torresqa: Maybe something got lost in the english but you cant "calculate the pressure inside a separator". The pressure in the separator is determined by your operating conditions. This includes upstream pressure, control valve set-points downstream conditions etc. If you are looking at upset scenerios (fire, blocked outlet etc) then these will determine the pressure.
Vapour pressure of the liquid in the separator is calculated by use of thermodynamics. If the pressure is higher than the vapour pressure at the operating temperature then it will be full of liquid - or you have some sort of inert gas added. Normally for separators its assumed that the liquid in the separator has a vapour pressure equal to the operating pressure - this determines the phase split.
Best regards
Morten