*2.6. Model-Free Methods*

In this work, the modeless methods of Friedman, OFW, and KAS were used to analyze the kinetic parameters [6,20].

The Friedman's method is a differential method which is expressed by the equation:

$$\ln\left[\beta\_i \left(\frac{d\alpha}{dT}\right)\_{a,i}\right] = \ln[A\_a f(\alpha)] - \frac{E\_\kappa}{RT} \tag{6}$$

where the subscript *i* is given heating rate value, and subscript *α* is given conversion degree. The OFW method is an integral method which is expressed by the equation:

$$\ln(\beta\_i) = \ln\left(\frac{A\_{a}E\_{a}}{R\_{\mathcal{S}}(\alpha)}\right) - 5.331 - 1.052 \frac{E\_{a}}{RT\_{ai}} \tag{7}$$

The KAS method used for kinetic determination is given in equation:

$$\ln\left(\frac{\beta\_i}{T\_{ai}^2}\right) = \ln\left(\frac{A\_{\text{A}}R}{E\_{\text{A}}\,\,\,\mathcal{g}(a)}\right) - \frac{E\_{\text{a}}}{RT\_{ai}},\tag{8}$$

where *g(α)* is constant with given conversion value.

#### *2.7. Reaction Model Determination for AIW Pyrolysis*

The master-plot method is used to predict solid state mechanisms in the thermal decomposition of biomass. The master graph is built either in a differential or in a differentialintegral form [37]. Various models are fitted to solid-phase kinetic data based on such reaction mechanisms as nucleation, geometric shape, diffusion, and reaction order [19,40]. The theoretical master plots do not depend on the heating rate, but strictly depend on the kinetic model used to model the reaction [41]. To construct a differential graph, a comparison is used at the control point *α* = 0.5 [42].

$$\frac{\frac{d\alpha}{d\theta}}{\left(\frac{d\alpha}{d\theta}\right)\_{0.5}} = \frac{f(\alpha)}{f(0.5)},\tag{9}$$

where *<sup>f</sup>*(*α*) *<sup>f</sup>*(0.5) – theoretically determined from the function, the expressions for which are given in [43]; *θ* denotes the reaction time taken to attain a particular *α* at infinite temperature. The left side of expression (9) is the experimental curve calculated using the following equation:

$$\frac{\frac{da}{d\theta}}{\left(\frac{da}{d\theta}\right)\_{0.5}} = \frac{\frac{da}{d\theta}}{\left(\frac{da}{d\theta}\right)\_{0.5}} \cdot \frac{\exp\left(\frac{E}{RT}\right)}{\exp\left(\frac{E}{RT\_{0.5}}\right)}\tag{10}$$

where *T*0.5 is the reaction temperature at *α* = 0.5.

### *2.8. Thermodynamic Parameters*

Estimating thermodynamic parameters is a useful tool for understanding biomass pyrolysis, determining the feasibility of a thermal decomposition process, and calculating energy performance. Enthalpy change Δ*H* (kJ/mol), Gibbs free energy Δ*G* (kJ/mol), and entropy change Δ*S* (J/mol·K) were calculated according to the equations derived from the activation complex theory (Eyring Theory) using the following formulas [44–46]:

$$
\Delta H = E\_a - R \cdot T\_{peak\prime} \tag{11}
$$

$$
\Delta G = E\_n + \left( R \cdot T\_{p\text{exak}} \cdot \ln \frac{K\_B \cdot T\_{p\text{exak}}}{h \cdot A} \right),
\tag{12}
$$

$$
\Delta S = \frac{\Delta H - \Delta G}{T\_{\text{peak}}},
\tag{13}
$$

where *Tpeak* is the temperature corresponding to the maximum mass loss rate, ◦C; *KB* is Boltzmann constant (1.38 · <sup>10</sup>−<sup>23</sup> J/K); *<sup>h</sup>* is Planck's constant (6.626 · <sup>10</sup>−<sup>34</sup> <sup>J</sup>·s).

#### **3. Results and Discussion**

*3.1. Results of Proximate and Ultimate Analyses*

To assess the possibility of using AIW as a bioenergy raw material, the main physical and chemical characteristics were considered (Table 1).


