Kinetic Modeling of Waste Tire Carbonization - Energy & Fuels (ACS

1650

Energy & Fuels 2008, 22, 1650–1657

Kinetic Modeling of Waste Tire Carbonization E. L. K. Mui, V. K. C. Lee, W. H. Cheung, and G. McKay* Department of Chemical Engineering, Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong ReceiVed October 10, 2007. ReVised Manuscript ReceiVed January 29, 2008

The pyrolysis of waste tire particles has been studied with a view to developing the understanding of this process in relation to using the product chars as precursors for activated carbon production. In the present work, the effects of heating rates have been studied using thermogravimetric analysis (TGA) and modeled. Two models have been studied and applied to the pyrolysis of waste tire particles. Models based on three-, four- and five-kinetic-step tire decompositions, assuming the component tire composition to be natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR), have been developed and tested. The five-kinetic-step mechanism is developed on the basis that BR and SBR both undergo two-step decomposition reactions and that NR only undergoes a one-step decomposition. Additional evidence was obtained by developing a five-step kinetic model based on a Runge–Kutta solution methodology which gave the lowest sum-of-squared error (SSE) values comparing several multistep model data and experimental data.

1. Introduction The disposal of waste tires is a serious concern in the area of environmental protection and sustainability. Recent processing techniques such as energy recovery (e.g., tire-derived fuel) have been proven successful;1 however, gaseous emission (e.g., polycyclic aromatic hydrocarbons, PAHs) evolved in the combustion process remains a barrier in the application.2 Alternative methods include the conversion of waste tire rubber to materials such as fuel oil3,4 and activated carbon5 via pyrolysis. For the latter, the process generally consists of two steps: thermal degradation under oxygen-deficient atmosphere to break down the cross linkage between carbon atoms, followed by activation in the presence of activating agents such as carbon dioxide or steam for further pore development. Some researchers also attempted to decompose tire rubber in a vacuum6 or pressurized hydrogen atmosphere.7 In the case of nitrogen * Author for correspondence. E-mail address: [email protected]. Phone: (852) 2358 8412. Fax: (852) 2358 0054. (1) Reisman J. I., Lemieux P. M. Air emissions from scrap tire combustion, report no. EPA-600/R-97-115, USEPA: Washington, DC, 1997. (2) Atal, A.; Yiannis, A.; Levendis, J. C.; Dunayevskiy, Y.; Vouros, P. Combust. Flame 1997, 110 (4), 462–478. (3) Li, S. Q.; Yao, Q.; Chi, Y.; Yan, J. H.; Cen, K. F. Ind. Eng. Chem. Res. 2004, 43 (17), 5133–5145. (4) Ucar, S.; Karagoz, S.; Ozkan, A. R.; Yanik, J. Fuel 2005, 84 (14– 15), 1884–1892. (5) Murillo, R.; Navarro, M. V.; Garcia, T.; Callen, M. S.; Aylon, E.; Mastral, M. A. Ind. Eng. Chem. Res. 2005, 44 (18), 7228–7233. (6) Sahouli, B.; Blacher, S.; Brouers, F.; Sobry, R.; van den Bossche, G.; Diez, B.; Darmstadt, H.; Roy, C.; Kaliaguine, S. Carbon 1996, 34 (5), 633–637. (7) Piskorz, J.; Majerski, P.; Radlein, D.; Wik, T.; Scott, D. S. Energy Fuels 1999, 13 (3), 544–551. (8) Williams, P. T.; Besler, S.; Taylor, D. T. Fuel 1990, 69 (12), 1474– 1482. (9) Teng, H.; Serio, M. A.; Wojtowicz, M. A.; Bassilakis, R.; Solomon, P. R. Ind. Eng. Chem. Res. 1995, 34, 3102–3111. (10) Lehmann, C. M. B.; Rostam-Abadi, M.; Rood, M. J.; Sun, J. Energy Fuels 1998, 12 (6), 1095–1099. (11) Kyari, M.; Cunliffe, A.; Williams, P. T. Energy Fuels 2005, 19 (3), 1165–1173.

