Pyrolysis kinetic modelling of abundant plastic waste (PET) and in-situ emission monitoring

Recycling the ever-increasing plastic waste has become an urgent global concern. One of the most convenient methods for plastic recycling is pyrolysis, owing to its environmentally friendly nature and its intrinsic properties. Understanding the pyrolysis process and the degradation mechanism is crucial for scale-up and reactor design. Therefore, we studied kinetic modelling of the pyrolysis process for one of the most common plastics, polyethylene terephthalate (PET). The focus was to better understand and predict PET pyrolysis when transitioning to a low carbon economy and adhering to environmental and governmental legislation. This work aims at presenting for the first time, the kinetic triplet (activation energy, pre-exponential constant, and reaction rate) for PET pyrolysis using the differential iso-conversional method. This is coupled with the in-situ online tracking of the gaseous emissions using mass spectrometry. The differential iso-conversional method showed activation energy (Ea) values of 165–195 kJ mol−1, R2 = 0.99659. While the ASTM-E698 method showed 165.6 kJ mol−1 and integral methods such as Flynn-–Wall and Ozawa (FWO) (166–180 kJ mol−1). The in-situ Mass Spectrometry results showed the gaseous pyrolysis emissions, which are C1 hydrocarbons and H–O-C=O along with C2 hydrocarbons, C5–C6 hydrocarbons, acetaldehyde, the fragment of O–CH=CH2, hydrogen, and water. From the obtained results herein, thermal predictions (isothermal, non-isothermal and step-based heating) were determined based on the kinetic parameters. They can be used at numerous scale with a high level of accuracy compared with the literature.


Background
Over 9 billion tonnes of plastic have been produced globally since the 1940s, with an annual growth rate of 8.7% [1]. Plastic materials are subdivided into seven different types and fulfil different purposes in our daily life such as in electronics, construction materials, agriculture, household items and packaging films. The widespread use is due to their intrinsic properties, i.e., chemical inertness, mechanical, pressure resistance, durability, versatility, flexibility, and cheap production cost, along with the thermal stability from the additives and stabilisers used in the production phase [2]. Over the last 60 years, consumer plastic use has increased by approximately 20 times, where the annual production had dramatically increased from 15 million tonnes (Mt) in 1964, to 335 Mt in 2016, and is expected to reach 1124 Mt by the year 2050 [3,4]. The annual consumption of water bottles alone has reached 500 billion units globally [5]. However, the disposal rate of these plastic debris has risen, making a substantial negative impact on the environment as well as public human health. The plastic waste generated in 2015 was 6300 Mt, where only 9% has been recycled, 12% incinerated, and the rest have been sent to landfills (79%) [6]. In the next 5 years, the plastic waste production rate will reach 220 Mt per annum, with its end-of-life destination deemed to be mainly in the sediment, biota, and aquatic ecosystem such as oceans and rivers [micro-plastic (< 5 mm) and nanoplastic (< 1.2 μm)], [7]. Where the complete degradation of its polymers could take centuries. Furthermore, direct burning of those plastic wastes generates hazardous emissions along with chemicals such as phosgene, dioxins, and carbon monoxide that are linked to human cancers and endocrine disruption [8,9]. However, it is possible to add additional value to this waste through processes such as pyrolysis, solvent dissolution, gasification, and other valorisation approaches while promoting the circular economy [10,11]. This approach of using a waste stream will complete the full cycle of plastic and, thus, directly support and facilitate the concept of the circular economy.
There are mainly four different technologies in dealing with plastic waste management which are: re-extrusion that requires semi-clean plastic scrap, along with mechanical (physical), chemical (solvolysis and pyrolysis), and energy recovery (incineration) [2,12,13]. Lopez et al. found out that the variability and inconsistency of the feed composition was the major challenge along with catalyst deactivation [14][15][16].
