Insights into Pyrolysis Kinetics, Thermodynamics, and the Reaction Mechanism of Wheat Straw for Its Resource Utilization

Abstract

To realize the energy recovery of wheat straw, the pyrolysis behavior of wheat straw was studied at three heating rates (10, 20, and 30 K/min) based on thermogravimetric analysis (TG–DTG). Kinetics and thermodynamics were analyzed using Flynn–Wall–Ozawa (FWO) and Kissinger–Akahira–Sunose (KAS) model-free methods, and the reaction mechanism was determined using the Coats–Redfern (CR) model-fitting method. The results show that there are three weightlessness stages in the pyrolysis process, of which the second stage was the main weightlessness stage and two distinct peaks of weightlessness were observed in this stage. With increasing heating rate, the main pyrolytic weightlessness peaks of the DTG curve shift to the high-temperature side. The pyrolysis activation energies calculated by the FWO and KAS methods are 165.17–440.02 kJ/mol and 163.72–452.07 kJ/mol, and the pre-exponential factors vary in the range of 2.58 × 10¹²–7.45 × 10³⁶ s⁻¹ and 1.91 × 10¹²–8.66 × 10³⁷ s⁻¹, respectively. The thermodynamic parameters indicate that wheat straw has favorable conditions for product formation and it is a promising feedstock. Its pyrolysis reaction was nonspontaneous and the energy output is stable. CR method analysis shows that the A_1/3 random nucleation model is the most suitable mechanism to characterize the pyrolysis process and random nucleation may be in charge of the main pyrolysis stage. This study can provide a theoretical basis for the thermochemical conversion and utilization of wheat straw.

1. Introduction

With the rapid development of social economy and technology, the excessive use of fossil energy has brought great disasters to the environment. Global warming, environmental pollution, energy shortage, and other issues have attracted high attention from the scientific community [1]. With the gradual depletion of fossil fuels, more and more attentions were paid to renewable energy. Biomass became the most potential renewable energy sources due to its “carbon neutral” feature [2], and was considered as the most promising alternative with the potential to abate carbon emissions. It can be converted into biomass gas, biochar, liquid fuels, and high value-added chemical raw materials through the thermochemical process [3]. The biomass gas can be used as a gaseous fuel for power generation and the liquid fraction can be used as biofuel after upgrading [4,5]. The biochar can be applied as soil amendment with the main component of carbon and inorganic materials [6,7]. Biomass includes agricultural residues and forest residues; as the world’s major agricultural country, the crop-straw output reaches about 910 million tons in China per year, among which the wheat-straw production reaches about 300 million tons. Its enormous output and ready availability make it extensively used as a fuel in China. Some of it is necessary to be left in the field after harvesting as organic fertilizer and most of the rest is burned instead of being used efficiently. However, the traditional utilization of wheat straw by simple combustion techniques often results in low combustion efficiency and high carbon emissions. Meanwhile, since pyrolysis has the advantage of less pollution emission, reasonable cost, and simple operation, it has become the most basic thermochemical transformation process. Therefore, the study of pyrolysis is helpful in effectively controlling the thermochemical transformation process, and the insights into kinetic and thermodynamic parameters and reaction mechanisms are the key to the design of large-scale pyrolysis reactors [8,9]. Through optimizing the pyrolysis process parameters, it is expected to maximize the yield of target products.

Thermogravimetric analysis (TGA) is widely used to understand the pyrolysis behavior of biomass. Based on the thermogravimetric data, the pyrolysis mechanism function and relevant dynamic parameters can be obtained. Currently, the study of the biomass pyrolysis process mainly includes model-fitting and model-free methods [10,11,12,13]. The activation energy gained by model-free methods is more credible since the pyrolysis mechanism functions are not taken into account, while both activation energy and pre-exponential factor can be calculated using model-fitting methods with the hypothesized mechanism functions. Thus, model-free methods and model-fitting methods are usually combined with each other to investigate the kinetic parameters and the reaction mechanism [14].

In order to provide theoretical guidance for the utilization of wheat straw and then provide a basis for the development of a large-scale pyrolysis reactor, in this work, the wheat straw was subjected to TGA at different heating rates with an aim to understand the pyrolytic behavior with the reaction mechanism. The kinetic and thermodynamics parameters of different pyrolysis processes were acquired by the recommended model-free models of Flynn–Wall–Ozawa (FWO) and Kissinger–Akahira–Sunose (KAS) [15,16,17] and the reaction mechanism for the pyrolysis process was gained by the Coats–Redfern (CR) model-fitting method [18,19].

