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Kinetic modelling of torrefaction of olive tree pruning
Accepted Manuscript Research Paper Kinetic modelling of torrefaction of olive tree pruning M.A. Martín-Lara, G. Blázquez, M.C. Zamora, M. Calero PII: DOI: Reference:
S1359-4311(16)33497-4 http://dx.doi.org/10.1016/j.applthermaleng.2016.11.147 ATE 9558
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 August 2016 3 November 2016 20 November 2016
Please cite this article as: M.A. Martín-Lara, G. Blázquez, M.C. Zamora, M. Calero, Kinetic modelling of torrefaction of olive tree pruning, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2016.11.147
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KINETIC MODELLING OF TORREFACTION OF OLIVE TREE PRUNING.
Authors: M.A. Martín-Lara*, G. Blázquez, M.C. Zamora, M. Calero * Corresponding author
* María Ángeles Martín-Lara Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) Phone: 34 958 240445 Fax: 34 958 248992 e-mail: [email protected]
Gabriel Blázquez García Department of Chemical Engineering University of Granada, 18071 Granada (Spain) Phone: 34 958 243311 Fax: 34 958 248992 e-mail: [email protected]
María Carmen Zamora Moreno Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) e-mail: [email protected]
Mónica Calero de Hoces Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) Phone: 34 958 243315 Fax: 34 958 248992 e-mail: [email protected]
Abstract The objective of this study is the proposal of a pyrolysis kinetic model that describes the thermal decomposition of olive tree pruning in different torrefaction conditions via thermogravimetrical measurements in nitrogen atmosphere. First, the determination of activation energies was performed by isoconversional methods of Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman. Three stages were distinguished in which the activation energy keeps approximately constant and were related to the thermal degradation of the different constituents of the material (cellulose, hemicellulose and lignin). Then, Coast-Redfern method was applied to determine the kinetic function. The kinetic function that seems to determine the mechanism of thermal degradation of main components of olive tree pruning was nth order reaction. Finally, a detailed pseudomechanistic model (using least squares fitting in a parallel reaction scheme) was analyzed. This model was appropriate to predict the pyrolysis behavior of the olive tree pruning in all torrefaction conditions studied.
Keywords: Kinetic; Modelling; Non-isothermal thermogravimetry; Olive tree pruning; Torrefaction
1. INTRODUCTION Torrefaction is a thermochemical treatment of biomass produced at temperatures between 200 and 300 °C in the absence of oxygen to produce beneficial changes in the composition of biomass: increases calorific value, improves grindability and resistance to degradation, among other properties (Van der Stelt et al., 2011). Torrefaction can be applied to a wide range of organic materials and can increase the use of biomass for power generation in conventional power plants and for producing a combustible gas in gasifiers (Shoulaifar et al., 2016). Kinetic modeling is a crucial tool to predict the performance of biomass during torrefaction (Repellin et al., 2010; Shang et al., 2013) and the most usual way of performing a kinetic analysis is through thermogravimetric analysis (TGA). In most of recent works (Ceylan and Topcu, 2014; Ma et al., 2015; Martín-Lara et al., 2016; Ren et al., 2013; Slopiecka et a., 2012; Zhao et al., 2013), an overall kinetic model has been developed to describe the mass loss or thermal degradation of lignocellulosic biomass. In general, most researchers compared different methods for predicting kinetic parameters (for example, Kisssinger model, Kissinger-Akahira-Sunose (KAS), FlynnWall-Ozawa (FWO) and Friedmann (FR) methods). However, other researchers have successfully applied the distributed activation energy model (DAEM) to describe biomass decomposition in an inert environment. This model assumes that several irreversible first order parallel reactions having unique kinetic parameters take place simultaneously (Chen et al., 2016; Soria-Verdugo et al., 2016). In addition, a great number of studied have proposed diverse reaction schemes consisting of multiple reactions that assume the decomposition of lignocellulosic materials as the sum of the decomposition of its major constituents, hemicellulose, cellulose and lignin. Most of these studies indicated that the different chemical steps can be characterized using a nth-
order reaction kinetic model (Anca-Couce et al., 2014; Conesa and Domene, 2011; Hashimoto et al., 2011). In mature olive trees, pruning is mainly required to renew the fruiting surface of the tree and achieve high yields, maintain vegetative growth of fruiting shoots, maintain the skeleton structure, favor air circulation and light penetration through the foliage to prevent bacterial and fungal diseases which grow more easily in humid, stagnant air. Also, it helps to decrease the alternation of production which naturally affect the olive and, finally, to eliminate dead wood and manage the size of the plant to engage the harvest in safe conditions. The objective of this study has been the proposal of a comprehensive pyrolysis kinetic model that describes the thermal decomposition process of olive tree pruning in different torrefaction conditions via thermogravimetrical measurements in nitrogen atmosphere. First, the determination of activation energies of the kinetics of biomass torrefaction was carried out by isoconversional methods, then, Coast-Redfern method was applied to determine kinetic function and, finally, a detailed pseudo-mechanistic model based in a parallel reaction scheme was analyzed. 2. MATERIAL AND METHODS 2.1. Biomass sample Olive tree pruning is a waste from olive pruning, characteristically required for maintenance and reshaping of olive trees. The OTP used for this study was obtained from olive plantation located in Vilches, province of Jaen (Spain). The solid was reduced to particles lower than 1.00 mm by powdering in an analytical mill (IKA MF10) and was stored for later use in all tests. A complete physic-chemical characterization of this material has been previously published in Calero et al., (2013). 2.2. Experimental method
A total of seven experiments were conducted under nitrogen atmosphere in a thermobalance Perkin Elmer, model STA 6000. Five experiments were carried out in dynamic conditions at five different heating rates (5, 10, 15, 20 and 25 °C/min), while two other tests were performed in dynamic + isothermal conditions, i.e. with a first stage at a constant heating rate of 15 °C/min and a second isothermal stage keeping constant the final temperature for a time of 60 min; specifically, an experiment to 200 °C and the other one to 300 °C. All experiments were performed by duplicate with an initial mass of sample about 25 mg (± 3 mg) and a nitrogen flow rate of 20 mL/min. In Table 1 the set of experimental conditions for each experiment are detailed. 2.3. Kinetic analysis In most developed kinetic formulations of thermal decomposition of biomass, the calculation of the kinetic parameters is based on the assumption that the decomposition rate (dα/dt) is a function of two variables, temperature (T) and degree of conversion or extend of reaction (α) related to the kinetic constant k(T) and the reaction model f(α), respectively, and described as a single reaction: (1) The function f(α) depends on the controlling mechanism and the extent of reaction or conversion can be calculated by the following equation: (2) where w0, w and w∞ correspond to the initial sample mass, the sample mass at any time and the final residual mass obtained at the end of the decomposition process, respectively. Moreover, the dependence of kinetic constant with temperature is described by Arrhenius equation: (3)
where k0 is the pre-exponential factor or frequency factor, E is the apparent activation energy and R is the gas constant. Also, as it is operated in dynamic regime (non-isothermal conditions) and the temperature increases linearly with time, a linear heating rate can be defined as: (4) So, an expression of the rate law for non-isothermal conditions can be obtained combining equations (1), (3) and (4): (5) Setting in order and integrating both sides of Eq. (5), can be obtained: (6) where p(x) in Eq. (6) is known as the temperature integral. The temperature integral does not have an exact analytical solution but it can be approximated by different empirical interpolation equations as term proposed by Doyle, Agrawal, Gorbatchev, etc. Determination of the activation energies by isoconversional methods of Flynn–Wall– Ozawa (FWO), Kissinger–Akahira–Sunose (KAS) and Friedman (FR). The isoconversional methods (also called “model-free” methods) are based on an isoconversional basis. They assume that the reaction rate at constant degree of conversion is only a function of the reaction temperature, allowing the determination of the values of the activation energy for the same degree of conversion, E α, without assuming any particular model. Hence, isoconversional methods do not require previous knowledge of the reaction mechanism for biomass thermal degradation. But, although it is not necessary to identify a particular model, it is assumed that the dependence of the conversion due to a differential model f(α) (Vyazovkin et al., 2011).
In this this work, activation energy for each degree of conversion is calculated by the integral isoconversional methods of Flynn-Ozawa-Wall (FOW) and Kissinger-AkahiraSunose (KAS) and the differential isoconversional method of Friedman (FR) as they are some of the most common model-free methods for the determination of kinetic parameters in a thermal decomposition. The main reason is easiness in treatment of the experimental data to obtain the values of the activation energy by simple linear representations.
Flynn-Wall-Ozawa (FWO) method
The equation used in the methodology developed by Flynn-Wall-Ozawa (Flynn, 1983; Flynn and Wall, 1966; Ozawa, 1965; 1970; 1992) uses the approximation of Doyle (Doyle, 1962). (7) The activation energy can be obtained from the plot of log (β) versus 1/T for different heating rates for each degree of conversion.
Kissinger-Akahira-Sinose (KAS) method
The approximation of the integral of Doyle may introduce some errors in the estimation of Eα, especially if it varies with the degree of conversion. Another widely used empirical approach is proposed by Murray and White (1955) that produces equation known as Kissinger-Akahira-Sinose (Akahira and Sunose, 1957; Kissinger, 1957). (8) Activation energy can be determined from the slope of the straight line obtained by plotting ln (β/T2) versus 1/T for a fixed degree of conversion.