The most common polymers studied are polyethylene terephthalate (PET), high-density polyethylene (HDPE), polypropylene (PP), and polystyrene (PS), where the pyrolysis and reforming conditions were around 500 and 700 °C, respectively. Nearly half of the total plastic market globally comes from PE (polyethylene) and PET with a contribution of 40% [17] in various sectors such as agriculture, drinking water bottles, food packaging, and construction materials. Thermoplastics account for 80% of the total plastic consumption [2]. PET (C 10 H 8 O 4 ) n ) is the most abundant thermoplastic due to its characteristics of existing in different forms such as a one-dimensional fibre, 2D films, and 3D bottles and containers [18,19]. It is the thirdmost consumed polymer in Europe after PP and LDPE, and the most widely used plastic in the packaging industry [20][21][22]. The global consumption and demand for PET reached 60 Mt by 2011 and is increasing by 4.5% each year [23]. It has been reported in the literature that PET plastic material has a similar energy content than that of soft coal, with a higher heating value of 46.2 MJ kg −1 and ultimate elemental analysis of > 45 wt.% carbon, 36 wt.% hydrogen, and 18 wt.% oxygen [20,24,25]. Most of those PET and plastic waste materials, in general, are non-biodegradable and their end-of-life destination is landfill or incineration. There is also another challenge that faces the recycling of these problematic materials, which is the difficulty of the selective and effective separation of the plastic mixture. For instance, a standard PET bottle contains about 10-15 wt.% PE in the form of printed labels and cups, where their separation is usually difficult [17].
One of the most convenient methods for plastic recycling is pyrolysis owing to its environmentally friendly nature. Furthermore, unlike other recycling processes such as mechanical and chemicals methods, pyrolysis is a flexible process where plastic waste could be treated alongside municipal solid waste such as e-waste, biomass, and others [26]. Interestingly, only 5% of the calorific value of the plastic waste is being used in the endothermic cracking process, which in the case of PET is 214 kJ kg −1 [27]. The pyrolytic products of plastic are oil (22-49 wt.%), gases (18-30 wt.%), and solid char (30-50 wt.%); where different operating parameters could affect the process and product composition (plastic type, residence time, pyrolytic temperature, ramping rate, and reactor type) [27]. As the operating parameters can shift the product composition and alter the reaction pathway, it is important to use kinetic modelling to help describe the reaction mechanism during the thermal cracking of plastic polymers. Ganeshan et al. [28], in their attempt to understand the PET pyrolysis process via kinetic modelling, used Coats-Redfern method that assumes the reaction is first order. They reported activation energies (E a ) value in the range of 133-251 kJ mol −1 ; however, the value of R 2 was low (< 0.8). Thus, they concluded that the Coats-Redfern method is not always suitable for calculating the kinetic parameters. Mishra et al. [29] studied kinetic modelling approaches (Coats-Redfern method, Kissinger-Akahira-Sunose, Flynn-Wall and Ozawa method, Friedman method, and Starink) for the copyrolysis of PET with biomass seeds. The KAS method of PET pyrolysis showed variation in the E a value from 210 to 241 kJ mol −1 within reaction progress α = 0.1-0.8, where the average E a -was 230.7 kJ mol −1 . Under the same conditions, the FWO and Starink methods showed similar variation in the E a value from 211-241 kJ mol −1 and 211-242 kJ mol −1 , respectively, with an E a average of 230.5 and 231.0 kJ mol −1 . The Friedman method showed a slightly lower difference in values under the same conditions with 208.6-236.0 kJ mol −1 and an average E a -of 225.6 kJ mol −1 . They performed the kinetic modelling based on three heating rates of 10, 30, and 50 °C min −1 , while for reliable evaluation of the kinetic parameters, it should be at low heating rates of less than 8 °C min −1 (with a ratio between the lowest and the highest heating rate of > 10) with four or five heating rates [30]. Das and Tiwari [18] measured the kinetic parameters for PET pyrolysis at high heating rates of 5, 10, 20, 40, and 50 °C min −1 using the iso-conversional method. They reported E a values in the range of 196-217 kJ mol −1 . Al-asadi and Miskolczi measured the emissions related to the uncatalysed along with Ni/zeolite catalytic pyrolysis of PET but only at a high-temperature range of 600-900 °C [17]. To the best of the authors' knowledge, this is the first detailed study in measuring and evaluating the kinetic triplet (activation energy, pre-exponential constant, and reaction rate) of PET plastic pyrolysis with the use of Advanced Kinetics and Technology Solutions (AKTS) software. This work aims at presenting for the first time, the kinetic triplet (activation energy, pre-exponential constant, and the rate of reaction) for PET pyrolysis using the differential iso-conversional method. This is coupled with the in-situ online tracking of the gaseous emissions using mass spectrometry, as there are a few and limited studies on oxygenated macromolecules such as PET in the literature [20,22]. The kinetic triplet can benefit in process modelling systems to help better understand the process at scale, as these values are not influenced based on scale. This ultimately aids in reactor optimization and design at scale as it gives a better insight into the reaction mechanism. This can be used by plastic recyclers worldwide and the predictions made here can be used to determine how the rate of reaction changes based on temperature and heating rate beyond experimental results using isothermal, non-isothermal and stepwise heating regimes.

