3.7b. Mass-transfer resistances during absorption.
For a system in which component A is transferring from the gas phase to the liquid phase, the equilibrium relation is given by
where pA,i is the equilibrium partial pressure in atm and xA,i is the equilibrium liquid concentration in molar fraction. At one point in the apparatus, the liquid stream contains 4.5 mole % and the gas stream contains 9.0 mole % A. The total pressure is 1 atm. The individual gas-film coefficient at this point is kG = 3.0 mole/m2-s-atm. Fifty per cent of the overall resistance to mass transfer is known to be encountered in the liquid phase. Evaluate
a) the overall mass-transfer coefficient, Ky;
Solution
b) the molar flux of A;
Solution
(yAe = yA*)
c) The liquid interfacial concentration of A.
Solution
3.8d. Absorption of ammonia by water: use of F-type mass-transfer coefficients.
Modify the Mathcad program in Figure 3.6 to repeat Example 3.5, but with yA,G = 0.70 and xA,L = 0.10. Everything else remains constant.
Solution
Initial guesses
3.9d. Absorption of ammonia by water: use of F-type mass-transfer coefficients.
Modify the Mathcad program in Figure 3.6 to repeat Example 3.5, but with FL = 0.0050 kmol/m2-s. Everything else remains constant.
Solution
Initial guesses
3.10b. Mass-transfer resistances during absorption of ammonia.
In the absorption of ammonia into water from an air-ammonia mixture a 300 K and 1 atm, the individual film coefficients were estimated to be kL = 6.3 cm/hr and kG = 1.17 kmol/m2-hr-atm. The equilibrium relationship for very dilute solutions of ammonia in water at 300 K and 1 atm is
Determine the following mass-transfer coefficients:
a) ky
Solution
b) kx
Solution
c) Ky
Solution
d) Fraction of the total resistance to mass transfer that resides in the gas phase.
Solution
3.11b. Mass-transfer resistances in hollow-fiber membrane contactors.
For mass transfer across the hollow-fiber membrane contactors described in Example 2.13, the overall mass-transfer coefficient based on the liquid concentrations, KL, is given by (Yang and Cussler, AIChE J., 32, 1910, Nov. 1986)
where kL, kM, and kc are the individual mass-transfer coefficients in the liquid, across the membrane, and in the gas, respectively; and H is Henry's law constant, the gas equilibrium concentration divided by that in the liquid. The mass-transfer coefficient across a hydrophobic membrane is from (Prasad and Sirkar, AIChE J., 34, 177, Feb. 1988)
where DAB = molecular diffusion coefficient in the gas filling the pores,
eM = membrane porosity,
tM = membrane tortuosity,
d = membrane thickness.
For the membrane modules of Example 2.13, eM = 0.4,tM = 2.2, and d = 25 ´ 10Ð6 m (Prasad and Sirkar, 1988).
a) Calculate the corresponding value of kM.
Solution
For oxygen in nitrogen at 298 K and 1 atm:
b) Using the results of part (a), Example 2.13, and Problem 2.25, calculate KL, and estimate what fraction of the total resistance to mass transfer resides in the liquid film.
Solution
From Example 2.13:
From Prob. 2.25:
Virtually all of the resistance resides in the liquid phase.
3.12c. Combined use of F- and k-type coefficients: absorption of low-solubility gases.
During absorption of low-solubility gases, mass transfer from a highly concentrated gas mixture to a very dilute liquid solution frequently takes place. In that case, although it is appropriate to use a k-type mass-transfer coefficient in the liquid phase, an F-type coefficient must be used in the gas phase. Since dilute liquid solutions usually obey Henry's law, the interfacial concentrations during absorption of low-solubility gases are related through yA,i = mxA,i.
a) Show that, under the conditions described above, the gas interfacial concentration satisfies the equation
Solution
In the gas phase:
In the liquid phase:
For Henry's Law:
Then:
Rearranging:
b) In a certain apparatus used for the absorption of SO2 from air by means of water, at one point in the equipment the gas contained 30% SO2 by volume and was in contact with a liquid containing 0.2% SO2 by mole. The temperature was 303 K and the total pressure 1 atm. Estimate the interfacial concentrations and the local SO2 molar flux. The mass-transfer coefficients were calculated as FG = 0.002 kmol/m2-s, kx = 0.160 kmol/m2-s. The equilibrium SO2 solubility data at 303 K are (Perry and Chilton, 1973):
kg SO2/100 kg water Partial pressure of SO2, mm Hg (torr)
0.0 0
0.5 42
1.0 85
1.5 129
2.0 176
2.5 224
Solution
Define: w = kg SO2/100 kg water
p = Partial pressure of SO2, mm Hg (torr)
Initial guess:
3.13d. Distillation of a mixture of methanol and water in a packed tower: use of F-type mass-transfer coefficients.
At a different point in the packed distillation column of Example 3.6, the methanol content of the bulk of the gas phase is 76.2 mole %; that of the bulk of the liquid phase is 60 mole %. The temperature at that point in the tower is around 343 K. The packing characteristics and flow rates at that point are such that FG = 1.542 ´ 10Ð3 kmol/m2-s, and FL = 8.650 ´ 10Ð3 kmol/m2-s. Calculate the interfacial compositions and the local methanol flux. To calculate the latent heats of vaporization at the new temperature, modify the values given in Example 3.6 using Watson's method (Smith, et al., 1996):
For water, Tc = 647.1 K; for methanol, Tc = 512.6 K
Solution
For methanol (A)
For water (B)
Parameters
Initial estimates