Deceptively difficult material balance problem. HELP

[Dan Feerst]

I have been working on what I thought was an easy problem. This was a one hour quiz in which the whole class failed, the instructor decided to give it as a homework assignment instead.


------problem start---------
Considerable interest exists in the conversion of coal into liquid products for production of desirable chemicals. Two of the main gases produced from in situ (in ground) coal combustion are H2 and CO. These product gases can be combined to form methanol (H2+CO-> CH3OH). The process is shown below:




Your system has the following specifications:

1. The fresh feed contains 55% mass H2, 44.3% mass CO and 0.7% mass CH4
2. The outputs from the condenser are a liquid stream (pure methanol) and a gas stream containing the un-reacted components, inert methane and uncondensed methanol (5% of the total methanol produced in the reactor)
3. The purge stream is used to maintain the CH4 concentration in the gas stream leaving the condenser at 4% mole.
4. The single pass conversion of CO is 25%

Assuming a production rate of methanol of 100 mol/h,

1. Draw and label the flow chart completely
2. Perform a degree of freedom analysis and show that all of the unknowns can be solved
Calculate the following:
3. Recycle ratio of the H2
4. Feed rate of CO
5. Purge gas composition and rate

------problem end-------

I have about 15 hours into this problem at this point. Unless the problem itself is messed up, or I'm setting up my flow chart wrong, it doesn't seem to work out.

Basically, what I have done so far is:
determine the there is 0 degrees of freedom on the system.
solve for the flow rate of the purge by setting a basis at the fresh feed and doing the inert balance. I can't seem to solve for anything else. Can anyone help?

 

[LightHero]

To solve this problem, you need to set up the flow diagram correctly and then use the degree of freedom analysis to determine the unknowns. The first step is to set up the flow diagram correctly. You need to consider the inputs to the system (fresh feed, recycle flow, and purge flow) and the outputs from the system (liquid stream and gas stream). Then calculate the flow rates of each component in each stream. Once you have the flow diagram and the flow rates, you can use the degree of freedom analysis to solve for the unknowns. You need to set a basis at the fresh feed and solve the inert balance. Once you have the flow rate of the fresh feed, you can then determine the recycle ratio of H2, the feed rate of CO, and the purge gas composition and rate. Good luck!