Introduction

Over the past few decades, the availability of agro-food wastes, particularly sugarcane by-products (S.C.B.) and waste (S.C.S. and S.B.P.), in large quantities on one hand, and the global tendency to address the energy crisis and invest in the renewable bioenergy sector, on the other hand, have led the scientists to identify a number of traditional and sophisticated thermochemical pathways to utilize and convert lignocellulosic materials, commonly referred to as biomass, into higher value-added products1,2. Among the various thermochemical processes, researchers have highly considered and evaluated the pyrolysis process3,4,5,6.

Pyrolysis of biomass and other degradable compounds is a multi-scale complicated process consisting of a large number of physicochemical interactions7,8,9. The physical changes at micro/particle and macro/reactor scales during pyrolysis can be described using the comprehensive transport phenomena formulations, while chemical conversions are predicted using various simple to detailed kinetic models10,11,12. Understanding the pyrolysis kinetics of a feedstock is important for the design, optimization, control, feasibility assessment, and scale-up of the pyrolysis reactors in industrial applications13,14.

In recent decades, several studies have used thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) to collect non-isothermal data and identify reaction mechanisms and compute kinetic parameters of thermal conversion processes15,16,17,18,19,20.

Generally, two commonly employed approaches to mathematical explanation for solid-state decomposition kinetics are model-free and model-fitting techniques. Model-fitting methods are the most frequently used to describe the conversion rate of the pyrolysis feed to product (i.e., global model) or a set of pseudo-component products (i.e., semi-global model). Pre-assumed reaction models and collected experimental data are used to approximate distinct kinetic parameters (also known as ‘kinetic triplets’) for each reaction through the application of linear or non-linear regression techniques21,22,23. Usually, the conversion mechanism and its reaction model differ depending on the feedstock properties and the reaction conditions.

In contrast to the model-fitting approach, model-free methods, commonly referred to as isoconversional methods24,25, operate under the premise that, at a predetermined conversion level, temperature is the sole variable influencing the reaction rate26. This implies that the activation energy (Ea) values for each specific conversion can be directly obtained without making assumptions about the underlying nature of the reaction model27.

Within the well-known realm of "model-free" methodologies, the determination of activation energy involves employing either a linear or nonlinear isoconversional procedure. The choice between these approaches depends on the assumptions underlying the selection of integral or differential isoconversional methods. It is worth mentioning that the differential isoconversional methods, owing to their reliance on instantaneous rate values, are susceptible to experimental noise, resulting in numerical instability. This issue can be effectively mitigated by adopting integral isoconversional approaches22,28.

Moreover, the pre-exponential factor (A) can be determined with noteworthy precision using sophisticated methods that adhere to a model-free approach29,30,31,32. Subsequently, the identification of activation energy and the pre-exponential factor allows for the generation of a tabular representation depicting an explicit version of the reaction model27,32.

International Confederation for Thermal Analysis and Calorimetry (ICTAC) kinetic researches shows that both model-fitting and isoconversional approaches can adequately describe the kinetics of single-step and multi-step processes, provided that the models in the model-fitting method are simultaneously fitted to several datasets gathered under various temperature programs21,22,33. However, when modeling multi-step reactions using model-fitting methods, various nontrivial issues arise, which is not the case when employing the model-free approaches22. In other words, isoconversional techniques can reduce the risk of mistakes in the model selection and parameter estimation.

Estimating the kinetic parameters of the pyrolysis process often involves the utilization of a model-free approach, which encompasses several methods, including Kissinger34, as well as various differential and integral isoconversional techniques such as Friedman35, Ozawa36, Ozawa-Flynn-Wall (OFW)36,37, Kissinger–Akahira–Sunose (KAS)38, and advanced non-linear (NLN) isoconversional (ANIC) methods39,40.

It was shown by Vyazovkin et al.27,28 that the OFW and KAS methods might produce relatively good values of the activation energy at E/RT > 13 due to the approximations made in these approaches. They also demonstrated that the ANIC and Friedman approaches are essentially independent of the E/RT value and can produce exceptionally low errors in the activation energy. As a result, ANIC and Friedman methods can be recommended to compute the activation energy necessary for the predictions and solve the other issues sensitive to activation energy accuracy27,28.

The pyrolysis kinetics of various biomass and agriculture waste materials have been extensively studied in the literature. These materials include sugarcane straw41, sugarcane bagasse41, soybean hull17, rice and corn18, tobacco waste42, plum and fig pomace43, olive mill solid waste44, coconut shell straws45, poplar wood46, pinewood sawdust47, bamboo sawdust48, maize straw, invasive lignocellulosic biomasses (i.e., Prosopis juliflora and Lantana camara)49 and digested organic fractions50. These studies employ a wide range of techniques, both model-fitting and model-free methods such as Kissinger, KAS, OFW, Friedman, ANIC, distributed activation energy model (DAEM) and other hybrid approaches51. To the best of our knowledge, the kinetic analysis of the pyrolysis reaction for S.B.P. has not been specifically discussed in the literature.

In this study, thermogravimetric and thermo-kinetic analysis of sugarcane bagasse pith (S.B.P.) was performed using a robust suite of experiments and kinetic analyses along with a comparative evaluation on the thermo-kinetic characteristics of two other major sugarcane residues, namely sugarcane straw (S.C.S.) and sugarcane bagasse (S.C.B.). In this regard, the thermogravimetric analysis is used to evaluate the pyrolysis behavior of sugarcane residues at seven distinct heating rates in a nitrogen atmosphere. The Kissinger34, Friedman35, and ANIC39,40 methods were utilized to obtain the activation energies. Moreover, the compensation effect theory29,32 and the combined kinetic analysis52 were employed to determine the samples pre-exponential factor and pyrolysis kinetic model using TG data. Simultaneously, a procedural and repeatable workflow for analyzing the results of the selected convergent approaches, in terms of determining the proper pyrolysis reaction model and estimating the kinetic parameters, is proposed based on the successful agreement between the study outcomes and the experimental data.

