Determination of kinetic parameters for biomass combustion

1 Determination of kinetic parameters for biomass combustion 1 Álvarez Aa, Pizarro Ca,*, García Rb, Bueno J.L.a, G. Lavín Aa 2 a Department of Chemical and Environmental Engineering. Faculty of Chemistry 3 University of Oviedo, Julián Clavería 8, 33006, Oviedo, Asturias, Spain. 4 b Instituto Nacional del Carbón, INCAR-CSIC, c/ Francisco Pintado Fe 26, 5 33011. Oviedo, Spain 6 7 ABSTRACT 8 The aim of this work is to provide a wide database of kinetic data for the most 9 common biomass by thermogravimetric analysis (TGA) and differential 10 thermogravimetry (DTG). Due to the characteristic parameters of DTG curves, a 11 two-stage reaction model is proposed and the kinetic parameters obtained from 12 model-based methods with energy activation values for first and second stages 13 in the range 1.75·104 – 1.55·105 J/mol and 1.62·104 – 2.37·105 J/mol, 14 respectively. However, it has been found that Flynn-Wall-Ozawa and Kissinger15 Akahira-Sunose model-free methods are not suitable to determine the kinetic 16 parameters of biomass combustion since the assumptions of these two 17 methods were not accomplished in the full range of the combustion process. 18 19 Keywords 20 Biomass, combustion, kinetic parameters, Coats-Redfern method, 21 thermogravimetric analysis 22 23 1. INTRODUCTION 24 2 The importance of waste biomass as an energy source is likely to increase 25 during the coming years as a result of European energy policy targets 26 (European Environment Agency (EEA), 2010). The total amount of potential 27 biomass in Spain is about 88,677,193 t/year (data from Spanish Renewable 28 Energies Plan 2011-2020 referencing in (Álvarez et al., 2015)), belonging to the 29 agricultural and harvesting residues the largest quantity (up to 37.8% of the total 30 potential biomass). 31 There are still some problems in current biomass combustion furnaces, such 32 as low thermal efficiency, instability of heat load, and slagging (Szemmelveisz 33 et al., 2009; Yang et al., 2004). Computational Fluid Dynamics (CFD) could be 34 useful in solving these problems (Dixon et al., 2005; Ma et al., 2007), but it is 35 absolutely essential having a deep knowledge of the composition (proximate, 36 ultimate and structural analysis) and thermal behaviour as well as the kinetics of 37 the combustion process of biomass. 38 The aim of this article is to determine the combustion kinetics parameters of 39 the most commonly used types of biomass in Spain using a thermogravimetric 40 analyser (TGA), since this technique is widely used in the analysis of weight 41 loss characteristics of biomass fuels (Garcia-Maraver et al., 2015; Kok and 42 Özgür, 2013; Maia and de Morais, 2016) 43 44 2. MATERIALS AND METHODS 45 2.1 Materials 46 Twenty eight different biomass samples were tested to obtain their activation 47 energy, Ea, and pre-exponential Arrhenius factor, ko, values for combustion. 48 3 These samples were selected trying to track a wide variety of different biomass 49 origins such as commercial fuels, industrial and forest wastes, energy crops and 50 cereals. Their proximate and ultimate analysis data and other properties are 51 available in a database previously published by this research group (García et 52 al., 2014a, 2014b) . These samples were pre-treated to assure homogeneity 53 and reproducibility of the carried-out tests and to that aim they were air-dried for 54 a day at room temperature, grinded and sieved to 250-500 µm. 55 56 