# GEM Method¶

### Briefly about Gibbs energy minimization (GEM)¶

The GEM approach to computing the chemical equilibrium phase assemblages and speciation is based on a mass balance for the entire complex chemical system, which is set up by the total amounts of chemical elements and zero charge. These elements and electric charge are called “Independent Components” (IC). All chemical species present in all phases are called “Dependent Components” (DC), as their stoichiometries can be built from ICs. Thermodynamic phases are defined each including one or more DCs and may have additional properties, such as the specific surface area. Multi-DC phases are called solutions, with mixing behavior described by a chosen activity model (ideal or non-ideal mixing). Each DC is provided at input with its elemental stoichiometry, and a value of the standard Gibbs energy per mole G0, which is taken from the database after correction to pressure P and temperature T of interest, if needed.

In the GEM method, the activities and concentrations of DCs are treated separately for each phase, taking into account the appropriate standard/reference states and activity coefficients. The equilibrium phase assemblage conforming to the Gibbs phase rule is selected automatically from a large list of feasible phases. The equilibrium partitioning in a multiphase system, including for example aqueous solution, gas mixture, one or several solid solutions, many pure solid phases, and, optionally, sorption phases, is computed simultaneously for all phases in a straightforward way.

The GEMS “Interior Points Method” (IPM-3) algorithm can do such computation efficiently because, in addition to the speciation vector x (mole amounts of DCs – the primal solution), it computes a complementary dual solution vector u (holding equilibrium chemical potentials of ICs at the state of interest). The power of GEM IPM lies in comparing the DC chemical potentials obtained from primal x and dual u vectors, wherever possible.