Materials and methods

Materials and experimental methods

The materials and experimental procedures utilized in this study have been previously described in our recent publication1. Sugarcane residues were collected from the CP69-1062 variety obtained from Karun Agro-Industry in Iran's Khuzestan province. It is important to mention that these materials are waste or by-products of the harvesting, juice extraction, and milling industrial processes of sugarcane, and do not involve the collection or utilization of live sugarcane plants. The use of these industrial residues complies with relevant institutional, national, and international guidelines and legislation governing the utilization of agricultural waste products for research purposes. All samples were prepared according to ASTM E1757-01 (2015) standards. Dry samples were crushed using a Retsch PM 100 planetary ball mill, sieved to a particle size of ≤ 212 μm (US Mesh 70), and then analyzed using a Mettler-Toledo TGA 1 thermal analyzer under high-purity nitrogen at a flow rate of 50 mL/min. The heating protocol involved ramping the temperature at 10 °C/min up to 105 °C, followed by a 10 min hold and further heating to 800 °C. Heating rates ranging from 10 to 40 °C/min were tested with approximately 10.7 mg of each sample. The entire TGA procedure was repeated three times, with an average deviation of less than 1.45%.

Theoretical methods

In thermogravimetric analysis (TGA), the degree of conversion (α) is defined as the mass fraction of the decomposed solid throughout the process. The degree of conversion (α) is calculated using the initial mass (m0), final residual mass (mf), and mass at any given time (mt) according to Eq. (1):

$$\alpha =\frac{{m}_{0}-{m}_{t}}{{m}_{0}-{m}_{f}}$$
(1)

Assuming that all of the components in solid or many condensed phases have the same reactivity and ignoring the influence of pressure on thermal analysis kinetics22,53, the kinetics of a single-step reaction can typically be described by the following rate equation. This equation can be considered as a product of two independent functions22:

$$\frac{d\alpha}{dt}=k\left(T\right)\cdot f\left(\alpha\right)$$
(2)

where in Eq. (2) α is the degree of conversion, t is the conversion time, dα/dt is the rate of the reaction process, k(T) is the reaction rate constant, T is the reaction temperature, and f(α) is a conversion function that demonstrates the reaction model used and relies on the controlling mechanism.

The effect of temperature on the reaction rate is typically assumed to follow the Arrhenius equation, as shown below22:

$$k\left(T\right)=A\mathit{exp}\left(\frac{-{E}_{a}}{RT}\right)$$
(3)

where A, Ea and R are the Arrhenius pre-exponential factor, the activation energy, and the universal gas constant, respectively.

In certain conditions, the non-isothermal reaction rate expressions can be represented under constant heating rate (β), alongside corresponding superficial transformation equations, as follows:

$$T={T}_{0}+\beta t$$
(4)
$$\frac{d\alpha}{dT}=\frac{d\alpha}{dt}\cdot \frac{dt}{dT}=\frac{1}{\beta}\frac{d\alpha}{dt}$$
(5)

By combining Eqs. (2), (3), and (5), Eq. (2) turns into:

$$\frac{d\alpha }{dt}=\beta \frac{d\alpha }{dT}=A\mathit{exp}\left(\frac{-{E}_{a}}{RT}\right)f\left(\alpha \right)$$
(6)

In the case where A remains a constant, the integral form of Eq. (6) can be represented by the following equation22,28:

$$g\left(\alpha \right)={\int }_{0}^{\alpha }\frac{d\alpha }{f\left(\alpha \right)}=A{\int }_{0}^{t}\mathit{exp}\left(\frac{-{E}_{a}}{RT}\right)dt=\frac{A}{\beta }{\int }_{{T}_{0}}^{T}\mathit{exp}\left(\frac{-{E}_{a}}{RT}\right)dT$$
(7)

Alternatively, Eq. (7) can be concisely reformulated as the temperature integral function:

$$g\left(\alpha \right)=A\left(J\left({E}_{a},T\left(t\right)\right)\right)=\frac{A}{\beta }\left(I\left({E}_{a},T\right)-I\left({E}_{a},{T}_{0}\right)\right)$$
(8)

In these expressions, g(α) signifies the integral representation of the reaction model, while I(Ea, T) or J(Ea, T(t)) denote temperature integral functions. Table 1 comprises a well-known set of the reaction models and their integral counterparts, highlighting the dependence on α in the reaction kinetics22,32. Equations (6) and (7) are considered as the basic equations of differential and integral methods, respectively.

Table 1 Common reaction models for the reaction kinetics in solid-state reactions.
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If the degree of conversion is kept constant, then f (α) is fixed at any temperature or temperature regime. In this scenario, the process mechanism becomes exclusively dependent on the conversion instead of the temperature22,28. Isoconversional methods, based on these assumptions, facilitate the estimation of activation energy without being constrained by a specific reaction model.

In accordance with the selected approach and associated hypotheses, various isoconversional methods have been extensively detailed in existing literature32,34,35,37,38,39,40. These techniques commonly determine the activation energy at a predetermined conversion degree using data obtained through a series of TG runs.

