Methanol can be produced by the gas phase catalytic reaction between carbon monoxide and hydrogen as follows: CO + 2H₂ → CH₃OH.
The feed to the process consists of a stoichiometric mixture of hydrogen and carbon monoxide, but it also contains 4% by volume of the inert gas, nitrogen. This stream is mixed with a recycle stream before being fed to the catalytic reactor. The product stream from the reactor is fed to a condenser where all of the methanol can be removed as a liquid, and the unreacted gases and the inert nitrogen are recycled to mix with the feed stream. However, as the inert gas will continue to be added to the system. With the aid of the following partially annotated PFD, answer the following.
Fie
FE Xg Y Z = 0.17
F X Y..
VF Xo X* Yo Y. Zo = 0.04 Z = 0.15
Reactor
Us
X-H Y-CO Z-N U-CH₃OH
100 kg/h
Note: Extra copies of this PFD are appended to this examination paper.
(a) Using an atom matrix, show that there are two independent atom species involved in the above reaction. [10%]
(b) Conduct a Degrees of Freedom analysis for the overall system, stating clearly the number of unknown variables, and the relationships that may be used to balance the overall system. Show that there is sufficient information provided to determine all of the molar flows and mole fractions for streams 0 and 5. [20%]
(c) Show, in the case of stream 5, by using the carbon and hydrogen atom balances for the overall process, that the following relationships hold:
CH₃OH = 2CO + 4H₂
Nâ‚‚ = 0
You may assume that the above relationships are true for all streams containing H, CO, and N only. [10%]
(d) Fill in all of the mole fractions for streams 0, 1, 4, 5, and 6. [5%]
(e) Determine the molar flows for streams 0 and 5. [15%]
(f) Using molecular balances on the mixing point, the flow splitter, and the condenser, solve for the remaining molar flows and mole fractions. [10%]
(g) Calculate the single pass conversion for CO and the overall fractional conversion of CO for the process. [10%]