The classic method would be to locate a gamma source on one side of the bed and number of gamma detectors on the opposite side of the bed.  This will work if the walls are relatively thin and the bed material is dense.  If the bed material I hydrogenous or of low atomic weight you could do the same thing with a neutron source and neutron detectors.  One other suggestion, which might work, is to use a very low density large diameter float level detector. You might use a free float containing a gamma source or tethered float designed not to bind with particles.

Dr. Lioyd， thank you very much for your answers. Your suggested methods may be very useful, but it seems they are not usually adopted in industrial fluidized reactor designs, e.g. FCC units. What I more want to know is the classical method that is used in industrial fluidized reactor based on pressure measurement.

Mr. Zhang,

Having worked in the fluidized bed field for (too) many decades here is a tried and true method we have used for decades:

Install two pressure taps ; one directly above the other;  at different heights about   1 ft or 100 cm apart in middle area of bed, depending on approximate bed height.

Pressure difference between the two taps indicates the solids density in the fluid bed as well as pressure drop per vertical distance of height in the bed.

Absolute pressure for the two taps is used to calculate the height of the top surface of the bed.

Suppose the two taps are 1 ft apart and lower tap measures 12 in WC and upper tap reads 10 in WC.

Pressure drop/linear height = (12-10)/1 ft = 2 in WC/ft

calculate surface height:

from lower tap

12 in WC/(2 in WC/ft)= 6 ft

10 in WC/2 in WC/ft)= 5 ft

So the surface of bed is 6 ft above lower pressure tap and 5 ft above the upper pressure tap.

I used this method on a recent fluid bed reactor in your country.

PS -

Can you estimate the solids density for the above example ?

It is equivalent to 2 in WC/ft of height.

If the fluid was water it would be 12 in WC per ft of height.

So the solids density is 2/12*62.4lbs/cubic ft = 10.4 lbs per cubic ft.

The above method is not perfect.  There is some inherent error due to the motion of the fluid bed which makes pressures fluctuate.  The trick is to average the readings and/or to dampen the readings electronically.

If budget allows it is desirable to use 3 pressure taps instead of two and depending on bed height locate the pressure taps a bit further apart.  Testing first using a cold flow rig can be helpful if you have the budget.

Hope this is helpful.

John D'Acierno

Thanks a lot for your answer, John. I understand the method you provided, which is also the traditional method used in industrial fluidized bed. A simple assumption of this method is the dense bed have a constant density throughout its height. However, I have measured the density profile of a fluidized bed throughout its height by multiple pressure taps. I found the density usually decreases with increasing height especially in high-velocity turbulent flow regimes. In an industrial fluidized bed design, how to properly locate the three taps (more commonly adopted as I observe) will influence the accuracy of the determined bed surface level. I think your suggestion to measure the bed density in the middle of the bed may be a good advice. Your suggestion to dampen or average the pressure signals is also good to encourage application in industrial DCS systems. Anyway, thank you very much, John.    Yongmin