July:
I sense that you "feel" or have been advised that there is an importance to attribute to "residence time" in a distillation column. While the time a quantity of liquid resides within a column may be of interest for some reason or other, the important thing to bear in mind is that for the distillation to succeed in effecting a separation it must have:
1. a constant and steady feed;
2. a positive liquid seal on each tray (assuming you are using trays - whether bubble cap, sieve, or valve) and on every downcomer; otherwise, you don't have a separation stage where you maintain a phase equilibria;
3. a liquid reservoir (or "sump") where you maintain a liquid level for postive control operations and also to serve as a source for feeding a reboiler requirement;
4. a certain amount of liquid reflux is also involved in the external piping and attached overheads condenser and reflux drum.
If you have a packed column instead of trays, you will have a certain amount of liquid hold-up ("wetting) amount within the packed bed. This usually is less than the amount required to maintain trays - although you could also have a substantial amount dedicated to intermediate, re-distribution trays.
Note that you have been very specific in your question and you haven't furnished specific data related to your question. Nevertheless, the important point is that the liquid holdup and required to carry out the operation is determined as per the type of operation and equipment employed. That is the most important thing to consider because otherwise the distillation operation won't work. Therefore, the "residence time" - as Doug infers - will vary for a variety of reasons. If you are looking for surge capacity due to downstream process needs, the usual economic answer is to install an appropriate surge tank on the bottoms product or the overheads product - whichever it is that you are concerned with.
In my experience, there is no such thing as "acceptable minimum residence times" for distillation columns - unless, as Doug points out, we are dealing with reactive distillation (which I assume is not the case since you don't mention it).
I hope these comments help you out.