Friedman (FR) method
Friedman method (Friedman, 1960) is also an isoconversional method in which the values of E for a given conversión value, are obtained plotting ln(dα/dT) versus 1/T, according to the following equation, (9) Determination of reaction model by Coats & Redfern (CR) method. Once the variation of the activation energy for the degradation process is evaluated, the next step is to determine what reaction mechanisms control the process obtaining the form of the function f(α). For this study, the method of Coats & Redfern, CR, applied at conversion ranges in which the activation energy can be considered approximately constant, is used. The method approximates p(x) using a Taylor series expansion to yield the following simplified expresion (Coast and Redfern, 1964, 1965): (10) By plotting ln[g(α)/T2] versus 1/T, the value of the activation energy is obtained. From the results, it can be set as a reaction mechanism which governs the decomposition process, in the different range of conversion tested, one with which the energy values are closest to the values obtained using the methods of FWO, KAS and FR. Some of the more important rate equations used to describe the kinetic behavior of solid state reactions and applied in this work on Coast & Redfern method are listed in Table 2. A pseudo-mechanistic model based on a parallel reaction scheme Finally, in this work, a devolatilization scheme has been proposed based on four parallel reactions considering the olive tree pruning a heterogeneous mixture formed by four independent fractions (moisture, hemicellulose, cellulose and lignin) that decompose at different temperatures following an independent reaction,
s1 Moisture
s1 Volatiles 1
s 2 Hemicellul ose ν2 Volatiles 2 c2 Char2 s3 Cellulose
ν3 Volatiles 3 c3 Char3
s4 Lignin ν4 Volatiles 4 c4 Char4
As an important part of this model, moisture evaporation has been included into the model. Actually, most of published works about thermal degradation of lignocellulosic materials don’t include this fraction as an independent reaction on their reaction schemes. However, it is important to highlight that some old works already included the moisture release in the chemical reaction model (Chan et al. 1983). Volatiles1, Volatiles2, Volatiles3 and Volatiles4 are the gases and condensable volatiles evolved in the decomposition reactions of moisture, hemicellulose, cellulose and lignin, respectively, and Char2, Char3 and Char4 refer to char formed in the decomposition reactions of hemicellulose, cellulose and lignin, respectively. Also, in the reaction scheme proposed, si is the initial contribution of the fraction or component 'i' to the total weight of the material and they have been experimentally obtained (7.7% moisture, 28.9% hemicellulose, 38.4% cellulose and 25.0% lignin); ʋi represents the maximum amount of volatile obtained by reaction 'i' at infinite time, that is, the yield coefficient of volatile that represents the maximum amount of volatiles that can be evolved during corresponding reaction when the substrate reacts completely and, likewise, ci refers to the maximum amount of carbonaceous residue obtained by reaction "i" (c = 1 - ʋ). For the moisture ʋ1 = s1 as any char is obtained from this fraction and total conversion of moisture in volatiles are supposed.
In this paper, according to results of Coast-Redfern method (see Results and Discussion, subsection 3.3.), an nth reaction model has been assumed. Therefore, given the mass balance of the products and reactants and the degree of conversion (α), the kinetic equations associated with independent reactions can be expressed as follows: (11) (12) (13) (14) In these equations ni is the order reaction, ki is the rate constant of the corresponding reaction “i”. These kinetic constants follow the Arrhenius law: (15) (16) (17) (18) where ki0 is the pre-exponential factor, Ei the apparent activation energy of reaction “i”. Total solid fraction, wcalc (unreacted solid and originated carbonaceous solid) are related to the other variables using the following expression: (19) Once the model was defined with its corresponding equations, the next step is to obtain the kinetic parameters of the reactions. The best parameters will be those that best correlate the calculated values with experimental thermogravimetric curves for all tests simultaneously (experiment 1 to 7).
The simultaneous solution of four differential equations system was carried out numerically with Euler's method in an Excel spreadsheet using as initial condition values of conversion factors equal to 0. The quality of the model was evaluated using an objective function that minimizing the differences of squares between experimental and calculated data in the integral and differential forms. (20) The parameter f is a scaling factor included to compensate the differences in the obtained numeric data for integral and differential forms. Moreover, m represents the number of heating rate studied and n the number of experimental data recorded in each test a specific heating rate. 3. RESULTS AND DISCUSSION 3.1. Analysis of thermogravimetric curves In Figure 1a, the experimental curves of mass loss versus temperature of dynamics experiments at five heating rates are shown. In Figure 1b, the experiments in dynamics+isotherms together with the dynamic experiments are shown. In this case, the representation of mass loss are versus time and logically, the displacement of curves with increasing the heating rate is to lower times, that is to say, the higher the heating rate faster decomposes the sample, because in this case the temperature in a given time is greater. Also, in figure 1a, an increase in the heating rate caused a shift of the curves at higher temperatures. This behavior usually occurs in any thermogravimetric analysis, and it can be interpreted as a consequence of the mathematical form of the kinetic law process, assuming infinitely fast heat transfer and kinetic parameters constant (Conesa and Rey, 2015; Martín-Lara et al., 2016). Moreover, the representations of the data of TGs curves by using the thermogravimetric derived curves (DTGs) provides useful information meaning that they allow to
appreciate more clearly small changes hardly observable in the curves TGs. In Figure 2, the values of dw/dT against the temperature have been shown. All curves present three different stages of mass loss, identified by peaks in the DTG curves. The first stage (first peak on DTG curves) can be attributed to the moisture release (Arteaga-Pérez et al., 2015; Basu 2013). The second peak corresponds to the decomposition of the hemicellulose (Carvalho et al., 2015; Martín-Lara et al., 2016). The third stage (third peak on DTG curves) is mainly attributed to the degradation of cellulose (Amutio et al., 2013). Hemicellulose usually appears as a shoulder to the left of the main degradation peak in the DTG curve corresponding to cellulose. Furthermore, a fourth stage of decomposition is found although it doesn’t appear as marked peak in the thermogravimetric derived curve and it corresponds to the thermal degradation of lignin, the fourth major component in olive tree pruning, whose decomposition takes place slowly over a greater temperature range (around 200-800 ºC) (Haykiri-Acma et al., 2010). These stages in TG and DTG curves are comparable to results found by Yang et al., 2007 in their study about hemicellulose, cellulose and lignin pyrolysis. Table 3 includes the information obtained from the TG and DTG curves for each stage of decomposition where Ti is the onset temperature of decomposition, T f is the temperature at which ends the stage of decomposition, T max is the temperature at which the decomposition in each stage has place at a higher rate (peak on the DTG curve), wvolatilized is the percentage of mass loss corresponding to each stage and (dw/dT)max is the value of maximum loss rate corresponding to each stage which has place a Tmax. Similar temperature ranges associated with these thermal degradations have been found by several authors who have used different vegetable waste, such as Gu et al., (2013) in his study of thermal degradation by pyrolysis of poplar sawdust, Gómez et al. (2016) in
their study of the pyrolysis of biomass relevant in the Mediterranean basin: olive pits, almond shell, pinewood and olive tree pruning, and Chen et al. (2013) in their kinetic analysis of pyrolysis of maize straw and wheat straw. As it is shown in thermogravimetric curves, the degradation process of organic materials such as residue from olive tree pruning is very complex, as they are involved multitude of chemical reactions and, in general, a superposition of different chemical processes. In addition, physical processes (for example diffusion of decomposition products) must be also considered, which make difficult to give an interpretation with a chemical/physical meaning to the mathematical equation describing the process. Still, in the bibliography simple models are presented to describe the kinetic of thermal decomposition process which isn’t known a priori, setting validation criteria such as the invariance of activation energy determined by isoconversionals methods. 3.2. Determination of the activation energies by isoconversional methods of Flynn– Wall–Ozawa (FWO), Kissinger–Akahira–Sunose (KAS) and Friedman (FR) In Figure 3, the results of the analysis based on isoconversionals models of FOW, KAS and FR for the range of values of the degree of conversion of 0.1 to 0.9 are shown. The fitting lines are shown only for those cases where the correlation coefficient was greater than 0.85. In Table 4, the parameters of the linear fits with correlation coefficients for each of the values of the degree of conversion studies are presented. Those adjustments have a correlation coefficient lower than 0.85 are marked in cursive. For the conversion value of 0.1 the adjustment linearity is rather low. In all cases, the worst fit is given to the extreme levels of conversion (0.1; 0.8; 0.85; 0.9) possibly due to the inherent error associated with the humidity difference samples (degrees of conversion low) and a more complex process in finalizing degradation (high degrees of conversion).
Moreover, Table 4 shows that activation energy determined by these conversional methods is not constant in function of conversion so, thermal decomposition under nitrogen atmosphere may not be represented by a single kinetic model, that is, the reaction mechanism is complex and cannot be described by a single reaction or a single type of degradation for the entire process of degradation. However, as it is shown in Figure 4, three stages can be distinguished in which the activation energy remains approximately constant meaning that the processes that controlling weight loss not vary significantly throughout the intervals (Flynn, 1988) and also, coincide with the intervals at which marked peaks appear in the DTG curve, that is, are related to the different degradation of the various constituents of the material. The first stage corresponds to the degree of conversion between 0.35 and 0.45 and is due to the thermal decomposition of hemicellulose. The second stage affects to conversion degrees between 0.5 and 0.7 with higher activation energies and may be associated mainly to degradation of cellulose, as is well known that cellulose has apparent activation energies greater the hemicellulose because the crystallinity of its components, and the third stage, with lower activation energy values correspond to degrees of conversion between 0.8 and 0.9. This decrease in activation energy in the last stage indicates that the degradation process takes place more easily and this behavior can be attributed to final lignin degradation. 3.3. Determination of reaction model by Coats & Redfern (CR) method Once the variation of activation energy for the degradation is known, the next step is to determine what reaction mechanisms direct the process, that is to say, the form of the function f(α). For this study, the method Coats & Redfern (CR) has been applied at intervals of conversion in which the activation energy can be considered approximately constant.
