A heterogeneous catalytic Reactor $($Packed bed reactor$)$ with three series reversible reactions. The following

reactions follows an elementary rate law. With the use of zinc oxide solid catalyst $($The density of catalyst

$0\mathrm{.}6\frac{kg}{dm3})$:

$C_{57}{H}_{104}{O}_{6(l)}+H_2{O}_{(l)}longrightarrow{C}_{39}{H}_{72}{O}_{5(l)}+C_{18}{H}_{34}{O}_{2(l)}$

Tri$-$olein Water Di$-$olein Faty Acid

$C_{39}{H}_{72}{O}_{5(l)}+H_2{O}_{(l)}longleftrightarrow{C}_{21}{H}_{40}{O}_{4(l)}+C_{18}{H}_{34}{O}_{2(l)}$

Di$-$olein Water Mono$-$olein Fatty Acid

$C_{21}{H}_{40}{O}_{4(l)}+H_2{O}_{(l)}longrightarrow{C}_3{H}_8{O}_{3(l)}+C_{18}{H}_{34}{O}_{2(l)}$

Mono$-$olein Water Glycerol Fatty Acid

Given:

Total volumetric flowrate flowrate in $=3\mathrm{.}14(\frac{d{m}^3}{(s)}).$

Outlet mass flowrate:

Flow rate of Triolein: $1274\mathrm{.}973901(\frac{Kg}{h}),$ Flow rate of Fatty Acid: $5521\mathrm{.}370293(\frac{Kg}{h}),$ Flow rate of Water:

$1008\mathrm{.}287825(\frac{Kg}{h}),$ Flow rate of Glycerol: $556\mathrm{.}0283631(\frac{Kg}{h}),$ Flow rate of Di$-$olein: $62\mathrm{.}16621933(\frac{Kg}{h}),$

Flow rate of Mono$-$olein: $222\mathrm{.}2383971(\frac{Kg}{h})$

Inlet mass flowrate:

Flow rate of Triolein: $7261\mathrm{.}523104(\frac{Kg}{h}),$ Flow rate of Water: $1334\mathrm{.}589612(\frac{Kg}{h})$

Outlet:

Triglyceride with mass fraction $=0\mathrm{.}1474,$ Fatty Acids with mass fraction $=0\mathrm{.}6385,$ Water with mass

fraction $=0\mathrm{.}1166,$ Glycerol with mass fraction $=0\mathrm{.}0643,$ Diglyceride with mass fraction $=0\mathrm{.}0072,$

Monoglyceride with mass fraction $=0\mathrm{.}0257$

Inlet:

Mass fraction for Tri$-$olein $=0\mathrm{.}8447449846,$ Mass fraction for Water $=0\mathrm{.}1552550154$

Outlet mole flowrate:

Tri$-$olein $=1\mathrm{.}439938497(Kmo\frac{l}{h}),$ Fatty Acid $=19\mathrm{.}54726422(Kmo\frac{l}{h}),$ Water $(H2O)=55\mathrm{.}97034335$

$(Kmo\frac{l}{h}),$ Glycerol$=6\mathrm{.}037701602(Kmo\frac{l}{h}),$ Di$-$olein $=0\mathrm{.}1001084905(Kmo\frac{l}{h}),$ Mono$-$olein $=$

$0\mathrm{.}6233186265(Kmo\frac{l}{h})$

Inlet mole flowrate:

Tri$-$Olein $=8\mathrm{.}201067216(Kmo\frac{l}{h}),$ water $=74\mathrm{.}08344816(Kmo\frac{l}{h})$

Densities At $250C$ :

Density of Tri$-$Olein $(L)$:$0\mathrm{.}753(\frac{g}{c}m3),$ Density of Water $(L)$:$0\mathrm{.}800(\frac{g}{c}{m}^3),$ Density of Glycerol$($L$)$: $1\mathrm{.}092$

$(\frac{g}{c}m3),$ Density of Oleic$-$Acid $(L)$:$0\mathrm{.}734(\frac{g}{c}m3),$ Density of Mono$-$Olein $(L)$:$0\mathrm{.}813(\frac{g}{c}m3),$ Density of

Di$-$Olein$($L$)$: $0\mathrm{.}818(\frac{g}{c}m3).$

Rate constants are:

Step $1($forward$)$: $K_f=5\mathrm{.}00{10}^{-3}(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s}),$ Step $1($reverse$)$: $K_r=2\mathrm{.}13{10}^{-2}(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s})$

Step $2($forward$)$: $K_f=8\mathrm{.}09{10}^{-0}(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s}),$ Step $2($reverse$)$: $K_r=6\mathrm{.}12{10}^{-0}(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s})$

Step $3($forward$)$: $K_f=1\mathrm{.}95{10}^0(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s}),$ Step $3($reverse$)$: $K_r=5\mathrm{.}52{10}^{-1}(\frac{m3}{\text{m}\text{o}\text{l}\text{e}s})$

Note: the constant rates of reactions are taken from different reference. If it is not suitable find the correct

values

Assume constant pressure within the reactor. The reaction is isothermal. Constant volume.

Questions:

$1-$Calculate the conversion rate for each reaction?

$2-$Calculate the concentration for each component?

$3-$Calculate the reaction rate?

$4-$Calculate the residence time?

$5-$Calculate the weight of catalyst for each bed?

$6-$Calculate the volume of the reactor?

$7-$Calculate the diameter and the length of the reactor?

$8-$What is the best material to construct the reactor from?