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Theoretical calculations were based on thermodynamic equilibrium in the multi-component and multi-phase system with heat and mass balance as well as the oxygen efficiency to take account for the effects of process kinetics. The variations of temperature, mass fractions of dissolved oxygen and sulfur in blister copper, partial pressures for O2, S2, SO2 in gas phase for the copper-making stage were calculated. The model predicted temperature, time of blowing as well as mass of the blister copper at end points for 6 heats showed a fairly good agreements with corresponding plant data. The calculated content of 0.065% and content of 0.87% in blister copper were both at reasonable levels. Compared with the so called Goto model, the present model has very much improved process description of copper-making stage as well as the prediction of end points for a copper converter by introducing the oxygen efficiency.