In the first coker I worked, the set up was 4 drums, 2 heaters and 3 heater charge pumps (2 running – 1 spare). So one pump would feed one heater and a pair of drums. Simple. No minimum flow line required because the pump could cover the operating range without going below minimum flow.
About a year ago I participated in a 4 drum coker startup in the Gulf Coast that had only 2 pumps. One running – one spare. The running pump would feed 2 heaters. (each heater – 2 drums). This system had minimum flow line to protect the pump from going below minimum flow if one heater tripped. (Or when running at reduced rates).
Because the heater charge feed has coke particles (as big as 1/2 inch) the minimum flow control valve has to be capable of passing coke particles this size. The pressure drop was 600 psig (pump discharge) to 15 psig (bottom of fractionator). This was done with two valves in series.
Hope this helps.