Packed beds coefficient

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

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... 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

The packed-bed-to-fluid heat-transfer coefficient has been investigated by Baumeister and Bennett [Am. In.st. Chem. Eng. J., 4, 69 (1958)], who proposed the equation... 

For larger diameter columns, and for low liquid rates, the distributor must be almost exactly level (e.g., within 6 mm for a 3-m diameter) or all pour points will not function. On the other hand, the rises must be high enough to accommodate the backup caused by high liquid rates. The needed head can be estimated from the orifice equation, with a discharge coefficient of 0.5. In some cases the orinces discharge directly into tubes that extend to the packed bed (the Tubed drip-pan distributor ). 

The axial dispersion coefficient [cf. Eq. (16-51)] lumps together all mechanisms leading to axial mixing in packed beds. Thus, the axial dispersion coefficient must account not only for moleciilar diffusion and convec tive mixing but also for nonuniformities in the fluid velocity across the packed bed. As such, the axial dispersion coefficient is best determined experimentally for each specific contac tor. 

FIG. 16"10 Sherwood mimher correlations for external mass-transfer coefficients in packed beds for e = 0.4 (adapted from Siiziild, gen. refs.). 

TABLE 16-10 Coefficients for Axial Dispersion Correlations in Packed Beds Based on Eq (16-79)... 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

Peclet number for dispersion Pe = uUD where t/ is a Bnear velocity, L is a hnear dimension, and is the dispersion coefficient. In packed beds, Pe = udp/De, where u is the interstitial velocity and dp is the pellet diameter. 

Re = R nolds number, dpS UolV Sc = Schmidt number, V/D D = axial dispersion coefficient dp = Diameter of particle or empty tube = Fraction voids in packed bed Uq = Superficial velocity in the vessel. 

As can be seen in the table above, the upper two results for heat transfer coefficients hp between particle and gas are about 10% apart. The lower three results for wall heat transfer coefficients, h in packed beds have a somewhat wider range among themselves. The two groups are not very different if errors internal to the groups are considered. Since the heat transfer area of the particles is many times larger than that at the wall, the critical temperature difference will be at the wall. The significance of this will be shown later in the discussion of thermal sensitivity and stability. 

The Peclet numbers decrease when the dispersion coefficients increase. In the Reynolds number range of 10-200, in a packed bed of pellets, Peii = 2 and PeH = 0.5 (119, 120). The dispersions in the transverse... 

Radial dispersion coefficient for heat in a packed-bed 9.3 Axial dispersion coefficient for temperature in PDE Sec. 9.1 model... 

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]. 

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. 

Speed-up of mixing is known not only for mixing of miscible liquids, but also for multi-phase systems the mass-transfer efficiency can be improved. As an example, for a gas/liquid micro reactor, a mini packed-bed, values of the mass-transfer coefficient K a were determined to be 5-15 s [2]. This is two orders of magnitude larger than for typical conventional reactors having K a of 0.01-0.08 s . Using the same reactor filled with 50 pm catalyst particles for gas/Hquid/solid reactions, a 100-fold increase in the surface-to-volume ratio compared with the dimensions of laboratory trickle-bed catalyst particles (4-8 mm) is foimd. 

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. 

The errors that result from the use of average transport coefficients are not particularly serious. The correlations that are normally employed to predict these parameters are themselves determined from experimental data on packed beds. Therefore, the applications of the correlations and the data on which they are based correspond to similar physical configurations. 

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... 

Other useful correlations of heat transfer coefficients in packed beds have been proposed. Among these is a simple relation of Calderbank and Pogorski (104)... 

FIG. 16-11 Axial disp ersion coefficient correlations for well-packed beds for 8 = 0.4. 

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