You are tasked with calculating the behavior of a packed bed. The pipe has a diameter of $10cm$

and a length of $45m.$ It is packed with spherical catalyst pellets with a void fraction of $30\%,$ and

each pellet has a diameter of $0\mathrm{.}25cm.$ The solid catalyst has a density of $1200k\frac{g}{m^3}.$ The

temperature across the pipe is constant at $215C.$

Flowing into the packed bed is a pure ideal gas feed of compound A preheated to $215C.$ Your

feed has a mass flow rate of $0\mathrm{.}01k\frac{g}{s},$ a viscosity of $1\mathrm{.}6{10}^{-5}k\frac{g}{m}s$ and a pressure of $\frac{20}{b}ar.$

Compound A has a molecular weight of $17\frac{g}{m}ol.$

a$)$ Calculate the pressure drop across the packed bed.

b$)$ Now consider the following second order reaction occurring in the packed bed:

$2AB+C$

$-r_A=k{C}_A^2$

$k=5*{10}^{-5}\frac{m^6}{(mol)*k{g}_{\text{c}\text{a}\text{t}}*s}$

c$)$ Calculate conversion with pressure drop. All assumptions and parameters previously

mentioned hold true.

d$)$ Calculate the conversion with no pressure drop.

e$)$ Compare the conversions you got in part b$)$ and part c$).$ What do you notice? Does this

match your expectation? Why? What are the physical phenomena that cause this

difference?