Theoretical prediction of product distribution of the

J. Anal. Appl. Pyrolysis 80 (2007) 427–438 www.elsevier.com/locate/jaap

Theoretical prediction of product distribution of the pyrolysis of high density polyethylene J.F. Mastral, C. Berrueco, J. Ceamanos * Department of Chemical and Environmental Engineering, CPS, University of Zaragoza, Marı´a de Luna 3, 50018 Zaragoza, Spain Received 21 January 2006; accepted 1 July 2006 Available online 18 May 2007

Abstract The main objective of this work is the formulation and development of a model that predicts the product distribution obtained in the pyrolysis of polyethylene. In order to do this a mechanistic model has been developed based on a radical mechanism. This model uses a small number of elementary kinetic steps, including initiation, b-scission, H-abstraction, aromatization and radical combination. The mechanism allows the prediction of the compounds obtained during the pyrolysis. Given the great number of species considered, the simulation of the pyrolysis process requires the solution of complex systems of ordinary differential equations. The results obtained have been validated with experimental results obtained in a free fall installation in which the pyrolysis process has been studied at different temperatures (500–1000 8C) and residence times (0.52–2.07 s). # 2007 Elsevier B.V. All rights reserved. Keywords: HDPE; Pyrolysis; Free fall reactor; Product distribution; Modelling; Kinetic mechanism

1. Introduction In the last 50 years there has been an unprecedented development in the use of plastics with a growth in consumption of 4% per year. This development has also originated an increase in the generation of plastic wastes, most of which (almost 90%) ends up in combustion plants and garbage dumps [1]. It is estimated that less than 15% of residual plastic materials are recovered or recycled. Being derivatives of non-renewable raw materials such as petroleum, plastics produce high energetic value wastes, abundant and relatively easy to recover in the MSW. However, only recently have they become subject to a selective collection and recovery. Pyrolysis appears to be an interesting technology for the treatment of mixtures of different plastic types, since a high yield in the separation of the wastes is not necessary [2]. In addition, a process of cracking, either thermal or catalytic, can be integrated in the operation of a refinery with consequent savings in costs. Due to the increasing interest in this type of process, the development of a model that simulates polyethylene pyrolysis was considered useful so that the influence of the operation * Corresponding author. Tel.: +34 976762160; fax: +34 976761879. E-mail address: [email protected] (J. Ceamanos). 0165-2370/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2006.07.009

variables on the behaviour of the system could be analyzed. This would lead to a possible optimization of the process and the development of new reactors. A detailed model for the analysis of a chemical process should include the differential equations of heat, mass and momentum balances and the physicochemical parameters of the system. These equations should be coupled to the kinetic system, so the mechanism, the kinetic equations and the values of the kinetic parameters must be known. In the work presented here the chemical stage has been studied in detail, trying to determine the reaction mechanisms. The characteristics of the experimental system allow a simplification of the study, since chemical reaction is the controlling step and no resistance of the heat transfer can be assumed. The first studies of the mechanism of thermal polyethylene decomposition already indicated that this occurs by means of a chain mechanism of free radicals of the Rice– Kossiakoff type [3]. The existing models [4–6] predict the generation of the main products, paraffins, olefins and diolefins, but not the influence of temperature and residence time on the product distribution. Neither is the formation of aromatics and polyaromatics included. The model presented here includes the polyethylene degradation step and the process of formation of aromatics and polyaromatics, and can be applied at different temperatures and residence times.

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J.F. Mastral et al. / J. Anal. Appl. Pyrolysis 80 (2007) 427–438

2. Experimental

Nomenclature Arn Bi Da Dn kf kpp kr kt k1ar k1s k2ar kb On Pn rib riArn rif ripp rir rit rj RDn ROn RPn Th

