Well, After 16 years working (design/operation) in Delay coker, the blowdown is the best system to handle these discharges, in fact the design criteria of the entire system of blowdown, is associated with the discharge of these safety valves during the cooling (quenching) with water (generally)
I have seen a couple of times open those valves (foamover and plugging the top line) and the system has handle that discharge very well, only afterwards that we had to implement was a procedure for cleaning the blowdown aircooler,
I think the most common design in the last 20 years is discharge this valve to the blowdown
Best Regards