Summer 2001 ChE n363, Unique No. 76085 UNIT OPERATIONS II: SEPARATION PROCESSES Solution to Homework 5 Assigned: Fri, June 29, 2001 Due: Fri, July 6, 2001 Exercise 7.13 A fractionation column operating at 101 kPa is to separate 30 kg/h of a solution of benzene and toluene containing 0.6 mass fraction toluene into an overhead produ product ct cont contai ainin ning g 0.97 0.97 mas masss frac fracti tion on benz benzene ene and a bott bottoms oms produc productt cont contain aining ing 0.98 0.98 mass fraction toluene. A reflux ratio of 3.5 is to be used. The feed is liquid at its boiling poin point, t, feed feed is is to to the the opt optim imal al tray, tray, and the the ref reflux lux is at satu satura rati tion on temp temper eratu ature re.. (a) Determine the quantity of top and bottom products. (b) Determine the number of stages required.
y x
EQUILIBRIUM DATA IN MOLE FRACTION BENZENE, 101 kPa 0.21 0.37 0.51 0.64 0.72 0.79 0.86 0.91 0.96 0.98 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95
Subject: Distillation of a mixture of benzene and toluene at 101 kPa for specified reflux ratio and product compositions. Given: Feed of 30 kg/h of saturated liquid feed containing 40 mass% benzene and 60 mass% toluene. Distillate to contain 97 mass% benzene and bottoms to contain 98 mass% toluene. Reflux ratio = 3.5 and feed is to optimal stage. Table of vapor-liquid equilibrium data in mole fractions at 101 kPa. Assumptions: Total condenser and partial reboiler. Saturated liquid reflux. Constant molar overflow. Find: (a) Flow rates of distillate and bottoms. (b) Number of equilibrium stages needed.
solve the material balance in mass units. Then convert to mole fractions Analysis: First solve so that the McCabe-Thiele method can be used for part (b) Overall mass balance: 30 = D + D + B B (1) Overall benzene mass balance: 0.4(30) 0.4( 30) = 12 = 0.97 0.9 7 D + D + 0.02 B B (2) Solving Eqs. (1) and (2): D = D = 12 kg/h B = B = 18 kg/h Converting to moles with molecular weights of 78.11 for benzene and 92.13 for toluene,
Product Prod uct Dist Distil illa late te Bottom Bottomss
Benzene Mass fraction Mole fraction 0.97 0.974 0.02 0.024
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Toluene Mass fraction Mole fraction 0.03 0.026 0.98 0.976
Solution for (a): D = 12 kg/h, B = 18 kg/h with compositions given by the previous table (b) Because benzene is the more volatile component of the feed the x and y coordinates will be those of benzene in the diagram. In mole fraction, the feed concentration for benzene is 0.44. For a saturated liquid feed, the q-line is vertical and passes through x = 0.44. The slope of the rectifying operating line, L/V , is obtained from Eq. (7-7), using the specified reflux ratio = 3.5 L R 3.5 = = = 0.778 V R + 1 4.5 For saturated liquid reflux, the rectifying line passes through the point (0.974, 0.974). See the McCabe-Thiele construction below, where it is seen that slightly more than 10 stages + a partial reboiler acting as an equilibrium stage are required. The top 5 stages are in the rectifying section.
