  The atmospheric composition of exoplanets with masses between 2 and 10
M$_\oplus$ is poorly understood. In that regard, the sub-Neptune K2-18b, which
is subject to Earth-like stellar irradiation, offers a valuable opportunity for
the characterisation of such atmospheres. Previous analyses of its transmission
spectrum from the Kepler, Hubble (HST), and Spitzer space telescopes data using
both retrieval algorithms and forward-modelling suggest the presence of H$_2$O
and an H$_2$--He atmosphere, but have not detected other gases, such as CH$_4$.
  We present simulations of the atmosphere of K2-18 b using Exo-REM, our
self-consistent 1D radiative-equilibrium model, using a large grid of
atmospheric parameters to infer constraints on its chemical composition.
  We show that our simulations favour atmospheric metallicities between 40 and
500 times solar and indicate, in some cases, the formation of H$_2$O-ice
clouds, but not liquid H$_2$O clouds. We also confirm the findings of our
previous study, which showed that CH$_4$ absorption features nominally dominate
the transmission spectrum in the HST spectral range. We compare our results
with results from retrieval algorithms and find that the H$_2$O-dominated
spectrum interpretation is either due to the omission of CH$_4$ absorptions or
a strong overfitting of the data. Finally, we investigated different scenarios
that would allow for a CH$_4$-depleted atmosphere. We were able to fit the data
to those scenarios, finding, however, that it is very unlikely for K2-18b to
have a high internal temperature. A low C/O ratio ($\approx$ 0.01--0.1) allows
for H$_2$O to dominate the transmission spectrum and can fit the data but so
far, this set-up lacks a physical explanation. Simulations with a C/O ratio $<$
0.01 are not able to fit the data satisfactorily.
