This article presents a process model of a phosphorus-producing, submerged arc furnace. The model successfully incorporates accurate, multifield thermodynamic, kinetic, and industrial data with computational flow dynamic calculations and thus further unifies the sciences of kinetics and equilibrium thermodynamics. The model is structurally three-dimensional and uses boundary conditions, initial values, and material specifications provided by industrial measurements, laboratory experiments, and a combination of empirical and thermodynamic data. It accounts for fully developed gas flows of gaseous product generated from within the packed bed; the energy associated with chemical reactions, heating, and melting, as well as thermal conductivity and the particle-particle radiation within the burden. The model proves the existence of a narrow, gas-solid reduction zone where the bulk of phosphorus is produced. It shows that fast reaction rates in this narrow reaction zone in combination with long residence times diminish the influence changing reaction rates have on the process. It indicates that most heat exchanged between the new pellets entering the furnace and the gaseous product produced in the reduction zone takes place in the top 0.5 m of the furnace bed. The gaseous product and flow information shows low and recirculating gaseous flow velocity areas that cause dust accumulation.

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