pyrolysis, typical product distribution varies between 33 and 38% char, 38 and 55% oil, and 10 and 30% gas.9–13 With the aid of thermogravimetric methods such as thermogravimetric analysis (TGA) and derivative thermogravimetry (DTG), a number of kinetic models have been developed for the study of the pyrolysis mechanism and kinetic parameters for waste tire or its components.14–20 A first-order reaction based on the Arrhenius theory is commonly assumed by researchers in the kinetic analysis of data for tire decomposition. A review of the current models and equations has been presented previously.21 Recently, these models18,22 have been based on the key component composition of the tires, namely, a three-elastomer and three-component model. A range of kinetic step models, varying from two to six have been reported using a variety of assumptions. In the present study, the pyrolysis of tire particles has been studied under various conditions of heating rates. Two models have been developed and tested to model the pyrolysis conditions, a Coats-Redfern model23 and a modified numerical solution to the model by Runge–Kutta algorithm.24 The quality (12) Cunliffe, A. M.; Williams, P. T. Energy Fuels 1999, 13 (1), 166– 175. (13) Senneca, O.; Chirone, R.; Masi, S.; Salatino, P. Energy Fuels 2001, 16, 653–660. (14) Chen, K. S.; Yeh, R. Z.; Chang, Y. R. Combust. Flame 1997, 108 (4), 408–418. (15) Yang, J.; Kaliaguine, S.; Roy, C. Rubber Chem. Technol. 1993, 66, 213–229. (16) Kim, S.; Park, J. K.; Chun, H. D. J. EnViron. Eng. 1995, 507–514. (17) Larsen, M. B.; Schultz, L.; Glarborg, P.; Skaarup-Jensen, L.; DamJohansen, K.; Frandsen, F.; Henriksen, U. Fuel 2006, 85 (10–11), 1335– 1345. (18) Leung, D. Y. C.; Wang, C. L. Energy Fuels 1999, 13, 421–427. (19) Senneca, O.; Salatino, P.; Chirone, R. Fuel 1999, 78, 1575–1581. (20) Chen, J. H.; Chen, K. S.; Tong, L. Y. J. Hazard. Mater. 2001, B84, 43–55. (21) Mui, E. L. K.; Ko, D. C. K.; McKay, G. Carbon 2004, 42, 2789– 2805. (22) Aylon, E.; Callen, M. S.; Lopez, J. M.; Mastral, A. M.; Murillo, R.; Navarro, M. V. J. Anal. Appl. Pyrolysis 2005, 74, 259–264. (23) Coats, A. W.; Redfern, J. P. Nature 1964, 201, 68–69. (24) Steiner, E. The chemistry maths book; Oxford: New York, 1997; p 269.

10.1021/ef700601g CCC: $40.75  2008 American Chemical Society Published on Web 04/16/2008

Modeling of Waste Tire Carbonization

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Figure 2. Derivative thermogram (DTG) of tire rubber (1000–2000 µm) at 5 K/min under nitrogen.

Figure 1. Effect of initial sample mass on pyrolysis. Table 1. Typical Composition of Tire Rubber rubber (SBR/BR/NR) carbon black zinc oxide sulfur additives a

passenger38

truck39a

61.9 31.5 1.4 0.8 4.4

60.0 29.3 2.7 1.3 6.7

Composition adjusted after excluding metals and textile.

of fits of the models has been compared using sum-of-squared error (SSE) based on the number of decomposition stages. It is believed that the models developed in this work offer beneficial understanding to both heat and mass transfer phenomenon in the thermal degradation of tire that eventually allows better design in the pyrolysis reactor in future. 2. Experiment and Apparatus 2.1. Materials. The shredded tire rubber particles are assumed to be a dry material of particle size below 5 mm. This rubber was supplied by a local tire reprocessing company in New Territory, Hong Kong. Using a microrotary mill, the rubber particles are further shredded to smaller sizes and sieved in the laboratory to obtain the fraction of 1000–2000 µm. 2.2. Apparatus. A thermogravimetric analyzer (Setaram, TGA/ DTA 92 Setaram II) was used in the analysis of tire rubber decomposition with respect to time. Nitrogen (UHP 99.999%) from a gas cylinder was used as a carrier gas (flowrate 180 mL/min). Samples were placed into a holder made of platinum and attached to a precise balance (sensitivity 1 µg). 2.3. Procedures. Approximately 10–12.3 mg of samples (1000–2000 µm) were heated to 773 K at the heating rate of 1-20 K/min and then held isothermal for 10 min. Preliminary study has shown that the initial sample mass in the range of 6–13 mg has no effect on the pyrolysis (Figure 1).

