The recent detection of gas-phase methanol (CH$_3$OH) lines in the disc of TW Hya by Walsh et al. provided the first observational constraints on the complex O-bearing organic content in protoplanetary discs. The emission has a ring-like morphology, with a peak at $sim 30-50$ au and an inferred column density of $sim 3-6times10^{12}$ cm$^{-2}$. A low CH$_3$OH fractional abundance of $sim 0.3-4times 10^{-11}$ (with respect to H$_2$) is derived, depending on the assumed vertical location of the CH$_3$OH molecular layer. In this study, we use a thermo-chemical model of the TW Hya disc, coupled with the ALCHEMIC gas-grain chemical model, assuming laboratory-motivated, fast diffusivities of the surface molecules to interpret the CH$_3$OH detection. Based on this disc model, we performed radiative transfer calculations with the LIME code and simulations of the observations with the CASA simulator. We found that our model allows to reproduce the observations well. The CH$_3$OH emission in our model appears as a ring with radius of $sim60$ au. Synthetic and observed line flux densities are equal within the rms noise level of observations. The synthetic CH$_3$OH spectra calculated assuming local thermodynamic equilibrium (LTE) can differ by up to a factor of 3.5 from the non-LTE spectra. For the strongest lines, the differences between LTE and non-LTE flux densities are very small and practically negligible. Variations in the diffusivity of the surface molecules can lead to variations of the CH$_3$OH abundance and, therefore, line flux densities by an order of magnitude.
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