Reaction Kinetics (Methanol Synthesis)

Your task is to convert syngas (CO, H 2 ) for further processing into methanol (CH 3 OH). To this end, a new copper/zinc catalyst has been developed which has promising potential. Reactions for methanol synthesis (new zinc-based catalyst):

���� 2��2 ⇆ ����3���� ∆H Rxn@298K: -91 kJ/mol

����2 + 3��2 ⇆ ����3���� + ��2�� ∆H Rxn@298K : -41 kJ/mol

(Note: In this report, we will consider only the forward reactions).

Your assignment is to produce a report ultimately detailing (1) the determination of reaction kinetics and (2) how you optimized your methanol synthesis reactor (3) the impact of reaction kinetics uncertainties on the optimized result.

(1) The following data has been obtained for the methanol synthesis reactions using a constant volume batch reactor. All reactions can be treated as irreversible.

��3

���� +2 → ����3������4

����2 + 3��2 → ����3����2��

Reaction conducted with excess hydrogen (H 2 ):

t(s) C CO (M) t(s) C CO2

(M)

0 0.500 0 1.400

1 0.330 1 0.570

2.5 0.221 3 0.270

5 0.142 5 0.170

10 0.083 7 0.130

20 0.045 10 0.090

40 0.024 15 0.060

60 0.016 30 0.030

t(s) C H2 (M)

0 0.900

0.5 0.502

��3

���� + 2��2 → ����3����

T( o C) ��3

300 0.86

400 1.81

500 3.07

600 4.88

700 6.62

����2 + 3��2 → ����3����2��

T( o C) ��4

500 17

600 21.1

700 25.4

800 29

900 33.1

1 0.352

1.5 0.258

3 0.122

6 0.043

12 0.012

t(s) C H2 (M)

0 0.750

0.2 0.600

0.5 0.444

1.0 0.269

2.0 0.098

3.0 0.036

4.0 0.013

5.0 0.005

Further examination of the reaction determines a temperature dependence of the reaction rate constants. The following data has been obtained for the reactions (Units for the reaction rate constant are M (mol/L) and s (seconds)):

In the appendix of the report, calculations and the figures should be clearly presented showing how the reaction rate expressions associated With the methanol synthesis were obtained.

(2) Use the reaction kinetics obtained to report the conversion for (a) 1m long PFR reactor (b) 10m long PFR reactor. Identify the optimal reactor volume numerically (using Excel Spreadsheet) for each case and discuss how you came to this decision based on your modeling and other supporting information. Explain how you determined the appropriate number of tubes and the diameter of the tubes inside the reactor – provide a sketch of the final reactor design showing major dimensions (this does not need to show every tube inside reactor! – only present an example of one and the geometric arrangement/spacing of the nearest

Neighbors). You should present a plot of conversion (X) as a function of reactor volume when discussing and justifying the determination of the optimal size (allowing V to become extremely large at a diminishing return on X is not a good answer!). For each reactor calculate the pressure drop using Ergun equation – plot pressure drop (∆P) as a function of reactor length, and also plot ∆P as a function of the catalyst means size (0.1mm to 10mm in increments of 0.1mm) – discuss the pros and cons of changing the catalyst size. Critically analyze adding CO 2 (up to 500kgmole/h) to the feed of the methanol synthesis reactor. For the optimal reactor, sizes plot the concentration profiles of reactants and products as a function of the length of reactors. Also, plot density vs. reactor length; Report the production of methanol (tonne/yr). (3) Perform a sensitivity analysis (± 10% for methanol synthesis reaction kinetic orders obtained in part (1) – you only need to identify maximum and minimum cases) w.r.t. Conversion (X), reactor volume (V), and methanol production for the methanol synthesis reactors. The impact of this error on the reactor conversion for the 1m and 10m PFR must be presented and discussed, and all values presented in the final report should contain the resultant errors (e.g., Methanol production = 300,000 (± 20,000) tonne/yr).

A final report must be produced, which addresses all the tasks above and discusses the choice of catalyst, reactors, and production rates w.r.t. Industrial process. You should read supplemental literature provided on LMS and use all pertinent information when discussing your final reactor design. Discuss in detail how well you think the PFR reactor models a real industrial reactor for methanol synthesis production – clearly identify to what extent PFR is appropriate and to what extent it is not.

Additional information:

Assume ideal gas law applies when determining thermodynamicproperties. Reactor feed rate is 5,000kgmol/h of syngas (feed ratio H 2

–to-CO is 2:1)).

Limits for methanol synthesis reaction conditions:

Temp = 300 o C.

Pressure = 20Bar.

Reaction is gas

phase.

The additional feed of CO 2: up to 500kgmol/h.

The catalyst used for methanol production reactions is a novel spherical Zinc based catalyst with the following information:

Mean Size: 3

mm Void

fraction: 0.5

Particle sphericity: 0.5

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