Bioenergy Potential of Salix alba Assessed Through Kinetics and Thermodynamic Analyses

  • Tanveer Rasool
  • Vimal Chandra Srivastava
  • M. N. S. Khan
Original Research Paper


Reutilizing the shavings of willow wood (Salix alba), a waste biomass from cricket bat manufacturing units of Kashmir (India) through pyrolysis, would prove to be a promising way for bioenergy production. The thermal degradation of this waste biomass was carried out under inert atmosphere using thermogravimetric analysis (TGA), at three different heating rates of 10, 25, and 50 K min−1. The kinetic and thermodynamic analyses were performed using isoconversional models of Kissenger-Akahira-Sunrose (KAS) and Ozawa-Flynn-Wall (OFW). The heating value of the willow wood shavings was found to be 18.03 MJ kg−1. The values of activation energy were found to be in the range of around 41.5 to 167.8 kJ mol−1 through conversion points of 0.2 to 0.8. The average value of change in Gibbs free energy were calculated to be of the order of 183.2 and 182 kJ mol−1 using KAS and OFW models, respectively. The thermal degradation reaction mechanism was predicted using Coats-Redfern method which showed that the one-dimensional diffusion model and first-order kinetic reaction model were best suited to represent the degradation process involving both exothermic and endothermic reactions. The thermodynamic parameters including pre-exponential factor, changes in enthalpy, and entropy reflect an enormous potential of the Salix alba shavings as low-cost waste biomass for bioenergy production.


Salix alba Thermal degradation Bioenergy, activation energy Diffusion 



Pre-exponential factor (s−1)




Diffusion-based reactor mechanism


Differential scanning calorimetry


Differential thermal analysis


Differential thermogravimetry


Activation energy (kJ mol−1)


Chemical reaction-based mechanism


Gibbs free energy (kJ mol−1)


Change in enthalpy (kJ mol−1)


High heating value (MJ g−1)



k (T)

Reaction rate constant


Boltzman constant (1.381× 10−23 J K−1)




Gas constant (8.314 J K−1 mol−1)


Change in entropy (kJ mol−1)


Temperature (K)


Peak temperature of DTG curve (K)


Thermogravimetric analyzer/analysis


Willow wood shavings


Thermal conversion process of waste biomass as non-edible alternative energy source has been an attractive subject of research and development owing to concerns of depletion of fossil fuels and increasing level of environmental pollution problems (Mehmood et al. 2017; Poskrobko 2012). The use of biomass and natural resources for production of high energy biofuels through thermal conversion processes has emerged as promising technology with satisfactory results. Moreover, biomass help in mitigating atmospheric carbon by sequestering it into biomass. The studies have proved biomass to be a promising non-conventional source of energy (Saqib et al. 2013; Skevas et al. 2014). Energy stored in biomass in the form of solar energy can be trapped via combustion, biological fermentation and pyrolysis with each method having its advantages and disadvantages. All these processes have been reported to depend on nature and composition of the biomass, in addition to other factors including heating rate, pressure, residence time, etc. (Slopiecka et al. 2012). However, pyrolysis of biomass has gained pragmatic importance in recent times as it converts biomass directly into biofuels or high value products in an inert atmosphere (Buryan and Staff 2008; Bridgwater 2012). The above facts necessitate the understanding of kinetic knowledge and process conditions of pyrolytic behavior of biomass, prior to their utilization as energy source. In this context, thermogravimetry (TG) facilitates a broad investigation of kinetic and process conditions of pyrolysis besides providing the fast and repeatable data collection of pyrolysis rate. Attempts have been made in recent years to evaluate kinetic parameters of various similar biomass wastes using TGA, such as polar wood (Bridgwater 2012), spruce wood (Rath and Staudinger 2001), saw dust (Heo et al. 2010), cotton stalks (El-Sayed and Mostafa 2015), and hazelnut husk (Ceylan and Topcu 2014). Although different other kinds of biomass or their wastes have been evaluated, but hard wood and its waste is main source of biomass with promising importance owing to its high yield applications, renewability and CO2 reduction as a result of its growth. An additional advantage of wood is its composite nature with cellulose, hemicellulose and lignin as its main constituents (Popescu et al. 2011).

