Lumped Kinetics for Homogeneous Reactions of n-Hexadecane and n-Decene as Model Compounds for PE Pyrolysis Primary Tars

: The focus of this paper is to establish a lumped kinetic scheme for secondary reactions of tar produced from pyrolysis of plastics or polymer-based wastes. Notably, the focus is not on the detailed yield of all reaction intermediates and products but on the propensity to form soot. Based on the assumption that that primary tar from pyrolysis of plastic wastes is mostly formed by aliphatics which can undergo progressive aromatization to polycyclic aromatic hydrocarbons (PAHs) and soot, a reaction network with 198 species and 6307 reactions proposed by Ranzi and coworkers was lumped into a very simple ﬁve reaction mechanism. The lumped kinetic model has been used to predict PAHs and soot formation in di ﬀ erent conditions and proved to be a good alternative to comprehensive kinetic models up for relatively low temperature and short residence times (of up to 1 min at 1200 K, up to 1 s at 1400 K). At higher temperature / longer residence times, the simpliﬁed model still provides reasonable qualitative trends but the amount of PAHs and soot is underestimated. The timescale of aromatization under inert conditions appears similar for all the alkanes and alkenes examined and also the yields in main reaction products seem to scale well with the number of carbon and hydrogen atoms of the parent alkane / alkene. Evolution of the young aliphatic tar into large aromatics is prevented as long as gaseous oxygen being available for oxidation. The lumped kinetic model has been used to highlight the e ﬀ ect of di ﬀ erent modes of oxygen feeding and of incomplete mixing of fuel and oxygen on the formation of PAH and soot. H C H CH 2 O, and C 3 H 6 start followed CH H , CO, CO 2 and H 2 O few Similar results are obtained for n-decene which at 1200 K decomposes in a time of the order of 0.5 ms forming mainly C 2 H 4 , CH 2 O, and C 3 H 6 . These species start to decrease after 2 ms while CH 4 , H 2 , CO, and H 2 O increase. CH 4 , H 2 , and CO start to decrease after 3 ms forming CO 2 and H 2 O. Formation of CO is complete by 3 ms. The e ﬀ ect of reaction temperature is to accelerate reactions: at 900 K with 20% of oxygen decomposition of n-hexadecane, for instance, requires 1 s and the maximum in CO production occurs at t = 2 s. At 1500 K thermal cracking occurs almost instantaneously (in roughly 0.01 ms) and oxidation requires less than 0.05 ms.


Introduction
Several well-known technologies for pyrolysis and gasification-such as entrained flow reactors, fluidized beds, rotary kilns, and fire grates-are nowadays receiving renewed attention as possible solutions to the problem of wastes disposal and for energetic exploitation of biomass and wastes. Within this context, considerable attention has been devoted to thermal recovery of plastic wastes . However, processing of non-conventional fuels is not straightforward. In fact, it has been reported that upon thermal treatment of biomass and wastes-like plastics, tires, automotive shredder residues (ASR), etc.-production of harmful compounds such as polyciclic aromatic hydrocarbons (PAHs) can be even more serious than for fossil fuels [14][15][16]24]. PAHs increase with pyrolysis temperature [25][26][27][28]. Rausa and Pollesel [26] report that the share of PAHs and substituted benzenes in products exceeds 80 wt% for pyrolysis of automotive shredder residue (ASR) at 1123 K. It is suggested that PAH formations is due to secondary reactions, is favored by high temperatures (>973 K) and long residence times [27,28].
Energies 2020, 13, 5466 3 of 18 order of 1000-1100 K. In line with these results, in the present work a simplified reaction scheme is proposed which considers only three categories of pyrolysis products: primary pyrolysis products are assimilated with alkanes and alkenes chains, secondary products with small aromatics, such as benzene and naphthalene, while larger PAHs and soot will be considered as tertiary products. The kinetics of the reactions of these species under inert and oxidative conditions will be obtained by a combination of laboratory and computational experiments. The proposed lumped kinetic scheme is reported in Figure 1.
Energies 2020, 13, x FOR PEER REVIEW 3 of 20 pyrolysis products are assimilated with alkanes and alkenes chains, secondary products with small aromatics, such as benzene and naphthalene, while larger PAHs and soot will be considered as tertiary products. The kinetics of the reactions of these species under inert and oxidative conditions will be obtained by a combination of laboratory and computational experiments. The proposed lumped kinetic scheme is reported in Figure 1.

