Plate efficiency definition

This presentation is limited to two models, the Murphree plate efficiency and the modified Murphree plate efficiency, and their applications to columns in the service of separating both binary and multicomponent mixtures. For convenience of application, these efficiencies are restated in terms of the vaporization plate efficiency. Definitions of the vaporization point and plate efficiency follow immediately and the Murphree plate efficiencies are defined in a subsequent section as they arise in the development of the perfectly mixed liquid phase model. 

Plate Efficiency Definitions and Relations. Over-all Column Eficiency, The relation between the performance of actual and theoretical plates is expressed as plate efficiencies. A number of different plate efficiencies have been proposed, but the two most commonly used are the over-all column efficiencywhich was proposed by Lewis (Ref. 20) and plate or point efficiencies suggested by Murphree (Ref. 24). The over-all column efficiency, is the number of theoretical plates necessary for a given separation divided by the number of actual plates required to perform the same separation i.e., it is the factor by which the number of theoretical plates is divided to give the actual number of plates. This efficiency has no fundamental mass-transfer basis, but it serves as an easily applied and valuable design factor and is therefore widely used. 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

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 utility of the vaporization efficiency rests on the fact that the equations for columns with perfect plates are readily transformed to those for columns with actual plates by the introduction of a single multiplier of. Unlike the Murph-ree plate efficiency, the vaporization plate efficiency does not arise from a particular model for the behavior of a plate. Instead it is a function which may be evaluated for any model which is assumed to describe the behavior of a plate. In this respect, the definition of the vaporization plate efficiency is analogous to the thermodynamic activity coefficient. 

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 ... 

If desired, (15-54) can be modified to permit real rather than theoretical stages to be computed. Values of the Murphree vapor-phase plate efficiency must then be specified. These values are related to phase compositions by the definition... 

On a tlieoretical plate, by definition [13,14] the average composition of the vapor leaving is the equilibrium value for the liquid leaving. The customairy index of comparison between actual behavior and the theoretical, or ideal, behavior is efficiency. There are several forms of plate efficiency, which may be related in various ways. It is important, therefore, to define plate efficiency and to realize which of the plate efficiencies are measured under particular experimental conditions. 

As mentioned previously, the number of actual plates in an absoiber is related to the number of theoietical plates by a factor known as the plate efficiency. In its simplest definition, the overall plate efficiency is defined as the ratio of theoretical to actual plates required for a given separation. For individual plates, the Murphree vapor efficiency (Murphree, 1935) more closely relates actual performance to the theoretical-plate standard. It is d ined by the following equation ... 

Theoretical Predictive Methods Tbe approach to equilibrium on a plate may be defined as tbe ratio of tbe aclual change in gas composition as it passes through tbe plate to tbe change that would have occurred if tbe gas bad reached a state of equibbrium with tbe liqmd. If a point on plate n is considered, this definition leads to tbe point efficiency ... 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

Scott and Kucera (49) have prepared a 500,000 plate colun n operated in GPC. High-efficiency GPC columns are easier to operate since all compounds are, in principle, eluted before the inert p>eak, i.e., by the definition used in this work, k is negative. 

The definition of separation efficiency known from chromatography, expressed as height equivalent to a theoretical plate (F1ETP), can be applied in the same way to CZE ... 

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