2.2. TG method 57 10 mg of the sample were subjected to thermal decomposition at 4 different 58 low heating rates (5, 10, 15 and 20 K/min) in a Perkin-Elmer STA 6000, using 59 40 ml/min of both purge (N2) and carrier (air) gas. 60 Particle diameter and, consequently, heating rates must be low, particle size 61 should be smaller than 500μm (Garcia-Maraver et al., 2015; Parthasarathy et 62 al., 2013; Shen et al., 2009), while oxidizing gas flux high in order to guarantee 63 chemical-kinetic reaction control, avoiding as possible temperature and 64 concentration gradients (Parthasarathy et al., 2013). 65 66 2.3. Kinetic models 67 In the case of combustion some authors consider just one global reaction 68 divided in three different stages (drying, pyrolysis and char combustion) (Fang 69 et al., 2013; Gangavati et al., 2005), others consider two parallel reactions with 70 three reaction stages (Wang et al., 2014). Finally (Gil et al., 2010) considers a 71 two stage reaction, with a first step between 200-365 ºC (oxidative degradation) 72 4 followed by combustion of char between 365-500 ºC. A similar model is 73 proposed by (Shen et al., 2009) and (Fang et al., 2006), who apply those 74 methods to a two reaction oxidation-reduction pyrolysis. 75 There are two main mathematical approaches to obtain the descriptors of 76 combustion kinetics of biomass samples: (a) model-free methods (iso77 conversional methods) and (b) model-based methods. Both approaches depart 78 from a general conversion-time relationship: 79 dα dt=k(T)∙f(α) (1) Where f(α) is the mechanistic temr and k(T) the thermal dependence term 80 that can be defined by Arrhenius law: 81 k(T)=k0∙e−EaRT ⁄ (2) Conversion rate can be defined as a relation between initial (m0), final 82 (m∞)and instantaneous (mt) sample mass. These data can be obtained from 83 each sample TG profile. 84 α= m0−m𝑡 m0−m∞ (3) The kinetic term f(α) depends on the conditions and the stage of the reaction 85 to study, but it can be usually expressed as (1-α) (Bahng et al., 2009; Fang et 86 al., 2006; Shen et al., 2009), if first reaction order is considered. If other reaction 87 model is required it should be substituted by one of the expressions shown at 88 Table 1. Combining both expressions, the experimental rate of reaction may be 89 formulate as: 90 dα dt=k0∙e−EaRT ⁄∙f(α) (4) 5 If the heating rate β=dT/dt, is included in the previous differential equation, 91 a new expression is obtained following a simple mathematical procedure which 92 can be seen in previous articles such as (Gil et al., 2010; Maia and de Morais, 93 2016): 94 dα dT=1 β·k0∙e−EaRT ⁄∙f(α) (5) Therefore: 95 dα f(α)=k β∙dT→dα f(α)=𝑘0 β∙e−EaRT ⁄dT (6) Then the following integer, that must be numerically solved, is obtained: 96 g(α)=∫ dα f(α)=k0 β∫ e−EaRT ⁄dT T T0 α 0=k0𝐸𝑎 𝛽𝑅 𝑃(𝐸𝑎 𝑅𝑇) (7) The function P(Ea/RT) has no exact solution. Thus Eq. (7) can be solved by 97 numerical methods or approximations as can be seen in (White et al., 2011). 98 2.3.1. Model-free methods 99 The model-free methods allow for evaluating the Arrhenius parameters 100 without choosing the reaction order (Janković et al., 2009; Ravi et al., 2012). 101 These methods rest upon the isoconversional principle, which states that, at a 102 constant extent of conversion, the reaction rate is a function only of the 103 temperature (Vyazovkin and Sbirrazzuoli, 2006). 104 2.3.1.1. Flynn-Wall-Ozawa method 105 The solution of Eq. 7 using Doyle’s approximation (Eq. 8) (Doyle, 1961), is 106 the Flynn-Wall-Ozawa (FWO) method (Eq. 9) (Flynn and Wall, 1966; Ozawa, 107 1965). 