2. Materials and Methods

2.1. Materials

The wheat straw used in this experiment was ground and sieved to pass through a 150-mesh screen. The proximate analysis and ultimate analysis of the wheat straw were conducted using the Chinese standard. The proximate analysis includes moisture, ash, volatiles, and fixed carbon. Moisture (M): taking a certain amount of wheat-straw raw materials in a drying oven at 383 K in a nitrogen stream until the mass is constant, the mass loss gives the moisture content. Ash (A): putting a certain amount of wheat straw into the muffle furnace, heating to 1088 K at a constant speed. When the carbon was burned to a constant mass, the residue mass was weighed as the ash content. Volatile (V): a certain amount of wheat straw was placed in a porcelain crucible with a cover at 1173 K and heated for 7 min, the weight loss in the wheat straw was defined as the volatile content. The fixed carbon (FC) content was then calculated by the difference (FC = 100 – M – V − A). The ultimate analysis of the wheat straw was carried out by the element analyzer to estimate the percentage weight content of the carbon, hydrogen, oxygen, nitrogen, and sulfur.

As shown in

Table 1. Proximate analysis and ultimate analysis of wheat straw.

Proximate Analysis/%				Ultimate Analysis/%
Moisture	Ash	Volatiles	Fixed Carbon	N	C	H	S	O
8.72	8.33	67.88	15.07	1.12	41.42	6.06	0.53	41.78

, the content of C and O elements in wheat straw is the highest and the content of S and N elements is the lowest. The C and H elements have a great influence on the calorific value of fuel and lower N and S content results in the lower emission of NOx and SOx into the atmosphere. The results of the proximate analysis show that the volatile content is as high as 67.88%, the fixed carbon content is 15.07%, and the ash content is only 8.33%. Low ash content is conducive to the improvement of heat-transfer efficiency during the pyrolysis process, while high volatile content and high fixed carbon content are helpful to the improvement of fuel performance.

2.1.1. Fourier Transform Infrared (FTIR) Analysis

In order to understand the functional groups of wheat straw, the Fourier transform infrared (FTIR) analysis was carried out. The spectra were collected within the wavenumber range of 400–4000 cm⁻¹, as shown in Figure 1. The absorption peak at 3405 cm⁻¹ is due to –OH stretching, which is ascribed to cellulose and lignin [20], while the sharp absorption peak at 2919 cm⁻¹ and 2852 cm⁻¹ are mainly caused by the asymmetric and symmetric stretching vibration of −CH₂. The absorption peak at 1656 cm⁻¹ is the stretching vibration of conjugated carbonyl C=O and the peak at 1247 cm⁻¹ is attributed to the stretching vibration of C–O. The absorption peak at 1162 cm⁻¹ is the antisymmetric stretching vibration of the C–O–C glycosioside bond contained in cellulose and hemicelluellulost [21] and the absorption peak at 1050 cm⁻¹ is the stretching vibration of primary alcohol C–O [22].

2.1.2. Field Emission Scanning Electron Microscopy (FESEM) Analysis

Field emission scanning electron microscopy (FESEM) was used to visualize the microstructural image of wheat straw, as shown in Figure 2. It can be seen that the wheat-straw sample presents an irregular rod-like shape with fibrous flakes on its surface without any pores. Some nano adsorption particles can be clearly seen on the surface.

2.1.3. X-ray Diffraction (XRD) Analysis

In order to study the crystallinity of the wheat straw, an X-ray diffraction (XRD) measurement was used. The XRD analysis was conducted within the angle 2θ range from 5° to 90° at a scanning speed of 2°/min, using a CuKα radiation source, as depicted in Figure 3. The XRD analysis shows that the wheat straw has a crystalline and amorphous structure. The peaks at 16.6° and 22.3° were ascribed to the diffraction planes of 101 and 002 in cellulose.

2.2. Experimental Procedure of TGA

Thermogravimetric testing was performed using a TGA5500 thermogravimetric analyzer, the schematic of the experimental equipment is shown in Figure 4. A thermogravimetric analysis system mainly consists of three parts: a temperature control system, a detection system, and a recording system. During the analysis process, the high-precision balance connected to the lower part of the sample holder senses the current weight of the sample at any time and transmits the data to the computer, which draws the curve of the sample weight against the temperature or time.

The mass of each sample, weighing about 8 mg, was placed in the alumina crucible and then heated from room temperature to 1173 K. The mass, time, temperature, and other signals of the sample were recorded online by a computer program. High purity nitrogen, with a purity of 99.999%, was used during the whole pyrolysis process. The gas flow rate was 60 mL/min and the heating rates were 10, 20, and 30 K/min, respectively. The experiment of each heating rate was repeated three times to ensure the accuracy of the experiment within the error range of ±3%. Before the experiment, the wheat straw was placed in a drying oven of 383 K for 12 h.

