  Modern observations of the interstellar medium (ISM) in galaxies detect a
variety of atomic and molecular species. The goal is to connect these
observations to the astrochemical properties of the ISM. 3D hydro-chemical
simulations attempt this but due to extreme computational cost, they have to
rely on simplified chemical networks and are bound to individual case studies.
We present an alternative approach which models the ISM at larger scales by an
ensemble of pre-calculated 1D thermo-chemical photodissociation region (PDR)
calculations that determine the abundance and excitation of atomic and
molecular species. We adopt lognormal distributions of column density (\avpdf
s) for which each column density is linked to a volume density as derived by
hydrodynamical simulations. We consider two lognormal {\avpdf}s: a diffuse, low
density medium with average visual extinction of $\overline{{\rm
A}_V}=0.75\,{\rm mag}$ and dispersion of $\sigma=0.5$ and a denser giant
molecular cloud with $\overline{{\rm A}_V}=4\,{\rm mag}$ and $\sigma=0.8$. We
treat the UV radiation field, cosmic-ray ionization rate and metallicity as
free parameters. We find that the low density medium remains fully HI- and
CII-dominated under all explored conditions. The denser cloud remains almost
always molecular (i.e. H$_2$-dominated) while its carbon phase (CO, CI and CII)
is sensitive to the above free parameters, implying that existing methods of
tracing H$_2$-rich gas may require adjustments depending on environment. Our
numerical framework can be used to estimate the PDR properties of large ISM
regions and quantify trends with different environmental parameters as it is
fast, covers wide parameter space, and is flexible for extensions.