3. Results and Discussion 3.1. General Kinetic Scheme. A general kinetic scheme is proposed to model the decomposition of tire rubber: tire rubber f volatiles + char The typical composition of tire rubber is shown in Table 1. Tire rubber is a composite material made of polymeric components such as styrene-butadiene rubber (SBR), natural rubber (NR), and butadiene rubber (BR) plus additives like carbon black, zinc oxide, and sulfur.4,9,25,26 Figure 2 is a (25) Williams, P. T.; Besler, S. Fuel 1995, 74 (9), 1277–1283. (26) Aguado, R.; Olazar, M.; Velez, D.; Arabiourrutia, M.; Bilbao, J. J. Anal. Appl. Pyrolysis 2005, 73, 290–298. (27) Lin, J. P.; Chang, C. Y.; Wu, C. H. J. Hazard Mater 1998, 58, 227–236.

Figure 3. Arrhenius plot for tyre rubber pyrolysis at different heating rates. Table 2. Kinetic Parameters Derived from Arrhenius Plots pre-exponential factor, A (1/min)

activation energy, E (kJ/mol)

component heating rate (K/min) 5 10 20

1

2

component 3

1

2

3

1.21 × 51.3 116.3 158.0 426 1.45 × 501 1.90 × 107 1.13 × 1017 50.3 102.8 237.1 114 2.98 × 105 3.16 × 1012 40.5 77.2 171.4 108

1011

thermogram of tire rubber pyrolyzed at 773 K at a heating rate of 5 K/min under nitrogen. The pyrolysis exhibited good repeatability and two distinct peaks were observed, revealing that more than one reaction is involved in the breakdown of polymeric components. Previous workers have developed pyrolysis models for a range of components from three up to six. In the present study, to take these components into the calculation, three models, namely, three-component, four-component, and five-component, were developed on the basis of the approximation suggested by Coats and Redfern23 as well as a numerical solution known as the fourth-order Runge–Kutta algorithm.24 The following is further assumed: (1) All reactions are first-order (i.e., n ) 1). (2) Carbon black is inert at temperatures below 773 K. (3) Polymeric components do not contribute significantly to the formation of chars. Researchers have shown that major polymeric components (i.e., NR, BR, and SBR) are almost completely converted to (28) Conesa, J. A.; Font, R.; Marcilla, A. J. Anal. Appl. Pyrolysis 1997, 43, 83–96. (29) Brazier, D. W.; Schwartz, N. V. J. Appl. Polym. Sci. 1978, 22, 113–124.

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Table 3. Kinetic Parameters Reported in the Literature pre-exponential factor, A (1/min)


component refs (1995)16

Kim et al. Conesa et al. (1997)28 Leung and Wang (1999)18 Gonzalez et al. (2001)40 Aylon et al. (2005)22 present work

1

2

934 5.25 × 1010 2.00 × 104 1.00 × 105 6.00 × 105 501

3.78 × 2.48 × 1018 6.30 × 1013 3.00 × 104 4.92 × 1016 1.90 × 107

component 3 8.75 × 3.58 × 1019 2.30 × 109 756 1.92 × 1019 1.13 × 1017

1016

108

1

2

3

38.7 70.0 52.5 66.8 70.0 50.3

209.0 212.6 164.5 44.8 212.0 102.8

127.3 249.3 136.1 32.9 265.0 237.1

Table 4. Pyrolysis Kinetic Parameters Derived from the Three-Component Model by the Coats-Redfern Method pre-exponential factor, A (1/min)


component heating rate (K/min)

1

1 5 10 20

3.69 × 2.88 × 105 1.26 × 105 1.18 × 104

component

2 105

3

1.96 × 2.02 × 1014 2.03 × 1014 3.43 × 1013 1014

1.95 × 3.98 × 107 1.64 × 108 3.55 × 107 108

1

2

3

SSE

71.2 67.4 67.6 49.3

179.4 180.0 180.9 167.2

122.2 111.0 117.9 105.4

0.0003 0.0008 0.0053 0.0068

Table 5. Pyrolysis Kinetic Parameters Derived from the Three-Component Model by the Runge–Kutta Method pre-exponential factor, A (1/min)


component

component

heating rate (K/min)