Computational Experiments
Computational experiments have been carried out with the module Aurora of the software Chemkin, which simulates a closed perfectly mixed reactor. The kinetic mechanism proposed by Ranzi and coworkers [33] for high temperature pyrolysis and oxidation of hydrocarbons has been used. This includes 6307 reactions and 198 species up to C20.
Four set of computational experiments have been carried out: Reaction of primary tar under inert conditions Reaction of secondary tar under inert conditions Combustion of primary tar Combustion of secondary tar In the first set of experiments, alkanes and alkenes of different length (up to n-hexadecane and n-decene) have been tested. In the second set of experiments small aromatics such as benzene, toluene, and naphthalene have been tested. The third and fourth sets of experiments were carried out with the same hydrocarbons as in the sets of experiment 1 and 2, respectively. The initial concentration value of the hydrocarbon was set to values between 0.0001 and 0.1, the temperature was varied between 700 and 1900 K and the holding time was varied between 0.001 and 10000 s. The oxygen concentration was varied between 0% and 20%.

Laboratory Experiments
A sample of fine particulate matter was recovered during tests with a mixture of plastic wastes in a pilot scale rotary kiln reactor (capacity of 100 kg/h, reactor length 3 m). The reactor was operated under lean oxygen conditions (the molar O/C in the feed was 0.3) and reached peak solids temperatures around 1200 K. The sample was collected by an isokinetic probe, cooled down, and soaked with isopropanol prior to further analysis.
The SEM pictures of the sample reveal Figure 2a sooty like structure. The elemental analysis performed by CHN LECO Analyzer shows that the sample contains over 75 wt% of carbon and 1.3 wt% of hydrogen. Notably, the carbon content is small compared to that of soot produced from gaseous hydrocarbons, which is constituted by more than 90% of carbon; however, this value is not surprising because the sample is produced from pyrolysis of a mixture of plastic wastes, which not contain only carbon and hydrogen, but also mineral matter from additives, colorants, etc.

Computational Experiments
Computational experiments have been carried out with the module Aurora of the software Chemkin, which simulates a closed perfectly mixed reactor. The kinetic mechanism proposed by Ranzi and coworkers [33] for high temperature pyrolysis and oxidation of hydrocarbons has been used. This includes 6307 reactions and 198 species up to C20.
Four set of computational experiments have been carried out: Reaction of primary tar under inert conditions Reaction of secondary tar under inert conditions Combustion of primary tar Combustion of secondary tar In the first set of experiments, alkanes and alkenes of different length (up to n-hexadecane and n-decene) have been tested. In the second set of experiments small aromatics such as benzene, toluene, and naphthalene have been tested. The third and fourth sets of experiments were carried out with the same hydrocarbons as in the sets of experiment 1 and 2, respectively. The initial concentration value of the hydrocarbon was set to values between 0.0001 and 0.1, the temperature was varied between 700 and 1900 K and the holding time was varied between 0.001 and 10000 s. The oxygen concentration was varied between 0% and 20%.

Laboratory Experiments
A sample of fine particulate matter was recovered during tests with a mixture of plastic wastes in a pilot scale rotary kiln reactor (capacity of 100 kg/h, reactor length 3 m). The reactor was operated under lean oxygen conditions (the molar O/C in the feed was 0.3) and reached peak solids temperatures around 1200 K. The sample was collected by an isokinetic probe, cooled down, and soaked with isopropanol prior to further analysis.
The SEM pictures of the sample reveal Figure 2a sooty like structure. The elemental analysis performed by CHN LECO Analyzer shows that the sample contains over 75 wt% of carbon and 1.3 wt% of hydrogen. Notably, the carbon content is small compared to that of soot produced from gaseous Energies 2020, 13, 5466 4 of 18 hydrocarbons, which is constituted by more than 90% of carbon; however, this value is not surprising because the sample is produced from pyrolysis of a mixture of plastic wastes, which not contain only carbon and hydrogen, but also mineral matter from additives, colorants, etc. The sample has been analyzed in a Netzsch 409-C thermogravimetric apparatus. Approximately 10 mg of the sample were loaded into the pan and heated in air from ambient temperature to 1125 K at the rate of 5 K/min. Tests have been repeated three times. The mass loss data have been worked out to calculate the carbon conversion degree, X = (mo − m)/(mo − m∞) (where mo and m∞ are the initial and final sample mass), and the instantaneous rate of carbon conversion: R = dX/dt, where t is time.

