Ponchon-Savarit Method Home -> Solved Problems -> Mass Transfer -> 1000 kg/hr of a mixture containing 42 mole percent heptane and 58 mole percent ethyl benzene is to be fractionated to a distillate containing 97 mole percent heptane and a residue containing 99 mole percent ethyl benzene using a total condenser and feed at its saturated liquid condition. The enthalpy-concentration data for the heptane-ethyl benzene at 1 atm pressure are as follows: xheptane 0
0.08
0.18
0.25
0.49
0.65
0.79
0.91
1.0
yhe ptane
0
0.28
0.43
0.51
0.73
0.83
0.90
0.96
1.0
Hl (kJ/kmol) x 10-3
24.3
24.1
23.2
22.8
22.05
21.75
21.7
21.6
21.4
Hv (kJ/kmol) x 10-3
61.2
59.6
58.5
58.1
56.5
55.2
54.4
53.8
53.3
Calculate the following: a. b. c. d. e.
Minimum reflux ratio Minimum number of stages at total reflux Number of stages at reflux ratio of 2.5 Condenser duty Reboiler duty
Calculations: Heptane = C7H16 Ethyl benzene = C6H5C2H5 Average molecular weight of feed solution = 0.42 x 100 + 0.58 x 106 = 103.48 Molal flow rate of feed, F = 1000/103.48 = 9.9937 kmol/hr The H-x-y diagram is constructed with the above data as given below:
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28/11/2011 9:28 PM
Ponchon-Savarit Method - Mass Transfer Solved Problems - msubbu
Reflux ratio, R = (Q' - HG1) / (HG1 - HL0) = (98.4391 - 53.70453) / (53.70453 - 21.53695) = 1.3907 Minimum Reflux ratio = 1.3907 With the x-y data, the following graph is drawn:
Minimum number of stages at total reflux is found from the x-y diagram and = 6.97 Number of stages at reflux ratio of 2.5: (Q' - 53.70453) / (53.70453 - 21.53695)= 2.5 Q' = 134.1235 x 103 kJ/kmol F = 9.9937 kmol/hr Material balance equations: F=D+W F zF = D xD + W xW
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Ponchon-Savarit Method - Mass Transfer Solved Problems - msubbu
i.e. 9.9937 = D + W 9.9937 x 0.42 = 0.97 D + 0.01 W Solving, 0.96 D = 4.0974 D = 4.2681 kmol/hr W = 9.9937 - 4.2681 = 5.7256 kmol/hr Energy balance equation: F HF = D Q' + W Q" Substituting for the known quantities, 9.9937 x 22.30098 x 103 = 4.2681 x 134.1235 x 103 + 5.7256 x Q" Q" = -61.0562 x 103 kJ/kmol Q' = HD + QC / D Q" = HW - QB / W Substituting for the known quantities in the above equations, 134.1235 x 103 = 21.53695 x 103 + QC / 4.2681 QC = 480.53 x 103 kJ/hr = 133.48 kW -61.0562 x 103 = 24.27584 x 103 - QB / 5.7256 QB = 488.58 x 103 kJ/hr = 135.72 kW Condenser duty = QC = 133.48 kW Reboiler duty = QB = 135.72 kW Number of stages is estimated from Ponchon-Savarit method as shown in the graph, and is equal to 11 (including the reboiler).
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Ponchon-Savarit Method - Mass Transfer Solved Problems - msubbu
