A Comprehensive Study on the Combustion of Sunflower Husk Pellets by Thermogravimetric and Kinetic Analysis, Kriging Method

Abstract

The combustion of sunflower husk pellets was investigated by kinetic analysis supplemented by the Kriging method. The nonisothermal thermogravimetric experiments in air were carried out at the temperatures from 20 to 700 °C and heating rates of 5, 10, and 20 °C/min. Kinetic analysis was carried out using the model-free OFW (Ozawa–Flynn–Wall) method and Coats–Redfern (CR) method. The activation energy values, calculated by the OFW method, ranged from 116.44 to 249.94 kJ/mol. These data were used to determine the combustion mechanism by the CR method. The kinetic triplet (E_α, A, g(α)) was determined in the conversion interval 0.2 to 0.8. The model of the chemical reaction F₈ was recommended to describe the mechanism of the thermochemical conversion process. The relationship between the kinetic parameters was analyzed using the Kriging method. The patterns between the kinetic parameters were represented as three-dimensional surfaces and two-dimensional projections. The distribution’s surfaces were uniform; there were local extremes as well as linear regions. A new approach to the data analysis will allow predicting parameters of a thermochemical conversion of the various raw materials and contributes to a deeper understanding of the characteristics and mechanism of biomass combustion.

1. Introduction

Currently, biomass is a main renewable energy source. The availability of this resource, its inexhaustibility, wide distribution, and practically neutral carbon dioxide emission, allow biomass to become a full-fledged alternative to traditional fuel [1]. Biomass is the fourth largest source of energy after coal, oil, and natural gas [2]. It accounts for 9% to 14% of total primary energy consumption in the industrialized countries and from 20% to 35% in developing countries [3]. It should also be noted that the main difference between biomass and coal is an absence of sulfides in its composition; therefore, the biomass power plants do not require a flue gas purification unit to remove sulfur dioxide before being released into the atmosphere [3]. Thermochemical conversion by direct combustion is the simplest and most basic way of valorization and conversion of biomass into useful energy [4].

The modern methods of heating include the use of automated boilers, running on pellet fuel. Usually, wood pellets are burnt in such boilers. The limited availability of wood biomass for energy purposes and the high demand for it from other industrial sectors have led to the need to increase the range of raw materials for the production of pellets [5]. The use of large-tonnage agricultural waste, such as sunflower husk, will solve this problem. In terms of fuel consumption density and output power, sunflower husk pellets are not inferior to hardwood pellets [6]. In addition, agropellets are the cheapest substitute for wood pellets [7].

Studying the chemical kinetics of combustion, using the thermal analysis methods, and obtaining the necessary kinetic parameters are important for optimizing the combustion process and designing industrial boilers, running on biomass pellets. Thermal analysis, in addition to determining the mass loss values, allows us to evaluate the combustion characteristics and reactivity of biomass at different heating rates. The biomass combustion mechanism, consisting of cellulose, hemicellulose, lignin, and extractives, is rather complex and multi-stage. Therefore, to determine the main kinetic parameters, two complementary methods have been developed: a model-free isoconversion method and a model-fitting one. The model-free methods, such as Friedman, Ozawa–Flynn–Wall (OFW), Starink, and Kissinger–Akahira–Sunose (KAS), allow us to determine only one value of the activation energy, which can be used for an analysis in the model fitting method [8,9]. According to the recommendations of the International Confederation for Thermal Analysis and Calorimetry (ICTAC) Kinetics Committee, the integral isoconversion OFW and KAS methods are accurate methods for calculating kinetic parameters [10,11]. A comparison of three model-free OFW, KAS, and Starink methods shows a similar distribution of activation energy values, while deviations between the obtained data can be neglected, and any of these methods can be used [12]. The model-fitting method (for example, Coats–Redfern (CR)) uses a number of kinetic models based on the type of reactions, and a heating rate is sufficient to calculate the kinetics [13]. The CR method was used to describe thermal degradation of various lignocellulosic fuels (wheat straw, rich husk, and bagasse) [14], mustard stalk [10], maize silage [15], and shells from different types of nuts (walnut, hazelnut, peanut, and pistachio) [16].

