A simple algorithm which always converges for estimating the phase com
position and compositions of multicomponent phases of a reacting heter
ogeneous multicomponent closed system has been proposed and its conver
gence proved. The thus obtained estimation serves as the first approxi
mation of a chemical equilibrium calculation at given temperature, pre
ssure and feed composition. The model of a totally immiscible system i
s applied and the blast furnace problem is presented as an example for
the demonstration of the algorithm. All mathematical proofs are conta
ined separately (see Appendix).