Mean particle diameter in fluidized bed

[MaticGrom]

Hi everyone!

I have problem in estimating mean particle diameter in fluidized bed material.

I have results of particle size analysis (please find it attached). According to Kunii and Levenspiel (Fluidization Engineering) or Perry's Chemical Engineers' Handbook, mean particle size to be used in fluidized bed equations is calculated by equation (1) in attached document.

Problem is, that if I take entire particle size distribution for calculation of mean particle size by equation (1), I obtain mean particle size of 16 micrometers. This would suggest, that material is in Geldard C group of particles. Group C materials are difficult to fluidize (they form "rathols" and pistons). My exerience shows however, that material behaves nice when fluidized, more like group B (I did not notice bubbles expansion range, it also defluidizes quickly).

If I exclude particles under 20 micrometers (representing about 9% of entire mass), a obtain mean particle diameter of 71 micrometers which is close to diameter calculated by more intutive equation (2) (68 micrometers).

My question is, what to do regarding this dilema? Is it justified to exclude particles below 20 micrometers? Does anyone have any similar experience?

Thank you very much for any answers and clues.

Best regards,

Matic

 

[MaticGrom]

Here is a document with equations

 

[Caloooomi]

Seems a bit weird that < 10% of the particles by mass, can shift the distribution so much...

 

[MortenA]

What i think you should do is to re-dístribute the "buckets". Your buckets becomes smaller and smaller (towards small size particles) and thats why your distribution does not looks "normal" (as in normal distribution). I think that you should try to draw the distrubutuion on a normal X axis (not log). If this shows you a "normal distribution" then i think you should calculate the diamter the "normal way (and this should then be around 2)

I may be totally of because i dont normally work with particles but it seem logical to me that the size should be normal distrubted and then 2) would give the same result as 1) i think

 

[MaticGrom]

Hello Caloooomi and MortenA,

thank you very much for your replies!

Please find attached Excel analysis of particles. If part of distribution, marked in yellow is taken for calculation, 70 microns are obtained and they represent 90% of distribution by mass. So it seems, that remaining 10% of mass can have so great influence.

I see no physical reason to redistribute buckets. Analysis was made by laser difraction and this is its result. Of course one could doubt on accuracy of measurement of smaller sizes. But unfortunately I do not have any knowledge, how accurate laser difraction is at smaller sizes.

Best regards,

Matic

 

[MortenA]

Its a statistical reason why you should redistribute!

 

[MaticGrom]

Hi MortenA,

can you explain more please and can you suggest how to do it?

There is no law, that would say, that distribution is normal. It could be Rosin Ramler distribution or any other.

Anyway, I am not calculating mean diameter from data for each size interval not any analytical expression based on distribution parameters. I also can not make distribution normal if it is not such in reality.

 

[Compositepro]

I've done a lot of work on fine grinding of materials over the years and particle size distribution is a very complex subject where many simplifying assumptions are required. There are number averages, surface area averages, and mass average distributions. A 10 micron particle weighs 1000 times as much a a 1 micron particle. Then how do you define the size of a particle that is the shape of a rod or a plate? Laser diffraction will measure a different number than other test methods. I've never found any of the test methods or mathematical modeling to be as useful as visual microscopic analysis. However, microscopic analysis requires a great deal of experience, and it is not quantitative.

Trying to define a particle size distribution with a single number is like trying to describe a person with a single word; it is generally not very useful, and often misleading.

 

[MortenA]

OK, its you job not ,ine anyway