Consider the first$-$order irreversible catalytic gas phase reaction $AB$ which is carried out in a

laboratory mixed flow reactor $($CSTR$).$ The reactor contains $10$ gram of $1\mathrm{.}2mm($diameter$)$ spherical

porous catalyst particles $(p=2000\frac{kg}{m^3}$;$D_{\text{e}\text{f}\text{f}}={1\mathrm{.}010}^{-7}\frac{m^2}{s}).$ The feed to the reactor is $4\mathrm{.}0c\frac{m^3}{s}$

pure A at $1\mathrm{.}0$ atmosphere $(1\mathrm{.}01325$ bar$)$ and $336C.$ A conversion of $80\%$ was obtained for this

experimertal setup. The flow pattern in the reactor is such that external diffusion effects are

negligible.

a$)$ Show that the experimental observed reaction rate in the experimental reactor is $6\mathrm{.}4$mmo$\frac{l}{k}{g}_{\text{c}\text{a}\text{t}}S$

$[4]$

b$)$ Motivate with detailed calculations, using the Weisz$-$Prater criterion, if the current operation of the

reaction with the laboratory experimental setup is internal diffusion or reaction controlled $[6]$

c$)$ Deternine the effectiveness factor of the catalyst used in the laboratory experiments $[5]$

A pilot scale reactor $($fluidised bed, which can be modelled as a CSTR$)$ was designed, which consists

of $10kg$ of catalyst $(1000$ times as much as the laboratory scale reactor$)$ with a feed flow of $4\mathrm{.}0d\frac{m^3}{s}$

$(1000$ times as much as the laboratory scale reactor$).$ The same operating conditions and $1$

atm., same catalytic material$)$ are used, but larger spherical catalyst particles $(D_p=2\mathrm{.}0(mm))$ are used

this time $($The effective diffusion coefficient remains the same, $D_{\text{e}\text{f}\text{f}}={1\mathrm{.}010}^{-7}\frac{m^2}{s}).$ Also in the pilot

scale reactor, the flow pattern is such that external diffusion effects are negligible.

d$)$ Do you expect a larger$/$equal$/$or lower conversion then $80\%($the conversion in the laboratory

experiments$)?$ Motivate! $[3]$

e$)$ Determine the conversion in the pilot scale reactor $[7]$