1

2

3

1

2

3

SSE

1 5 10 20

5.79 × 104 5.02 × 104 1.32 × 104 2.01 × 103

1.58 × 1011 1.41 × 1012 1.75 × 1013 2.72 × 1011

6.87 × 106 3.97 × 106 1.45 × 107 2.89 × 106

52.6 50.3 47.4 36.3

123.9 133.6 146.1 126.2

90.5 85.7 91.2 82.1

0.0003 0.0009 0.0051 0.0068

volatiles in pyrolysis.17,18,22,25 Williams and Besler25 pointed out that the char yield of each elastomer is generally less than 4% w/w. Adding this value (i.e., 4% w/w of 61% w/w elastomers) up with the carbon black (31.5% w/w; see Table 1) and ash content (ca. 2.2% w/w), the solid residue is ca. 36.1% w/w, which is within the range of literature values (33–38% w/w).9–13 It agrees with the assumption above that polymeric components do not contribute significantly to the formation of chars, as the amount of chars from elastomers only contribute to less than 8% of the total char (2.4% of 36.1% w/w). 3.2. Estimation of Kinetic Parameters. The pre-exponential factor (A) and activation energy (E) can be determined from the slopes of curves shown in the Arrhenius plot (Figure 3). There are three different reaction regions in the temperature range ca. 442–606, 606–667, and 700–773 K. Table 2 is a summary of the kinetic parameters at different heating rates. For comparison, literature data were compiled in Table 3. As shown, the derived parameters in this work are of the same range with data in the literature, revealing the suitability of these parameters in the role of initial guess. 3.3. Three-Component Model. Assuming that three independent, parallel reactions are involved in the course of pyrolysis, a three-component model was developed in accordance with solutions by Coats-Redfern and Runge–Kutta. The pyrolysis scheme is given as below:

The first reaction is initiated at approximately 473 K, followed by two consecutive reactions occurring in the range of 553 and 723 K.

For each component, the reaction rate is as follows:

( )

Ei dRi ) Ai exp (1 - Ri) (1) dt RT The overall reaction rate is given as the sum of the individual decomposition rates, which is: dRT dR1 dR2 dR3 ) m1 + m2 + m3 (2) dt dt dt dt where mi is the mass fraction of each component with respect to the overall decomposable portion of tire rubber. The sum of m is 1. Using kinetic parameters derived from the Arrhenius plots as the basis for an initial guess, iterations were carried out to yield the optimized parameters at different heating rates (see Tables 4 and 5). Both Coats-Redfern and Runge–Kutta solution methods developed during the present work were able to produce kinetic parameters with high correlation coefficients (SSE: 0.0006– 0.0066). Data further revealed that the calculated pre-exponential factor and activation energy of all components decreased with increasing heating rates, showing that the thermal lag effect is significant at higher heating rates. The activation energies for components 1, 2, and 3 calculated based on the Coats-Redfern solution method developed in the present study were 49.3–71.2, 167.2–180.9, and 105.4–122.2 kJ/mol, respectively, whereas the values derived from the Runge–Kutta solution method developed in the present study were 36.3–52.6, 123.9–146.1, and 82.1–91.2 kJ/mol. These values were in the range of other three-component models in the literature in which the activation energy of components 1, 2, and 3 varied between 38.7 and 168.8, 83.1 and 212.6, and 127.3 and 265 kJ/mol.9,16,19,22,28 Comparing the sum-of-squared error (SSE) values between the Coats-Redfern and Runge–Kutta methods, it can be seen that the Runge–Kutta model is able to obtain kinetic parameters with a better fit to



Figure 4. Comparison between data from experiments and the Coats-Redfern method prediction (three-component model).

Figure 7. Effect of activation energy (E) on component 3 decomposition.

Figure 5. Comparison between data from experiments and the Runge–Kutta method prediction (three-component model). Figure 8. Step-size (H) effect on component 3 decomposition. Table 6. Sensitivity Analysis of Component 3 Decomposition in Terms of SSEs variationa

pre-exponential factor, A (1/min)


step-size, H (min)

-25% 0% +25%

0.0160 0.0013 0.5926

0.1316 0.0013 0.1186

0.0017 0.0013 0.0010

a

For activation energy (E), the variation is -5%, 0%, and +5%.

