A general Gibbs energy minimization algorithm for modelling solid-fluid equilibria in binary systems involving totally and partially miscible solids, pure solids, hydrates and co-crystals

At a fixed temperature and pressure, a mixture is at equilibrium if and only if the Gibbs energy of the system is at its global minimum. In other words, phase equilibrium calculations can be treated as optimization problems, as the minimization of the Gibbs energy represents the sufficient condition for thermodynamic equilibrium. However, the necessary condition of equilibrium resulting from the iso-fugacity criterion of each individual component in each guess equilibrium phase is more used. Despite being computationally simpler, this approach may lead to metastable solutions. On the whole, the minimization of Gibbs energy should be prioritized as it is the only approach that provides the true thermodynamic state of a given mixture since it considers the overall Gibbs energy of the system. This work presents a general algorithm based on the Gibbs energy minimization approach for binary systems. Provided that suitable fluid-phase and solid-phase models are chosen, the algorithm is able to evaluate the most stable thermodynamic state of a system for a given global composition, temperature, and pressure without prior assumptions about the number, nature, or compositions of equilibrium phases. To the authors’ knowledge, this is the first Gibbs energy minimization approach capable of handling solid-fluid phase equilibria involving diverse solid types: from totally miscible solids (e.g., N 2 +Ar, CH 4 +Kr systems), partially miscible solids (e.g., N 2 +O 2 , CH 4 +Ar systems), pure solids (e.g., N 2 +CO 2 , CH 4 +C 2 H 6 systems), and hydrates (e.g., CH 4 +H 2 O system), to cocrystals with both congruent and incongruent melting (e.g., C 6 H 6 +C 2 H 3 N, CH 3 OH+H 2 O systems).