Computing multi-species chemical equilibrium with an algorithm based on the reaction extents

• A mathematical and numerical model for multi-species and multiphase chemical equilibrium problems is detailed described.
• The model consists of a root-finding method of the chemical potential function iterating on the reaction extents.
• Convergence strategies include: (1) refining the numerical parameters, and (2) ignore solid precipitation/dissolution reactions for kinetic considerations.

A mathematical model for the solution of a set of chemical equilibrium equations in a multi-species and multiphase chemical system is described. The computer-aid solution of model is achieved by means of a Newton–Raphson method enhanced with a line-search scheme, which deals with the non-negative constrains. The residual function, representing the distance to the equilibrium, is defined from the chemical potential (or Gibbs energy) of the chemical system. Local minimums are potentially avoided by the prioritization of the aqueous reactions with respect to the heterogeneous reactions. The formation and release of gas bubbles is taken into account in the model, limiting the concentration of volatile aqueous species to a maximum value, given by the gas solubility constant.The reaction extents are used as state variables for the numerical method. As a result, the accepted solution satisfies the charge and mass balance equations and the model is fully compatible with general reactive transport models.