Reaction of Primary Tar Under Inert Conditions
As examples of results of computational pyrolysis experiments, Figure 3a-c show the concentration obtained with 0.1% n-hexadecane in nitrogen at 1200 and 1900 K. Hydrocarbon mole fractions have been multiplied by the number of carbon atoms in each molecule to normalize values on a carbon basis. At 1200 K (Figure 3a) n-hexadecane, in less than 1 ms, fragments into relatively small hydrocarbons (nC10H20, nC7H14). By the time of 2 milliseconds, further cracking leads to even smaller products: C2H4 appears to be the most abundant product. Over the timescale of few seconds (Figure 3a), further small alkanes, alkines, and aromatics are formed, in particular CH4, C6H6, and C2H2. Formation of C10H8 and of progressively larger aromatics takes on over longer times. Production of C10H8 is indeed maximum at 52 s. Notably the kinetic mechanism used for Chemkin simulations does not include aromatics larger than C20, therefore the appearance of C20H10 has been assumed in the present work as indicative of the formation of progressively larger PAHs and eventually soot. Hydrogen is produced at all stages of reaction as a consequence of cracking and dehydrogenation. For temperatures up to 1600 K, the general trend is similar but reaction time scales are shorter, maximum production of naphthalene occurring at approximately 0.2 s at 1500 K. For higher temperatures, formation of C2H2 is predominant over PAHs (Figure 3c).
Results of pyrolysis experiments with n-decene resemble those observed in Figure 3a, since nhexadecane transforms into n-decene in the very early instances of reaction. The sample has been analyzed in a Netzsch 409-C thermogravimetric apparatus. Approximately 10 mg of the sample were loaded into the pan and heated in air from ambient temperature to 1125 K at the rate of 5 K/min. Tests have been repeated three times. The mass loss data have been worked out to calculate the carbon conversion degree, X = (m o − m)/(mo − m ∞ ) (where m o and m ∞ are the initial and final sample mass), and the instantaneous rate of carbon conversion: R = dX/dt, where t is time.

Reaction of Primary Tar Under Inert Conditions
As examples of results of computational pyrolysis experiments, Figure 3a-c show the concentration obtained with 0.1% n-hexadecane in nitrogen at 1200 and 1900 K. Hydrocarbon mole fractions have been multiplied by the number of carbon atoms in each molecule to normalize values on a carbon basis. At 1200 K (Figure 3a) n-hexadecane, in less than 1 ms, fragments into relatively small hydrocarbons (nC 10 H 20 , nC 7 H 14 ). By the time of 2 milliseconds, further cracking leads to even smaller products: C 2 H 4 appears to be the most abundant product. Over the timescale of few seconds (Figure 3a), further small alkanes, alkines, and aromatics are formed, in particular CH 4 , C 6 H 6 , and C 2 H 2 . Formation of C 10 H 8 and of progressively larger aromatics takes on over longer times. Production of C 10 H 8 is indeed maximum at 52 s. Notably the kinetic mechanism used for Chemkin simulations does not include aromatics larger than C20, therefore the appearance of C 20 H 10 has been assumed in the present work as indicative of the formation of progressively larger PAHs and eventually soot. Hydrogen is produced at all stages of reaction as a consequence of cracking and dehydrogenation. For temperatures up to 1600 K, the general trend is similar but reaction time scales are shorter, maximum production of naphthalene occurring at approximately 0.2 s at 1500 K. For higher temperatures, formation of C 2 H 2 is predominant over PAHs (Figure 3c).
Results of pyrolysis experiments with n-decene resemble those observed in Figure 3a, since n-hexadecane transforms into n-decene in the very early instances of reaction.   Based on the above considerations the following simplified reactions have been assumed to describe pyrolysis of n-hexadecane (reaction 1a) and n-decene (reaction 1b) Notably, all aromatics have been represented as C 10 H 8 , in accordance with the simplified reaction scheme of Figure 1. This simplification required some minor adjustment of the stoichiometric factors in order to respect the elemental mass balance.
The general formula of Equations (1) and (2) can be expressed as: The time τ when concentration of C 10 H 8 is maximum can be roughly assumed as the timescale of formation of secondary tar according to pyrolysis Equation (1) or (2) The stoichiometric coefficients of reaction products have been obtained from the concentration of the different species measured at time τ normalized with respect to n and m.
The values of the normalized stoichiometric coefficients (a to e) obtained at different temperatures have been plotted in Figure 4 for n-C 16 Table 1. From the analysis of the trends of Figure 4, it can be noted that H 2 and C 2 H 2 progressively increase with temperature, while other products decrease.

Reaction of Secondary Tar Under Inert Conditions
The formation of PAHs from secondary tar is addressed in Figures 5 and 6a,b. It is recalled that in the present work C10H8 has been chosen as representative of secondary tar. However, as shown in previous figures, naphthalene is formed along with C2H2. In order to investigate PAHs formation The expressions obtained from the fit of stoichiometric coefficients of reaction 1 as a function of temperature are reported in Table 1.

