Thermogravimetric pyrolysis of waste polyethylene-terephthalate and polystyrene: A critical assessment of kinetics modelling

Resources, Conservation and Recycling 55 (2011) 772–781

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Thermogravimetric pyrolysis of waste polyethylene-terephthalate and polystyrene: A critical assessment of kinetics modelling Anke Brems a,∗ , Jan Baeyens b , Johan Beerlandt a , Raf Dewil a a b

Katholieke Universiteit Leuven, Chemical and Biochemical Process Technology and Control Section, Department of Chemical Engineering, 3001 Heverlee, Belgium University of Warwick, School of Engineering, Coventry CV 4 7 AL, United Kingdom

a r t i c l e

i n f o

Article history: Received 24 January 2011 Received in revised form 9 March 2011 Accepted 11 March 2011 Keywords: Pyrolysis Waste plastics Polyethylene-terephthalate (PET) Polystyrene (PS) Kinetics Modelling

a b s t r a c t Pyrolysis is considered as possible technique to thermally convert waste plastics into chemicals and energy. Literature on experimental findings is extensive, although experiments are mostly performed in a dynamic heating mode, using thermogravimetric analysis (TGA) and at low values of the heating rate (mostly below 30 K/min). The present research differs from literature through the application of far higher heating rates, up to 120 K/min. The use of these dynamic results to define the reaction kinetics necessitates the selection of an appropriate reaction mechanism, and 21 models have been proposed in literature considering the rate limiting step being diffusion, nucleation or the reaction itself. The current research studied the cracking of PET and PS by TGA at different heating rates (temperature ramps). Results were used to check the validity of the proposed mechanisms. Several conclusions are drawn: (i) to obtain fair results, the heating ramp should exceed a minimum value, calculated at 30 K/min for PET and 80 K/min for PS; (ii) application of the majority of the models to experimental findings demonstrated that they do not meet fundamental kinetic considerations and are questionable in their use; and (iii) simple models, with reaction order 1 or 2, provide similar results of the reaction activation energy. A further comparison with literature data for dynamic and isothermal experiments confirms the validity of these selected models. Since TGA results are obtained on a limited amount of sample, with results being a strong function of the applied heating rate, the authors believe that isothermal experiments, preferably on a large scale both towards equipment and/or sample size, are to be preferred. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The total plastic consumption in Western Europe exceeded 52 million tonnes in 2008 (Baeyens et al., 2010). These plastics include mostly polyethylene (PE – 37 wt%), polypropylene (PP – 19 wt%), polyvinyl chloride (PVC – 19 %), polystyrene (PS – 6 %) and polyethylene terephthalate (PET – 6 wt%). Thermoplastics are widely applied in industrial and commercial products, and usually contain stabilisers and additives. Household solid waste (HSW) consists of 7–8 wt%, or up to 20 vol% of the post-consumer plastic solid waste (PSW) (Al-Salem et al., 2010; Baeyens et al., 2010). Treatment and disposal of post-consumer plastics have become an important environmental concern, with recovery and recycling, landfilling and (co-)incineration as most applied methods. Incineration gains interest, due to increasing landfilling constraints and taxes, and due to the difficulties encountered when attempting to

∗ Corresponding author. Tel.: +32 15 31 69 44; fax: +32 15 31 74 53. E-mail addresses: [email protected] (A. Brems), [email protected] (J. Baeyens), [email protected] (R. Dewil). 0921-3449/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.resconrec.2011.03.003

recycle mixed plastic wastes (Al-Salem et al., 2009a,b, 2010). The research focus has recently shifted towards pyrolysis or gasification as thermal treatments. Whereas high temperature gasification targets the production of a syngas, to be further upgraded to fuelgrade organics or directly used in electricity generation, pyrolysis takes place in the absence of oxygen at moderate temperatures and recycles plastic solid waste (PSW) into chemicals and/or fuel: the polymer structure is decomposed into smaller intermediate products, usable as fuel or as raw materials for the petrochemical industry. By producing value-added products (such as liquid and gaseous fuel, polymer monomers and/or a carbonaceous residue as a candidate for possible upgrading to activated carbon or carbon black), pyrolysis can overcome certain disadvantages of incineration and recycling (Brems et al., 2011). The low temperature of the process and the absence of oxygen, moreover, reduce emission problems as encountered during incineration, where large volumes of combustion gas and toxic pollutants are produced (Everaert and Baeyens, 2002; Bhandare et al., 1997). Co-incineration is moreover controlled by stringent emission standards as e.g. set by the EU Hazardous Waste Incineration Directive (EU, 2000). It is difficult to treat or recycle mixed PSW, due to its complex nature and composition,