108 6 𝑙𝑛[𝑝(𝐸𝑎 𝑅𝑇)]≃−5.331−1.052𝐸𝑎 𝑅𝑇 (8) 109 ln(𝛽)=𝑙𝑛(k0𝐸𝑎 𝑅𝑔(𝛼))−5.331−1.052𝐸𝑎 𝑅𝑇 (9) Eq. 8 is valid only if 20 ≤ Ea/RT ≤ 60 (Flynn and Wall, 1966). For a series of 110 measurements with different heating rates at the fixed conversion value α=αi, 111 the plot of ln (β) vs. T-1 is a straight line with the slope m = –1.052 Ea/R. 112 2.3.1.2. Kissinger-Akahira-Sunose method 113 The Kissinger–Akahira–Sunose method (KAS) is obtained using Eq. 10, 114 which is valid for 20 ≤ Ea/RT ≤ 50 (Sbirrazzuoli et al., 2009). 115 p(Ea RT)≃e−EaRT ⁄ (Ea RT)2 (10) In KAS method, the relation between the temperature and heating rate is 116 given by Eq. 11 (Kissinger, 1957). 117 ln(β T2)=ln(k0R Eag(α))−Ea RT (11) The plot of the left side of Eq. 11 vs. T-1 at constant conversion value is a 118 straight line with the slope m=-Ea/R. 119 2.3.2. Model-based methods. Coats-Redfern method. 120 Coats-Redfern method uses the asymptotic series expansion for 121 approximating the exponential integral in Eq. 7 (Coats and Redfern, 1964). 122 ln(g(α) T2)=ln(k0R βEa(1−2RT  Ea))−Ea RT (12) 7 If term 2RT/Ea is much lower than one it can be ignored, being the right 123 logarithmic term constant: 124 ln(g(α) T2)=ln(k0R βEa)−Ea RT (13) Plotting the left side of Eq. 13 vs. T-1, Ea and k0 are obtained from the slope 125 and intercept respectively. Finally, the model that gives the best linear fit is 126 selected as the chosen model. 127 Several reaction model for g(α) and f(α) are listed at Table 1. With these 128 mathematical approach the kinetic triplet (decomposition model/reaction order, 129 pre-exponential Arrhenius factor and activation energy) can be obtained from 130 thermal decomposition data in a thermobalance scale (Bahng et al., 2009). 131 132 3. RESULTS AND DISCUSSION 133 3.1 Parameters of DTG curves 134 The characteristic parameters of DTG plots, which are presented in Fig. 1, 135 are shown in Table 2. As shown in Table 2, the combustion behaviour of 136 biomass samples studied is almost the same. There are two steps in 137 combustion of biomass, except for charcoal, lignin and cellulose which 138 presented only one step. The first step is related with combustion of cellulose 139 and hemicelluloses and the second one is related with the lignin fraction. All the 140 temperatures at maximum DTG (Tpeak) of first stage are in the range between 141 249-353 ºC, while the range for second stage is 414-627 ºC. Temperature at 142 maximum weight loss rate of cellulose is 338 ºC, which correspond to the first 143 stage while in the case of lignin this temperature is 548 ºC belonging to second 144 8 stage. Thus, the first step is related with combustion of cellulose and 145 hemicelluloses and the second one is related with the lignin fraction. 146 Due to the data in Table 2, a two-stage reaction kinetic scheme has been 147 proposed in this article: 148 A (solid)  A’ (solid) + B1 (gas) (stage 1) A’ (solid)  B2 (gas) + D (ash) (Stage 2) (14) 149 3.2 Kinetic parameters 150 The samples of biomass fuels were subjected to four heating ramps at 5, 10, 151 15 and 20 K/min. Obtained data was adjusted using previously described FWO, 152 KAS and Coats-Redfern method as well as numerically using Scientist software, 153 supposing first reaction order in all cases, which showed a really good 154 mathematical adjust. In that way, a four point straight line was obtained for each 155 conversion value from 10 to 90%, so a value of Ea is obtained for each 156 conversion (FWO and KAS methods) while only one heating ramp data (15 157 K/min) were necessary when Coats-Redfern or numerical methods were used 158 to obtain the kinetic triplet. The obtained kinetic data are shown at Table 3 and 159 Table 4 for Coats-Redfern and numerical solutions respectively. 