A kinetic study of thermochemical conversion in an inert atmosphere (pyrolysis) of sunflower husks in order to determine the activation energy, the conversion rate constant, as well as understanding the process mechanism is presented in [17,18,19,20,21]. The authors of the study [5] carried out TGA sunflower husk pellet combustion both separately and in a mixture with oats at a heating rate of 10 °C/min without studying the kinetics of the process. The thermogravimetric study of the sunflower husk pellets combustion at three heating rates of 5, 10, and 20 °C/min is presented in the work [22]. Studies [23,24] showed that torrefaction significantly affects the thermal characteristics of sunflower husks. The risk assessment of sunflower husk ignition and the combustion process were investigated at a heating rate of 10 °C/min, the kinetic parameters were determined using the reaction rate constant method [25]. In the work [26] the oxygen burning of the mixture of corn and sunflower husk was studied, the combustion kinetics was evaluated using OFW and Vyazovkin’s methods. The sunflower shell combustion was evaluated by the thermogravimetric analysis at the heating rates of 5, 10, 20, and 40 °C/min [27]. The kinetic parameters were determined using the distributed activation energy model and the global kinetic model. It should be noted that currently there are no works, devoted to the study of the kinetics and characteristics of the sunflower husk pellet combustion based on TGA data.

Nowadays the optimization of the thermochemical conversion process and the study of the relationship of various parameters, while performing a smaller number of experimental studies, are of great interest. For these purposes, the statistical response surface methodology (RSM) is often used, which combines 3D surface graphs and 2D contours [28,29,30,31]. However, RSM is more suitable for solving low-order nonlinear problems. For a high order nonlinear problem, it is better to use the Kriging or Gaussian process regression method [32]. This is a well-known geostatistical method, used to construct grids and graphs [33,34]. When solving a number of problems, it was found that the Kriging method is a good alternative to RSM [35]. In this study, the relationship between the kinetic parameters is proposed for the first time to be evaluated using this method.

The literature review reveals that the data on the combustion of sunflower husk pellets and their kinetics are rare and need more attention. Therefore, the aim of the present work was to study the thermal behavior of sunflower husk pellets during combustion; determination of the kinetic parameters using the model-free OFW approach and the model-fitting CR method; and analysis of the relationship between the kinetic parameters using the Kriging method. The current study contributes to a deeper understanding of the characteristics and mechanism of biomass pellets combustion.

2. Materials and Methods

2.1. Agropellets

Sunflower husk pellets were produced at the Oil Extraction Plant. Proximate analysis was performed according to ISO standards (18134–3:2015, 18122:2015, 18123:2015) using a drying chamber (ShSL-43/250 V, AnalytPromPribor, Moscow, Russia) and a muffle furnace (PMLS-2/1200, Milaform, Kazan, Russia). Ultimate analysis was performed on an elemental analyzer (Euro EA 3000, Eurovector, S.p.A., Milan, Italy). The chemical composition and ash content of the sample are shown in Figure 1.

Pellets contained 77.6% volatile matters, 12.5% fixed carbon, 6.7% moisture, and their higher heating value was 18.9 MJ/kg. Sunflower husk pellets were crushed to a powder by SM-450, normal type (MRC Ltd-LABORATORY EQUIPMENT, Holon, Israel). The pellets had a cellulose content of 46.4%, hemicellulose 31.6%, and lignin 17.1% (Oil Extraction Plant data).

2.2. Thermogravimetric Analysis

The experiments on pellets combustion were carried out on the thermal analyzer SDT Q600 (TA Instrument, New Castle, DE, USA). The samples were crushed and placed in the equipment 10 mg. The temperature was uniformly increased from 20 to 700 °C at heating rates of 5, 10, and 20 °C/min. The oxidizing atmosphere was maintained by a continuous supply of air flow at a rate of 100 mL/min. The repeatability error of the experiment corresponded to 1.5% in accordance with [36].

2.3. Kinetic Theory

The kinetic equation for thermal decomposition reactions of a solid-phase substance is based on the conversion rate:

$$\frac{d\alpha }{dt}=k\left(T\right)f\left(\alpha \right),$$

(1)

where α is the conversion degree; dα/dt is the conversion rate; t is the time period (s); T is the absolute temperature (K); k(T) is the reaction rate constant; and f(α) is the reaction model.

The rate of sunflower husk pellets conversion is determined by the following equation:

$$\alpha =\frac{m_0-m_a}{m_0-m_f},$$

(2)

where $m_0$ is the initial weight of the sample (mg); $m_a$ is the current weight of the sample (mg); and $m_f$ is the final weight of the sample (mg).

The constant k(T) is expressed by the Arrhenius equation:

$$k\left(T\right)=A{e}^{-E_{\alpha }/RT},$$

(3)

where E_α is the activation energy (kJ/mol); R is the universal gas constant (8.314 J/K∙mol); and A is the pre-exponential factor (1/s).

