Dimensioning Tray Columns

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Dimensioning Tray Columns
Prof. Dr. Marco Mazzotti - Institut für
Verfahrenstechnik
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GEOMETRICAL VALUES hw,weir height hcl, Skirt
clearence height of the downcomer hL, Clear
liquid height hp, pressure drop between downcomer
inlet and outlet. hf, froth height H, tray
spacing lcl,, skirt clearance lw,weir length d,
diameter
SURFACES Aac, active area Ah, hole area a,
interfacial area f, relative free area
PHYSICAL PROPERTIES ML, molar mass of the liquid
phase MG, molar mass of the gas phase DL,
diffusion coefficient of the liquid DG,
diffusion coefficient of the gas rL, density of
the liquid phase rG, density of the gas phase s,
surface tension hG, viscosity of the gas phase m,
slope of the equilibrium line (linear case)
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VELOCITIES/ FLOWS V, gas/liquid flow uLd,
velocity of clear liquid in the downcomer uG,
superficial velocity F, gas load vo, velocity of
gas in the holes Fh, gas load in the holes uG,
superficial velocity of the gas (VG/Aac) ed,
volume fraction of the dispersed phase eL,
relative liquid holdup
COEFFICIENTS CG, capacity factor Co, discharge
factor xsp, friction coefficient a, discharge
coefficient b, mass transfer coefficients zsp,fric
tion factor of the drop eLd, relative liquid
content
PRESURE DROP Dpd, pressure drop on a dry
tray DpL, pressure drop in the clear liquid
height (hL) DpR, pressure drop by several
phenomena
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OTHER yn-1, composition of the gas entering the
tray y(x), composition of the gas at equilibrium
with a liquid of composition x yn, composition of
the gas going out from the tray y(xn),
composition of the gas at equilibrium with a
liquid of composition xn xn, composition of the
liquid in the outlet downcomer EOG, point
efficiency EOGM, tray efficiency or Murphree NOG,
gas side overall transfer units NG, gas side
transfer units NL, liquid side transfer units
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PART I Operating region of tray columns

• Maximum gas load
• Minimum gas load
• Maximum liquid load
• Minimum liquid load
• Operating region of tray columns

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Maximum Gas Load
The gas load in a tray column can be increased up
to a point where the gas blows the liquid off the
tray in form of fine droplets. The liquid then no
longer flows countercurrently to the gas, and
proper column operation ends.
Souders and Brown were the first to develop in
1934 a systematic approach for calculating the
maximum gas load of a tray. They considered a
single drop suspended above the tray and
formulated the equilibrium of friction force and
weight force minus buoyancy
The gas load is usually expressed by the F-factor
that represents the square root of the kinetic
energy of the gas flow. It is defined by
Combining the two expressions we arrive to
another expression of F. Finally it can be
expressed in terms of the capacity factor, CG.
See correlations for the gas capacity factor,
Souders and Brown, Kirschbaum, Wenzel, etc...
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cont. Maximum Gas Load
The maximum gas load is expressed as a function
of the Weber-number (Wer u2d/s). There is a
critical value of the Weber number that gives us
the critical gas load
Using equation I-2 in the Weber-number definition
and then, isolating d, we get
Where Fh is the gas load in the holes of the
tray. To write the expression in terms of the gas
load, F, we use the definition of relative free
area (f)
Combining the last two equations with equation
I-3
According to Wallis the value of the critical
Weber number is approximately 12 for liquids with
low viscosity. If the friction coefficient (xsp)
is assumed to be 0.4 (the value for rigid spheres
in turbulent flow), the equation I-6 becomes
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Minimum Gas Load
The gas load of the column tray can be decreased
to a point where either the gas no longer flows
uniformly though all the tray openings or the
liquid leaks though the tray. Both modes of
operation should be avoided because they diminish
tray efficiency.
According to Mersmann, gas flows uniformly
through all the holes of a sieve tray when the
Weber-number in the hole (hole diameter and hole
velocity) , exceeds a critical value of 2. From
this condition follows
According to Ruff, the liquid is prevented from
leaking though a sieve tray if the Froude-number,
Fr, exceeds a critical value. From this condition
follows
At small hole diameters (up to approximately 2 or
3 mm, the uniform gas flow through all the holes
is the limiting mechanism the minimum gas load
decreases with increasing the hole diameter. At
hole diameter grater than 2 or 3 mm, weeping of
liquid through the tray becomes the decisive
factor the minimum gas load increases with
increasing hole diameter.
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Maximum Liquid Load
Liquid flows down the column through the
downcomers due to gravity. The limited driving
force permits a limited liquid flow rate VL
only. The following four empirical rules are
often used to determine the maximum liquid flow
rate (Hoppe and Mittelstrass)
1. The weir load VL/lw (where lw is the weir
length) should not be less than 60m3/(m h)
2. The liquid velocity in the downcomer should
not exceed a value of 0.1 m/s
3. The volume of the downcomer should permit a
liquid residence time of more than 5 s.
4. The height of the clear liquid, hcl, in the
downcomer should not exceed half of the tray
spacing
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cont. Maximum Liquid Load
The flow of liquid through the downcomer is, in
essence, comparable with the flow of a liquid
trough the opening of a vessel. This classical
flow problem has been solved by Torricelli early
in 1644. Torricellis equation is
To apply this equation to the dowcomer situation,
other phenomena must be taken into account
1. The downcomer does not contain clear liquid
but a liquid gas mixture with a relative liquid
content of eLd.
2. The velocity of clear liquid in the downcomer
exit is expressed by
3. The density of the gas, rG, must not be
neglected against the density of the liquid, rL
4. The liquid flows onto a tray with a clear
liquid height hL.
5. Between downcomer inlet and downcomer outlet
exists a pressure difference due to the pressure
loss Dp of a tray. It can be expressed in terms
of clear liquid height that is defined by
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cont. Maximum Liquid Load
Considering all these phenomena, the Torricellis
equation turns into (Stichlmair)
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Minimum Liquid Load
A column tray can, in principle, be operated even
with very small liquid loads becasue the height
of the two-phase layer on the tray is kept at a
minimum value by the exit weir. However at
extremely low liquid loads, liquid flows unevenly
across the tray (maldistribution), which
decreases the mass transfer efficiency.
Accordingly, the minimum height of the weir
overflow is usually set at approximately 5 mm
this corresponds to a minimum liquid weir load of
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Operating region of tray columns
The operating region of a tray column can be
represented in a diagram with x-coordinate VL and
y-coordinate VG. Often these two loads are
referred to the Active area (Aac)
The upper borders for the gas for gas and liquid
flow are absolute borders that can never be
crossed.
The lower borders (dashed lines), however, may be
exceeded to a certain extent without encountering
any flow problems. However the mass transfer
efficiency my gradually decrease
The shape and size of the operating region
depends on the design parameters. An example is
the relative free area, f, that affects the upper
and lower borders of the operating region.
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PART II Two Phase Flow in Tray Columns