2.3. Kinetic Method

Pyrolysis of biomass is a complex reaction. The thermal reaction in the pyrolysis process follows the following reaction: A(solid) → B(solid) + C(gas). For a nonisothermal and heterogeneous reaction, the conversion rate of biomass pyrolysis can be expressed by the following formula [23].

$$\frac{\mathrm{d}\alpha }{\mathrm{d}t}=k\left(T\right)f(\alpha )$$

(1)

where α is the conversion rate, t is the pyrolysis time, k(T) is the pyrolysis-reaction rate constant, and f(α) is the differential expression of the kinetic mechanism function. The α can be calculated from the data obtained by thermogravimetric analysis, as shown in Equation (2).

$$\alpha =\frac{m_0-m_t}{m_0-m_{\infty }}$$

(2)

where m₀, m_t, and m_∞ represent the initial mass of the biomass, the mass of the biomass at time t, and the final mass of the biomass, respectively.

According to Arrhenius’s law, k(T) can be represented by Equation (3).

$$k\left(T\right)=A\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{E}{RT})$$

(3)

where T represents the reaction temperature (K), A is the pre-exponential factor (1/s), E is the activation energy (kJ/mol), and R represents the universal gas constant (8.314 J/mol/K).

When the temperature rises at a given rate (β = dT/dt), Equation (3) can be obtained as follows:

$$\frac{\mathrm{d}\alpha }{\mathrm{d}T}=\frac{A}{\beta }\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{E}{RT})f(\alpha )$$

(4)

The integrated form of f(α) can be expressed as follows:

$${\int }_0^{\alpha }\frac{\mathrm{d}\alpha }{f(\alpha )}=g\left(\alpha \right)=\frac{A}{\beta }{\int }_{T_0}^T{e}^{-\frac{E}{RT}}\mathrm{d}T$$

(5)

2.3.1. Model-Free Methods

In order to analyze the kinetic parameters, two model-free methods of Flynn–Wall–Ozawa (FWO) and Kissinger–Akahira–Sunose (KAS) were employed in this work.

The FWO method can be expressed as Equation (6) [24]; there is a linear relationship between ln(β) and 1/T at different heating rates β. The activation energy can be calculated from the ramp rate −1.052E/R of the fitting equation.

$$\mathrm{l}\mathrm{n}\beta =\mathrm{l}\mathrm{n}\frac{AE}{g(\alpha )R}-5.331-1.052\frac{E}{RT}$$

(6)

The KAS method can be written as Equation (7) [25]; there is a linear relationship between ln(β/T²) and 1/T at different heating rates β. The pyrolysis activation energy can be obtained from the ramp rate −E/R of the fitting equation.

$$\mathrm{l}\mathrm{n}\frac{\beta }{T^2}=\ln \frac{AE}{g(\alpha )R}-\frac{E}{RT}$$

(7)

2.3.2. Model-Fitting Methods

With the hypothesized mechanism functions, the model-fitting methods can help to obtain the fittest reaction-mechanism function. In this study, the reaction mechanism was studied by the Coats–Redfern (CR) method [26,27], which is derived from the Arrhenius equation as follows.

$$\mathrm{l}\mathrm{n}\frac{g(\alpha )}{T^2}=\ln \frac{AR}{\beta E}-\frac{E}{RT}$$

(8)

The E can be calculated by plotting lng(α)/T² versus 1/T in terms of the algebraic expressions for g(α). If the average E value acquired by the model-fitting method (CR method) with a given reaction model is equal to that calculated by the model-free methods (FWO and KAS), the corresponding reaction model may be utilized to describe the thermal conversion process. The reaction mechanisms of biomass pyrolysis are broadly classified into five major categories, namely diffusion, chemical reaction order, random nucleation, diffusional, phase-boundary reaction, and exponential nucleation. In this study, 20 common pyrolysis-reaction models were selected in five categories of reaction mechanisms, which are listed in

Table 2. Common solid-state thermal reaction mechanisms.