1
2
1
3 4 0.8
5
Equilibrium Curve
r o p a v n i 0.6 n o i t c a r f e l o m e n e z 0.4 n e b , y
R. S. op. line 6
7
S. S. op. line 8 q-line
9 0.2
10 R 0
zF 0
0.2
0.4
0.6
0.8
x, benzene mole fraction in liquid
Figure 1. McCabe-Thiele Diagram for Exercise 7-13
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Exercise 7.15 A continuous distillation operation with a reflux ratio ( L/ D) of 3.5 yields a distillate containing 97 wt% B (benzene) and bottoms containing 98 wt% T (toluene). Due to weld failures, the 10 plates in the bottom section of the column are ruined, but the 14 upper plates are intact. It is suggested that the column still be used, with the feed ( F ) as saturated vapor at the dew point, with F = 13,600 kg/h containing 40 wt% B and 60 wt% T. Assuming that the plate efficiency remains unchanged at 50%: (a) Can this column still yield a distillate containing 97 wt% B, (b) How much distillate can we get, and (c) What will the composition of the residue be in mole percent? For vapor-liquid equilibrium data, see Exercise 7.13
Subject: Effect of loss of plates in a distillation column separating a benzene-toluene mixture. Given: Saturated vapor feed of 13,600 kg/h of 40 wt% benzene and 60 wt% toluene. Column with 14 plates above the feed location. Plate efficiency is 50%. Reflux ratio is 3.5. Previously, with 10 plates in the stripping section, column could achieve a distillate of 97 wt% benzene and a bottoms of 98 wt% toluene. Vapor-liquid equilibrium data in Exercise 7.13. Assumptions: Total condenser and partial reboiler. Constant molar overflow. Find: (a) If column with 10 inoperable plates can yield a distillate of 97 wt% benzene, assuming that we no longer can achieve the 98 wt% bottoms product. (b) The distillate flow rate. (c) The composition of the bottoms Analysis: (a) First convert the mass fraction of benzene to mole fraction, using molecular weights of 78.11 for benzene and 92.13 for toluene. z F = 0.44. For a distillate of 97 wt% benzene, the mole fraction is 0.974 With a reflux ratio of 3.5, from Eq. (7-7), the slope of the rectifying section operating line is 0.778 The q-line is a horizontal line at y = 0.44. For 14 plates with 50% efficiency, the column has the equivalent of 7equilibrium stages + 1 for the partial reboiler, The McCabe-Thiele construction is shown on the next page, where it is seen that it is possible to obtain the desired distillate composition.
(b) and (c) From the McCabe-Thiele diagram, the mole fraction of benzene in the bottoms is x B = 0.25. As a weight fraction this corresponds to 0.25( 78.11) = 0.22 weight fraction or 22 wt% benzene 0.25( 78.11) + 0.75(92.13) Compute the distillate rate by overall mass balances. Overall total mass balance: 13,600 = D + B (1) Overall benzene mass balance: 5,440 = 0.97 D + 0.22 B (2) Solving Eqs. (1) and (2): D = 3,264 kg/h, B = 10,336 kg/h
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1
2
1
3 4 0.8
5
Equilibrium Curve
r o p a v n i 0.6 n o i t c a r f e l o m e n e z 0.4 n e b , y
6
R. S. op. line
7 q-line
R
0.2
0
0
0.2
0.4
0.6
0.8
x, benzene mole fraction in liquid
Figure 1. McCabe-Thiele Diagram for Exercise 7-15
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Exercise 10.25 Use the Chao-Seader or Grayson-Streed correlation for thermodynamic properties to calculate product compositions, stage temperatures, interstage flow rates and compositions, reboiler duty, and condenser duty for the distillation specifications in Figure 10.32 Compare your results with those given in the Chemical Engineers’ Handbook , Sixth Edition, pp. 13-42 to 13-45. Why do the two solutions differ?
