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

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

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

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

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

Dr.Riham Hazzaa

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 0.872. 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

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

Dr.Riham Hazzaa

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

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