4.19c,d. Batch wastewater aeration using spargers; effect of liquid depth.
Consider the situation described in Problem 4.18. According to Eckenfelder (2000), for most types of bubble-diffusion aeration systems the volumetric mass-transfer coefficient will vary with liquid depth Z according to the relationship
where the exponent n has a value near 0.7 for most systems. For the aeration pond of Problem 4.18, calculate kLa at values of Z = 3m, 4m, 6m, and 7 m. Estimate the corresponding value of n from regression analysis of the results. Hint: Remember that the total volume of the pond must remain constant, therefore the cross-sectional area of the pond must change as the water depth changes.
Solution
Using the program developed in Prob 4.18, the following vector of results is generated
4.20c. Flooding conditions in a packed cooling tower.
A cooling tower, 2 m in diameter, packed with 75-mm ceramic Hiflow rings, is fed with water at 316 K at a rate of 25 kg/m2-s. The water is contacted with air, at 300 K and 101.3 kPa essentially dry, drawn upward countercurrently to the water flow. Neglecting evaporation of the water and changes in the air temperature, estimate the volumetric rate of airflow, in m3/s, which would flood the tower.
Solution
LMV = liquid mass velocity GMV = gass mass velocity
Introduce a units conversion factor in Fp
Initial estimate of GMV
4.21c,d. Design of a sieve-tray column for ethanol absorption
Repeat the calculations of Examples 4.6, 4.7, 4.8, and 4.9 for a column diameter corresponding to 50% of flooding.
Solution
From the Sieve-Plate Design Program, the following results are obtained for f = 0.5
D = 1.176 m t = 0.6 m DP = 590 Pa/tray
Froude No. = 1.22 (no excessive weeping) E = 0.0165
EOG = 0.8123 EMG = 0.8865 EMGE = 0.878
4.22c,d. Design of a sieve-tray column for aniline stripping.
A sieve-tray tower is to be designed for stripping an aniline (C6H7N)-water solution with steam. The circumstances at the top of the tower, which are to be used to establish the design, are:
Temperature = 371.5 K Pressure = 100 kPa
Liquid:
Rate = 10.0 kg/s Composition = 7.00 mass % aniline
Density = 961 kg/m3 Viscosity = 0.3 cP
Surface tension = 58 dyne/cm
Diffusivity = 4.27 ´ 10Ð5 cm2/s (est.) Foaming factor = 0.90
Vapor:
Rate = 5.0 kg/s Composition = 3.6 mole % aniline
Density = 0.670 kg/m3 Viscosity = 118 mP (est.)
Diffusivity = 0.116 cm2/s (est.)
The equilibrium data at this concentration indicates that m = 0.0636 (Treybal, 1980).
(a) Design a suitable cross-flow sieve-tray for such a tower. Take do = 5.5 mm on an equilateral-triangular pitch 12 mm between hole centers, punched in stainless steel sheet metal 2 mm thick. Use a weir height of 40 mm. Design for a 75% approach to the flood velocity. Report details respecting tower diameter, tray spacing, weir length, gas-pressure drop, and entrainment in the gas. Check for excessive weeping.
Solution
For aniline, the molecular weight = 93. The average molecular weight of the gas = 20.7.
The composition of the liquid is calculated as 1.4 mole % aniline, the average molecular weight = 19.1.
From the Sieve-Plate Design Program, the following results are obtained for f = 0.75
D = 1.93 m t = 0.6 m DP = 435 Pa/tray
Froude No. = 0.93 (no excessive weeping) E = 0.045
Weir length = 1.40 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.716 EMG = 0.722 EMGE = 0.720
4.23c,d. Design of a sieve-tray column for aniline stripping.
Repeat Problem 4.22, but for a 45% approach to flooding. Everything else remains the same as in Problem 4.22.