Sample preparation and in-situ gaseous emission detection using mass spectrometry
The PET sample was collected from used water bottles, then washed with deionized water, dried, and finally crushed down into a form of small particles and sieved in the range of less than 100 µm to avoid the mass and heat transfer limitations during the kinetic modelling and pyrolysis tests, as shown in Additional file 1: Figure S1. The PET pyrolysis was performed in a fixed bed reactor, where the output of the reactor is coupled and attached to a mass spectrometer (MS) through a heated quartz capillary tube. To prevent any condensation, dissolution, or adsorption on the tube wall, all the lines were heated to 150 °C, where the evolved gas mixtures were then directly fed to the mass spectrometer. The MS (Hiden Analytical instrument) was performed under vacuum and the rapid in-situ detection of the characteristic fragment ion intensity of the associated gaseous emissions such as hydrocarbons and other related emissions including characteristic ion species according to its mass-tocharge ratio (m/z) such as m/z = 15 (

Kinetic modelling of PET waste via AKTS
The evaluation of the kinetic parameters of PET pyrolysis was determined using the TGA data (at different heating rates of 0.5, 1, 2, 4, and 8 °C min −1 ) under N 2 atmosphere with a ratio of 16 between the lowest and the highest heating rate. The heating rate of 4 °C min −1 was repeated for the reproducibility and accuracy of results. The TGA experiments were conducted in a simultaneous thermal analysis Mettler Toledo (TGA/DSC) Thermogravimetric analyser Pyris TGA/DSC1, and changes in the mass of the sample were recorded during the ramping operation.
The TGA instrument was also calibrated for buoyancy effects to allow quantitative estimation of weight changes. Experiments were performed twice to ensure reproducibility and the standard error was found to be ± 1 °C. The ICTAC Kinetics Committee published the problems and reported the essential principals that should be followed to obtain thermal analysis data that are adequate to the kinetic computations [31]. To determine the kinetic parameters more accurately and to better understand the PET pyrolysis, Advanced Kinetics and Technology Solutions (AKTS) software was utilized. AKTS software correlated and validated the practical experiments with theoretical calculations for the kinetic modelling of the pyrolysis process of the PET plastic waste along with calculating the activation energy (E a ) and the preexponential factor. Different kinetic modelling methods were employed such as ASTM-E698, Flynn-Wall and Ozawa (FWO), and differential iso-conversional (modelfree) method such as the Friedman method. The latter method measures E a and pre-exponential constant at different extents of reaction progress α without requiring prior knowledge of the reaction mechanism [32]. Consequently, the iso-conversional (differential) method was used herein to measure the kinetic parameters using heating rates ranging from 0.5 to 8 °C min −1 as a function of reaction progress (α). Where the rate of the thermal decomposition of the waste PET plastic can be expressed according to the iso-conversional method as a function of reaction temperature and α, where the latter is calculated from the initial, actual, and final masses of PET waste. The Arrhenius equation defined the temperaturedependent function of the kinetic parameters as shown in Eq. 1: The non-isothermal iso-conversional method usually utilizes different heating rates, β = dT dt −1 , and thus, the PET plastic pyrolysis can be expressed as shown in Eq. 2: One of the examples of iso-conversional methods (the non-isothermal) such as ASTM-E698 is shown in Eq. 3: whereas the Flynn-Wall and Ozawa (FWO) method is shown in Eq. 4: The equation for the Kissinger-Akahira-Sunrose (KAS) methods is shown below in Eq. 5: Finally, the isothermal iso-conversional method is represented in the Friedman method as shown below in Eq. 6:

Results and discussion
