Radionise:
The following follows the way I interpret your two questions.
First, which “inlet flow rate will vary from time to time...” – the inflow to the Liquid Control Valve? I presume so, if the inlet to the production separator is also varying.
Secondly, engineers normally are only interested and deal in gaseous fluids achieving sonic velocity. I see no practical reason or purpose to impose sonic velocity on a liquid fluid inside a pipe (assuming you could design for, and handle, a sonic-level liquid hammer in your piping). Therefore, the only way that you are going to tolerate sonic velocity (“choked” flow) inside your drain pipe is for the drained liquid to “vaporize” – actually, an isenthalpic flash – across the drain valve (LCV). This may be true in your case, but it depends on the liquid fluid we are talking about. Production separators can handle a variety of hydrocarbon liquids as well as water – it depends on your production characteristics. Only you can tell us that.
Based on a material balance, the liquid fluid that enters the separator must exit through the LCV. I believe that is a basic premise for your continuous operation. There is NO liquid accumulated in the separator. In my opinion, the vapor (or gas) flow at choked condition CAN EXIST at the LCV outlet – if you want it that way or if there is enough gaseous volumetric flowrate through a fixed, small pipe diameter. Normally, this is not what you want – and, therefore not what happens. I can safely control the separator’s liquid level by expanding the liquid content down to whatever pressure I need to drain down to and handle it accordingly - without causing choked, gas flow. If I find that my LCV will be actually flashing, I need to take this into consideration immediately at its sizing and design stage. If this is true you will find that you probably will also inherit other problems: the isenthalpic expansion will cause cooling – perhaps down to the sub-zero range - due to the hydrocarbon refrigerants being flashed. This is exactly the same principle and technique employed in mechanical refrigeration. The expansion (“refrigeration”) valve is nothing more than a fancy LCV acting in exactly the same manner that you describe – except that it’s signal is reversed: it opens more on liquid level depletion in the evaporator. For many years, before the advent of turboexpanders, that’s the way we produced liquid hydrocarbons at low temperature in order to subsequently apply de-ethanizers, de-propanizers, de-butanizers, etc., etc.
Like Milton, I also have never heard of choked liquid flow affecting the ability of an interface level controller on a three-phase (or 2-phase) separator and not allowing it to work properly. In fact, I dare say that anyone attempting to design for choked liquid flow is begging for trouble in the form of a sonic-speed water bullet trying to make a 90o degree turn at the first elbow it meets. I wouldn't give the elbow much chance to continue existing were that the case. So why tolerate/design for sonic liquid flow?
I've handled/designed dozens of these same applications and never have come up with what is being questioned or posed. Neither have I heard of anyone else coming up with the same. Perhaps I don't understand the questions correctly.