160 When FWO or KAS method were applied, their particular assumptions were 161 only accomplished in the a range of conversion belonging to hemicelluloses and 162 cellulose fractions, while at the level of conversion for which the combustion of 163 lignin starts the assumptions were not accomplished (Fig 2). In Fig 2 the values 164 of Ea/RT for FWO and KAS methods are plotted against temperature as well as 165 dotted lines for maximum and minimum Ea/RT values for both methods. It can 166 9 be seen clearly that the assumptions of FWO and KAS methods were only 167 accomplished in the first stage with Ea/RT values (red and green lines) between 168 dotted lines while these coloured lines are below minimum dotted line when the 169 second stage takes place. In commercial lignin and charcoal samples, the 170 assumptions were not accomplished at all. Taking into account that charcoal is 171 mainly composed of lignin, it is clear that FWO and KAS methods cannot 172 predict activation energy of biomass combustion when lignin decomposition 173 takes place. 174 Regarding Coats-Redfern and numerical method kinetic data, the activation 175 energy in both stages is almost the same although it must be stated that in most 176 samples this value is slightly higher in second stage. However, the activation 177 energy of lignin is lower than cellulose, this is thought to be because of the 178 synergistic effect. Since both stages are overlapped, in the Coats-Redfern 179 method a 𝛾-factor is used in order to link both stages: 180 dα dT=γ(dα dT)stage 1+(1−γ)(dα dT)stage 2 (15) 181 The 𝛾-factor is modelled as a modified Gomperzt function (Collado et al., 182 2016): 183 𝛾=1 − 𝐴 𝑒𝑥𝑝{−exp(𝜇𝑒 𝐴(𝑇𝑐−𝑇)+1)} (16) Figures 3a and 3b show the simulations of the Coats-Redfern method. As it 184 can be seen in Table 5, where the Gomperzt parameters are shown, A values 185 are close to 1 and Tc is the turning point between both stages, while µ values 186 are related with the rate of change of the 𝛾-factor. 187 16 Table 2. DTG data of biomass samples 322 Sample First stage Second stage Tpeak(ºC) Temperature range (ºC) Tpeak(ºC) Temperature range (ºC) Cellulose 338 300-360 - - Lignin - - 548 450-600 Almond shell 298 250-390 477 400-720 Apple tree leaves 311 220-350 414 410-600 Beetroot pellets 342 210-380 541 400-640 Briquette 343 260-400 509 410-550 Charcoal - - 490 400-900 Chestnut tree chips 335 260-370 473 400-520 Cocoa bean husk 312 225-350 627 425-634 Coffee bean husk 319 220-360 502 440-520 Corncob 289 250-340 454 400-550 Eucalyptus tree chips 340 250-370 486 420-520 Extracted olive pomace 328 230-360 550 400-725 Gorse 339 250-390 560 450-570 Grape seed flour 340 255-375 546 400-775 Miscanthus 307 240-340 550 450-550 Olive stone 340 260-360 418 400-820 Olive tree pruning 342 250-375 469 430-570 Pepper plant 311 220-374 460 400-807 Pine and pineapple leave pellets 324 250-360 422 400-740 Pine kernel shell 249 270-370 515 400-820 Pineapple leaf 344 250-380 496 420-570 Rice husk 334 260-360 450 400-540 Sainfoin 301 230-330 456 390-522 Scrubland pruning 334 260-370 538 400-760 Thistle 345 240-400 473 420-550 Vine shoot 318 250-380 468 420-500 Wheat straw 312 260-360 543 420-650 Wheat straw pellets 300 230-365 458 400-528 323 17 Table 3. Kinetic parameters obtained by means of Coats-Redfern method. 