Felder Exe.4.26
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Transcript of Felder Exe.4.26
ChE 201 Washington State University
Chemical Process Principles and Calculations Voiland School of Chemical Engineering
and Bioengineering
Fall, 2011 Richard L. Zollars
Problem 4.26, Felder and Rousseau
Gas absorption or gas scrubbing is a commonly used method for removing
environmentally undesirable species from waste gases in chemical manufacturing and
combustion processes. The waste gas is contacted with a liquid solvent in which the
potential pollutants are highly soluble and the other species in the waste gas are relatively
insoluble. Most of the pollutants go into solution and emerge with the liquid effluent
from the scrubber, and the cleaned gas is discharged to the atmosphere. The liquid
effluent may be discharged to a waste lagoon or subjected to further treatment to recover
the solvent and/or to convert the pollutant to a species that can be released safely to the
environment.
A waste gas containing SO2 (a precursor to acid rain) and several other species
(collectively designated as A) is fed to a scrubbing tower where it contacts a solvent (B)
that absorbs SO2. The solvent feed rate to the tower is 1000 L/min. The specific gravity
of the solvent is 1.30. Absorption of A and the evaporation of B in the scrubber may be
neglected.
The gas in the scrubber rises through a series of trays (metal plates perforated with many
small holes), and the solvent flows over the trays and through downcomers to the trays
below. Gas bubbles emerge from the holes in each tray and rise through the covering
liquid, and SO2 diffuses out of the bubbles and into solution.
The volumetric flow rate of the feed gas is determined with an orifice meter, with
a differential mercury manometer being used to measure the pressure drop across the
orifice. Calibration data for this meter are tabulated here:
h (mm) ⁄
100 142
200 204
300 247
400 290
The molar density of the feed gas may be determined from the formula
(
)
where P and T are the absolute pressure and temperature of the gas. An electrochemical
detector is used to measure the SO2 concentration in the inlet and outlet gas streams: SO2
in the samples gas is absorbed in a solution across which a fixed voltage is applied, and
the mole fraction of SO2 in the gas is determined from the resulting current. The
calibration curve for the analyzer is a straight line on a semilog plot of y (mol SO2/mol
total) versus R (analyzer reading), which passes through the following points:
y (log scale) R (rectangular scale)
0.00166 20
0.1107 90
The following data are taken:
(a) Draw and completely label a process flowchart. Include in the labeling the molar
flow rates and SO2 mole fractions of the gas streams and the mass flow rates and SO2
mass fractions of the liquid streams. Show that the scrubber has zero degrees of
freedom.
(b) Determine (i) the orifice meter calibration formula by plotting versus h on
logarithmic axes and (ii) the SO2 analyzer calibration formula.
(c) Calculate (i) the mass fraction of SO2 in the liquid effluent stream and (ii) the rate at
which SO2 is removed from the feed gas (kg SO2/min).
(d) The scrubber column trays commonly have diameters on the order of 1 – 5 meters
and the perforation holes on the order of 4 – 12 mm in diameter, leading to the
formation of many tiny bubbles in the liquid on each tray. Speculate on the
advantages of making the bubbles as small as possible.
SOLUTION
(a) The flowchart that was requested is shown below
There are eight unknowns shown in the process flow diagram shown above. There
are three components (SO2, solvent (B), and the remaining gas species (A) ) so we
can write three independent material balances. We are given two analyzer readings
which can be converted to mole fractions giving two more equations. There is also an
orifice meter reading which can be converted to a volumetric flow rate (one more
equation). For stream 1 we also know the temperature and pressure so the volumetric
flow rate can be converted to a molar flow rate via the equation given in the problem
statement. Finally we are given a specific gravity for stream 2 so the volumetric flow
rate can be converted to a mass flow rate. Thus there are eight equations (3 material
balances, 2 analyzer equations, 1 orifice meter equation, 1 conversion between
volume and moles, and 1 equation for converting volume to mass) so there are zero
degrees of freedom.
b) i) The requested plot is shown below
Det
Scrubbing
Tower
Or
Det
𝑚
1000 L/min B
SG = 1.3
x2,B = 1.0
2
1
3
4
𝑛1
𝑉1
T = 75ºF
P = 150 psig
h = 210 mm Hg
R = 82.4
y1, SO2
y1,SO2
𝑛
R = 11.6
y3,SO2
𝑚4 x4,SO2
The fact that this is a straight line indicates that an equation of the form
represents the data. Following the example from the text (p. 24) we can use Excel to
determine the best fit values for m and b. The Excel spreadsheet shown below does
this.
ii) There are only two points for the analyzer. Since the data is supposed to be a
straight line on semilog axes we know that the equation relating analyzer reading (R)
to SO2 mole fraction (y) should be of the form
The slope and intercept are given by
Thus the formulae for the orifice meter and analyzer are
( )
100
1000
100 1000
Vo
l. F
low
rat
e (
m3
/min
)
h (mm Hg)
Prob 4.26 b) i), Felder and Rousseau
Vol flow h ln(vol. flow)ln(h)
100 142 4.60517 4.955827
200 204 5.298317 5.31812 slope (m) = 0.511
300 247 5.703782 5.509388 intercept (b) = 2.638
400 290 5.991465 5.669881
c) For stream 1 we can compute the following values
( 1)
1
(
)
1
(
)
( 1 )
1
For stream 2
(
)
For stream 3
( )
This leaves only three unknowns from the process diagram ( , 4 , and y4,SO2).
Doing a mole balance on species A gives
1 ( 1 ) ( )
Doing a mass balance on B gives
1 4 ( 4 )
4 ( 4 )
Since this equation has two unknowns we need another equation, a balance on SO2.
However, we have molar quantities in streams 1 and 3 but mass quantities in streams
2 and 4. We need to be consistent in the units. Thus, we will perform a mass balance
on SO2 by multiplying any molar quantities by the molecular weight of SO2 (MW =
64.07 from Appendix A).
1 1 4 4
(
)
(
) 4 4
4 4
Substituting this value into the mass balance for B gives
4 ( 4 ) 4 4 4 4
4
4
So the mass fraction of SO2 in the liquid effluent (x4,SO2) is 0.246. The rate at which
SO2 is removed from the gas stream is the rate at which SO2 leaves the tower in the
liquid effluent. This is 4 4 which was calculated above as 424 kg/min.
d) SO2 can only transfer from the gas to the liquid when the two are in contact. If there
is more contact between the gas and liquid (more surface area) the transfer of SO2
will be promoted. Making smaller bubbles, but more of them, increases the surface
area. Thus making small bubbles increases the total surface area and promotes
transfer between the gas and liquid phases.