## Tray Columns Performance

conditions in the column such as weeping, flooding or high vapour entrainment.

Numerous geometrical factors have to be selected by the designer such as: (i) column diameter; (ii) tray spacing; (iii) top and bottom downcomer area; (iv) number of flow passes; (v) hole diameter and density; (vi) tray thickness; and (vii) weir design. This is a highly empirical process which depends on empirical design equations that describe the tray hydraulics and rule-of-thumb guidelines that have evolved over several decades of operating experience. Thus, the design of sieve tray columns has remained an art, although commercial process simulation software packages such as ASPEN, PRO II, HYSIM, etc., are trying to codify these procedures into their design packages. The conceptual steps in the design procedure together with the rule-of-thumb guidelines have been presented in the Tray Columns: Design article. Since frequent reference will be made to that article, we will henceforth refer to it simply as Part I.

In contrast, the performance analysis problem is relatively more scientific, in the sense that a series of well-defined steps leads to the estimation of the Murphree tray efficiency, the column efficiency and the actual number of trays. The overall column efficiency, Eo, is defined as:

Ne equilibrium

actual

Figure 1

comer.

(A) Murphree tray efficiency. (B) Head in the down-

Figure 1

comer.

(A) Murphree tray efficiency. (B) Head in the down-

where Nequilibnum is obtained from stagewise equilibrium design calculations. Performance evaluation boils down to estimating Eo so that the actual number of trays, Nactual, can be determined. The overall column efficiency, Eo, is related to the Murphree tray efficiency, EMV, through the Lewis relationship (assuming constant slopes of equilibrium and operating lines), given by:

Figure 1A illustrates various compositions. yn is the actual composition of the vapour stream leaving tray n, while yH is the composition that is in equilibrium with the exit liquid stream.

These two compositions would be the same, if and only if the condition of ideal equilibrium tray is satisfied. Since it is never satisfied in practice, it is important to be able to predict the tray efficiency. In fact, the compositions are not even uniform across the tray deck. Hence the above definition is applied at a local point on the tray and the point efficiency is integrated with the variations in flow conditions to predict a tray efficiency. The relationship between the inputs and the sequence of calculations is shown in Figure 2.

In Figure 2 the point efficiency is a function of local flow conditions such as local mass transfer coefficients in the liquid and vapour phases. The dry Mur-phree tray efficiency incorporates the effects of liquid and vapour distribution on the point efficiency, while the wet Murphree tray efficiency incorporates the additional effects of entrainment and weeping.

where X = mG/L is the separation factor, m is the slope of the equilibrium line, and (G, L) are the vapour and liquid flow rates in kmols-1. Thus the Murphree tray efficiency, EMV, must be estimated in order to determine the column efficiency. The urphree tray efficiency is defined to provide a measure of departure from the assumption of ideal equilibrium tray that is used to determine the number of ideal stages required to achieve a given separation. It is defined as:

The tray efficiency, EMV, clearly depends on: (i) the geometrical design parameters chosen as outlined in Part I; (ii) the physical properties of the system such as density, viscosity, surface tension, etc.; and (iii) the operating conditions like the vapour/liquid flow rates.

Having selected the design parameters identified in Part I, the objective of the performance analysis step is to predict: (i) the tray hydraulics (including the pressure drop, the flow regime, the froth density, the entrainment and weeping factors); (ii) the point efficiency; (iii) the Murphree tray efficiency; and (iv) the column efficiency. In the initial stages of designing a new tray column, there is feedback between the design and performance analysis steps to arrive at a set of optimal design parameters, as outlined in the flow chart (Figure 5 of part I). But the performance analysis steps to be outlined in this part, are also useful in analysing the performance of an existing tray column, although the opportunity to pick optimal design conditions is not present as one is forced to deal with an existing tray.

An excellent summary of the equations used to study the performance of a sieve tray column can be found in Zuiderweg (1982), Lockett (1986) and Kister (1992) (see Further Reading). The detailed steps involved in the performance analysis include: (i) the pressure drop prediction; (ii) froth height and density calculations; (iii) point efficiency prediction; and (iv) tray efficiency prediction. The inputs required are: (i) tray geometry; (ii) physical properties; and (iii) flow conditions.

weir geometry. One such equation that predicts the liquid height is given by:

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