#### 2.1. Vine Wood Sample Preparation

Vine wood was obtained from grubbed vines from a vineyard replanting operation in Pacs del Penedés, Barcelona, Spain. The vine wood was left aside in the vineyard to be dried and crushed in a hammermill until it passed through a mesh size of less than 10 mm. This size was selected in order to reduce the heterogeneous structure of the biomass. The observed heterogeneity is due to the different vine plant families in the vineyard and the soil residues that remain in the wood after sample collection.

Biomass was then dried for 24 h and left to cool at room temperature to ensure similar moisture content in the samples. Then, it was sieved, and the particle size distribution (PSD) was analyzed. Subsamples of non-leached biomass (NL-B) and leached biomass (L-B) were prepared according to the PSD reported in

Table 1. In L-B samples, the average particle size fraction under 1 mm was removed because this fraction would be eliminated in the leaching process.

After sieving, the L-B sample fraction was leached in order to remove soluble salts and dirt by washing with hot water. One liter of distilled water was used to leach 20 g of each fraction at 80 °C for 1 h. Afterward, the sample was vacuum-filtered and dried for 24 h in an oven at 100 °C. These conditions were chosen from methodologies reported by other authors in the literature [

20,

21]. Hot water was used because it is better for dissolving mineral material [

22,

23]. Then, the particle size was reduced by using a ball mill until the particles could pass through a sieve with a mesh size of 0.5 mm, which was deemed an adequate size to avoid heat transfer effects and successfully perform thermogravimetric tests [

24].

The NL-B sample was prepared by (1) reducing the particle size and by (2) sieving each fraction to 0.5 mm separately. Finally, as performed for L-B, the NL-B sample fractions were weighed and mixed according to their PSD. This process was performed to ensure a homogeneous particle size in the final sample since each fraction has different grinding behaviors.

#### 2.3. Thermogravimetric Data Processing: Deconvolution

The thermal degradation of biomass is a complex process that can be explained by analyzing the pyrolysis kinetic parameters obtained using distributed activation energy models (DAEM) [

12,

14,

25,

26]. Recently, other models based on the Fraser–Suzuki function have allowed new and improved ways to fit kinetic curves. In these studies, independent decomposition profiles of the main components of lignocellulosic biomass were obtained, and the thermal degradation of samples was successfully described after applying the Fraser–Suzuki function [

27,

28,

29,

30].

In the present study, multiple overlapping phases from TGA were detected; they were separated by a deconvolution methodology using the Fraser–Suzuki function shown in Equation (1).

where y is the sample mass; T is the temperature; and h, p, s, and w are different adjustment parameters that correspond to the amplitude (

$\frac{\mathrm{dW}}{\mathrm{dT}}$_{max} in this case), position (T

_{max} in this work), asymmetry, and half-width of the TG curve, respectively. The parameter values were obtained by fitting TGA data using nonlinear regression [

31].

The derivative of the mass loss,

$\frac{\mathrm{dy}}{\mathrm{dT}}$, which is input deconvolution data (Equation (1)), was obtained directly by derivative TG (DTG) [

32].

By integrating Equation (1), Equation (2) was obtained. This mathematical expression is used to determine the percentages of each degradation phase of the global reaction by using Erf as the error function.

If symmetric functions are assumed and the s parameter is considered to be null, Equation (2) can be simplified by avoiding the use of the error function and without taking initial conditions. With these approximations, the percentages of each phase were obtained by Equation (3).

Afterward, two assumptions were made: the samples have an ideal behavior, and the component percentages are independent of the chosen heating ramp. With these considerations, two relationships between deconvolution process parameters were established by using Equation (3). Finally, rearranging Equation (3) resulted in Equation (4).

From Equation (4), the parameter w must be constant for the same pseudo-component with every heating ramp used if a symmetric function is considered and if ${\frac{\mathrm{d}\mathsf{\alpha}}{\mathrm{dT}}}_{\mathrm{max}}$ is assumed to be constant.

In a study of two similar pseudo-components, it can be assumed that $\frac{\mathrm{d}\mathsf{\alpha}}{\mathrm{dT}}{\left(\mathsf{\beta}\right)}_{\mathrm{max}}$ remains constant. Hence, by comparing their amplitudes ($\frac{\mathrm{dW}}{\mathrm{dT}}$_{max}) at different heating rates, Equation (3) can be transformed into Equation (5), where p_{1} and p_{2} refer to the maximum temperature reached by β_{1} and β_{2}, respectively.

In light of this last relation, it can be shown that the decomposition of two similar pseudo-components at the same heating rate must take place at the same T_{max} if they have common kinetic parameters.

For all these assumptions to be correct, T

_{max} (or p) must vary by rearranging Equation (5) as follows:

Although Equation (6) looks artificial, it has a strong correlation with the famous Kissinger equation [

12], where if two different T

_{max} values (with their respective β values) are compared, Equation (7) can be obtained.

Finally, rearranging Equation (7) results in Equation (8), which is nonlinear. The similarity between Equations (6) and (8) is apparent. In addition, both equations are easy to implement by computational methods.

#### 2.4. Isoconversional Method

The kinetic rates of non-isothermal processes have been thoroughly described in the literature [

5,

6,

27,

33,

34] and can generally be described by Equation (9).

where β is the heating rate; α is the conversion degree; and E, f(α), and A are the kinetic triplet parameters: activation energy, reaction model, and preexponential factor, respectively.

In this work, the differential isoconversional method proposed by Friedman [

14,

35] and presented by Equation (10) was applied. The Friedman model was selected because of the weakness of integral methods relative to differential ones, despite the noise in the results [

17].

Finally, for runs performed at different heating rates, Af(α) is constant at a fixed conversion degree, α. By measuring the temperature T and the reaction rate dα/dt at the fixed conversion degree α for all experiments performed at different heating rates, the activation energy can be calculated from the slope of ln(dα/dt) vs. 1/T, whereas ln(Af(α)) is obtained from the intercept [

14]. In the end, the recommendations proposed by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC) were considered [

36] by reporting the variation in E vs. α.

To calculate the kinetic parameters, the global reaction was considered as the sum of the contributions of the different components. From this assumption, Equation (11) was obtained. In this equation, c_{i} denotes the ith contribution of phases formed by the four main pseudo-components considered (moisture, cellulose, hemicellulose, and lignin).

For the latest reaction stages, a modified Friedman equation, Equation (12), was used.

where α values are sought when a single pseudo-component was involved in the overall reaction. These α values were different for each sample because of the delay in conversion degree; the delay is caused by different amounts of inert material.

When different samples are compared, kinetic parameters are similar if a similar and single reaction takes place in both samples. In this case, the activation energy was obtained by taking the logarithm of Equation (12) and rearranging the resultant mathematical expression. Thus, E values are associated with Equation (13).

where the subscripts in Equation (13) denote the two different biomasses with different values of the conversion degree for each sample. This difference corresponds to the delay in α values.