Transfer units definition

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

In which R/S is the required product purity and aR and as are the distribution ratios of the R- and -enantiomers over the two chiral liquids, respectively (by definition aR = l/as). NTU is the number of transfer units required for the separation. From the data given in Table 5-1 it can be concluded that enantioselectivities typically are in the range between 1.05 and 1.20. According to Equation (4), the number... 

Similar equations of definition are obtained with the other transfer units ... 

Under certain assumptions (discussed below), the cost per transfer unit Yx is independent of the number of transfer units x, as shown following Eqn. (20) below. Figure 4 displays the minimum of this dimensionless total cost for a feedwater heater with constant parameters Yx, y, Xu, Tc, M, cp, and U. Similar curves result for condensers and boilers. The values used for the dimensionless parameters y and Yx/XfjTQ are shown in the figure. From the definition x = UA/Mcp, it is seen that x is directly proportional to the heat transfer area A (since U, M, and Cp are constant). 

Recalling the definitions for various heights of a transfer unit we end up with... 

The prime on Ni appears because an alternative definition of the number of transfer units for the liquid phase has been suggested by Lockett to deal with some fundamental deficiencies in the definition of While Lockett is undoubtedly right that the conventional derivations of are at fault, there is no ambiguity in the calculation of... 

By combining these definitions with Equation 14.25, the number of overall mass transfer units can be expressed in terms of the individual phase mass transfer units ... 

Table 6.3 Definition for the number of transfer units and the height of a transfer unit [5], Reprinted by permission of John Wiley and Sons, Inc. Copyright 1980.

The number of transfer units for the large column can be calculated from the definition of N and the correlation for k a... 

From the definition of the height of a transfer unit HTU, given by Eq. (13-33), it is evident that the multiplication of Eq. (13-35) by the total depth of packing yields the following relationship used by Bolles and Fair in their analysis... 

Since hA, is the volume of this section of the column, (hAc)/Q and (hAj,)/V are measures of the residence time of the vapor. Thus, the number of transfer units is proportional to (ka) x (residence time). This is true of all definitions of number of transfer units in Table 16-1 with appropriate changes in ka and residence times. 

There is obviously a similar equation that can be written in terms of X and L. The quantity on the left is unity when the change in composition is equal to the mean driving force over an interval. This serves as the definition of a mass-transfer unit. In terms of the whole stream flow rather than on the olute-fi basis used above, it becomes... 

Full understanding of the transfer-unit concept requires some elaboration. If we apply the definition of Eq. (17) to the two phases in turn, the numbers of transfer units achieved in a given process are not generally the same. Consider absorption of a component from a gas. Figure 9.5 shows the concentration or fugacity profiles across the interfacial films. In terms of the mass-transfer coefficients, we write for the overall process... 

From the experimental data, we obtain yj, Xj, L, and G , and we need to solve the equation for each point. We are going to use gPROMS to model the column and determine the number of transfer units. We start with fitting the equilibrium line. We do in piecewise due to the complexity and the range of data. For the sake of the room, we present the parameter and variable definition as well as the values in Table 9.6. 

The computation of the number of transfer units for dilute mixtures can be greatly simplified. When the gas mixture is dilute, for example, the second term of the definition of [Eq. (8.35)] becomes entirely negligible and can be discarded... 

Other values often used instead of the mass transfer coefficient and die average driving force are the height of a mass transfer unit and the number of mass transfer units. To definite them, let us proceed fitan equations (194) and (198) and fi om the equation of the mass balance of the apparatus. From these equations it follows ... 

Unit definition One methyl transfer unit catalyzes the transfer of 1 pmol of [ H]methyl groups in 30 min at 37°C. 

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