Figure 6. Effect of pre-exponential factor (A) on component 3 decomposition.

the experimental values as the latter have smaller or the same SSEs. Figures 4 and 5 show the comparison of predicted pyrolysis rates under different heating rates with the experimental data. As mentioned in earlier sections, the peaks shown in the DTG curve could be attributed to the volatilisation of different

components. The decomposition initiated at approximately 473 K and reached the maximum decomposition rate at 543 K. This range is believed to be low-boiling point additives, processing oil, and plasticizer, followed by the pyrolysis of certain linear polymers such as BR or NR.4,16 When the temperature was elevated to 573 K or higher, the decomposition of SBR was triggered, leading to the occurrence of the second peak under the influence of residual BR or NR22 or, possibly, the secondary reactions of volatiles such as aromatization or depolymerization.12,19,30–32 The ability of the Runge–Kutta solution for a threecomponent model developed in this work to correlate the experimental data at four heating rates is as good or better than any of the results reported in the literature, based on the SSE values in Table 5. 3.4. Sensitivity Analysis. Sensitivity analysis on the major factors affecting the numerical solution was carried out in order to find out the implications of these factors on the SSEs. Table 6 shows the results of the sensitivity analysis of component 3 by varying three factors in the extent up to 25%. These factors include (1) pre-exponential factor, A; (2) activation energy, E; and (3) step-size, H. As component 3 contributes to over 60% of the overall decomposable fraction, it is reasonable to take this component as a model to demonstrate the effect of different factors to the simulated reaction rate. Figure 6 shows the effect of increasing the pre-exponential factor of component 3 by 25%. A significant shift of peak (30) Laresgoiti, M. F.; de Marco, I.; Torres, A.; Caballero, B.; Cabrero, M. A.; Chomon, M. J. J. Anal. Appl. Pyrolysis 2000, 55, 43–54. (31) de Marco Rodriguez, I.; Laresgoiti, M. F.; Cabrero, M. A.; Torres, A.; Chomon, M. J.; Caballero, B. Fuel Proc. Tech. 2001, 72 (1), 9–22. (32) Fernandez-Berridi, M. J.; González, N.; Mugica, A.; Bernicot, C. Thermochim. Acta 2006, 444, 65–70.


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Table 7. Pyrolysis Kinetic Parameters Derived from the Four-Component Model by the Coats-Redfern Method pre-exponential factor, A (1/min)


component heating rate (K/min)

1

2a

1 5 10 20

8.13 × 1.27 × 107 1.74 × 106 7.10 × 105 105

component 2b

1.01 × 2.21 × 1013 2.80 × 1013 1.58 × 1014 1013

3

2.80 × 1.29 × 1014 8.21 × 1013 1.09 × 1016 1011

2.35 × 3.17 × 109 2.82 × 106 6.58 × 108 107

1

2a

2b

3

SSE

74.0 83.9 93.0 67.0

165.3 170.6 190.6 174.9

159.7 175.1 176.1 204.8

111.1 136.1 89.2 122.9

0.0003 0.0004 0.0050 0.0050

Table 8. Pyrolysis Kinetic Parameters Derived from the Four-Component Model by the Runge–Kutta Method pre-exponential factor, A (1/min)