Kissinger method

The Kissinger method relies on obtaining the maximum reaction peak temperature and the corresponding maximum reaction rate from each heating rate series generated by thermal analysis instruments, such as DSC and TGA. The method's basic equation is Eq. (6), where the maximum rate takes place when d2α/dt2 is zero22,34:

$$\frac{{d}^{2}\alpha }{d{t}^{2}}=\left[\frac{{E}_{a}\beta }{R{T}_{m}^{2}}+A{f}{\prime}\left({\alpha }_{m}\right)\mathit{exp}\left(\frac{-{E}_{a}}{R{T}_{m}}\right)\right]{\left(\frac{d\alpha }{dt}\right)}_{m}=0$$
(9)

here, f′(α) = df(α)/dt, and the subscript m specifies the variables related to the maximum reaction rate. If the reaction model is assumed to be first order (Table 1) and the natural logarithm is used, Eq. (9) can be stated as follows22,34:

$$ln\left(\frac{\beta }{{T}_{m,i}^{2}}\right)=ln\left(\frac{AR}{{E}_{a}}\right)-\frac{{E}_{a}}{R{T}_{m,i}}$$
(10)

where i represents the index of the individual heating rate (β). The activation energy (Ea) and pre-exponential factor (A) can be determined by plotting ln(β/T2m,i) against 1/Tm,i and fitting all the data with a straight line.

Friedman method

Performing a natural logarithmic transformation to Eq. (6) gives:

$${\mathit{ln}\left(\frac{d\alpha }{dt}\right)}_{\alpha ,i}=\mathit{ln}\left[f\left(\alpha \right){A}_{\alpha }\right]-\frac{{E}_{a}}{R{T}_{\alpha ,i}}$$
(11)

in Eq. (11), known as Friedman’s method35, i is the individual heating rate (β) index, and Tα,i is the temperature at which the degree of conversion α is accomplished. For any specified value of α, the slope of a plot of ln(dα/dt)α,i against 1/Tα,i yields the value of Ea, and the mathematical function f(α), which describes the reaction model, can be determined from the intercept of the plot. Equation (11) can be used with any temperature program, in addition to its applicability to linear heating programs.

Advanced NLN isoconverstional method

Integrating Eq. (7) over small time intervals (tα-Δα) → tα provides the following results for each given value of α27,40:

$$g{\left(\alpha \right)}_{\alpha }=A{\int }_{{t}_{\alpha -\Delta \alpha }}^{{t}_{\alpha }}\mathit{exp}\left(\frac{-{E}_{a,\alpha }}{RT\left(t\right)}\right)dt=\frac{A}{\beta }{\int }_{{T}_{\alpha -\Delta \alpha }}^{{T}_{\alpha }}\mathit{exp}\left(\frac{-{E}_{a,\alpha }}{RT}\right)dT$$
(12)

Equation (12) lacks a fully analytical solution; hence Ea,α must be calculated numerically. Following the isoconversional method assumptions, it is presumed that g(α) is constant at equivalent conversions (at each heating rate). In other words, the response reaction model remains mostly unchanged and maintains a consistent structure at the given conversion. Consequently, based on Eqs. (8) and (12), for a particular conversion and relying on the outcomes of a series of experiments conducted at a discrete heating rate (βi), the following can be expressed:

$$J\left({E}_{a,\alpha },T\left({t}_{\alpha }\right)\right)={\int }_{{t}_{\alpha -\Delta \alpha }}^{{t}_{\alpha }}\mathit{exp}\left(\frac{-{E}_{a,\alpha }}{RT\left(t\right)}\right)dt$$
(13)

under a constant heating rate, one could express:

$$\frac{I\left({E}_{a,\alpha },{T}_{\alpha ,i}\right)}{{\beta }_{i}}={\int }_{{T}_{\alpha -\Delta \alpha }}^{{T}_{\alpha }}\mathit{exp}\left(\frac{-{E}_{a,\alpha }}{RT}\right)dT$$
(14)

This implies that for a given conversion and a set of experiments performed at nth arbitrary heating rates, the following results could be obtained, according to Eqs. (8) and (12):27,54

$$g{\left(\alpha \right)}_{\alpha ,{\beta }_{1}}=g{\left(\alpha \right)}_{\alpha {,\beta }_{2}}=\cdots =g{\left(\alpha \right)}_{\alpha {,\beta }_{n}}= \text{ constant}$$
(15)

or

$${A}_{\alpha }J\left({E}_{a,\alpha },{T}_{1}\left({t}_{\alpha }\right)\right)={A}_{\alpha }J\left({E}_{a,\alpha },{T}_{2}\left({t}_{\alpha }\right)\right)=\cdots ={A}_{\alpha }J\left({E}_{a,\alpha },{T}_{n}\left({t}_{\alpha }\right)\right)= \text{ constant}$$
(16)

Equation (16) can be generalized by dividing both sides of Eq. (15) by one another and summing. The result is54:

$$min\left|{\sum }_{i=1}^{n}{\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^{n}\frac{J\left({E}_{a,\alpha },{T}_{i}\left({t}_{\alpha }\right)\right)}{J\left({E}_{a,\alpha },{T}_{j}\left({t}_{\alpha }\right)\right)}\right|={\Omega }_{\alpha }=n\left(n-1\right)$$
(17)

In Eq. (17), the optimization indicator is designated by the symbol Ωα, signifying the minimum achievable value of the equation. Additionally, the temperature integral functions (J) can be calculated using the trapezoidal rule40, or the Senum and Yang approximation27,39,55,56. Eα can be determined as the value that minimizes Ωα by repeating the optimization procedure for each α value using Eq. (17)40,54. Equation (17) is applicable to a wide range of temperature programs, and its accuracy depends on the size of the integral step28,57.

