Felder Exe.4.26

6
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 SO 2 (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 SO 2 . 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 SO 2 diffuses out of the bubbles and into solution.

Transcript of Felder Exe.4.26

Page 1: 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.

Page 2: Felder Exe.4.26

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.

Page 3: Felder Exe.4.26

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

Page 4: Felder Exe.4.26

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

Page 5: Felder Exe.4.26

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).

Page 6: Felder Exe.4.26

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.