**Table 1.** The results of the proximate and ultimate analyses of AIW sample.

Humidity and ash content in the AIW sample corresponds to the range of values typical for commercial biomass fuels (humidity up to 25.6 wt.%, ash content up to 9.8 wt.%) [47]. The test sample has a high content of volatile substances; therefore, it is suitable for various thermochemical processes due to its high flammability. The obtained value of volatile substances is comparable with the values obtained for other agricultural wastes suitable for energy use [47,48]. In addition, this means that the AIW sample is more reactive than traditional energy sources such as coal. The HHV of the sample corresponds to the commercial fuel olive stone (17.88 MJ/kg), energy crops–thistle (17.75 MJ/kg) [47], as well as such biomass as: apple tree branches (17.82 MJ/kg), feijoa leaves (17.81 MJ/kg), hazelnut tree leaves (17.87 MJ/kg), kiwi branches (17.81 MJ/kg), and olive stone (17.88 MJ/kg) [49].

#### *3.2. Pyrolysis Products Yields and Their Quality*

The pyrolysis products of AIW are shown in Figure 1. The presented values are consistent with the data obtained from the pyrolysis of rice husks [34], switchgrass [50], algal waste [51], and poultry litter [52]. The maximum mass fraction of 37.1 wt.% is characteristic of the pyrolysis liquid. In connection with the subsequent use of pyrolysis liquid for energy purposes, it was separated into oil and aqueous fractions. It is important to use a homogeneous fuel to ensure timely ignition, as well as efficient atomization in the combustion zone and maintaining flame stability in combustion devices [53].

The aqueous fraction of the pyrolysis liquid contains 85.72% water, 10.4% acetic acid, and 3.88% unidentified components. Water is the main component in the liquid, which is explained by the humidity of the AIW sample, dehydration reactions at temperatures below 550 ◦C, and the occurrence of secondary cracking reactions of oxygen-containing macromolecular compounds at high temperatures [54]. The oil fraction has a diverse and rich composition. Approximately 70.85% of the relative content of the total peak area was identified (GC-MS analysis). The identified compounds were classified into the following main chemical categories: hydrocarbons, phenols, alcohols, ketones, ethers, and N-containing heterocycles. Components with a peak area ≥ 1% are presented in Table 2. Saturated hydrocarbons tetratetracontane and tetracontane are present in large quantities. It is known that the oil fraction from red amaranth seeds is a rich source of squalene, so the content of 2,6,10,14,18,22-Tetracosahexaene, 2,6,10,15,19,23-hexamethyl-, (all-E) equals 5.44% [55]. All identified compounds (including peak area ≤ 1%) are grouped and shown in Figure 2. The oil fraction contains 41.8% hydrocarbons, which characterizes it as a high-quality fuel.

**Figure 1.** AIW pyrolysis products.

**Table 2.** The main components of the oil fraction (peak area ≥ 1%).


**Figure 2.** Pyrolysis Liquid: (**a**) photograph and (**b**) composition of the oil fraction.

It should also be noted that there are no organic acids in the oil fraction; they are present only in the composition of esters. Accordingly, the pH value is high and the liquid is characterized by an alkaline reaction, which is also important for the design of power plants.

The concentrations of the detected pyro-gas components, converted to nitrogen-free composition, are shown in Table 3. It was found that the predominant components in AIW pyrolysis are CO2 and CO. The total concentration of these gases reaches 94.44%. The combustible part of the pyrolysis gas includes 52.7% of the components, which is consistent with the data of other authors [52,56,57].

**Table 3.** Pyro—gas composition.


The main physicochemical characteristics of AIW biochar (Table 4) correspond to biochars obtained by pyrolysis (process temperature 500 ◦C) of different biomass [58]. The elemental composition of AIW biochar is typical, in which the content of carbon is in the range of 50–87.2%, hydrogen 0.7–4.5%, nitrogen 0.08–6.94%, and oxygen 6–30% [59]. Figure 3 shows the microelement composition of the ash of the solid carbonaceous residue. The predominant components of the ash were K and Ca, and their total content was 81.8% of the total mass.