In the following, the integral methods can be employed to obtain the mathematical function that describes the reaction model through the application of Eq. (18):31

$${G\left(\alpha \right)=g\left(\alpha \right)-g\left(\alpha -\Delta \alpha \right)={\int }_{\alpha -\Delta \alpha }^{\alpha }\frac{d\alpha }{f(\alpha )}=}A_{\alpha }J\left({E}_{a,\alpha },T\left({t}_{\alpha }\right)\right)$$
(18)

By applying the presumption that the reaction model is constant over a small conversion interval and is independent of the heating rate to the integral function on the left side of Eq. (18), the mathematical function f(α) describing the reaction model can be obtained from Eq. (19):

$${A}_{\alpha }f\left(\alpha \right)=\frac{\Delta \alpha }{J\left({E}_{a,\alpha },T\left({t}_{\alpha }\right)\right)}$$
(19)

Determining the pre-exponential factor

Finding the reaction model and pre-exponential factor may be accomplished by combining the outcomes of a model-free approach and a model-fitting method for a particular heating rate22. Several methods exist in the model-free and isoconversional computations to estimate the pre-exponential factor. These methods can be classified as model-based or model-free22,29. Researchers28,29,30,31 have demonstrated that when the Eα varies significantly with α, as it does in a multi-step process, the application of model-free based procedures leads to outstanding results, notably for the Friedman and ANIC methods. The objective is to take advantage of the compensation effect (CE), expressed as follows58:

$$ln{A}_{i}=a{E}_{i}+b$$
(20)

In order to compute the pre-exponential factor, after evaluating Ea using an isoconversional technique, several values of Ea and A could be determined by the model-fitting method based on TG experimental data gathered at a single heating rate for each reaction model presented in Table 1. Finally, by utilizing these values and Eq. (20), and obtaining values for a and b, the pre-exponential factor can be calculated based on each pre-evaluated value of Ea.

Identification of the kinetic model

Adaptable theoretical models are commonly utilized to accurately represent and justify deviations from idealized processes28,59,60. The most well-known model is a modified form of Sestak and Berggren's truncated equation (tSB)22,52.

Pérez-Maqueda52 revealed that the findings of the combined kinetic analysis (CKA) (i.e., Ea, A, and f(α)), obtained from linear model-fitting of TG analysis data collected from arbitrary temperature programs to the tSB reaction model, could be reconciled with a number of theoretical reaction models (e.g., Table 1). This method has the advantage that the reaction model is not confined to Table 1 or comparable kinetic models. Considering the CKA approach, the following generic form is used to determine the kinetic model52:

$$f\left(\alpha \right)=c {\alpha }^{m}{\left(1-\alpha \right)}^{n}$$
(21)

In fact, Eq. (21) could be adjusted by modifying the values c, n, and m to match different ideal kinetic models developed under particular mechanistic assumptions52.

The combined kinetic analysis is relied on rearranging Eq. (6) and replacing f(α) with Eq. (21):

$$ln\left[\frac{d\alpha }{dt}\frac{1}{{\alpha }^{m}{\left(1-\alpha \right)}^{n}}\right]=\mathit{ln}\left(cA\right)-\frac{{E}_{a}}{RT}$$
(22)

The unknown kinetic parameters of Eq. (22) can be effectively determined using the nonlinear optimization method and thermogravimetric data collected at one or more heating rates. Afterwards, the optimization results are employed to evaluate the maximum correlation coefficient (R2). This assessment is carried out using the linear representation of Eq. (22), within specific conversion (α) ranges. The indicated evaluation provides the values of n and m, along with the intercept (ln(cA)) and slope (Ea) of Eq. (22) over the specified conversion (α) range. If the values of n and m do not fall within the expected range of one of the ideal kinetic models (see Table 1), it becomes impossible to separate the variables c and A in the intercept (ln(cA)) of Eq. (22). However, studies have demonstrated that the impact of c on the pre-exponential factor, commonly denoted as ln(A), is negligible and can be disregarded under certain conditions due to the relatively small value of c22.

In conclusion, it can be stated that although the effect of conversion on the reaction rate as determined by the CKA method (i.e., f(α)) may not be entirely consistent with any ideal kinetic model, the results obtained can still be used to compare isoconversional methods for identifying a correct reaction model22.

Thermodynamic parameters calculation

The following general equation can be written using Eyring's active complex theory to derive the thermodynamic parameters61:

$$k\left(T\right)=\kappa \frac{{\kappa }_{B}T}{h}\mathit{exp}\left(\frac{\Delta {S}^{*}}{R}\right)\mathit{exp}\left(\frac{-\Delta {H}^{*}}{RT}\right)$$
(23)

In Eq. (23), \(\frac{{\kappa }_{B}T}{h}\) is the frequency of vibration of the high-energy, active complex surmounting the transition state energy barrier62. The probability that a chemical reaction will occur once the system has attained the active state is indicated by the transmission coefficient (κ). The transmission coefficient quantifies the probability that a complex would dissociate into products rather than reactants61,63. Theoretically, κ might range from zero to one, but it often takes unity61.

Whether the reaction is monomolecular or bimolecular, the difference between ∆H* in Eq. (23) and Ea in Eq. (3) is only one or two R.T. values. Since this discrepancy typically falls within the expected range of experimental activation energy uncertainty, which is around 5–10%, it can be overlooked29,64. By comparing Eqs. (3) and (23) and assuming ∆H*≈ Ea, the change of the activation entropy at the formation of an activated complex from the reactant is obtained:

$$\Delta {S}^{*}=R\mathit{ln}\left(\frac{Ah}{{\kappa }_{B}T}\right)$$
(24)

and,

$$\Delta {H}^{*}={E}_{a}-RT$$
(25)

The following thermodynamic relationship is used to calculate the Gibbs free energy of the activated complex formation:

$$\Delta {G}^{*}=\Delta {H}^{*}-T\Delta {S}^{*}$$
(26)

In contrast, by substituting Eq. (3) in Eq. (23) and considering Eq. (26), the value of \(\Delta {G}^{*}\) can also be obtained from the following equation:

$$\Delta {G}^{*}={E}_{a}+\mathit{RT} \mathit{ln}\left(\frac{{\kappa }_{B}T}{Ah}\right)$$
(27)

According to the equations, two approaches for determining the thermodynamic parameters are compared in Eqs. (24)–(27). Method I, consists of Eqs. (24)–(26), while Method II consists of Eqs. (25)–(27). In Eqs. (23)–(27) κB is the Boltzmann constant (1.38065 × 10–23 J/K), h is the Planck constant (6.62607 × 10–34 J.s), the value of κ is assumed to be one, ∆S* (J/mol.K), ∆H* (kJ/mol) and ∆G* (K.J./mol) are the entropy, enthalpy and Gibbs free energy of activation, respectively. All thermodynamic parameters based on Method I or II can be obtained by substituting T = Tp, the maximum decomposition temperature from the differential thermogravimetry (DTG) data, in Eqs. (24)–(27).