The cricket bat industry of Kashmir is believed to be one of the oldest and most important wood industry of Kashmir province of India. The industry manufactures cricket bats for both soft and leather balls. According to Haq et al. (2013), the total registered small manufacturing units in the valley amount to around 300 with each unit manufacturing around 25,000 bats per annum. The willow wood (Salix alba) of Kashmir is abundantly used for manufacturing of cricket bats thereby generating lot of waste during finishing of the product including saw dust, shavings, chips, etc. Willow wood (Salix alba) shavings (WWS) are used only as domestic low-cost fuel, being a waste of cricket bat industry. The abundance of this waste biomass additionally with low cost has been the main reason for evaluating its energy potential through pyrolytic characterization. The present study is aimed to investigate thermodynamic and kinetic behavior of WWS for energy conversion. Salix alba also known as cricket bat willow is grown as specialized timber crop mainly for production of cricket bats. It produces a light weight but tough wood that does not splinter easily. White willow is another species of willow, a native of Europe, western and central Asia. It is a medium sized to large tree growing up to 10–30 m tall with variable sized trunk up to 1 m thick. The present study is probably the first attempt of pyrolytic analysis of this biomass at three heating rates of 10, 25 and 50 K min−1 under inert atmosphere. The biomass waste was subjected to TG, differential thermogravimetry (DTG), differential thermogravimetric analysis (DTA), and differential scanning calorimetry (DSC) analysis with an aim to understand the pyrolytic behavior with reaction mechanism of WWS. The results show that the WWS can prove to be highly potential energy source through pyrolysis under wide range of heating conditions.

Materials, Method, and Experiments

Materials and Physicochemical Analyses

The WWS were collected and used for this study sourced from the cricket bat manufacturing units of Pulwama town of Kashmir, India. The shavings were air dried under sun for three consecutive days followed by oven drying at 75 ± 10 °C for 3 h. The dried biomass was milled on cutting mill and fractionated on sieve shaker over a period of 10 min. The 400-500 μm fractions obtained were stored and sealed in air tight containers. For analytical and pyrolytic purpose, the 400-500 μm fraction were oven dried at 110 °C for around 12 h to a constant weight, prior to analysis. The material was kept in air tight container/(desiccators) till other investigations were carried on it.

Proximate Analysis and HHV

The proximate analysis of WWS was carried out to estimate percentage of volatile matter (VM%), moisture (M%), ash content and fixed carbon. The fixed carbon content (%) was calculated as: 100-(ash content+ moisture+ volatile matter content). The analysis was carried out following the procedure laid down in ASTME871–72 (2013), ASTME872–82 (2013), ASTME1534–93 (2013) and ASTME1755-01 (2007). An elemental analyzer (Euro vector-Italy) was used to determine percentage of C, H, S, N and O of the biomass waste using helium (He) as a carrier gas. Measuring the higher heating value (HHV, MJ kg−1) of biomass is an important parameter while observing out its potential as energy source. As the experiments used to estimate HHV are time consuming with greater possibilities of experimental errors (Nhuchhen and Salam 2012), several correlations have been established to estimate the HHV of biomass based on its proximate analysis (Shen et al. 2010; Ahmaruzzaman 2008). In the present study, correlation developed by Nhuchhen and Salam (2012) has been used. To have more accurate value of HHV, the calculations were made using an average value of at least three reproduced experiments for primate analysis.

TG-DTG and DSC Experiment

The pyrolytic characterization of WWS was carried out using simultaneous DTA which combines a heat-flux type DTA with TGA (Exstar DTA/TG 6300) having DTA sensitivity of ± 0.1 μV, temperature measurement accuracy of ± 0.1 K and microbalance sensitivity of ± 0.1 μg. The analysis was conducted under nitrogen atmosphere at steady flow rate of 100 mL min−1 into the pyrolytic chamber. The sample after initial pre-treatment of preheating and equilibrium conditioning was heated to 1000 °C at pre-set heating rates of 10, 25, and 50 K min−1. The loss of mass as a function of temperature along with its derivative were recorded through analytical computer system. An aluminum oxide crucible to hold the sample was placed in a furnace wherein the temperature increases linearly with the time. The temperature is measured by platinum-rhodium thermocouple while the corresponding change in the mass of the sample was recorded by the recorder. An arrangements for N2 or air as input and corresponding outputs was also incorporated. The schematic diagram of the thermal analyzer is presented in Fig. 1.
Fig. 1

Schematic diagram of thermal analyzer

DSC experiments were carried out separately under same conditions at three pre-set heating rates of 10, 25, and 50 K min−1 on Swiss made Mettler-Teledo GmbH-8606 TGA/DSC.