In general, in the studies of thermal degradation of biomass is admitted a model of first or nth order (Baroni et al., 2016; Ceylan and Topçu, 2014; Damartzis et al., 2011; Slopiecka et al., 2012). However, polymeric materials, as in the case of lignocellulosic residues studied in this work, can also present a mechanism of degradation of sigmoidal or diminishing type different from the reaction of first or nth order so, the assumption of first or nth order is not recommended without verification because, perphaps, another kinetic model could be more convenient to describe the degradation process in a given interval conversion (Hatakeyama and Quinn, 1999). In Table 2, the possible mechanisms that have been considered in this study are shown. The first conversion interval to be analyzed, from the point of view of the reaction mechanism, includes the degradation temperature of hemicellulose which, as dicussed above, has associated the second peak obtained in the thermogravimetric derived curve. The second interval includes the temperature to the rate of thermal degradation is maximum and occurs most volatile emissions, that is, includes the largest peak obtained for the thermogravimetric derived curve (the third peak) and is the interval of the temperature-conversion which is associated with the degradation of cellulose. Finally, with the third interval will be evalueted the reaction mechanism, which would correspond to lignin because high conversion values where practically only this component is degraded. The numerical results obtained for the activation energy, in kJ/mol, applying the method of CR are shown in Table 5. Only results obtained for three of the five heating rates studied in this work have been reported in order to simplify and improve the clearness of Table 5, however, similar results were found for the other two heating rates. Based on the results presented in Table 5 and the main research strategy of choosing one model that provides a good fit to the experimental data and provides an activation
energy close to that estimated by the isoconversionals methods of FWO, KAS and FR, the kinetic function f(α) that seems to determine the kinetic model of the mechanism of thermal degradation for cellulose and lignin components is the reaction of nth order, being the most common reaction order the fourth or fifth order. The activation energy values of the other models are significantly different to the values obtained by isoconversional methods. Moreover, the function capable of reproducing the first stage considered in this method (α = 0.35 – 0.45) which correspond to part of the thermal degradation of hemicellulose, seem to be nth reaction model but with order of reaction higher to 5, but, also is important to remake that activation energy in this stage is not constant, it increases slightly with increasing conversion degree. 3.4. Proposal of a pseudo-mechanistic model based on a parallel reaction scheme In the thermal degradation of organic materials, even the simplest, are involved multitudes of chemical reactions. One way to study the kinetics of the thermal decomposition is to propose pseudo-mechanistic models. In them, the products of decomposition in an inert atmosphere are divided in solids (non-volatile residue with a high carbon content), tars (mixtures of a large number of compounds of high molecular weight which are volatile at the temperature of pyrolysis or torrefaction but condense at ambient temperature) and gases (volatile products with low molecular weight at ambient temperature). Because in a thermobalance is not possible to distinguish between the fractions corresponding gases and tars, these fraction are grouped into a single fraction, and in the proposed models is considered only solids and volatiles as products. Moreover, the reactions include a set of several simple reactions, and kinetic parameters that have been obtained are representative of each global reaction. The kinetic reaction schemes proposed for torrefaction can be very different (reactions in parallel, series, competitive, etc.), and there are proposed in function of the shape of
the thermogravimetric curves, the nature of the material (homogeneous or heterogeneous sample) and information provided by the analysis of the generated products
(by TG
coupled
with
mass
spectrometry (TG-MS)
or
infrared
spectrophotometry (TG-FTIR), for example). The kinetic parameters obtained for the fit of the experimental data are shown in Table 6. The kinetic parameters obtained are similar to those found by other authors in previous works. For example, Sharma et al. (2016) found apparent activation energies between 53 and 68 kJ/mol for reaction of moisture release. Grønly et al. (2002) studied the kinetics of devolatilization of wood and obtained apparent activation energies of 100 kJ/mol for the thermal decomposition of hemicellulose, 236 kJ/mol for the decomposition of cellulose and 46 kJ/mol for the decomposition of lignin. Also, Abreu Naranjo et al., (2012) presented values of 88.36, 171.96 and 54.05 kJ/mol for hemicellulose, cellulose and lignin, respectively. With respect to the reaction order, authors as Ceylan y Topçu (2014), working with hazelnut shell, found that thermal degradation of this residue in an inert atmosphere of nitrogen is adequately described with a model reaction of twelve order. Moreover, the reaction orders obtained through the pseudo-mechanistic model and presented in Table 6, are consistent with the results obtained by applying the method of CR (see Table 5). Regarding the values of yield coefficients to volatiles (ʋ), these are in conformity with the results presented by other authors who have analyzed the thermal decomposition in an inert atmosphere of similar lignocellulose residues. For example, Anca-Couce et al., (2014) had yields of char (1-ʋ) for hemicellulose and cellulose fractions comparable to those found in this work. Also, Haykiri-Acma et al., (2010) obtained a char yield of 36.9 wt.% of the initial weights for lignin. Similarly, Font et al., (2009) studied the pyrolytic decomposition of pine leaf and pinecone shell and found values of yield
coefficient to volatiles very similar to those shown in Table 6, for each pseudocomponent. Finally, Figures 5 and 6 present experimental and calculated TG and DTG curves. These figures show the evolution of experimental and calculated solid fractions for the torrefaction process at 200 ºC and 300ºC to simulate the lower and higher temperatures of torrefaction. Also, pyrolytic decomposition of each pseudocomponent is presented. At 200 ºC only the moisture of the sample is lost and is very slightly begins to degrade part of lignin and hemicellulose, however cellulose is unaffected. Moreover, in curves of the torrefaction performed at 300 ºC is observed as cellulose and hemicellulose have an evident degradation. 4. CONCLUSIONS In this work, kinetic of torrefaction of olive tree pruning was evaluated based on thermogravimetric data in nitrogen atmosphere. Torrefaction of olive tree pruning could not be modeled by isoconversional kinetics for one-step global reaction. The torrefaction activation energies ranged from 61.56 to 217.83 kJ/mol. A pseudomechanistic model based on four independent parallel reactions was proposed to modeling torrefaction kinetics of olive tree pruning. This pseudo-mechanistic model provided a good agreement with the experimental data; therefore, the kinetic parameters obtained could be used to predict olive tree pruning torrefaction.
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LIST OF FIGURES Figure 1: Experimental thermogravimetric curves (TG) of the olive tree pruning waste. a) Representation of mass fraction (w) versus temperature (T), b) Representation of mass fraction (w) versus time (t). Figure 2: Experimental thermogravimetric derived curves (DTG). Representation of dw/dT versus temperature (only dynamics tests). Figure 3: Representation of isoconversional methods of FOW (a), KAS (b) and FR (c) for the analysis of thermal degradation of olive tree pruning waste under inert atmosphere (β is heating rate, α is conversion degree). Figure 4: Dependence of activation energy (Eα), obtained with isoconversionals methods of FOW, KAS and FR for analysis of thermal degradation under nitrogen atmosphere of olive tree pruning waste, on conversion degree (α). Figure 5: Simulation of TG (a) and DTG (b) curves of torrefaction of olive tree pruning at 200ºC at a heating rate of 15ºC/min and a holding time of 60 min at 200 ºC. Figure 6: Simulation of TG (a) and DTG (b) curves of torrefaction of olive tree pruning at 300ºC at a heating rate of 15ºC/min and a holding time of 60 min at 300 ºC.
1.0
5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min
w = m/m0
0.8
0.6
0.4
0.2
0.0 200
400
600
800
T, ºC
Figure 1a
1.0 5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min 15 ºC/min + 200 ºC during 60 min 15 ºC/min + 300 ºC during 60 min
w=m/m0
0.8
0.6
0.4
0.2
0.0 0
2000
4000
6000
t, s
Figure 1b
8000
10000
0.000
-0.001
5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min
dw/dT, ºC-1
-0.002
-0.003
-0.004
-0.005
-0.006 200
400
T, ºC
Figure 2
600
800
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1.4
log, K/min
1.2
1.0
0.8
0.6
0.0010
0.0015
0.0020
1/T, K
0.0025
0.0030
-1
a) FOW
-12 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
ln, 1/K·min
-11
-10
-9
0.0010
0.0015
0.0020
1/T, K-1
b) KAS
0.0025
0.0030
-7 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
-6
ln[(d/dT)]
-5
-4
-3
-2
-1 0.0010
0.0015
0.0020
1/T, K
-1
c) FR
Figure 3
0.0025
0.0030
250
E, kJ/mol
200
150
100
50
FOW KAS FR
0 0.0
0.2
0.4
0.6
Figure 4
0.8
1.0
1.0
0.8 Experimental Calculated Hemicellulose Cellulose Lignin Moisture
w
0.6
0.4
0.2
0.0 0
1000
2000
3000
4000
5000
Time, s
Figure 5a
0.0000
dw/dt, s-1
-0.0001
Experimental Calculated Hemicellulose Cellulose Lignin Moisture
-0.0002
-0.0003
-0.0004 0
1000
2000
3000
Time, s
Figure 5b
4000
5000
1.0 Experimental Calculated Hemicellulose Celullose Lignin Moisture
0.8
w
0.6
0.4
0.2
0.0 0
1000
2000
3000
4000
5000
Time, s
Figure 6a
0.0000
dw/dt, s-1
-0.0002 Experimental Calculated Hemicellulose Celullose Lignin Moisture
-0.0004
-0.0006
-0.0008
-0.0010 0
1000
2000
3000
Time, s
Figure 6b
4000
5000
Table 1. Set of experimental conditions for each thermal decomposition test in thermobalance.