Vapor distillate 48.9 lbmol/h
1 Feed bubble-point liquid at 120 psia C3 iC4 nC4 iC5
lbmol/h 5 15 25 20
126.1 lbmol/h 5
120 psia throughout
9
Bottoms
Figure 10-32 Data for Exercise 10.25 Subject: Distillation of a hydrocarbon mixture and comparison with solution in Perry’s Handbook. Given: Bubble-point liquid feed of composition given below. Column has partial condenser, partial reboiler, and 9 equilibrium stages in the column, with operation at 120 psia. Refluz rate = 126.1 lbmol/h and vapor distillate rate = 48.9 lbmol/h. Grayson-Streed correlation for K - values and the Lee-Kesler model for enthalpies. Find: Product compositions, stage temperatures, insterstage flow rates and compositions, reboiler duty, and condenser duty. Analysis: The calculations were made with the RADFRAC model of the Aspen Plus v10.1simulator, with the following specifications: Number of stages: 11 (includes partial condenser and partial reboiler) Partial condenser Distillate rate: 48.9 lbmol/h Reflux rate: 126.1 lbmol/h
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Feed stage: 6 from the top Stage 1/Condenser pressure: 120 psi (no pressure drop) The feed is given as a bubble-point liquid (vapor fraction = 0) at 120 psia. Using the Grayson-Streed correlation, the temperature is computed to be 180.3oF. Based on the feed composition, the distillate rate of 48.9 lbmol/h corresponds to a desired split between n-butane and isopentane. The calculations converged rapidly in 2 outer-loop iterations with results given below and on the following pages. Condenser duty = 1,047,318 Btu/h Reboiler duty = 1,495,715 Btu/h Top temperature = 161.3oF Bottom temperature = 231.3o F Stream Temperature F Pressure PSI Vapor Frac Mole Flow LBMOL/HR Mass Flow LB/HR Volume Flow CUFT/HR Enthalpy MMBTU/HR Mole Flow LBMOL/HR C3 IC4 NC4 IC5 NC5
1 180.3 120.00 0.000 100.000 6513.684 198.821 -6.584
2 161.3 120.00 1.000 48.900 2850.829 2313.789 -2.650
3 231.3 120.00 0.000 51.100 3662.855 113.891 -3.486
5.000 15.000 25.000 20.000 35.000
4.998 14.798 23.493 3.482 2.129
0.002 0.202 1.507 16.518 32.871
Temp Pressure Liquid flow Stage F psi lbmol/hr 1 161.3 120 126.10 2 174.4 120 122.59 3 184.8 120 120.35 4 192.7 120 119.18 5 198.0 120 118.62 6 201.5 120 220.08 7 210.9 120 221.78 8 218.4 120 223.38 9 224.0 120 224.78 10 228.2 120 225.85 11 231.3 120 51.10
Vapor Liquid flow feed lbmol/hr lbmol/hr 48.90 0 175.00 0 171.49 0 169.25 0 168.08 0 167.52 100 168.98 0 170.68 0 172.28 0 173.68 0 174.75 0
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Vapor Mixed Liquid Vapor feed feed product product lbmol/hr lbmol/hr lbmol/hr lbmol/hr 0 0 0 48.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 51.1 0
Vapor Composition Profiles
6 . 0 5 5 . 0 5 . 0 5 4 . 0 4 . 0 ) 5 c 3 . a r 0 f e 3 l . o 0 m ( 5 2 . Y 0 2 . 0 5 1 . 0 1 . 0 5 0 . 0
1
C3 IC4 NC4 IC5 NC5
2
3
4
5 6 . 0 6 . 0 5 5 . 0 5 . 0 5 4 . 0 4 . ) 0 c a r 5 f 3 . e 0 l o 3 m . ( 0 5 X 2 . 0 2 . 0 5 1 . 0 1 . 0 5 0 . 0
1
5
6 Stage
7
8
9
10
11
Liquid Composition Profiles
C3 IC4 NC4 IC5 NC5
2
3
4
5
6 Stage
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7
8
9
10
11
The above results for the product compositions are compared to the results in Perry’s Handbook as follows:
Component Propane Isobutane n-Butane Isopentane n-Pentane Total
Feed, lbmol/h 5.00 15.00 25.00 20.00 35.00 100.00
Perry’s Handbook Distillate, Bottoms, lbmol/h lbmol/h 5.00 0.00 14.82 0.18 23.60 1.40 3.21 16.79 2.30 32.70 48.93 51.07
This exercise Distillate, lbmol/h 5.00 14.80 23.49 3.48 2.13 48.90
Bottoms, lbmol/h 0.00 0.20 1.51 16.52 32.87 51.10
The example in Perry’s Handbook is for a column with a total condenser, while this exercise calls for a partial condenser. Thus, this exercise has 11 instead of 10 equilibrium stages. Nevertheless, the solution from Perry’s Handbook shows a slightly sharper separation. This is probably due to the differences in K -values. For example at a midcolumn temperature of 210oF, the Grayson-Streed correlation predicts a relative volatility between n-butane and isopentane of 1.84, while the graphical correlation used in Perry’s Handbook predicts a higher value of 1.94
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