Task $4$: Adsorption $(13$P$)$

For the purification of a flue gas of a waste combustion plant, volatile organic compounds $($VOC$)$ shall

be removed by adsorption on pure activated carbon $($AC$)$ up to the allowable emission limit of

$10mg$ voc $\frac{?}{N{m}_{\text{a}\text{i}\text{r}}^3}.$ The flue gas contains organic compounds with an amount of $800m\frac{g_{\text{v}\text{o}\text{c}}}{N}{m}_{\text{a}\text{i}\text{r}}^3.$ The

adsorption takes place in two fixed$-$bed reactors, which will be alternately loaded or regenerated

every three hours. The activated carbon is fully regenerated.

Required data is given at the end of this task.

e$)$ Determine the required mass of activated carbon for each adsorber for the case in which the

activated carbon can be loaded up to a maximum of $80\%$ of the thermodynamically possible

loading. $(3$P$)$

f$)$ Calculate the length and diameter of one adsorber $($cylindric$)$ for the acceptable superficial

velocity $("$Leerrohrgeschwindigkeit$")$ of $0\mathrm{.}5\frac{m}{s}.$ Further calculate the interstitial velocity

$("$Zwischenkorngeschwindigkeit$")$ in the fixed$-$bed of the adsorber. $(4$P$)$

g$)$ Because of an error $($drop in the temperature of the desorber$)$ the activated carbon won't be

fully regenerated anymore. So some organic compounds remain on the activated carbon. Explain

its consequences for the adsorption process, using the Langmuir$-$adsorption isotherm. $($No

calculation! Only graphical explanation with arguments$)(3$P$)$

h$)$ For the determination of the specific surface area of the activated carbon used in the fixed bed

adsorber a BET$-$analysis is performed. From the adsorption isotherm of nitrogen $)$ a loading

for the monomolecular layer of $q_{\text{m}\text{o}\text{n}\text{o}\text{m}\text{o}\text{l}\text{e}\text{c}\text{u}\text{l}\text{a}\text{r}}=300\frac{g_{N2}}{k}{g}_{AC}$ is obtained. Use the result of the BET$-$

analysis for the calculation of the specific surface area of the activated carbon. $(3$P$)$

Additional information:

flowrate of the flue gas: $V_{\text{f}\text{l}\text{u}\text{e}\text{g}\text{a}\text{s}}^{}=300\frac{m^3}{h}$

ratio of volumetric flow rate of air in the adsorber at operating conditions and norm conditions:

$\frac{V_{\text{a}\text{i}\text{r}}}{V_{N,\text{a}\text{i}\text{r}}}=1\mathrm{.}2\frac{m_{\text{a}\text{i}\text{r}}^3}{N}{m}_{\text{a}\text{i}\text{r}}^3$

time of loading $/$ regeneration: $t_{\text{l}\text{o}\text{a}\text{d}\text{i}\text{n}\text{g}}=3h$

thermodynamically possible loading: $q=5g$ voc $\frac{?}{k{g}_{ac}}$

bulk density of activated carbon $("$Sch$$ttdichte$")$: ${}_{\text{b}\text{u}\text{l}\text{k}}=400k\frac{g}{m^3}$

porosity of the activated carbon fill: $=0\mathrm{.}4$

molar mass of nitrogen: $M_{N2}=28\frac{g}{m}ol$

area of a nitrogen molecule: $A_{N2}=0\mathrm{.}162n{m}^2$