3.4.1. Gaussian Model

Table 5 shows E0, σ, and h computed through the Gaussian model at different heating rates for the various substrates, while Figure 5 shows the experimental data compared with the modeling curves for pyrolysis (data and curves relevant to oxidation are available in Supplementary Materials Figure S3). Experimental data are the starting point to compute DTGA curves reported in Figure 2.


**Table 5.** Values of E0 and σ for the Gaussian model for the different substrates and heating rates; per moles of dry feedstock. k0 is let constant and equal to 1.67 <sup>×</sup> 1013 <sup>s</sup><sup>−</sup>1.

Data demonstrate that for both pyrolysis and oxidation, the effect of the heating rate on E0 and σ is negligible. Therefore, every substrate can be associated with one single pair of E0 and σ, regardless of the heating rate, which agrees with previous studies performed on other biomass substrates [28]. Under both inert and oxidative atmospheres, the Gaussian DAEM adopted does not highlight the effects of both HTC and its severity on the starting feedstock (their maximum relative difference is 3.7%). This is not surprising: the model basis on the assumption of approximating the entire decomposition profile, which includes more stages, through a one-step profile characterized by a Gaussian distribution. Therefore, the final values of E0 and σ can be considered as a sort of weighted average among the values of the single components (biomass constituents), i.e., hemicellulosic, lignin-like plus cellulosic compounds, and oil. Probably, the difference in the relative composition of the hydrochars is not enough to affect the final values. In particular, under an inert atmosphere, E0 passes from 193 kJ/mol of grape seeds to 200–209 kJ/mol of hydrochars, while σ ranges between 14 and 17 kJ/mol. Values agree with those reported in the literature on the single components. For example, during pyrolysis, the activation energies usually range in 80–116 kJ/mol for hemicellulose, 195–286 kJ/mol for cellulose, and 176–300 kJ/mol for lignin [35,42]. The pyrolysis of oil alone has an E0 of 218 kJ/mol. With values between 211 and 215 kJ/mol, the activation energy of oxidation is the same for grape seeds and hydrochars obtained at 180 and 220 ◦C. Meanwhile, it slightly increases at 220 kJ/mol for the 250 ◦C hydrochar.

**Figure 5.** 1-α vs. temperature: comparison between experimental data (dots) and predicted data (lines) computed through the Gaussian model, during pyrolysis of different samples. (**a**) hydrochar 180 ◦C; (**b**) hydrochar 220 ◦C; (**c**) hydrochar 250 ◦C.
