Material balance- purge cycle help

In summary, hydrogen is used to reduce iron oxide to metallic iron in a chemical reaction. The water produced is condensed and the unreacted hydrogen is recycled, but due to impurities in the fresh feed, some of the hydrogen must be purged. To limit the impurity CO2 in the reactor feed, a material balance is used to calculate the flow rate and composition of the purge stream. The result is a flow rate of 23.76 kmol h^{-1} with 3.1% CO2 and 96.9% H2. The flow rate of the purge stream is equal to that of the fresh feed stream, which may be confusing but is a result of the material balance calculation.
  • #1
simon.23
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Hydrogen is used to reduce 2.3 tonne per hour, Fe2O3 to metallic iron according to the reaction

[tex] Fe_{2}O_{3} + 3H_{2} = 2Fe + 3H_{2}O [/tex]

The water is condensed and the unreacted hydrogen is recycled (see diagram attached). Because the hydrogen in the fresh feed contains 1.1% CO2 as an impurity, some of the unreacted hydrogen must be purged. Calculate the flow rate and the composition of the purge stream required to limit the CO2 in the reactor feed to 2.8% if the ratio of recycle to fresh feed is 11:2 on a molar basis.
MW(Fe) = 55.85, MW(H) = 1.01, MW(O) = 16.00.


I am really struggling to get to grips with this question, ( struggling with material balance overall!)

I can do dimple material balance however for things with a recycle stream or purge stream, really confuses me.

I have the solution which I will post up, but I still don't get 'why' it is solved in this manner. I would really appreciated it, if someone explains to me why. Or if you have simpler way of working the flow rate of the purge stream?

thank you,
 

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  • #2
SOLUTION;

CO2- Balance;


[tex] 0.011x + y = 6.5x (0.028) [/tex]

[tex] y = 0.0171x [/tex] in the recycle stream.

[tex] \frac{0.0171x}{5.5x} \times 100 = 3.1 \% [/tex] of CO2 in purge stream,
100 - 3.1 = 96.9 % H2 in purge stream. Flow rate of purge:

CO2 BALANCE-

[tex] 0.011x = 0.031p , x = \frac{0.031p}{0.011} [/tex]

H2 Balance-
[tex] 0.989x = 43.204 + 0.969p [/tex]

[tex] 2.787p = 43.204 + 0.969p [/tex]

[tex] p = 23.76 kmol h^{-1} [/tex]

Firstly, I don't get why the flow rate of the purge stream is equal to the flow rate of the fresh feed stream?

Surely it won't be the same, as some CO2 is being recycled? Your also loosing water and Fe iron, from the fresh fee, you have two outputs, so surely the flow rate of the fresh feed would be more than the flow rate of the purge stream, so you can't set them equal to each other?
 

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1. What is material balance and why is it important in a purge cycle?

Material balance is the accounting of all the materials entering and exiting a system. In a purge cycle, it is important to maintain a balance in order to ensure that the system is functioning properly and to avoid any potential safety hazards.

2. How does material balance affect the efficiency of a purge cycle?

Material balance directly impacts the efficiency of a purge cycle. If there is an imbalance, it can lead to incomplete purging and contamination of the system, resulting in reduced efficiency and potential damage to equipment.

3. What factors can affect material balance in a purge cycle?

Some factors that can affect material balance in a purge cycle include the flow rate of the purging gas, the temperature and pressure of the system, and any leaks or losses in the system. It is important to consider all of these factors when designing a purge cycle.

4. How can an engineer determine the required purge time for a system?

The required purge time for a system can be determined by considering the volume of the system, the flow rate of the purging gas, and the desired level of purging. Engineers can also use mathematical models and simulations to calculate the required purge time.

5. What are some strategies for maintaining material balance in a purge cycle?

One strategy is to continuously monitor and adjust the flow rate of the purging gas to maintain a balance. Another strategy is to perform regular leak checks and repairs to minimize any losses in the system. It is also important to properly size and design the purge cycle for the specific system to ensure efficient purging and material balance.

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