Murphree raffinate stage efficiency

Similarly the Murphree raffinate stage efficiency EMr is defined as... 

Emr Murphree raffinate stage efficiency, as a fraction, dimensionless... 

One can look at the progress toward equilibrium based on the extract phase also. The extract-phase composition exiting the real device is xjy, corresponding to a raffinate composition of xyj. If, however, the extract phase of composition, XjE, leaving the mixer were in equilibrium with the raffinate phase, the hypothetical raffinate composition would have been X iR> corresponding to point B on the equilibrium curve. An estimate of this difference is provided by the Murphree raffinate-stage efficiency, Emr, which is defined as... 

Murphree e3ctract stage efflciency, Murphree raffinate stage efficiency (6.4.70), (6.4.71) Murphree vapor efficiency (8.1.198) Newton particle separation efficiency (2.4.14a) total efficiency in solid-fluid separation (2.4.4a), overall Alter efficiency (6.3.45), (7.2.201) reduced efficiency of KelsaU (2.4.16a) Ej- for ith solid-fluid separator (2.4.17c,d)... 

The Murphree stage efficiencies are also in common use. In terms of the extract the Murphree extract stage efficiency Eme is defined as the ratio of the number of moles of solute actually transferred to the number which would be transferred if the final extract were in equilibrium with the actual final raffinate. Preservation of a material balance does not permit such final equilibrium concentrations actually to develop, but in terms of the concentrations shown in Fig. 2 this becomes... 

In practice, when the extraction process is completed in the mixer and the two phases are separated in a settler, the two phases are often not at equilibrium with each other. In such a case, the end of the process is located at a point R (xjR, Xie). The extent of approach to equilibrium achieved by each phase is frequently estimated in the following way. The extract-phase final composition achieved is X( . However, if the raffinate phase leaving the mixer at a composition Xir were in equilibrium with this extract phase of composition Xjg, then this hypothetical extract composition would have a higher value, xj (corresponding to point C on the equilibrium curve in Figure 6.4.8(c)). An estimate of this deficiency is called the Murphree extract-stage efficiency, Eme-... 

As in gas-liquid contact, the performance of individual extraction stages can be described in terms of the approach to equilibrium actually realized by the effluent extract and raffinate streams. The Murphree stage efficiency can be expressed in terms of extract compositions as or in terms of raffinate... 

Sometimes, however, the extractions in staged cascades are much less effective than expected even when the mass transfer is fast. In other words, the Murphree efficiencies are much less than one even when the quantity KyaVjGA) is expected to be much greater than one. Such poor performance is often due to backflow of either the raffinate or the extract. Such backflow may occur because of entrained liquid. While the cause varies, the effect is the same a lower apparent stage efficiency. We explore these ideas in the example that follows. 

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