Mass-transfer coefficients and

To use all of these equations, the heights of the transfer units or the mass transfer coefficients and must be known. Transfer data for packed columns are often measured and reported direcdy in terms of and and correlated in this form against and... 

The values of k and hence Sb depend on whether the phase under consideration is the continuous phase, c, surrounding the drop, or the dispersed phase, d, comprising the drop. The notations and Sh are used for the respective mass-transfer coefficients and Sherwood numbers. 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

For consistency, clearance here is expressed in cm /s although the more common clinical units, and those used later in this chapter, are ml,/min. Combination and rearrangement of equations 6—8 allows clearance to be estimated from mass-transfer coefficient and vice versa the conditions of countercurrent flow with no dialysate recycling are shown below. 

Volumetric Mass-Transfer Coefficients and Kia Experimental determinations of the individual mass-transfer coefficients /cg and /cl and of the effective interfacial area a involve the use of extremely difficult techniques, and therefore such data are not plentiful. More often, column experimental data are reported in terms of overall volumetric coefficients, which normally are defined as follows ... 

Experimental values of Hqg -nd Hql for a number of distillation systems of commercial interest are also readily available. Extrapolation of the data or the correlations to conditions that differ significantly from those used for the original experiments is risky. For example, pressure has a major effect on vapor density and thus can affect the hydrodynamics significantly. Changes in flow patterns affeci both mass-transfer coefficients and interfacial area. 

Note that the product of the mass-transfer coefficient and the interfacial area is a volumetric coefficient and obviates the need for a value of the interfacial area. While areas for mass transfer on plates have been measured, the experimental contacting equipment cuffered significantly from that used for commercial distillation or gas absorption, and the reported areas are considered unreliable for design purposes. 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

TABLE 23-14 Continuous-Phase Mass-Transfer Coefficients and Interfacial Areas in Liquid/Liquid Contactors ... 

This is the most accurate method of measuring the mass transfer coefficient and it can be used in the actual fermentation system. It depends on accurate oxygen analyses and... 

El), Oldshue (Ol), and Johnson et al. (J4)] have been concerned with the determination of the volume transfer coefficient KtAb (liter/hr), where Kx is the mass-transfer coefficient and Ab is the total gas-liquid interfacial area. The results obtained using a turbine impeller and an open pipe sparger can be correlated in terms of the nominal gas velocity wg(ft/hr) and the horsepower input to the impeller HP by an expression of the following form ... 

A summary of a number of correlations proposed for volumetric mass-transfer coefficients and specific interfacial area is presented in Table II, which includes data additional to those of Westerterp et al. (W4). It is apparent that disagreement exists as to the numerical values for the exponents. This is due, in part, to the lack of geometric similarity in the equipment used. In addition, variation in operating factors such as the purity of the system (surfactants), kind of chemical system, temperature, etc., also contribute to the discrepancies. To summarize Table II ... 

The principal applications of mass transfer are in the fields of distillation, gas absorption and the other separation processes involving mass transfer which are discussed in Volume 2, In particular, mass transfer coefficients and heights of transfer units in distillation, and in gas absorption are discussed in Volume 2,. In this section an account is given of some of the experimental studies of mass transfer in equipment of simple geometry, in order to provide a historical perspective. 

Lowe and Christie 17 used a 1.3 m square experimental column fitted with a number of different types of packing and measured heat and mass transfer coefficients and pressure... 

The whole of die resistance to heat and mass transfer may be considered as being within the gas phase and the product of the mass transfer coefficient and the transfer surface per unit volume of column (hpa) may be taken as 0.2 s"1. 

Water is to be cooled in a small packed column from 330 to 285 K by means of air flowing countercurrently. The rate of flow of liquid is 1400 cm3/m2 s and the flow rate of the air, which enters at a temperature of 295 K and a humidity of 60%, is 3.0 m3/m2 s. Calculate the required height of tower if the whole of the resistance to heat and mass transfer may be considered as being in the gas phase and the product of the mass transfer coefficient and the transfer surface per unit volume of column is 2 s-1. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

In Table 1.4, the characteristic time-scales for selected operations are listed. The rate constants for surface and volume reactions are denoted by and respectively. Furthermore, the Sherwood number Sh, a dimensionless mass-transfer coefficient and the analogue of the Nusselt number, appears in one of the expressions for the reaction time-scale. The last column highlights the dependence of z p on the channel diameter d. Apparently, the scale dependence of different operations varies from dy f to (d ). Owing to these different dependences, some op-... 

Simple algebra, based on a combination of the film and overall mass transfer rate equations, lead to the following equations, relating the respective overall mass transfer coefficients and the coefficients for the two films... 

Their correlations were based on a large amount of data on gas absorption and distillation with a variety of packings, which included Pall rings and Berl saddles. Their method for estimating the effective area of packing can also be used with experimentally determined values of the mass-transfer coefficients, and values predicted using other correlations. 

First, there is a term to account for turbulent gas-phase mixing between adjacent subchannels. This is accounted for by a term that has the form of a concentration difference between the subchannels multiplied by a mass transfer coefficient and the area available for transfer. This representation was used, as it is similar to the equation used for deposition. 

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