The kinetic modelling results AKTS thermokinetics package was utilized in this study to facilitate kinetic analysis of PET plastic bottle samples using conventional thermo-analytical data, which, in the case of this study, was in the form of TGA. This can allow for the study of the thermal behaviour of the PET samples within the discrete areas of quality assurance and research and development (R&D). The analysis begins with the importations of ASCII files from the TGA instrument. A derivation filter is then applied to provide the DTG reading of the sample. The DTG signal then has a baseline constructed to integrate the curve and provide the evaluation of the kinetic parameters such as rate of reaction, activation energy and pre-exponential constant (also commonly known in the literature as the kinetic triplet). Herein, baselines were constructed to integrate the DTG results with respect to the PET plastic pyrolysis profile. The type of baseline used herein was horizontal. AKTS has numerous possibilities for advanced baseline construction such as spline, sigmoid, tangential first point, tangential last point, etc. as baseline construction is the most crucial step in kinetic data treatment, and these constructed baselines can be optimized numerically. Additionally, the parameters for the Arrhenius equation can be determined for multi-step complex reactions, which cannot be visually seen if the thermo-analytical curves potentially overlap. Based on the obtained kinetic parameters, simulation curves are generated for the reaction rate and the reaction progress, which were compared with the experimental data to check the accuracy of the modelling. As the PET pyrolysis reaction progresses, there is a change in the specific heat of the reactant-product mixture, thus changing the heat of reaction and, consequently, the kinetic parameters. Specifically, using the AKTS package, the progress/extent of reaction (α) and the reaction rate can be predicted for a wide variety of temperature profiles (non-isothermal, isothermal, modulated, or periodic temperature variations or step base heating).
The software ultimately provides a robust and accurate result due to strict thermokinetic criteria of average correlation coefficient R having to be greater than 0.95 and the plotting of high-resolution data over 10,000 specific data points for the parameters and alpha values. Additional file 1: Figure S2 shows the practical results, their integration, and the subsequent simulated results from the TGA kinetic modelling results at different heating rates from 0.5 to 8 °C min −1 . Similar TGA results were reported in the literature [22,27,33,34]. The high mass loss in PET pyrolysis is due to the high volatile matter content as reported by Lee [34] in PET pyrolysis. While the DSC results of two heating rates (0.5 and 1 °C min −1 ) showed two endothermic peaks, along with a small shoulder of an exothermic peak, as shown in Additional file 1: Figure  S3. The first two endothermic peaks at 252 and 460 °C are due to the PET melting and pyrolysis, while the third peak at around 800 °C is characteristic of the graphitization of the residual carbon material. This agrees with the work reported by Kamali et al., where the three peaks appeared at 254, 466, and 791 °C, respectively [5]. It is obvious that there is a good match between the practical and theoretical simulation, as shown in Additional file 1: Figure S2 from the lowest to the highest heating rate with There is a clear shift towards a higher decomposition temperature by increasing the heating rate 16 times (from 0.5 to 8 °C min −1 ), as shown in Table 1 with R 2 = 0.99659. For instance, the temperature range for the pyrolysis reaction to occur at 0.5 °C min −1 was 261-442 °C, while at 8 °C min −1 , it increased to 328-535 °C. Furthermore, the onset temperature increased from 351 to 413 °C, respectively. By increasing the heating rates by 16 times, the offset temperature increased by 56 °C, as shown in Table 1. Thus, it is not surprising that the peak maximum was shifting towards a higher reaction temperature with increasing the heating rates, as 0.5, 1, 2, 4, and 8 °C min −1 showed peak maximum at 374, 389, 402, 417, and 433 °C, respectively. On the other hand, the time required for the pyrolysis reaction to finish has dramatically decreased by 13 times with increasing the heating rates by 16 times. Table 1 shows that the required time for completion at 0.5 °C min −1 was 49,447 s, while at 8 °C min −1 was 3789 s. Based on the integrated DTG curves from the five heating rates shown in Additional file 1: Figure S2, the average PET plastic weight loss up to 600 °C was 82.898 ± 1.2 wt.% of its initial mass.
