Task $6$: Adsorption $(13$P$)$

Methanol is removed from a carrier gas stream $((V^{})=600\frac{m^3}{h})$ with the help of adsorption on

activated carbon. The initial loading content of methanol in the gas stream equals $0\mathrm{.}08kgk{g}^{-1}.$ The

final loading contents of the outlet gas stream should not be higher than $0\mathrm{.}0001kgk{g}^{-1}.$ There are

three fixed bed adsorbers $($bulk density$/$ Sch$$ttdichte $300k\frac{g}{m^3})$ available, which operate alternately

every $60$ minutes.

a$)$ Determine the maximum possible bed loading for the process at $25C$ and $50C$ graphically

from the given adsorption isotherms. Which temperature is more reasonable from a process

engineer point of view? $(2$P$)$

An optimization in the pore structure of the activated carbon enables a new maximum bed loading

for the process of $0\mathrm{.}4k\frac{g}{k}g.$

b$)$ How much activated carbon $($mass$)$ is needed, if the regeneration of the adsorber leaves a

final bed loading of $0\mathrm{.}05kgk{g}^{-1}?(3$P$)$

If you couldn't solve task b$),$ resume with $m_{\text{A}\text{d}\text{s}\text{o}\text{r}\text{b}\text{e}\text{r}}=220kg$ and a mass stream which has to be

adsorbed of $76k\frac{g}{h}.$

c$)$ The superficial velocity $($Leerrohrgeschwindigkeit$)$ is $0\mathrm{.}8\frac{m}{s}.$ Calculate the interstitial velocity

$($Zwischenkorngeschwindigkeit$),$ the volume, the diameter and the length of the adsorber.

$(4$P$)$

If you couldn't solve task c$),$ resume with an adsorber length of $3m.$

d$)$ Calculate the pressure drop over the adsorber with the Ergun$-$equation! $(1$P$)$

The adsorption is now considered as non$-$isothermal. The adsorber is operated adiabatic and the

adsorption enthalpy equals $500k\frac{J}{k}{g}_{\text{m}\text{e}\text{t}\text{h}\text{a}\text{n}\text{o}\text{l}}.$

e$)$ Calculate the adsorbent temperature after one working cycle, under the consideration, that

the released heat only heats the fixed bed. $(c_p=760\frac{J}{k}gK)$ The start temperature of the fixed

bed is $25C.(2$P$)$

f$)$ Now a heat exchange with the environment is considered. The temperature of the

environment is $20C.$ How does the gas loading at the exit of the adsorber change

qualitatively? $(1$P$)$

$\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{L}}=150\frac{(1-{)}^2{}_g{v}_g}{{}^3{d}_P^2}+1,75\frac{(1-){}_G{v}_g^2}{{}^2{d}_p},$

$d_p$: Korndurchmesser $(particle$ diameter$)0,005m$

$v_g$ : Leerrohrgeschwindigkeit $(superficial$ velocity$)[\frac{m}{s}]$

$$ : Porosit$t(porosity)0,5$

${}_g$: Viskosit$t$ des Gases $(visocosityof$ the gas$)1,81**{10}^{-5}$ Pas

${}_g$: Gasdichte $(gas$ density$)1,6k\frac{g}{m^3}$

Figure $1$ : experimental adsorption isotherms of methanol on activated carbon at $25C$ and $50C$

Task $7$: Theory $-$ TVT $(8$P$)$

a$)$ Draw a membrane module and label it completely. $(1$P$)$