Model Development for Kinetic and Thermodynamics Study

Pyrolysis of biomass is mostly outlined as a solid state single decomposition reaction wherein the biomass degrades and decomposes mainly to char residue, condensable gases and volatiles. The main reason of the kinetic study being the evaluation of kinetic parameters viz, activation energy (Ea), pre-exponential or frequency factor (A) and the reaction model f (α). The reaction mechanism can however be described by various data processing methods available in the literature, generally classified as model free and model-fitting methods. The present study will use model free methods of Kissenger-Akahira-Sunrose (KAS) and Ozawa-Flynn-Wall (OFW) to estimate the kinetic parameters, widely used in earlier studies too (Bridgwater 2012; Ceylan and Topcu 2014; El-Sayed and Mostafa 2015). Coats-Redfern method (model-fitting method) was used to find the probable reaction mechanism among most common mechanisms including contacting geometry, diffusion and chemical reaction (White et al. 2011). In thermogravimetric experiments, the mass change in the initial weight of biomass sample is used to express the extent of reaction (α) as:

$$ \alpha =\frac{m_s-{m}_i}{m_i-{m}_f} $$
where, ms, mi and mf are the initial, instantaneous and final mass of the sample, respectively.

The conversion rate dα/dt at constant heating rate of β can be expressed as:

$$ \frac{d\alpha}{d t}=\beta \frac{d\alpha}{d t}=k(T)f\left(\alpha \right) $$
where, T and k(T) represent the temperature and k(T) the rate constant described by Arrhenius Law as:
$$ k(T)=A\exp \left(-{E}_a/ RT\right) $$

Using initial conditions of α = 0 at T = T0 and combining Eqs. (2) and (3) gives:

$$ P\left(\alpha \right)=\underset{0}{\overset{\alpha }{\int }}\frac{d\alpha}{f\left(\alpha \right)}=\underset{T_0}{\overset{T}{\int }}\frac{A}{\beta }{e}^{-{E}_a/ RT} dT=\frac{A\kern0.5em {E}_a}{\beta R}U\left(\chi \right) $$

In Eq. (4), χ represents Ea/RT. However the function U(χ) has no exact solution and is solved by using various approximations generating different isoconversional methods.

Model Free Methods

Kissinger-Akahira-Sunrose Method (KAS Method)

The method is based on Coats-Redfern approximation of U(χ) ≅ χ−2e−χ and after simplification and rearrangement, Eq. (4) yields

$$ 1\mathrm{n}\frac{\beta }{T^2}=1\mathrm{n}\frac{AR}{E_af\left(\alpha \right)}-\frac{E_a}{RT} $$

Equation (5) represents a straight line with a slope −Ea/R, used to calculate activation energy for constant value of α.

Ozawa-Flynn-Wall Method (OFW Method)

The method is an integral method and is based on application of Doyle’s approximation1nU(Ea/RT) ≅  − 3.315 + Ea/RT (Doyle 1965), which on substitution in Eq. (4) and rearrangement, gives

$$ 1\mathrm{n}\left(\beta \right)=1\mathrm{n}\left(\frac{AE_a}{Rf\left(\alpha \right)}\right)-2.135-0.4567\frac{E_a}{RT} $$

The plot of 1n(β) versus 1/T, the inverse of pyrolysis temperature for a constant conversion value α obtained at several heating rates of should be a straight line with a slope of−Ea/R, used to calculate activation energy Ea for almost entire conversion range.

Model-Fitting Method

Coats-Redfern Method

This method is derived from the Arrhenius equation. Accordingly, Ceylan and Topcu (2014) have used it to calculate the order of the reaction in addition to activation energy and pre-exponential factor.

