A 3 way refrigerator does not have a compressor for cooling action on AC like a residential traditional fridge has. I don't know the full science but all it is a heating element that causes the ammonia and sodium gas mixture or something like that, rise into an evaporator system which cools the fridge. should be essentially silent on all modes, aside from an occasional click for the control relay on and off, no hum like a regular fridge.
On propane it works really quickly because the small flame can put out a decent amount of heat compared to say a 275 watt AC heating element.
12 volt mode is even slower because the heating element may be even smaller, and the heat output is highly sensitive to whatever the system voltage is. Could be 11.5 v with a low battery, could be as much as 14.4v with the converter's full output.
Expect on 120 mode it will take at least 8 hours to cool, and that means no food in fridge.
12 volt mode needs 24h I would say.
Gas? 6 hours.
Finally, sometimes the process takes longer if the fridge has been sitting for a while unused.