Results and discussion

In this section, following a thorough examination and analysis of laboratory results, the investigation unfolds in a systematic sequence. Firstly, the outcomes related to the activation energy and the ‘ln(f(α)Aα)’ quantity, derived through the application of the Friedman and ANIC isoconversional methods, are presented. Subsequently, the assessment of the reaction model is conducted using the CKA procedure. Employing the CE methodology, the values of the pre-exponential factor are scrutinized. Additionally, using both the CKA and CE results, the ‘ln(f(α)Aα)’ quantity is computed and compared with the values obtained through the isoconversional methods. Finally, the thermodynamic parameters of the process are computed and examined using the final results in all three tested samples. The procedural workflow of the kinetic analysis in this study is shown in Fig. 1.

Figure 1
figure 1

Procedural workflow of the kinetic analysis.

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Experimental and TG analysis

The summary of the experimental analysis of sugarcane residues is presented in Table 2 [In the table, the reported values represent the average of three replicate experiments, ‘ ± S.D.’ indicates standard deviation, ‘db.’ denotes the dry basis, fixed carbon calculated by difference (dry basis): 100-VM-Ash, and oxygen content calculated by difference (dry basis): 100-(C + H + N + Ash)]. These experimental results are derived from our recent study1.

Table 2 Experimental analysis of S.C.S., S.C.B., and S.B.P.
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The composition of biomass polysaccharides and their monosaccharide components significantly impact both the rate of thermal decomposition and the thermal stability of biomass1. Thermogravimetric analysis (TGA) findings (see Fig. 2) have allowed the categorization of the thermal decomposition of three biomass samples, namely S.C.S., S.C.B., and S.B.P., into four distinct stages1:

  1. 1.

    Dehydration Stage (< 423 K): This stage involves the removal of internal and external water from the biomass.

  2. 2.

    Torrefaction Stage (423–548 K): During this stage, extractives and a portion of hemicellulose undergo decomposition.

  3. 3.

    Active Pyrolysis Stage (548–673 K): In this zone, hemicellulose, cellulose, and a portion of lignin are decomposed. The derived thermogravimetry (DTG) curve typically exhibits two prominent peaks, with the dominant peak attributed to the devolatilization of cellulose.

  4. 4.

    Passive Pyrolysis Stage (673–1073 K): This stage primarily involves the decomposition of lignin.

Figure 2
figure 2

TG and DTG curves of (a) S.C.S., (b) S.C.B., and (c) S.B.P. at various heating rates.

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According to Fig. 2 and Table 3 [In the table, ‘ ± S.D.’ indicates standard deviation], comparing weight changes at different temperature ranges, it was observed that S.C.S. and S.B.P. experienced greater weight loss than S.C.B. during the torrefaction stage. The weight loss in S.C.S. was mainly attributed to extractive materials, while in S.B.P., the type of hemicellulose and its interactions with other polysaccharides affected the rate of weight loss within this stage1. In the active pyrolysis zone, S.C.B. demonstrated the highest weight loss and thermal degradation rate due to its elevated levels of hemicellulose and cellulose content1,41.

Table 3 Temperature-dependent average weight loss of S.C.S., S.C.B., and S.B.P.
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The peak temperature analysis of the DTG profile for S.C.S., S.C.B., and S.B.P. at the different heating rates in the active pyrolysis zone is shown in Table 4. Accordingly, the decomposition rate and peak temperature are increased with increasing the heating rate for all samples. The results showed that the average first and second peak temperature (mainly related to the hemicellulose and cellulose, respectively) of S.C.B. is equal to 602 and 644 K and are higher than the average peak temperature of S.B.P. (i.e., 600 and 642 K) and S.C.S. (i.e., 576 and 619 K), respectively. Accordingly, a similar result can be obtained for the decomposition rate at the different heating rates as follows: S.C.S. < S.B.P. < S.C.B.

Table 4 DTG curve peak analysis of S.C.S., S.C.B., and S.B.P. at different heating rates.
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Isoconversional analysis

In this investigation, the kinetic parameters were determined employing the in-house kinetic calculation software known as XTKinetic, developed on the Python platform. The results of the linear regression parameters obtained using the Kissinger method are shown in Table 5 [In the table, the uncertainty ( ±) was determined using the traditional standard error approach with 95% confidence intervals65]. Additionally, Tables 6 and 7 [In the table, \({\Omega }_{\alpha }^{*}={\Omega }_{\alpha }-n\left(n-1\right)\)] present outcomes for activation energies (Ea) and ln(f(α)Aα, along with their error metrics (i.e., R2 and \({\Omega }_{\alpha }\)), for S.C.S., S.C.B., and S.B.P. samples determined using Friedman and ANIC methods. Both methodologies involved computing Ea within a conversion factor (α) range of 0.1–0.7 and a heating rate (β) of 10–40 K/min.

Table 5 Kissinger method results.
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Table 6 Friedman method results.
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Table 7 Advanced NLN isoconverstional method results.
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It is worth mentioning that, in this study, the conversion factors greater than 0.7 were not considered due to their potential non-linear behavior and the increased likelihood of precision loss, particularly in the vicinity of the TGA/DTG peak tail20. A critical observation suggests that an accurate assessment of the Ea dependency is achievable by approximating the temperature integral with a small Δα, specifically 0.0228,30. Therefore, in our research, the computation was executed for every α value within the range of 0.1 to 0.7, utilizing a step size of 0.01.