component

component


1

2a

2b

3

1

2a

2b

3

SSE

1 5 10 20

4.06 × 108 7.31 × 104 9.54 × 103 4.73 × 103

1.61 × 1013 1.29 × 1012 3.07 × 1012 9.50 × 109

7.73 × 1012 6.82 × 1013 4.48 × 107 1.98 × 1010

1.59 × 109 2.54 × 108 3.79 × 107 7.90 × 107

85.1 52.1 53.4 38.3

145.5 132.7 138.9 110.2

136.5 155.3 82.8 112.7

116.0 106.6 96.6 97.9

0.0008 0.0008 0.0048 0.0035

temperature (from ca. 693 to 623 K) and reaction rate (from 0.07 to 0.09 1/min) were observed. It should be pointed out that the peak temperature of 623 K is unlikely as component 3, which is believed to be SBR, does not decompose at temperatures that low. In contrast, such changes were much less in the case of decreasing the factor by 25%, in which both peak temperature (from 693 to 713 K) and reaction rate varied only in the extent of within 10%. While comparing the SSEs one can see that increasing pre-exponential factor may result in larger deviation from the experimental values. The order of SSEs in terms of pre-exponential factor can be expressed in this way: 0.5926 (+25%) > 0.0160 (-25%) > 0.0013 (base case), showing that the simulation is sensitive to the change of preexponential factor. It is preferred to adjust the value of A toward lower temperature region as it may reduce the deviation between predicted and experimental values. Figure 7 demonstrates the implication of varying activation energy to the component 3 decomposition. It appears that the simulation is much more sensitive to the factor of activation energy as even a narrow adjustment within (5% may result in a shift of peak temperature ((30 K) having the trend that the higher the activation energy the larger the peak temperature. Comparing the deviation between simulated values with experimental data in terms of SSE, it can be expressed in descending order: 0.1316 (-5%) > 0.1186 (+5%) > 0.0013 (base case). The effect of step-size to the component 3 decomposition is shown in Figure 8. It is found that all three curves are super positioned with each other, suggesting that the variation of (25% in step-size has limited implication on the simulation process. The SSE is mildly improved when the step-size was elevated from 0.0017 (-25%) to 0.0013 (base case) and further to 0.0010 (+25%). Although the SSE test outcome favors a larger step-size, in applying the numerical solution such as Runge–Kutta algorithm lower step-size is often preferred 23,24 as it means smaller difference between the simulated and exact values. The step-size selected is the base case, hence, it was regarded as a justified response to the requirements of lower SSEs as well as smaller step-sizes. In summary it appears that the reaction rate is sensitive to both pre-exponential factor and activation energy, particular the latter. Although the step-size is significant to the curve-fitting, it did not shift the peak temperature and reaction rate similar to other two kinetic parameters, A and E, in the Arrhenius theory. While selecting the appropriate parameters in kinetic modeling

the implication of these factors should be considered together with the actual experimental data. 3.5. Four-Component Model. The three-component model did not take into account the secondary reaction in the pyrolysis process. Literature data28,34,35 suggested that the thermal decomposition of styrene-butadiene rubber in the range 553 to 713 K is initiated from the butadiene part of the copolymer, followed by a consecutive reaction that degrades the aromatic styrene at a higher temperature. This two-step process, as Senneca et al.19 pointed out, that the tire rubber pyrolysis is similar to other thermal degradation reactions of polymeric substances which consist of different stages such as main-chain scission and depolymerisation at lower temperature (primary pyrolysis), followed by cyclization and degradation of cyclized products at higher temperatures (secondary pyrolysis). Considering these facts, component 2 is split into two subcomponents known as component 2a and 2b, representing the “active” intermediates or oil fraction evolved after the primary pyrolysis.

The reaction rates of the individual components and overall decomposition are identical to the three-component model, which is:

( )

Ei dRi ) Ai exp (1 - Ri) dt RT

(3)

dR1 dR2a dR2b dR3 dRT ) m1 + m2a + m2b + m3 dt dt dt dt dt

(4)

where the sum of all mass fractions is 1. Tables 7 and 8 list the kinetic parameters derived from the Coats-Redfern and Runge–Kutta models. It could be seen that the four-component models generally have lower SSEs in comparison with the three-component models, revealing a better (33) Kreyszig, E. AdVanced engineering mathematics, 7th ed.; Wiley: New York, 1993; p 1041. (34) Erdogan, M.; Yalcin, T.; Tincer, T.; Suzer, S. Eur. Polym. J. 1991, 27 (4–5), 413–417. (35) Conesa, J. A.; Martin-Gullon, I.; Font, R.; Jauhiainen, J. EnViron. Sci. Technol. 2004, 38 (11), 3189–3194.



comparison of the predicted pyrolysis rates under different heating rates with the experimental data. 3.6. Five-Component Model. To further investigate the implication of different components to the overall decomposition rate, component 3 in the four-component model was split into two subcomponents, namely, component 3a and component 3b. These two subcomponents represented a series of secondary reactions occurring at a higher temperature (623 K and above), which is likely triggered by the two-stage degradation of styrene-butadiene rubber (SBR) and butadiene (BR) due to their aromatic structure.25,28 The reaction scheme now becomes the following: Figure 9. Comparison between data from experiments and the Coats-Redfern method prediction (four-component model).

