Fluid Flow through Solids Beds

In the moving-bed system of Figure 7, solid is moving continuously in a closed circuit past fixed points of introduction and withdrawal of liquid. The same results can be obtained by holding the bed stationary and periodically moving the positions at which the various streams enter and leave. A shift in the positions of the introduction of the liquid feed and the withdrawal in the direction of fluid flow through the bed simulates the movement of solid in the opposite direction. 

These few examples of percolation problems evidence the influence that percolation structures may have cxi fluid flow hydrodynamics when fluid-solid interaction is the factor determining fluid flow through packed beds (i.e. at low gas-liquid interactions). 

Filtration is the concentration of solids (or clarification of liquor) from slurry by fluid flow through a permeable medium. This normally takes the form of a membrane, filter leaf or packed bed, which restricts the particles, more than the fluid (Figure 4.4). 

This fraction could be viewed as a fixed-bed wetting efficiency. If he t = s and hyt= 1, the bed is completely filled with fluid (fully wetted). The term is analogous to the catalyst wetting efficiency/w for trickle beds (Section 3.7.3). However, this equality is valid solely in fixed beds where a single fluid flows through. The active volume of the solid, which is occupied by the fluid, amounts to the fixed-bed volume occupied by the fluid minus the volume occupied by fluid ... 

Ergun s equation on drop of fluid pressure when flowing through a bed of solid particles [1] ... 

Solids of group C are very fine-grained, cohesive powders (e.g. flour, fines from cyclones, and electrostatic filters) that virtually cannot be fluidized without fluidization aids. The adhesion forces between particles are stronger than the forces that the fluid can exert on the particles. Gas flow through the bed forms channels extending from the grid to the top of the bed, and the pressure drop across the bed is lower than the value from cq 1. Fluidization properties can be improved by the use of mechanical equipment (agitators, vibrators) or flowability additives such as Aerosil. 

Now, the actual linear velocity with respect to the retaining vessel of a fluid flowing through a fluidized bed of voidage e is m0/e, where u0 is the superficial fluid velocity, that is, the volumetric fluid flow rate divided by the horizontal cross-sectional area of the otherwise empty retaining vessel, being positive for the upward direction. Similarly, the actual linear velocity of the particles with respect to the retaining wall is ud/(l - e), where ud is the solid mass flow rate... 

In porous solids made of larger elements such as fixed packed beds, where the characteristic dimension of the packing is d (for example the diameter of a packed solid), the frequency of the velocity change is a = v/d (after each flow through an element of the packed bed, the local fluid velocity v changes its direction). Now if we use this value of a in the dispersion coefficient, we obtain the famous relation Pe = (vd)/D = 2, which gives the value of the dispersion coefficient when a fluid flows through a packed bed [4.90]. 

When a fluid flows through a porous solid or a porous bed, the species forming the fluid can present some affinities with the solid particles. The affinity of species with respect to the contacting solid, which here form what is called a stationary phase, can be the result of different phenomena such as adsorption, ion exchange, steric exclusion and absorption. 

The term fluidization is applied to processes in which a loose, porous bed of solids is converted to a fluid system, having the properties of surface leveling, flow, and pressure-depth relationships, by passing the fluid up through the bed. 

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