  We present a detailed analysis of ALMA Bands 7 and 9 data of CO, HCO+, HCN
and CS, augmented with Plateau de Bure Interferometer (PdBI) data of the ~ 200
pc circumnuclear disk (CND) and the ~ 1.3 kpc starburst ring (SB ring) of
NGC~1068, a nearby (D = 14 Mpc) Seyfert 2 barred galaxy. We aim at determining
the physical characteristics of the dense gas present in the CND and whether
the different line intensity ratios we find within the CND as well as between
the CND and the SB ring are due to excitation effects (gas density and
temperature differences) or to a different chemistry. We estimate the column
densities of each species in Local Thermodynamic Equilibrium (LTE). We then
compute large one-dimensional non-LTE radiative transfer grids (using RADEX) by
using first only the CO transitions, and then all the available molecules in
order to constrain the densities, temperatures and column densities within the
CND. We finally present a preliminary set of chemical models to determine the
origin of the gas. We find that in general the gas in the CND is very dense (>
10^5 cm^-3) and hot (T> 150K), with differences especially in the temperature
across the CND. The AGN position has the lowest CO/HCO+, CO/HCN and CO/CS
column density ratios. RADEX analyses seem to indicate that there is chemical
differentiation across the CND. We also find differences between the chemistry
of the SB ring and some regions of the CND; the SB ring is also much colder and
less dense than the CND. Chemical modelling does not succeed in reproducing all
the molecular ratios with one model per region, suggesting the presence of
multi-gas phase components. The LTE, RADEX and chemical analyses all indicate
that more than one gas-phase component is necessary to uniquely fit all the
available molecular ratios within the CND.
