Height equivalent of a theoretical stage

Equilibrium-stage methods are usually adequate for nearly ideal distillation systems when coupled with calculations of plate efficiency to estimate actual trays or, in the case of packed towers, when HETS (height equivalent of a theoretical stage) or HETP (height equivalent to a theoretical plate) values are known from experience or from experiment to enable the estimation of packed height. For absorbers, strippers, and nonideal distillation systems, mass-transfer models are preferred, but their use requires a value for the tower diameter and a tray layout or type and size of packing. Even when mass-transfer models are preferred, initial calculations are usually made with equilibrium-stage models. Also, note that data for reliable mass-transfer coefficients is often difficult to obtain. 

Height of gas transfer unit, ft Hei t of liquid transfer unit, ft Liquid holdup, ft liquid/ft bed volume Height equivalent of a theoretical stage, ft Height of a transfer unit, defined by Eq. (9.9), ft... 

Design data for separation of the particular or similar mixture in a packea column are not available. Design procedures are better estabhshed for tray-type columns than for packed columns. This is particularly so with respect to separation efficiency since tray efficiency can be estimated more accurately than packed height equivalent to a theoretical stage (HETP). 

The height equivalent to a theoretical stage (HETS) in an extraction tower is simply the height of the tower Zt divided by the number of theoretical stages achieved [Eq. (15-29)]. 

N = number of theoretical stages HETP = height equivalent of a theoretical plate... 

An additional expression of performance used for countercurrent cascades, particularly for those in the design of towers (see below), is HETS, the height equivalent to a theoretical stage. 

Prediction of the height equivalent to a theoretical stage presents a difficult problem. A lack of fundamental data necessitates an empirical approach, and at the present time... 

These terms sometimes are used interchangeably with height equivalent to a theoretical stage (HETS), but they are nearly the same only when the ratio kjka is a large number in the case of HTUa. Example 13.12 studies this difference. 

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height equivalent to a theoretical stage (HETS) in ft or m. 

In order to permit sizing a tower, data must be available of the height of a transfer unit (HTU). This term often is used interchangeably with the height equivalent to a theoretical stage (HETS), but strictly they are equal only for dilute solutions when the ratio of the extract and raffinate flow rates, E/R, equals the distribution coefficient, K = xE/xR (Treybal, 1963, p. 350). Extractor performance also is expressible in terms of mass transfer coefficients, for instance, KEa, which is related to the number and height of transfer units by... 

Eckert [9] showed that a relative height equivalent to a theoretical stage (HETS) vs. the dispersed-phase velocity revealed the packed-column efficiency, or simply the required height, to make one theoretical stage. (See Fig. 7.10). Eckert and others [6, 8] have shown that normally the theoretical packed-column stage requires 2.5 ft of column packed height. All this of course refers strictly to liquid-liquid extraction processing. Also, the continuous-phase velocity Vc (ft/h) and the dispersed-phase velocity VD (ft/h) are referenced to the liquid-phase... 

Distillation stage calculations are usually performed with ideal stages, The number of ideal stages required for the separation is divided by the overall column efficiency (Sec, 7,1,1) to obtain the required number of trays. In packed towers, the number of stages in the column is multiplied by the HETP (Height Equivalent of a Theoretical Plate, see Sec. 9.1,2) to obtain the packed height. 

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