324 Sample Stage 1 Stage 2 ko Ea (J/mol) R2 ko Ea (J/mol) R2 Cellulose 9.47E+17 2.12E+05 0.997 - - - Lignin - - - 6.87E+03 6.95E+04 0.98 Almond shell 2.07E+03 4.82E+04 0.994 1.00E+00 1.71E+04 0.94 Apple tree leaves 3.54E+01 2.94E+04 0.997 2.65E+00 2.06E+04 0.996 Beetroot pellets 5.36E+00 2.16E+04 0.998 3.99E+00 2.32E+04 0.98 Briquette 4.65E+02 4.28E+04 0.997 2.24E+03 5.55E+04 0.96 Charcoal - - - 9.17E-01 2.29E+04 0.98 Chestnut tree chips 1.35E+03 4.66E+04 0.998 2.83E+03 5.38E+04 0.98 Cocoa bean husk 2.86E+01 2.90E+04 0.995 6.28E-01 1.51E+04 0.99 Coffee bean husk 1.06E+02 3.46E+04 0.998 7.10E+03 6.25E+04 0.96 Corncob 1.65E+07 8.69E+04 0.994 3.20E+00 1.95E+04 0.93 Eucalyptus tree chips 4.60E+02 4.18E+04 0.9995 1.03E+04 6.30E+04 0.98 Extracted olive pomace 5.96E+01 3.23E+04 0.993 5.08E-01 1.46E+04 0.92 Gorse 3.07E+01 3.07E+04 0.997 3.31E+02 4.71E+04 0.95 Grape seed flour 8.85E+00 2.56E+04 0.995 3.09E+02 5.70E+04 0.96 Miscanthus 2.56E+02 3.79E+04 0.996 6.76E+02 5.09E+04 0.97 Olive stone 1.37E+03 4.63E+04 0.98 7.33E+01 4.76E+04 0.91 Olive tree pruning 1.48E+02 3.64E+04 0.9991 2.26E+00 1.92E+04 0.92 Pepper plant 4.58E+00 2.14E+04 0.9993 7.02E+01 4.73E+04 0.95 Pine and pineapple leave pellets 1.05E+03 4.51E+04 0.994 1.09E-01 7.35E+03 0.97 Pine kernel shell 2.84E+02 4.05E+04 0.996 7.91E+01 4.81E+04 0.97 Pineapple leaf 1.31E+02 3.69E+04 0.997 5.33E+02 4.92E+04 0.95 Rice husk 7.31E+03 5.39E+04 0.9991 4.13E+01 3.28E+04 0.92 Sainfoin 1.64E+02 3.49E+04 0.996 1.88E+02 4.09E+04 0.995 Scrubland pruning 2.26E+01 2.90E+04 0.995 2.86E+00 2.09E+04 0.92 Sorghum 2.93E+03 4.99E+04 0.998 2.01E+00 1.81E+04 0.98 Thistle 9.64E+01 3.46E+04 0.998 5.61E+01 3.50E+04 0.99 Vine shoot 5.12E+03 5.16E+04 0.998 8.68E+02 4.82E+04 0.96 Wheat straw 1.93E+06 7.75E+04 0.96 4.13E+00 2.34E+04 0.92 Wheat straw pellets 1.35E+04 5.46E+04 0.995 1.51E+01 2.75E+04 0.96 325 18 Table 4. Kinetic parameters obtained by numerical solution. 326 Sample Stage 1 Stage 2 ko Ea R2 ko Ea R2 Cellulose 3.24E+10 1.26E+05 0.997 - - - Lignin 4.49E+05 9.73E+04 0.99993 Almond shell 2.97E+02 3.83E+04 0.9997 7.11E+01 4.36E+04 0.999996 Apple tree leaves 1.29E+02 3.42E+04 0.9998 2.57E+01 3.23E+04 0.999998 Beetroot pellets 3.26E+00 1.75E+04 0.999996 1.26E+03 6.04E+04 0.9999995 Briquette 1.98E+04 5.98E+04 0.99996 3.90E+09 1.48E+05 0.9999997 Charcoal 1.09E+00 2.10E+04 0.9996 Chestnut tree chips 1.76E+05 6.88E+04 0.9998 3.01E+08 1.24E+05 0.99995 Cocoa bean husk 2.48E+02 3.77E+04 0.9998 9.87E+00 2.91E+04 0.999997 Coffee bean husk 9.03E+02 4.35E+04 0.999996 4.70E+10 1.62E+05 0.999997 Corncob 3.99E+07 9.06E+04 0.998 1.30E+03 5.29E+04 0.999996 Eucalyptus tree chips 2.02E+03 4.79E+04 0.99995 3.69E+11 1.72E+05 0.9999997 Extracted olive pomace 2.04E+02 3.69E+04 0.9994 4.11E+01 4.11E+04 0.99998 Gorse 1.28E+03 4.72E+04 0.999995 3.64E+08 1.38E+05 0.999997 Grape seed flour 1.19E+02 3.64E+04 0.99991 5.80E+00 2.84E+04 0.99997 Miscanthus 3.11E+03 4.87E+04 0.9998 4.30E+07 1.22E+05 0.999998 Olive stone 2.00E+02 3.63E+04 0.9995 1.80E+00 2.09E+04 0.99998 Olive tree pruning 2.31E+03 4.85E+04 0.99995 2.15E+03 5.89E+04 0.999991 Pepper plant 2.10E+01 2.68E+04 0.999993 3.58E+11 2.37E+05 0.999999994 Pine and pineapple leave pellets 7.78E+04 6.46E+04 0.99995 1.20E+00 1.62E+04 0.999994 Pine kernel shell 7.07E+03 5.51E+04 0.99997 2.03E+02 5.66E+04 0.999998 Pineapple leaf 3.53E+03 5.15E+04 0.999995 3.13E+04 7.61E+04 0.9999991 Rice husk 1.57E+04 5.69E+04 0.99991 1.85E+04 