Atmosphere
Flow rate, mL/min
Initial temperature, ºC
Final temperature, ºC
Dynamic stage: Heating rate, ºC/min
Isothermal stage: Time at final temperature, min
Nitrogen
20
30
800
5
0
Nitrogen
20
30
800
10
0
Nitrogen
20
30
800
15
0
Nitrogen
20
30
800
20
0
Nitrogen
20
30
800
25
0
Nitrogen
20
30
200
15
60
Nitrogen
20
30
300
15
60
Table 2. Common mechanisms of degradation of a solid state material. Degradation Model
f(α) = (1/k)·(dα/dt)
g(α) = k·t
Nucleation Avrami-Erofeev
A2
2·(1-α)·[-ln(1-α)]1/2
[-ln(1-α)]1/2
Nucleation Avrami-Erofeev
A3
3·(1-α)·[-ln(1-α)]2/3
[-ln(1-α)]1/3
Nucleation Avrami-Erofeev
A4
4·(1-α)·[-ln(1-α)]3/4
[-ln(1-α)]1/4
Contraction area
R2
2·(1-α)1/2
1-(1-α)1/2
Contraction volume
R3
3·(1-α)2/3
1-(1-α)1/3
Undimensional diffusion
D1
1 2
α2
Bidimensional diffusion
D2
1 ln1 α
(1-α)·ln(1-α)+α
Three-dimensional diffusion (Jander)
D3
3 1
2/ 3
2 1 1 α
1/ 3
[1-(1-α)1/3]2
Three-dimensional diffusion (Ginstling-Brounshtein)
D4
3 1 / 3 2 1 α 1
1-2/3·α-(1-α)2/3
First order reaction
F1
(1-α)
-ln(1-α)
Nth order reaction
Fn
(1-α)n
Table 3. Summary of the different stages on thermal decomposition of olive tree pruning under nitrogen atmosphere to different heating rates. β, ºC/min
First stage of decomposition (Moisture)
Second stage of decomposition (Hemicellulose)
Third stage of decomposition (Cellulose)
Fourth stage of decomposition (Lignin)
5
10
15
20
25
Ti, ºC
30
30
30
30
30
Tf, ºC
128
133
135
140
142
Tmáx, ºC
59
76
89
93
96
wvolatilized (%)
7.7
7.7
8.0
7.7
7.8
(dw/dT)máx, ºC-1
-1.520·10-3
-1.333·10-3
-1.445·10-3
-1.287·10-3
-1.394·10-3
Ti, ºC
165
170
172
174
180
Tf, ºC
320
325
330
333
335
Tmáx, ºC
-
310
312
314
317
wvolatilized (%)
32.4
31.6
30.3
31.1
30.7
(dw/dT)máx, ºC-1
-4.203·10-3
-4.434·10-3
-4.345·10-3
-4.385·10-3
-4.214·10-3
Ti, ºC
320
325
330
333
335
Tf, ºC
388
390
393
395
400
Tmáx, ºC
346
352
359
360
365
wvolatilized (%)
24.1
22.2
23.6
23.1
23.6
(dw/dT)máx, ºC-1
-5.644·10-3
-5.256·10-3
-5.133·10-3
-5.104·10-3
-5.096·10-3
Ti, ºC
388
390
393
395
400
Tf, ºC
800
800
800
800
800
Tmáx, ºC
-
-
-
-
-
wvolatilized (%)
14.4
17.2
17.4
19.4
18.6
(dw/dT)máx, ºC-1
-
-
-
-
-
Ti is the onset temperature of decomposition Tf is the temperature at which ends the stage of decomposition Tmax is the temperature at which the decomposition in each stage has place at a higher rate wvolatilized is the percentage of mass loss corresponding to each stage. (dw/dT)max is the value of maximum loss rate corresponding to each stage which has place a Tmax.
Table 4. Activation energy values (E α) and correlation coefficients (r2) determined by FOW, KAS and FR methods for thermal degradation of olive tree pruning under nitrogen atmosphere. Method Conversion degree
FWO
KAS
FR
Eα, kJ/mol
r2
Eα, kJ/mol
r2
Eα, kJ/mol
r2
0.05
64.03
0.980
61.56
0.997
64.03
0.980
0.10
41.52
0.399
36.68
0.319
37.49
0.370
0.15
126.96
0.921
125.04
0.911
126.96
0.921
0.20
144.57
0.947
143.14
0.941
160.07
0.976
0.25
160.85
0.967
160.02
0.963
160.85
0.967
0.30
173.18
0.985
172.79
0.984
185.03
0.994
0.35
185.34
0.994
185.40
0.993
185.34
0.994
0.40
195.32
0.998
195.73
0.997
209.60
1.000
0.45
202.53
1.000
203.15
1.000
202.53
1.000
0.50
208.75
0.999
209.53
0.999
215.89
0.998
0.55
211.88
0.999
212.66
0.999
211.88
0.999
0.60
214.52
0.999
215.29
0.999
217.83
0.999
0.65
213.78
0.999
214.39
0.999
213.78
0.999
0.70
205.58
0.999
205.64
0.999
180.30
0.988
0.75
172.35
0.987
170.51
0.985
172.35
0.987
0.80
108.83
0.955
103.27
0.945
82.13
0.899
0.85
94.40
0.935
87.35
0.918
94.40
0.935
0.90
90.74
0.936
82.48
0.916
82.73
0.892
Table 5. Numerical results obtained for the activation energy (in kJ/mol) using the method of CR for the heating rates of 5, 15 and 25 ºC/min compared with the values obtained by FOW, KAS and FR. 5 ºC/min Hemicellulose Mechanism E
r
A2
12.99
A3
2
15 ºC/min
Cellulose
Lignin
Hemicellulose
7.11
0.993
-8.50
0.998
0.992
2.71
0.975
-9.71
0.998
32.89
0.999
31.05
0.999
-5.43
0.982
0.983
31.02
0.999
27.73
0.999
-7.00
0.986
-5.25
0.939
64.79
0.999
53.85
1.000
-5.41
0.949
1,000
-1.28
0.464
71.69
0.999
65.25
1.000
-1.38
0.557
80.74
0,999
6.21
0.974
79.46
1.000
79.63
0.999
6.20
0.985
0.999
71.13
0,999
1.07
0.408
74.27
0.999
70.00
0.999
1.00
0.449
40.42
1.000
42.87
0,997
1.24
0.905
38.83
1.000
42.26
0.998
1.14
0.955
0.989
54.42
1.000
70.79
0,994
22.76
0.993
52.29
1.000
70.32
0.994
22.87
0.988
48.63
0.996
70.57
1.000
105.46
0,991
51.59
0.991
67.81
1.000
105.24
0.991
51.99
0.987
0.986
78.43
0.997
88.71
1.000
145.43
0,989
82.82
0.991
85.23
1.000
145.49
0.990
83.55
0.987
0.985
108.65
0.998
108.60
1.000
189.02
0,987
114.59
0.991
104.33
1.000
189.34
0.988
115.66
0.988
r
E
r
E
r
E
r
1.000
16.94
0.992
-6.15
0.969
15.33
0.999
16.27
0,995
-5.90
0.995
14.49
5.50
0.999
7.92
0.985
-8.30
0.989
6.97
0.998
7.40
0,991
-8.28
0.997
A4
1.75
0.993
3.41
0.959
-9.37
0.993
2.79
0.994
2.97
0,971
-9.47
R2
29.98
1.000
32.18
0.997
-5.81
0.941
34.25
0.999
31.68
0,999
R3
28.25
0.999
28.69
0.998
-7.24
0.966
32.31
0.999
28.36
D1
59.43
0.999
54.84
0.999
-6.11
0.919
67.02
0.999
D2
65.80
1.000
66.77
0.999
-2.56
0.566
74.16
D3
73.00
1.000
81.91
0.997
4.40
0.726
D4
68.19
1.000
71.76
0.998
-0.39
F1
35.47
1.000
44.01
0.995
F2
47.93
1.000
73.78
F3
62.29
1.000
F4
78.42
F5
96.09
2
Lignin
0.997
E
2
Cellulose
-6.09
r
2
Hemicellulose
0.996
E
2
Lignin
r2
r
2
Cellulosa
E
E
2
25 ºC/min
E
r
0.999
15.89
6.37
0.998
0.998
2.32
-5.26
0.975
0,999
-6.81
54.96
1,000
0.999
66.39
82.24
1.000
0.026
76.85
0.29
0.027
0.991
20.96
110.97
0.988
1.000
153.85
0.999
200.51
2
FOW
156.60
210.90
97.99
156.60
210.90
97.99
156.60
210.90
97.99
KAS
155.85
211.50
91.03
155.85
211.50
91.03
155.85
211.50
91.03
FR
161.80
207.94
86.42
161.80
207.94
86.42
161.80
207.94
86.42
Table 6. Kinetic parameters obtained for the pyrolitic thermal decomposition of olive tree pruning according to the pseudo-mechanistic model proposed.
Parameter
Moisture
Hemicellulose
Cellulose
Lignin
ki0 (s-1)
4.64·109
3.53·1012
8.98·1015
3.78·1014
Ei (kJ/mol)
74.55
151.65
209.25
76.56
ni
6.99
3.90
4.83
4.51
ʋi
1.00
1.00
0.99
0.57
37
KINETIC MODELLING OF TORREFACTION OF OLIVE TREE PRUNING
Highlights
Thermogravimetric analysis of material under torrefaction conditions was studied.
Mass loses during torrefaction was modeled by a pseudo-mechanistic model.
The model included moisture, hemicellulose, cellulose and lignin content.