A. Brems et al. / Resources, Conservation and Recycling 55 (2011) 772–781

2. Materials and methods As stated before, the thermal behaviour of polymers is usually investigated by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). These methods provide useful information on the thermal characteristics of materials, e.g. melting point, weight loss during thermal degradation, glass transition temperature, heat of crystallisation, etc. Based on these parameters, a kinetic model can be established to predict the reactor behaviour and a product distribution can be determined when TGA and MS are coupled. In literature, very different experimental TGA-conditions have been used with broad ranges of sample amount, heating rates, temperatures and reaction atmospheres. Most experiments are performed in a dynamic mode, i.e. at a fixed heating rate or temperature ramp ˇ, and the thermal decomposition is often described by a power law equation, although the reaction order is commonly assumed close to 1. For the thermogravimetric analysis, a Hi-res TGA 2950 Thermogravimetric Analyser was used at atmospheric pressure with a nitrogen flow of 50 ml/min. The TGA scale was made of platinum and the weight was registered every 0.5 s. The different heating rates ˇ = T/t enable the determination of the weight loss as a function of the temperature, shown by the TGA-profiles. Transformation to results of conversion with time is straightforward, due to the known value of ˇ, relating time and temperature. The dynamic thermogravimetry was conducted on the polymer samples using 4 constant heating rates, i.e. ˇ = 15, 50, 100 and 120 K/min. Literature reports are mostly conducted at a low value of ˇ (below 30 K/min)· The runs were conducted in triplicate and average results are reported hereafter.

100

A

Weight (%)

80 60 40 20 0 300

350

400

450

500

550

600

650

700

750

Temperature (°C) β = 15 °C/min

β = 50°C/min

β = 100°C/min

β = 120°C/min

100

B

80 Weight (%)

the contamination with various residues (organic, inorganic or biological), and the possible structural deterioration of the polymeric compounds. When pyrolysing PSW, only 5% of the energy content is used in the endothermic cracking process (Brems et al., 2011). Pyrolysis is therefore considered as one of the most promising methods to recover material and energy from PSW. Furthermore, almost all types of plastics (commingled or mixed with other materials such as wood, paper, ink, paint) can be treated. Pigments, inorganic fillers, supports and other additives, possibly present in minor concentrations in the polymers, are mostly retained in the solid residue. Due to possible interactions during decomposition and interactions between the components of the mixture and the low molecular weight products and free radicals formed by the scission of the polymeric chains, thermal degradation of polymer mixtures gets more complex than degradation of single polymers (Williams and Williams, 1999). These interactions can affect the quality of the products formed and are hence important when high quality standards have to be met for use as feedstock or fuel (Al-Salem et al., 2009b, 2010). The objectives of the present research were twofold, i.e. (i) to study the experimental pyrolytic degradation of 2 important thermoplastics, PET and PS; and (ii) to critically assess the multiple model treatment methods proposed in literature to determine the Arrhenius-based kinetic parameters of the pyrolysis reaction as often experimentally determined by TGA. There is indeed some literature controversy concerning the applicability of simple TGA experiments to define the pyrolysis kinetics, with results widely different according to the conversion model applied. TGA experiments are, however, easy and fast and can provide correct kinetic values, comparable with isothermal results, if the correct data treatment is applied (Brems et al., 2011; Al-Salem et al., 2010). A study of isothermal pyrolysis of polyethylene is e.g. recently proposed by Al-Salem and Lettieri (2010).

773

60 40 20 0 0

100

200

300

400

500

600

700

Temperature (°C) β = 15 °C/min

β = 50 °C/min

β = 100 °C/min

β = 120 °C/min

Fig. 1. (A) TGA curves of PET at different heating rates, ˇ. (B) TGA curves of PS at different heating rates, ˇ.

