The in-line scavenging of hydrogen sulfide is the preferred method for minimizing the corrosion and operational risks in offshore oil production. We model hydrogen sulfide removal from multiphase produced fluids prior to phase separation and processing by injection of triazine solution into their gas phase. Using a kinetic model and multiphase simulator, the flow regimes, amounts, and composition of three phases are determined along the horizontal and vertical flow path from subsea well to separator tank. The flow regimes were found to be slug flow or intermittent flow. The highly reactive triazine is destroyed on contact with water phase flowing near the wall. We have simulated the hydrogen sulfide concentration profiles for different amounts of gas injection. The results are compatible with the available field data from an offshore oil well and are useful in determining the injection rates of expensive chemical scavengers and optimal gas injection rates.