Toluene hydrodealkylation to benzene is given by the reaction: $C_6{H}_5-C{H}_3+H_2{C}_6{H}_6+C{H}_4$

The rate of reaction can be calculated by $r=k{C}_T*C_H^{0\mathrm{.}9}$

$k=A*exp(-\frac{E}{R}T),A=3{10}^{10}$ and $E=209\mathrm{.}213kJ*mo{l}^{-1},$

A stream containing $70.$kmol$*h^{-1}$ toluene, $160$kmol$*h^{-1}C{H}_4,$ and $4$kmol$*h^{-1}$ benzene at $800C$ and $26$ bar is mixed with $370$kmol$*h^{-1}{H}_2$ at $50C$ and $26$ bar then fed to plug flow reactor $.$ Considering a multitube reactor with a length of $10m$ and $500$ tubes with $0\mathrm{.}02m$ inner diameter. The reactor effluent at $815C$ is cooled to $120C$ and $1\mathrm{.}5$ bar then fed to absorber column $(5$ trays$).n-$dodecane is used as liquid solvent with $500$kmol$*h^{-1}$ at $100C$ to separate benzene from gas mixture. The efficiency of the column is $20\%.$Pressure and temperature at the column top and bottom of column is $1\mathrm{.}5$ bar and $100C$

$1-$ Calculate the flow rate of each stream and duty in cooler and reactor

$2-$Reaction conversion,

$3-$Plot the gradient of composition with reactor length.

$4-$Plot the gradient of gas and liquid composition on each tray

$5-$Calculate the conversion ratio of reaction with feed florrate of $H_2(200-800)kmol*h^{-1}$