Exam$-$Like question $($Main Diet $2023)$

Absorption

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A gas stream containing $0\mathrm{.}008$ mole fraction of A in nitrogen is passed through a column with $8$

m high packing, recovering $60\%$ of A by absorption in pure water. The absorber operates at $20$

${?}^{0}C$ and $\frac{10}{b}ar.$ The inlet water flow rate is $50000kg{h}^{-1}$ and at the outlet the mole fraction of A

in water is $0\mathrm{.}0025.$ The equilibrium of $A$ in water can be described by $y^{**}=1\mathrm{.}3x.$

You can assume dilute conditions.

a$)$ Determine the flowrate of the gas stream and the minimum water flowrate, in $mol{s}^{-1},$ required

for the separation in the original configuration with one column. $(15)$

b$)$ Determine the number of transfer units $N_{OG}$ and the height of the transfer units, $H_{OG}.(15)$

c$)$ A second identical column is to be added in series with the first to increase the recovery of A$,$

maintaining the overall flow countercurrent.

Assume that the height of the transfer units $(H_{OG})$ remains the same in the two$-$column

configuration.

Determine the new value of the recovery and the mole fraction of $A$ in water at the outlet of the

second column, $x_{b2.}(20)$