From the dynamic TGA experiments, the reaction rate constant k can be determined by using the reaction rate equations as developed in Section 3.2, with the conversion, ˛, defined as: ˛=

M0 − Mt M0 − M∞

(1)

with M0 , Mt and M∞ being respectively the weight of the plastic sample prior to pyrolysis, at time t during pyrolysis and at the end of the reaction. The relative amount of feedstock remaining at any time is hence (1 − ˛). The reaction rate constant is defined by the Arrhenius equation: k = Ae−Ea /RT

(2)

with k the reaction rate constant (in s−1 ) for a first order reaction, or in appropriate units in function of the conversion model used), Ea the activation energy (J/mol) and A the pre-exponential factor (in the units of k). As the weight of the sample is continuously registered, M0 , Mt and M∞ are defined and the reaction rate constant can be derived at every moment, since the known heating rate of the TGA relates the temperature ramp to the time scale. The Arrhenius equation can be applied after data transformation and plotting of the results in function of the reaction mechanism, as discussed in Section 3.2. As far as the possible chemical reactions are concerned, the pyrolysis of PET is described in detail in Brems et al. (2011). The pyrolysis reaction scheme of PS is more complex, and given in detail in Faravelli et al. (2001), Kruse et al. (2001) and Hu and Li (2007). 3. Results and discussion 3.1. Thermogravimetric degradation results of PET and PS Figs. 1 and 2 show the TGA and DTG curves of PET and PS, DTG being determined from the TGA as Mt /t versus T. The curves were obtained during the pyrolysis process under inert N2 atmosphere at different heating rates, ˇ. The data obtained for

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Rate of weight loss (%/°C)

0

-0.5

-1

-1.5

A -2 300

350

400

450

500

550

600

650

700

750

Temperature (°C) β = 15 °C/min

β = 50 °C/min

β = 100 °C/min

β = 120 °C/min

Rate of weight loss (%/min)

0.0

-0.5

-1.0

-1.5

B

-2.0 300

350

400

450

500

550

600

Temperature (°C) β = 15 °C/min

β = 50 °C/min

β = 100 °C/min

β = 120 °C/min

Fig. 2. (A) DTG curves of PET at different heating rates, ˇ. (B) DTG curves of PS at different heating rates, ˇ.

temperatures below 350 and 300 ◦ C are omitted in the figures, since the loss of weight recorded is minimum. As seen from the figures, the pyrolysis stage is clearly defined between 380 and 470 ◦ C for PET and 395–450 ◦ C for PS respectively, and virtually independent of the ˇ value applied when fast heating rates are used (ˇ ≥ 50 K/min). For PET, irrespective of ˇ, a carbonaceous residue of about 10 wt% remains at the end of the main pyrolysis stage, and this residue is slowly decomposed at higher temperatures, as shown by the slightly continued loss of weight above 475 ◦ C with a second small DTG-valley around 650 ◦ C. For PS, and provided a fairly fast heating rate is applied, the amount of residual carbonaceous residue (char) is very limited and between 0 and 2 wt% at 465 ◦ C, function of ˇ. This confirms previous investigations where the amount of char in PET pyrolysis in isothermal fluidized bed pyrolysis is indicated between 5 and 25 wt% (Brems et al., 2011), whereas a maximum char content in the case of PS is 1 wt% (Smolders and Baeyens, 2004; Onwudili et al., 2009).

f(˛). The resulting equation is: d˛ = k · f (˛) dt

(3)

The rate constant, k, can be described by the Arrhenius expression of Eq. (2). The overall expression of the reaction rate takes the form of: d˛ = k · f (˛) = Ae−Ea /RT f (˛) dt

(4)

During the experiments, 4 specific heating rates, ˇ = dT/dt, were used. The conversion, ˛, can thus be written as a function of the temperature, T: d˛ dT d˛ d˛ = =ˇ dt dT dt dT

(5)

Combination of Eqs. (4) and (5) results in the following expression:

3.2. Kinetic analysis of dynamic TGA experiments

A d˛ = e−Ea /RT f (˛) dt ˇ

3.2.1. The conversion function In the non-isothermal TGA experiments, the weight of the sample is measured as a function of temperature, while the reaction proceeds for a fixed regime of temperature ramps, ˇ (K/min). The degradation can thus also be expressed as function of time, t, since T and t are linked in the experiments. The rate of degradation or conversion, d˛/dt, is a function of the temperature-dependent rate constant, k, and a temperature-independent function of conversion,

Integration and recombination of Eq. (6) gives (EbrahimiKahrizsangi and Abbasi, 2008):

 g(˛) = 0

˛

d˛ f (˛)



