Deriving model-based T$_e$-consistent chemical abundances in ionised
  gaseous nebulae
  The derivation of abundances in gaseous nebulae ionised by massive stars
using optical collisionally excited emission lines is studied in this work
comparing the direct or $T_e$ method with updated grids of photoionisation
models covering a wide range of input conditions of O/H and N/O abundances and
ionisation parameter. The abundances in a large sample of compiled objects with
at least one auroral line are re-derived and later compared with the $\chi^2$
weighted-mean abundances from the models. The agreement between the abundances
using the two methods both for O/H and N/O is excellent with no additional
assumptions about the geometry or physics governing the HII regions. Although
very inaccurate model-based O/H are obtained when no auroral lines are
considered, this can be overcome assuming empirical laws between O/H, log $U$,
and N/O to constrain the considered models. In this way, for 12+log(O/H) $>$
8.0, a precision better than 0.1dex consistent with the direct method is
attained. For very low-$Z$, models give higher O/H values and a high
dispersion, possibly owing to the contamination of the low-excitation
emission-lines. However, in this regime, the auroral lines are usually
well-detected. The use of this procedure, in a publicly available script,
HII-CHI-mistry}, leads to the derivation of abundances in faint/high redshift
objects consistent with the direct method based on CELs.