• Flow regimes
• Relative liquid holdup
• Froth height
• Liquid entrainment
• Interfacial area
• Pressure drop

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Flow regimes
After determination of the operating region of
the column, the characteristic data on the
two-phase flow on the tray must be studied to
ensure safe column operation. The behavior and
properties of the two-phase layer on trays are
important for the effectiveness of tray columns.
The different regimes are

• Buble regime the liquid forms a continuous
  phase. The gas is in form of discrete bubbles in
  the liquid.

• Drop regime The gas forms continuous phase
  and the liquid is dispersed into fine droplets.

• Froth regime This regime represents the
  intermediate state between the bubble and the
  drop regime. No clearly dispersed phase exists.

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Relative liquid holdup, eL
This is a very important characteristic parameter
of the two-phase layer on a tray. It is defined
as the ratio of clear liquid height and froth
height
From hf and eL, the height of clear liquid can be
calculated.
Equation II-2 is valid only when the term...
...is larger than 50.
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Froth height, hf
A knowledge of the froth height on a tray is very
essential since it must be considerably lower
than tray spacing, H. If the froth extends up to
next tray it may block the openings in the tray
and cause a sharp increase on pressure drop and,
finally, flooding.
The following correlation can be used
(Stichlmair)
( II-3)
The last term takes into account spraying of
liquid, and therefore, it should be considered
only when
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Liquid entrainment
Gas flowing though the two-phase layer on a tray
always entrains some liquid in form of fine
droplets. This liquid entrainment is unfavorable
because it affects the countercurrent flow of a
gas and a liquid within the column and, in turn,
decreases mass transfer efficiency of a tray.
Even at very low gas loads (e.g bubble regime)
fine droplets are formed by busting bubbles. At
drop regime all the liquid of the tray is
dispersed into fine droplets of different sizes.
Liquid drops are entrained by the gas flow if
their terminal velocity is lower than gas
velocity. After having reached a certain height,
most droplets fall down again into the two-phase
layer on the tray. The smaller the drops the
higher they rise.
- The load Factor,F, is the dominant factor in
the liquid entrainment phenomena. An increase of
the gas load by a factor of 10 increases liquid
entrainment by a factor of 1000 or 10000.
- Another major factor is the surface tension
becasue it influences the drop size.
- Liquid viscosity is only of influence in high
viscous systems.
- The relative free area, f, and the tray
spacing, H, have also an influence on the
entrainment.
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Liquid entrainment
The correlation shown in the next diagram
describes the major entrainment factors.
Liquid entrainmetn is inevitable in tray
operation. However, too large an entrainment
affects mass transfer efficiency since a pure
countercurrent flow of gas and liquid no longer
exists. A rule of thumb says that an entrainment
rate of up to 10 of the liquid flow onto the
tray may be tolerated.
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Interfacial area
A high interfacial area in the two-phase layer on
the tray is the most essential prerequisite for
good mass transfer. The interfacial area, A, is
usually referred to the volume of the froth, Vf,
and expressed as
An estimation of the interfacial area order of
magnitude is given by
This equation may be used in the drop and bubble
regime, but not in the froth regime
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Pressure drop
The basic equation for calculating the pressure
drop of a tray is
The pressure drop in the clear liquid can be
formulated
The last term of equation II-8 accounts for
several residual factors including bubble
formation, liquid mixing and vertical
acceleration of the liquid. This term can be
neglected in most cases.
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Pressure drop in the sieve tray, Dpd
The pressure drop of a gas as it passes through a
tray is given by
The discharge coefficient can be calculated by
the following equation
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PART III Mass Transfer in the two-phase layer on
column trays

