The prediction multi-phase, multi reactant equilibria by minimizing the Gibbs energy of the system : Review of available techniques and proposal of a new method based on a Monte Carlo technique

International audienceSince already a few decades, researchers developed tools to predict chemical reactions in the context of the chemical industry. Numerical tools are now available to predict final chemical equilibriums using the principle of minimizing the Gibbs free energy of the reactions. In this paper, after recalling some basis on thermochemical equilibria, a brief review of the most renown techniques available to find the minimum of the Gibbs energy is presented. From this, limitations are discussed. Mathematically, the equations are always strongly non-linear, and the standard step by step resolution techniques may fail to find the global minimum. When non-mixed phases are present (solids, for instance), the calculations often fail. An example is given with biphenyl-CO2 mixtures. Especially when many phases are postulated. An alternative resolution method is proposed based on a Monte Carlo method which does not require nor a linearization of the Gibbs equation neither a step by step resolution. The method can solve any multi-phase and any multi-reactant equilibrium but is much more computer resource demanding than the traditional methods. It was implemented in a home-made code (CIRCE) briefly described in Appendix A