Displacement of fluid from a pulse

[RiverRunner]

Hi,

The following question is related to my individual design for an engineering subject.

I am trying to calculate the fluid displacement in a packed vessel when air is pulsed through a pulse leg, which is connected to the bottom of the vessel. Using equations from literature, I have calculated the amplitude and frequency of the pulse to be 0.4m and 1 s^-1, respectively.The following picture shows the general setup, although the pulse leg is above the vessel.

Help/Tips/Suggestions to do this would be fantastic, I only need a starting point.

Information:

There are two fluids inside the vessel.
The ratio of fluid 1 to fluid 2 is 2:1.
The density of fluid 2 is 1100 kg/m^3
The density of fluid 1 is 850 kg/m^3
The space the packing takes up in the column is 70%

The diameter of the vessel is 0.4m.
The height of the vessel is 1.7m
The height of the pulse leg is 2.2m
The amplitude of the pulse is 0.4m
The frequency of the pulse is 1s^-1

Many thanks

 

[CWatters]

Not sure I'm the best person to answer but...

Air cannot be injected unless the air pressure is sufficient to overcome the pressure in the vessel due to the density of the fluids etc. If the pressure is "only just" sufficient then the volume displaced initially will be the same as the volume of air injected. If the air pressure is much higher then the air bubble will expand as soon as it's injected displacing more fluid. I'm not sure there is enough info to proceed unless you assume that the air pressure is "only just" enough for injection?

Then the air bubble may expand as it rises through the fluids and the pressure reduces causing more fluid to be pushed out.

So I'd start by working out the volume of air injected. What do you mean by "The amplitude of the pulse is 0.4m"? Could you just multiply that by the cross sectional area of the pulse pipe to get the volume of air per pulse?