After applying an asymptotic approximation on Eq. (4) with supposition of 1n(1 − 2RT/Ea) → 0for Doyle’s approximation (Doyle 1965) gives:

$$ 1\mathrm{n}\frac{f\left(\alpha \right)}{T^2}=1\mathrm{n}\frac{AR}{\beta {E}_a}-\frac{E_a}{RT} $$

Using various algebraic expressions of f(α) for various kinetic mechanisms as given in Table 2, the activation energy values as calculated from model free methods of KAS and OFW are validated. The Ea is calculated after plotting 1n f(α)/T2 versus 1/T in terms of the algebraic expressions for f(α) for the most frequently used reaction mechanisms (Vyazovkin and Wight 1997).

The thermodynamic parameters like change in enthalpy (ΔH), Gibbs free energy (ΔG) and entropy (ΔS) were calculated using the following equations:

$$ \Delta H={E}_a- RT $$
$$ \Delta G={E}_a+{RT}_p\kern0.5em 1\mathrm{n}\left({K}_b{T}_p/ hA\right) $$
$$ \Delta S=\Delta H-\Delta G/{T}_p $$
where, Kb is the Boltzmann constant (1.381 × 10−23 J K−1), Tp is peak temperature of DTG (K) and R the universal gas constant (8.314 J K−1 mol−1).

Results and Discussion

Physicochemical Characterization

After pre-treatment of biomass samples as reported in section 2.2, the samples were subjected to proximate analysis. An interesting factor which emerges is that WWS shows higher volatile matter (81.23%) and lower ash content (2.01%) when subjected to combustion. The proximate and ultimate analysis of WWS are compared with various biomasses already reported in the literature in Tables 1 and 2, respectively. The HHV of WWS was calculated using the proximate analysis results using correlation developed by Nhuchhen and Salam (2012). It was calculated as 18.03 MJ kg−1. It is known that as the ash content decreases, the heating value of the biomass generally increases, unless affected by some other factors like structure and density. Thus, these two factors may be responsible for little lower value of HHV for WWS. The HHV value of WWS after comparison with different energy crops like babui grass, spruce wood, hazelnut husk and pine (Table 1) (Ahmad et al. 2017; Ceylan and Kazan 2015; Ceylan and Topcu 2014; El-Sayed and Mostafa 2015) clearly shows that WWS possesses a considerable potential as an energy production.
Table 1

Proximate analyses of the willow wood shavings (WWS) and other biomass (wt.%)


Volatile matter (VM)



Fixed carbon (FC)

HHV (MJ kg−1)


Sugarcane bagasse






El-Sayed and Mostafa (2015)

Walnut shell






Acikalm (2011)

Saw dust





Mythili et al. (2013)






Butler et al. (2013)

Sweet sorghum stem





Yan et al. (2017); Monti et al. (2008)

Pine sawdust






Ningbo et al. (2015)







Present study

Table 2

Ultimate analyses of the willow wood shavings (WWS) and other biomass (wt.%)







Sugarcane bagasse





El-Sayed and Mostafa (2015)

Walnut shell





Acikalm (2011)

Saw dust





Mythili et al. (2013)






Butler et al. (2013)

Pine sawdust





Ningbo et al. (2015)






Present study

Thermal Behavior of Willow Wood (Salix alba) Shavings

The general shape of pyrolysis TG (mass loss) and DTG curves for WWS at heating rates of 10, 25 and 50 K min−1 under nitrogen atmosphere is presented together in Fig. 2, while the results are summarized in Tables 3 and 4.
Fig. 2

TG-DTG curves willow (Salix alba) wood shavings showing percentage mass loss

Table 3

Critical temperatures associated with pyrolysis of WWS

Heating rate (K min−1)

Temperature (K)
















Average temp. (K)




Table 4

Stages of decomposition with mass loss


Heating rate, β (K min−1)




Stage-I, (%WL)




Stage-II, (%WL)




Stage-III, (%WL)




Final residues beyond 1000–1025 K




The curves clearly reveal the three different stages of pyrolysis, usually described as initial stage (stage-I), the pyrolysis stage (stage-II) and char decomposition stage, followed by a long steady tail (stage-III). Stage-I shows the mass loss ranges between 8.1 and 8.97%, between room temperature to around 520 K. The same can be attributed to loss of water or moisture retained by the biomass. As per the findings of Braga et al. (2014), a biomass with less than 10% water content is feasible for combustion. This aspect thus signifies the combustible characteristics of WWS. The second stage (stage-II) ranges between 526 and 651 K. At different heating rates under study, the mass loss percentage at beginning of this stage is around 10% and eventually increases to 61.3%, indicating mass loss of more than 50% in this stage. The sudden increase in mass loss in lesser temperature range can be attributed to degradation of main components of biomass viz. cellulose and hemicellulose along with pectin. However, as per Kim et al. (2010), the components are reported to get degraded in the temperature range of 493–588 K. The middle stage is followed by char pyrolysis beginning at around 660 K continuing to 865 K. This stage is followed by long tail corresponding to the degradation of lignin and the formation of char.