Solution
From the Sieve-Plate Design Program, the following results are obtained for f = 0.45
D = 2.49 m t = 0.6 m DP = 399 Pa/tray
Froude No. = 0.491 ( excessive weeping) E = 0.0173
Weir length = 1.81 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.660 EMG = 0.666 EMGE = 0.665
4.24c,d. Design of a sieve-tray column for methanol stripping.
A dilute aqueous solution of methanol is to be stripped with steam in a sieve-tray tower. The conditions chosen for design are:
Temperature = 368 K Pressure = 101.3 kPa
Liquid:
Rate = 0.25 kmol/s Composition = 15.0 mass % methanol
Density = 961 kg/m3 Viscosity = 0.3 cP
Surface tension = 40 dyn/cm
Diffusivity = 5.70 ´ 10Ð5 cm2/s (est.) Foaming factor = 1.0
Vapor:
Rate = 0.1 kmol/s Composition = 18 mole % methanol
Viscosity = 125 mP (est.) Diffusivity = 0.213 cm2/s (est.)
The equilibrium data at this concentration indicates that m = 2.5 (Perry and Chilton, 1973).
(a) Design a suitable cross-flow sieve-tray for such a tower. Take do = 6.0 mm on an equilateral-triangular pitch 12 mm between hole centers, punched in stainless steel sheet metal 2 mm thick. Use a weir height of 50 mm. Design for 80% approach to the flood velocity. Report details respecting tower diameter, tray spacing, weir length, gas-pressure drop, and entrainment in the gas. Check for excessive weeping.
Solution
From the Sieve-Plate Design Program, the following results are obtained for f = 0.80
D = 1.174 m t = 0.6 m DP = 386 Pa/tray
Froude No. = 0.878 (no excessive weeping) E = 0.052
Weir length = 0.853 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.5987 EMG = 0.707 EMGE = 0.700
4.25c,d. Sieve-tray column for methanol stripping; effect of hole size.
Repeat Problem 4.24, but changing the perforation size to 4.5 mm, keeping everything else constant.
Solution
From the Sieve-Plate Design Program, the following results are obtained for f = 0.80
D = 1.174 m t = 0.6 m DP = 686 Pa/tray
Froude No. = 1.561 (no excessive weeping) E = 0.076
Weir length = 0.853 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.793 EMG = 0.936 EMGE = 0.918
4.26c,d. Design of sieve-tray column for butane absorption.
A gas containing methane, propane, and n-butane is to be scrubbed countercurrently in a sieve-tray tower with a hydrocarbon oil to absorb principally the butane. It is agreed to design a tray for the circumstances existing at the bottom of the tower , where the conditions are:
Temperature = 310 K Pressure = 350 kPa
Liquid:
Rate = 0.50 kmol/s Average molecular weight = 150
Density = 850 kg/m3 Viscosity = 1.6 cP
Surface tension = 25 dyn/cm
Diffusivity = 1.14 ´ 10Ð5 cm2/s (est.) Foaming factor = 0.9
Vapor:
Rate = 0.3 kmol/s Composition = 86% CH4, 12% C3H8, 2% C4H10
Viscosity = 113 mP (est.) Diffusivity = 0.035 cm2/s (est.)
The system obeys Raoult's law; the vapor pressure of n-butane at 310 K is 3.472 bar (Reid et al., 1987).
(a) Design a suitable cross-flow sieve-tray for such a tower. According to Bennett and Kovak (2000), the optimal value of the ratio Ah/Aa is that which yields an orifice Froude number, Fro = 0.5. Design for the optimal value of do on an equilateral-triangular pitch 12 mm between hole centers, punched in stainless steel sheet metal 2 mm thick. Use a weir height of 50 mm. Design for a 75% approach to the flood velocity. Report details respecting tower diameter, tray spacing, weir length, gas-pressure drop, and entrainment in the gas.
Solution
The slope of the equilibrium curve is approximately 1.0. The average molecular weight of the gas is 20.2. By trial-and-error, using the Sieve-Plate Design Program, it was found that the orifice diameter that results in a Froude number = 0.5 is do = 3.43 mm.
