The Transfer Unit Concept

Since the volume of the element is AT dH (Fig. 9.1a), the number of moles transferred per unit volume over the section is given by (N is in pound-moles per hour per cubic foot) 

The number of moles transferred per unit volume can also he calculated from the mass transfer equation 

The above applies for a differential section. Integrating over a packed bed H feet tall 

A more detailed derivation which spells out the assumptions is gives  

Height of transfer unit (HTU). The height of a transfer unit is best defined from Eq. (9.7) as the height of packing which gives a change composition equivalent to one transfer unit. It is therefore a diretf measure of column efficiency. 

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The HETP (Height Equivalent to a Theoretical Plate (stage or plate)) is the tray spacing divided by the fractional overall tray efficiency [82]. The transfer unit concept has been useful for generalized correlations [89]. Because packed towers operate with continuously changing compositions through the packed height, the concept... 

Cornell, Knapp, and Fair [12, 13, 14] proposed the use of the transfer-unit concept for distillation, where ... 

The transfer unit concept is also applicable to distillation in packed towers. Height of the packing required is ... 

Although the transfer unit concept allows for the effects of mass transfer rate, in the simplified form given here it... 

Nonequilibrium methods attempt to get around the difficulty of predicting efficiencies by doing away with the equilibrium-stage concept. Instead, they apply a transport phenomena approach for predicting mass transfer rates. The mass transfer rates are calculated continuously along the column length and not in discrete equilibrium stages. This process is similar to the transfer unit concept (Sec. 10.3.1). 

Packings for columns are available in a variety of shapes and sizes. Modern models for predicting their efficiency utilize the transfer unit concept. For the multicomponent case, NTU values are found from theoretical stages ... 

The performance of the continuous membrane column was characterized earlier (28) in a manner analogous to the transfer unit concept for packed columns. The expressions developed for NMU (difficulty of separation) and HMU (efficiency) were... 

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... 

Fair [11] systematized and correlated results obtained in direct-contact systems. He showed the use of both volumetric heat-transfer coefficients and the transfer-unit concept. For the case of simple heating or cooling without a phase change,... 

Another and in some ways a more useful design method of packed towers is the use of the transfer unit concept. For the most common case of A diffusing through stagnant and nondiffusing B, Eqs. (10,6-14)- 10.6-17) can be rewritten as... 

Because the transfer unit is defined on a differential countercurrent basis, it is usually assumed to be more correct for the design of packed towers than the stepwise countercurrent procedure of the theoretical plate. This is probably true, but there is a serious question whether the transfer unit is on a sound theoretical basis. Most distillation operations are of a degree that requires a number of theoretical plates, and for su h cases it is doubtful whether at the present stage of development the transfer-unit concept has any advantage over the theoretical-plate basis for the design of packed towers. The latter is easier to employ. 

In the transfer unit concept there is a clear separation between the number of transfer units (Nqg) which is based on driving forces, and the height of a transfer unit (Hqg) > which represents the rate of mass transfer. Thus, the specification for the amount of solute transferred from the gas phase determines the number of transfer units required. The height of a transfer unit depends mainly on the choice of tower packing. 

In an attempt to obtain more consistency with mass transfer theory, the transfer unit concept has been proposed. The number of gas-phase transfer units (Nqg) be calculated by the Souders and Brown procedure using the absorption factor [11]. This equation assumes linear, although not parallel, operating line and equilibrium curve. 

The usefulness of the transfer unit concept may be seen with the aid of Fig. 2, in which heat balance curves are drawn for the countercurrent cooling of warm... 

Unlike in distillation and absorption, very little is known about HETP values in adsorption. As a consequence, it may be preferable to use the transfer unit concept for continuous flow adsorbers like the solids in plug flow unit. A differential mass balance on the sorbate across an incremental length of bed, dz, as shown in Figure 6.6, yields ... 

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