You really have 4 questions:
1. What gravities I should use for criteria?
2. What is this term of time?
3. And what it is used for??
4. It is surge time and hold-up time value is absolute?
The answers are:
1. What you are seeking is the size (height) of the liquid-containing sump volume at the bottom of the vertical separator (“liquid collection section”; page 10, API 12J) – here, I’m presuming you are talking about a vertical unit since you haven’t told us if you have a vertical or horizontal unit. Based on the expected liquid input, the total liquid inventory in the separator represents a “liquid retention time”. Because you are proposing to use the separator in varying load services, you would be wise to design it for the worse case and use a liquid density that is conservative – i.e., use the lowest liquid density. But bear in mind that it is actually two prime factors that determine the correct vessel size with respect to the liquid collection section:
a. The time required for your instrumentation or operator actions during the process changes or procedures – both normal and extraordinary.
b. The need to have a HH and LL liquid level instrument set points for operational and shutdown procedures.
These two factors have much more importance than any “general” rule of thumb or typical value given by anyone – including the API. Note that API states that these are “typical” times – not those specific to your application. As is the usual case, you must design to your specific needs and requirements, using good and logical engineering decisions. Do not depend on the API (or anybody else, for that matter) to give you a “magically” specific equation to your application or problem.
2. If you are to reasonably have liquid surges into the vessel and must account for some hold-up of the same, then you must design for that event as well. In other words, you must add more liquid collection volume to the separator. This is not only common sense, it is mandatory good engineering judgment.
3. The additional liquid collection volume is used to handle the additionally imposed liquid volumes under the surge conditions. If it is reasonable to expect surge conditions, you must design for it.
4. This question is unintelligible. I don’t know what to make of it.
You are basically applying the simple Brown-Souders equation to a 2-phase separator and possibly allowing for surging liquid flows. This classical 1930's equation was derived by both venerable gentlemen for determining the proper distances between distillation trays. The diameter of the vertical vessel is dependent on the densities of the gas and the liquids involved. If you allow for a conservative and low superficial vapor velocity the only items that can cause you problems are the disengagement distances above the sump’s liquid level, the distance above the demister pad (if one is used), and the amount of liquid inventory designed into the unit. These factors are decided mainly by considering process needs and requirements set by you or the nature of the operation. Only you can furnish the real basic data and, consequently, the basis for design. Neither API, text books, or this Forum can do that. But I hope this helps you out in assessing your application.