Oxidation of SO2 (the exam contains 4 pages)
The catalytic (V2O5) oxidation of SO2 to SO3 is an important step in a Sulfuric Acid production plant.
with:
In the equations above, T is in K and P in bar. In your further calculations you may assume to be constant. The conversion of the reaction is limited by thermodynamic equilibrium.
The reactor that needs to be designed is for a plant that produces 0.5 million ton H2SO4 per year ( 1 year = 8000 hours). The SO2 conversion needs to be higher than 96% in order to meet the emission requirements. The composition of the feed stream is 8 vol% SO2, 11 vol% O2, 0 vol% SO3, rest is N2. The inlet temperature is: 420 °C. Inlet pressure is 1.2 bar and the maximal allowable pressure drop is 0.2 bar. The maximal superficial velocity is the reactor is 5 m/s. The reactor is a fixed bed.
Question A: Select a suitable fixed bed configuration. You may choose from: A1) single adiabatic bed, A2) single externally cooled bed, B) cooled multi-tubular reactor and C) multi adiabatic beds with interstage cooling. Schematics are given below. Motivate your choice! Use (simple) calculations to support your reasoning. Do not only advocate your selection, also show the disadvantages / impossibilities of the others. (35 pts)
Molten salt at 410 °C (you can assume a constant temperature) is available for cooling the multi-tubular reactor (B) and the single bed(A2). With interstage cooling the temperature is reduced to 430 °C after each stage.
Data and equations that you might use to support your reasoning for question A can be found on the pages below.
Question B: Design (size) the reactor of your choice. You may assume that the conversions of the other reactors in the plants are 100%. (65 pts)
You may use a 1D model.
The molar concentration can be calculated with the ideal gas law and may be assumed constant (use for the calculation the inlet P and T). For the density of the gas (kg/m3) you make the value for N2 (28 g/mol). You may further assume that the velocity does not change in the reactor. In the model you can also assume the pressure to be constant. The pressure drop can be calculated based on the inlet conditions.
Provide:
1) The diameter and length of the bed (A), the diameter and length of the tubes and the number of tubes required (B), the diameter and length of the beds (C)
2) Axial profiles of the concentrations (mole fractions) and temperature in the bed(s)/tubes.
3) The particle size of the catalyst.
4) The pressure drop. (you don’t have to solve the pressure drop equation as ODE, instead it can be evaluated at inlet conditions).
As catalyst you may select particles with a characteristic length (dp) of 3mm, 7 mm, 1 cm or 2 cm.
In case you selected the multi-tubular system, tubes with a diameter of 5, 10 and 15 cm are available. (you may neglect the wall thickness).
The reaction kinetics are described by:
p is in bar, K1-3 are defined below with T in K. There are no heat / mass transfer limitations at the level of the catalyst particles.
The calculate the pressure drop the equation below is given:
In this equation, u is the superficial velocity and the density of the gas.
To calculate the overall heat transfer from tube (bed) to coolant the following relation can be used.
dt is he diameter of the bed and U is the overall heat transfer coefficient (W/m2/K).
Further constants are given in the table below:
Constant Unit Value
R J/mol/K 8.314
Cp J/mol/K 30
?cat kgcatalyst / m3reactor 1500
?? - 0.5
?g W/m/K 0.05
?g Pa.s 2.5x10-5
Molar masses: SO2 = 64 g/mol
SO3 = 80
H2SO4 = 98
O2 = 32