Furthermore, the uncertainty of the activation energy (Ea) obtained from the Friedman method was estimated using the traditional linear regression standard error approach, in line with 95% confidence intervals65. This analysis was performed in conjunction with Vyazovkin and Sbirrazzuoli modifications66. Also, the uncertainty in the Ea value calculated by the ANIC method was assessed by applying the approach recommended by Vyazovkin and Wight67, incorporating 95% confidence intervals. Figure 3 depicts the dependency of the activation energy (Ea) on the conversion factor and its uncertainty for three samples.

Figure 3
figure 3

Dependence of activation energy (Ea) on conversion factor (α) of (a) S.C.S., (b) S.C.B., and (c) S.B.P.

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As can be observed in Fig. 3, the pyrolysis activation energies of each biomass sample increase until the conversion degrees of 0.45, then decrease slightly until the conversion degrees of 0.6 before increasing significantly for the conversion degrees higher than 0.7. The likelihood of an accelerated decomposition process for the primary composition, which approaches equilibrium at early stages, is inferred by the minor increase in activation energy (Ea) for S.C.S. and S.C.B. before the conversion value of 0.2. It should be highlighted that this expedited degradation process may differ from the one at the start of the thermal conversion, which is mainly caused by the degradation of low-molecular composition68. The decrease in the activation energy (Ea) for S.B.P. at α < 0.2 could be attributed to the type of hemicellulosic material present in this biomass1,69,70 as well as the depithing process71, which involves the lignin softening and rearrangement of fibers. Furthermore, the larger drop in activation energy (Ea) for S.C.B. and S.B.P. at α > 0.45 may be attributed to the reduced lignin concentration of S.C.B. and S.B.P. compared to S.C.S. The limited deviation of activation energy (Ea) values at 0.15 < α < 0.3 for S.C.S. indicates that the hemicellulose degradation mechanism in S.C.S. remains similar throughout the selected conversion range. Moreover, the deviation from linearity in the final conversions of S.C.S., S.C.B., and S.B.P. can be ascribed to intricate multi-step reaction mechanisms unfolding across a spectrum of temperatures under various heating rates, all influenced by heat and mass transport mechanisms68,72. The Friedman plot for S.C.S., S.C.B., and S.B.P. are shown in Fig. 4. The conversion factors of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 were employed in the regression analyses. All potential conversions produce almost parallel fitted lines, consistent with similar activation energy across the conversions. Besides, when the fitting lines are not parallel, it can be inferred that a shift from one set of reaction mechanisms to another has occurred68,73.

Figure 4
figure 4

Friedman plot of (a) S.C.S., (b) S.C.B., and (c) S.B.P. at different conversion factor (α).

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The findings of the Friedman method indicated that the activation energies of S.C.S., S.C.B., and S.B.P. are around 171–199 (avg., 188), 144–185 (avg., 170), and 136–164 (avg., 151) kJ/mol, respectively. As can be seen, the application of the ANIC method leads to results that are extremely close to the specified ranges. Specifically, Kissinger74 demonstrated that his approach causes the Ea values to be underestimated. The results presented in Table 5 confirm this proposition. Investigations show that the obtained Ea values are comparable and close to the values reported in the literature for thermal decomposition of S.C.S. and S.C.B.41,60,72,73,75. However, no analogous results were found for the pyrolysis of S.B.P. As shown in Fig. 3, if the conversion step (Δα) in the ANIC method is lower than 0.02 (here 0.01 is chosen), then the values of the activation energy and ln(f(α)Aα) obtained will be quite near to those obtained from Friedman method, even though the trend and Ea values deviate significantly from Friedman method for larger values of Δα (e.g., Δα > 0.02).

Kinetic model analysis

Table 8 [The uncertainty ( ±) was determined using the traditional standard error approach with 95% confidence intervals65] and Fig. 5 present the findings of the combined kinetic analysis (CKA) for S.C.S., S.C.B., and S.B.P. across seven heating rates. According to the results for S.C.B., a conversion factor (α) of 0.1–0.75 yields the highest R2 value, whereas, for S.C.S. and S.B.P., the corresponding ranges were 0.1–0.7. Comparing the results of activation energies in Table 6 and Table 8 show that the activation energies (Ea) obtained using CKA for S.C.S., S.C.B., and S.B.P. differ by 4.78%, 2.62%, and 1.66%, from the average Friedman method results, respectively. Similarly, comparable outcomes can be achieved through the application of the ANIC method. In this context, it becomes evident that the outcomes from both the Friedman and ANIC methods are in close agreement. Based on this and the findings already described, also by ignoring the calculation of c in Eq. (22), the optimization outcomes will be analysed and compared in the following sections.

Table 8 Combined kinetic analysis and the modified truncated Sestak-Berggren kinetic equation optimization parameters.
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Figure 5
figure 5

Combined kinetic analysis plot for (a) S.C.S., (b) S.C.B., and (c) S.B.P.

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Compensation effect analysis

In order to determine the pre-exponential factor, TGA data and a model-fitting method were used to evaluate 15 reaction models presented in Table 1 in accordance with the compensation effect (CE) study described in Section "Determining the pre-exponential factor". The statistical parameters mentioned in Table 9 [In the table, in Eqs. (28)–(34), n: number of data points, \({\omega }_{i}\): the weight corresponding to ith value of the variable, p: number of model parameters, \({y}_{i}\): ith value in a sample, \({\widehat{y}}_{i}\): ith value of the variable to be predicted, \(\overline{y }\): mean value of a sample] were utilized to compare the obtained results. It was also shown that one of the most useful metrics for the model selection and statistical analysis is the normalized root means square error (nRMSE) parameter. Accordingly, besides Bayesian information criterion (BIC) and Akaike's information criterion (AIC), nRMSE has also been utilized as an accuracy metric in the model selection76,77,78. In this analysis, the model accuracy has been marked as “outstanding” when nRMSE was less than 10%, “good” when nRMSE was between 10 and 20%, “fair” when nRMSE was between 20 and 30%, and “poor” when nRMSE was greater than 30%77.

