Msia:
Your information is incomplete and misleading. You are not being specific when you state you have problems with the reboiler liquid level.
The basic fact of the matter here is that you have a kettle reboiler - as you have shown in the sketch supplied. This type of reboiler has a vertical WEIR inside the shell that is 100% seal-welded. In other words, the amine solution on the tube bundle side of the weir cannot enter the other side of the weir (the part that is being measured by a liquid level gauge) without going over the weir's horizontal cut. This is what sets and ensures that the tube bundle will be 100% + covered by amine solution being vaporized.
The level you are seeing is the liquid level that DOES NOT COVER THE TUBE BUNDLE. Therefore, you have no reason to be concerned by this level "fluctuating" (which I seriously doubt, if you are operating the reboiler the way you should). The level over the tubes CANNOT FLUCTUATE. It is being held constant by the weir. There is no "nucleate boiling" taking place; all the reboiler does is creaste a gentle, simmering vaporization of a portion of the solution. I know, because I have designed and built these type of amine reboilers in the past and I installed sightglasses on some of these in order to disprove the existance of so-called "foaming" - and I did. The boiling is very gentle, with no wave action or level fluctuation.
Besides all of the above facts, you should know that the level seen in the reboiler level gauge should be steady and constant because it is being held there and controlled by the level control valve on the lean amine going to the contactor tower. This control valve fixes the steady flow rate of amine going to the contactor.
Without you furnishing a decent, detailed sketch of your reboiler and where your level gauge is located and what you have "fixed", we are unable to add any further advice, comments, experience, or expertise on this topic. What you furnished as your reboiler sketch was a downloaded illustration from the Penn State website offering hydrocarbon phase equilibria information. You should generate your own, specific sketch.