From the Sieve-Plate Design Program, the following results are obtained for f = 0.75
D = 2.73 m t = 0.6 m DP = 811 Pa/tray
Froude No. = 0.5 (no excessive weeping) E = 0.013
Weir length = 2.28 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.833 EMG = 1.038 EMGE = 1.034
4.27c,d. Design of sieve-tray column for ammonia absorption.
A process for making small amounts of hydrogen by cracking ammonia is being considered, and residual uncracked ammonia is to be removed from the resulting gas. The gas will consist of H2 and N2 in the molar ratio 3:1, containing 3% NH3 by volume. The ammonia will be removed by scrubbing the gas countercurrently with pure liquid water in a sieve-tray tower. Conditions at the bottom of the tower are:
Temperature = 303 K Pressure = 200 kPa
Liquid:
Rate = 6.0 kg/s Average molecular weight = 18
Density = 996 kg/m3 Viscosity = 0.9 cP
Surface tension = 68 dyn/cm
Diffusivity = 2.42 ´ 10Ð5 cm2/s (est.) Foaming factor = 1.0
Vapor:
Rate = 0.7 kg/s
Viscosity = 113 mP (est.) Diffusivity = 0.230 cm2/s (est.)
For dilute solutions, NH3-H2O follows Henry's law, and at 303 K the slope of the equilibrium curve is m = 0.85 (Treybal, 1980).
(a) Design a suitable cross-flow sieve-tray for such a tower. Take do = 4.75 mm on an equilateral-triangular pitch 12.5 mm between hole centers, punched in stainless steel sheet metal 2 mm thick. Use a weir height of 40 mm. Design for an 80% approach to the flood velocity. Report details respecting tower diameter, tray spacing, weir length, gas-pressure drop, and entrainment in the gas. Check for excessive weeping.
Solution
From the Sieve-Plate Design Program, the following results are obtained for f = 0.80
D = 0.775 m t = 0.5 m DP = 624 Pa/tray
Froude No. = 1.033 (no excessive weeping) E = 0.048
Weir length = 2.28 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.806 EMG = 0.85 EMGE = 0.847
4.28c,d. Design of sieve-tray column for toluene-methylcyclohexane distillation.
A sieve-tray tower is to be designed for distillation of a mixture of toluene and methylcyclohexane. The circumstances which are to be used to establish the design, are:
Temperature = 380 K Pressure = 98.8 kPa
Liquid:
Rate = 4.8 mole/s Composition =48.0 mol % toluene
Density = 726 kg/m3 Viscosity = 0.22 cP
Surface tension = 16.9 dyne/cm
Diffusivity = 7.08 ´ 10Ð5 cm2/s (est.) Foaming factor = 0.80
Vapor:
Rate = 4.54 mole/s Composition =44.6 mole % toluene
Density = 2.986 kg/m3 Viscosity = 337 mP (est.)
Diffusivity = 0.0386 cm2/s (est.)
The equilibrium data at this concentration indicates that m = 1.152.
(a) Design a suitable cross-flow sieve-tray for such a tower. Take do = 4.8 mm on an equilateral-triangular pitch 12.7 mm between hole centers, punched in stainless steel sheet metal 2 mm thick. Use a weir height of 50 mm. Design for a 60% approach to the flood velocity. Report details respecting tower diameter, tray spacing, weir length, gas-pressure drop, and entrainment in the gas. Check for excessive weeping.
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
a) From the Sieve-Plate Design Program, the following results are obtained for f = 0.60
D = 0.6 m t = 0.5 m DP = 295 Pa/tray
Froude No. = 0.585 (no excessive weeping) E = 0.007
Weir length = 0.436 m
(b) Estimate the tray efficiency corrected for entrainment for the design reported in part (a).
Solution
EOG = 0.611 EMG = 0.712 EMGE = 0.710