Murphree stage efficiency

Murphree plate efficiency, 8 767-768 Murphree stage efficiency, 70 758 Murphree vapor plate efficiency, 7 84, 87-89... 

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... 

Murphree-stage efficiency Time for distillation Parameter in Underwood equations... 

Liquid viscosity Chemical potential of component t in phase I Mixture mean viscosity defined in Eq. (15-180) Reference viscosity (of water) MOSCED asymmetry factor Efficiency of a batch e3q)eriment [Eq. (15-175)] Efficiency of a continuous process [Eq. (15-176)] Murphree stage efficiency Murphree stage efficiency based on dispersed phase Overall stage efficiency Solvatochromic polarity parameter... 

The fundamental stage efficiency is referred to as the Murphree stage efficiency The Murphree efficiency based on the dispersed phase... 

The overall stage efficiency is related to the Murphree stage efficiency and the extraction factor ( ) ... 

The approach to equilibrium for a contacting stage is called the Murphree stage efficiency, defined as the composition change in vapor across the stage divided by the composition change that would be achieved if true equilibrium existed ... 

FIGURE 12.11 Modified McCabe-Thiele plot to show approach to equihbrium on real stages. The relative height of the real stage to the equilibrium stage height denotes Murphree stage efficiency. 

The Kremser equation and its various modified forms consider only the number of theoretical plates, sot the number of actual plates in absorbers and strippers. For cases where the Murphree stage efficiency is known and relatively constant over the length of the tower, a correlation proposed by Nguyen can be used to estimate the total required number of actual plates NT as follows ... 

The Murphree stage efficiency for leaching is given by the equations... 

Equation (7-18) is valid for EF 1. If the Murphree stage efficiency expressed in terms of extract compositions, EM , is constant, then the overall efficiency for the cascade is given by... 

When dispersion is complete and uniform, the contents of the vessel are perfectly mixed with respect to both phases. In that case, the concentration of the solute in each of the two phases in the vessel is uniform and equal to the concentrations in the two-phase emulsion leaving the mixing tank. This is called the ideal CFSTR (continuous-flow-stirred-tank-reactor) model, sometimes called the perfectly mixed model. Next we develop an equation to estimate the Murphree-stage efficiency for liquid-liquid extraction in a perfectly mixed vessel. 

Em Murphree stage efficiency in terms of extract composition dimensionless. Emg Murphree gas-phase tray efficiency dimensionless. 

As we show by example, there are widely accepted methods to account for practical inefficiencies that arise, by introducing, for example, Murphree Stage efficiency, and so on. 

When other variables are specified, the stage-by-stage calculation is still trial and error. The basic procedure remains the same. That is, calculate and plot everything you can first, guess the needed variable, and then check whether the separation can be obtained with the existing number of stages. Murphree stage efficiencies are easily enployed in these calculations. 

Because extraction mixer-setders typically operate at stage efficiencies above 80% and often in the range from 95% to 100%, the equilibrium stage analysis in Section 13.14 is often used with an assumed value for the stage efficiency. However, a more accurate design will result if a mass-transfer analysis is used to estimate the stage efficiency. The purpose of the analysis will be to estimate the value of the dispersed-phase Murphree stage efficiency, Ej. ... 

To determine the actual number of required stages Np for the extraction column, the number of theoretical stages M, and the stage efficiency factor Md (Murphree stage efficiency factor) have to be known. For the case of mass transfer from the continuous to the disperse phase with respect to the dispersed phase, is... 

There are several versions of this column. The earliest model was introduced around 1948 and it was the flrst to epjoy wide commercial application. It provides alterrurting compartments to aid dispersion with impellers and coalescence with a wire mesh (about 97% void space). Capa and mass transfer data have been developed for columns with diameters from 25 to 300 nun and in three different liquid-liquid systems. The reported column capacity depends on the system properties but varies from about 14,000 to 24,000 L/h m (or 350-600 gal/h ft ). The Murphree-stage efficiency for a 12 in. diameter column can be conelated as... 

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... 

Equation (6.4.84) provides a relation between Nior and one of the Murphree stage efficiencies for a continuous well-mixed extractor. In a well-mixed batch extractor, the difficulty or ease of separation will he determined hy the time needed to achieve the desired change in composition. Thus, the numher of transfer units N,qe based on the extract phase in this case may be obtained from equation (6.4.77) as... 

Eq. (2.3) is particularly important because it involves the efficiency factor. The efficiency factor typically refers to the Murphee efficiency factor. Many real-world fractionation systems do not operate with the ideal stage assumption used in standard distillation algorithms. A popular method to deal with the non-ideal stage behavior is the Murphree stage efficiency ... 

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