Comparison between the model and observations of G328.25, G335.58 and G335.78. Middle left: lower and upper bounds of the model that best cover the observations at a given time of 6 × 10⁴ yr with a grain size of 0.5 μm. These areas of best coverage relate to various locations in the envelope; they are marked by the lines in the top and bottom panels, which are colour-coded by temperature. Comparisons with the 0D model (UCLCHEM-0D with G₀=1 and Garrod et al. 2022) are also provided; mean prediction values are shown with ‘x’ symbols and asterisks, while the hatched lines boxes mark a factor of 5 scatter around these mean values. Middle right: temperature profile for all locations in our model.