Reaction of Secondary Tar Under Inert Conditions
The formation of PAHs from secondary tar is addressed in Figures 5 and 6a,b. It is recalled that in the present work C 10 H 8 has been chosen as representative of secondary tar. However, as shown in previous figures, naphthalene is formed along with C 2 H 2 . In order to investigate PAHs formation from secondary tar, computational experiments have been performed with C 10 H 8 alone in nitrogen and with mixtures of naphthalene and acetylene in nitrogen at different concentration values. In Figure 6a, we report results of the computational experiment with 0.033% naphthalene and 0.1% acetylene in nitrogen at 1200 K. We chose these values for concentration of naphthalene and acetylene in order to respect the ratios between the stoichiometric coefficients measured at this temperature (see Table 1). Apparently, naphthalene and acetylene initially form C12H8 which further on evolve into C14H10 and eventually PAHs. Increasing the temperature up to 1900 K ( Figure 5), we observe that naphthalene is consumed in about 20 ms while acetylene concentration tends to a constant value and PAHs are formed only by naphthalene.
Stoichiometric coefficients for conversion of naphthalene are reported in the following formulas: As an example, results of pyrolysis of 0.1% naphthalene in nitrogen at 1200 K are shown in Figure 5. We can observe a progressive increase of C 20 H 10 , C 20 H 16 and H 2 as naphthalene is consumed. The timescale of reaction at 1200 K is in the order of 1000. For the sake of brevity, results of computational experiments of secondary tar reactions at higher temperature have not been reported, since the trends of concentration profiles are quite similar, but reaction timescales sensibly decrease with temperature, dropping to 10 s at 1500 K.
In Figure 6a, we report results of the computational experiment with 0.033% naphthalene and 0.1% acetylene in nitrogen at 1200 K. We chose these values for concentration of naphthalene and acetylene in order to respect the ratios between the stoichiometric coefficients measured at this temperature (see Table 1). Apparently, naphthalene and acetylene initially form C 12 H 8 which further on evolve into C 14 H 10 and eventually PAHs. Increasing the temperature up to 1900 K ( Figure 5), we observe that naphthalene is consumed in about 20 ms while acetylene concentration tends to a constant value and PAHs are formed only by naphthalene.
Stoichiometric coefficients for conversion of naphthalene are reported in the following formulas: on evolve into C14H10 and eventually PAHs. Increasing the temperature up to 1900 K ( Figure 5), we observe that naphthalene is consumed in about 20 ms while acetylene concentration tends to a constant value and PAHs are formed only by naphthalene. Stoichiometric coefficients for conversion of naphthalene are reported in the following formulas:

Combustion of Primary Tar
For sake of brevity only the results of computational experiments of combustion of n-hexadecane ( Figure 7) and of naphthalene ( Figure 8) at 1200 K and 20% oxygen are reported. Under these conditions n-hexadecane decomposes in less than 1 ms (Figure 7) forming mainly smaller alkenes (C2H4, C3H6, and n-decene), CH2O, CO, and H2. Soon after C2H4, CH2O, and C3H6 start to decrease followed by CH4, H2, and CO, while CO2 and H2O progressively increase. Oxidation is complete within few milliseconds with a maximum in CO production at t = 3 ms.
Similar results are obtained for n-decene which at 1200 K decomposes in a time of the order of 0.5 ms forming mainly C2H4, CH2O, and C3H6. These species start to decrease after 2 ms while CH4, H2, CO, and H2O increase. CH4, H2, and CO start to decrease after 3 ms forming CO2 and H2O. Formation of CO is complete by 3 ms. The effect of reaction temperature is to accelerate reactions: at 900 K with 20% of oxygen decomposition of n-hexadecane, for instance, requires 1 s and the maximum in CO production occurs at t = 2 s. At 1500 K thermal cracking occurs almost instantaneously (in roughly 0.01 ms) and oxidation requires less than 0.05 ms.
Increasing the oxygen concentration above 20% does not significantly affect the reaction times and path. The only effect that can be observed is an acceleration of the formation of H2O at the expense of H2. Reducing the value of oxygen concentration, instead, has a remarkable effect. For instance, at 1200 K when the oxygen concentration is reduced from 20% to 5% and 2% the time of maximum formation of CO from n-hexadecane increases from 3 ms to 9 ms and 60 ms. Further decrease of

Combustion of Primary Tar
For sake of brevity only the results of computational experiments of combustion of n-hexadecane ( Figure 7) and of naphthalene ( Figure 8) at 1200 K and 20% oxygen are reported. Under these conditions n-hexadecane decomposes in less than 1 ms (Figure 7) forming mainly smaller alkenes (C 2 H 4 , C 3 H 6 , and n-decene), CH 2 O, CO, and H 2 . Soon after C 2 H 4 , CH 2 O, and C 3 H 6 start to decrease followed by CH 4 , H 2 , and CO, while CO 2 and H 2 O progressively increase. Oxidation is complete within few milliseconds with a maximum in CO production at t = 3 ms.
Similar results are obtained for n-decene which at 1200 K decomposes in a time of the order of 0.5 ms forming mainly C 2 H 4 , CH 2 O, and C 3 H 6 . These species start to decrease after 2 ms while CH 4 , H 2 , CO, and H 2 O increase. CH 4 , H 2 , and CO start to decrease after 3 ms forming CO 2 and H 2 O. Formation of CO is complete by 3 ms. The effect of reaction temperature is to accelerate reactions: at 900 K with 20% of oxygen decomposition of n-hexadecane, for instance, requires 1 s and the maximum in CO production occurs at t = 2 s. At 1500 K thermal cracking occurs almost instantaneously (in roughly 0.01 ms) and oxidation requires less than 0.05 ms.  Figure 7. Combustion of 0.1% n-hexadecane at 1200K with 20% oxygen.

