The technique employed by ChemApp to calculate complex, multicomponent, multiphase chemical equilibria is called Gibbs energy minimisation (GEM). An outline of this technique can be found in an article on ChemSage, which internally uses the same calculational engine as ChemApp [Eri90].
More information on the GEM technique can be obtained from the following references –
[Smi82] – W. R. Smith and R. W. Missen: Chemical Reaction Equilibrium Analysis, Wiley-Interscience, New York, NY, 1982.
[Mat86] – A. E. Mather: Fluid Phase Equilib., 1986, vol. 30, pp. 83-100.