It is required to design an Isothermal Packed Bed Reactor $($PBR$)$ to handle a gas

phase reaction $A+2B2D$ with a feed temperature of is $55C$ and pressure

of $P$ atm. For safety reasons, feed contains inert gas. If the mole fractions of the

feed streams are $20\%,50\%$ and $30\%$ for A$,$ B and Inert I respectively. The total

volumetric feed rate is Volumetric flow rate $d\frac{m^3}{m}in.$ The properties of the gas

are similar to those of air at this temperature and pressure.

Given: The reaction follows a reaction rate expression of $rA=2\mathrm{.}5C_A^{0\mathrm{.}5}{C}_B^1$

$(kmo\frac{l}{m^3}*min).$

The Molecular weight of A is $100\frac{g}{m}ol$ and Molecular weight of B is $50\frac{g}{m}ol.$

Inert molecular weight is $28\frac{g}{m}ol.$

Assume Variable density Case and without ignoring the pressure drop in the

reactor:

How much catalyst weight is needed to be filled in a $20ft$ length reactor packed

with catalyst $($a $C_{?}$ inches diameter catalyst particles and bed porosity of $45\%)$

to achieve $95\%$ conversion of A$.$ The catalyst density is $2000k\frac{g}{m^3}.$

How many $D_{?}$ inch diameter tube of $20ft$ legth is needed?

Plot the concentrations of all species, volumetric flow rate, pressure, and

conversion as a function of weight of catalyst?

Perform a sensitivity analysis to investigate the impact of the catalyst particle

size $($C$)$ on the pressure drop in accordance with your design parameters $,$

$D,P,$ and volumetric flow rate$).$ Determine the minimum particle size required

to maintain a non$-$zero exit pressure?