I have a relatively small column with 10 bubble cap trays.  It is in a dirty service with approximately 1% phenolic tars.  Feed is 96% toluene and ~2% each of water and methanol.  Feed enters on top tray and there is no reflux.  Solvent and tars are the bottoms.  Over time the bubble caps get dirty and stuck closed causing high dP across the column which limits capacity.  We often see damage and/or buckling of the bottom trays during our annual shutdown.  I am considering removing a certain percenage of the caps.  Does anyone have any advice on this?

you needn't change all the trays, only a few trays at the bottom. The best way is to change the trays to the type of anti-fouling. I am not sure the measures to remove some caps is effective, because you can not determine the fouling is caused by which factor(crystallization,reaction or precipitation). If you increase the velocity of the gas, maybe decrease the fouling,but it also increase the  pressure drop, which will results small capacity. So you should be careful. 

You use the phrase "bubble caps get dirty and stuck closed causing high dP".

Bubble caps are fixed orifice devices and basically prevent liquid weepage by creating a seal between the upper and lower parts of the tray.  They also aren't that commonly used any more other than for some speciality applications.

Unlike valve trays, there are no moving parts in a bubble cap.  the opening for the vapor can become plugged but they can't be 'stuck closed' in the true sense of the word.

Are these bubble cap or valve/Globe valves trays in the column?  If you have bubble cap trays, then there are no moving parts to get stuck closed.  The orifices can still plug.  A valve tray has moving orifice covers that can get stuck open, closed, or in between due to fouling.

Assuming these are have bubble cap trays, removing the cap will lower tray efficiency.  The cap forces the vapor to pass through the liquid and results in mass transfer.  Without the cap, the vapor will blow through to the next tray and short circuit the mass transfer that did occur in the tray below.

I think that replacing the bubble cap with a sieve trays will give better column operation.  A sieve tray may be more tolerant to fouling and will have lower pressure drop than bubble caps.  The lower pressure drop means that you column can run longer between cleanings before high DP becomes a problem.

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