This paper demonstrates a new modeling method of the complex heterogeneous processes between a metal and slag based on a pattern of formation of the crystallization fields of phases.The theoretical justification was provided pentair hose for the using of the osmotic coefficients of Bjerrum-Guggenheim with the reduction reactions of elements from the liquid oxide melts into metal.As an example, the equilibrium procedure of a carbon-saturated Fe-Si melt with liquid CaO-SiO2-Al2O3 slag was presented and a mathematical model of the fr5947 complex phase equilibrium in a metal-slag system was provided.