P$6\mathrm{.}6-$ ELEMENTS OF CHEMICAL REACTION NGINEERING FIFTH EDITION$($H$.$ SCOTT FOGLER$)$

$($Membrane reactor$)$ The first$-$order, gas$-$phase, reversible reaction

$AB+2C$

is taking place in a membrane reactor. Pure A enters the reactor, and $B$ diffuses out through the

membrane. Unfortunately, a small amount of the reactant A also diffuses through the membrane.

$($a$)$ Plot and analyze the flow rates of $A,B,$ and $C$ and the conversion $x$ down the reactor, as well

as the flow rates of A and $B$ through the membrane.

$($b$)$ Next, compare the conversion profiles in a conventional PFR with those of a membrane reactor

from part $($a$).$ What generalizations can you make?

$($c$)$ Would the conversion of $A$ be greater or smaller if $C$ were diffusing out instead of $B?$

Additional information:

$k=10mi{n}^{-1}$

$K_C=0\mathrm{.}01mo\frac{l^2}{d}{m}^6$

$k_{CA}=1mi{n}^{-1}$

$k_{CB}=40mi{n}^{-1}$

$F_{A0}=100mo\frac{l}{m}in$

$v_0=100d\frac{m^3}{m}in$

$V_{\text{r}\text{e}\text{a}\text{c}\text{t}\text{o}\text{r}}=20d{m}^3$