Combustion of Secondary Tar
Combustion of naphthalene ( Figure 8) requires longer times compared to n-hexadecane and ndecene formation of smaller alkenes (C2H6, C3H3) is not evident, whereas CO and H2 seem to be the main products in the first milliseconds. The presence of ketene (CH2CO) is also observed in the initial stages. Formation of CO is completed at 1200 K by 9 ms (against the 3 ms obtained for n-decene and n-hexadecane). At longer times, complete combustion takes on producing CO2 and H2O.  Figure 8. Combustion of 0.1% naphthalene at 1200K with 20% oxygen. Figure 9 reports the DTG curve (dX/dt versus T) obtained from thermogravimetric experiment in air on the soot like sample produced from pyrolysis of plastics in rotary kiln. The derivative curve shows a first sharp peak at T = 660 K, followed by a well-resolved peak at 710 K. The first peak accounts for a mass loss of less than 10% and is likely associated to some residual tar survived on the sample. The second peak is more likely due to combustion of the sooty carbon.   Figure 7. Combustion of 0.1% n-hexadecane at 1200K with 20% oxygen.

Combustion of Secondary Tar
Combustion of naphthalene ( Figure 8) requires longer times compared to n-hexadecane and ndecene formation of smaller alkenes (C2H6, C3H3) is not evident, whereas CO and H2 seem to be the main products in the first milliseconds. The presence of ketene (CH2CO) is also observed in the initial stages. Formation of CO is completed at 1200 K by 9 ms (against the 3 ms obtained for n-decene and n-hexadecane). At longer times, complete combustion takes on producing CO2 and H2O.  Figure 8. Combustion of 0.1% naphthalene at 1200K with 20% oxygen. Figure 9 reports the DTG curve (dX/dt versus T) obtained from thermogravimetric experiment in air on the soot like sample produced from pyrolysis of plastics in rotary kiln. The derivative curve shows a first sharp peak at T = 660 K, followed by a well-resolved peak at 710 K. The first peak accounts for a mass loss of less than 10% and is likely associated to some residual tar survived on the sample. The second peak is more likely due to combustion of the sooty carbon. Increasing the oxygen concentration above 20% does not significantly affect the reaction times and path. The only effect that can be observed is an acceleration of the formation of H 2 O at the expense of H 2 . Reducing the value of oxygen concentration, instead, has a remarkable effect. For instance, at 1200 K when the oxygen concentration is reduced from 20% to 5% and 2% the time of maximum formation of CO from n-hexadecane increases from 3 ms to 9 ms and 60 ms. Further decrease of oxygen concentration below stoichiometric conditions results in patterns approaching those of pyrolysis experiments.

Combustion of Secondary Tar
Combustion of naphthalene ( Figure 8) requires longer times compared to n-hexadecane and n-decene formation of smaller alkenes (C 2 H 6 , C 3 H 3 ) is not evident, whereas CO and H 2 seem to be the main products in the first milliseconds. The presence of ketene (CH 2 CO) is also observed in the initial stages. Formation of CO is completed at 1200 K by 9 ms (against the 3 ms obtained for n-decene and n-hexadecane). At longer times, complete combustion takes on producing CO 2 and H 2 O. Figure 9 reports the DTG curve (dX/dt versus T) obtained from thermogravimetric experiment in air on the soot like sample produced from pyrolysis of plastics in rotary kiln. The derivative curve shows a first sharp peak at T = 660 K, followed by a well-resolved peak at 710 K. The first peak accounts Energies 2020, 13, 5466 10 of 18 for a mass loss of less than 10% and is likely associated to some residual tar survived on the sample. The second peak is more likely due to combustion of the sooty carbon.

Assessment of Kinetic Rate Expressions
Results of the computational experiments carried out for different hydrocarbons and operative conditions have been worked out in order to estimate lumped kinetic expressions for the reactions indicated as 1, 2, 3, 4 in Figure 1 and describing, respectively, the formation of aromatics from primary tar (reaction 1), evolution into PAHs/Soot (reaction 2), oxidation of primary (reaction 3), and secondary tar (reaction 4).
A first order approximation of the timescale of reaction 1 (primary tar  secondary tar) has been obtained from the computational experiments of hydrocarbons pyrolysis as the time τ required to reach the maximum concentration of C10H8. This species was selected as representative of secondary tar. It can be observed that this choice is of course arbitrary. Smaller building blocks such as C6H6 might have been chosen as well. Notably, in order to check if this timescale is affected by the length of the original hydrocarbon, we have carried out computational experiments also with smaller alkanes and alkenes, such as nC10H22 and nC7H14. The concentration profiles obtained from these experiments have been worked out by the same procedure to calculate the reaction times τ and results are reported as data points in the Arrhenius plot of Figure 10. It can be observed that the timescale of reaction 1 is very similar for all the alkenes and alkanes investigated, regardless of the length of hydrocarbon, so much so that-for sake of simplicity and within the scope of the present work-a single set of kinetic parameters could be used to describe the rate of reaction 1, regardless of the specificity of primary tar. The solid line plotted in Figure 10 and labeled as reaction 1 is in fact the result of the linear regression performed over the data points relative to all the alkanes and alkenes investigated.

