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

§ 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

§ 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

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

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

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

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

More Equations [5.6] Chapter 5 CHEM ENG 1007

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

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 0.002 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

Example 5.5 - Solution Chapter 5 CHEM ENG 1007

Example 5.5 - Solution Chapter 5 CHEM ENG 1007

Example 5.5 - Solution Chapter 5 CHEM ENG 1007

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

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

Example 5.6 - Solution Chapter 5 CHEM ENG 1007

Toluene instead of Benzene Example 5.6 - Solution Toluene instead of Benzene Chapter 5 CHEM ENG 1007

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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

Example 5.6 - 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 (= 4 + 54)  Check: inlet = outlet  100 = 42 + 58 Chapter 5 CHEM ENG 1007

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

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