Mechanism	Symbol	$\mathit{f}(\mathit{\alpha })$	$\mathit{g}(\mathit{\alpha })$
Diffusion	D	Differential form	Integral form
One-way transport	D1	$1/2\alpha$	${\alpha }^2$
Two-way transport	D2	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{-1}$	$\alpha +(1-\alpha )\mathrm{l}\mathrm{n}(1-\alpha )$
Three-way transport	D3	$\left[\left(3/2\right){\left(1-\alpha \right)}^{2/3}\right]/[1-{(1-\alpha )}^{1/3}]$	${[1-{(1-\alpha )}^{1/3}]}^2$
Ginstling–Brounshtein	D4	$\left(3/2\right){[{\left(1-\alpha \right)}^{1/3}-1]}^{-1}$	$(1-2\alpha /3{)-(1-\alpha )}^{2/3}$
Zhuravlev, Lesokin, Tempelman	D5	$\left[\left(3/2\right){\left(1-\alpha \right)}^{4/3}\right]/[{\left(1-\alpha \right)}^{-1/3}-1]$	${[{\left(1-\alpha \right)}^{-1/3}-1]}^2$
Chemical reaction order	F	Differential form	Integral form
First order	F1	$1-\alpha$	$-\mathrm{l}\mathrm{n}(1-\alpha )$
Second order	F2	${(1-\alpha )}^2$	${(1-\alpha )}^{-1}-1$
Third order	F3	${(1-\alpha )}^3$	${[(1-\alpha )}^{-2}-1]/2$
Random nucleation	A	Differential form	Integral form
Avrami–Erofeyev (n = 2)	A2	${2(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{1/2}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{1/2}$
Avrami–Erofeyev (n = 3)	A3	${3(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{2/3}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{1/3}$
Avrami–Erofeyev (n = 4)	A4	${4(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{3/4}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{1/4}$
Avrami–Erofeyev (n = 1/2)	A1/2	${1/2(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{-1}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^2$
Avrami–Erofeyev (n = 1/3)	A1/3	${1/3(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{-2}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^3$
Avrami–Erofeyev (n = 1/4)	A1/4	${1/4(1-\alpha )[-\mathrm{l}\mathrm{n}(1-\alpha )]}^{-3}$	${[-\mathrm{l}\mathrm{n}(1-\alpha )]}^4$
Phase-boundary reaction	R	Differential form	Integral form
Contracting disk	R1	1	$\alpha$
Contracting cylinder	R2	${2(1-\alpha )}^{1/2}$	$1-{(1-\alpha )}^{1/2}$
Contracting sphere	R3	${3(1-\alpha )}^{2/3}$	$1-{(1-\alpha )}^{1/3}$
Exponential nucleation	P	Differential form	Integral form
Power law (n = 1/2)	P1/2	${2\alpha }^{1/2}$	${\alpha }^{1/2}$
Power law (n = 1/3)	P1/3	${3\alpha }^{2/3}$	${\alpha }^{1/3}$
Power law (n = 1/4)	P1/4	${4\alpha }^{3/4}$	${\alpha }^{1/4}$

[28,29,30].

2.4. Thermodynamic Method

According to the activation energy calculated by the FWO and KAS methods, for the pre-exponential factor A, thermodynamic parameters, such as enthalpy ΔH, Gibbs free energy ΔG, and entropy ΔS at a given heating rate, can be calculated by the following equations [31,32].

$$A=\frac{\beta E\mathrm{e}\mathrm{x}\mathrm{p}(\frac{E}{{RT}_m})}{{RT}_m^2}$$

(9)

$$\mathsf{\Delta }H=E-RT$$

(10)

$$\mathsf{\Delta }G=E-{RT}_m\mathrm{l}\mathrm{n}(\frac{K_B{RT}_m}{hA})$$

(11)

$$\mathsf{\Delta }S=\frac{\mathsf{\Delta }H-\mathsf{\Delta }G}{T_m}$$

(12)

Here, T_m is the maximum decomposition temperature of the DTG peak, K_B represents the Boltzmann constant (1.381 × 10⁻²³ J/K), and h is the Planck’s constant (6.626 × 10⁻³⁴ J/s).

3. Results

3.1. Thermogravimetric Analysis

The TG and DTG curves of wheat straw at different ramp rates of temperature are shown in Figure 5. The pyrolysis process of wheat straw can be divided into three stages: dehydration, main pyrolysis, and carbonization. The first stage (room temperature to 453 K) is the initial stage of pyrolysis, which is mainly the removal of water and some small molecules of volatile substances. When the heating rate is 10, 20, and 30 K/min, the weight loss is 8.69%, 8.71%, and 8.72%, respectively, which is very close to the water content in Table 1. The second stage (453 K to 773 K) is the main stage of the pyrolysis process. The hemicellulose, cellulose, and most lignin are pyrolyzed in this stage since they are the main component of biomass [33]. A shoulder and sharper peaks can be clearly seen on the DTG curve, the shoulder peak is related to the pyrolysis of hemicellulose and lignin, and the sharper peak is caused by the pyrolysis of cellulose and lignin of wheat straw. At the heating rates of 10, 20, and 30 K/min, the maximum pyrolysis rates are 7.92, 17.25, and 30.72%/min, respectively. The third stage (773 K to 1173 K) is the continuous decomposition of residual lignin, carbon precipitation, and ash formation. At this stage, less volatile components are released and a slight weight loss can be seen. At the end of the pyrolysis process, the residual masses are 17.65%, 17.58%, and 17.52% at different heating rates, respectively.