• Definition of mass transfer efficiencies
• Relationship between point annd tray
  efficiencies
• Point efficiency
• Tray efficiencies

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Mass transfer efficiency
The difficulty of a separation is given by the
number of required equilibrium stages. When this
number of stages is high, the separation is
difficult. The number of equilibrium stages must
be transformed into the real number of stages to
get the real height required. This is because a
tray is not working like the equilibrium stage.
In most cases the concentration changes achieved
by a tray are significantly smaller.
To solve this problem, one uses the mass transfer
efficiencies, defined as the ratio of the
concentration changes of an actual tray and an
equilibrium stage.
Mass transfer efficiencies can be defined either
as gas side efficiency EOG, by considering the
concentration changes in the gas phase or as
liquid side efficiency EOL by considering the
concentration changes in the liquid phase.
Two definitions of gas side mass transfer
efficiencies have to be distinguished

• Point efficiency
• Tray efficiency

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Point efficiency
The concentration change along an individual
stream line of the gas flow is considered. The
definition is
The subscript OG expresses that the overall
resistance has been formally placed into the gas
phase. The actual change in concentration of the
gas (yi1 , y) as it flows through the tray i is
related to the maximum concentration change
attainable, (yi1 - y(x)).
y(x) is the gas concentration in equilibrium
with liquid concentration x at the point on the
tray where the gas stream line passes through the
two-phase layer.
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Tray efficiency
The tray efficiency, EMGi or Murphree efficiency,
is defined as follows
( III-2)
Here the overall gas flow through the column is
considered. The actual concentration change,
(yi1 - yi), is related to the maximum possible
concentration change (yi1 - y(xi) ).
Here y(xi) is the gas concentration in
equilibrium with liquid concentration xi going
out from tray i. This definition is arbitrary
because the gas concentration usually is
different at each point on the tray. Thus,
efficiencies higher than 100 may be obtained in
some cases.
Although the theoretical definition is
unsatisfactory, it is of practical interest
because it describes the separation efficiency of
a real tray.
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Relationship between Point and Tray efficiency
According to Lewis, when the liquid flows across
the tray without mixing (plug flow), the two
efficiencies are related by the following
equation
The gas under each tray is assumed to be
completely mixed.
For complete liquid mixing, tray efficiency and
point efficiency have the same value
The normal condition lies between the two extreme
cases described by equations II-3 and III-4.
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Cont. Relationship between Point and Tray
efficiency
The degree of liquid mixing is expressed in terms
of the Peclet number (Pe)
That we can also express as
In which the eddy diffusion coefficient can be
calculated
In plug-flow (no mixing) the value of
Peclet-number becomes infinite
In the case of complete liquid mixing the value
of Peclet-number is zero
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Point efficiency calculation
The prediction of the mass transfer efficiency is
based on the following fundamental equation
(Taylor and Krishna)
The overall number of gas phase transfer units
can be calculated from
Using expressions for the mass transfer
coefficients, b, we obtain the next equation for
the the point efficiency at froth regime
So NOG is a function j of the variables hf and
uG, what agrees well with the experimental data.
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Practical determination of tray efficiency
Usually empirical values of trays efficiencies
are used and in most cases large safety factors
are included to reduce the risk of malfunction of
the separation column.
Empirical tray efficiency data lie in the order
of 70 for distillation systems under normal
conditions. However, in absorption and desorption
processes, values of tray efficiencies are
reported to be as low as 1 or even 0.1.
In practice, empirical correlations are sometimes
used for calculating the number of gas units and
liquid side transfer units NG and NL,
respectively
For sieve trays
For bubble cap trays
The correlations are dimensionally incorrect!!