(6)

T

e−Ea /RT dT

(7)

0

where g(˛) represents the integrated form of the conversion dependence, however without specific analytical solution. Several

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775

Table 1 Kinetic integration functions g(˛) for different reaction mechanisms (Ebrahimi-Kahrizsangi and Abbasi, 2008; Chen and Wang, 2007). n◦

Function Diffusion models Parabolic law Valensi (Barrer)

1 2

Mechanism

g(˛)

Diffusion, 1D Diffusion, 2D

˛2 ˛  + (1 − ˛)ln(1  − ˛)

3

Ginstling-Broushtein

Diffusion, 3D (column symmetry)

4 5

Jander Anti-Jander

Diffusion, 3D (spherical symmetry) Diffusion, 3D

6

Zhrualev, Lesokin and Tempelmen

Diffusion, 3D

15 16

Nucleation models Avrami-Erofeev Power law Power law Power law Reaction order and geometric contraction models Shrinkage geometry Shrinkage geometry

17-20 21

Reaction order Mampel

7–11 12 13 14

expressions for g(˛) have been proposed in the literature as a function of different reaction mechanisms, all of which are based on three concepts: diffusion, nucleation and the order of the reaction. Expressions of g(˛) were summarized from previous literature and are given in Table 1, showing the 21 models available. These models differ only by considering the rate limiting step to be diffusion, nucleation or the reaction itself. Using x as Ea /RT, Eq. (7) can be rewritten in a more useable form:



∞

p(x) = x

e−x dx x2

(8)

g(˛) can then be solved as (Chen and Wang, 2007): g(˛) =

AEa ˇR

 x

∞

e−x AEa p(x) dx = ˇR x2

(9)

A solution for the function p(x) can be found by solving the integral and using a Taylor approximation. 3.2.2. Solutions of the kinetic expressions 3.2.2.1. Flynn–Wall–Ozawa (FWO) method. Using the approximation of Doyle (1965) with ln(p(x)) = −2.315 − 0.4567x, the following

1−

2˛ 3

2/3

− (1 − ˛)

(1 − (1 − ˛)1/3 )2 [(1 + ˛)1/3 − 1]2



1 1−˛

1/3

2

−1

n = 1; 1.5; 2; 3; 4

[−ln(1 − ˛)]1/n ˛ ˛1/2 ˛1/3

Column symmetry Spherical symmetry

1 − (1 − ˛)1/2 1 − (1 − ˛)1/3

n = 0.25; 1.5; 2; 3 n=1

−ln(1 − ˛)

(1−˛)1−n −1 n−1

expression can be found: ln(ˇ) = ln

 AE  a Rg(˛)

− 2.135 − 0.4567

Ea RT

(10)

The activation energy, Ea , can be found by plotting ln(ˇ) versus 1/T, which results in a straight line, with Ea defined from the slope of this line multiplied by R/0.4567 (Akiyama et al., 1998; Bianchi et al., 2008). The shortcoming of the FWO approach is that the values of Ea are a function of ˇ only. As shown in the discussions below, this is only the case for low values of ˇ, whereas Ea assumes nearly constant values at higher heating rates. Applying the FWO approach for the PET TGA experiments results in values of Ea between 229 and 245 kJ/mol for ˇ = 100–120 K/min, as further discussed in Section 4. The ˇ dependence of the activation energy was previously discussed by Van de Velden et al. (2010) and Brems et al. (2011) through considerations of heating rate and reaction progress, concluding that relevant values for Ea can only be obtained for ˇ > 30 K/min (PET). When applying appropriate data for PS (Brems et al., 2011), the minimum value for ˇ should exceed 80 K/min. In bubbling or circulating fluidised beds, the heat transfer coefficient to the particles, h, ranges from 100 to 500 W/m2 K (Baeyens and Geldart, 1980). Since particles used in pyrolysis are of small size,

Fig. 3. Diffusion models of PET with heating rates of 15 and 120 ◦ C/min.

