Overall stage efficiency

The overall stage efficiency of a staged extraction system is simply the number of theoretical stages divided by the number of actual stages times 100 [Eq. (15-28)]. 

Overall Stage Efficiencies The mixer-settler extractors described have generally produced overall stage efficiencies in excess of 80 percent, usually nearly 90 to 95 percent. 

The calculation of the overall stage efficiency must also include losses encountered in the diffuser. Thus, the overall actual adiabatic head attained will be the actual adiabatic head of the impeller minus the head losses encountered in the diffuser from wake caused by the impeller blade the loss of part of the kinetic head at the exit of the diffuser (A(/ed), and the loss of head from frictional forces (A(/osf) encountered in the vaned or vaneless diffuser space... 

It should be emphasized that the overall stage efficiency from Equation 9.61 should only be used to derive a first estimate of the actual number of distillation trays. More elaborate methods are available but are outside the scope of this text. In practice, the stage efficiency varies from component to component, and more accurate calculations require much more information on tray type and geometry and physical properties of the fluids. 

A first estimate of the overall stage efficiency can be obtained from the empirical correlation4 ... 

To calculate the overall stage efficiency for absorbers, the liquid viscosity and density need to be specified at average conditions. 

These two effects are major factors for the need to define an overall stage efficiency, which is the ratio of the number of ideal stages theoretically required for a given separation to the number actually required. 

Mujtaba (1989) used CMH model to simulate the operations considered by Domenech and Enjalbert (1974). Since the overall stage efficiency in the experimental column was 75%, the number of theoretical plates used by Mujtaba was 3. The column was initialised at its total reflux steady state values. Soave-Redlich-Kwong (SRK) model was used for the VLE property calculations. Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the... 

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

If 95% sugar is to be recovered and the extract phase leaving the system is to contain 12% sugar, determine the number of actual stages required if each kilogram of the dry pulp retains 2.5 kg of solution. Assume an overall stage efficiency of 85%. In Figure 32,... 

Once the overall stage efficiency has been calculated, it is possible to determine the specific volume at stage outlet from the inlet and outlet pressures and the specific volume at stage inlet. Here we use the equations developed in Section 15.3, namely ... 

If the stage is the first stage and is an impulse stage, calculate overall stage efficiency from equation (16.17) ... 

Determinatidn of separator flow capacity and stage efficiency is best done by proprietary data, methods, and experience. However, Chapter 13 briefly presents acceptable methods for rapid preliminary estimates of separator diameter and overall stage efficiency. An introduction to synthesis, the determination of optimal arrangements of separators for processes that must separate a mixture into more than two products, is presented in Chapter 14. 

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