The model can predict the mass yield under different operating conditions.
38
S1359-4311(16)33497-4 http://dx.doi.org/10.1016/j.applthermaleng.2016.11.147 ATE 9558
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 August 2016 3 November 2016 20 November 2016
Please cite this article as: M.A. Martín-Lara, G. Blázquez, M.C. Zamora, M. Calero, Kinetic modelling of torrefaction of olive tree pruning, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2016.11.147
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KINETIC MODELLING OF TORREFACTION OF OLIVE TREE PRUNING.
Authors: M.A. Martín-Lara*, G. Blázquez, M.C. Zamora, M. Calero * Corresponding author
* María Ángeles Martín-Lara Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) Phone: 34 958 240445 Fax: 34 958 248992 e-mail: [email protected]
Gabriel Blázquez García Department of Chemical Engineering University of Granada, 18071 Granada (Spain) Phone: 34 958 243311 Fax: 34 958 248992 e-mail: [email protected]
María Carmen Zamora Moreno Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) e-mail: [email protected]
Mónica Calero de Hoces Department of Chemical Engineering. University of Granada, 18071 Granada (Spain) Phone: 34 958 243315 Fax: 34 958 248992 e-mail: [email protected]
Abstract The objective of this study is the proposal of a pyrolysis kinetic model that describes the thermal decomposition of olive tree pruning in different torrefaction conditions via thermogravimetrical measurements in nitrogen atmosphere. First, the determination of activation energies was performed by isoconversional methods of Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman. Three stages were distinguished in which the activation energy keeps approximately constant and were related to the thermal degradation of the different constituents of the material (cellulose, hemicellulose and lignin). Then, Coast-Redfern method was applied to determine the kinetic function. The kinetic function that seems to determine the mechanism of thermal degradation of main components of olive tree pruning was nth order reaction. Finally, a detailed pseudomechanistic model (using least squares fitting in a parallel reaction scheme) was analyzed. This model was appropriate to predict the pyrolysis behavior of the olive tree pruning in all torrefaction conditions studied.
Keywords: Kinetic; Modelling; Non-isothermal thermogravimetry; Olive tree pruning; Torrefaction
1. INTRODUCTION Torrefaction is a thermochemical treatment of biomass produced at temperatures between 200 and 300 °C in the absence of oxygen to produce beneficial changes in the composition of biomass: increases calorific value, improves grindability and resistance to degradation, among other properties (Van der Stelt et al., 2011). Torrefaction can be applied to a wide range of organic materials and can increase the use of biomass for power generation in conventional power plants and for producing a combustible gas in gasifiers (Shoulaifar et al., 2016). Kinetic modeling is a crucial tool to predict the performance of biomass during torrefaction (Repellin et al., 2010; Shang et al., 2013) and the most usual way of performing a kinetic analysis is through thermogravimetric analysis (TGA). In most of recent works (Ceylan and Topcu, 2014; Ma et al., 2015; Martín-Lara et al., 2016; Ren et al., 2013; Slopiecka et a., 2012; Zhao et al., 2013), an overall kinetic model has been developed to describe the mass loss or thermal degradation of lignocellulosic biomass. In general, most researchers compared different methods for predicting kinetic parameters (for example, Kisssinger model, Kissinger-Akahira-Sunose (KAS), FlynnWall-Ozawa (FWO) and Friedmann (FR) methods). However, other researchers have successfully applied the distributed activation energy model (DAEM) to describe biomass decomposition in an inert environment. This model assumes that several irreversible first order parallel reactions having unique kinetic parameters take place simultaneously (Chen et al., 2016; Soria-Verdugo et al., 2016). In addition, a great number of studied have proposed diverse reaction schemes consisting of multiple reactions that assume the decomposition of lignocellulosic materials as the sum of the decomposition of its major constituents, hemicellulose, cellulose and lignin. Most of these studies indicated that the different chemical steps can be characterized using a nth-
order reaction kinetic model (Anca-Couce et al., 2014; Conesa and Domene, 2011; Hashimoto et al., 2011). In mature olive trees, pruning is mainly required to renew the fruiting surface of the tree and achieve high yields, maintain vegetative growth of fruiting shoots, maintain the skeleton structure, favor air circulation and light penetration through the foliage to prevent bacterial and fungal diseases which grow more easily in humid, stagnant air. Also, it helps to decrease the alternation of production which naturally affect the olive and, finally, to eliminate dead wood and manage the size of the plant to engage the harvest in safe conditions. The objective of this study has been the proposal of a comprehensive pyrolysis kinetic model that describes the thermal decomposition process of olive tree pruning in different torrefaction conditions via thermogravimetrical measurements in nitrogen atmosphere. First, the determination of activation energies of the kinetics of biomass torrefaction was carried out by isoconversional methods, then, Coast-Redfern method was applied to determine kinetic function and, finally, a detailed pseudo-mechanistic model based in a parallel reaction scheme was analyzed. 2. MATERIAL AND METHODS 2.1. Biomass sample Olive tree pruning is a waste from olive pruning, characteristically required for maintenance and reshaping of olive trees. The OTP used for this study was obtained from olive plantation located in Vilches, province of Jaen (Spain). The solid was reduced to particles lower than 1.00 mm by powdering in an analytical mill (IKA MF10) and was stored for later use in all tests. A complete physic-chemical characterization of this material has been previously published in Calero et al., (2013). 2.2. Experimental method
A total of seven experiments were conducted under nitrogen atmosphere in a thermobalance Perkin Elmer, model STA 6000. Five experiments were carried out in dynamic conditions at five different heating rates (5, 10, 15, 20 and 25 °C/min), while two other tests were performed in dynamic + isothermal conditions, i.e. with a first stage at a constant heating rate of 15 °C/min and a second isothermal stage keeping constant the final temperature for a time of 60 min; specifically, an experiment to 200 °C and the other one to 300 °C. All experiments were performed by duplicate with an initial mass of sample about 25 mg (± 3 mg) and a nitrogen flow rate of 20 mL/min. In Table 1 the set of experimental conditions for each experiment are detailed. 2.3. Kinetic analysis In most developed kinetic formulations of thermal decomposition of biomass, the calculation of the kinetic parameters is based on the assumption that the decomposition rate (dα/dt) is a function of two variables, temperature (T) and degree of conversion or extend of reaction (α) related to the kinetic constant k(T) and the reaction model f(α), respectively, and described as a single reaction: (1) The function f(α) depends on the controlling mechanism and the extent of reaction or conversion can be calculated by the following equation: (2) where w0, w and w∞ correspond to the initial sample mass, the sample mass at any time and the final residual mass obtained at the end of the decomposition process, respectively. Moreover, the dependence of kinetic constant with temperature is described by Arrhenius equation: (3)
where k0 is the pre-exponential factor or frequency factor, E is the apparent activation energy and R is the gas constant. Also, as it is operated in dynamic regime (non-isothermal conditions) and the temperature increases linearly with time, a linear heating rate can be defined as: (4) So, an expression of the rate law for non-isothermal conditions can be obtained combining equations (1), (3) and (4): (5) Setting in order and integrating both sides of Eq. (5), can be obtained: (6) where p(x) in Eq. (6) is known as the temperature integral. The temperature integral does not have an exact analytical solution but it can be approximated by different empirical interpolation equations as term proposed by Doyle, Agrawal, Gorbatchev, etc. Determination of the activation energies by isoconversional methods of Flynn–Wall– Ozawa (FWO), Kissinger–Akahira–Sunose (KAS) and Friedman (FR). The isoconversional methods (also called “model-free” methods) are based on an isoconversional basis. They assume that the reaction rate at constant degree of conversion is only a function of the reaction temperature, allowing the determination of the values of the activation energy for the same degree of conversion, E α, without assuming any particular model. Hence, isoconversional methods do not require previous knowledge of the reaction mechanism for biomass thermal degradation. But, although it is not necessary to identify a particular model, it is assumed that the dependence of the conversion due to a differential model f(α) (Vyazovkin et al., 2011).
In this this work, activation energy for each degree of conversion is calculated by the integral isoconversional methods of Flynn-Ozawa-Wall (FOW) and Kissinger-AkahiraSunose (KAS) and the differential isoconversional method of Friedman (FR) as they are some of the most common model-free methods for the determination of kinetic parameters in a thermal decomposition. The main reason is easiness in treatment of the experimental data to obtain the values of the activation energy by simple linear representations.
Flynn-Wall-Ozawa (FWO) method
The equation used in the methodology developed by Flynn-Wall-Ozawa (Flynn, 1983; Flynn and Wall, 1966; Ozawa, 1965; 1970; 1992) uses the approximation of Doyle (Doyle, 1962). (7) The activation energy can be obtained from the plot of log (β) versus 1/T for different heating rates for each degree of conversion.
Kissinger-Akahira-Sinose (KAS) method
The approximation of the integral of Doyle may introduce some errors in the estimation of Eα, especially if it varies with the degree of conversion. Another widely used empirical approach is proposed by Murray and White (1955) that produces equation known as Kissinger-Akahira-Sinose (Akahira and Sunose, 1957; Kissinger, 1957). (8) Activation energy can be determined from the slope of the straight line obtained by plotting ln (β/T2) versus 1/T for a fixed degree of conversion.