Here, the percentage mass loss was found to fall between 13 and 27%. The results indicate that no appreciable mass conversion reaction took place at temperatures more than 865 K. Moreover, it can be conferred that the favorable temperature for thermal conversion of this biomass lies in the range of 526–865 K. However, the same may vary according to the products required. As the average biochar yield is more than 20% at 950 K (just above the stage-III), the findings when compared with biochar yield of some common biomasses (Ahmad et al. 2017) reveal that willow (Salix alba) wood shavings are an appropriate option of biomass for biochar production. An additional advantage of having very high volatile matter content (81.23%) compared to sugar bagasse (73.5%), walnut shell (78.04%) and spruce (76.6%) (Ceylan and Topcu 2014; Ahmaruzzaman 2008; Ceylan and Kazan 2015), prove WWS as a better choice for pyrolysis.

Effect of Heating Rate

The influence of heating rate on the thermal degradation process of WWS was studied at three different heating rates of 10, 25and 50 K min−1 in an inert atmosphere (nitrogen gas atmosphere). Because of the change in heat transfer flux within the sample and surroundings additionally with very less time of exposure of samples at higher heating rates, the DTG curves show a shift to higher temperature range with increasing heating rate without any considerable change in the decomposition behavior (Table 3). The curves of TG and DTG conclude that pyrolysis temperatures required to get similar weight loss increases with increasing heating rate. The behavior is often termed as thermal lag or thermal hysteresis and has been reported in thermal degradation studies of other biomasses (Yahiaoui et al. 2015; Ahmad et al. 2017). The behavior can be attributed to change in the rate of heat and mass transfer with increased heat input to the system. While more temperature or increased heating rate sets off decomposition process of biomass quickly, lesser residence time is provided for volatile matter to evolve fully. The increased heating rate thus affects the total weight loss and increase in yields of volatiles. The findings are in complete agreement with TG and DTG behavior of other cellulose-based biomass wastes (Bridgwater 2012; Ceylan and Topcu 2014; Vyazovkin and Wight 1997; Braga et al. 2014).

Heat Flow Measurements and DSC

DSC is an analytical technique highlighting the difference in the amount of heat required (heat flow) to increase the temperature of the sample and reference as a function of temperature. The same heat flow (mW mg−1) to WWS is shown in Fig. 3. Initially, the heat flow shows an increasing trend followed by decreasing heat flow at different temperatures corresponding to a particular heating rate. The initial stage of increasing heat flow culminates around 725, 925 and 980 °C corresponding to heating rates of 10, 25 and 50 K min−1, respectively. The increasing trend of the heat flow at all heating rates show that the degradation follows the same but active reaction mechanism in early stages. Subsequently after crossing certain temperature levels, the reaction rates or heat flow shows some stabilization or even a decrease at higher heating rates. While at lower heating rate of 10 K min−1, a stabilization zone is prominent extending from 725 to 925 °C, however, a sharp decline in heat flow is observed at heating rates of 25 and 50 K min−1. The decrease in heat flow occurs only after around 900 K. The total mass lost by the sample by this temperature is around 80–90%. Therefore, the mass left is biochar. There is of course depletion of the reactants as already observed in TG data. Therefore, peaks and abrupt decrease in rate of heat flow is either due to ceasing of the degradation reaction (as no reactants are present) or due to change of degradation mechanism (on the basis of new reactant biochar). However, this requires more experimental investigation using other sophisticated instruments. The behavior of curves signify an intense interactions of various thermodynamic functions during pyrolytic reactions and are in complete agreement with previous studies on biomass materials like Eulaliopsis binata, Typha latifolia, Potamoge toncrispus (a fresh water plant) and Sargassam thunbergii, a marine macro alga (Mehmood et al. 2017; Ahmad et al. 2017; Li et al. 2012).
Fig. 3

