Kiyomi,
If the warm up vapors are routed back to the fractionator, the pressure drop through the coke drum overhead vapor line is a part of the driving force bringing vapors back into the coke drum to warm the drum. The reduced temperature of the coke drum as compared to the overhead vapor temperature results in condensation that reduces the pressure in the coke drum and draws vapor back into it.
Most systems have a “forcing valve” in the combined overhead vapor line. This is sometimes referred to as the SP-3 valve that is sometimes a ring valve and sometimes a gate valve with a minimum stop. I have also heard of a butterfly style valve being used in this service. The purpose is to impose more pressure drop in the combined overhead vapor line to force more vapors back into the drum being warmed and increase the rate of heating and the maximum temperature of the drum prior to switch.
The warm-up line has to be adequately sized out of the utility header to prevent a two-phase choked flow limiting the mass flow rate and the warm-up of the drum.