Tray efficiency defined

Defining tray efficiency as the difference between the actual and the equilibrium vaporization, the efficiency is ... 

The foregoing define the number of theoretical states. Actual stages depend upon the tray efficiency, which will probably be the weakest number in the design. Using operating data from a similar system is certainly best where possible. Table 8-1 gives some shortcut correlations. 

The reciprocal 1/Ka of Ka measures how far the system is from equilibrium. The equilibrium stages are naturally the most efficient ones and they occur for high Ka values. For lower Ka values the system efficiency decreases. Here the tray efficiency is defined as the ratio between the separation efficiency for specific low Ka values and that for high Ka values. Note that high Ka values indicate that the system is very close to equilibrium. 

Enter an alpha value if you have chosen F or T for the method. Enter a K value for a light key component if you chose A. Input the factor alpha or K. Alpha is defined as simply the light key K divided by the heavy key K component. The K factor is simply the particular component s vapor phase mole fraction divided by its liquid mole fraction. The alpha value is therefore a ratio of the chosen two key components. These key components should be those that readily point to how well the fractionator is doing its job of separation. For example, for a depropanizer tower, choose propane as the light key component and butane as the heavy key, since you wish to separate the propane from the butane to make a propane product specification. For a multicomponent system, you may try several components to determine a controlling alpha and/or to factor an average tray efficiency. 

For tray columns, an alternative approach uses Murphree tray efficiencies (Sec, 7,1.1). This efficiency is easy to incorporate into an x-y diagram, and the diagram construction can he performed using actual rather than ideal stages. The Murphree tray efficiency is defined as... 

Below the dump point (100 percent weep), tray efficiency is a small fraction of its normal value, and mass transfer is extremely poor. Since no liquid enters the downcomers, they lose the liquid seal that prevents vapor from rising through them. Operation below the dump point can be accompanied by severe hydraulic instability due to unsealing of downcomers, as was demonstrated by field experience (76). The startup stability diagram (1), which defines the range of vapor and liquid rates needed for satisfactory startup, has the dump point as the lower limit- The tendency of dumping increases when (77-79)... 

The intersection of the operating and equilibrium lines (X, Y ) represents the scrubber outlet gas and liquid conditions for a theoretical stage which represents 100% overall tray efficiency. The overall tray efficiency E is defined as ... 

Overall tray efficiency is defined as the number of theoretical trays required for a service divided by the number of actual trays. 

Murphree tray efficiency is defined as the approach to equilibrium on an individual tray by ... 

The Murphree vapor-phase tray efficiency is defined by (refer to Fig. 12.1, which pictures vapor-liquid contacting on a distillation tray)... 

In practice the tray efficiency is estimated from a model that combines information about the tray hydrodynamics, with a model for the point efficiency that is defined analogously to the tray efficiency but applied to a narrow vertical slice of the froth (see Fig. 12.1). The Murphree vapor-phase point efficiency, for example, is defined by... 

A horizontal concentration gradient will develop in the liquid due to mass transfer into and from the liquid as the liquid flows across the tray. Thus, the composition of the vapor above the froth will change as we traverse the tray even if the composition of the vapor just below the tray is uniform. The point efficiency defined in the preceding section models the mass transfer processes at a particular point on the tray but does not take into account the fact that the liquid may have a significant concentration change as it crosses the tray. Thus, the point efficiency must be related to the tray efficiency before it can be used in column design calculations. 

The Murphree tray efficiency for component i as defined by Eq. 13.1.2 can be expressed... 

The vapor phase Murphree tray efficiency for tray j is defined as... 

The Murphree tray efficiency relates to the tray as a whole and is defined as the ratio of the actual change in a component vapor concentration as it flows through the tray to the change that would occur at equilibrium conditions. The Murphree tray efficiency is expressed in vapor terms as... 

Murphree tray efficiency is defined specifically for a given component and may have... 

A process is defined similar to Example 17.2, with the same components, initial charge and composition, the same constant distillate rate and required composition, and the same column pressure. In this case the reflux ratio is maintained at twice the minimum value. The column has six actual trays plus the reboiler, the equivalent of seven actual trays. The overall tray efficiency is 65%, and the relative volatility of butane to pentane is assumed constant at 2.315. 

The number of actual trays required in a tower to attain the perforomnce of a calculated number of theoretical stages is detemiined by the tray efficiency. Several types of tray efficiency have been proposed however, the two most widely used are the Murptuee vapor efficiency CMV, defined in Section 6.2 [Eq. (6.2-1)], which refers to individual trays, and the overall column efficiency Eq, which is defined simply as... 

A third type of tray efficiency, the Murphree point efficiency, is used sometimes in attempts to correlate efficiency with fundamental mechanisms occurring on the iray, The point efficiency . is defined as follows ... 

For a given separation, the ratio of the required number of equilibrium stages N to the number of actual trays Na defines an overall tray efficiency. 

In practice, tray efficiencies (Murphree Efficiency) are used that are defined by... 

Factor used in the Chan and Fair tray efficiency correlation, defined by Eq. (7.25). 

Overall tray efficiency. The overall tray or plate efficiency Eq concerns the entire tower and is simple to use but is the least fundamental. It is defined as the ratio of the number of theoretical or ideal trays needed in an entire tower to the number of actual trays used. 

Parameter defined by Equation 13.22 Parameter defined by Equation 13.23 Total number of components Component balance function on tray j Average heat capacity on tray j Enthalpy balance function on tray j Murphree tray efficiency in vapor terms Eugacity... 

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