DSC curves representing heat flow across willow (Salix alba) wood shavings

Kinetic and Thermodynamic Parameters

The comparative assessment of kinetic parameters including activation energies and pre-exponential factor were carried out at three heating rates of 10, 25 and 50 K min−1. These parameters were calculated using KAS and OFW methods, using Eqs. 5 and 6, respectively. The values of activation energies calculated at progressive conversion rates along with the thermodynamic parameters, using KAS and OFW model are presented in Tables 5 and 6, respectively. The mean or average value of activation energies calculated using KAS and OFW method are 124.42 and 128.27 kJ mol−1, respectively. However, the activation energies varied at different conversion points ranging between 41.56 and 167.86 kJ mol−1, much higher than hazelnut husk (127.8–131.1 kJ mol−1), switch grass (60.9 to 152.9 kJ mol−1), sugar bagasse (81.77 kJ mol−1) and cotton stalks (84.75 kJ mol−1) (Ceylan and Topcu 2014; Ceylan and Kazan 2015; El-Sayed and Mostafa 2015). The variation of activation energy with conversion (α) is presented in Fig. 4, reflecting that the activation energy is highly dependent on conversion. It further confirms the complexity of the process of pyrolysis of biomass. The rapid increase in activation energy E after around 40% conversion (both in KAS and OFW model) is indicative of initiation of major degradation reactions. The decline of activation energy after 60% conversion however indicates the gradual transition of reaction mechanism from one type to another one. The transition of reaction mechanism is again proved by this study too. The compensation effect observed for KAS and OFW models is presented in Fig. 5. Plotting ln(A) against Ea for both models gives an excellent linear relationship (Fig. 5) which can be expressed as:
Table 5

Conversion points and the corresponding function values using KAS method

Conversion (α)

E (kJ mol−1)

R 2

A (s−1)

ΔH (kJ mol−1)

ΔG (kJ mol−1)

ΔS (Jmol−1)




1.27 × 101



− 0.237




6. 89 × 108



− 0.089




7.34 × 1011



− 0.032




5.35 × 1011



− 0.035




6.11 × 109



− 0.072




1.34 × 108



− 0.104




6.02 × 106



− 0.130






Table 6

Conversion points and the corresponding function values using OFW method

Conversion (α)

E (kJ mol−1)

R 2

A0 (s−1)

ΔH (kJ mol−1)

ΔG (kJ mol−1)

ΔS (Jmol−1)




8.30 × 101



− 0.221




1.49 × 109



− 0.083




1.07 × 1012



− 0.028




7.74 × 1011



− 0.031




1.05 × 1010



− 0.067




2.66 × 108



− 0.098




1.38 × 107



− 0.124






Fig. 4

Activation energy change with progressive conversion for KAS and OFW models

Fig. 5

Linear fit plots of for compensation effects (ln(A) against (E) of willow (Salix alba) wood shavings (WWS) for KAS and OFW models

$$ 1\mathrm{n}\left(\mathrm{A}\right)=-3.3825+0.1955\kern0.5em {\mathrm{E}}_{\mathrm{a}}\kern0.5em {\mathrm{R}}^2=0.9987 $$
$$ 1\mathrm{n}\left(\mathrm{A}\right)=-1.5048+0.1840\kern0.5em {\mathrm{E}}_{\mathrm{a}}\kern0.5em {\mathrm{R}}^2=0.9967 $$

A mere difference of around 5 kJ mol−1 between the values of Ea with corresponding value of enthalpies (ΔH) of activation at any specific conversion point shows that an activated complex gets created with low potential energy barrier. All the values of changes in entropies of activation for WWS have negative values in the range (− 0.237 to − 0.028 J mol−1) indication higher degree of disorder of products when compared to biomass under study. The complexity of thermal conversion of WWS is thus reflected by this fact and the products thus produced leave a provision for their characterization in future studies.

The values of Gibbs free energy (ΔG) of activation of WWS were calculated and found to fall in the range of ~ 183 kJ mol−1 higher than some similar biomasses investigated earlier like Camel grass, pepper waste and Eulaliopsis binata (Mehmood et al. 2017; Maia and de-Morais 2016; Ahmad et al. 2017). The values suggest willow (Salix alba) wood shavings (WWS) as potential biomass waste feedstock for bioenergy.