To obtain the kinetic parameters, first, the reaction progress (α) was plotted versus the reaction temperature as shown in Fig. 1, where the practical and theoretical results are shown in coloured and dashed-grey lines, respectively. Again, it is obvious that there is a good match between practical and theoretical results. Figure 2 shows the practical and theoretical reaction rate against reaction temperature, where the coloured and dashed-grey curves show the practical and theoretical calculations, respectively, with good matching in all of the five heating rates. The maximum reaction rate of the PET pyrolysis at heating rates of 0.5, 1, 2, 4, and 8 °C min −1 was found to be 0.000089, 0.000449, 0.00092, 0.00188, and 0.00386 s −1 , respectively. Thus, the reaction rate increased by approximately 43 times with increasing the heating rates by 16 times, i.e., from 0.5 to 8 °C min −1 .
One of the kinetic modelling methods, ASTM-E698 (Eq. 3), was used to calculate the E a and showed 165.6 kJ mol −1 with R 2 = 0.9989, as shown in Fig. 3a. This is in agreement with the E a value reported by Saha and Ghoshal which was 162.15 kJ mol −1 using the ASTM-E698 method [35].
While the Flynn-Wall and Ozawa (FWO) method (Eq. 4) showed a variation of E a during the reaction progress in the range of 166-180 kJ mol −1 , as shown in Fig. 3b. The results herein are lower than those reported by Yao et al. [36], who reported 184-269 kJ mol −1 . This is maybe due to the fact that they did not specify the plastic waste that they used along with the high heating rates used (15,25, and 35 °C min −1 ).
The differential iso-conversional method also was used to calculate the kinetic parameters [E a along with the pre-exponential factor (k o )] using the AKTS software by plotting of the natural logarithm of the reaction rate in (s −1 ) against the inverse of the temperature (T −1 ), as shown in Fig. 4a. In Fig. 4b, a variation in the E a value was shown to be in the range of 165-195 kJ mol −1 . Interestingly, the results herein are in line with the work done by Jenekhe and Sun, where they reported E a values of 173.6-205.8 kJ mol −1 using the differential iso-conversional method [37]. At the start of the PET pyrolysis reaction where α = 0, the activation energy was 165 kJ mol −1 . This is in agreement with work done by Cooney and Wiles [38], where the E a value of the initial pyrolysis stage using Kissinger's Method was 163 kJ mol −1 . This activation energy value stayed relatively constant, while the reaction progress was increasing up to α = 0.3, i.e., 30% of the reaction progress, while the pre-exponential factor; ln(A(α) f(α) is ~ 22 s −1 . This high E a value at the start of the pyrolysis reaction could be attributed to the depolymerization of the polyethylene terephthalate polymer, which requires high energy to cleave the bonding within the polymer structure for the PET pyrolysis reaction, to initiate and progress. With the pyrolysis reaction progressing > α = 0.3, the activation energy value slightly increased to reach 195 kJ mol −1 at α = 0.9, while the preexponential factor; ln(A(α) f(α) is ~ 26 s −1 . This is again in line with the work reported by Cooney and Wiles [38], where the E a value increased to 202 kJ mol −1 .

