Theoretical, or ideal, stages have the wonderful property that their prod-uct streams are in equilibrium with each other. Of course in reality, ideal stages, like ideal-anything, are seldom encountered.
When a liquid and vapor are brought into contact, mass moves across the phase boundary until an equilibrium is reached and the net mass transfer of each component ceases. The time required to reach equilibrium is dependent on the rate of mass transfer, the contact time, and also how the phases are brought into contact. Consider the stages shown in Figure 38.
For the reasons indicated in the figure, the small bubble contactor is closer to an equilibrium stage than the large-bubble contactor.
Figure 38:
Effect of Bubble Size on Stage Efficiency
PRO/II performs calculations in terms of theoretical stages, which means that you will have to translate actual trays into theoretical stages. You can use efficiency factors to describe how close a given stage is to theo-retical. Efficiencies depend both on the design and operating conditions of the tray. Under low flow conditions, for example, a bubble cap tray may be more efficient than a sieve tray, and a bubble cap tray near the top of a column may be more efficient than the same tray close to the bottom of the column.
PRO/II has three tray efficiency models: Murphree, vaporization, and equilibrium.
■ The Murphree model, illustrated in Figure 39, has a simple interpre-tation on McCabe-Thiele diagrams. Instead of stepping all the way to the equilibrium line, you only step part way. Unfortunately, Mur-phree values are not widely available.
Figure 39:
■ The vaporization model is the simplest of the three models, and con-sists of a multiplier, c, applied to the equilibrium K values for a com-ponent.
(15)
That is, the vaporization for that component is artificially adjusted versus the vaporization predicted by equilibrium. This model has the advantage that it can be extended to multicomponent distillation by defining different multipliers for different components or groups of components. PRO/II even allows you to provide a different set of multipliers on each tray.
■ The equilibrium model replaces K values with numbers that are closer to 1.0, resulting in less-than-theoretical splits.
(16)
Typically the equilibrium efficiency, Eeq, is between 0 and 1. In terms of x and y this equation is:
(17)
As with the vaporization model, you can enter different efficiencies for any component on any tray.
All of these tray efficiency models result in vapor leaving a tray that is not at its dew point. This violates the basic assumption of equilibrium used to derive the distillation column model. Therefore these tray effi-ciency models should be used sparingly. Apply them only to a few trays as needed to “tune” a model. Advanced users can use PRO/II's CON
-TROLLER to automatically determine the efficiencies that allow the col-umn to meet survey values.
yA
The recommended method for determining tray efficiencies is the appli-cation of overall efficiencies. The overall efficiency is defined as the ratio of the number of theoretical stages to the number of actual stages required to carry out a given separation. Of course the number of actual trays must be greater than the number of theoretical trays. These factors are well known for many applications, and satisfactory models may be attained by using typical values.
A good practice is to divide the column into zones, and adjust the effi-ciencies within the zones until the desired fractionation is achieved at the measured temperatures and reflux quantities. The inherent advantage of this approach over the supplied tray efficiency models is that the vapors leaving the trays are always at their dew points. Table 20 gives some typ-ical values for overall tray efficiencies.
Treat all condensers and kettle reboilers as true equilibrium stages (100% efficient). Although subcooled condensers do not actually behave as equilibrium stages, you should count them as 100% efficient when you translate your column to a PRO/II model. PRO/II will make internal
,
Note: The above efficiency models have serious implications for the column top tray in particular, since the condenser duty is defined as the duty to condense the overhead vapor from its dew point to the desired condensing temperature. Using a tray efficiency on the condenser can result in a mixed phase leaving the condenser. For this reason, PRO/II does not allow you to apply efficiency factors to condensers. For similar reasons, you cannot apply efficiency factors to reboilers.Table 20: Typical Overall Tray Efficiencies
Unit Efficiency (%)
Simple Absorbers/Strippers 20-30 Reboiled Absorbers/Strippers 40-50
Deethanizers 60-65
Depropanizers 65-75
Debutanizers 80-90
Deisobutanizers (Refluxed) 85-95 Splitters
C2, C2- 85-95
C3, C3- 95-100
C4's or C5's 90-100
Notes:
1) Assume 65-75% for most columns with reboilers and condensers.
2) At low reflux, split insensitive to number of trays in the model.
3) Pumparounds usually modeled as 2 stages.
adjustments to ensure that subcooled condensers are simulated appropri-ately.
You can reasonably expect a tray efficiency in the range of 65 to 75 per-cent for any column with several distributed components and both reboiling and condensing systems. The overall tray efficiencies increase as the reflux ratio increases and the number of components in the system decreases.
Pumparound circuits produce a zone of nearly constant liquid composi-tion in a column. This reduces the fraccomposi-tionacomposi-tion in the zone and two stages are adequate to represent the zone. The bottom stage is the draw-off (usually also a product draw stage) and the top stage is the return stage.