Friedman (FR) method
Friedman method (Friedman, 1960) is also an isoconversional method in which the values of E for a given conversión value, are obtained plotting ln(dα/dT) versus 1/T, according to the following equation, (9) Determination of reaction model by Coats & Redfern (CR) method. Once the variation of the activation energy for the degradation process is evaluated, the next step is to determine what reaction mechanisms control the process obtaining the form of the function f(α). For this study, the method of Coats & Redfern, CR, applied at conversion ranges in which the activation energy can be considered approximately constant, is used. The method approximates p(x) using a Taylor series expansion to yield the following simplified expresion (Coast and Redfern, 1964, 1965): (10) By plotting ln[g(α)/T2] versus 1/T, the value of the activation energy is obtained. From the results, it can be set as a reaction mechanism which governs the decomposition process, in the different range of conversion tested, one with which the energy values are closest to the values obtained using the methods of FWO, KAS and FR. Some of the more important rate equations used to describe the kinetic behavior of solid state reactions and applied in this work on Coast & Redfern method are listed in Table 2. A pseudo-mechanistic model based on a parallel reaction scheme Finally, in this work, a devolatilization scheme has been proposed based on four parallel reactions considering the olive tree pruning a heterogeneous mixture formed by four independent fractions (moisture, hemicellulose, cellulose and lignin) that decompose at different temperatures following an independent reaction,
s1 Moisture
s1 Volatiles 1
s 2 Hemicellul ose ν2 Volatiles 2 c2 Char2 s3 Cellulose
ν3 Volatiles 3 c3 Char3
s4 Lignin ν4 Volatiles 4 c4 Char4
As an important part of this model, moisture evaporation has been included into the model. Actually, most of published works about thermal degradation of lignocellulosic materials don’t include this fraction as an independent reaction on their reaction schemes. However, it is important to highlight that some old works already included the moisture release in the chemical reaction model (Chan et al. 1983). Volatiles1, Volatiles2, Volatiles3 and Volatiles4 are the gases and condensable volatiles evolved in the decomposition reactions of moisture, hemicellulose, cellulose and lignin, respectively, and Char2, Char3 and Char4 refer to char formed in the decomposition reactions of hemicellulose, cellulose and lignin, respectively. Also, in the reaction scheme proposed, si is the initial contribution of the fraction or component 'i' to the total weight of the material and they have been experimentally obtained (7.7% moisture, 28.9% hemicellulose, 38.4% cellulose and 25.0% lignin); ʋi represents the maximum amount of volatile obtained by reaction 'i' at infinite time, that is, the yield coefficient of volatile that represents the maximum amount of volatiles that can be evolved during corresponding reaction when the substrate reacts completely and, likewise, ci refers to the maximum amount of carbonaceous residue obtained by reaction "i" (c = 1 - ʋ). For the moisture ʋ1 = s1 as any char is obtained from this fraction and total conversion of moisture in volatiles are supposed.
In this paper, according to results of Coast-Redfern method (see Results and Discussion, subsection 3.3.), an nth reaction model has been assumed. Therefore, given the mass balance of the products and reactants and the degree of conversion (α), the kinetic equations associated with independent reactions can be expressed as follows: (11) (12) (13) (14) In these equations ni is the order reaction, ki is the rate constant of the corresponding reaction “i”. These kinetic constants follow the Arrhenius law: (15) (16) (17) (18) where ki0 is the pre-exponential factor, Ei the apparent activation energy of reaction “i”. Total solid fraction, wcalc (unreacted solid and originated carbonaceous solid) are related to the other variables using the following expression: (19) Once the model was defined with its corresponding equations, the next step is to obtain the kinetic parameters of the reactions. The best parameters will be those that best correlate the calculated values with experimental thermogravimetric curves for all tests simultaneously (experiment 1 to 7).
The simultaneous solution of four differential equations system was carried out numerically with Euler's method in an Excel spreadsheet using as initial condition values of conversion factors equal to 0. The quality of the model was evaluated using an objective function that minimizing the differences of squares between experimental and calculated data in the integral and differential forms. (20) The parameter f is a scaling factor included to compensate the differences in the obtained numeric data for integral and differential forms. Moreover, m represents the number of heating rate studied and n the number of experimental data recorded in each test a specific heating rate. 3. RESULTS AND DISCUSSION 3.1. Analysis of thermogravimetric curves In Figure 1a, the experimental curves of mass loss versus temperature of dynamics experiments at five heating rates are shown. In Figure 1b, the experiments in dynamics+isotherms together with the dynamic experiments are shown. In this case, the representation of mass loss are versus time and logically, the displacement of curves with increasing the heating rate is to lower times, that is to say, the higher the heating rate faster decomposes the sample, because in this case the temperature in a given time is greater. Also, in figure 1a, an increase in the heating rate caused a shift of the curves at higher temperatures. This behavior usually occurs in any thermogravimetric analysis, and it can be interpreted as a consequence of the mathematical form of the kinetic law process, assuming infinitely fast heat transfer and kinetic parameters constant (Conesa and Rey, 2015; Martín-Lara et al., 2016). Moreover, the representations of the data of TGs curves by using the thermogravimetric derived curves (DTGs) provides useful information meaning that they allow to
appreciate more clearly small changes hardly observable in the curves TGs. In Figure 2, the values of dw/dT against the temperature have been shown. All curves present three different stages of mass loss, identified by peaks in the DTG curves. The first stage (first peak on DTG curves) can be attributed to the moisture release (Arteaga-Pérez et al., 2015; Basu 2013). The second peak corresponds to the decomposition of the hemicellulose (Carvalho et al., 2015; Martín-Lara et al., 2016). The third stage (third peak on DTG curves) is mainly attributed to the degradation of cellulose (Amutio et al., 2013). Hemicellulose usually appears as a shoulder to the left of the main degradation peak in the DTG curve corresponding to cellulose. Furthermore, a fourth stage of decomposition is found although it doesn’t appear as marked peak in the thermogravimetric derived curve and it corresponds to the thermal degradation of lignin, the fourth major component in olive tree pruning, whose decomposition takes place slowly over a greater temperature range (around 200-800 ºC) (Haykiri-Acma et al., 2010). These stages in TG and DTG curves are comparable to results found by Yang et al., 2007 in their study about hemicellulose, cellulose and lignin pyrolysis. Table 3 includes the information obtained from the TG and DTG curves for each stage of decomposition where Ti is the onset temperature of decomposition, T f is the temperature at which ends the stage of decomposition, T max is the temperature at which the decomposition in each stage has place at a higher rate (peak on the DTG curve), wvolatilized is the percentage of mass loss corresponding to each stage and (dw/dT)max is the value of maximum loss rate corresponding to each stage which has place a Tmax. Similar temperature ranges associated with these thermal degradations have been found by several authors who have used different vegetable waste, such as Gu et al., (2013) in his study of thermal degradation by pyrolysis of poplar sawdust, Gómez et al. (2016) in
their study of the pyrolysis of biomass relevant in the Mediterranean basin: olive pits, almond shell, pinewood and olive tree pruning, and Chen et al. (2013) in their kinetic analysis of pyrolysis of maize straw and wheat straw. As it is shown in thermogravimetric curves, the degradation process of organic materials such as residue from olive tree pruning is very complex, as they are involved multitude of chemical reactions and, in general, a superposition of different chemical processes. In addition, physical processes (for example diffusion of decomposition products) must be also considered, which make difficult to give an interpretation with a chemical/physical meaning to the mathematical equation describing the process. Still, in the bibliography simple models are presented to describe the kinetic of thermal decomposition process which isn’t known a priori, setting validation criteria such as the invariance of activation energy determined by isoconversionals methods. 3.2. Determination of the activation energies by isoconversional methods of Flynn– Wall–Ozawa (FWO), Kissinger–Akahira–Sunose (KAS) and Friedman (FR) In Figure 3, the results of the analysis based on isoconversionals models of FOW, KAS and FR for the range of values of the degree of conversion of 0.1 to 0.9 are shown. The fitting lines are shown only for those cases where the correlation coefficient was greater than 0.85. In Table 4, the parameters of the linear fits with correlation coefficients for each of the values of the degree of conversion studies are presented. Those adjustments have a correlation coefficient lower than 0.85 are marked in cursive. For the conversion value of 0.1 the adjustment linearity is rather low. In all cases, the worst fit is given to the extreme levels of conversion (0.1; 0.8; 0.85; 0.9) possibly due to the inherent error associated with the humidity difference samples (degrees of conversion low) and a more complex process in finalizing degradation (high degrees of conversion).
Moreover, Table 4 shows that activation energy determined by these conversional methods is not constant in function of conversion so, thermal decomposition under nitrogen atmosphere may not be represented by a single kinetic model, that is, the reaction mechanism is complex and cannot be described by a single reaction or a single type of degradation for the entire process of degradation. However, as it is shown in Figure 4, three stages can be distinguished in which the activation energy remains approximately constant meaning that the processes that controlling weight loss not vary significantly throughout the intervals (Flynn, 1988) and also, coincide with the intervals at which marked peaks appear in the DTG curve, that is, are related to the different degradation of the various constituents of the material. The first stage corresponds to the degree of conversion between 0.35 and 0.45 and is due to the thermal decomposition of hemicellulose. The second stage affects to conversion degrees between 0.5 and 0.7 with higher activation energies and may be associated mainly to degradation of cellulose, as is well known that cellulose has apparent activation energies greater the hemicellulose because the crystallinity of its components, and the third stage, with lower activation energy values correspond to degrees of conversion between 0.8 and 0.9. This decrease in activation energy in the last stage indicates that the degradation process takes place more easily and this behavior can be attributed to final lignin degradation. 3.3. Determination of reaction model by Coats & Redfern (CR) method Once the variation of activation energy for the degradation is known, the next step is to determine what reaction mechanisms direct the process, that is to say, the form of the function f(α). For this study, the method Coats & Redfern (CR) has been applied at intervals of conversion in which the activation energy can be considered approximately constant.
