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There are 3 basic types of relief valves:
Conventional Relief Valve
The conventional relief valve is a differential pressure device. Back pressure on the outlet of the relief valve effects it. They are really only any use if they discharge to atmosphere. Discharging to a relief/flare header is not practical as the back pressure is always variable and will effect when they conventional relief valve pops.
Balanced Bellows Relief Valve
The balanced bellows relief valve addresses the back pressure problem with conventional relief valves but is not a complete solution. The balanced bellows relief valve flow performance starts getting impacted at back pressures in excess of 30% of relief valve set point. Also the bellows that eliminates the effect of back pressure on the ability of the relief to pop has mechanical integrity issues. Large balance bellows relief valves ( such as 6x8 ) cannot take more than 60 psig back pressure without it causing a failure of the bellows.
Piloted Operated Relief Valves
The pilot operated relief valve is not normally effected by back pressure (as to its ability to pop at set). The effect of back pressure on the performance of the relief valve is also minimal. They can have up to 80% back pressure with it only derating the capacity by 20%. There is one interesting effect: if the back pressure exceeds the upstream pressure of the relief valve the relief valve pops even if it is not at set. This can be prevented by purchasing a back flow preventor. PORVs also can handle high inlet losses by using a remote pilot. The sensing line for the remote pilot must use a special pickup to allow it to capture the dynamic pressure part of the gas.
Inlet lines to PSVs
Inlet lines are sized based on the rated capacity of the relief valve at rated conditions. In the case of multiple relief valves, rated capacity and conditions will be at 10% accumulation for purposes of inlet line calculations. The allowable pressure drop is 3%. The pressure drop is based on the difference of stagnation pressures. The stagnation pressure is the static pressure plus the velocity head. The stagnation pressure is the total pressure. The 3% pressure loss is essentially the frictional losses not changes in pressure as a result of conversion of static pressure to velocity head.
Intial assumptions of inlet lines should be one line size larger than the relief valve inlet. The gate valve should be on the large line. All valves on relief valve inlets and outlets are required to be full port. Note that api gate valves 4 inch and larger are full port. 3 inch and smaller gate valves can be either reduced port of full port, so in the case of relief valve isolation specify full port.
Outlet lines from PSVs
The lines running from the relief valves to the common header are also sized based on rated capacity. The common relief header is sized based on required capacity of any relief valves that can conceivable relieving at the same time.