Reaction Mechanism

The Coats-Redfern method is one of the frequently used methods to determine the probable model for thermal degradation and reaction mechanism. The models used along with the corresponding integral expressions of associated function f(α) are given in Table 7. The heterogeneous processes are generally governed by three broader areas as transport of matter (diffusion), phase boundary reactions and nucleation and growth of nuclei. Accordingly using Eq. 7, an apparent activation energy for every given f(α) function was computed at different heating rates under study. Using Coats-Redfern method, the apparent activation energy values along with correlation coefficient and pre-activation energy values at 10 K min−1 is tabulated in Table 7. In the progress of non-isothermal thermogravimetric pyrolysis, these energies are critical. To elucidate the thermal degradation mechanism of WWS, the activation energies obtained from Coats-Redfern method were compared with each other. As observed, one-dimensional diffusion (D1) model has the lowest value of activation energy E (110.8 kJ mol−1) than two-dimensional (D2) and three-dimensional (D3) model, 140.6 and 181.8 kJ mol−1, respectively. Thus in diffusion mechanism, D1 kinetics dominate the thermal degradation of WWS. Similarly, while comparing the values of activation energies corresponding to chemical reaction kinetic models F1 and F2, the F1 kinetic with lower value of Ea (108.3 kJ mol−1) seems more dominant than the other one, F2 (196.4 kJ mol−1). Among all the values of Ea calculated, the values corresponding to D1 and F1 are closer to the average values of activation energies calculated via KAS and OFW models. The findings thus reveal that one-dimensional diffusion model (D1) followed by first-order kinetic model (F1) are the rate controlling mechanisms followed by pyrolytic degradation of WWS. The findings are in complete agreement with some previous studies on pyrolysis of biomass materials (Khawam and Flanagan 2006; Ahmad et al. 2017).
Table 7

Algebraic expression for p(α) for the most frequently used reaction mechanisms with corresponding activation energy and pre-exponential factor values at heating rate of 10 K min−1


Integral form

R 2

Ea (kJ/mol)

A (min−1)

Power law (P3/2)




6.47 × 105

Power law (P1/2)





Power law (P1/3)





Power law (P1/4)





Contracting cylinder (R2)




1.8 × 105

Contracting sphere (R3)




1.04 × 106

1-D diffusion (D1)




2.3 × 108

2-D diffusion (D2)

(1-α)ln(1-α) + α



5.8 × 1010

3-D diffusion (D3)




6.12 × 1013





2.1 × 1011

Avrami-Erofeev (A2)




2.52 × 103

Avrami-Erofeev (A3)





Avrami-Erofeev (A4)





Chemical reaction model(F1)




3.5 × 108

Chemical reaction model (F2)




2.36 × 1016


The present study focused on understanding the pyrolysis of willow (Salix alba) wood shavings, a waste biomass generated by cricket bat industry of Kashmir (India). The kinetic analysis, thermodynamic parameters along with the reaction mechanism of pyrolysis, were predicted using TGA at three different heating rates of 10, 25 and 50 K min−1 using Kissenger-Akahira-Sunrose (KAS), Ozawa-Flynn-Wall (OFW) and Coats-Redfern methods. It was found that the major pyrolytic degradation of this biomass waste is achieved between 526 and 651 K. However, with an increasing heating rate, there is a shift in the maximum rate of mass loss to higher temperatures. The mean apparent activation energies (Ea) of pyrolysis and ΔG of alba shavings ranged between 124–128 kJ mol−1 and 182–182 kJ mol−1, respectively. The best fit plots obtained by comparing the experimental data with predicted data points showed that the most probable model for pyrolysis process adopted by Salix alba shavings agrees with the one-dimensional diffusion mechanism (D1) followed by first-order chemical reaction (F1) mechanism. The outcome from this study is vital for future application of Salix alba shavings as potential feed stock for bioenergy production.


Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Tanveer Rasool
    • 1
  • Vimal Chandra Srivastava
    • 2
  • M. N. S. Khan
    • 1
  1. 1.Department of Chemical EngineeringNational Institute of Technology SrinagarSrinagarIndia
  2. 2.Department of Chemical EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia

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