It is desired to produce methane from captured carbon dioxide in a single packed bed

reactor $($diameter of $0\mathrm{.}0254m$ and $2m$ length$)$ operated isothermally at $314C$ with

an inlet pressure of $30$atm by the following gas phase reaction. Molar feed rate of

carbon dioxide is $50$kmo$\frac{l}{h}.$ The reactants are fed to the reactor in stoichiometric

ratio.

$C{O}_{2(g)}{?}_{(A)}+4H_{2(g)}{?}_{(B)}harrC{H}_{4(g)}{?}_{(C)}+2H_2{O}_{(g)}{?}_{(D)}$

$($C$)$

$($D$)$

Reaction rate law in terms of the partial pressures of the reactants is expressed as :

$-r_A=\frac{k*P_A*P_B^4}{(1+K_1*P_B+K_2*P_A{)}^5}$

a$)$ Derive the mole balance equations for all species.

b$)$ Calculate molar flow rates of reactants and conversion in the absence of

pressure drop for the $5m$ of reactor length.

DATA:

$=0\mathrm{.}45$

${}_{\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}}=,2000k\frac{g}{m^3}$

Your report must include the derivation of model equations, screenshots of solutions

performed by Polymath and MATLAB.