2. Consider a packed bed column to absorb component A in the bulk gas stream usi
ID: 703739 • Letter: 2
Question
2. Consider a packed bed column to absorb component A in the bulk gas stream using a solvent. It is assumed that the content of A in the feed gas is high, and variation of V (molar flow rate of gas) along z is non-negligible whereas variation of L (molar flow rate of solvent) along z is negligible. (a) Derive the operating line equation that relates x and y when?(0) y(0), L(0), and V (0) are specified where a and y represent mole fractions of A in the solvent and gas streams, respectively. (b) Set up the component mass balance equation for A and also the total mass balance for the gas phase under a steady state around differential control volume with thickness dz.
Explanation / Answer
Assume that only solute is transferred from one phase to another (no vaporization of liquid or condensation of gas carriers).
Feed to column:
Lo= Liquid molar rate In with xo concentration of A
Vo= Vapour molar rate In with yo concentration of A
La= Liquid molar rate Out with xa concentration of A
Va= Vapour molar rate Out with ya contration of A
Overall Balance: Lo + Vo = La + Va
Component balance over A: Lo xo + Vo yo = La xa + Va ya
yo = (La/Vo) xa + (Va ya - Lo xo)/Vo
Operating Line equation is:
y = (L/V) x + (Va ya - Lo xo)/V..............(1)
The amount of solute in gas is significant and the absorption across differential height dz is d (Vy), since both V & y decreases as the gsa passes through the tower.
Only A is being transferred, dNa is same as dV,
dNa = Vdy + ydNa
dNa=Vdy/(1-y)
Effect of one way diffusion in the gsa film is to increase mass transfer rate for gas film by factor 1/(1-y)L, so the effective overall coefficient Kyá is larger than normal value of Kya.
1/Kyá = ((1-y)L/Kya) + m/Kxa
When solubility of gas is more in liquid, m is negligible.
So, dNa = Vdy/(1-y) = Kyá S dz (y-y*)
Column height can be found by integrating above equation.
Zt = (1/S) ?Vdy/((1-y)(y-y*)Kyá) from a to b
Kya varies with about V^0.7
Kya will alomot is same as there is no variation.
Zt= ((V/S)/(Kya)?dy/(y-y*)
Zt = Hoy Noy
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