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Relief valve calculations use API Std 521 (ISO 23251) as guidance. For a total power failure, the steam system will likely be compromised as well and not be available so no heat removal can be credited for any of the pump around streams. Each company has made decisions about the probability of simultaneous loss of power and steam and the level of risk associated with that decision.
Control valves are typically assumed to be in the normal operating condition at the time of the over pressure event, unless they are the source of the over pressurization and then they are considered to be fully open or fully closed, whichever causes the relief rate to be higher. For a local or individual power failure event, steam can be considered to be a back up. These pump arounds may still be lost as the heat balance causes the liquid to dry up on the trays and no liquid is available to pump around. Dynamic analysis can be used in this case to determine the potential for relief load reduction before the pump around liquid is lost, but a heat decay curve from the coke drum is needed to properly evaluate that case. As a total power failure case is more severe, sizing the relief valves to cover that case removes the incentive to perform a dynamic analysis.
The back pressure in the flare header is another variable to be considered. During the total power failure case the flare load will likely be at its maximum. A back pressure assumption of less than 35% of the relief valve set pressure for a balanced bellows relief valve during the maximum relieving case should minimize the size of the flare header and the required relief area. Back pressures of up to 50% of the relief valve set pressure can be tolerated by balanced bellows relief valves, but with a reduction in capacity. The relief valve manufacturer should be consulted to confirm the required capacity de-rating for the imposed back pressure on their relief valve.
The total power failure case does typically result in a very large relief load. The coke drum is a source of stored energy that is uncontrolled and there is no heat removal available except for the air coolers of the overhead condenser (if they are present, some percentage of their typical duty can be assumed due to natural convection. Typically this value is 20%) until the overhead accumulator becomes full of liquid. As the source of energy input into the fractionator is from the stored energy in the coke drum, there are not suitable instrumented systems that could reduce the relief load in this case.