Assessment of Kinetic Rate Expressions
Results of the computational experiments carried out for different hydrocarbons and operative conditions have been worked out in order to estimate lumped kinetic expressions for the reactions indicated as 1, 2, 3, 4 in Figure 1 and describing, respectively, the formation of aromatics from primary tar (reaction 1), evolution into PAHs/Soot (reaction 2), oxidation of primary (reaction 3), and secondary tar (reaction 4).
A first order approximation of the timescale of reaction 1 (primary tar → secondary tar) has been obtained from the computational experiments of hydrocarbons pyrolysis as the time τ required to reach the maximum concentration of C 10 H 8 . This species was selected as representative of secondary tar. It can be observed that this choice is of course arbitrary. Smaller building blocks such as C 6 H 6 might have been chosen as well. Notably, in order to check if this timescale is affected by the length of the original hydrocarbon, we have carried out computational experiments also with smaller alkanes and alkenes, such as nC 10 H 22 and nC 7 H 14. The concentration profiles obtained from these experiments have been worked out by the same procedure to calculate the reaction times τ and results are reported as data points in the Arrhenius plot of Figure 10. It can be observed that the timescale of reaction 1 is very similar for all the alkenes and alkanes investigated, regardless of the length of hydrocarbon, so much so that-for sake of simplicity and within the scope of the present work-a single set of kinetic parameters could be used to describe the rate of reaction 1, regardless of the specificity of primary tar. The solid line plotted in Figure 10 and labeled as reaction 1 is in fact the result of the linear regression performed over the data points relative to all the alkanes and alkenes investigated.
It is worth underlining that, by reaction 1, we mean the formation of aromatics (in particular naphthalene) from the original hydrocarbon. This process must be distinguished from thermal cracking of the original hydrocarbon into smaller fragments, which is in fact a much faster process, and therefore has not been explicitly considered in the reaction scheme of Figure 1, but rather included in reaction 1. In order to check the validity of this approach, the timescale of thermal cracking of hydrocarbons has also been estimated from the computational experiments as the time required to decompose 95% of the original hydrocarbon into smaller alkanes, alkenes, and alkines. At 1200 K, thermal cracking occurs over the timescale of 1 ms (see  for the alkanes and alkenes. The regression line over the data points obtained from the computational experiments for thermal cracking is plotted in Figure 10 as a function of temperature, in order to compare the timescale of thermal cracking with the timescale of reaction 1 over a broad temperature range (the individual data points have not been reported, instead, to improve the readability of the figure). It can be observed that thermal cracking is moderately slower for alkenes than for alkanes, but it is always faster than formation of aromatics (reaction 1) by at least an order of magnitude. It is worth underlining that, by reaction 1, we mean the formation of aromatics (in particular naphthalene) from the original hydrocarbon. This process must be distinguished from thermal cracking of the original hydrocarbon into smaller fragments, which is in fact a much faster process, and therefore has not been explicitly considered in the reaction scheme of Figure 1, but rather included in reaction 1. In order to check the validity of this approach, the timescale of thermal cracking of hydrocarbons has also been estimated from the computational experiments as the time required to decompose 95% of the original hydrocarbon into smaller alkanes, alkenes, and alkines. At 1200 K, thermal cracking occurs over the timescale of 1 ms (see  for the alkanes and alkenes. The regression line over the data points obtained from the computational experiments for thermal cracking is plotted in Figure 10 as a function of temperature, in order to compare the timescale of thermal cracking with the timescale of reaction 1 over a broad temperature range (the individual data points have not been reported, instead, to improve the readability of the figure). It can be observed that thermal cracking is moderately slower for alkenes than for alkanes, but it is always faster than formation of aromatics (reaction 1) by at least an order of magnitude.
The timescales of Equations (2a) (secondary tar  PAHs) and (2b) (naphthalene + acetylene  PAHs) have been obtained from computational experiments of C10H8 pyrolysis and reaction between C10H8 and C2H2 respectively, as the time τ required to obtain 95% conversion of naphthalene. Results for Equations (2a) and (2b) (for a concentration of acetylene equals to 0.1%) are reported in the Arrhenius plot of Figure 10.
