What was flow rate through furnace prior to 10 m3/hr increase?

Flow rate was 44 m3/ hour before increase

10/44 is a 23% increase in flow rate. Pressure drop goes as the square of the flow change, or 1.23 squared = 1.51. That means pressure drop would increase 51%, so your increase from 3.5 kg/cm2 to 5.0 kg/cm2 is not unreasonable, though still higher than expected. A 1.5 kg/cm2 DP increase would mean the DP prior to the rate increase was 3.0 kg/cm2, which only leaves 0.5 kg/cm2 (~7 psig) for coke drum back pressure, which is unreasonably low. Possibly coke has spalled and is creating additional pressure drop in the piping circuit.

Dear guest

Thanks for your reply can you please tell me whether can we suspect the. Possibility of a choke or coke formation in between switch valve and feed valve which may also be the reason for back pressure

Coke can be lodged anywhere in the piping system between furnace and coke drum. Most typically large coke pieces can become stuck in elbows or reductions in piping diameter. Clean out flanges at elbows are usually provided to allow piping inspection during drum cuts or maintenance windows.