**Table 4.** The results of the proximate and ultimate analyses for biomass biochars.


\* calculated.

**Figure 3.** Biochar: (**a**) photography; (**b**) elemental composition of mineral part.

Thus, the studied biochar can serve as a direct source of potassium, which is the most important element—a biophile, the removal of which with the harvest of agricultural crops is always greater than that of phosphorus and nitrogen. An analysis of the literature showed that elevated values of K, Mg, and Ca in the solid pyrolysis product make it possible to use it for liming and neutralizing acidic soils [60,61].

#### *3.3. Thermal Degradation Analysis*

The results of pyrolysis of AIW samples at heating rates of 10, 15, and 20 ◦C/min in an argon atmosphere are shown in Figure 4. The TG curves are the change in weight loss with temperature, and the DTG curves are the rate of weight loss with temperature. According to the shape of the curves, it can be judged that the thermal degradation of the studied AIW sample occurs similarly to the general trend of biomass pyrolysis.

**Figure 4.** (**a**) TG−curves; (**b**) DTG−curves.

Based on the analysis of the obtained TG data, the AIW pyrolysis process can be divided into 3 main stages (Table 5).


**Table 5.** Main stages of thermal decomposition.

The first stage in the temperature range from 40 ◦C to 190 ◦C corresponded to the process of evaporation of physically bound moisture from samples of AIW. It is also possible to release light volatile components at this stage [46]. The average weight loss at this stage was 9.25 wt.% for three heating rates (Table 6). The first stage has a small peak characterized by an endothermic reaction, which is associated with the absorption of heat in the process of moisture evaporation [44].

The main stage, corresponding to the main pyrolysis, occurred in the temperature range from 190 ◦C to the temperature range of 530–560 ◦C for three heating rates and was accompanied by the main loss of organic matter mass. During this stage, there was an active decomposition of the biomass components and the release of volatile substances associated with the thermal destruction of hemicellulose, cellulose, and lignin [62,63]. The average weight loss during the release of volatiles was 59.63 wt.%. As can be seen from Figure 4, rapid weight loss begins above a temperature of 190 ◦C, which is associated with the rapid breakdown of thermally unstable components of hemicellulose and extractives [37,64]. Hemicellulose consists of short chain heteropolysaccharides and is an amorphous and branched structure [8,19,33,37,39,41,65,66]. Furthermore, with an increase in the pyrolysis temperature, cellulose is involved in the degradation process, which is characterized by a higher decomposition temperature (315–400 ◦C) due to the presence of a long polymer of glucose units and a large number of hydrogen bonds in its composition [67]. Cellulose, due to its chemical structure, is more resistant to thermal degradation; its decomposition is typical for the temperature range of 270–350 ◦C [68,69].


**Table 6.** Mass loss characteristics of AIW obtained from TGA analysis.

On the DTG-curves (Figure 4) at the stage of devolatilization, one can note the maximum temperature peak, which has values of 317.7, 322.6, and 328.5 ◦C for the three heating rates. This peak is characterized by an endothermic reaction. In addition, a small temperature exothermic peak is found at 402.7–422.1 ◦C, which can be associated with the beginning of the decomposition of lignin in the test sample. The literature data indicate that the onset of lignin decomposition for various types of biomass occurs in the temperature range of 280–550 ◦C [16]. The mechanism of lignin pyrolysis is more complex than that of cellulose and hemicellulose; it includes reactions of free radicals [70,71]. Due to the fact that lignin has the highest thermal stability, it decomposes slowly throughout the thermal degradation up to a temperature of 900 ◦C [16].

