As I discussed in my reply for hot spots in coke drums (https://refiningcommunity.com/forums/topic/hotspots-in-coke-drums/) the coking reactions take between 60 and 75 minutes at 825 F (440 C). The reaction mass in the bubbly liquid layer on top of the coke pile is approximately 60% converted, so over approximately 30 minutes after switching feed out, all the hydrocarbons reactions have been completed and no further products are exiting the drum.
My guess is the decay is a first order exponential decay as coking reactions are first order kinetics. The mass flow rate will go from full design to zero in roughly 30 minutes once feed is lost, unless the temperatures drop. As you know, at lower temperatures the time required for complete reaction increases.
Is your question in relation to trying to size relief valves for the fractionator or some other piece of equipment? If so, you should work with the licensor to understand the assumptions and basis for the relief valve calculations. The amount of vapor and the enthalpy balance needed to properly size relief valves is tricky and a thorough understanding of your feeds and unit are necessary to ensure the relief valves are adequately sized.