The Length of a Transfer Unit

A well-established concept in the design of stripping operations in the chemical processing industries is the use of equations in which the height of the unit required is expressed as the product of two terms the number of transfer units (NTU), a measure of the difficulty of the operation to be carried out, and the height of a transfer unit (HTU), a measure of the height required in order to carry out an operation of unit difficulty. The advantage of this procedure is that the effectiveness of a particular unit is directly reflected in the value of the HTU. On the other hand, the advan- 

Collins et al. (1 3) have suggested that this same concept can be applied to polymer devolatilization processes, except that the HTU might be more appropriately termed the LTU when screw extruders are used since these need not be vertical. By analogy, the following expressions can be written  

The subscripts 1 and 2 refer to liquid inlet and outlet conditions, respectively. If the mode of operation is known and the value of e is measured, NTU can be calculated. If, in addition, X is known or measured, then the LTU can be determined experimentaUy. In some cases, however, an analytic expression for the LTU can be obtained. For a wiped film processor—such as a screw extruder—in which mass transfer occurs by diffusion through a wiped film into a vsqrar phase that has negligible resistance, Eq. (35) can be used and the LTU is given by 

As pointed out earlier, stripping operations are usually conducted under conditions of reduced pressure and in these circumstances NTU is given by 

Equations (83) and (87)-(89) have been used to estimate values for the LTU in the studies conducted by Coughlin and Canevari (1%9) and by Werner (1980). These results are summarized in Table II along with the results from the study of Collins et ah (1983). The results in this table provide support for the idea that the LTU can be used as a measure of the effectiveness of the extraction unit. 

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Again referring to Fig. 13, the same general trend is apparent in both the pressure-drop and number-of-transfer-unit curves. This suggests that another empirical correlating procedure could be arrived at for example, an approximate relationship exists between the length of a transfer unit (LTU) and the Lockhart-Martinelli parameters, X. 

The length of a transfer unit and the number of transfer units appropriate for good design are discussed later under Drying Equipment. ... 

The unusually small volume ratio of gas to liquid makes stripping plate efficiencies low. Yokota s model of the process assumes that liquid travels across a plate in uniform flow with no transverse mixing but that vertical mixing is perfect. He then characterizes a plate by the length of linear travel of the liquid. Correlation of the experimental data is in terms of the length of a transfer unit. This is the distance that liquid must travel to undergo an amount of mass transfer equivalent to one transfer unit. A plate then provides a (normally fractional) number of transfer units given by... 

The length of a transfer unit generally decreases as gas flow rate increases. Figure 7.100 illustrates the effect, which tends to level off at a gas velocity of about 2.8cms . Experimentally, L j at that gas rate is proportional to the 0.6 power of liquid mass... 

Results of diying tests can be correlated empirically in terms of overall heat-transfer coefficient or length of a transfer unit as a function of operating variables. The former is generally apphcable to all types of dryers, while the latter applies only in the case of continuous diyers. The relationship between these quantities is as follows. 

For design purposes it is convenient to write equations 11.97 and 11.98 in terms of transfer units (HTU) where the value of integral is the number of transfer units, and the group in front of the integral sign, which has units of length, is the height of a transfer unit. 

The expression in from or the integral has the units of length and is called the height of a transfer unit (HTU) or, for this cuse, the height of a gas-phase transfer unit, H0. which is defined as... 

In analogy to similar problems in heat and mass transfer, the length of the apparatus is the number of transfer units Ng, multiplied with the height of a transfer unit Hg. From this and for the case of. 9s = const., the temperature of the gas in the dryer can be evaluated to be... 

Could the height of a transfer unit change over the length of a column ... 

For those condensing duties where permissible pressure loss is less than 0.07kpf/cm there is no doubt but that the tubular unit is most efficient. Under such pressure-drop conditions only a portion of the length of a plate heat exchanger plate would be used and a substantial surface area would be wasted. However, when less restrictive pressure drops are available the plate heat exchanger becomes an excellent condenser, since very high heat transfer coefficients are obtained and the condensation can be carried out in a single pass across the plate. 

The Noq in Eq. (16e) is termed the overall number of transfer units. It is dimensionless and is the ratio of the change of bulk-phase concentration to the average concentration driving force. It is essentially a measure of the ease of separation. The H0G in Eq. (16d) is termed the overall height of a transfer unit. It has the dimension of length and defines the vertical height of contactor required to provide a change of concentration equivalent to one transfer unit. 

In this section we outline the systems of units which are used throughout the book. One must be careful not to confuse the meaning of the terms units and dimensions. A dimension is a physical variable used to specify the behavior or nature of a particular system. For example, the length of a rod is a dimension of the rod. In like manner, the temperature of a gas may be considered one of the thermodynamic dimensions of the gas. When we say the rod is so many meters long, or the gas has a temperature of so many degrees Celsius, we have given the units with which we choose to measure the dimension. In our development of heat transfer we use the dimensions... 

H has the dimensions of a length and has been called the height of a reactor unit, by analogy with heights of transfer units and equivalent theoretical plates. Interpret Eq. (6.5.4) to show that H is the sum of a height for external mass transfer HTU) and a term dependent on the reaction, the so-called height of a catalytic unit (HCU). Examine the contribution of these terms when the mass transfer, diffusion, and kinetic regimes are dominant. 

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