The distribution of oxygen between the gaseous and liquid oxidation products at the hot spot is modeled. The simplified model accurately describes the interaction of the gas jet exiting the lance nozzles with the gaseous surrounding of the jet. This interaction changes the chemical composition of the gas jet influencing the subsequent interaction with the hot spot. The iterative procedure then calculates the chemical composition of the gas exiting the cavity. The characterization of the exiting gas flowing past the lance head as well as the generation rate of FeO is attained by combining the modeled gas composition exiting the cavity with an oxygen mass balance based on a quasi-stationary BOF operation.