Tray efficiencies definitions

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

The point and Murphree efficiency definitions above are expressed in terms of vapor concentrations. Analogous definitions can be made in terms of liquid concentrations. Further discussion is elsewhere (Lockett, Distillation Tray Fundamentals, Cambridge University, Press, Cambridge, England, 1986). 

Alternative definitions of tray efficiency are sometimes used. Lockett (12) reviewed the pros and cons of several efficiency definitions. He cited the industry s experience that the more rigorous and theoretically correct a definition is, the more difficult it is to use, For instance, the Standart efficiencies are often considered the soundest fundamentally, but apparently have never been used for a design. For the design and operation engineer, the overall column (or section) efficiency is by far the most important. 

The above derivation assumes that vapor flows upward in plug flow and that there is no horizontal vapor mixing, while liquid flows horizontally in plug flow and there is no vertical mixing. Lockett and Uddin (12,122) and Standart (123,124) showed that these liquid flow assumptions are poor, unnecessary, and lead to incorrect implications regarding tray efficiency. By modifying the definition of NL, Lockett derived a fundamentally superior equation analogous to Eq. (7.13). Most theoretical models, however, use Eq. (7.13). Equation (7.13) is also the equation used for packed columns, but for packed columns, it is based on sounder assumptions (12). 

There are many different definitions of stage (or tray) efficiency, with that of Murphree [Ind. Eng. Chem., 17, 960-964... 

Considerable work on methods for pre-predicting fractionator tray efficiency continues to the present. Shortcut methods from the past differed rather widely. The AIChE 1958 calculation method is 90% accurate,but definitely cannot be termed shortcut. 

Two efficiency definitions are in common use for engineering design overall tray efficiency and Mur-phree tray efficiency. Murphree tray efficiency basis can be set on either the vapor phase or the liquid phase. Most literature reports data on a vapor phase... 

The tray efficiencies follow from the definition of the Murphree tray efficiency (Eq. 13.1.2)... 

The overall tray efficiency E fy (often called Murphree efficiency ) takes into account concentration gradients on the tray. It has an arbitrary definition based on the average total vapor composition leaving the froth and the specific liquid composition leaving the tray [not the average composition on the tray (see Figure 12.58)]. Because of this arbitrariness, the overall tray efficiency valne can exceed 1.0. When there are no composition gradients on the tray, = Ey,y... 

FIGURE 12.58 Compositions leading to the definition of overall tray efficiency, Em... 

At the present state of the art the mass transfer on a tray is expressed by tray efficiencies. Two definitions of tray efficiencies have to be distinguished, i.e., point efficiency qg and tray efficiency qgm-... 

There are two common definitions of tray efficiency (rj). The Fenske tray efficiency is applied to the whole column... 

The location of a point of coordinates (JCjocai.J itcai) be obtained by trial, to fit the definition of Eqq, Eq. (6.47). Equations (6.51) and (6.52) show that the lower the solubility of the vapor (the larger the w), the lower the tray efficiency will be. 

The number of actual trays required in a column can be determined from the calculated number of theoretical stages by invoking an efficiency. Various definitions of efficiency... 

The most commonly used definition of efficiency is the overall efficiency, defined as the number of theoretical trays required for a separation divided by the number of actual trays. A theoretical tray is defined as a contacting stage for which the vapor and the liquid streams leaving would be in thermodynamic equilibrium. The overall efficiency is inexact because separation... 

This curve is constructed based on the definition of the tray vapor efficiency by marking off vertical segments between the operating line and the equilibrium curve such that... 

This definition has the advantage of being very simple to use however, it does not take into account the variation in efficiency from one stage to another due to changes in physical properties of the system caused by changes in composition and temperature. In addition, efficiencies for various species and for various tray designs may differ. 

A stage efficiency frequently used to describe individual tray performance for individual components is the Murphree plate efficiency. This efficiency can be defined on the basis of either phase and, for a given component, is equal to the change in actual composition in the phase, divided by the change predicted by equilibrium considerations. This definition as applied to the vapor phase is expressed mathematically as ... 

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