Question

500 kgmol/h of a gas stream containing 2% of component A is to be purified using gas absorption. The vent from the absorber can contain no more than 0.5 kgmol/h of A. Two scrubbing liquids, P and Q, are available.

a. For liquid Q, m=0.45. How many stages are required in the scrubber for 1.5 times the minimum liquid rate? The incoming Q contains no A. 2

b. For liquid P, m=0.25. If liquid P is used in the scrubber specified in part a, at the same rate as Q is used in part a, what recovery can be achieved? The incoming P contains no A.

c. How would the answer to b change if the incoming P contains 0.1% A?

Answer 1

Here,

for Gas:

solute free gas G= 500*(1-0.02) = 490 kmol/hr
inlet: composition of A = Y_N+1= (moles of A/moles of solute free gas) = 0.02/(1-0.02) = 0.0204

outlet: Y₁ = 0.5/490 = 0.0010204

part (a): (m=0.45)

for liquid Q:

inlet composition of A in Liquid = X₀ = 0

outlet composition of A in Liquid :X_N
using equlibrium relation X_N=Y_N+1/m = 0.0204/0.45 = 0.0453

Material Balance: Q*X₀ + G*Y_N+1 = Q*X_N + G*Y₁

Q*(0) + (490)*(0.0204) = Q*(0.0453) + (490)*(0.0010204)

Q = 209.62 kmol/hr

Actual liquid(Q) flow rate = 1.5*209.62 = 314.43 kmol/hr

to find no. of stage using KREMSER equation:

Absorption factor: = (314.43)/(0.45*490) = 1.425

Striping factor S=(1/A) = 0.7017

Np = 5.355 = No. of STAGES.

Part (b): (m=0.25)

X₀ = 0

X_N = Y_N+1 / m = 0.0204/0.25 = 0.0816

Material Balance: P*X₀ + G*Y_N+1 = P*X_N + G*Y₁

P*(0) + (490)*(0.0204) = P*(0.0816) + (490)*(0.0010204)

P = 116.37 kmol/hr

Actual liquid(P) flow rate = 1.5*116.37 = 174.55 kmol/hr

to find no. of stage using KREMSER equation:

Absorption factor: = (174.55)/(0.25*490) = 1.425

so, no. of STAGES are remain same. = 5.355

Recovery = (1-(Y₁/Y_N+1))*100%

= (1-(0.0010204/0.0204))*100%

= 95%

Part (c): if X₀ = 0.001

X_N = Y_N+1 / m = 0.0204/0.25 = 0.0816

Material Balance: P*X₀ + G*Y_N+1 = P*X_N + G*Y₁

P*(0.001) + (490)*(0.0204) = P*(0.0816) + (490)*(0.0010204)

P = 117.82 kmol/hr

Actual liquid(P) flow rate = 1.5*117.82 = 176.72 kmol/hr

to find no. of stage using KREMSER equation:

Absorption factor: = (176.72)/(0.25*490) = 1.4426

Np = 5.2418

(Here, no. of stages are decreses but solvent flowrate increses which is not economical).