Solve the odes from part b for the hydrocarbon concentration

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Reference no: EM132803985

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:

Rate Constant	K0	E (kcal/mol)	Units
k1,f	4.65e13	65.2	s-1
k1,r	8.75e8	32.7	m³ kmol^-1s^-1
k2	3.85e11	65.25	s-1
k3,f	9.81e8	36.92	s-1
k3,r	5.87e4	7.04	m³ kmol^-1s^-1
k4	1.03e12	41.26	m³ kmol^-1s^-1
k5	7.08e13	60.43	m³ kmol^-1s^-1

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?

Reference no: EM132803985

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