Distillation columns play key roles for separating compounds in many chemical processes. Most commonly, the columns rely on trays or packing to accomplish mass transfer. Each stage in a trayed distillation column essentially is a flash drum where vapor from below contacts liquid from above. Ideally, the phases mix, reach equilibrium and then separate. The tower is just a convenient method of arranging multiple mixing stages and handling the internal recycles (boil-up and reflux) with minimum fuss.
Of course, real trays don’t provide ideal performance. They must contend with constraints imposed by operating phase regime, relative rates of the liquid and vapor, vapor/liquid surface area, system properties, liquid bypassing (leaks), vapor bypassing, maldistribution (unequal liquid-to-vapor ratios), entrainment of liquid, carry-under of vapor, back-mixing, and many other issues. Additionally, most trays, even if working with mechanical perfection, are cross-flow devices, not true counter-current ones. Many things can affect tray efficiency.
The best starting point for coming up with tray efficiency for design is to gather operating data. Take advantage of the published data available on many systems and specific trays. For evaluating current tray efficiency, begin with operating data from the plant; this allows for estimating section efficiencies.
Life becomes more complex when observed efficiency departs from expected values or when no data are available.
Much research has gone into developing fundamental relations that predict efficiency for a specific tray. Unfortunately, different methods can give very different results. This underscores a common problem with engineering correlations. If you see something that has lots of different prediction methods, the usual reason is that none work very well. The most important reason to create a new correlation is because the old ones don’t suffice. There isn’t much point for another research project on tray efficiency prediction if an existing method already does the job well.
The practicing engineer’s problem still remains. What’s a useful way to predict tray efficiency and how well can it be done?
Tray efficiency can be defined multiple ways. The most commonly used ones are the Murphree tray efficiency, EM, and overall tray efficiency, EO. You can consider EM as the fraction of composition change in the vapor phase compared to what a single ideal stage would accomplish. In contrast, EO compares the separation across a number of trays to how many ideal stages would accomplish the same separation. For example, if the data show that 10 trays in a real tower match the separation expected with 7 ideal stages, the efficiency would be 7/10 or 70%. For design and plant operation, EO has the most practical value.
The first solid attempt at correlating fractionation tray efficiency was the O’Connell method from 1946. A good, simplified curve fit is:
EO = 50.3(µLα)-0.226 (1)
where EO is section efficiency in percent, μL is liquid viscosity in centipoise, and α is the relative volatility of the light key to the heavy key. This correlation gives results that are within ±10% for 90% of the data. Different graphs/equations have been generated for absorber services.
A recent update by Duss and Taylor modified this by decreasing the importance of relative volatility changes:
EO = 50.3(µL)-0.226α-0.08 (2)
Equations 1 and 2 give slightly different results; you can use either. As with any correlation, applicability ranges and limits are important. If tray efficiency variations become a significant factor for you, investigate the specifics and how they fit your case.
Generally, the more-complex methods rarely reward the effort required. They are more difficult to evaluate and don’t give significantly more accurate results.
One lesson here is that, lacking data, a ±10% prediction of tray efficiency is the realistic limit. For design purposes, adding an extra tray to a 10-tray tower may not pose much of an economic penalty. However, putting 12 more trays on a tower with 120 probably would be expensive. As the cost of the design margin rises, generating accurate data in a test unit becomes increasingly worthwhile.
In the plant, the best way to understand efficiency changes is to test the tower to determine efficiency at the start-of-run. A performance test will give you something to check against to help diagnose operating problems. Trying to evaluate tray efficiency and determine if it’s the problem are extremely difficult if you lack data of a “good” operation.