For packed beds

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

E] Based on freely falling, evaporating spheres (see 5-24-C). Has been applied to packed beds. Prediction is low compared to experimental data for packed beds. Liuiit of 2.0 at low Nr. is too high. 

For packed beds Gamson et al (1943) developed Colburn-type correlation for heat and mass from many experimental measurements for Rep >350 as ... 

Air Flow. Typical gas flow rates for packed-bed wet scrubbers are 0.25 to 35 standard cubic meters per second (smVsec) (500 to 75,000 standard cubic feet per minute (scfm)). 

The specific cake resistance r(nr ) depends on particulate bed characteristics e and According to the Carman-Kozeny equation for packed beds (Chapter 2)... 

By far the major portion of the available gas-absorption data have been obtained for countercurrent flow, which is the normal mode of operation for packed-bed absorbers. Special mention may be made of the results of Dodds et al. (D6), who examined mass transfer by the absorption of gas in liquid under cocurrent downward flow at flow rates higher than those corresponding to the flooding point for countercurrent operation. 

Date for mass transfer across the liquid-solid interface are virtually nonexistent for packed-bed gas-liquid-particle operations. The smaller particle size that may be employed in suspended-bed operations should be an advantage in this respect, but the packed-bed operations have, on the other hand, the advantage of having higher possible relative velocities between liquid and solid. 

For packed beds in either turbulent or laminar flow, the Ergun equation is often satisfactory ... 

Geometrically Similar Scaleups for Packed Beds. As was the case for scaling packed beds in series, the way they scale with geometric similarity depends on the particle Reynolds number. The results are somewhat different than those for empty tubes because the bed radius does not appear in the Ergun equation. The asymptotic behavior for the incompressible case is... 

Constant-Pressure Scaleups for Packed Beds. A scaleup with constant pressure drop can be achieved in a packed bed just by increasing the diameter to keep a constant gas velocity m. This gives... 

FIGURE 9.7 Peclet number Pe = u dp/D, versus Reynolds number. Re = pdpuj p, for packed beds. 

The first eight chapters of this book treat homogeneous reactions. Chapter 9 provides models for packed-bed reactors, but the reaction kinetics are pseudohomogeneous so that the rate expressions are based on fluid-phase concentrations. There is a good reason for this. Fluid-phase concentrations are what can be measured. The fluid-phase concentrations at the outlet are what can be sold. 

The global design equations for packed beds—e.g.. Equations (10.1), (10.9), (10.39), and (10.40)—all have a similar limitation to that of the axial dispersion model treated in Chapter 9. They all assume steady-state operation. Adding an accumulation term, da/dt accounts for the change in the gas-phase inventory of component A but not for the surface inventory of A in the adsorbed form. The adsorbed inventory can be a large multiple of the gas-phase inventory. 

The central difficulty in applying Equations (11.42) and (11.43) is the usual one of estimating parameters. Order-of-magnitude values for the liquid holdup and kiA are given for packed beds in Table 11.3. Empirical correlations are unusually difficult for trickle beds. Vaporization of the liquid phase is common. From a formal viewpoint, this effect can be accounted for through the mass transfer term in Equation (11.42) and (11.43). In practice, results are specific to a particular chemical system and operating mode. Most models are proprietary. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

Cylinders have the advantage that they are cheap to manufacture. In addition to varying the shape, the distribution of the active material within the pellets can be varied, as illustrated in Figure 6.7. For packed-bed reactors, the size and shape of the pellets and the distribution of active material within the pellets can be varied through the length of the reactor to control the rate of heat release (for exothermic reactions) or heat input (for endothermic reactions). This involves creating different zones in the reactor, each with its own catalyst designs. 

Normally, such heat transfer coefficients for packed beds are significantly greater than those for empty tubes at the same gas flow rate. Early reports of such data were usually reported as... 

Temperature and Conversion Profiles for Packed Bed Reactor Network... 

D. Validation of CFD Simulations for Packed Beds 1. Flow Field Validation... 

In cake filtration, the filter medium acts as a strainer and collects the solid particles on top of the initial layer. A filter cake is formed and the flow obeys the Carman-Kozeny equation for packed beds. 

The chromatographic parameters discussed above were calculated for packed beds (increased dispersion and bed length), and for expanded beds with moderate, higher and lower dispersion. The results indicated that the corresponding separation parameters of packed beds and expanded beds are commensurable, therefore, expanded beds can be successfully employed in liquid chromatography even in the case of trace analysis of synthetic dyes in waste water and sludge [75],... 

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