The characteristic parameters of the main pyrolysis stage were obtained by TG and DTG curves, as shown in

Table 3. Characteristic parameters of the main pyrolysis stage.

Heating Rates/(K/min)	Starting Temperature/K	Temperature of First Shoulder Peak/K	Temperature of Second Sharper Peak/K	Ending Temperature/K	Percentage of Weight Loss/%
10	454.6	549.6	597.4	740.9	63.24
20	460.9	563.3	613.9	758.3	63.82
30	470.5	567.7	617.2	773.4	64.08

. It can be drawn that the heating rate has little difference in the weight loss in the main pyrolysis stage. With the increase of the heating rate, the starting pyrolysis temperature of the main pyrolysis stage and the temperature corresponding to the weight-loss peak gradually increased. This is because that, at a higher heating rate, the rate of chemical bond breaking is fast, which easily produces volatile polymer materials and, thus, increases the pyrolysis temperature. Within the same temperature range, the higher the heating rate, the shorter the residence time of wheat straw, which is not conducive to heat transfer, resulting in a larger temperature difference between the surface and the interior. Therefore, the overall pyrolysis DTG curve shifts to the high-temperature side.

3.2. Kinetics Analysis

Activation energy is the minimum amount of energy required for a molecule to change from a normal to an active state, where a chemical reaction takes place. In order to enhance the accuracy of the calculation results, the pyrolysis process with a conversion rate of 0.2–0.8 was analyzed. The linear correlations of the pyrolysis process fitted by the FWO and KAS methods are shown in Figure 6.

The kinetic parameters calculated by the two different methods are listed in

Table 4. Kinetic parameters calculated by the two different methods.

α	FWO			KAS
	E/(kJ/mol)	A/(1/s)	R2	E/(kJ/mol)	A/(1/s)	R2
0.20	184.00	1.27 × 1014	0.952	184.46	1.40 × 1014	0.949
0.25	181.24	7.20 × 1013	0.950	181.39	7.42 × 1013	0.941
0.30	201.28	4.52 × 1015	0.951	202.33	5.61 × 1015	0.951
0.35	195.62	1.40 × 1015	0.954	196.23	1.59 × 1015	0.951
0.40	184.10	1.30 × 1014	0.974	183.95	1.26 × 1014	0.972
0.45	181.90	8.24 × 1013	0.990	181.51	7.60 × 1013	0.989
0.50	190.82	5.21 × 1014	0.999	190.86	5.26 × 1014	0.999
0.55	171.52	9.61 × 1012	0.991	170.46	7.73 × 1012	0.990
0.60	165.17	2.58 × 1012	0.978	163.72	1.91 × 1012	0.976
0.65	182.89	1.01 × 1014	0.982	182.27	8.91 × 1013	0.980
0.70	203.96	7.85 × 1015	0.973	204.34	8.50 × 1015	0.971
0.75	424.12	2.92 × 1035	0.994	435.75	3.12 × 1036	0.994
0.80	440.02	7.45 × 1036	0.958	452.07	8.66 × 1037	0.950
Average	223.59			225.33

. It can be seen from Table 4 that the correlation coefficients R² of FWO (0.950 < R² < 1) and KAS (0.941 < R² < 1) are both above 0.940, indicating the ideal linear fitting and high reliability of calculation results. The activation energy calculated by the FWO and KAS methods ranges from 165.17 to 440.02 kJ/mol and 163.72 to 452.07 kJ/mol, and the average values are 223.59 kJ/mol and 225.33 kJ/mol, respectively.

