Portfolio 03: Isothermal reactor design

CHEN3010/ CHEN5040: chemical reaction engineering

Solutions

Answers to the portfolio questions are uploaded at Portfolio 3 answers

Introduction

Ethylene oxide (EO) (\ce{C2H4O}), 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 4.07% during the forecast period until 2032. With a selling price of $1913 per tonne, the commercial value of EO 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:

\ce{C2H4 + 1/2 O2 -> C2H4O}

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 (as air) are fed in stoichiometric proportions to a packed-bed reactor operated isothermally at 280 ^\circ C.

Ethylene and oxygen are fed in stoichiometric proportions to a packed-bed reactor operated isothermally at 280 ^\circ C. Ethylene is fed at a rate of 200 mol/s at a pressure of 10 atm (1013 kPa). It is proposed to use 10 banks of 25.4 mm diameter schedule 40 tubes packed with catalyst with 100 tubes per bank. Consequently, the molar flow rate to each tube is to be 0.2 mol/s.

The rate law for the reaction is

-r'_A = k P_A^{1/3} P_B^{2/3}

with k = 0.00392 \frac{mol}{atm \ kg-cat\ s} at 260 ^\circ C. The heat of reaction, \Delta H is -106.7 kJ/mol and the activation energy, E is 69.49 kJ/mol.

Questions

1. 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.

2. 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 6.35 mm catalyst particles is 1925 kg/m^3, the bed void fraction is 0.45, and the gas density is 16 kg/m^3. For these catalyst properties, the pressure drop parameter \alpha is 0.0367 1/kg

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

   2. Draw the profiles of concentrations of reactants and products, conversion, volumetric flow rate ratio (\upsilon/\upsilon_0), and pressure ratio (P/P_0) as a function of catalyst weight.

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