For nonisothermal experiments of thermal decomposition of a solid at a linear heating rate $\beta =dT/dt$, the generalized fundamental equation has the following form:

$$\frac{d\alpha }{dT}=\frac{A}{\beta }\cdot \exp \left(-\frac{E_{\alpha }}{R\cdot T}\right)\cdot f\left(\alpha \right)$$

(4)

Integrating Equation (4) makes it possible to analyze the kinetic data obtained by the TGA method. Integration can be performed using isoconversion methods [37].

2.3.1. OFW Method

The model-free isoconversion method OFW is one of the most common methods to calculate the kinetic characteristics of the processes of solid biomass thermal decomposition according to thermogravimetric curves [38]. This method can be used to obtain activation energy values without a preknown reaction model based on the conversion rate at several heating rates. According to the OFW theory based on the Doyle approximation [39], the equation for calculating the activation energy has the following form [40]:

$$\ln \left({\beta }_i\right)=\ln \left(\frac{A\cdot E_{\alpha }}{R\cdot g\left(\alpha \right)}\right)-5.331-1.052\frac{E_{\alpha }}{R\cdot T}$$

(5)

The activation energy E_α calculated by the angle value of an inclination of the line, plotted in the coordinates lnβ−1/T at an equivalent conversion degree α for the different heating rates. To determine the pre-exponential factor, the following formula is used [41]:

$$A=\frac{-\beta R}{E_{\alpha }}\left(\ln \left[1-\alpha \right]\right)\cdot {10}^{\delta },$$

(6)

where $\delta$ is the numerical integration constant based on the Doyle approximation.

2.3.2. CR Method

The CR method is based on a model fitting and is expressed by the following equation [42]

$$\ln \frac{g\left(\alpha \right)}{T^2}=\ln \left(\frac{A\cdot R}{E_{\alpha }\cdot \beta }\right)-\frac{E_{\alpha }}{R\cdot T}$$

(7)

where g(α) is the integral form of reaction model (Table 1).

By plotting a graph $\ln g\left(\alpha \right)/T^2$ depending on $1/T_{\alpha }$, the activation energy E_α, and the pre-exponential factor A can be obtained. This method can be used even for one heating rate [40,43]. To calculate the kinetic parameters using the CR method, the solid-phase reaction model should be determined in advance. These can be a variety of models based on nucleation and growth (An), interphase reaction (Rn), chemical reaction (Fn), and diffusion (Dn).

Table 1. Various kinetic models and the corresponding mechanism of the solid-state process [40,44].

Symbol	Model	Integral Form g(α)	Differential Form f(α)	Rate-Determining Mechanism
1. Sigmoidal rate equations or random nucleation and subsequent growth
A1	Avrami−Erofeev equation	−ln(1 − α)	1 − α	Assumed random nucleation and its subsequent growth, n = 1
An	Avrami−Erofeev equation	[−ln(1 − α)]1/n	n(1 − α)[−ln(1 − α)]1/n(n−1)	Assumed random nucleation and its subsequent growth, n ≠ 1
2. Chemical process or mechanism non−invoking equations
F1	First order	−ln(1 − α)	1 − α	Chemical reaction
Fn	n-th order	(1 − α)−(n−1) − 1	(1 − α)n	Chemical reaction
3. Acceleratory rate equations
P2	Mampel power law	ln(α1/2)	2(α)1/2	Nucleation
4. Deceleratory rate equations
4.1. Phase boundary reaction
R2	Power law	1 − (1 − α)1/2	2(1 − α)1/2	Contracting cylinder, cylindrical symmetry
R3	Power law	1 − (1 − α)1/3	3(1 − α)2/3	Contracting sphere, spherical symmetry
4.2. Based on the diffusion mechanism
D1	Parabola low	α2	1/2α	1D diffusion
D2	Valensi equation	(1 − α)ln(1 − α) + α	[−ln(1 − α)]−1	2D diffusion
D3	Jander equation	[1 − (1 − α)1/3]2	1.5(1 − α)2/3[1 − (1 − α)1/3]−1	3D diffusion, spherical symmetry
D4	Ginstling−Brounstein equation	(1 − 2α/3) − (1 − α)2/3	1.5[(1 − α)−1/3 − 1]−1	3D diffusion, cylindrical symmetry
D5	Zhuravlev, Lesokin, Tempelman equation	[(1 − α)−1/3 − 1]2	1.5(1 − α)4/3[(1 − α)−1/3 − 1]−1	3D diffusion
D6	Anti-Jander equation	[(1 + α)1/3 − 1]2	1.5(1 + α)2/3[(1 + α)1/3 − 1]−1	3D diffusion
D7	Anti-Ginstling−Brounstein equation	1 + 2α/3 − (1 + α)2/3	1.5[(1 + α)−1/3 − 1]−1	3D diffusion
D8	Anti-Zhuravlev, Lesokin, Tempelman equation	[(1 + α)−1/3 − 1]2	1.5(1 + α)4/3[(1 + α)−1/3 − 1]−1	3D diffusion
5. Another kinetics equations with unjustified mechanism
G1	-	1 − (1 − α)2	1/2(1 − α)	-
G2	-	1 − (1 − α)3	1/3(1 − α)2	-

Table 1. Various kinetic models and the corresponding mechanism of the solid-state process [40,44].

