Please do the calculations and mole balances by hand firstly than do it in matlab and polymath. Calculations need to be made from appropriate numerical analysis method $($e$.$g newton raphson, eugler method or other$)$Question: 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.It is desired to produce methane from captured carbon dioxide in afdssingle 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.