Question

a sorbent planned for use in separating methane from hydrogen is tested in the lab. initial conditions for the sorbent bed are only hydrogen present, a pressure of 3 atm and a tempera- ture of 298 k. the column containing the sorbent is 50 cm in length and has a diameter of 2 cm. a methane feed of 5 liters per minute at 10 mole% is started, and the center of the outlet wave passes 35 seconds later, with a total width of 12 seconds (0.5 to 9.5 mole%) and was observed to be symmetric. (a) determine the shock velocity for methane, the width of the mass transfer zone, and the fractional use of the bed using the lub method.

Answer 1

Property Value

Shock velocity (u_s) 0.0143 m/s

Mass transfer zone

width (delta_z) 0.171 m

Fractional use of

bed (epsilon) 0.343 .

The Lub method is a simple and effective way to estimate the shock velocity, mass transfer zone width, and fractional use of the bed for a sorbent bed used to separate two gases.

The method is based on the assumption that the outlet wave is symmetric and that the width of the mass transfer zone is small compared to the length of the bed.

The shock velocity is the velocity at which the methane concentration wave travels through the bed.

The mass transfer zone width is the width of the region in the bed where the methane concentration is changing.

The fractional use of the bed is the fraction of the bed that is being used to separate the methane from the hydrogen.

The Lub method is a good approximation for cases where the shock velocity is much greater than the mass transfer zone width.

In this case, the shock velocity is 0.0143 m/s and the mass transfer zone width is 0.171 m.

This means that the shock velocity is about 12 times greater than the mass transfer zone width, so the Lub method is a good approximation.

The fractional use of the bed is 0.343, which means that about 34% of the bed is being used to separate the methane from the hydrogen.

This is a relatively low fractional use of the bed, which means that the sorbent is very effective at separating the methane from the hydrogen.