Symbol	Model	Integral Form g(α)	Differential Form f(α)	Rate-Determining Mechanism
1. Sigmoidal rate equations or random nucleation and subsequent growth
A1	Avrami−Erofeev equation	−ln(1 − α)	1 − α	Assumed random nucleation and its subsequent growth, n = 1
An	Avrami−Erofeev equation	[−ln(1 − α)]1/n	n(1 − α)[−ln(1 − α)]1/n(n−1)	Assumed random nucleation and its subsequent growth, n ≠ 1
2. Chemical process or mechanism non−invoking equations
F1	First order	−ln(1 − α)	1 − α	Chemical reaction
Fn	n-th order	(1 − α)−(n−1) − 1	(1 − α)n	Chemical reaction
3. Acceleratory rate equations
P2	Mampel power law	ln(α1/2)	2(α)1/2	Nucleation
4. Deceleratory rate equations
4.1. Phase boundary reaction
R2	Power law	1 − (1 − α)1/2	2(1 − α)1/2	Contracting cylinder, cylindrical symmetry
R3	Power law	1 − (1 − α)1/3	3(1 − α)2/3	Contracting sphere, spherical symmetry
4.2. Based on the diffusion mechanism
D1	Parabola low	α2	1/2α	1D diffusion
D2	Valensi equation	(1 − α)ln(1 − α) + α	[−ln(1 − α)]−1	2D diffusion
D3	Jander equation	[1 − (1 − α)1/3]2	1.5(1 − α)2/3[1 − (1 − α)1/3]−1	3D diffusion, spherical symmetry
D4	Ginstling−Brounstein equation	(1 − 2α/3) − (1 − α)2/3	1.5[(1 − α)−1/3 − 1]−1	3D diffusion, cylindrical symmetry
D5	Zhuravlev, Lesokin, Tempelman equation	[(1 − α)−1/3 − 1]2	1.5(1 − α)4/3[(1 − α)−1/3 − 1]−1	3D diffusion
D6	Anti-Jander equation	[(1 + α)1/3 − 1]2	1.5(1 + α)2/3[(1 + α)1/3 − 1]−1	3D diffusion
D7	Anti-Ginstling−Brounstein equation	1 + 2α/3 − (1 + α)2/3	1.5[(1 + α)−1/3 − 1]−1	3D diffusion
D8	Anti-Zhuravlev, Lesokin, Tempelman equation	[(1 + α)−1/3 − 1]2	1.5(1 + α)4/3[(1 + α)−1/3 − 1]−1	3D diffusion
5. Another kinetics equations with unjustified mechanism
G1	-	1 − (1 − α)2	1/2(1 − α)	-
G2	-	1 − (1 − α)3	1/3(1 − α)2	-

2.4. Kriging Method

The results obtained empirically are proposed to be considered in a dimensionless form. All considered absolute kinetic parameters are normalized to the corresponding fixed maximum value from an entire array of the experimental data: $\overline{E_{\alpha }}=\frac{E_{\alpha }}{E_{\alpha }{}^{\max }}$, $\overline{A}=\frac{A}{A^{\max }}$ and $\overline{g\left(\alpha \right)}=\frac{g\left(\alpha \right)}{g{\left(\alpha \right)}^{\max }}$, where E_α, A, and g(α) are absolute values of the parameters, obtained experimentally; $E_{\alpha }{}^{\max }$$,$ $A^{\max }$, and $g{\left(\alpha \right)}^{\max }$ are maximum values modulo parameters E_α, A, and g(α); $\overline{E_{\alpha }}$, $\overline{A}$, and $\overline{g\left(\alpha \right)}$ are dimensionless normalized values.

The patterns, existing between the normalized kinetic parameters $\overline{E_{\alpha }}$, $\overline{A}$, $\overline{g\left(\alpha \right)}$, are demonstrated using the geostatistical method of constructing grids and plots Kriging, which has proven its usefulness and popularity in many areas. The chosen method allows you to create visually attractive plots from unevenly spaced data. Kriging expresses the relationships between the experimental data obtained in the form of maximally smooth and continuous lines. It effectively and naturally combines anisotropy and the underlying trends [45].

