A semipermeable membrane is used for the partial removal of...

A semipermeable membrane is used for the partial removal of oxygen from air that is blown through a grain elevator storage facility. Ambient air (79\% nitrogen, 21\% oxygen on a mole basis) is compressed to an appropriate pressure, cooled to ambient temperature $25^{\circ} \mathrm{C},$ and then fed through a bundle of hollow polymer fibers that selectively absorb oxygen, so the mixture leaving at $120 \mathrm{kPa}, 25^{\circ} \mathrm{C}$, contains only $5 \%$ oxygen, shown in Fig. $\mathrm{P} 12.128 .$ The absorbed oxy. gen is bled off through the fiber walls at $40 \mathrm{kPa}$, $25^{\circ} \mathrm{C},$ to a vacuum pump. Assume the process to be reversible and adiabatic and determine the minimum inlet air pressure to the fiber bundle.

Key Concepts

Ideal Gas Behavior and Partial Pressures

Assuming that gases behave ideally simplifies the analysis of separation processes by allowing the use of the ideal gas law. Under this assumption, properties such as partial pressures and mole fractions can be directly related, which is fundamental in calculating equilibrium conditions and determining the necessary process parameters, like the inlet pressure required for selective separation.

Minimum Work of Separation

This principle involves calculating the theoretical minimum amount of work required to separate a mixture into components of specified compositions. It is derived from the change in free energy during the separation and sets the benchmark for evaluating the efficiency of practical separation systems.

Adiabatic Process

An adiabatic process is one in which there is no heat exchange with the surroundings, meaning all changes in the system’s energy are due to work. When a process is both adiabatic and reversible, it is also isentropic, allowing for simplifications in determining work interactions and state changes in gas mixtures during separation.

Reversible Process Analysis

A reversible process is an idealization in thermodynamics where the process proceeds infinitesimally slowly with no increase in entropy. Its analysis provides a theoretical lower bound on the energy (or work) required, which is crucial for determining the minimum input conditions needed for efficient separation processes.

Membrane Separation

This concept involves using a semipermeable membrane that selectively allows certain gas species to pass through while retaining others. It is a key separation technology where the membrane's differential permeability is exploited to separate a gas mixture into streams with differing compositions.

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