The prediction of PET pyrolysis The step-based prediction of PET pyrolysis
The predictions of PET pyrolysis using a step-based heating regime are shown in Fig. 5a-d. For all of the four predictions, the final pyrolysis temperature was set to 500 °C, as this was in line with total decomposition from the TGA results. Additionally, all heating regimes began at 20 °C to indicate heating from ambient room temperature. In Fig. 5a, the PET was heated from 20-420 °C at 50 °C min −1 and then from 420-500 °C at 25 °C min −1 . It is evident that the reaction had appeared to complete after 11 min from the reaction rate curve. Interestingly, the maximum reaction rate observed was 0.014 s −1 at approximately 9.77 min. In Fig. 5b, the heating regime of 20-400 °C at 100 °C min −1 and 400-500 °C at 50 °C min −1 was utilized. For this sample condition, the peak reaction rate was shown to be 0.029 s −1 after approximately 5.42 min. From the reaction rate curve, it can be seen that the curve does not reach its baseline of 0 and is incomplete, therefore, implying an incomplete reaction. This is likely due to the heating rates used of 100 and 50 °C min −1 , respectively. If the reaction had occurred for longer at 50 °C min −1 or dwelled at the final reaction temperature of 500 °C, it would have reached completion. Figure 5c, on the other hand, is subjected to a heating regime of 100 °C min −1 from 20-320 °C and then 20 °C min −1 from 320-500 °C, respectively. However, in this case, the lower latter heating rate supplied allowed the observed reaction to reach completion. In this instance, the peak reaction rate observed was 0.010 s −1 after 9.86 min. Finally, Fig. 5d is heated from 20 to 450 °C at a heating rate of 100 °C min −1 and then from 450-500 at a heating rate of 5 °C min −1 . The maximum observed reaction rate was 0.011 s −1 after 5.42 min.  Interestingly, the curve in this sample appeared to have a shoulder and this is likely due to the rapid change in heating rate from 100 to 5 °C min −1 , respectively.

Isothermal prediction of PET pyrolysis
The isothermal prediction of PET pyrolysis showing 14 different isotherms at every 10 °C temperature change over the temperature range of 420-550 °C is shown in Fig. 6a, b. Figure 6a shows the reaction progress over the first minute, whereas Fig. 6b shows the reaction profile over the first 5 min. Evidently, from Fig. 6a, at reaction temperatures of 490 °C and above, the reaction reached completion (α = 1) in the short timeframe of 1 min. This rapid decomposition indicates that these temperatures would be ideal for rapid conversion. However, at lower than 490 °C, for example, 480, 470, and 460 °C, the reaction progress only reached α values of 0.93, 0.81, and 0.55, respectively, after the first minute. As Fig. 6b shows the decomposition over a broader time range, it is worth noting that temperatures such as 450-480 °C that did not reach (α = 1) in Fig. 6a have reached reaction completion when the timeframe is expanded to 5 min of operation. Below 450 °C shows a much slower reaction and indicates that the reaction has not reached completion in this case. This further indicates that in order for successful pyrolysis to occur of PET temperatures exceeding 450 °C should be used. Figure 7 shows the non-isothermal prediction of PET pyrolysis over the temperature range of 350-500 °C. It is not surprising that the decomposition temperature shifted slightly toward higher reaction temperatures. For example, by increasing the heating rates from 10 up to 30 °C min −1 , the peak reaction rates observed were 0.0051, 0.0077, 0.0104, and 0.0159 s −1 , respectively. In all of the four heating rates used (10,15,20, and 30 °C min −1 ) for the prediction, the reaction profile and reaction rate curves appeared to be consistent.

The in-situ gaseous monitoring of PET pyrolysis
During the pyrolysis process, two main reactions occur: cracking which breaks down the carbon chain and the charring reaction which aids to re-build up higher molecular weight products [39]. For instance, polyolefins (PP and HDPE) are composed of a saturated hydrocarbon chain, where the thermal decomposition takes place randomly by a radical scission mechanism [40,41]. However, due to the aromatic nature of PS, it decomposes into styrene monomers (70.6 wt.%), oligomers, and other secondary aromatic products. On the other hand, PET is composed of terephthalic acid and ethylene glycol monomers, and thus upon pyrolysis, various oxygenates and aromatics products are produced. The pyrolysis residue in the case of polyolefins was negligible, unlike PET that showed a value of 7 wt.% residue [40]. Barbarias et al. reported that the main PET pyrolysis fraction was a gaseous stream (CO and CO 2 ), with a product yield of 42.8 wt.%, along with 37.4 wt.% for the solid residue (benzoic and benzoyl formic acid) and 12.8 wt.