When constructing surfaces $S_{\overline{E_{\alpha }}}$, $S_{\overline{A}}$, and $S_{\overline{g\left(\alpha \right)}}$; it is assumed that the function, linking all values together, can be represented by analogy with the interpolation formula of a surface in space:

$$z=f(x,y)={\displaystyle {\sum }_{i=1}^n{z}_i}{b}_i(x,y)$$

(8)

where x, y, z are Cartesian coordinates, $z_i$ is the value at the i-th point, and $b_i(x,y)$ is the basis function on the plane (x, y) at the i-th point.

As a result, the surface $S_{\overline{E_{\alpha }}}$ is described by the formula:

$$\overline{E_{\alpha i}}\left(\overline{g\left(\alpha \right)},\overline{A}\right)={\displaystyle {\sum }_j{\lambda }_{ij}C\left(d_j\left(\overline{g\left(\alpha \right)},\overline{A}\right)\right)}$$

(9)

The surface $S_{\overline{A}}$ is represented as follows:

$$\overline{A_i}\left(\overline{E_{\alpha }},\overline{g\left(\alpha \right)}\right)={\displaystyle {\sum }_j{\lambda }_{ij}C\left(d_j\left(\overline{E_{\alpha }},\overline{g\left(\alpha \right)}\right)\right)}$$

(10)

Accordingly, the surface $S_{\overline{g\left(\alpha \right)}}$:

$$\overline{g_i\left(\alpha \right)}\left(\overline{E_{\alpha }},\overline{A}\right)={\displaystyle {\sum }_j{\lambda }_{ij}C\left(d_j\left(\overline{E_{\alpha }},\overline{A}\right)\right)}$$

(11)

In these formulas ${\lambda }_{ij}$ is unknown Kriging weights; they are calculated from the corresponding systems of linear equations. $C\left(d_j\left(*,**\right)\right)$ is the basis function at the i-th point.

3. Results

3.1. Thermogravimetric Analysis

Figure 2 shows the thermogravimetric (TG) and derivative thermogravimetric (DTG) curves of the mass change and the rate of mass change from the temperature during pellets combustion. At all heating rates, an identical trend in the TG–DTG curves can be seen. With an increase in the heating rate from 5 to 20 °C/min, a shift towards a higher temperature is noticeable on the TG curves.

A comparison of TGA data for the combustion of sunflower husks obtained in Poland [5], Spain [26], and China [27] was carried out. The nature of the TG and DTG curves is similar. The DTG curve shows two peaks, and the peak temperatures almost coincide. The differences are due to different conditions of origin of raw materials, processing methods (loose or granulated husks), as well as physicochemical parameters. Thus, in loose sunflower husks [26,27], which had a higher moisture content and lower density, weight loss began earlier than in granulated husks [5], this study, but the magnitude of the peaks on the DTG curves was smaller. For granulated sunflower husks, the TG curves shifted towards higher temperatures, and the rate of weight loss was higher.

The process of thermal destruction of biomass during combustion is a complex phenomenon due to differences in the chemical composition of its structural components, which is confirmed by several peaks on the DTG curves [13,46]. Two significant inflection points were obtained on the TG curves, which were confirmed in the form of the main and secondary peaks on the DTG curves. It can be noticed that on the DTG curves, the height and width of the peaks increased with an increase in the heating rate, which indicates a high rate of thermal destruction. A similar character of the TG/DTG curves was obtained during the combustion of rice husks [2], sunflower husk pellets [5], and corn straw [47].

The process of pellet combustion can be divided into three stages: drying (I), devolatilization (II), and coke combustion (III). The stage I (20–210 °C) corresponds to the initial mass loss of pellets, associated with the evaporation of moisture and the release of light volatile substances. The slope of the TG curves in this area indicates a relatively slow rate of mass loss. The average mass loss at this stage for all heating rates was about 7.4%. With increasing temperature, the combustion intensity and the release rate of volatile substances became increased.

The stage II is in the temperature range from 210 to 400 °C; it is the main stage of thermochemical destruction of sunflower husk pellets. At this stage, there is an active interaction of the decomposition components of hemicellulose and cellulose with oxygen in the air. The degradation of hemicellulose and cellulose was reflected in the TG curves in the form of a steep decline, which indicated an increase in the mass loss rate. For all heating rates, the greatest mass loss (47 to 51%) occurred in the temperature range of 250 to 315 °C. The presence of oxygen increased the thermo-oxidative destruction rate of sunflower husk pellets at stage II, which was reflected in the DTG curves in the form of the first peak. The authors [2] obtained a similar result during the combustion of corn straw and rice husks.

