Question $3$

The first$-$order irreversible gas phase calalytic reaction, $AB,$ was carried out and the following experimental data were obtained $($Table P$3).$ The conditions for all experiments were the same, where the reaction was caried out in an isothermal and isobaric differential reactor at a pressure of $1\mathrm{.}0$ bar and a temperature of $700K$ using pure A$.$ Assume negligible extemal mass transfer resistance.

$($Aiote that part e$)$ and ff$)$ of this question can be mate withetat ansurering $($i$)-$ di$)$

Table P$3$: Experimentally observed reaction rate as a function of catalyst size

$\backslash$table$[[,\backslash$table$[[$Observed reaction rale$],[$ mol$/$gcat s$]]],$Catalyst radius $($mm$)],[$Run $1,3\mathrm{.}0*{10}^{-5},10],[$Run $2,15\mathrm{.}0*{10}^{-5},1\mathrm{.}0]]$

a$)$ Motivate, without doing any calculations, that internal diffusion limits the reaction rate in this conversion process $($do not use more than $25$ words$).$

b$)$ Estimate the Thiele modulus and effectiveness factor for each catalyst size.

Thiele, $16\mathrm{.}5$ and $1\mathrm{.}65,$ eff factor $0\mathrm{.}17$ and $0\mathrm{.}86$

c$)$ How small should the pellets be made to eliminate nearly all internal diffusion resistance?

$0\mathrm{.}5mm$

d$)$ Determine the intrinsic reaction rate constant $(k)$ and the ratio of the catalyst density to the effective diffusivity $(\frac{{}_{ca}}{D_{lon}})$ of this catalytic reaction.

$k1=1\mathrm{.}0e-5m\frac{3}{g}$cats

These studies were carried out in order to select a reactor that will operate at the reaction conditions similar to the experimental conditions $,$ pure A feed$).$ The company has $2$ choices of reactor, and since the catalyst is excessive expensive, the company prefers the reactor that needs the least catalyst:

Option $1$: A fluidised bed reactor operating with catalytic particles of $3\mathrm{.}0mm$

Option $2$: A fixed bed reactor operating with catalytic particles of $10mm$

$($If you did not find an answer in d$)$ continue the problem with $k^{\text{'}}=1\mathrm{.}5*{10}^{-2}\frac{m^3}{k}{g}_{\text{c}\text{a}\text{r}}S,ra{t}_{\text{c}\text{a}\text{t}}=2000k\frac{g}{m^3}$ and $D{e}_e=7\mathrm{.}5*{10}^{-6}\frac{m^2}{s})$

e$)$ What reactor would you advise? If:

$(7)$

i$)$ The conversion should be $98\%$

i$)$ The conversion should be $10\%$

CSTR

$($Hint: Assume that the fluidised bed reactor can be modelled as a CSTR while the fixed bed reactor does not sho axial dispersion, and also assume isobaric and isothermal conditions$)$

f$)$ Determine the catalyst weight, which when used in both reactors, would yield the san conversion.

equal catalyst used at $83\%$