Correlations of Mass Transfer Coefficients

TABLE 23-12 Correlations of Mass-Transfer Coefficients in Stirred Tanks... 

The above correlation is valid for a bioreactor size of less than 3000 litres and a gassed power per unit volume of 0.5-10 kW. For non-coalescing (non-sticky) air-electrolyte dispersion, the exponent of the gassed power per unit volume in the correlation of mass transfer coefficient changes slightly. The empirical correlation with defined coefficients may come from the experimental data with a well-defined bioreactor with a working volume of less than 5000 litres and a gassed power per unit volume of 0.5-10 kW. The defined correlation is ... 

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 II Useful Correlations of Mass Transfer Coefficients for Fluid-Fluid Interfaces... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

Onda s Correlations for Randomly Packed Columns Onda et al. (1968) developed correlations of mass transfer coefficients for gas absorption, desorption, and vaporization in randomly packed columns. The vapor-phase mass transfer coefficient is obtained from... 

Although reliable correlations of mass transfer coefficients for the components of a multicomponent mixture remain to be developed, a development of the equations required to describe simultaneous mass and heat transfer in a packed column follows. 

Kikuchi K, Sugawara T, Ohashi H. Correlation of mass transfer coefficient between particles and liquid in liquid fluidized beds, J Chem Eng Japan 16 426-428, 1983. 

Mass-transfer rates The correlations of mass-transfer coefficients for the standard packings discussed in Chap. 6 are suitable for the operations discussed here (see particularly Illustration 6.7). Additional data for humidification with Berl saddles [9] Intalox saddles, and Pall rings [18t] are available. Data for some of the special tower fillings generally used for water-cooling towers are available in texts specializing in this type of equipment [15, 19]. 

It is only recently that a beginning has been made in systematizing axial-mixing data, and reliable correlations of mass-transfer coefficients must wait upon this. Practical applications are advanced far ahead of sound design data. 

In short, the determination of mass transfer coefficient of two-component system is still relied on experimental measurement although the use of dimensionless group in the data regression can be helpful and reasonable. The collection of published correlations of mass transfer coefficient by Wang et al. [65] and Zhou [64] can be used as reference. 

Data correlations of mass transfer coefficient employ empirical equations similar to the theoretical one. Equation 2.28 above. These use of the Sherwood number (dimensionless), Sh = kaL/D, as the dependent variables ... 

This chapter discusses mass transfer coefficients for dilute solutions extensions to concentrated solutions are deferred to Section 9.5. In Section 8.1, we give a basic definition for a mass transfer coefficient and show how this coefficient can be used experimentally. In Section 8.2, we present other common definitions that represent a thicket of prickly alternatives rivaled only by standard states for chemical potentials. These various definitions are why mass transfer often has a reputation with students of being a difficult subject. In Section 8.3, we list existing correlations of mass transfer coefficients and in Section 8.4, we explain how these correlations can be developed with dimensional analysis. Finally, in Section 8.5, we discuss processes involving diffusion across interfaces, a topic that leads to overall mass transfer coefficients found as averages of more local processes. This last idea is commonly called mass transfer resistances in series. 

In this book, we will frequently use the first definition in Table 8.2-2, implying that mass transfer coefficients have dimensions of length per time. If the flux is expressed in moles per area per time we will express the concentration in moles per volume. If the flux is expressed in mass per area per time, we will give the concentration in mass per volume. This choice is the simplest for correlations of mass transfer coefficients reviewed in this chapter and for predictions of these coefficients given in Chapter 9. Expressing the mass transfer coefficient in dimensions of velocity is also simplest in the cases of chemical reaction and simultaneous heat and mass transfer described in Chapters 16, 17, and 21. 

Correlations of mass transfer coefficients are conveniently divided into those for fluid-fluid interfaces and those for fluid-solid interfaces. The correlations for fluid-fluid interfaces are by far the more important, for they are basic to absorption, extraction, and distillation. These correlations of mass transfer coefficients are also important for aeration and water cooling. These correlations usually have no parallel correlations in heat transfer, where fluid-fluid interfaces are not common. 

The film theory is valuable for two reasons. First, it provides simple physical insight into mass transfer, for it shows in very simple terms how resistance to mass transfer might occur near an interface. Second, it often accurately predicts changes in mass transfer caused by other factors, like chemical reaction or concentrated solution. As a result, the film theory is the picture around which most people assemble their ideas. In fact, we have already implicitly used it in the correlations of mass transfer coefficients in Chapter 8. These correlations are almost always written in terms of the Sherwood number ... 

The restriction to dilute solution is less serious than it might first seem. While correlations of mass transfer coefficients like those in Chapter 8 are often based on dilute solution experiments, these correlations can often be successfully used in concentrated solutions as well. For example, in distillation, the concentrations at the vapor-liquid interface may be large, but the large flux of the more volatile component into the vapor will almost exactly equal the large flux of the less volatile component out of the vapor. There is a lot of mass transfer, but not much diffusion-induced convection. Thus constant molar overflow in distillation implies a small volume average velocity normal to the interface, and mass transfer correlations based on dilute solution measurements should still work for these concentrated solutions. 

Our goal was to predict the experimentally based correlations of mass transfer coefficients. This prediction would then clarify the basis of mass transfer, giving us a physical picture relating mass transfer and diffusion coefficients. Such a picture could potentially show us how to make mass transfer faster and more efficient. 

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