CL 351                                   Homework # 6

 

Due date: 6 October 2005

 

 

  1. The following questions concern the distillation of benzene and p-xylene, available as a saturated vapour mixture at 1 atm pressure, containing 40 mol% benzene.  The vapour liquid equilibrium can be described with a constant relative volatility of 4.82.  For saturated liquid products with purities of 95 mol%, answer the following questions by making McCabe Thiele construction on a graph sheet.  The average latent heat of the mixture is 33.37 kJ/mol.

a.       The minimum number of equilibrium stages.

b.       The minimum reflux and reboil ratios.

c.       The minimum vapour flows (relative to feed flow) in each column section, and the corresponding energy requirements.

d.       The number of equilibrium stages in each column section, and the energy requirements at a reflux ratio 60% larger than the minimum.

e.       Make a plot of reflux ratio Vs. number of plates.  Use Matlab program to produce data; start with a high reflux ratio, gradually reduce it and make sure you have enough data to generate a smooth curve.

 

2.       Consider the distillation of a mixture containing methanol and 1,4-dioxane in a column operating at 1 atmosphere.  The feed contains 3,000 lb/hr of methanol and 7,000 lb/hr of dioxane (Mol. Wt. = 88 g/gmol) as a saturated liquid mixture, also at 1 atm pressure.  The VLE data are tabulated below.  It is desired to recover 98% of the methanol, which should have a purity of 95 mol%.  For a reflux ratio of 2.5, plot the liquid composition, vapour composition and temperature profiles in the column.

 

T, oC

101.1

94.9

89.6

82.2

76.9

73.1

70.7

68.8

67.5

66.2

65.1

64.7

64.5

x (MeOH)

0

0.05

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.95

1

y (MeOH)

0

0.21

0.37

0.54

0.66

0.74

0.78

0.82

0.85

0.89

0.95

0.97

1

 

1.       A 600 lbmol/hr mixture of 40 mol% propane and 60 mol% propylene is to be separated to produce a distillate that is 99% pure in propane and a bottoms product 95% pure in propylene.  The mixture is available at 70oF and 1 atm pressure. To what pressure the mixture must be compressed in order to use cooling water as cooling medium in the condenser.  The water can be supplied at 25oC and the overhead from the column is 20oC above the cooling water temperature.  Refer to Wankat’s book for equations to compute K values for propane and propylene.

 

2.       An equimolar saturated liquid feed containing ethanol and water is being separated in a distillation column with ten equilibrium stages to produce a distillate with 80 mol% ethanol and bottoms with 1 mol% ethanol.  What is the required reflux ratio?  To play it safe, operator runs the column so that distillate is 82 mol% pure in ethanol.  At what reflux ratio is the column being operated?  What is the percentage rise in the steam consumption in the reboiler for this reflux ratio?  In order to drive home the point that raising product composition, even by small percentage, may rise the steam consumption dramatically, make a plot of steam consumption Vs. purity as the purity is changed in steps of 0.01 from 0.8 to 0.85.  Saturated steam at 120oC is available for the reboiler. (enthalpy of steam = 39641.4 kJ/kmol, enthalpy of saturated water at 100oC = 40624.2 kJ/kmol).  Use Matlab program to solve this problem.

 

3.       Ethylbenzene(1), ortho-xylene(2), p-xylene(3) and m-xylene(4) having same molecular formula are produced in naphtha reforming units in oil refineries.  The xylene isomers are intermediates in the manufacture of polyesters, films, fibers and, ethylbenzene is raw material for styrene and poly styrene production.  The boiling points of four compounds are quite close; 136.2, 144.4, 138.3, and 139.1 degrees Celsius in the order stated above and their mole fractions in the feed are 0.25, 0.16, 0.14 and 0.45.  The relative volatilities of ethylbenzene, para and meta xylenes with respect to ortho xylene are 1.235, 1.170, 1.147, respectively.  Ortho xylene and sometimes ethylbenzene are separated by distillation; relative volatility between para and meta isomers is too low to warrant distillation as a means of separating them.

 

The mixture can be separated in two distillation schemes as shown in the Figures below.  In Figure a, ortho xylene is separated in the first column and then ethylbenzene is distilled off in the second column.  Bottoms purity in the first column is 95 mol% o-xylene and its fractional reovery is 99.9%.  Distillate purity in the second column is 99.7% ethylbenzene and its fractional recovery is 90.3%.  Treat 1, 3 and 4 as one compound in the first column and take relative volatility of this compound with respect to ortho xylene as 1.147.  In the second column, group 2, 3 into one compound and approximate its relative volatility with respect to ethylbenzene as 1.056.

 

In Figure b, ethylbenzene is distilled off in the first column and then ortho xylene is removed in the second column.  Consider same purities and fractional recoveries of ethylbenzene and o-xylene as in Figure a.  For the first column in Figure b, group 2, 3, 4 as one compound whose relative volatility with respect to 1 is 1.056.  In the second column, treat 2, 3 as one mixture with its relative volatility with respect to 4 as 1.147.

 

Which configuration do you recommend?  Make comparison of minimum vapour rate and minimum number of stages for your recommendation.  Use Matlab programs to solve this problem.