The reaction rates of the individual component and overall decomposition are identical to the three-component model, which is

( )

Ei dRi ) Ai exp (1 - Ri) (5) dt RT dR1 dR2a dR2b dR3a dR3b dRT ) m1 + m2a + m2b + m3a + m3b dt dt dt dt dt dt (6) Figure 10. Comparison between data from experiments and the Runge–Kutta method prediction (four-component model).

where the sum of all mass fractions is 1. Tables 9 and 10 show the kinetic parameters derived from the two methods and the SSEs in comparison with the experimental data. Both the Coats-Redfern and Runge–Kutta models appear capable to fit experimental data with sufficiently low SSEs (SSE: 0.0002–0.0066), but the latter are generally lower (Table 11), suggesting that the pyrolysis is better described by the model obtained by the Runge–Kutta method. Figures 11 and 12 compared the experimental data with predicted values by the Coats-Redfern and Runge–Kutta methods. Similar to the three- and four-component models, there is a lateral shift in the peak temperature to higher temperatures as the heating rate was elevated. It can be explained by the sudden release of volatiles at higher heating rates. Figure 13 demonstrated the decomposition of individual components predicted by Runge–Kutta method. From the peak

fit of the modeling result when the secondary reaction effect is taken into consideration. The activation energies for the pseudocomponent 2a compounds were generally lower than the component 2b processes, showing that the secondary pyrolysis occurred at a relatively lower temperature (below 623 K). With increased heating rates the activation energies of both components decreased which could be explained by the rapid release of lighter hydrocarbons that further converted to noncondensable gaseous products such as CO and CO2. On the basis of the SSE values, one can see that the Runge–Kutta model was able to generate model data that fit better to the experimental data. Figures 9 and 10 show the

Table 9. Pyrolysis Kinetic Parameters Derived from the Five-Component Model by the Coats-Redfern Method pre-exponential factor, A (1/min)


component

component


1

2a

2b

3a

3b

1

2a

2b

3a

3b

SSE

1 5 10 20

4.99 × 105 3.41 × 106 2.91 × 105 1.22 × 105

1.21 × 1014 5.69 × 1015 9.06 × 1013 1.67 × 1015

9.19 × 1011 5.71 × 1012 8.80 × 1012 1.41 × 1010

5.23 × 109 1.21 × 1011 4.79 × 1012 1.05 × 1011

1.20 × 107 6.50 × 109 3.56 × 109 1.80 × 1011

72.0 78.0 65.6 58.9

177.8 196.6 176.3 185.9

152.8 178.2 163.7 136.7

139.0 144.3 180.1 153.8

108.1 140.7 130.0 142.7

0.0003 0.0006 0.0006 0.0047

Table 10. Pyrolysis Kinetic Parameters Derived from the Five-Component Model by the Runge–Kutta Method pre-exponential factor, A (1/min)


component

component


1

2a

2b

3a

3b

1

2a

2b

3a

3b

SSE

1 5 10 20

8.09 × 104 6.22 × 104 4.40 × 104 1.69 × 104

5.65 × 1012 5.49 × 1012 6.14 × 1012 5.26 × 1012

9.31 × 1010 5.12 × 1010 4.80 × 1012 9.08 × 1012

6.27 × 109 1.58 × 1011 1.09 × 1011 1.82 × 107

1.75 × 104 3.40 × 106 7.05 × 107 9.60 × 109

53.9 50.2 48.4 42.7

140.6 140.4 139.2 141.1

131.0 119.1 140.8 139.1

121.8 140.3 139.1 86.1

63.5 81.2 94.7 124.5

0.0003 0.0002 0.0003 0.0044


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Table 11. Summary of SSEs between Experimental Data and Predicted Values by Different Models heating rate (K/min)

three-component Coats-Redfern/Runge–Kutta

four-component Coats-Redfern/Runge–Kutta

five-componen Coats-Redfern/Runge–Kutta

1 5 10 20 total

0.0003/0.0003 0.0008/0.0009 0.0053/0.0051 0.0068/0.0068 0.0132/0.0131

0.0008/0.0004 0.0004/0.0008 0.0050/0.0048 0.0050/0.0035 0.0112/0.0095

0.0003/0.0003 0.0006/0.0002 0.0006/0.0003 0.0047/0.0044 0.0062/0.0052

temperature of individual components, one can assign the component 1 is oil from elastomers or additives at a peak temperature ca. 563 K,18,22 followed by two overlapping decomposition of components 2a and 2b at ca. 643 K, which can be attributed to NR or oil from BR.14,29,36,37 When the temperature was raised to ca. 693 K, component 3b reached its maximum degradation rate that can be assigned to SBR.32,34 At

Figure 11. Comparison between data from experiments and the Coats-Redfern method prediction (five-component model).