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Fig. 4. Nucleation models of PET with heating rates of 15 and 120 ◦ C/min. Table 2 Activation energies and deviations for the diffusion models of PET. Model

Ea (J/mol) ˇ = 15

1 2 3 4 5 6

351,782 331,587 352,896 398,260 291,827 559,185

ˇ = 50 428,233 381,265 390,918 410,307 325,600 472,133

ˇ = 100 416,393 441,569 446,824 457,334 403,814 489,668

the heat transfer resistance by internal conduction can be omitted (Van de Velden et al., 2008). Since the rate of particle heating is proportional with the heat transfer coefficient and the driving temperature difference, and inversely proportional with the particle size, the ˇ values obtained in fluidised beds are of the order

ˇ = 120 355,507 447,489 459,254 482,917 381,240 558,786

Average Ea



(J/mol)

(J/mol)

387,979 400,478 412,473 437,204 350,620 519,943

34,614 47,470 42,961 34,406 44,299 39,532

%

8.9 11.9 10.4 7.9 12.6 7.6

of tens of K/s, hence certainly exceeding the TGA limit value.

3.2.2.2. Coats–Redfern method. The method of Coats and Redfern (1964) solves Eq. (9) by limiting the number of terms in the Taylor

Table 3 Activation energies and deviations for the nucleation models of PET. Model

7 8 9 10 11 12 13 14

Average Ea



ˇ = 15

Ea (J/mol) ˇ = 50

ˇ = 100

ˇ = 120

(J/mol)

(J/mol)

230,542 149,742 109,343 68,943 48,739 170,021 79,136 48,839

230,799 149,959 109,542 69,118 48,914 207,403 97,860 61,335

253,930 165,348 121,058 76,759 54,617 202,289 103,955 65,384

214,403 138,867 101,186 63,497 44,657 171,825 84,167 52,181

232,419 150,979 110,282 69,579 49,232 187,885 91,280 56,935

14,084 9431 7076 4721 3545 17,069 10,025 6688

%

6.1 6.2 6.4 6.8 7.2 9.1 11.0 11.7

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Table 4 Activation energies and deviations for the models of reaction order and geometric contraction of PET. Model

Ea (J/mol)

15 16 17 18 19 20 21

196,428 193,202 154,398 297,381 376,368 562,344 335,253

ˇ = 15

series expansion: AEa g(˛) ∼ = ˇR =



e−x



x2

ART 2 ˇEa



1−

1−

ˇ = 50



2

=

x

2RT Ea



 g(˛)  T2

= ln

 AR  ˇEa

1−

AEa ˇR



(Ea /RT )

2RT Ea



−

ˇ = 120

226,800 242,473 214,221 283,704 316,089 388,258 316,089



e−Ea /RT

e−Ea /RT

Eq. (11) can be rewritten:

ln

ˇ = 100

218,893 222,809 213,106 243,138 255,926 282,798 255,926

2

1−

2 Ea /RT



(11)

Ea RT

(12)

By plotting the left hand side of the equation versus 1/T, the activation energy, Ea , can be determined from the slope of the linear expression. Introduction of the experimental data into the different equations, together with a statistical analysis of the data-fitting, will define both the equation-specific val-

192,046 201,508 181,695 238,415 264,556 322,474 264,556

Average Ea



(J/mol)

(J/mol)

208,542 214,998 190,855 265,660 303,234 388,968 232,377

14,658 19,189 24,769 25,403 48,083 106,950 14,137

%

7.0 8.9 13.0 9.6 15.9 27.5 6.1

ues of Ea , and the validity of the different g(˛) model approaches. This will be assessed and discussed in Section 3.3 below. 3.3. Assessment and discussion of the experimental results 3.3.1. Preliminary remarks The complete graphical presentation of the transformed results, for 4 ˇ-values, 21 possible model approaches and 2 plastics (i.e. PET and PS) would lead to a vast amount of figures. We therefore prefer to limit the number of illustrations to what is strictly necessary to support the observations and discussions. According to the treatment of Section 3.2, first pre-requisites in the assessment stems from the fact that linear relationships should be obtained, and that the linear representations of ln(g(˛)/T2 ) versus 1/T should be parallel, irrespective of ˇ, since the activation energy is supposed to a con-

Fig. 5. Reaction order and geometric contraction models of PET with heating rates of 15 and 120 ◦ C/min.

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Fig. 6. Diffusion models of PS with heating rates of 15 and 120 ◦ C/min.

stant for the given plastic. The pre-exponential factor of the Arrhenius equation will however be different since expected to be a function of the heat transfer rate to the particles, and hence higher at faster rates, i.e. increasing ˇvalues.

