Mass-transfer coefficients in packed beds

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

Wakao, N. and Funazkri, T. Chem. Eng. Sci. 33 (1978) 1375. Effect of fluid dispersion coefficients on particle-fluid mass transfer coefficients in packed beds. 

Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds various correlations exist in terms of dimensionless numbers. In Table 1 the most appropriate ones for laboratory reactors are given [5, 7, 30, 31]. Values of k( and h for gases in laboratory systems range between O.l-lOms-1 and 100-1000JK-1s-1 m-2, respectively. In the case of monoliths, other correlations should be used because of the different geometry [32-34],... 

Wakao N., and T. Funazkri, Effect of Fluid Dispersion Coefficients on Particle-to-fluid Mass Transfer Coefficients in Packed Beds, Chem. Engr. Sci., 33,1375 (1978). 

Wakao, N., Particle-to-fluid heat/mass transfer coefficients in packed bed catalytic reactors, in Recent Advances in the Engineering Analysis of Chemically Reacting Systems (Ed. L.K. Doraiswamy), Wiley Eastern, New Delhi, 1984. 

Numerous investigations have been conducted of mass transfer coefficients in vessels with a variety of kinds of packings. Many of the mote acceptable results are cited in recent books on mass transfer, for instance, those of Sherwood et al. (Mass Transfer, McGraw-Hill, New York, 1975), Cussler (Diffusion, Cambridge, 1984), and Hines and Maddox (1985). A convenient correlation of mass transfer coefficients in granular beds covering both liquid and vapor films is that of Dwivedi and Upadhyay [Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)], namely,... 

Table I. Correlations to calculate mass and heat transfer coefficients in packed beds [S, 7, 30, 31] and monoliths [32-34],...

The methods of experimental measurement of heat and mass transfer coefficients are summarized in Table 4.8, and resulted mainly from heat and mass transfer investigations in packed beds. Heat transfer techniques are either steady or unsteady state. In steady-state methods, the heat flow is... 

The mass transfer coefficient between the surface of the particles and the flowing fluid varies along the surface of each particle, but an average value can be measured from mass transfer experiments in packed beds. Large numbers of... 

From tests on systems of known area, Catchpole et aL [94] and several previous workers [95-98] have shown that the solvent film mass transfer coefficient for the transport of solute into solvents under near-critical conditions can be predicted successfully from appropriate correlations. These correlations require values for the solute diffusivity into the solvent as well as the viscosity and density of the solvent. Based on determinations of mass transfer rates in packed beds using benzoic acid [94], 2-napthol [95] and naphthalene [96] as solutes, Catchpole et al. [94] recommend the equation... 

Example 8.2-4 Log mean mass transfer coefficients Consider again the packed bed of benzoic acid spheres shown in Fig. 8.1-1(b) that was basic to Example 8.1-2. Mass transfer coefficients in a bed like this are sometimes reported in terms of a log mean driving force ... 

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... 

Most recently. Kirillov and Nasamanyan15 carried out a very interesting unsteady-state analysis of liquid-solid mass transfer for cocurrent upflow in a fixed-bed reactor. The analysis was compared and verified by the steady-state measurements of liquid-solid mass-transfer coefficients in a 10-cm x 10-cm square column with a height of 50 cm. Three types of packings, 30-mm and 8-mm... 

Kato and Wen (5) found, for the case of packed beds,that there was a dependency of the Sherwood and Nusselt numbers with the ratio dp/L. They proposed that the fall of the heat and mass transfer coefficients at low Reynolds numbers is due to an overlapping of the boundary layers surrounding the particles which produces a reduction of the available effective area for transfer of mass and heat. Nelson and Galloway W proposed a new model in terms of the Frossling number, to explain the fall of the heat and mass transfer coefficients in the zone of low Reynolds numbers. 

It is desired to double the capacity of the existing plant by processing twice the feed of reactant A while maintaining the same fractional conversion of A to B in the reactor. How much larger a reactor, in terms of catalyst weight, would be required if all other operating variables are held constant You may use the Thoenes-Kramers correlation for mass transfer coefficients in a packed bed. Describe the effects of the flow rate, temperature, particle size at conversion. 

In order to assess transport mechanisms due to convection various correlation for heat and mass transfer coefficients in a packed bed have been derived. For the present application the transfer coefficient in the bed is related to the transfer coefficient of a single particle in a gas flow according to [15]. Due to the outflow of the gases during pyrolysis and char conversion the calculated transfer coefficient is decreased, thus Stefan correction is included to calculate the transfer coefficient at a finite flow over the boundary. 

Heat and mass transfer coefficients in a fluidised bed lie between the values for a packed bed and those for a single particle. The fundamental pattern of the Nusselt or Sherwood number as functions of the Reynolds number is illustrated in Fig. 3.40. In this the Nusselt number Nu = adP/A or the Sherwood number Sh = l3dP/rj and the Reynolds number Re = wmdP/v are all formed with the particle diameter, which for non-spherical particles is the same as the equivalent sphere diameter according to (3.273). In the Reynolds number wm is the mean velocity in the imaginary empty packing. 

Example 2.3 Mass-Transfer Coefficient in a Packed-Bed Distillation Column... 

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