At stage III (400–700 °C), lignin pyrolysis occurs with the formation of coke and its subsequent combustion, which is also accompanied by mass loss of pellets [47]. An increase in the mass loss rate was observed, which was reflected in the form of the second peak on the DTG curves. It should be noted that the other authors also correlated the second peak on the DTG curves with coke combustion during the burning of poplar wood chips and rice husk [2], as well as corn straw [48]. The mass loss at this stage was ≈20–30%. After the combustion process was completed, no mass loss was observed on the TG and DTG curves. The average value of the residual mass in all experiments was 1–3%.

3.2. Kinetic Study of Sunflower Husk Pellets

3.2.1. Kinetic Analysis by OFW Method

In this study, the widely recognized OFW method was used to determine the activation energy and pre-exponential factor at the several heating rates [40,49]. Kinetic parameters were determined at the degree of conversion of sunflower husk pellets from 0.1 to 0.9 in increments of 0.05, which corresponds to the recommendations of the ICTAC Kinetics Committee [12,50]. The Figure 3 shows the isoconversion lines lnβ from 1/T, obtained by OFW method at the various degrees of conversion.

The obtained values E_α and A are presented in

Table 2. Kinetic parameters of sunflower husk pellets obtained by OFW method.

α	Eα (kJ/mol)	A (1/s)	R2
0.1	116.44	6.26 × 101³	0.9556
0.15	133.42	2.07 × 1015	0.9930
0.2	141.66	7.77 × 1015	0.9901
0.25	147.64	2.78 × 1016	0.9968
0.3	155.68	1.66 × 1017	0.9948
0.35	165.80	8.86 × 1017	0.9951
0.4	179.20	2.29 × 1019	0.9905
0.45	196.30	5.71 × 1020	0.9912
0.5	210.96	4.99 × 1021	0.9856
0.55	217.37	1.59 × 1022	0.9620
0.6	192.97	3.81 × 1019	0.9009
0.65	156.17	3.94 × 1015	0.9765
0.7	148.70	5.60 × 1014	0.9109
0.75	151.43	2.17 × 1014	0.9470
0.8	214.00	7.36 × 1018	0.9984
0.85	249.94	4.06 × 1021	0.9996
0.9	203.99	1.34 × 1018	0.9990
Average	175.39

. These data indicate a complex multistage mechanism of thermo-oxidative destruction of pellets. The values of the correlation coefficient R² for all α were close to 1.00, indicating the reliability of the calculation and the accuracy of the data.

The mechanism of sunflower husk combustion is quite complicated due to the lignocellulose composition of biomass [51]. The initial tendency to increase the activation energy in the conversion degree from 0.10 to 0.55 is noticeable. Subsequent fluctuations in the values E_α in the conversion degree of 0.60 to 0.90 indicate the course of complex or autocatalytic reactions in the several stages, which is associated with decomposition and salinization of the solid residue [4]. A similar trend in changing the values E_α was obtained during the loose sunflower husk combustion [28]. The average value E_α for the pellets was 175.39 kJ/mol, indicating their high thermal stability. Thus, a significant amount of energy is required for a chemical reaction to occur. Taking into account the various sources and characteristics of biomass, the values of the activation energy of sunflower husk pellets obtained by the OFW method generally agree well with the data presented for biomass pellets [52,53,54].

3.2.2. Kinetic Analysis by CR Method

Kinetic analysis has the aim of finding three kinetic parameters, namely, E_α, A, and g(α), together called a “kinetic triplet”. Finding a reaction mechanism is an important final step in evaluating the kinetics of thermochemical conversion [55,56]. The mechanism of the sunflower husk pellets combustion was evaluated on the basis of the widely used CR method for the entire process at the values $\alpha \in \left(0.2;0.8\right)$. The biomass combustion process, based on a solid-phase reaction, can be described by any of the 30 reaction rate models given in Table 1. Since the OFW method is sufficiently reliable [11,12], the values E_α, calculated by this method, were taken as a basis to determine the most appropriate combustion mechanism (dominant reaction model). The average values E_α, obtained by the CR method at three heating rates β = 5, 10, and 20 °C/min, were compared with the E_α values, obtained by the OFW method.

The mechanism of the sunflower husk pellet combustion process was studied using 30 reaction models (Figure 4). It was found that for all heating rates, thermochemical destruction is best described by the 8th order chemical reaction model (F₈). F8 is the best reaction model, because it has the maximum R-squared value, as well as the E_α value, which corresponds to that calculated by method OFW.