Table 9 Statistical metrics for evaluation of the model accuracy.
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To achieve the maximum possible R2 from the model-fitting procedure, the optimal range of conversion factor (α) of TGA data for S.C.S. was 0.1–0.7, while the corresponding ranges for S.C.B. and S.B.P. were 0.1–0.75 and 0.1–0.8, respectively.

In the present study, the best set of the calculated model-fitting kinetic parameters based on the heating rate that leads to the appropriate CE-dependent parameters was chosen. This decision was made based on comparing the relative error between ln(f(α)Aα) calculated from CE parameters at different heating rates and the reaction model obtained from CKA with the results obtained from the Friedman and ANIC method. On the basis of this information, the heating rate of 15 K/min was found to produce the best results considering the agreement with the TGA experiments. It should be noted that, a comparative analysis revealed that the values of the pre-exponential factor (ln(Aα)), obtained through the compensation effect methodology and involving fitting 15 reaction models at different heating rates, exhibit a standard deviation ranging from 0.02 to 0.1 for all three samples.

Figure 6 and Table 10 illustrate the CE plot and the outcomes of the model-fitting method for the heating rate of 15 K/min across all three samples. Also, Table 11 provides the acquired CE parameters. From Table 10 and in accordance with the defined range for nRMSE, it can be seen that the results of the reaction models F1, F2, A2, A3, and A4 for S.C.S., F1, F2, A2, A3, A4, R2, and R3 for S.C.B., and F1, A2, A3, A4, R2, R3 and D3 for S.B.P., have “good” accuracy compared to other models, while the results from other models do not. It is worth noting that the related conclusions can be deduced for other heating rates.

Figure 6
figure 6

Compensation effect plot (dot line) for (a) S.C.S., (b) S.C.B., and (c) S.B.P. The data points on the graph represent the ln(A) and Ea values that were determined for the 15-reaction models in Table 1 using a heating rate of 15 K/min.

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Table 10 Non-linear model-fitting results for S.C.S., S.C.B., and S.B.P. with 15-reaction models based on a heating rate of 15 K/min.
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Table 11 Compensation effect parameters derived from 15- and 4-reaction models.
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The AIC, BIC, and R2 all confirm the accuracy evaluation. The results indicate that nRMSE can be used to select the optimal model for all three samples, whereas the level of empirical support of the model (e.g., AIC-AICmin) with different selection ranges, as well as the R2, could only verify the selected model. Additionally, while certain models assessed in this work have an AIC-AICmin that does not meet the threshold of acceptability (less than 10), it has been shown that for the non-nested models, this threshold might be greater79. It should be emphasized that although the R2 comparison results are compatible with other statistical metrics, caution should still be taken when relying on R2 alone since it is defined as a pseudo-R283 and is not directly attainable from the nonlinear optimization techniques.

Kinetic results validation

A comparison of the results obtained in the previous three sections reveals that the ln(f(α)Aα) values, calculated using the CE and CKA procedures for S.C.S., S.C.B., and S.B.P. are, on average, approximately 5% higher, 6% higher, and 7% lower than those obtained through Friedman and ANIC methods, respectively. However, the trend of ln(f(α)Aα) calculated based on ln(Aα) derived from the chosen reaction models and that of f(α) produced by CKA are consistent with the outcomes obtained using these methods. Furthermore, according to Sbirrazzuoli31, using the 4-reaction models Avrami-Erofeev (A2, A3, A4) and Mampel (F1) for CE parameter computation can result in trustworthy values. This study demonstrates that while all of the 4-reaction models are among all of the selected reaction models, calculating ln(f(α)Aα) with the 4-reaction approach could increase its value by as much as 18% for S.C.S., 6% for S.C.B., and 20% for S.B.P. compared to the ln(f(α)Aα) obtained using Friedman and ANIC methods.

In general, it can be stated that using a 4-reaction or the selected reaction model based on the statistical metrics of the model-fitting findings to calculate the CE parameters yields the final results of ln(f(α)Aα) with the same trend as those of the model-free methods. However, the final values of ln(f(α)Aα) might be produced with an absolute relative error of 5–20% due to the type of raw material, the accuracy of the experimental results, and the error-prone nature of the non-linear optimization approaches. This could be supported by similar findings in the published literature84.

According to the provided explanations and the experimental TG data of the present study (see Fig. 2), the optimal ln(f(α)Aα) is resulted by selecting all 15 reaction models for CE parameters computation and employing the CKA reaction model for f(α) calculation.

Assuming that c is equal to one, Fig. 7 and Table 12 depict the comparison between the results obtained from the Friedman method (see Table 6) and the computed value for the quantity ln(f(α)Aα) with CE-CKA findings. To calculate ln(f(α)Aα), Aα is computed using Eq. (20), with the CE parameters obtained from the 15 and 4-reaction models, as shown in Table 11. Additionally, values of f(α) are determined based on the CKA results presented in Table 8 and Eq. (21).

Figure 7
figure 7

Comparison of ln(f(α)Aα) based on the Friedman method and CE + CKA results for (a) S.C.S., (b) S.C.B., and (c) S.B.P.

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Table 12 Comparison of ln(f(α)Aα) values obtained from CE (15-reaction models)—CKA procedure and the Friedman method results.
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Based on these findings, it can be concluded that the average relative error for ln(f(α)Aα) estimated using the CKA and CE methods for S.C.S., S.C.B., and S.B.P., compared to the values obtained using the Friedman method, is 0.407%, 0.526%, and 0.492%, respectively. The application of ANIC method yields comparable results; however, there is a slight increase in the average relative error for the estimated ln(f(α)Aα), which is 0.507%, 0.565%, and 0.698% for S.C.S., S.C.B., and S.B.P., respectively.