The variation trend of activation energy upon the conversion rate has been manifested in Figure 7. The activation energy obtained by the FWO and KAS methods are similar and the activation energy calculated by the FWO method is slightly lower than that of the KAS method. The trend of the activation energy upon the conversion rate can be divided into three stages. When the conversion rate is from 0.2 to 0.3, the activation energy begins to increase slightly, which is mainly due to the decomposition of hemicellulosic and cellulose of wheat straw. When the conversion rate ranges from 0.3 to 0.6, the activation energy shows a decreasing trend, which corresponds to the pyrolysis of cellulose of wheat straw. A large amount of volatile substances are produced at this stage and the semicrystal structure of cellulose was destroyed, making the pyrolysis process easy to occur. When the conversion rate ranges from 0.6 to 0.8, the activation energy increases rapidly, especially when the conversion rate is above 0.7. This is mainly because a large amount of lignin starts to pyrolyze and produces coke with low reactivity in this stage.

Activation energy is a sensitivity criterion for the determination of a reaction rate. The higher value of activation energy indicates more difficulty for the reaction to start [34]. Thus, low activation energy is desirable for biomass utilization. In order to further explore the energy utilization value of wheat straw, a restrictive comparison of the activation energy of wheat straw, with the reported works of the literature, is listed in

Table 5. Comparison of activation energy of wheat straw with the reported works of the literature.

Biomass	Average Activation Energy/(kJ/mol)		References
	FWO	KAS
Wheat straw	223.59	225.33	Present study
Bean straw	250.48	253.70	[35]
Wheat-straw hull	224.60	226.60	[36]
Mustard straw	202.19	201.80	[37]
Argan shell	302.87	308.56	[38]
Date seed	273.91	278.62	[38]

. It reveals that the average activation energies for wheat straw are nearly equal to the biomass materials, such as wheat-straw hull, mustard straw, and bean straw, indicating that wheat straw shows a competitive reactivity with these biomass types. The relatively low activation energy of wheat straw indicates that it is more promising for pyrolysis applications when compared with date seed and argan shell, as lower activation energy is conducive to reducing the operating cost and improving the process efficiency. Comparisons with other biomass in the reported literature show that wheat straw is a superior feedstock.

The pre-exponential factor A is a pivotal index reflecting the surface structure of the sample or the complexity of the reaction during pyrolysis. When the value of A is <10⁹ s⁻¹, the reaction is the surface reaction; when the value of A is ≥10⁹ s⁻¹, it means the occurrence of a complex reaction [39]. As can be seen in Table 4, the pre-exponential factors calculated by the FWO and KAS methods vary in the range of 2.58 × 10¹² to 7.45 × 10³⁶ s⁻¹ and 1.91 × 10¹² to 8.66 × 10³⁷ s⁻¹, respectively, with a ramp function of 10 K/min. This indicates that the pyrolysis process of wheat straw involves multiple parallel reactions and it is very complicated. The variation trend of the pre-exponential factor upon the conversion rate is consistent with that of the activation energy.

3.3. Thermodynamic Analysis

Thermodynamics analysis is favored for the study of the energy changes in the pyrolysis process. The thermodynamics parameters, such as enthalpy ΔH, Gibbs free energy ΔG, and entropy ΔS, along with the change trend upon the conversion rate at the heating rate of 10 K/min, are shown in

Table 6. Thermodynamic parameters of wheat straw calculated by KAS and FWO methods.

α	FWO			KAS
	ΔH/(kJ/mol)	ΔG/(kJ/mol)	ΔS/(J/mol/K)	ΔH/(kJ/mol)	ΔG/(kJ/mol)	ΔS/(J/mol/K)
0.20	179.50	172.45	11.80	179.96	172.44	12.58
0.25	176.66	172.53	6.92	176.80	172.52	7.17
0.30	196.63	172.01	41.22	197.68	171.98	43.01
0.35	190.90	172.15	31.39	191.51	172.13	32.43
0.40	179.31	172.45	11.49	179.16	172.45	11.23
0.45	177.05	172.51	7.60	176.66	172.52	6.93
0.50	185.92	172.27	22.85	185.96	172.27	22.92
0.55	166.58	172.80	−10.42	165.53	172.83	−12.23
0.60	160.20	172.99	−21.41	158.74	173.03	−23.92
0.65	177.87	172.48	9.02	177.25	172.50	7.95
0.70	198.89	171.94	45.11	199.27	171.93	45.77
0.75	418.92	168.31	419.56	430.55	168.17	439.25
0.80	434.63	168.12	446.15	446.68	167.99	466.55
Average	218.70	171.77	78.56	220.44	171.75	81.51

.