The timescale of oxidation of primary tar and secondary tar (reaction 3 and 4) has been assumed equal to the time required to reach the maximum of CO concentration. Data for reactions 3 and 4 have also been reported in the Arrhenius plots of Figure 10. For primary tar, the timescales evaluated from computational experiments with both n-hexadecane and n-decene and 20% oxygen are shown as data points. It can be noted that the timescale of oxidation of alkanes and alkenes is quite similar (and lower than that of naphthalene by a factor of 10) so much so that for sake of simplicity and within the scope of the present work, a single set of kinetic parameters could be used to describe the timescale of reaction 3, regardless of the specificity of primary tar, similarly to what already suggested for reaction 1. Oxidation reactions 3 and 4 are two-to-three orders of magnitude faster than reactions 1 and 2, suggesting that under oxidative conditions evolution of primary tar into PAHs would be prevented by combustion. It is worth underlining that, by reaction 3-4, we mean the formation of CO from original hydrocarbon. This process must be distinguished from thermal cracking of the hydrocarbon into smaller fragments, which occurs in the first instances of reaction. The timescale of thermal cracking of hydrocarbons under oxidative conditions has also been calculated from the computational experiments under oxidative conditions as the time required to decompose 95% of the The timescales of Equations (2a) (secondary tar → PAHs) and (2b) (naphthalene + acetylene → PAHs) have been obtained from computational experiments of C 10 H 8 pyrolysis and reaction between C 10 H 8 and C 2 H 2 respectively, as the time τ required to obtain 95% conversion of naphthalene. Results for Equations (2a) and (2b) (for a concentration of acetylene equals to 0.1%) are reported in the Arrhenius plot of Figure 10.
The timescale of oxidation of primary tar and secondary tar (reaction 3 and 4) has been assumed equal to the time required to reach the maximum of CO concentration. Data for reactions 3 and 4 have also been reported in the Arrhenius plots of Figure 10. For primary tar, the timescales evaluated from computational experiments with both n-hexadecane and n-decene and 20% oxygen are shown as data points. It can be noted that the timescale of oxidation of alkanes and alkenes is quite similar (and lower than that of naphthalene by a factor of 10) so much so that for sake of simplicity and within the scope of the present work, a single set of kinetic parameters could be used to describe the timescale of reaction 3, regardless of the specificity of primary tar, similarly to what already suggested for reaction 1. Oxidation reactions 3 and 4 are two-to-three orders of magnitude faster than reactions 1 and 2, suggesting that under oxidative conditions evolution of primary tar into PAHs would be prevented by combustion. It is worth underlining that, by reaction 3-4, we mean the formation of CO from original hydrocarbon. This process must be distinguished from thermal cracking of the hydrocarbon into smaller fragments, which occurs in the first instances of reaction. The timescale of thermal cracking of hydrocarbons under oxidative conditions has also been calculated from the computational experiments under oxidative conditions as the time required to decompose 95% of the original hydrocarbon into smaller species. The result of linear regression over these results is also plotted in the Arrhenius plot of Figure 10 (again the individual data points have not been reported to improve the readability of the figure). It can be observed that oxidative cracking is moderately faster than cracking under inert conditions at the lower temperatures investigated. Differences level off at 1500 K. For both alkenes and alkanes, oxidative cracking is faster than the oxidation reaction 3 by an order of magnitude, and therefore can be included in reaction 3.
Regression over experimental results allowed estimating kinetic expressions of each reaction assuming a typical Arrhenius law. The kinetic parameters are reported in Table 2 and have been used to calculate the rates shown as solid lines Figure 10. Notably for the combustion reactions, the dependence of the rate of reaction from oxygen concentration has been found negligible for values Energies 2020, 13, 5466 12 of 18 of oxygen concentration above 20% consistently with the fact that only minor differences have been observed in the overall rate of combustion form computational experiments with different, but large values of O 2 concentration. At much lower values of oxygen, the dependence of the rate of combustion from oxygen concentration is instead relevant. The rate of reaction 5 of soot combustion has been obtained from results of TGA on the carbon rich sample recovered from pyrolysis in the rotary kiln. The Arrhenius plot obtained from TGA is reported in Figure 11. The same figure reports also the rate of naphthalene combustion obtained from computational experiment. Interestingly the rate of soot combustion from TGA and the rate of naphthalene combustion from computational experiments nicely overlap, for this reason the same kinetics have been used in the model for reactions 4 and 5.