In general, in the studies of thermal degradation of biomass is admitted a model of first or nth order (Baroni et al., 2016; Ceylan and Topçu, 2014; Damartzis et al., 2011; Slopiecka et al., 2012). However, polymeric materials, as in the case of lignocellulosic residues studied in this work, can also present a mechanism of degradation of sigmoidal or diminishing type different from the reaction of first or nth order so, the assumption of first or nth order is not recommended without verification because, perphaps, another kinetic model could be more convenient to describe the degradation process in a given interval conversion (Hatakeyama and Quinn, 1999). In Table 2, the possible mechanisms that have been considered in this study are shown. The first conversion interval to be analyzed, from the point of view of the reaction mechanism, includes the degradation temperature of hemicellulose which, as dicussed above, has associated the second peak obtained in the thermogravimetric derived curve. The second interval includes the temperature to the rate of thermal degradation is maximum and occurs most volatile emissions, that is, includes the largest peak obtained for the thermogravimetric derived curve (the third peak) and is the interval of the temperature-conversion which is associated with the degradation of cellulose. Finally, with the third interval will be evalueted the reaction mechanism, which would correspond to lignin because high conversion values where practically only this component is degraded. The numerical results obtained for the activation energy, in kJ/mol, applying the method of CR are shown in Table 5. Only results obtained for three of the five heating rates studied in this work have been reported in order to simplify and improve the clearness of Table 5, however, similar results were found for the other two heating rates. Based on the results presented in Table 5 and the main research strategy of choosing one model that provides a good fit to the experimental data and provides an activation
energy close to that estimated by the isoconversionals methods of FWO, KAS and FR, the kinetic function f(α) that seems to determine the kinetic model of the mechanism of thermal degradation for cellulose and lignin components is the reaction of nth order, being the most common reaction order the fourth or fifth order. The activation energy values of the other models are significantly different to the values obtained by isoconversional methods. Moreover, the function capable of reproducing the first stage considered in this method (α = 0.35 – 0.45) which correspond to part of the thermal degradation of hemicellulose, seem to be nth reaction model but with order of reaction higher to 5, but, also is important to remake that activation energy in this stage is not constant, it increases slightly with increasing conversion degree. 3.4. Proposal of a pseudo-mechanistic model based on a parallel reaction scheme In the thermal degradation of organic materials, even the simplest, are involved multitudes of chemical reactions. One way to study the kinetics of the thermal decomposition is to propose pseudo-mechanistic models. In them, the products of decomposition in an inert atmosphere are divided in solids (non-volatile residue with a high carbon content), tars (mixtures of a large number of compounds of high molecular weight which are volatile at the temperature of pyrolysis or torrefaction but condense at ambient temperature) and gases (volatile products with low molecular weight at ambient temperature). Because in a thermobalance is not possible to distinguish between the fractions corresponding gases and tars, these fraction are grouped into a single fraction, and in the proposed models is considered only solids and volatiles as products. Moreover, the reactions include a set of several simple reactions, and kinetic parameters that have been obtained are representative of each global reaction. The kinetic reaction schemes proposed for torrefaction can be very different (reactions in parallel, series, competitive, etc.), and there are proposed in function of the shape of
the thermogravimetric curves, the nature of the material (homogeneous or heterogeneous sample) and information provided by the analysis of the generated products
(by TG
coupled
with
mass
spectrometry (TG-MS)
or
infrared
spectrophotometry (TG-FTIR), for example). The kinetic parameters obtained for the fit of the experimental data are shown in Table 6. The kinetic parameters obtained are similar to those found by other authors in previous works. For example, Sharma et al. (2016) found apparent activation energies between 53 and 68 kJ/mol for reaction of moisture release. Grønly et al. (2002) studied the kinetics of devolatilization of wood and obtained apparent activation energies of 100 kJ/mol for the thermal decomposition of hemicellulose, 236 kJ/mol for the decomposition of cellulose and 46 kJ/mol for the decomposition of lignin. Also, Abreu Naranjo et al., (2012) presented values of 88.36, 171.96 and 54.05 kJ/mol for hemicellulose, cellulose and lignin, respectively. With respect to the reaction order, authors as Ceylan y Topçu (2014), working with hazelnut shell, found that thermal degradation of this residue in an inert atmosphere of nitrogen is adequately described with a model reaction of twelve order. Moreover, the reaction orders obtained through the pseudo-mechanistic model and presented in Table 6, are consistent with the results obtained by applying the method of CR (see Table 5). Regarding the values of yield coefficients to volatiles (ʋ), these are in conformity with the results presented by other authors who have analyzed the thermal decomposition in an inert atmosphere of similar lignocellulose residues. For example, Anca-Couce et al., (2014) had yields of char (1-ʋ) for hemicellulose and cellulose fractions comparable to those found in this work. Also, Haykiri-Acma et al., (2010) obtained a char yield of 36.9 wt.% of the initial weights for lignin. Similarly, Font et al., (2009) studied the pyrolytic decomposition of pine leaf and pinecone shell and found values of yield
coefficient to volatiles very similar to those shown in Table 6, for each pseudocomponent. Finally, Figures 5 and 6 present experimental and calculated TG and DTG curves. These figures show the evolution of experimental and calculated solid fractions for the torrefaction process at 200 ºC and 300ºC to simulate the lower and higher temperatures of torrefaction. Also, pyrolytic decomposition of each pseudocomponent is presented. At 200 ºC only the moisture of the sample is lost and is very slightly begins to degrade part of lignin and hemicellulose, however cellulose is unaffected. Moreover, in curves of the torrefaction performed at 300 ºC is observed as cellulose and hemicellulose have an evident degradation. 4. CONCLUSIONS In this work, kinetic of torrefaction of olive tree pruning was evaluated based on thermogravimetric data in nitrogen atmosphere. Torrefaction of olive tree pruning could not be modeled by isoconversional kinetics for one-step global reaction. The torrefaction activation energies ranged from 61.56 to 217.83 kJ/mol. A pseudomechanistic model based on four independent parallel reactions was proposed to modeling torrefaction kinetics of olive tree pruning. This pseudo-mechanistic model provided a good agreement with the experimental data; therefore, the kinetic parameters obtained could be used to predict olive tree pruning torrefaction.
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LIST OF FIGURES Figure 1: Experimental thermogravimetric curves (TG) of the olive tree pruning waste. a) Representation of mass fraction (w) versus temperature (T), b) Representation of mass fraction (w) versus time (t). Figure 2: Experimental thermogravimetric derived curves (DTG). Representation of dw/dT versus temperature (only dynamics tests). Figure 3: Representation of isoconversional methods of FOW (a), KAS (b) and FR (c) for the analysis of thermal degradation of olive tree pruning waste under inert atmosphere (β is heating rate, α is conversion degree). Figure 4: Dependence of activation energy (Eα), obtained with isoconversionals methods of FOW, KAS and FR for analysis of thermal degradation under nitrogen atmosphere of olive tree pruning waste, on conversion degree (α). Figure 5: Simulation of TG (a) and DTG (b) curves of torrefaction of olive tree pruning at 200ºC at a heating rate of 15ºC/min and a holding time of 60 min at 200 ºC. Figure 6: Simulation of TG (a) and DTG (b) curves of torrefaction of olive tree pruning at 300ºC at a heating rate of 15ºC/min and a holding time of 60 min at 300 ºC.
1.0
5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min
w = m/m0
0.8
0.6
0.4
0.2
0.0 200
400
600
800
T, ºC
Figure 1a
1.0 5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min 15 ºC/min + 200 ºC during 60 min 15 ºC/min + 300 ºC during 60 min
w=m/m0
0.8
0.6
0.4
0.2
0.0 0
2000
4000
6000
t, s
Figure 1b
8000
10000
0.000
-0.001
5 ºC/min 10 ºC/min 15 ºC/min 20 ºC/min 25 ºC/min
dw/dT, ºC-1
-0.002
-0.003
-0.004
-0.005
-0.006 200
400
T, ºC
Figure 2
600
800
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1.4
log, K/min
1.2
1.0
0.8
0.6
0.0010
0.0015
0.0020
1/T, K
0.0025
0.0030
-1
a) FOW
-12 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
ln, 1/K·min
-11
-10
-9
0.0010
0.0015
0.0020
1/T, K-1
b) KAS
0.0025
0.0030
-7 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
-6
ln[(d/dT)]
-5
-4
-3
-2
-1 0.0010
0.0015
0.0020
1/T, K
-1
c) FR
Figure 3
0.0025
0.0030
250
E, kJ/mol
200
150
100
50
FOW KAS FR
0 0.0
0.2
0.4
0.6
Figure 4
0.8
1.0
1.0
0.8 Experimental Calculated Hemicellulose Cellulose Lignin Moisture
w
0.6
0.4
0.2
0.0 0
1000
2000
3000
4000
5000
Time, s
Figure 5a
0.0000
dw/dt, s-1
-0.0001
Experimental Calculated Hemicellulose Cellulose Lignin Moisture
-0.0002
-0.0003
-0.0004 0
1000
2000
3000
Time, s
Figure 5b
4000
5000
1.0 Experimental Calculated Hemicellulose Celullose Lignin Moisture
0.8
w
0.6
0.4
0.2
0.0 0
1000
2000
3000
4000
5000
Time, s
Figure 6a
0.0000
dw/dt, s-1
-0.0002 Experimental Calculated Hemicellulose Celullose Lignin Moisture
-0.0004
-0.0006
-0.0008
-0.0010 0
1000
2000
3000
Time, s
Figure 6b
4000
5000
Table 1. Set of experimental conditions for each thermal decomposition test in thermobalance.