6.95E+04 0.99997 Sainfoin 2.00E+03 4.53E+04 0.9998 2.11E+04 6.88E+04 0.999994 Scrubland pruning 4.09E+03 5.24E+04 0.99998 3.57E+03 6.21E+04 0.99998 Sorghum 1.09E+04 5.54E+04 0.9997 1.79E+01 2.81E+04 0.999980 Thistle 3.65E+03 5.08E+04 0.999991 2.35E+05 8.64E+04 0.999998 Vine shoot 3.24E+04 5.97E+04 0.99992 3.31E+10 1.54E+05 0.9999992 Wheat straw 2.59E+13 1.55E+05 0.9998 1.25E+01 3.06E+04 0.99997 Wheat straw pellets 6.25E+06 8.21E+04 0.99992 3.90E+04 1.54E+05 0.999998 327 19 Table 5. Gompertz model parameters of the biomass samples analysed. 328 Sample A µ (K-1) Tc (K) Almond shell 0.999 0.016 597.9 Apple tree leaves 1.292 0.074 591.3 Beetroot pellets 0.852 0.029 638.8 Briquette 0.957 0.031 637.8 Charcoal - - - Chestnut tree chips 1.000 0.064 633.7 Cocoa bean husk 1.000 0.145 594.5 Coffee bean husk 0.879 0.032 606.9 Corncob 1.014 0.028 573.2 Eucalyptus tree chips 0.949 0.019 621.2 Extracted olive pomace 0.996 0.017 589.7 Gorse 0.976 0.012 603.6 Grape seed flour 1.372 0.018 603.2 Miscanthus 1.000 0.017 583.0 Olive stone 1.011 0.035 616.0 Olive tree pruning 1.016 0.023 605.2 Pepper plant 0.677 0.050 593.6 Pine and pineapple leave pellets 1.251 0.029 595.8 Pine kernel shell 1.000 0.011 595.2 Pineapple leaf 0.988 0.021 613.0 Rice husk 1.002 0.029 606.9 Sainfoin 1.509 0.056 586.2 Scrubland pruning 1.031 0.019 600.4 Sorghum 1.000 0.052 600.5 Thistle 1.944 0.016 612.1 Vine shoot 0.991 0.018 593.9 Wheat straw 1.000 0.068 588.7 Wheat straw pellets 0.976 0.023 570.8 329 20 FIGURE CAPTIONS 330 Fig. 1. DTG curves of the combustion process (β = 15 K/min) of biomass 331 samples analysed. (PPLP in b is the pine and pineapple leave pellet sample). 332 Fig 2. Matches between DTG and Ea values in FWO and KAS methods. 333 Fig. 3a. Simulations for CR method; 1. Almond shell; 2. Apple tree leaves; 3. 334 Beetroot pellets; 4. Briquette; 5. Charcoal; 6. Chestnut tree chips; 7. Cocoa 335 bean husk; 8. Coffee bean husk; 9. Corncob; 10. Eucalyptus tree chips; 11. 336 Extracted olive pomace; 12. Gorse; 13. Grape seed flour; 14. Miscanthus; 15. 337 Olive stone; 16. Olive tree pruning. 338 Fig. 3b. Simulations for CR method; 17. Pepper plant; 18. Pine and pineapple 339 leave pellets; 19. Pine kernel shell; 20. Pineapple leaf; 21. Rice husk; 22. 340 Sainfoin; 23. Scrubland pruning; 24. Sorghum; 25. Thistle; 26. Vine shoot; 27. 341 Wheat straw; 28. Wheat straw pellets. 342 21 343 Fig. 1. DTG curves of the combustion process (β = 15 K/min) of biomass 344 samples analysed. (PPLP in b is the pine and pineapple leave pellet sample) 345 22 346 Fig 2. Matches between DTG and Ea values in FWO and KAS methods 347 0 10 20 30 40 50 60 70 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 100 200 300 400 500 600 700 800 900 Ea/RT DTG, %weight/ºC Temperature, ºC DTG Chestnut tree chips Ea/RT (FWO) Ea/RT (KAS) Ea/RT min (FWO and KAS) Ea/RT maximum (FWO) 23 348 Fig. 3a. Simulations for CR method; 1. Almond shell; 2. Apple tree leaves; 3. 349 Beetroot pellets; 4. Briquette; 5. Charcoal; 6. Chestnut tree chips; 7. Cocoa 350 bean husk; 8. Coffee bean husk; 9. Corncob; 10. Eucalyptus tree chips; 11. 351 Extracted olive pomace; 12. Gorse; 13. Grape seed flour; 14. Miscanthus; 15. 352 Olive stone; 16. Olive tree pruning. 353 24 354 Fig. 3b. Simulations for CR method; 17. Pepper plant; 18. Pine and pineapple 355 leave pellets; 19. Pine kernel shell; 20. Pineapple leaf; 21. Rice husk; 22. 356 Sainfoin; 23. Scrubland pruning; 24. Sorghum; 25. Thistle; 26. Vine shoot; 27. 357 Wheat straw; 28. Wheat straw pellets. 358