3.3.2. Kinetic parameters for PET pyrolysis The transformation of the experimental results using the model equations of g(˛) is hereafter represented at ˇ = 15 and 120 K/min per mechanism investigated, i.e. diffusion (Fig. 3), nucleation (Fig. 4) and reaction order and shrinkage (Fig. 5). Mechanism-applications

Fig. 7. Nucleation models of PS with heating rates of 15 and 120 ◦ C/min.

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779

Fig. 8. Reaction order and geometric contraction models of PS with heating rates of 15 and 120 ◦ C/min.

are numbered according to the reference of Table 1. The defined values of Ea for all ˇ-values is added in the corresponding Table 2 (diffusion), Table 3 (nucleation) and Table 4 (reaction order). The illustrations in Fig. 3 relate to the diffusion approaches. Except for mechanism 6, a linear fit is not obtained for values of ˇ = 15 K/min (and 50 K/min, not shown in the figure). At ˇ = 120 K/min (and 100 K/min, although not shown), only models 4 and 6 show a linearity. From considerations of heating rate and reaction progress, it was already pointed out by Van de Velden et al. (2010) and by Brems et al. (2011), that relevant values for Ea can only be obtained for higher values of ˇ. This is confirmed by the present extensive results and also shown in the statistical evaluation of Ea -values and their respective standard deviation, , as presented in Table 2. Even for the clearly non-linear plots at low ˇ, an Ea value was tentatively determined. A standard deviation in excess of 5% should certainly not be taken into consideration, leading to the conclusion that none of the diffusion-approaches can be judged appropriate. A similar assessment can be made for the nucleation models, as represented in Fig. 4 and Table 3, although the required linearity and parallelism of the fitting is reasonable for models 7, 8 and 10. Other models do certainly not meet these requirements. Although standard deviations are a lot lower for the selected models, it is very distressing that calculated Ea -values vary from ∼78 kJ/mol (model 10) to 232 kJ/mol (model 7). This discrepancy will be further examined in Section 4, when a comparison will be made of the present TGA-experiments and isothermal experiments in a fluidized bed at constant temperature.

The illustrations of Fig. 5 relate to the reaction models. Most often, a linear fit is not obtained for values of ˇ = 15 K/min and 50 K/min, except for reaction orders of 1 (model 21) and 1.5 (model 18). Only these 2 models maintain the required linearity at higher ˇ-values, all other models showing a non-linear plot. Models 16, 17, 19 and 20 should moreover be discarded on the basis of the high value of the standard deviation. It is also noteworthy that the activation energies determined by application of model-approaches 15, 18 and 21 are very similar, and of the order of 230 kJ/mol, on average. Evidently, the kinetic simulation using reaction order models seems more appropriate than when using diffusion or nucleation approaches. 3.4. Kinetic parameters for PS pyrolysis The data treatment is even more distressing when models are used in the fitting of PS conversions, as shown in Figs. 6–8, with corresponding Tables 5–7. Linearity is completely absent at low ˇvalues, and even doubtful at 120 ◦ C/min, except in a narrow range of 1/T. The tentatively calculated values of Ea and their corresponding standard deviations vary within a wide range. If a selection had to be made, certainly models 18 and 21 appear to present some degree of accuracy, with activation energy values within a fair range of 249–300 kJ/mol. 4. Comparison with literature data and data obtained in isothermal pyrolysis results The present results for PET can be compared with both a previous literature survey, and dynamic or isothermal (flu-

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Table 5 Activation energies and deviations for the diffusion models of PS. Model

Ea (J/mol) ˇ = 15

1 2 3 4 5 6

335,203 377,432 423,053 480,182 292,692 685,797

ˇ = 50 398,052 447,689 470,213 517,172 358,983 687,784

ˇ = 100 336,209 367,613 381,515 410,457 308,789 514,728

ˇ = 120 328,701 351,167 360,196 378,530 305,696 439,690

Average Ea



(J/mol)

(J/mol)

349,542 385,975 408,744 446,585 316,540 582,000

%

28,155 36,845 42,076 54,882 252,38 108,099

8.1 9.5 10.3 12.3 8.0 18.6

Average Ea



%

Table 6 Activation energies and deviations for the nucleation models of PS. Model

Ea (J/mol) ˇ = 15

ˇ = 50

ˇ = 100

ˇ = 120

(J/mol)

(J/mol)