Thermodynamic parameter evaluations

To calculate the thermodynamic parameters, it is necessary to determine the reaction's kinetic characteristics at first and then assess the reaction's maximum peak or the decomposition temperature. The maximum peak temperature (Tp) value can be obtained in a few different ways: (1) using the highest possible degradation temperature in the DTG curve at each heating rate or at the lowest heating rate, (2) by taking the average of the highest possible temperatures across all heating rates85,86. In this research, the maximum peak temperature is considered corresponding to β → 0, and it is determined by solving the quadratic equation, a0 + a1.β + a2.β2, where a0, a1, and a2 are the numerical coefficients, and the reciprocal value of the a0 coefficient is identical to Tp at β → 068,87,88. In this regard, the value of maximum peak temperature according to Table 4 for S.C.S., S.C.B., and S.B.P. has been calculated as 591.38, 612.13, and 605.52 K, respectively.

Table 13 presents the average values of ∆S*, ∆H*, and ∆G* that were obtained by two distinct methods (Method I and II) based on the findings of the Friedman method. It should be noted that similar outcomes to those of the Friedman method could be obtained using the ANIC method.

Table 13 Average thermodynamic parameters based on the Friedman method.
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The values of ∆S* and ∆H* are seen to increase up to the range of conversion 0.45, then decrease relatively up to the conversion reaches of 0.6, after which they rise again. In contrast, ∆G* exhibits a relative decline up to the conversion range of 0.45, then increases up to the range of 0.6 before declining again. Singh et al.89 have also observed a similar trend in this regard.

The value of ∆S* signifies the extent to which a reaction tends to be in either the transition state or the ground state. A decreased or negative value of ∆S* indicates that the reaction can proceed with less energy and difficulty. In such cases, ∆S* often suggests an associative mechanism in which two reactants form a single active complex90.

∆S* values close to zero (e.g., S.C.B.) during pyrolysis indicate that the feedstock experienced only slight chemical or physical change, resulting in a new condition close to its thermodynamic equilibrium. A low value of ∆S* lengthens the time required for the pyrolysis reaction (referred to as "slow" reactions)91,92.

Larger negative values of ∆S* (e.g., S.B.P.) indicate that the degree of disorder in the products is significantly lower compared to the initial reaction state, while positive values reveal the opposite93. In these circumstances, the reaction can involve a bimolecular step and is most likely a second-order reaction. ∆S* in such instances indicates the entropy loss caused by the unification of the two reaction partners into a single transition state90. The devolatilization stage of all three samples produced negative ∆S* values, which is a significant finding. A high or positive value of ∆S* indicates that the activated complex, which is about to dissociate, has a high reactivity (associated with “fast” reactions) and is distant from the thermodynamic equilibrium state. Naturally, if the value of ∆S* is more positive (e.g., S.C.S.), a fast reaction can have a higher activation energy90,91,92.

A significant factor in assessing whether a decomposition process is endothermic or exothermic is the value of the enthalpy change parameter ∆H*, which may be positive or negative. Moreover, ∆H* is an important thermodynamic parameter for determining the energy required to convert the biomass into bioenergy products. Positive values of ∆H* indicate that an external heat source is necessary for biomass pyrolysis to produce biofuels and bio-based compounds, as is typical of an endothermic reaction92. The activation energies are consistent with the value of ∆H* being equal to the difference between the reagent and the activated complex94. The difference between activation energy (Ea) values and ∆H* reveals the likelihood of the pyrolysis reaction93. More specifically, a lower ∆H* value suggests that the product formation was easier, whereas a larger ∆H* value shows that the product formation was more complex95.

∆G* is a parameter that reveals the amount of energy available from the feedstock throughout the pyrolysis process. It is also used to determine the spontaneity of the decomposition process, which is another essential factor92,93,94,95. Positive results for ∆G* and ∆H* in the thermodynamic parameters of S.C.S., S.C.B., and S.B.P. support the conclusion that the pyrolysis process is non-spontaneous, endothermic, and the event was also endergonic.

Conclusions

This research explored the thermo-kinetic characteristics of sugarcane bagasse pith (S.B.P.) and conducted a comparative evaluation with two other significant sugarcane residues, namely sugarcane straw (S.C.S.) and sugarcane bagasse (S.C.B.), throughout the pyrolysis process. The study utilized rigorous thermogravimetric analysis and kinetic computations. Key findings include the robust agreement between the ANIC and Friedman methods, demonstrating consistency in ln(f(α)Aα) and activation energy values. Furthermore, the study demonstrates that if a small step size (e.g., Δα ≈ 0.01) is chosen for the ANIC method, the activation energy range calculated for S.C.S. (171–199 kJ/mol), S.C.B. (144–185 kJ/mol), and S.B.P. (136–164 kJ/mol) using Friedman's method were vin close agreement with ANIC results.

The method of calculating the ln(f(α)Aα) quantity using two different methodologies, including CE and CKA, and comparing the results with those of the isoconversional method, along with accuracy assessments, exhibits scalability and precision in our approach. Additionally, the study shows that the application of different reaction models in the CE method to obtain the pre-exponential factor may lead to final results of ln(f(α)Aα) with an absolute relative error of 5–20%.

Thermogravimetric analysis in the study reveals an accelerated decomposition process in the early stages, shaped by factors such as low-molecular composition and the influence of hemicellulosic material, providing qualitative insights into the distinctive thermal characteristics of each sample.

Thermodynamic analysis affirms the non-spontaneous and endothermic nature of pyrolysis for S.B.P., S.C.S., and S.C.B. Moreover, a distinct trend is revealed through the results obtained from activation energy and thermodynamic calculations, indicating that S.B.P. has lower thermal stability compared to S.C.B. and S.C.S. These findings align with physicochemical characterizations, emphasizing operational considerations for samples and highlighting the bioenergy potential of S.B.P., S.C.S., and S.C.B.