  The physical properties of brown dwarf discs, in terms of their shapes and
sizes, are still largely unexplored by observations. To what extent brown dwarf
discs are similar to scaled-down T Tauri discs is currently unknown, and this
work is a step towards establishing a relationship through the eventual
modelling of future observations.
  We use observations of the brown dwarf disc $\rho$ Oph 102 to infer a
fiducial model around which we build a small grid of brown dwarf disc models,
in order to model the CO, HCN, and HCO+ line fluxes and the chemistry which
drives their abundances. These are the first brown dwarf models to be published
which relate detailed, 2D radiation thermochemical disc models to observational
data.
  We predict that moderately extended ALMA antenna configurations will
spatially resolve CO line emission around brown dwarf discs, and that HCN and
HCO+ will be detectable in integrated flux, following our conclusion that the
flux ratios of these molecules to CO emission are comparable to that of T Tauri
discs. These molecules have not yet been observed in sub-mm wavelengths in a
brown dwarf disc, yet they are crucial tracers of the warm surface-layer gas
and of ionization in the outer parts of the disc.
  We present the prediction that if the physical and chemical processes in
brown dwarf discs are similar to those that occur in T Tauri discs -- as our
models suggest -- then the same diagnostics that are used for T Tauri discs can
be used for brown dwarf discs (such as HCN and HCO+ lines that have not yet
been observed in the sub-mm), and that these lines should be observable with
ALMA. Through future observations, either confirmation (or refutation) of these
ideas about brown dwarf disc chemistry will have strong implications for our
understanding of disc chemistry, structure, and subsequent planet formation in
brown dwarf discs.
