1. Material balance on single unit process
Degree of freedom analysis
Dr.Riham Hazzaa

2. Degree of Freedom Analysis
Draw and label flow chart
Count the unknown variables on the flow chart, nunknowns
Count the independent equations relating them, nindep eqns
ndf = nunknowns - nindep eqns
If ndf = 0, the problem is solvable
If ndf>0, the problem is underspecified, need to provide more information/equations.
If ndf˂0, the problem is overspecified, more equations than unknowns, redundant and possibly inconsistent information.
Dr.Riham Hazzaa

3. General Procedure for Material Balance Calculations
Choose as a basis of calculations an amount or flow rate of one of the process streams
Draw a flowchart of the process. Include all the given variables on the chart and label the unknown stream variables on the chart
Write the expressions for the quantities requested in problem statement
Convert all mass and molar unit quantities to one basis
Do the degree of freedom analysis. For any given information that has not been used in labeling the flowchart, translate it into equations in terms of the unknown variables
If nDF = 0, write material balance equations in an order such that those involve the fewest unknowns are written first
Solve the equations and calculate the additional quantities requested in the problem statement
Scale the quantities accordingly

4. Example A stream of humid air enters a condenser in which 95% of the water vapor in the air is condensed. The flow rate of the condensate (the liquid leaving the condenser) is measured and found to be 225 L/h. Dry air may be taken to contain 21 mole% oxygen, with the balance nitrogen.
Calculate the new rate of the gas stream leaving the condenser and the mole fractions of oxygen, nitrogen, and water in this stream.
Dr.Riham Hazzaa

5. Solution: Basis: 225 L/h Condensate
Suppose that the entering air contains 10.0 mole% water
Dr.Riham Hazzaa

6. Dr.Riham Hazzaa

7. Example: Material Balances on a Distillation Column A liquid mixture containing 45.0% benzene (B) and 55.0% toluene (T) by mass is fed to a distillation column. A product stream leaving the top of the column (the overhead product) contains 95.0 mole% B, and a bottom product stream contains 8.0% of the benzene fed to the column (meaning that 92% of the benzene leaves with the overhead product). The volumetric flow rate of the feed stream is 2000 L/h and the specific gravity of the feed mixture is
Determine the mass flow rate of the overhead product stream and the mass flow rate and composition (mass fractions) of the bottom product stream.
Dr.Riham Hazzaa

8. Draw and label the flowchart.
Choose a basis. feed stream flow rate (2000 L/h) as the basis of calculation.
Draw and label the flowchart.
Dr.Riham Hazzaa

9. Dr.Riham Hazzaa

10. Volumetric flow rate conversion
The benzene in the bottom product stream is 8% of the benzene in the feed stream
Dr.Riham Hazzaa

11. additional quantities requested in the problem statement
The results are ṁl = 1744 kg/h, ṁB3 = 62.8 kg benzene/h, ṁ2 = 766 kg/h , and ṁT3 = 915 kg toluene/h. A total mass balance (which is the sum of the benzene and toluene balances) may be written as a check on this solution:
additional quantities requested in the problem statement
Dr.Riham Hazzaa