Discussion
In order to check the ability of the simplified kinetics of scheme in Figure 1, to predict PAHs and soot formation, calculations have been performed in MATLAB of the fate of nC16H34 at different

Discussion
In order to check the ability of the simplified kinetics of scheme in Figure 1, to predict PAHs and soot formation, calculations have been performed in MATLAB of the fate of nC 16 H 34 at different temperature and holding times. Oxidizing vs. inert conditions have also been considered. For a stirred tank reactor (STR) or equivalently a plug flow reactor (PFR), the following set of equations applies when the reaction scheme of Figure 1 is used. The change of overall volume due to reaction is neglected since very diluted conditions are considered: The stoichiometric coefficients and kinetic parameters reported in Tables 1 and 2 have been used in the calculations.
The maximum value of PAHs predicted under inert conditions are reported in Figure 12 as a function of holding time and temperature and compared with the corresponding results obtained using the original comprehensive kinetic scheme of Ranzi and coworkers with 6307 reactions [33]. For a holding time of 1 s, typical of flow reactors, the simplified and the comprehensive kinetic schemes provide results in good agreement. The PAHs concentration increases with temperature up to 1500 K and then decreases as a result of the competitive effect of PAHs and C 2 H 2 formation. For holding times of 10 s and 100 s, more typical of fixed beds, both the simplified and the comprehensive kinetic schemes predict higher values of the PAHs' maximum and a shift towards lower temperatures. The simplified model apparently underestimates the amount of PAHs at large residence times and high temperature, probably because the simplified model considers only the main path of formation of PAHs, that is from naphthalene and acetylene, whereas the comprehensive kinetic schemes include also other paths of formation which become more important the longer the holding time and the higher the temperature.
Under oxidative conditions, the formation of PAHs decreases thanks to the competition between reactions leading to PAHs formation (reactions 1 and 2) and combustion reactions (reactions 3 and 4). Figure 13 compares the formation of PAHs at 1200 K under inert conditions with formation of PAHs when oxygen is fed to the reactor, together with C 16 H 34 at the reactor inlet, or distributed along the reactor. The molar fraction of nC16H34 in the feed is fixed at 0.001, and the oxygen molar fraction is either 0.001 or 0.01. In both cases the feed of oxygen is understoichiometric: 6% and 60% of the oxygen necessary for oxidation of nC 16 H 34 to CO and H 2 O are fed respectively (E = 0.06 and 0.6). In the first case, the amount of the PAHs formed under inert conditions is reduced by 6% and in the second case it is reduced by 60%. Figure 14 shows the case of oxygen being added in 13 steps throughout the reaction time/reactor length, keeping the same cumulative amount of fed oxygen. The idea is to investigate the effect of ineffective mixing with alternation of inert and oxidative regions or the case of purposely distributed oxygen feed. It can be observed that PAHs initially increase but eventually are consumed by combustion reactions. The decrease of PAHs compared to inert conditions is approximately 10% and 85% when oxygen is distributed; therefore, it is larger than in the case of a single oxygen feed. Results can be explained by the fact that the presence of oxygen does not only consume PAHs but to some extent prevents its very formation throughout the process.

Conclusions
Laboratory and computational experiments carried out in present work did not aim to a detailed speciation of the gaseous and liquid products of pyrolysis of plastics, but rather to investigate the possibility of formation of PAHs and soot from primary pyrolysis tar over its residence time in a reactor where fuel rich conditions establish or where incomplete mixing determines fuel rich/fuel lean regions. Primary tar was considered to be constituted mainly by aliphatics. n-hexadecane and n-decene were chosen as representative compounds but similar results have been obtained regardless of the length of the alkanes and alkenes. After a very fast cracking event, all alkanes and alkenes undergo a similar destiny: in the absence of oxygen they evolve into progressively larger aromatics and over prolonged time into PAHs and soot. Naphthalene can be assumed as representative of small aromatic-intermediate products. The timescale of initial aromatization is similar for the different alkanes and alkenes considered and drops from 100 s at 1200 K to 0.2 s at 1500 K. The timescale of further evolution into larger aromatics is larger by approximately a factor of 10. Similar yields in reaction products as a function of temperature have also obtained when they are normalized with respect to the number of carbon and hydrogen atoms of the parent fuel. Oxidation reactions of primary (reaction 3) and secondary tar (reaction 4) are order of magnitude faster than reactions 1 and 2 respectively, therefore evolution of the young aliphatic tar into aromatics is prevented as long as gaseous oxygen is available for oxidation. Similarly, combustion of young aromatic is always much faster and favored over reactions of PAH formation, provided oxygen is available for oxidation.
From the kinetic point of view evolution of primary tar into secondary tar and ultimately into PAHs can be described by two consecutive lumped reactions each characterized by first order kinetics, with activation energy in the order of 67-69 kcal/mol and different pre exponential factors. Oxidation reactions are also described by power law kinetics, with activation energy of 46 kcal/mol. The reaction order with respect to oxygen is 1.4-1.5 at low values of oxygen concentration. An increase of oxygen concentration above 20% does not have further effect on the rate of combustion. The lumped kinetic model has been used to estimate the tendency to produce PAHs and soot in different conditions and, in particular, to highlight the effect of different modes of oxygen feeding and of incomplete mixing of fuel and oxygen. The simplified approach proved to be a good alternative to comprehensive kinetic models up to 1400 K and for relatively small residence times as far as the propensity to for PAHs and soot is concerned. At higher temperature and long residence times, the simplified model still provides reasonable qualitative trends but formation of PAHs and soot is underestimated compared to more comprehensive kinetic schemes.
Author Contributions: O.S.: conceptualization, writing original draft, writing review and editing, supervision, methodology. T.T.: investigation, conceptualization, data curation. All authors have read and agreed to the published version of the manuscript.