% for oil fraction. PET plastic consists of chain-like backbones of synthetic polymers that are made of bis-hydroxyethyl-terephthalate monomer, and with thermal cracking or pyrolysis, it evolved various gaseous emissions. The PET pyrolysis is a complex process that releases different types of products such as aromatic compounds, such as benzene and toluene and aliphatic hydrocarbons C 1 -C 4 such as methane and ethane along with the typical pyrolytic emissions (CO 2 , CO, H 2 , and H 2 O) [20,[42][43][44]. Furthermore, other species could be released such as aldehydes, carboxylic acids (benzoic acid, acetyl benzoic acid, methyl benzoic acid, and ethyl benzoic acid), esters (vinyl benzoate and its derivatives), ketones (benzophenone and acetophenone), and terephthalic acid and vinyl terephthalate [20,[45][46][47]. The complexity of such reaction is due to the possibility of several side interactions between free radicals during the scission of the polymeric hydrocarbon chain such as intramolecular or intermolecular exchange and six-membered transition state reactions [27]. Figure 8 shows the in-situ monitoring of the evolved gaseous emissions using the mass spectrometer which offers rapid analysis and is not limited to the shape, colour, impurities, or dimensional limit as in other techniques such as Fourier-transform infrared spectroscopy (FTIR) and Raman spectroscopy [1]. Herein, the temperature was recorded using a thermocouple that was set in the middle of the fixed bed reactor as shown from the bluedashed line in Fig. 8. The PET pyrolysis herein occurred in one stage, which is in line with the TGA results with a similar heating rate, while the DSC results in Additional file 1: Figure S3 showed that the pyrolysis occurred in two stages. Figure 8 shows  [48]. Acetaldehyde was the first gaseous product that evolved and finished, as shown in Fig. 8, and this was confirmed by the m/z = 44 and 29 with the same evolution trend. This is in line with the work reported by Dhahak et al. [20], as they reported that acetaldehyde was the first detected gas followed by the following gases; benzoic acid, terephthalic acid, and benzene. Traces of benzene was detected herein in two peaks as shown in Additional file 1: Figure S4, with a large peak and small shoulder. This is also in agreement with the literature, as it was explained that those two peaks are due to the decarboxylation of benzoic acid (first peak) and terephthalic acid (second peak) [33]. Dhahak et al. reported that the major three gaseous compounds detected during the pyrolysis of PET were acetaldehyde, benzoic acid, and vinyl terephthalate [20]. During the PET pyrolysis, the depolymerisation reaction starts to occur at the weak bonding points within the ester polymeric structure, such as the C-O bonding and the polymer chain near the C=O bonding [27]. It is worth noting that the evolved short-chain hydrocarbon (C 1 -C 4 hydrocarbons) emissions can be combusted to provide some of the required reaction heat during the pyrolysis process [27].

Conclusion
Herein, with the aid of thermo-analytical data (TGA and DSC) along with kinetic modelling software, we evaluated and measured the kinetic triplet of polyethylene terephthalate pyrolysis to better understand the process at scale. Furthermore, three types of predictions (step prediction, non-isothermal, and isothermal) were made at higher heating rates to represent a realistic scenario that would occur in the industry. The differential iso-conversional method  . Future work could involve the use of kinetic modelling approaches such as the methods used herein to help determine how certain impurities or mixed wastes alongside PET can affect kinetic parameters and the predictions made in this study to help visualise problems that may occur in real-world scenarios such as industrial pyrolysis processes. This work can be used as a baseline kinetic modelling benchmark for pure PET bottle samples. The kinetic parameters evaluated herein can be used as a prerequisite in process modelling applications and the scale-up of PET pyrolysis worldwide. This will effectively allow this abundant waste stream to be converted into useful products such as energy and help to promote concepts such as the circular economy and the waste management hierarchy. Additionally, it will alleviate the amount of waste plastic that is conventionally sent to landfill or end in the aquatic ecosystem, by providing another end-of-life pathway for this non-biodegradable waste.

Supplementary information
Supplementary information accompanies this paper at https ://doi. org/10.1186/s1230 2-020-00390 -x.  Figure S1. The PET sample used herein. Figure S2. The % integrated mass derived from TGA results of PET pyrolysis at heating rates of 0.5, 1, 2, 4 and 8 °C min −1 . The integration of the DTG curve is shown in yellow and simulation results are shown by black lines. Figure S3. The DSC-TGA thermogram of the PET pyrolysis at heating rate of 0.5 °C min −1 (a) and 1 °C min −1 (b) under nitrogen atmosphere. Figure S4. Benzene evolution during the PET pyrolysis.