A detailed numerical analysis is performed in the torch and in the test chamber of an inductively coupled plasma facility. The main purpose is the analysis of the plasma jet in the test chamber and the assessment of its degree of non equilibrium together with the level of elemental demixing. To this end three different mathematical formulations have been used: an extended chemical non-equilibrium formalism including finite-rate chemistry and two forms of equation valid in the limit of local thermo-chemical equilibrium: the LTE-VEF formulation, that takes into account the demixing of chemical elements and the LTE-CEF formulation, where the molar fraction of elements is supposed to be constant. In order to assess the influence of the finite rate chemistry model on the results, two models have been used. Simulations at various operating pressures indicate that the model dependency is strongly reduced at sufficiently high pressures while relevant at lower pressure. As the operating pressure is increased, chemistry becomes increasingly fast and the non-equilibrium results correctly approach both in the torch and in the test chamber those obtained assuming local thermo-chemical equilibrium, provided that elemental fraction variations are correctly taken into account.