The gas$-$phase production of compound C $($Shown in reaction $1)$ will be undertaken in a PBR:

$A+BC+D$

Reaction $1$

Unfortunately, a side reaction $($Shown in reaction $2)$ also occurs consuming reactant A and desired

product C:

$A+CE$

Reaction $2$

Both reactions are endothermic with the activation energy of Reaction $2$ greater than the activation

energy of Reaction $1(E_2>E_1).$ The reactor is heated with medium pressure saturated steam $($note

that the condensate is not subcooled$).$ In addition, the pressure drop can be modeled using the

Ergun Equation. The rate laws for the reactions are determined to be:

$r_1=k_1{C}_A^2{C}_B^{\frac{1}{2}},$ and $,r_2=k_2{C}_A{C}_C$

a$)$ Sketch out concentration of $C(Cc)$ and the operating temperature versus the catalyst mass.

Please use the figure on the following page. $(5$ points$)$

b$)$ Sketch out the selectivity $(F\frac{c}{F}E)$ as a function of catalyst weight. $(5$ points$)$

c$)$ Suggest and briefly discuss $2$ methods to optimize the yield of C$.(5$ points$)$

d$)$ Use the following reaction conditions and material properties to derive all of the equations

required to numerically plot the figures from part a$)$ using Polymath $($or equivalent

program$).$ Please fill out the sections on pages $6$ and $7$ with the required equations. $(25$

points$)$

Inlet conditions:

Feed temperature of $A$:$T_{A0}$

Feed temperature of B: T$0$

Flow rate of $A$:$F{A}_0$

Flow rate of $B$:$F_{B0}$

Concentration of reactants: $C_{A0}=C_{B0}$

Pressure of feed streams: $P_0$

Molecular weight of reactants and products: $M{W}_A,MW,MWc,MWD,$MWE

Reactor conditions:

Reactor volume $=V$

Heat transfer coefficient $=U$

Heat transfer area per reactor volume $=$ a

Pressure drop term: $$

Steam flow rate: $m_{\text{s}\text{t}\text{e}\text{a}\text{m}}$

Steam condensate temperature: $T_a$

Catalyst density: $c$

Material properties:

Heat capacities: CPA,$CPB,CPC,CPD,$CPE

Heats of formation $($at $T^0)$: $HA,HB,Hc,HD,HE$

Rate constant of reaction $1T_{\text{r}\text{e}\text{f}\text{:}}{k}_1,$ref

Rate constant of reaction $2$ at $T_{\text{r}\text{e}\text{f}}{k}_{2,\text{r}\text{e}\text{f}}$

Activation energy of reaction $1$: $E_1$

Activation energy of reaction $2$:$E_2$