The energy contained in the system is defined as enthalpy. Change in enthalpy ΔH determines the loss or gain of energy. Table 6 shows that the ΔH calculated by the FWO and KAS methods vary in the ranges of 160.20 to 434.63 kJ/mol and 158.74 to 446.68 kJ/mol, and the average values are 218.70 and 220.44 kJ/mol, respectively. The ΔH, when calculated by the two methods, has the same trend upon conversion and both are positive, indicating that the parallel reaction involved in the pyrolysis process of wheat straw is dominated by the endothermic reaction. In addition, the difference between ΔH and E calculated by the two methods is about ±6 kJ/mol at the same conversion rate, implying that the pyrolysis process is highly reactive and occurs easily, which is conducive to the formation of activation complexes with low energy [40,41].

Gibbs free energy represents the energy available for the chemical conversion of biomass and the formation of active complexes. Table 6 shows that the ΔG, when calculated by the FWO and KAS methods, ranges from 168.12 to 172.99 kJ/mol and 167.99 to 173.03 kJ/mol, and the average values are 171.77 kJ/mol and 171.75 kJ/mol, respectively. In addition, the values of ΔG vary within ±5 kJ/mol corresponding to each conversion rate, indicating that wheat straw has a stable energy output during the whole pyrolysis process.

Entropy denotes molecular disorder and randomness of the system. Lower entropy may be related to physical changes or minor chemical reactions, while higher entropy indicates higher reactivity and the formation of activated complexes. Table 5 shows that the change in entropy, when calculated by the FWO and KAS methods, ranges from −21.41 to 446.68 J/(mol × K) and −23.92 to 466.55 J/(mol × K), respectively. The ΔS values calculated by the two methods were observed to be negative for the conversion rate 0.55–0.60, while positive values were shown for the rest of the conversion rate. Where negative ΔS values imply that a thermally stable product is produced and the thermodynamic equilibrium was established, whereas positive ΔS values indicate that the disorder degree of pyrolysis products was larger than that of the initial reactants [42]. Especially when the conversion rate is above 0.7, the entropy shows a large increase, indicating that the system has greater disorder at the end of the pyrolysis reaction and the pyrolysis reaction has difficulty reaching thermodynamic equilibrium [43].

According to the variation trend of the thermodynamic parameters upon the conversion rate in Table 6, it can be clearly seen that the variation trend of ΔG is opposite to that of ΔH and ΔS. The values of ΔH and ΔS increase slightly when the conversion rate is 0.2 to 0.3. In this process, hemicelluloses and cellulose in wheat straw begin to decompose gradually and the disorder of the reaction system increases. This process corresponds to the first shoulder peak in the DTG curve of the second stage in Figure 5. When the conversion rate ranges from 0.3 to 0.6, the disorder of the system begins to decrease due to the gradual decomposition of hemicellulose and cellulose and the values of ΔH and ΔS decrease gradually, which corresponds to the second weight-loss sharper peak in the DTG curve. When the conversion rate varies from 0.6 to 0.8, the lignin of wheat straw begins to decompose and produce coke with low reactivity; thus, the values of ΔH and ΔS increase significantly. The results of the thermodynamic analysis show that the wheat straw has a massive quantity of potential energy to be developed.

These analyses can provide a good parameter reference for a pilot-scale pyrolysis of wheat straw. In the previous part, two important parameters: pyrolysis temperature and heating rate have been discussed. A suitable pyrolysis temperature and heating rate can obtain high-quality pyrolysis products, such as bio-oil, biomass gas, and biochar. According to the above thermogravimetric analysis, when the temperature is in the range of 460–760 K, the temperature has a significant effect on the pyrolysis-reaction process. The pyrolysis gas yield increases with the increase of temperature but the influence degree is not obvious when the temperature exceeds 760 K. Taking the change of weight loss and activation energy against temperature into account, a temperature of about 620 K is more suitable for industrial application selection. The heating rate directly affects the time consumption of the pyrolysis process. The higher the heating rate, the shorter the residence time of wheat straw, which is not conducive to heat transfer, resulting in a larger temperature difference between the surface and the interior, and then reduces the yield of bio-oil. The lower heating rate is beneficial to increase the liquid phase yield but the reaction time is increased and the weight-loss rate is also low. Based on these, the heating rate of 20 K/min is optimal to avoid the instability of heating caused by a fast heating rate and the inefficiency caused by a slow heating rate.

3.4. Reaction Mechanism

The reaction mechanism during the main pyrolysis process at a heating rate of 10 K/min was investigated using the CR method. The reaction mechanisms selected are listed in Table 2. It is manifested that the values of activation energy changed little in the conversion range of 0.2–0.7, as shown in Table 4, while the changes in activation energy were remarkable when the conversion rate is above 0.7. Therefore, a conversion range of 0.2–0.7, which is the main pyrolysis stage based on the primary analysis, was studied in detail. If the average activation-energy values acquired by the discussed mechanism functions are almost equal to the energy values acquired by the FWO and KAS methods, it indicates that this mechanism function should be the best-fit reaction mechanism of the main stage of the pyrolysis process.