Figure 12. Comparison between data from experiments and the Runge–Kutta method prediction (five-component model).

a temperature of ca. 733 K, the major decomposition of component 3a can be attributed to the residual BR. It is also possible that a portion of the BR decomposed originated from the SBR decomposed at lower temperature.25,32,34,36,37 4. Conclusion Table 11 is a summary of SSEs of different models developed by the Coats-Redfern and Runge–Kutta methods. It appears that there is no significant difference in the SSEs between the three- and four-step models regardless of the method adopted, revealing that the reaction of component 2 not in a critical role that determined the decomposition of component 3. Furthermore, increasing the number of steps in the reaction may have the effect of improving the SSEs purely on a statistical basis, namely, that it is adding an additional mathematical variable. However, in the literature it can be seen from the single component studies on NR, BR, and SBR, that SBR and BR are best explained by twostep decomposition and NR by a one-step decomposition. Therefore, the mechanism also supports the SSE results of our overall five-step model. However, in the case of that five-step model, the Runge–Kutta method yielded the lowest SSEs at all heating rates. One possible explanation is that the five-component model placed the key secondary reactions occurring in components 2 and 3 into the calculation, particularly the latter reaction step, since the aromatic structure of component 3 (probably SBR) leads to a two-stage degradation, and the introduction of secondary reactions in this component to the overall model also improved the SSEs significantly. Similar situations can also be found in the five-step model solved by the Coats-Redfern solution method, which suggested that the concept of “five-steps” is reasonable. It is believed that the five-step model solved by the Runge–Kutta method described the tire decomposition process best. In conclusion, it is possible to state that the five-step model solved using the fourth-order Runge–Kutta solution method, developed in the theory section of this paper, gives excellent model predictions over a wide range of heating rates, from 1 to 20 K/min, for the pyrolysis of tire rubber. The present Runge–Kutta model analysis/solution method provides better correlation of experimental tire pyrolysis data than any other literature model. Acknowledgment. The authors are grateful to the Hong Kong Research Grant Council (RGC) and Green Island Cement (GIC)

Figure 13. Decomposition of individual components derived from the Runge–Kutta method (five-component model, heating rate 10 K/min).

(36) Cui, H.; Yang, J.; Liu, Z. Thermochim. Acta 1999, 333, 173–175. (37) Seidelt, S.; Muller-Hagedorn, M.; Bockhorn, H. J. Anal. Appl. Pyrolysis 2006, 75, 11–18. (38) Mark, H. F.; Kroschwitz, J. I. Encyclopedia of polymer science and technology; John Wiley & Sons, Inc.: New York, 1989; Vol. 16, p 842. (39) Hird, A. B.; Griffiths, P. J.; Smith, R. A. Tyre waste and resource management: A mass balance approach; TRL Limited: UK, 2002; p 4. (40) Gonzalez, J. F.; Encinar, J. M.; Canito, J. L.; Rodriguez, J. J. J. Anal. Appl. Pyrolysis 2001, 58–59, 667–683.

Modeling of Waste Tire Carbonization Company Limited for providing the financial support for this research project. Nomenclature

A ) pre-exponential factor (1/min) E ) activation energy (kJ/mol) H ) step-size (min) m ) mass fraction (dimensionless) R ) universal gas constant (8.314 J/mol · K) SSE ) sum-of-squared error ) Σ((dR/dt)exp - (dR/dt)cal)2 T ) temperature (K) t ) time (min)


R ) fraction decomposed (dimensionless) R ) (w0 - w)/(w0 - wf) w )weight (mg) Subscripts 0 ) initial f) final i ) component i a ) subcomponent a b ) subcomponent b T ) total

EF700601G

Kinetic Modeling of Waste Tire Carbonization - Energy & Fuels (ACS

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