The E_α values for heating rates of 5, 10, and 20 °C/min were 177.32, 184.10, and 189.56 kJ/mol, and R² were 0.9895, 0.9824, and 0.9730, respectively. It should be noted that when describing the thermochemical conversion process, the pseudo-order n has no physical meaning, but it plays an important role in determining the reaction mechanism as a correlation parameter of the model [57,58]. The obtained value of the reaction order in this study is comparable to the values, obtained for combustion of palm oil wastes (n = 7) [59], bean straw, and maize cob (n = 9–10) [60], as well as for pyrolysis of Douglas fir (n = 6) [61], soybean straw (n = 8.2–17.3) [58], and hazelnut husk (n = 12) [62].

Table 3. Kinetic parameters and fitted linear regression equations.

β (K/min)	Reaction Model	Fitted Linear Regression Equation	g(α)	Eα (kJ/mol)	A (1/s)
5	F8	y = −20.12x + 27.153	7828.84	177.32	7.16 × 1017
10	F8	y = −20.194x + 26.584	7828.84	184.10	2.11 × 1018
20	F8	y = −20.6x + 26.799	7828.84	189.56	3.00 × 1019

shows the obtained values of the kinetic parameters g(α), E_α, A and fitted linear regression equations.

3.2.3. Relationship between the Kinetic Parameters

The study of the relationship between the kinetic parameters was carried out for heating rate 20 °C/min by the Kriging method. The proposed method of the parameter normalization allows obtaining universal kinetic parameters in a range of the values [0; 1]. For this reason, it was possible to construct visual comparative plots for the results obtained. The graphs were plotted under the following conditions: the kinetic parameters were considered dimensionless, absolute, and normalized to the corresponding fixed maximum value (

Table 4. Kinetic parameters in absolute and normalized form.

α	Eα (kJ/mol)	$\overline{{\mathit{E}}_{\mathit{\alpha }}}$	A (1/s)	$\overline{\mathit{A}}$	g(α)	$\overline{\mathit{g}\left(\mathit{\alpha }\right)}$	T (K)
0.20	141.66	0.65	7.77 × 1015	4.89 × 10−7	3.768	0.00005	546.90
0.25	147.64	0.68	2.78 × 1016	1.75 × 10−6	6.492	0.00008	554.68
0.30	155.68	0.72	1.66 × 1017	1.05 × 10−5	11.143	0.00014	560.97
0.35	165.80	0.76	8.86 × 1017	5.58 × 10−5	19.399	0.00025	566.43
0.40	179.20	0.82	2.29 × 1019	1.44 × 10−3	34.722	0.00044	571.74
0.45	196.30	0.90	5.71 × 1020	3.59 × 10−2	64.684	0.00083	577.43
0.50	210.96	0.97	4.99 × 1021	3.14 × 10−1	127.000	0.00163	584.12
0.55	217.37	1.00	1.59 × 1022	1.00	266.616	0.00341	593.47
0.60	192.97	0.89	3.81 × 1019	2.40 × 10−3	609.352	0.00780	610.29
0.65	156.17	0.72	3.94 × 1015	2.48 × 10−7	1553.260	0.01988	641.92
0.70	148.70	0.68	5.60 × 1014	3.53 × 10−8	4571.474	0.05852	672.71
0.75	151.43	0.70	2.17 × 1014	1.36 × 10−8	16,383.000	0.20971	691.03
0.80	214.00	0.98	7.36 × 1018	4.63 × 10−4	78,124.000	1.00000	706.70

).

Figure 5 illustrates the changes in the normalized kinetic parameters obtained for the combustion of sunflower husks pellets over time. The analysis of the plots in Figure 5a,b shows the relationship between the activation energy and the pre-exponential factor. Since the value $\overline{E_{\alpha }}>0.6$, the range of the absolute values $E_{\alpha }$ cannot fall below 60% of the values $E_{\alpha }^{\max }$. This is consistent with the data of other authors [40,63,64].

In this case, the dimensionless parameter $\overline{E_{\alpha }}$ reaches a maximum value equal to one at the moment when the dimensionless parameter $\overline{A}$ will also have a peak value equal to one. The E_α value is the minimum energy needed for a molecule to become active in reaction, and parameter A is the number of molecules with effective collision [65,66]. Increase of the pre-exponential factor would speed up the reaction rate, and increase of activation energy makes reaction become hard to happen, so there is a compensation effect between these values. Thus, the presence of a compensation effect leads to the identical first peak on the curves Figure 5a,b. Figure 5c clearly shows the change in the algebraic g(α) function corresponding to the thermochemical conversion process, the eighth pseudo-order.

