Packed Bed flooding.pdf - Youngstown State University's Personal ...

comparison to Example 14 isn’t possible because at the 1.5 m/s velocity of
Example 14, the system becomes a froth. But at about one-fifth the velocity of
Example 14, an estimate of interfacial area is possible.
If the bubble size is 10,000 µm and fractional holdup is 0.4, Eqs. (14-177) and
(14-178) give an interfacial area of
a = (6/0.01)(0.4) = 240 m 2 /m 3
Measured interfacial area in distillation trays is consistent with this high value.
Note the much higher interfacial area than in the droplet systems of
Examples 14 and 15. The higher interfacial area when the gas is dispersed
explains why bubbling and froth systems often give better performance
than droplet systems. The big difference in interfacial area stems from the
much larger volume per unit of mass of gas, i.e., lower density of the gas
than the liquid.
RATE MEASURES, TRANSFER UNITS, APPROACH
TO EQUILIBRIUM, AND BYPASSING
What Controls Mass/Heat Transfer: Liquid or Gas Transfer
or Bypassing Either gas side or liquid side of the interface can be
controlling.
Liquid-Controlled In fractionation systems with high viscosity
or component relative volatility that greatly exceeds 1, the liquid side
will be controlling. This is clearly illustrated by Fig. 14-47 which
shows a sharp decline in efficiency with either a rise in liquid viscosity
or a rise in component relative volatility.
Note that high component relative volatility means the same
thing as sparingly soluble. Oxygen dissolving in a fermentation
reactor is an example of a system being liquid-controlled due to a
sparingly soluble gas. Another application that is liquid-controlled
is the removal of high relative volatility components out of residual
oil.
Still another case where liquid controls is in condensing a pure
vapor, as in Example 23, or absorbing a pure gas, as in Example 24.
Gas-Controlled The gas side dominates in gas cooling applications.
An example is the quenching of a furnace effluent with a vaporizing
liquid. In this application the liquid is nearly uniform in
temperature. Restated, the reduction in driving force across the liquid
side of the interface is unimportant.
Other applications that are gas-side-controlled include removal of a
component such as NH3 from a gas by using an acidic liquid, or
removing a component such as SO2 from a gas with a basic liquid. See
Examples 19 through 22.
Bypassing-Controlled Trayed or packed columns operate with
countercurrent flow and can achieve many equilibrium stages in
series by good distribution of gas and liquid, and careful control of
details. Other devices such as sprays are vulnerable to bypassing and
are limited to one equilibrium stage.
Rate Measures for Interfacial Processes Terminology used
for reporting rate data can be confusing. Normally rate data are
reported on a volumetric basis with transfer rate and effective area
combined. For example, kLa denotes mass-transfer data per unit volume.
The L subscript means it is referenced to the molar concentration
difference between the interface and the bulk liquid. This is
commonly used on data involving a sparingly soluble (high relative
volatility) component. Note that the lowercase k means the data deal
only with the resistance in the liquid phase.
Less commonly, data are given as kGa. The G subscript means it is
referenced to the molar concentration difference between the interface
and the gas. This might be used for data on absorbing a gas such
as NH3 by a highly acidic liquid. Note that kGa only deals with the
resistance in the gas phase.
When one is dealing with direct contact heat transfer, the corresponding
terms are hLa and hGa. Here the driving force is the temperature
difference. The L subscript means that we are dealing with a
liquid-limited process such as condensing a pure liquid. How to convert
kLa data to an hLa value is illustrated by Example 23.
There are ways to combine the liquid and gas resistance to get an
overall transfer rate such as KGa (as denoted by the uppercase K).
However, data are rarely reported in this form.
PHASE DISPERSION 14-89
Approach to Equilibrium Although rate measures such as k Ga
and h Ga are often cited in the literature, they are often not as useful to
designers as the simpler concept of approach to equilibrium. Approach
to equilibrium compares the transfer between liquid and gas phases to
the best possible that could be achieved in a single backmixed equilibrium
stage.
Approach to equilibrium is easy to understand and easy to apply.
Examples 17 through 23 illustrate its use.
Example 17: Approach to Equilibrium—Perfectly Mixed, Complete
Exchange This would be approximated by a very long pipeline contactor
where an acidic aqueous stream is injected to cool the gas and remove NH 3.
If the adiabatic saturation temperature of the gas is 70°C, at the exit of the
contactor, the gas would be cooled to 70°C.
Similarly, at the exit of the contactor, the NH 3 in the gas would be zero,
regardless of the initial concentration.
Example 18: Approach to Equilibrium—Complete Exchange
but with 10 Percent Gas Bypassing A spray column is used, and an
acidic liquid rains down on the gas of Example 17. If the initial NH3 is 1000 ppm
and 10 percent of the gas bypasses, the NH3 in the exit gas would be
0.1(1000) = 100 ppm
Similarly, if the gas enters at 120°C, at the exit we would find 10 percent of the
differential above the adiabatic saturation temperature. For an adiabatic saturation
temperature of 70°C, the exit gas temperature would be
70 + 0.1(120 − 70) = 75°C
Approach to Equilibrium—Finite Contactor with No Bypassing
When there is no bypassing, the measure that sets the approach
is the ratio of change to driving force. This ratio is called the number
of transfer units NG. It is dimensionless. For heat-transfer applications,
it can be envisioned as a conventional heat exchanger where a
vaporizing liquid cools a gas:
No. of gas-phase transfer units = �� =NG (14-180)
(TG − TL)av
Where T G = gas temperature and T L = liquid temperature. The
number of transfer units N G can also be calculated as the capability
for change divided by the thermal capacitance of the flowing
streams.
N G =
(gas contact time)(hGa)
= ���
(14-181)
ρGcG
TG,out − TG,in
(system volume)(hGa)
���
(volumetric flow rate)ρGcG
where a = interfacial area per unit volume
h G = heat-transfer coefficient from interface to gas
ρ G = gas density
c G = gas specific heat
Note that in the above, performance and properties all refer to the
gas, which is appropriate when dealing with a gas-limited transfer
process.
This leads to a way to estimate the approach to equilibrium.
E = 1 − e−N G (14-182)
where E = “approach to equilibrium” fractional removal of NH3 or
fractional approach to adiabatic liquid temperature
N G = number of transfer units calculated relative to gas flow
Example 19: Finite Exchange, No Bypassing, Short Contactor
A short cocurrent horizontal pipeline contactor gives 86 percent removal of
NH 3. There is no bypassing because of the highly turbulent gas flow and injection
of liquid into the center of the pipe. What would we expect the exit gas temperature
to be?