*3.5. Aspen Plus Model*

Figure 8a,c show the trend of heat produced/required as computed by Aspen Plus under pyrolytic and oxidative atmosphere.

Regarding pyrolysis, all samples follow a similar trend, characterized by an exothermic behavior at low temperatures and an endothermic one at high temperatures. Figure 9 reports the trends of the products at different pyrolysis temperatures resulting from the 180 ◦C hydrochar (the other samples present the same qualitative trends) and can help to interpret the heat trends. At low temperatures, thermodynamics favors exothermic reactions like char oxidation to CO2 and CO, oxidation of hydrogen, and methanation. Conversely, higher temperatures enhance endothermic reactions, like the Boudouard reaction (and therefore the conversion of CO2 into CO), and methane steam reforming (thus the conversion of CH4 and H2O to CO and H2). At low temperatures, more carbonized substrates show a higher exothermic behavior due to a higher carbon partial oxidation and methane production (they present a higher C/H ratio than less carbonized substrates). Conversely, at higher temperatures, less carbonized samples show a higher endothermic behavior, probably due to the higher production of CO. As expected from its high C/O ratio and low volatile matter content, the profile of coal is flatter than hydrochar, and it is always endothermic. The different starting points can be explained by the higher ash content of coal than hydrochars (13.7% vs. 1.9–2.5%): ash, being not reactive, lowers the energy input/output per unit of mass involved. The slight difference in the coal profile with the previous work of our group [40] is due to the different inlet temperatures (isotherm to the reactors here vs. at ambient temperature in [31]).

**Figure 9.** Aspen Plus results: main products from pyrolysis of hydrochar 180 ◦C.

Besides, Figure 8b shows the progressive integration of pyrolytic DSC data; computing the energy integral is necessary because DSC measures the instantaneous heat flow absorbed or released (which depends on the "history" of the sample due to the thermal program), while thermodynamics considers the energy absorbed or released when converting all the reactants into products at that determined temperature (and therefore the values obtained from thermodynamics do not depend on the thermal history of the sample). Over-

all, DSC data show a trend towards a cumulative exothermic behavior, whose final value corresponds to the integral reported in Table 4. The different behavior concerning Aspen data can be due to the nature of the thermodynamic approach. Indeed, real systems do not behave as predicted by thermodynamics at low temperatures because of reaction kinetics constraints. Moreover, as previously mentioned, thermodynamics does not consider the "history" of what happened before a certain condition. Indeed, inside the DSC, the starting material progressively undergoes pyrolysis, and the material at every time is the result of what happened before (i.e., the thermal program). In addition, thermodynamics does not consider typical "out of equilibrium" products, like tarry compounds, always present in real systems. Therefore, the thermodynamic approach requires particular attention and criticism before being used.

Regarding oxidation, both thermodynamic and DSC curves are clearly exothermic, with values that progressively increase with temperature. Under both atmospheres, absolute values differ between the Aspen and DSC approaches. This is due to the mass involved: DSC curves measure the energy absorbed/released by an amount of material that progressively decreases with time (the process is occurring), while Aspen predicts the energy absorbed/released by the same mass at every temperature. Since the energy is normalized by the amount of starting feedstock (and not the mass measured at every temperature), the amount of heat computed through the DSC approach is smaller than the Aspen one. Finally, it is interesting to note that in an oxidative environment, and for the whole range of temperature investigated, the thermodynamic approach foresees the complete oxidation of the biomass with the production essentially of CO2, H2O, and residual ash (equal to about 2% of the biomass fed to the reactor, Table 1). Conversely, in an oxidative environment in DSC, at the maximum temperature reached of 600 ◦C, there is still a substantial mass of non-oxidized carbon: the residual mass at 600 ◦C is of the order of 30% (Table 4). Through this critical comparison, the two approaches, thermodynamic and DSC, turn out to actually be very distant from each other, which is an aspect worthy of interest.

#### **4. Conclusions**

This work investigated the kinetic behavior during pyrolysis and oxidation of hydrochars derived from an agro-industrial residue (grape seeds). The topic was approached through experimental techniques (TGA and DSC) that were used to develop two different DAEMs for biomass decomposition. Indeed, there is a certain lack in the literature regarding hydrochar decomposition, especially for the computation of the kinetic parameters. Therefore, this work covers both the experimental aspects and the comparison of two DAEMs using a critical approach. Thermogravimetric analysis and differential scanning calorimetry highlighted the importance of the HTC severity on the decomposition profiles. Indeed, hydrochars obtained at 180 and 220 ◦C still decompose with two/three stages (pyrolysis/oxidation) due to the presence of lignocellulosic constituents and oil that only partially degraded during HTC. Meanwhile, the 250 ◦C hydrochar shows a more stable profile, with one/two decomposition peaks, highlighting that HTC temperature hugely affected the structure of the biomass. Interestingly, all hydrochars show a certain exothermic behavior during pyrolysis.

DAEMs predicted the kinetic parameters involved during the pyrolysis and oxidation processes, i.e., the activation energy and the pre-exponential factor. The single-stage Gaussian model does not highlight differences among the various hydrochars obtained at different HTC temperatures, with average values of activation energy in the range 203–206 kJ/mol for pyrolysis and 213–220 kJ/mol for oxidation. Actually, the Gaussian DAEM turned out to be unsatisfactory to model complex feedstock such as hydrochars characterized by multi-decomposition peaks. Meanwhile, the Miura–Maki model, even if not applicable over the entire decomposition region, enabled the determination of the distribution of activation energies: the more severe the HTC process, the lower the activation energy values.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/en15030950/s1, Figure S1: (1-α) at different temperatures of feedstock during: (a) pyrolysis; (b) oxidation. Heating rate: 10 ◦C/min.; Figure S2: Comparison between DTGA and DSC curves during pyrolysis at 10◦C/min of: (a) grape seeds and hydrochar 180 ◦C; (b) hydrochars 220 and 250 ◦C; Figure S3: Comparison between experimental and predicted data (1-α vs temperature) computed through the Gaussian model, during oxidation of different samples: (a) hydrochar 180 ◦C; (b) hydrochar 220 ◦C; (c) hydrochar 250 ◦C; Table S1: Details of Miura-Maki model, pyrolysis (on a dry basis); Table S2: Details of Miura-Maki model, oxidation (on a dry basis); Gaussian DAEM – MATLAB code.

**Author Contributions:** G.G.: methodology, software, data curation, writing—original draft preparation; G.I.: data curation, visualization, writing—original draft preparation; L.F. (Luca Fambri): experimental planning, writing—review and editing, supervision, project administration; L.F. (Luca Fiori): writing—review and editing, supervision, project administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** All the authors acknowledge Claudia Gavazza for thermal analysis. G.I. acknowledges the financial support provided by the ERICSOL project of the University of Trento, which partially covered her Ph.D. scholarship. All individuals included in this section have consented to the acknowledgement.

**Conflicts of Interest:** The authors declare no conflict of interest.