The third stage, which is typical for the temperature range of 529.5 ◦C and up to 1000 ◦C for three heating rates, is associated with the process of degradation of char and minerals. At this stage, after the completion of the release of volatiles and the main thermal destruction, the process of enrichment with carbon and the formation of the structure of carbonaceous matter continue. Although small, inorganic minerals in biomass can have a significant effect on the pyrolysis process. In this regard, the process of thermal degradation of mineral components is primarily associated with the decomposition of CaCO3 in the temperature range from 780 to 1000 ◦C [72]. In addition, pyrolysis products can interact with inorganic elements in the residual carbonaceous matter [73]. In this case, the mineral components act as catalysts in the reactions of gas formation from pyrolysis products [72]. The residual fraction as a result of AIW pyrolysis was 25.5 wt.% for the three heating rates. As a result of the experiments, it was revealed that the nature of the TG and DTG curves of the studied samples is similar to the biomass of herbaceous plants, which were reported in [16,17,74].

#### *3.4. Kinetic Analysis*

In this work, a kinetic analysis was carried out for the main stage of pyrolysis devolatilization—since at this stage, the maximum mass loss occurs [75]. AIW kinetic parameters were determined using three model-free methods: Friedman, KAS, and OFW, based on TGA data. Figure 5 shows the results of linear regression in the range of conversions from 0.1 to 0.9 of the kinetic analysis of the total thermal decomposition reactions of the AIW samples. Straight line slope data obtained from each model-free method were used to calculate the *Eα* values presented in Table 7.

**Figure 5.** Plots for determination *Eα* of AIW pyrolysis using: (**a**) Friedman; (**b**) KAS; (**c**) OFW.



The dynamics of *Eα* values obtained by the Friedman, KAS, and OFW methods highlight the complexity of the AIW sample kinetics. *Eα* gradually increases until reaching its maximum at a conversion rate of 0.8 for the OFW and KAS methods, and *α* conversion rate of 0.7 for the Friedman method. A similar trend in *Eα* values was found during pyrolysis of such biomass as bark of *Ficus natalensis* [7], water hyacinth [76], elephant grass [77], and mustard stalk [78].

The pre-exponential factor A characterizes the frequency of collisions of reacting molecules. This indicator makes it possible to explain the chemistry of reactions, which is important for optimizing the pyrolysis process [36]. Almost all obtained A values are in the range from 10<sup>4</sup> to 109, which indicates a low reactivity of the test sample and the occurrence of a surface reaction, as well as a tight junctional complex (closed complex) [36,39].

The *Eα* values are in the range of 152.52–291.94 kJ/mol (Friedman), 156.78–265.25 kJ/mol (KAS), and 157.00–265.43 kJ/mol (OFW). The value of *Eα* shows a measure of the minimum energy required to start a chemical reaction, as well as a potential measure of reactivity [79,80]. According to the literature data, the KAS and OFW methods are less accurate than the Friedman method [39,79], since it does not contain assumptions and approximations [39,81]. It should be noted that the Eα values calculated by the KAS, OFW, and Friedman methods for the AIW sample agree with each other. The average value of *Eα* obtained by the Friedman method is only 3.7% higher than that calculated by the OFW and KAS methods. Comparative analysis of *Eα* values for different types of biomass is presented in Table 8.


**Table 8.** Comparison of biomasses activation energy.

Figure 6 compares the theoretical differential plots of *f*(*α*))/*f*(0.5) versus *α* with the experimental plot of (d*α*/d*θ*)/(d*α*/d*θ*) 0.5 versus α for a heating rate of 10 ◦C/min to draw a conclusion about the reaction mechanism of solid-phase pyrolysis.

**Figure 6.** Comparison of experimental and theoretical master plots for samples AIW.

In the range of *α* from 0.1 to 0.5, the AIW degradation mechanism refers to the onedimensional diffusion (D1) process, i.e., heat transfer in the sample occurs by diffusion. When α values are greater than 0.5, the AIW degradation mechanism tends to random nucleation with one nucleus in a single particle (F1). In the range of *α* from 0.7 to 0.9, the mechanism is reduced to random nucleation with two nuclei in the individual particle (F2). The F1 and F2 degradation mechanisms are initiated from random points that act as growth centers for the development of the degradation reaction [87]. Similar results were obtained for other types of biomass [88]. A slight discrepancy between the experimental curves of the master plot for the studied AIW samples can be explained by the deviation of the ideal conditions adopted in the kinetic models from the actual pyrolysis conditions.
