivalent diameters for different particle shapes as used in packed bed reactors are presented in Table 8.1. ... 

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