You are developing a process for the synthesis of proprietary chemical $D$ from reagent $A.$ The process involves three process units. First, reagent A $($as a solution in water$)$ is fed to a continuous stirred tank reactor $($CSTR$)$ with an enzyme catalyst pre$-$immobilized on silica particles. The enzyme catalyst contains two unique active sites and is capable of transforming A into $B$ at active site $1,$ and A into $C$ at active site $2.$ The enzyme can be retained inside the CSTR$,$ such that the only species in the output stream are A$,B,C,$ and water. Second, a separation unit then recovers the water and vaporizes the remaining $A,B,C.$ Finally, the vapor stream is fed to an isothermal equilibrium gas phase reactor $($GPR$)$ in which $D$ is produced. Unfortunately, two undesired side reactions also occur, producing byproducts $F$ and $G.$ For this assignment, you are only concerned with this final product gas stream, which contains unreacted $A,$ B$,$ and C $,$ together with all three products, D $($desired$),$ F $($undesired$),$ and G $($undesired$).$

Description of the CSTR

The CSTR has a volume of $100$ L and is to be run with input and output flow rates of $1\frac{L}{m}in.$ The concentration of $A$ in the feed is held at $2mo\frac{l}{L}.$ The enzyme $($E$)$ concentration inside the reactor is fixed at $1mo\frac{l}{L}($assuming the enzyme remains active and not degraded during the entire process runtime$).$ The reactions can be described as follows:

$A+E{}_{k_{1-18}}^{k_{18}}[AE]k_{2B}B+E$

$A+E{}_{k_{-1c}}^{K_c}[AE{]}^0$ hat$(scc{)}_{2c}C+E$

where $k_i$ represents the reaction rate constant for the direction indicated by the arrow. The reaction rates for these enzyme$-$catalyzed reactions follow Michaelis$-$Menten kinetics, which result in the following rate expressions:

where the rates are in $mo\frac{l}{m}in,K_{MB}=\frac{k_{-1B}+k_{2B}}{k_{1B}},$ and $,K_{MC}=\frac{k_{-1C}+k_{2C}}{k_{1C}}.$

The useful expressions at the right of each rate equation $($boxed$)$ were derived from recognizing that at steady state, the concentration of species A in the reactor is identical to that in the output $($CSTR assumption$),$ such that:

$[A]=\frac{n_{A,D}}{V_{cSTR}}=\frac{n_{A,ad}^{}}{V_{\text{o}\text{d}\text{A}}^{}}$

For the enzyme developed:

$\backslash$table$[[$rate constant,$x=B,x=C$