Slides for the eLearning course Separation and purification processes in biorefineries (https://open-learn.xamk.fi) in IMPRESS project (https://www.spire2030.eu/impress). Subject: 2.4 Plate efficiencies.

1. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
Plate
efficiencies

2. Reasons for efficiency drops
• In practice, column trays are less than
ideal. There are several reasons for that:
1. Contact time is too short for the vapor
and liquid to reach equilibrium.
2. Weeping: Some of the liquid leak
through the holes to the tray below.
Weeping occurs at low vapor velocities.
3. Entrainment: The vapor entrains
droplets of liquid and carry them into the
tray above. Entrainment is caused by
high vapor flow rates.
Weeping and entrainment in a distillation column.
Reference: M.R. Resetarits, M.J. Lockett, in
Encyclopedia of Physical Science and Technology
(Third Edition), 2003.

3. Types of efficiency
• We use column efficiency to estimate the
required numer of actual trays. To translate the
number of ideal trays to the number of actual
trays, we must know the plate efficiency.
• Three kinds of tray efficiencies are used:
1. Overall efficiency
• Concerns the entire column
2. Murphree efficiency
• Determines the efficiency of a single tray
3. Local efficiency
• Pertains to a specific location on a single plate

4. Overall efficiency
• The overall efficiency 𝜂𝑂 is defined as the
ratio of number of ideal plates needed to the
number of actual plates.
• 𝜂𝑂 =
number of equilibrium stages
number of actual plates
• From the steps determined in theMcCabe-
Thiele diagram, you need to take away the
partial condenser and reboiler.
• The reboiler and partial condenser are
outside of the column and they are assumed
to be in perfect equilibrium.
• Total condenser is not an equilibrium stage.

5. Murphree efficiency
• The Murphree efficiency 𝜂𝑀 is defined by 𝜂𝑀 =
𝑦𝑛−𝑦𝑛+1
𝑦𝑛
∗ −𝑦𝑛+1
where
• 𝑦𝑛= actual concentration of vapor leaving plate n
• 𝑦𝑛+1= actual concentration of vapor entering plate n
• 𝑦𝑛
∗= concentration of vapor in equilibrium with liquid leaving from plate n
• Most empirical correlations for the Murhree efficiency are based on the
samples taken of the liquid on the plates, and the vapor compositions are
determined from the McCabe-Thiele diagram.
• A plate efficiency can also be defined using liquid concentrations, but this
method is rarely used in distillation.
• The plate efficiency is lower in the columns operated at high velocity,
because of significant entrainment.

6. Local efficiency
• The local efficiency 𝜂′ is defined by 𝜂′ =
𝑦𝑛
′ −𝑦𝑛+1
′
𝑦𝑒𝑛
′ −𝑦𝑛+1
′ where
• 𝑦𝑛
′ = concentration of vapor leaving specific location on plate n
• 𝑦𝑛+1
′
= concentration of vapor entering plate n at same location
• 𝑦𝑒𝑛
′ = concentration of vapor in equilibrium with liquid at same location
• Local efficiency cannot be greater than 1, because 𝑦𝑛
′
cannot be greater
than 𝑦𝑒𝑛
′
.
• In small columns with sufficient agitation, there are no measurable
concentration gradients in the liquid as it flows across the plate.
• Then the local efficiency and Murphree efficiency are equal.
• In larger columns, the local efficiency is lower than the Murphree efficiency.

7. Murphee efficiency and McCabe-Thiele diagram
• The Murphree efficiency can be used in
the McCabe-Thiele diagram.
• Triangle ABC represents an ideal plate
and triangle ADE the actual plate.
• The Murphree efficiency is the ratio
AD/AB.
• The effective equilibrium curve 𝑦𝑒
′ can
be calculated from the equation
• 𝑦𝑒
′ = 𝑦 + 𝜂𝑀(𝑦𝑒 − 𝑦)
• Position of the equilibrium curve 𝑦𝑒
′ is
depended on both the operating line
and the true equilibrium curve.
A
B C
D E

8. Number of actual plates
• When determining the number of actual plates, it is common practice to
assume the plates to be ideal and then estimate the number of actual plates
by column efficiency.
• The number of ideal plates (equilibrium plates) can be a fraction, but the
number of actual trays has to be rounded to the next higher integer.
• Example: Determine the number of actual plates, if the number of ideal
plates is 14.7 and the column has a reboiler and a partial condenser. The
overall efficiency of the column is 0.7.
• At first, we need to reduce the reboiler and the partial condenser, because
they are assumed to be equilibrium stages.
•
14.7−2
0.7
=
12.7
0.7
= 18.14 … ⟹ 19 plates

9. Relation between Murphree and overall efficiencies
• The overall efficiency is not the same as the average of Murphree
efficiencies of the individual plates.
• Typically, in stripping section, where the equilibrium line is steeper than
the operating line, the overall efficiency is greater than the Murphree
efficiency.
• At the top of the rectifying section, the equilibrium line is less steep than
the operating line and the overall efficiency is smaller than the Murphree
efiiciency.
• In a distillation column (including both a stripping and a rectifying section),
the difference between the overall efficiency and the average of Murphree
efficiencies is so minor that it is ignored in calculations 𝜂𝑜 ≈ 𝜂𝑀 .

10. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
References
Corripio, A. B. 2013. Binary Distillation Design. pp. 49-50.
Dutta, B. K. 2007. Principles of mass transfer and separation processes. New Delhi: Prentice-Hall,
pp. 371-373.
McCabe, W. L., Smith, J. C. & Harriott,, P. 2005. Unit Operations of Chemical Engineering. 7 th
Edition. New York: McGraw-Hill, pp. 712-722.
Videos:
• Flux units & tray efficency: https://youtu.be/HOGREUb49bA (7:22)
• Murphee efficiency: https://youtu.be/n1o2k_Ez-08 (6:22)
• Flooding and entrainment in a Distillation tray: https://youtu.be/q7u3NkpeatY (1:01)