1. Reading Materials: Chapter 5
Steady-State
Material
Balances
LECTURE 12
Chapter 5
CHEM ENG 1007

2. § 5.2 Material Balances for Multiple Species
Sometimes, streams containing more than one chemical compound or specie. Performing balance on an individual compound is called a species balance.
In contrast to total mass, which is neither created nor destroyed, a particular compound (e.g., A) can be “created” or “destroyed”.
Rate that Rate that Rate that Rate that Rate that
A enters + A is formed = A leaves + A is cons. + A accum
the system in the system the system in the sys. in the sys.
[5.3]
Chapter 5
CHEM ENG 1007

3. § 5.2 Material Balances for Multiple Species
For steady-state, equation 5.3 becomes
Rate that Rate that Rate that Rate that
A enters A is formed = A leaves A is cons.
the system in the system the system in the sys.
[5.4]
[5.5]
Chapter 5
CHEM ENG 1007

4. Example 5.4
Natural gas, which is essentially pure methane, undergoes steady-state combustion by injecting it into a small burner into which air is also injected. The methane flow rates in the steady input and output streams are:
Natural gas input stream: methane mass flow rate = 4.61 g/s
Air input stream: contains no methane
Output (Flue gas) stream: Flow rate of unburned methane = 0.09 g/s
At what rate (in g/s) is methane being burned?
Chapter 5
CHEM ENG 1007

5. From Lecture 10
The mass flow rates of methane in both streams are measured and found to be different!
What possibly happened?
Chapter 5
CHEM ENG 1007

6. Example 5.4 - Solution Flue gas Natural Gas Input burner Air Input
Chapter 5
CHEM ENG 1007

7. Example 5.4 - Solution The methane mass balance is Chapter 5
CHEM ENG 1007

8. More Equations
[5.6]
Chapter 5
CHEM ENG 1007

9. § 5.2.1 Material Balances with formation and/or consumption where chemical reaction is not given
Chapter 5
CHEM ENG 1007

10. Example 5.5
Penicillin is produced in reactors containing the bacteria Penicillium chrysogenum. One such method involves continuous (steady-state) production in a constantly-stirred tank reactor, where optimum Penicillin production has been reported when:
The penicillin concentration inside the reactor is mol/L
The inlet volumetric flow rate is 0.25 L/hr for a 10 L reactor
A nutrient stream (containing no Penicillin) is fed to a 10 L reactor containing the Penicillium chrysogenum bacteria. A product stream containing Penicillin leaves the reactor (the bacteria stay in the reactor, and the Penicillin concentration in the product stream is the same as inside the reactor). The densities of the nutrient and product streams can be assumed to be equal.
What is the production rate of Penicillin under these conditions? (MW Penicillin = 334.4)
Chapter 5
CHEM ENG 1007

11. Example Solution
Chapter 5
CHEM ENG 1007

12. Example Solution
Chapter 5
CHEM ENG 1007

13. Example Solution
Chapter 5
CHEM ENG 1007

14. § 5.2.2 Material Balances with no formation / consumption
Chapter 5
CHEM ENG 1007

15. Example 5.6
Benzene and toluene (two similar compounds) are partially separated using a distillation column. The feed (input) stream of 100 kg/hr contains benzene at a mass fraction of 0.40 with the balance being toluene. In the overhead product output stream, the benzene flow rate is 36 kg/hr, and in the bottom output stream, the toluene flow rate is 54 kg/hr. What is the toluene flow rate in the overhead output stream and the benzene flow rate in the bottoms output stream?
Chapter 5
CHEM ENG 1007

16. Example Solution
Chapter 5
CHEM ENG 1007

17. Toluene instead of Benzene
Example Solution
Toluene instead of Benzene
Chapter 5
CHEM ENG 1007

18. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene
Toluene
Total
100
Chapter 5
CHEM ENG 1007

19. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene
40 (=0.4x100)
Toluene
Total
100
Chapter 5
CHEM ENG 1007

20. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40
Toluene
60 (=0.6x100)
Total
100
Chapter 5
CHEM ENG 1007

21. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36
Toluene 60
Total
100
Chapter 5
CHEM ENG 1007

22. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36
Toluene 60 54
Total
100
Chapter 5
CHEM ENG 1007

23. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36
4 (=40-36)
Toluene 60 54
Total
100
Chapter 5
CHEM ENG 1007

24. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36 4
Toluene 60
6 (=60-54) 54
Total
100
Chapter 5
CHEM ENG 1007

25. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36 4
Toluene 60 6 54
Total
100
42 (=36+6)
Chapter 5
CHEM ENG 1007

26. Example Solution
Alternatively, we can set up our work as shown in the below table
Basis: 100 kg/hr of feed stream
Component
Feed
Overhead
Bottoms
Benzene 40 36 4
Toluene 60 6 54
Total
100 42
58 (= ) 
Check: inlet = outlet  100 =
Chapter 5
CHEM ENG 1007

27. Note
Problems may also often involve specifications such as “95% of species A in the feed stream leaves in the overhead stream.” Therefore,
Chapter 5
CHEM ENG 1007

28. HW # 1
A feed stream consisting of C8 and C10 hydrocarbons is separated by distillation into three products A, B and C. The flow rate of the feed is 2500 kg/hr and its composition is 30 wt% C8 hydrocarbons, 70 wt% C10 hydrocarbons. The compositions of the products A, B and C are 60 wt%, 35% and 15% C8 hydrocarbons respectively. Of the C8 hydrocarbons which enter in the feed, one half appears in product A. Calculate the mass flowrates (kg/min) of the three product streams.
Chapter 5
CHEM ENG 1007