Mass-transfer Correlations

Mass transfer coefficients in packed columns are influenced by the packing type and size, by the liquid and vapor velocities in the column, and by the diffusivities of the solute in the liquid and vapor. Mass transfer coefficients are usually correlated in terms of these parameters by empirical correlations based on extensive experimental data (Seader and Henley, 1998). 

Gas Bubble to Bulk Liquid(kj) A persistent problem in measuring transport coefficients from bubbles is the evaluation of the interfacial area. Calder-bank. solved this problem by using a light-transmission method. His data and other results in the literature were reasonably well correlated by the equation 

Pi J Pi where Ap = difference in density between liquid phase and gas bubbles 

Pi = viscosity of liquid phase g = acceleration of gravity Pi = density of liquid phase ki = mass-transfer coefficient, cm/sec 

This correlation is for bubbles rising through the liquid phase because of the gravitational force. Mechanical stirring is absent. It is applicable for small (less than 2.5 mm diameter) rigid bubbles of the size likely to be encountered in slurry reactors. Equation (10-49) has been applied with apparent success to transport from bubbles to liquid in systems containing catalyst particles in slurry form.  

CHAPTER 10 EXTERNAL TRANSPORT PROCESSES IN HETEROGENEOUS REACTIONS 

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Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

Units employed in diffusivity correlations commonly followed the cgs system. Similarly, correlations for mass transfer correlations used the cgs or Enghsh system. In both cases, only the most recent correlations employ SI units. Since most correlations involve other properties and physical parameters, often with mixed units, they are repeated here as originally stated. Common conversion factors are listed in Table 1-4. 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

TABLE 5-21 Mass Transfer Correlations for a Single Flat Plate or Disk—Transfer to or from Plate to Fluid... 

TABLE 5-22 Mass Transfer Correlations for Falling Films with a Free between Gas and Liquid... 

TABLE 5-23 Mass-Transfer Correlations for Flow in Pipes and Duets—Transfer is from Wall to Fluid... 

TABLE 5-24 Mass Transfer Correlations for Flow Past Submerged Objects... 

TABLE 5-25 Mass-Transfer Correlations for Drops and Bubbles... 

TABLE 5-26 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems... 

TABLE 5-27 Mass Transfer Correlations for Fixed and Fluidized Beds... 

TABLE 5-28 Mass Transfer Correlations for Packed Two-Phase Contactors—Absorption, Distillation, Cooling Towers, and Extractors (Packing Is Inert)... 

Heat Transfer Heat-transfer rates are gener ly large despite severe axial dispersion, with Ua. frequently observed in the range 18.6 to 74.5 and even to 130 kW/(m K) [1000 to 4000 and even to 7000 Btu/(h fF °F)][see Bauerle and Ahlert, Ind. Eng. Chem. Process Des. Dev., 4, 225 (1965) and Greskovich et al.. Am. Tn.st. Chem. Eng. J., 13,1160 (1967) Sideman, in Drewet al. (eds.). Advances in Chemical Engineering, vol. 6, Academic, New York, 1966, p. 207, reviewed earlier work]. In the absence of specific heat-transfer correlations, it is suggested that rates be estimated from mass-transfer correlations via the heat-mass-transfer analogy. 

The mass transfer correlations are obtained by replacing Nu by Sh and Pr by Sc according to the heat and mass transfer analogy. 

There has to be a relation between kLa with aeration rate and agitation speed, and scale-up factor has to be determined. To eliminate the effect of viscous forces, the rheology of the media and broth for a large vessel have to be similar to that of a bench-scale vessel. For scale-up based on geometric similarity, the constant values a and b are proposed for the mass-transfer correlation in Table 13.1. 

Table 13.1. Constants in mass transfer correlation for various fermenter size...

This article presents a brief account of theory and practical aspects of rotating hemispherical electrodes. The fluid flow around the RHSE, mass transfer correlations, potential profile, and electrochemical application to the investigations of diffusivity, reaction rate constants, intermediate reaction products, passivity, and AC techniques are reviewed in the following sections. 

Fig. 6. Comparison between mass transfer correlations and results of limiting current measurements [14, 22],...

Another survey by Ibl (13) in 1963 listed 13 mass-transfer correlations established by the limiting-current method, only four of which were derived from quantitative considerations. At the time of writing the total number of publications is more than 200. The majority of these concern flow conditions under which theoretical predictions are, at best, qualitative. More recently, an increasing number of publications deal with model hydrodynamic studies of more complex situations, for example, packed and fluidized beds. 

The mass-transfer correlation obtained by Bohm et al. (B9), Eq. (33), in Table VII, is conspicuous for its remarkably high exponent (0.85) on the GrSc product. Since the current is almost independent of diffusivity, this must mean that the reacting ion is depleted at the downstream end of the narrow slit between the cathode and diaphragm. The total current then is determined largely by the convective transport of reactant into the slit, which, in turn, depends on the density difference but not on diffusivity. 

Sirkar and Hanratty (S13) showed, by means of refined measurements using strip electrodes at different orientations with respect to the mean flow, that transverse velocity fluctuations play a significant part in the turbulent transport very close to the wall, and that the eddy diffusivity may well be dependent on the cube of the distance y+, leading to a Sc1/3 dependence of mass-transfer correlations, which is often found experimentally. 

Bubble columns, 15 698-703, 726 estimating shear rates for, 15 689 gas-liquid mass transfer correlations for, 15 70 l-702t... 

In most cases, mass transfer coefficients are derived from experimental observations. There are full accounts in Treybal [24] and in Sherwood et al. [25]. The former gives a useful table [49] summarizing mass transfer correlations in simple situations. 

Here we review some of the correlations of convective mass transfer. We will find that many reactors are controlled by mass transfer processes so this topic is essential in describing many chemical reactors. This discussion will necessarily be very brief and qualitative, and we win summarize material that most students have encountered in previous courses in mass transfer. Our goal is to write down some of the simple correlations so we can work examples. The assumptions in and validity of particular expressions should of course be checked if one is interested in serious estimations for particular reactor problems. We will only consider here the mass transfer correlations for gases because for liquids the correlations are more comphcated and cannot be easily generalized. 

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