The aim is to treat the gaseous effluent from a textile industry containing diethylamine $($DEA$)$

$((C2H5)2NH)$ as a pollutant. The effluent will be treated using a fixed$-$bed adsorption column, which will undergo adsorption$-$regeneration cycles. The characteristics of the gaseous effluent to be treated and the emission limit value for the DEA are:

The characteristics of the gaseous effluent to be treated, and the emission limit value for the DEA are:

Characteristics of the gaseous effluent: dry air $+$ DEA

Emission limit value: DEA concentration, CDEA$=60$ ppmv

$T=30C$;

$P=101$kPa;

volumetric flow rate of gaseous effluent, $Gv=15\frac{m3}{s}$;

DEA concentration: CDEA$=1000$ ppmv$.$

Characteristics to consider when sizing the adsorption column:

Isothermal operation at $30C$ and $101$kPa;

consider that the gaseous species behave like ideal gases;

Isothermal adsorption: $Y=129.x^{2\mathrm{.}4}$

$Y-$ Mass ratio of pollutant in the gas, kgpollutant$/$kfluent without pollutant

$x-$ Mass ratio of pollutant adsorbed in the solid phase, kgadsorbate$/$kgadsorbent

Recommended gas flow velocity in the free section of the column equal to $1\mathrm{.}0\frac{m}{s}$

Volume mass of the clean adsorbent in the fixed bed equal to $400\frac{kg}{m3}$

Adsorption zone thickness equal to $0\mathrm{.}10m$

Residual adsorption capacity of the adsorption zone equal to $0\mathrm{.}50$

Dry sea $=29\frac{g}{\text{m}\text{o}\text{l}}$ and MDEA$=73\frac{g}{\text{m}\text{o}\text{l}}.$

a$)$ Calculate the height of the adsorption column, bearing in mind that the operating time of the

adsorption column must be equal to $1\mathrm{.}5$ hours;

b$)$ Calculate the mass of pollutant permanently adsorbed in the adsorption zone;

c$)$ Calculate the speed at which the adsorption zone moves.