Hülsmann, MarcoMarcoHülsmannKlaassen, BernhardBernhardKlaassenKrämer, AndreasAndreasKrämerKrämer-Fuhrmann, OttmarOttmarKrämer-FuhrmannPangalela, TosawiTosawiPangalelaReith, DirkDirkReithHack, KlausKlausHackLinden, JohannesJohannesLinden2022-03-052022-03-052017https://publica.fraunhofer.de/handle/publica/25140610.1007/978-3-319-62458-7_1The paper describes methods for calculating chemical equilibria based on a constrained Gibbs free energy minimization. The methods allow the treatment of multicomponent systems with multiple phases, including gaseous phases, condensed phases, and stoichiometric phases. A special aspect is the detection and treatment of miscibility gaps. The underlying mathematical problem is described in detail together with the algorithmic approach for its solution. Results are presented for some test cases, including the computation of phase diagrams for ternary systems.enbook article