7 8 9 10 11 12 13 14

281,609 183,798 134,901 85,996 61,543 188,645 104,429 65,708

291,927 190,707 140,089 89,480 64,171 193,152 90,702 63,514

223,516 145,169 105,992 66,815 47,226 162,339 75,401 46,419

198,074 128,216 93,288 58,355 40,890 158,597 73,548 45,196

248,781 161,973 118,568 75,161 53,457 175,683 86,020 55,209

39,207 26,095 19,540 12,986 9707 15,356 12,541 9443

15.8 16.1 16.5 17.3 18.2 8.7 14.6 17.1

Average Ea



%

(J/mol)

(J/mol)

Table 7 Activation energies and deviations for the models of reaction order and geometric contraction of PS. Model

Ea (J/mol) ˇ = 15

15 16 17 18 19 20 21

213,389 234,183 126,944 315,731 428,092 694,976 281,609

ˇ = 50 235,605 252,716 170,728 355,457 467,752 730,437 291,927

ˇ = 100 188,895 199,462 170,761 296,982 372,527 547,985 223,516

idized bed) experiments as published by Brems et al. (2011): the isothermal activation energy was determined as 237 kJ/mol, whereas TGA experiments were modelled using the FWOmethod to determine Ea for ˇ = 100–120 K/min between 229 and 245 kJ/mol. These values in excess of 200 kJ/mol were also confirmed by Buyck (2007) and by Girija et al. (2005). Encinar and González (2008) observed values of 117–255 kJ/mol, obtained at low values of ˇ (5–20 K/min), and hence questionable. Clearly the values obtained in the present paper by applying models 15, 18 and 21, with an average of 230 kJ/mol are in fair agreement with the literature findings. For PS, literature data vary widely, and this is ascribed to the complex cracking mechanisms that are strongly affected by the operating temperature (Ahmed and Gupta, 2010; Poutsma, 2009; Hu and Li, 2007). For TGA experiments at increasing, albeit low ˇ of 5–20 K/min, Encinar and González (2008) determined Ea at 236–286 kJ/mol, whereas Buyck (2007) measured 213 kJ/mol at ˇ = 100 K/min. Isothermal experiments in a fluidized bed of 450 ◦ C (Suk et al., 2006), determined very low Ea values between ∼50 and 72 kJ/mol only. Recent experiments (Brown et al., 2011) treating a continuous feed of 10 kg/h of PS in an isothermal fluidized bed at ∼450 ◦ C, confirm the higher range of Ea -values, in the order of 250 kJ/mol. The findings of these continuous fluidized bed experiments will be published in a follow-up paper. The data for PS obtained by the present selected models 18 and 21 have an average Ea of 275 kJ/mol, and are in-line with most of the literature-cited values.

ˇ = 120 176,772 183,507 160,277 230,858 268,131 354,343 198,074

203,665 217,467 157,177 299,757 384,125 581,935 248,781

22,672 27,383 17,971 45,035 75,026 148,140 39,207

11.1 12.6 11.4 15.0 19.5 25.5 15.8

From the above analysis, the use of models 18 and 21 therefore appears to provide a fair value of Ea , in a fair agreement with both dynamic (TGA) and isothermal experimental results and literature data. Since TGA results are obtained on a limited amount of sample, with results being a strong function of the applied heating rate, the authors believe that isothermal experiments, preferably on a large scale both towards equipment and/or sample size, are to be preferred. 5. General conclusions According to the model assessment, the concepts of a first or second order kinetics provide the most suitable design approach. A first order kinetics is commonly proposed in literature for a variety of plastics (Al-Salem et al., 2009a,b; Al-Salem and Lettieri, 2010; Brems et al., 2011). For both concepts, the activation energy is identical, since a function only of the plastic under scrutiny. The pre-exponential factor of the Arrhenius equation will however differ both in value and dimensions, being respectively s−1 for a first order, and m3 /mol s for a second order approach. The paper used dynamic TGA-results to define the reaction kinetics of PET and PS pyrolysis, comparing activation energies as obtained by the application of 21 models proposed in the literature. Results were used to check the applicability of the proposed mechanisms. Results obtained at low values of the heating ramp mostly overestimate the activation energy. Application of the majority of the models to experimental findings demonstrated that they do not meet fundamental kinetic considerations of required linearity of ln(g(˛)/T2 ) versus 1/T and are

A. Brems et al. / Resources, Conservation and Recycling 55 (2011) 772–781

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