Turn down ratio in separators is a term that is very often mis-applied, but it is reasonably easy.
If we start at the top end, we have the mist pad. Mist pads tend to have a narrow operating range, and it is much worse to go under the design velocity than to exceed the design velocity. The design velocity used by competent vessel designers is around 10 ft/s. This requirement is the reason that on larger vessels the mist extractor is often placed inside a plenum that is smaller than the bulk vessel diameter. Velocity greater than 10 ft/s will reduce performance, but very slowly and 30 or 40 ft/s tends to give you results indistinguishable from 10 ft/s.
The maximum velocity is determined by a constant based on vessel orientation and length times the square root of the term difference in species density divided by gas density.
Turn these two velocities into mass flow rates (or volume flow rates at standard conditions) being careful to use the mist-pad plenum diameter for the top end if appropriate and divide the small flow rate into the big flow rate and you have turndown ratio.
For a separator, residence time is a bit messier than ashtree's tank example. The reason we talk about it at all is that many volatile components in crude oil can take some non-trivial time to evolve out of the liquid phase. Allowing that time is important to keeping these valuable components from gong out the tank vents. Most often we calculate the volume of liquid represented by the level controller just opening the dump valve minus the volume in the vessel as the level controller shuts the dump valve with that difference divided by the liquid flow rate into the vessel. If someone is talking about residence time in a gas/water 2-phase separator they are quoting rote "learnings" that they really didn't comprehend.
Foaming service is just what it says, fluids that tend to foam either before or inside the separator. Foam is very persistent and difficult to deal with, which is why it is common to use foam breaker chemicals before the separator to keep the mess under control. It is very difficult to deal with foam mechanically.
"Slugging" is a flow stream that is prone to the multi-phase condition of "slug flow". I'm not sure what you are looking for beyond that.
I'm not familiar with the term "H&MB Case".
[bold]David Simpson, PE[/bold]
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist