Problem $3$:

$[25$ marks$]$

Consider the first$-$order reaction of $AB$ which is carried out in an experimental mixed

flow reactor $($CSTR$).$ The reactor contains $10$ gram of $0\mathrm{.}50mm($diameter$)$ spherical

catalyst particles $(=2000k\frac{g}{m^3}$; Deff $={1\mathrm{.}010}^{-6}\frac{m^2}{s}).$ The feed to the reactor is $4\mathrm{.}0$

$c\frac{m^3}{s}$ pure A at $1\mathrm{.}0$ atmosphere $(\frac{1\mathrm{.}01325}{b}ar)$ and $336C.$ A conversion of $80\%$ was

obtained for this experimental setup. The flow pattern in the reactor is such that

external diffusion effects could be considered negligible.

a$)$ Show that the experimental observed reaction rate in the experimental reactor is

$6\mathrm{.}4$mmo$\frac{l}{k}g$ cat $s.$

b$)$ Motivate with detailed calculation, using the Weisz Prater criterion, that the

current operation of the reaction within the experimental setup is not affected by

internal diffusion limitations$.$

negligeble internal mass transfer effects

c$)$ Determine the reaction rate constant $(\{$:$k^{\text{'}})$ at the given conditions.

$k^{\text{'}}=1\mathrm{.}6E-3m\frac{3}{k}gs$

d$)$ Show that the volumetric reaction constant $($k$)$ equals $3\mathrm{.}2s^{-1}$ and confirm using the

Thiele modulus that reaction control applies for the experiments. Use this value for

further calculations in $3e).$

There is a need to design a commercial$-$sized reactor to treat large amounts of pure $A$

to $80\%$ conversion. The same operating conditions $($temperature and pressure$)$ will be

used as described above. Our choice is between $($a$)$ a fluidized bed of $1\mathrm{.}0mm$ particles

and $($b$)$ a packed bed of $1\mathrm{.}5cm$ particles. For the fluidized bed one could assume

mixed flow of the gas $($CSTR behaviour$),$ and for the packed bed one can assume

PFR behaviour for the gas.

e$)$ Give detail calculations with motivation which reactor system you would prefer if

minimisation of catalyst use is the objective.