Atmosphere
Flow rate, mL/min
Initial temperature, ºC
Final temperature, ºC
Dynamic stage: Heating rate, ºC/min
Isothermal stage: Time at final temperature, min
Nitrogen
20
30
800
5
0
Nitrogen
20
30
800
10
0
Nitrogen
20
30
800
15
0
Nitrogen
20
30
800
20
0
Nitrogen
20
30
800
25
0
Nitrogen
20
30
200
15
60
Nitrogen
20
30
300
15
60
Table 2. Common mechanisms of degradation of a solid state material. Degradation Model
f(α) = (1/k)·(dα/dt)
g(α) = k·t
Nucleation Avrami-Erofeev
A2
2·(1-α)·[-ln(1-α)]1/2
[-ln(1-α)]1/2
Nucleation Avrami-Erofeev
A3
3·(1-α)·[-ln(1-α)]2/3
[-ln(1-α)]1/3
Nucleation Avrami-Erofeev
A4
4·(1-α)·[-ln(1-α)]3/4
[-ln(1-α)]1/4
Contraction area
R2
2·(1-α)1/2
1-(1-α)1/2
Contraction volume
R3
3·(1-α)2/3
1-(1-α)1/3
Undimensional diffusion
D1
1 2
α2
Bidimensional diffusion
D2
1 ln1 α
(1-α)·ln(1-α)+α
Three-dimensional diffusion (Jander)
D3
3 1
2/ 3
2 1 1 α
1/ 3
[1-(1-α)1/3]2
Three-dimensional diffusion (Ginstling-Brounshtein)
D4
3 1 / 3 2 1 α 1
1-2/3·α-(1-α)2/3
First order reaction
F1
(1-α)
-ln(1-α)
Nth order reaction
Fn
(1-α)n
Table 3. Summary of the different stages on thermal decomposition of olive tree pruning under nitrogen atmosphere to different heating rates. β, ºC/min
First stage of decomposition (Moisture)
Second stage of decomposition (Hemicellulose)
Third stage of decomposition (Cellulose)
Fourth stage of decomposition (Lignin)
5
10
15
20
25
Ti, ºC
30
30
30
30
30
Tf, ºC
128
133
135
140
142
Tmáx, ºC
59
76
89
93
96
wvolatilized (%)
7.7
7.7
8.0
7.7
7.8
(dw/dT)máx, ºC-1
-1.520·10-3
-1.333·10-3
-1.445·10-3
-1.287·10-3
-1.394·10-3
Ti, ºC
165
170
172
174
180
Tf, ºC
320
325
330
333
335
Tmáx, ºC
-
310
312
314
317
wvolatilized (%)
32.4
31.6
30.3
31.1
30.7
(dw/dT)máx, ºC-1
-4.203·10-3
-4.434·10-3
-4.345·10-3
-4.385·10-3
-4.214·10-3
Ti, ºC
320
325
330
333
335
Tf, ºC
388
390
393
395
400
Tmáx, ºC
346
352
359
360
365
wvolatilized (%)
24.1
22.2
23.6
23.1
23.6
(dw/dT)máx, ºC-1
-5.644·10-3
-5.256·10-3
-5.133·10-3
-5.104·10-3
-5.096·10-3
Ti, ºC
388
390
393
395
400
Tf, ºC
800
800
800
800
800
Tmáx, ºC
-
-
-
-
-
wvolatilized (%)
14.4
17.2
17.4
19.4
18.6
(dw/dT)máx, ºC-1
-
-
-
-
-
Ti is the onset temperature of decomposition Tf is the temperature at which ends the stage of decomposition Tmax is the temperature at which the decomposition in each stage has place at a higher rate wvolatilized is the percentage of mass loss corresponding to each stage. (dw/dT)max is the value of maximum loss rate corresponding to each stage which has place a Tmax.
Table 4. Activation energy values (E α) and correlation coefficients (r2) determined by FOW, KAS and FR methods for thermal degradation of olive tree pruning under nitrogen atmosphere. Method Conversion degree
FWO
KAS
FR
Eα, kJ/mol
r2
Eα, kJ/mol
r2
Eα, kJ/mol
r2
0.05
64.03
0.980
61.56
0.997
64.03
0.980
0.10
41.52
0.399
36.68
0.319
37.49
0.370
0.15
126.96
0.921
125.04
0.911
126.96
0.921
0.20
144.57
0.947
143.14
0.941
160.07
0.976
0.25
160.85
0.967
160.02
0.963
160.85
0.967
0.30
173.18
0.985
172.79
0.984
185.03
0.994
0.35
185.34
0.994
185.40
0.993
185.34
0.994
0.40
195.32
0.998
195.73
0.997
209.60
1.000
0.45
202.53
1.000
203.15
1.000
202.53
1.000
0.50
208.75
0.999
209.53
0.999
215.89
0.998
0.55
211.88
0.999
212.66
0.999
211.88
0.999
0.60
214.52
0.999
215.29
0.999
217.83
0.999
0.65
213.78
0.999
214.39
0.999
213.78
0.999
0.70
205.58
0.999
205.64
0.999
180.30
0.988
0.75
172.35
0.987
170.51
0.985
172.35
0.987
0.80
108.83
0.955
103.27
0.945
82.13
0.899
0.85
94.40
0.935
87.35
0.918
94.40
0.935
0.90
90.74
0.936
82.48
0.916
82.73
0.892
Table 5. Numerical results obtained for the activation energy (in kJ/mol) using the method of CR for the heating rates of 5, 15 and 25 ºC/min compared with the values obtained by FOW, KAS and FR. 5 ºC/min Hemicellulose Mechanism E
r
A2
12.99
A3
2
15 ºC/min
Cellulose
Lignin
Hemicellulose
7.11
0.993
-8.50
0.998
0.992
2.71
0.975
-9.71
0.998
32.89
0.999
31.05
0.999
-5.43
0.982
0.983
31.02
0.999
27.73
0.999
-7.00
0.986
-5.25
0.939
64.79
0.999
53.85
1.000
-5.41
0.949
1,000
-1.28
0.464
71.69
0.999
65.25
1.000
-1.38
0.557
80.74
0,999
6.21
0.974
79.46
1.000
79.63
0.999
6.20
0.985
0.999
71.13
0,999
1.07
0.408
74.27
0.999
70.00
0.999
1.00
0.449
40.42
1.000
42.87
0,997
1.24
0.905
38.83
1.000
42.26
0.998
1.14
0.955
0.989
54.42
1.000
70.79
0,994
22.76
0.993
52.29
1.000
70.32
0.994
22.87
0.988
48.63
0.996
70.57
1.000
105.46
0,991
51.59
0.991
67.81
1.000
105.24
0.991
51.99
0.987
0.986
78.43
0.997
88.71
1.000
145.43
0,989
82.82
0.991
85.23
1.000
145.49
0.990
83.55
0.987
0.985
108.65
0.998
108.60
1.000
189.02
0,987
114.59
0.991
104.33
1.000
189.34
0.988
115.66
0.988
r
E
r
E
r
E
r
1.000
16.94
0.992
-6.15
0.969
15.33
0.999
16.27
0,995
-5.90
0.995
14.49
5.50
0.999
7.92
0.985
-8.30
0.989
6.97
0.998
7.40
0,991
-8.28
0.997
A4
1.75
0.993
3.41
0.959
-9.37
0.993
2.79
0.994
2.97
0,971
-9.47
R2
29.98
1.000
32.18
0.997
-5.81
0.941
34.25
0.999
31.68
0,999
R3
28.25
0.999
28.69
0.998
-7.24
0.966
32.31
0.999
28.36
D1
59.43
0.999
54.84
0.999
-6.11
0.919
67.02
0.999
D2
65.80
1.000
66.77
0.999
-2.56
0.566
74.16
D3
73.00
1.000
81.91
0.997
4.40
0.726
D4
68.19
1.000
71.76
0.998
-0.39
F1
35.47
1.000
44.01
0.995
F2
47.93
1.000
73.78
F3
62.29
1.000
F4
78.42
F5
96.09
2
Lignin
0.997
E
2
Cellulose
-6.09
r
2
Hemicellulose
0.996
E
2
Lignin
r2
r
2
Cellulosa
E
E
2
25 ºC/min
E
r
0.999
15.89
6.37
0.998
0.998
2.32
-5.26
0.975
0,999
-6.81
54.96
1,000
0.999
66.39
82.24
1.000
0.026
76.85
0.29
0.027
0.991
20.96
110.97
0.988
1.000
153.85
0.999
200.51
2
FOW
156.60
210.90
97.99
156.60
210.90
97.99
156.60
210.90
97.99
KAS
155.85
211.50
91.03
155.85
211.50
91.03
155.85
211.50
91.03
FR
161.80
207.94
86.42
161.80
207.94
86.42
161.80
207.94
86.42
Table 6. Kinetic parameters obtained for the pyrolitic thermal decomposition of olive tree pruning according to the pseudo-mechanistic model proposed.
Parameter
Moisture
Hemicellulose
Cellulose
Lignin
ki0 (s-1)
4.64·109
3.53·1012
8.98·1015
3.78·1014
Ei (kJ/mol)
74.55
151.65
209.25
76.56
ni
6.99
3.90
4.83
4.51
ʋi
1.00
1.00
0.99
0.57
37
KINETIC MODELLING OF TORREFACTION OF OLIVE TREE PRUNING
Highlights
Thermogravimetric analysis of material under torrefaction conditions was studied.
Mass loses during torrefaction was modeled by a pseudo-mechanistic model.
The model included moisture, hemicellulose, cellulose and lignin content.
The model can predict the mass yield under different operating conditions.
38