After comparing the average activation energy E with that of the model-free methods obtained in the previous section, the detailed results are shown in

Table 7. The activation energy acquired by the CR method in the conversion range of 0.2–0.7.

Mechanism	Symbol	E/(kJ/mol)	R2
One-way transport	D1	91.96	0.999
Two-way transport	D2	104.67	0.999
Three-way transport	D3	119.97	0.998
Ginstling–Brounshtein	D4	109.73	0.999
Zhuravlev, Lesokin, Tempelman	D5	153.69	0.993
First order	F1	62.74	0.995
Second order	F2	90.53	0.986
Third order	F3	123.99	0.977
Avrami–Erofeyev (n = 2)	A2	26.51	0.993
Avrami–Erofeyev (n = 3)	A3	14.43	0.991
Avrami–Erofeyev (n = 4)	A4	8.39	0.985
Avrami–Erofeyev (n = 1/2)	A1/2	128.68	0.997
Avrami–Erofeyev (n = 1/3)	A1/3	192.84	0.997
Avrami–Erofeyev (n = 1/4)	A1/4	266.92	0.997
Contracting disk	R1	40.99	0.999
Contracting cylinder	R2	51.119	0.998
Contracting sphere	R3	54.829	0.997
Power law (n = 1/2)	P2	15.649	0.997
Power law (n = 1/3)	P3	7.169	0.993
Power law (n = 1/4)	P4	2.93	0.975
Average activation energy (0.2–0.7)	FWO	185.68 kJ/mol
	KAS	185.59 kJ/mol

. It is indicated that the average E value (192.84 kJ/mol) calculated by the mechanism function A_1/3 (${g\left(\alpha \right)=[-\mathrm{l}\mathrm{n}(1-\alpha )]}^3$), corresponding to random nucleation mechanism, is nearly equal to the value (185.68 kJ/mol⁻¹ and 185.59 kJ/mol⁻¹) estimated based upon the FWO and KAS methods in the conversion range of 0.2–0.7. The relative error is less than 4% and the correlation coefficients R² exceeds 0.997. Therefore, it is credible that the A_1/3 random nucleation model is the optimal mechanism function to characterize the pyrolysis process. It implies that during the pyrolysis process, in the conversion range of 0.2–0.7, the random nucleation may play a pivotal role.

4. Conclusions

In this work, the pyrolysis behavior of wheat straw was identified using TGA experiments. The dynamics parameters of pyrolysis at three different heating rates and the thermodynamics parameters at the heating rate of 10 K/min were obtained using the model-free methods (FWO and KAS). Meanwhile, the pyrolysis mechanism was determined by the model-fitting method (CR).

The following conclusions are drawn:

• The thermogravimetric analysis results show that there are three main weight-loss stages in the pyrolysis of wheat straw. A shoulder and sharper peaks can be clearly seen on the DTG curve, which ascribes to the synergistic effect of the decomposition of different components in wheat straw. With an increasing heating rate, the DTG curve of pyrolysis shifts to the high-temperature side;
• The activation energy gained by the FWO and KAS methods are 165.17–440.02 kJ/mol and 163.72–452.07 kJ/mol, respectively, indicating the ideal linear fitting and high reliability of the calculation results. The pre-exponential factors obtained by the FWO and KAS methods are in the range of 2.58 × 10¹²–7.45 × 10³⁶ s^–1 and 1.91 × 10¹²–8.66 × 10³⁷ s^–1 at the heating rate of 10 K/min;
• The variation trend of thermodynamic parameters ΔG upon the conversion rate is opposite to that of ΔH and ΔS during wheat-straw pyrolysis. Thermodynamic analysis shows that the potential energy barrier between ΔE and ΔH is about 6 kJ/mol, indicating the favorable conditions for product formation;
• The wheat straw is a promising energy feedstock and contains a massive quantity of potential energy to be developed. In order to provide an optimal parameter reference for pilot-scale pyrolysis of wheat straw, the temperature of 620 K and the heating rate of 20 K/min can be taken into account;
• It was found that the mechanism function A_1/3 (${g\left(\alpha \right)=[-\mathrm{l}\mathrm{n}(1-\alpha )]}^3$) is the most suitable mechanism function to characterize the main pyrolysis stage. Random nucleation may be in charge of the pyrolysis process in the conversion range of 0.2–0.7.