Question

Your engineering consulting firm has been retained to develop an absorption process that removes 98% of the SO2 from an air stream. The column operates at 30 oC and 5 atm. The design assumes 250 mol/min of an air stream contaminated with 10 mol% SO2 fed to the bottom of the column. Regenerated absorbent is fed to the top of the column. The absorbent is an aqueous solution, where the absorbent species is non-volatile. Some water will vaporize based on its vapor pressure at 30 oC (approximately 35 mmHg), so the treated gas will contain air, residual SO2, and water vapor. The absorbent stream leaving the column contains SO2 in a molar ratio of 15:1 (solvent:SO2). The absorbent is recovered in a stripping column operating at 120 oC and 2 atm. The stripping gas is 250 mol/min steam which is fed to the bottom of the stripping column and removes 98% of the SO2. Some of the steam condenses in the absorbent phase at a ratio of 2:1 (aqueous solvent:condensate). The absorbent is non-volatile, so the exiting steam only contains water and SO2. Your task is to analyze this process. Follow the problem solving procedure outlined in your notes and the textbook. You must: prepare a fully labeled process flow diagram, conduct a degree of freedom analysis on each system (overall, absorber, and stripper), clearly identify unknown variables and units, write all appropriate equations (materials balances, etc.) needed to solve for the unknowns, solve the problem.

Answer 1

in this question two process are happening simultaneously

first is adsorption followed by stripping and both the process is happening in counter current manner

First we take Absorption process and define some data

the top of the column is numbered as 2 and bottom of the column is numbered as 1

Y₁ is the mole ratio of SO₂ and air in the feed stream

similarly Y₂ for the exit sream

Y₁  = 25/225 and Y₂ = 0.5/225

these terms is for gas phase

for solvent (absorbent)

X₁ mole ratio of SO₂ and absorbent coming out of the column from the bottom

X₂ is the molar ratio of SO₂ and absorbent at the top of the column

X₂ should be equal to zero as in the question absorbent is pure

we have to define the molar flow rate of gas phase and liquid phase on the solute (SO₂) basis

let G_s be the molar flow rate of pure air (SO₂ free basis) fed from the bottom of the column

and L_s be the molar flow rate of the absorbent fed to the column from the top

from the given data we have to remove 24.5 moles of SO₂ from the air stream to the absorbent sream

so the mass balance can be written as below for the steady state process is

the unknown is L_s and X₁

In the question given "The absorbent stream leaving the column contains SO2 in a molar ratio of 15:1(Solvent:SO₂)"

24.5 moles of SO₂ is absorbed in the absorbent hence the molar flow rate of the absorbent should be 24.5*15 .....i..e 367.5 moles of absorbent per minute

For stripping Column

the nomenclature is same for both the columns but here values is changed

G_s = 250 mol/min

Y₁ = 0 (pure steam is fed from the bottom)

Y₂ = 24.01/250 (98% of SO₂ is stripped from the liquid )

L_s = 367.5 mol/min

X₁ = 0.49/367.5 (only 2% of SO₂ is left in the liquid)

X₂ = 24.5/367.5

degree of freedom for both the cases

F = C + P - 2

C = Number of component is 3(Air, SO₂ and Liquid)

P = Number of phases (liquid and gas )

F = 3+2-2= 3