Field-Resolved Three-Phase Dephosphorisation in Molten Steel: Euler–Euler–DPM Modelling of Bottom-Blown Oxygen–Lime-Powder Injection

Dephosphorisation in oxygen steelmaking depends on more than the equilibrium phosphorus partition ratio. It also depends on where gas, slag, metal and injected lime powder coexist while the bath is being stirred. We develop a gas–slag–metal–particle reaction model for bottom-blown oxygen–CaO powder injection by coupling Euler–Euler transport of liquid steel, mixed slag and gas with discrete CaO-particle motion. The local source terms include oxygen dissolution, FeO/Fe2O3 conversion, CO/CO2 buffering, competitive C/Si/P oxidation, P2O5 formation, C2S–C3P fixation, reaction heat and phase-wise mass conservation. Instead of resolving every bubble or slag droplet, the model represents bubble swarms, dispersed slag and emulsified metal–slag contact through mean-field interfacial area densities tied to local phase fractions and mixing. Two cases with the same initial phosphorus content but different carbon levels are used to test reaction selectivity. In the high-carbon bath, bottom-blown oxygen is consumed first by decarburisation; the generated CO sustains plume buoyancy but reduces FeOx retention during flotation. CaO addition improves local slag formation, but it contributes to dephosphorisation only where FeOx supply, P2O5 generation and C2S–C3P fixation coincide at an active slag–metal interface. The stable dephosphorisation window therefore lies mainly in the upper slag–metal mixing zone, not in the bottom gas column. The model provides a computable basis for analysing bottom powder injection, combined blowing and low-carbon endpoint dephosphorisation in gas–slag–metal reactive flows.