Introduction

Ethylene oxide $($EO$)(C_2{H}_{4}O),$ also known as oxirane, is a colorless, flammable gas with a sweet, ether$-$like smell. EO is an important industrial chemical used primarily to make ethylene glycol $($a key ingredient in antifreeze and polyester fiber$)$ and other chemicals, such as surfactants, detergents, and solvents.

In $2022,$ global production of EO was nearly $28$ millions of tons and s expected to grow at a steady CAGR of $4\mathrm{.}07\%$ during the forecast period until $2032.$ With a selling price of $$1913$ per tonne, the commercial value of $E0$ is around $$53$ billion.

The primary route for EO production involves the direct vapor phase oxidation of ethylene in the presence of a silver catalyst:

$C_2{H}_4+\frac{1}{2}{O}_{2}longrightarrow{C}_2{H}_{4}O$

This reaction is highly exothermic and requires careful control to manage the risk of runaway reactions. The process typically involves a recovery stage to separate EO from water and other byproducts.

We want to design a reactor achieve a desired conversion of ethylene. Ethylene and oxygen are fed in stoichiometric proportions to a packed$-$bed reactor operated isothermally at $260C.$

Ethylene and oxygen are fed in stoichiometric proportions to apacked bed reactor operated isothermally at $280C.$ Ethylene is fed at a rate of $200mo\frac{l}{s}$ at a pressure of $10$atm$(1013$kPa$).$ It is proposed to use $10$ banks of $25\mathrm{.}4mm$ diameter schedule $40$ tubes packed with catalyst with $100$ tubes per bank. Consequently, the molar flow rate to each tube is to be $0\mathrm{.}2mo\frac{l}{s}.$

The rate law for the reaction is

$-r_A^{\text{'}}=k{P}_A^{\frac{1}{3}}{P}_B^{\frac{2}{3}}$

PBR

with $k=0\mathrm{.}00392\frac{\text{m}\text{o}\text{l}}{\text{a}\text{t}\text{m}\text{k}\text{g}-\text{c}\text{a}\text{t}\text{s}}$ at $260C.$ The heat of reaction, $H$ is $-106\mathrm{.}7k\frac{J}{m}ol$ and the activation energy, $E$ is $69\mathrm{.}49k\frac{J}{m}ol.$

Questions

Isobaric reactor

$(10$ marks$)$

Using the mole balances developed in portfolio $02,$ determine the weight of catalyst required to achieve $60\%$ conversion in a PBR$.$ Show your working by following the reaction engineering algorithm. State your assumptions if any.

Effect of pressure drop

$(20$ marks$)$

As this is a gas phase reaction carried out in a PBR$,$ there is a significant pressure drop. The properties of the reacting fluid are to be considered identical to those of air at this temperature and pressure. The density of the $6\mathrm{.}35mm$ catalyst particles is $1925k\frac{g}{m^3},$ the bed void fraction is $0\mathrm{.}45,$ and the gas density is $16k\frac{g}{m^3}.$ For these catalyst properties, the pressure drop parameter $$ is $\frac{0\mathrm{.}03671}{k}g$

$3$

a$.$ How will the equations change when you consider pressure drop?

b$.$ Draw the profiles of conversion, volumetric flow rate ratio $(\frac{v}{v_0}),$ and pressure ratio $(\frac{P}{P_0})$ as a function of catalyst weight.

c$.$ Estimate the catalyst weight required to achieve $60\%$ conversion considering pressure drop. Compare the results with those obtained in question $1.$