Reference no: EM132803962
Modeling Assignment
Question 1. You are looking at the thermal cracking of ethane into its constituents based on a model by Sundaram and Froment (Model III, Chem. Eng. Sci., Vol 32, p. 601).
k1
C2H6 ↔ C2H4 + H2
k2
2C2H6 ↔ C3H8 + CH4
k3
C3H8 ↔ C2H2 + CH4
k4
C2H2 + C2H4 ↔ C2H6
k5
C2H4 + C2H6 ↔ C3H6 + CH4
The mixture at the outlet should contain ethane (E), ethylene (Y), Hydrogen (H), propane (p), methane (M), propylene (L), Acetylene (a), and 1,3-butadine (B). The kinetic parameters are:
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Rate Constant
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K0
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E (kcal/mol)
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Units
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k1,f
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4.65e13
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65.2
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s-1
|
|
k1,r
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8.75e8
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32.7
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m3 kmol-1s-1
|
|
k2
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3.85e11
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65.25
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s-1
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k3,f
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9.81e8
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36.92
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s-1
|
|
k3,r
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5.87e4
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7.04
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m3 kmol-1s-1
|
|
k4
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1.03e12
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41.26
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m3 kmol-1s-1
|
|
k5
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7.08e13
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60.43
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m3 kmol-1s-1
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Where the reverse rate constants come from the reaction equilibrium. Assume all but reaction 2 are elementary and that reaction 2 is complex and first order. These parameters are probably not valid outside the temperature range of the data so you do not want the reaction temperature to vary by more than 15%. Assume feed is 99% ethane (by mole) with the remainder unseparated ethylene. The Feed is 100 moles per second. Assume 40% steam by mole.
a) Predict the Reynolds number at the inlet conditions and show that the flow is turbulent at the inlet. You will have to find correlations for the viscosity of each component as a function of temperature - Use the formulae from the DIPPR database. Assume 820 ºC.
b) Set up the system of equations for the change in flux of each component along the length of the reactor, including an expression for the velocity in the reactor and the pressure change inside the reactor. Assume isothermal conditions and P0 of 11 atm. Assume ideal gas.
c) Solve the ODEs from part b for the hydrocarbon concentration as a function of length.
d) Plot the mole fractions of ethane and ethylene as a function of length out to 95 meters.
e) The reactor will coke up too much if the conversion goes above 60%. What would you change in order to maximize the selectivity to ethylene while keeping the conversion at or below this value?
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