Deceptively difficult material balance problem. HELP

In summary, the conversation discusses the problem of converting coal into liquid products using in situ coal combustion. The process involves combining H2 and CO to form methanol and has specific specifications, including the desired production rate of 100 mol/h. The solution involves setting up a flow diagram and using degree of freedom analysis to determine the unknowns, such as the recycle ratio of H2, feed rate of CO, and the purge gas composition and rate.
  • #1
Dan Feerst
12
0
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?
 

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  • #2
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!
 

What is a material balance problem?

A material balance problem is a type of mathematical problem used in engineering and science to determine the amount of a substance present in a system, based on known inputs and outputs.

Why is a material balance problem considered deceptively difficult?

A material balance problem can be deceptively difficult because it requires a thorough understanding of the system and all of its inputs and outputs. It may also involve complex equations and multiple variables, making it challenging to solve.

What are some strategies for solving a material balance problem?

Some strategies for solving a material balance problem include creating a mass balance table, using algebraic equations, and simplifying the problem by assuming certain conditions or using simplifying assumptions.

What are some common mistakes made when solving a material balance problem?

Common mistakes when solving a material balance problem include incorrect unit conversions, missing or incorrect inputs, and not considering all of the inputs and outputs in the system. It is important to double-check all calculations and assumptions to avoid errors.

How can I improve my skills in solving material balance problems?

Practice is key to improving your skills in solving material balance problems. It is also helpful to review key concepts, such as mass balance equations, before attempting a problem. Collaborating with others and seeking help from a tutor or instructor can also be beneficial.

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