(a) Consider the hollow-fiber BFW deaerator described in Example 2.14. If only oxygen diffuses across the membrane, calculate the gas volume flow rate and composition at the lumen outlet. The water enters the shell side at \(298 \mathrm{~K}\) saturated with atmospheric oxygen, which means a dissolved oxygen concentration of \(8.38 \mathrm{mg} / \mathrm{L}\).

(b) Calculate the mass-transfer coefficient at the average conditions inside the lumen. Neglect the thickness of the fiber walls when estimating the gas velocity inside the lumen.

Data From Example 2.14:-

Boiler feed water (BFW) must be deaerated to avoid corrosion problems in the boilers. Hollow fibers made of microporous polypropylene can be used for extremely fast removal of dissolved oxygen from water, therefore making a compact BFW deaerator possible (Yang and Cussler, 1986). For a given boiler, 40,000 kg/h of BFW is needed. Design a hollow-fiber membrane module for that purpose, if the unit can remove 99% of the dissolved oxygen present in natural waters at 298 K.