The HETP Concept

The concept of HETP (height equivalent of a theoretical plate) was introduced to enable comparison of efficiency between packed and plate columns. HETP iB defined as 

A similar HETP value can be obtained for a plate column if the tray spacing is known 

Relationship between HTU and HETP. The relationship between HETP and HTU has been shown to be (111,113,114) 

HETP versus HTU. Packed-height computations can be carried out using either the HTU or the HETP approach. Both approaches should give essentially the same resnlt. The HETP approach is usually preferred because it has the following edvantages  

The HETP approach is suitable for multicomponent systems, while the HTU approach is difficult to apply for thses. 

Rtlattonahip between HTU and HETP. The relationship between HETP 

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Packed column performance can use either the HETP or HTU concepts, the HTU is somewhat more complicated but no more correct than the HETP concept. The latter adapts itself to direct use from tray-by-tray digital computer calculations, and is thereby a litde more direct. 

In practice, the HETP concept is used to convert empirically the number of theoretical stages to packing height. As most data in the literature have been derived from small-scale operations, these do not provide a good guide to the values which will be obtained on full-scale plant. The values given in Table 11.5 may, however, be used as a guide. 

In spite of its empirical nature, the HETP concept remains in universal use for the description of packing performance by manufacturers and users. 

The HETP equation is not simply a mathematical concept of little practical use, but a tool by which the function of the column can be understood, the best operating conditions deduced and, if required, the optimum column to give the minimum analysis time calculated. Assuming that appropriate values of (u) and (Dm) and (Ds)... 

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... 

Where F is the variance of analyte molecides about their mean in the analyte broadening zone which have a concentration profile in the Gaussian distribution shape, and the Lz is the distance the zone has moved (please note that Lz does not necessarily refer to column length here). Obviously, this is a more meaningful and useful concept, which views the HETP as the length of column necessary to achieve equihbrium between the Hquid and mobile phase. In addition, equation 27 can be related to the random diffusion process (actually, the movement of analyte molecules between the two phases is hke the molecule motion in a random diffusion process) defined by the Einstein diffusion equation ... 

Packed columns operate in the counterflow mode, and thus it is not really appropriate to utilize stagewise concepts for their analysis and design. Despite this, the HETP approach [Equation... 

The concept of HETP was described in Chapter 3, p. 26. The same concept applies here except that HETP for a distillation differs from an HETP for a chromatographic separation, because in a distillation, the entire column is in use at the same time, whereas in a chromatographic column, only a small portion is being used at any one time. 

For the special case where the equilibrium and operating lines are perallet, that is. mGM/LM = I, HETP and HTU values are equal. The height of the packing zone. Z, may he estimeted using either HTU or HETP concepts diet is,... 

Figure 2.7 Comparison of the treatment of the additivity of the contributioos to the HETP from convection and dispersion after the dasrical ooncqit and Giddings coupling concept. The HETP derived from the coupling equation is always less than both/f, and Afo, and the dassk HETP is always greater than either of these. (Rquinted from Ref. 9, p. SS by courtesy of Mated Dekker, Inc.)...

The concepts of reduced velocity v and reduced plate height h are powerful ideas that allow us to compare columns to each other under a broad range of mobile-phase conditions and over a range of particle sizes. We use the principle of corresponding states to form dimensionless parameters from the HETP and the linear velocity. The HETP has the dimension of length. To make it dimensionless, we simply divide it by the particle diameten... 

Giddings (9,10) argued that the origin of the problem rests with a basic conjecture of the van Deemter concept the assumption that the different contributions to the HETP are independent of each other and that therefore the variances of these different contributions can be summed up ... 

A comparison of the results of the classic concept and the coupling concept is shown in Figure 2.7. Oiddings (9) pointed out that the HETP derived from the coupling equation is always less than both Hf and Ha, while the classic H... 

We are able to show that in a well-packed (i.e., a uniform column), this concept gives rise to a term that is practically constant over the range of interest, that is, in accordance with the van Deemter equation. In a nonuniform bed, on the other hand, it gives rise to the curvature of the increasing branch of the HETP-velocity plot that has been observed experimentally. Consequently, a uniform, well-packed bed can be described by the van E>eemter equation, while a poorly packed bed needs to be described by an equation that contains a term incorporating the curvature. 

To relate packed tower performance to trays, packing performance is defined occasionally in terms of the height equivalent to a theoretical plate (HETP). The HTU concept is theoretically more correct for packed towers, in which mass transfer is accomplished by a differential action rather than a series of discrete stages. However, some data still are presented as HETPs. When the operating and equilibrium lines are straight, the two concepts can be related as follows ... 

Remember, though, that the old concept of the HETP (height equivalent to a theoretical plate) can be evaluated as equal to around 25 times the nominal size of the packing. Thus, we can quickly gain a rough estimation of the height of a distillation colunm or even an isothermal absorption column. However, this way of working is imprecise, because there is no rational justification for the concept of the HETP. 

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