Process Engineering & Applied ScienceCHEE3634
Due by 4pm, Nov. 24th.
Be sure to include the assignment number, and your name and student number at
the top of each page. Pages should be stapled together in the top-left corner
Consider a gas-phase system with the following two reactions taking place in miniature packed
C2H4 + 0.5 O2 → C2H4O
C2H4 + 3O2 → 2 CO2 + 2H2O
The kinetics for these reactions is based on the partial pressures, rather than concentrations:
1.33 × 105 [𝑔 𝑠 𝑏𝑎𝑟 1.58 ] exp (−
) 𝑃𝐶2𝐻4 𝑃𝑂2
(1 + 6.50 [𝑏𝑎𝑟] 𝑃𝐶2𝐻4 )
1.80 × 10 [𝑔 𝑠 𝑏𝑎𝑟 1.30 ] exp (−
) 𝑃𝐶2𝐻4 𝑃𝑂2
(1 + 4.33 [𝑏𝑎𝑟] 𝑃𝐶2𝐻4 )
The reactor consists of 15 cm long, 0.75 cm diameter tube which was uniformly packed with 7.2
grams of catalyst with particle diameters of 0.6 mm. The density of the particles is roughly
1500 g/L, and so you can determine the solid holdup, 𝜖𝑠 , in the reactor as the volume of particles
(7.2 / 1500) divided by the reactor volume (15 cm long, 0.75 cm diameter). Check for unit
Note the units for the kinetics is mmol of C2H4 consumed per second, per gram of catalyst, with
the pressure added to cancel out the pressure units later in the equation. This problem is solved
on a catalyst weight basis, dW, not a volume basis. The design equations for this problem have
the general form of 𝑑𝑊
= 𝑟𝐶2𝐻4 , where W is the weight of catalyst (solved from 0 to 7.2
grams). Note that the partial pressures can be determined based on the total pressure at any
given point, P, and the mole fraction (𝑃𝑎 = 𝐹𝑎 𝑃)
The inlet pressure that you can achieve with your current up-stream compressor ranges from 1.5
to 4 Bar, and the inlet temperature is 230°C. The inlet gas mixture is fed at 200 standard cubic
centimeters per minute (SCCM, with standard conditions defined as 298K and 1Bar pressure).
The gas consists of Ethylene (6% by moles), Oxygen (6% by moles), and the remainder being
inert Argon. The gas viscosity can be approximated at 0.000009 kg/m s and is assumed to be
fairly constant. The Gas density, which varies, is ~1.4 kg/m3 at 1.5 bar and 200°C. The outlet
pressure must be at least 1 Bar.
1) If the reactor operates isothermally, based on all of this information, what inlet operating
pressure would you choose to maximize the production of your desired product C2H4O.
justify your answer by showing plot of molar flow rate of C2H4O at the outlet (y-axis)
vs. Pinlet (x-axis) for at least 4 different conditions.
For your chosen Optimum, plot the total pressure and the partial pressures of ethylene
and ethylene oxide as a function of W (ranging from 0 to 7.2).
Be sure to account for pressure drop through the packed bed and the impact on density, as
these gases are compressible.
2) Isothermal operation is only accomplished through heat removal. The heat of reaction for
the first reaction at operating conditions is -100 kJ/mol C2H4 reacted, and the heat of
reaction of the second reaction is -1300 kJ/mol C2H4 reacted. These values do not
change significantly over the temperature range of these experiments (i.e. you can assume
these values are Δ𝐻𝑅 , and are constant. When operated properly, there is minimal need to
remove energy… but if the 2nd reaction starts occurring too much, the significant heat of
reaction can lead to hot spots in the reactor and unsafe conditions…
For your optimum found in 1, Plot the heat removal rate (Q) along the reactor (i.e. use W
as the x-axis, going from 0 to 7.2 grams). Note that the heat removal rate required for
isothermal conditions is determined by solving for the value of Q that results in dT/dVrx
(or dT/dW) = 0. You may assume the mixture has an average heat capacity of 0.52 J/g K,
and that this does not change significantly during the reaction.
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