The graphical representation is a suitable way to find the optimal combination of kinetic parameters. In [67] it is noted that, “Two types of graph may be helpful: the surface in the three-dimensional space and the graph of contours, which is the projection of the surface on a plane, represented as lines of constant value”. Traditional representations of the dependencies in the form of curves are proposed to be supplemented from a new point of view of the analysis of the results obtained. The patterns between the kinetic parameters were represented as three-dimensional distribution surfaces of the parameters $\left(\overline{E_{\alpha }},\overline{g\left(\alpha \right)},\overline{A}\right)\in S$. Figure 6a–c shows the distribution surfaces of the kinetic parameters. The distributions surfaces are uniform; there are local extremes as well as linear regions. The required optimal value can be found by a simple visual inspection of the three-dimensional surface [67].

The results shown in Figure 7 are very indicative. The projections of the surface on the corresponding planes are illustrated on these plots. Figure 7a shows a projection of the surface $S_{\overline{E_{\alpha }}}$ in the system $\left(\overline{A},\overline{g\left(\alpha \right)}\right)$. The fields of the normalized dimensionless parameter of the activation energy change smoothly and uniformly and take maximum values in the range $\left(0.3;1\right)\in \overline{A}$ and $\left(0;1\right)\in \overline{g\left(\alpha \right)}$. Figure 7b shows a projection of the surface $S_{\overline{A}}$ in the system $\left(\overline{E_{\alpha }},\overline{g\left(\alpha \right)}\right)$. It can be seen that the zone with a local extremum for the $\overline{A}$ is a section with a range of the values $\left(0.95;1\right)\in \overline{E_{\alpha }}$ and $\left(0;0.05\right)\in \overline{g\left(\alpha \right)}$. The fields for the $\overline{A}$ can be constructed only in a range of the values of the normalized dimensionless activation energy parameter within $\left(0.6;1\right)\in \overline{E_{\alpha }}$.

The plot in Figure 7c shows a projection of the surface $S_{\overline{g\left(\alpha \right)}}$ in the coordinate system $\left(\overline{A},\overline{E_{\alpha }}\right)$. It is easy to see that the distributions of the parameter $\overline{g\left(\alpha \right)}$ are curvilinear and can be described by homogeneous second-order functions in the range $\left(0.95;1\right)\in \overline{E_{\alpha }}$ and $\left(0;0.4\right)\in \overline{A}$. If we expand the range of consideration $\left(0;0.95\right)\in \overline{E_{\alpha }}$ and $\left(0.4;1\right)\in \overline{A}$ the linear nature of the parameter change is observed $\overline{g\left(\alpha \right)}$. The extreme value of the function $\overline{g\left(\alpha \right)}$ is located in the interval $\left(0.95;1\right)\in \overline{E_{\alpha }}$ and $\left(0;0.12\right)\in \overline{A}$. The fields of the surfaces $S_{\overline{E_{\alpha }}}$, $S_{\overline{A}}$, and $S_{\overline{g\left(\alpha \right)}}$ vary uniformly and can be described by the second-order functions. Thus, when parameter normalization is used, the relationship between the parameters $\overline{E_{\alpha }},\overline{g\left(\alpha \right)},\overline{A}$ becomes more predictable and can be described using simpler and more visual mathematical formulas. In addition, visual plots can be constructed to compare the results obtained for various materials, process rates, and methods of thermochemical conversion of raw materials. However, this requires the analysis of more experimental data.

4. Conclusions

In this research, the kinetic characteristics of sunflower husk pellets combustion process were identified by TGA experiments coupled with the isoconversional analysis method (OFW) and model fitting (CR). The temperature range from 210 to 400 °C is the main stage of the thermochemical destruction of the sunflower husk pellets. The average value E_α, calculated by OFW method, was 175.39 kJ/mol, and by CR method for the heating rates of 5, 10, and 20 °C /min was 177.32, 184.10, and 189.56 kJ/mol, respectively. The A value shows variations in a wide range from 10¹³ to 10²² 1/s, which implies the complex composition of sunflower husk pellets and the complex chemical reactions that occur during the combustion. The model of the chemical reaction of eighth order F₈ allows us to describe the mechanism of the entire combustion process of the raw materials under study. The relationship between the kinetic parameters was first analyzed using the Kriging method and presented in the form of three-dimensional surfaces and their projections. In the future, it can be described using simple mathematical formulas. A new approach to the data analysis will allow predicting the parameters of thermochemical conversion of various agricultural raw materials and contributes to a deeper understanding of the characteristics and mechanism of biomass pellets combustion.