2.1. Installation and experimental procedure

molar flow of n carbon atoms aromatic (mol/m3) Biot dimensionless number Damkholer dimensionless number molar flow of n carbon atoms diolefin (mol/m3) kinetic constant of H-abstraction reaction (m3/ mol s) kinetic constant of initial scission reaction (s1) kinetic constant of H-abstraction reaction (m3/ mol s) kinetic constant of termination reaction (m3/ mol s) kinetic constant of production of aromatics 1 reaction (m3/mol s) kinetic constant of secondary gas production reaction (s1) kinetic constant of production of aromatics 2 reaction (m3/mol s) kinetic constant of b-scission reaction (s1) molar flow of n carbon atoms olefin (mol/m3) molar flow of n carbon atoms paraffin (mol/m3) rate of production of i via b-scissio´n (mol/ m3 s) rate of production of i via aromatization (mol/ m3 s) rate of production of i via H-abstraction (mol/ m3 s) rate of production of i via initial scission (mol/ m3 s) rate of production of i via H-abstraction (mol/ m3 s) rate of production of i via termination (mol/m3 s) rate of production of the j reaction (kg/m3 s) molar flow of n carbon atoms radical diolefin (mol/m3) molar flow of n carbon atoms radical olefin (mol/ m3) molar flow of n carbon atoms radical paraffin (mol/m3) Thiele dimensionless number

The raw material used was high density polyethylene, HOSTALEN GH 4765 from HOECHST, with an average particle size of 225 mm. The experimentation was carried out in an installation consisting of two free fall reactors in series with independent external heating. This type of reactor allows high heating rates, between 500 and 2000 K/s [7,8], and is adapted to carry out flash pyrolysis. The system allows the temperature of the two reactors to be established separately and the use of reactors of different volume in the second zone for studying a broad range of residence times. Therefore, a more detailed analysis can be performed of this important variable in the development of secondary reactions. The system of stepped cooling used allows the condensation and collection of the reaction products. Analysis was carried out by means of chromatography. Two gas chromatographs were used: HEWLETT PACKARD 5890 series II provided respectively with detectors of thermal conductivity (TCD) and ionization of flame (FID). In the chromatograph provided with the TCD the concentrations of H2, O2, N2, CO and CO2 were determined. Two packed columns connected in series were used: a 10 ft Porapak N, 1/8 in. external diameter with a 80/100 mesh and a 3 ft Molecular Sieve 13, 1/8 in. of external diameter with a 45/60 mesh. The hydrocarbons obtained in the gaseous fraction (one to eight carbon atoms) were analyzed using the chromatograph equipped with the FID. This chromatograph has a semicapillar column: HP-PLOT/Al2O3, 50 m in length, 0.53 mm external diameter. For the detailed analysis of the waxes and oils obtained a HEWLETT PACKARD GCD Series G 1800 A gas chromatograph, was used, equipped with a mass detector and a SGE column, HT5 Aluminium Clad 25 m 0.32 mm 0.1 mm. The identification of compounds was made by means of a Wiley 275. Two series of experiments were carried out. In the first series only the primary reactor was used, and the temperature of the first furnace was varied between 500 and 1000 8C. In the second series two reactors were used, the temperature and N2 flowrate in the first reactor being kept constant. The experiments were duplicated and the experimental conditions selected are shown in Table 1.

Table 1 Experimental conditions Run

Temperature oven 1 (8C) Temperature oven 2 (8C) tr (s) Fed PE (g/min) Fed N2 (g/min) Run time (min) Reactor 1 volume (l) Reactor 2 volume (l)

A

B

1a

1b

2a

2b

3a

3b

4a

4b

1a

1b

2a

2b

3a

3b

500 – 0.81 0.16 2.56 16.0 0.09 –

500 – 0.79 0.05 2.52 22.0 0.09 –

600 – 0.69 0.17 2.62 15.0 0.09 –

600 – 0.70 0.16 2.56 17.0 0.09 –

700 – 0.62 0.34 2.50 16.4 0.09 –

700 – 0.64 0.30 2.52 18.0 0.09 –

800 – 0.57 0.19 2.52 9.0 0.09 –

800 – 0.47 0.25 2.63 15.0 0.09 –

600 600 2.11 0.15 2.50 22.4 0.09 0.18

600 600 2.04 0.18 2.63 15.0 0.09 0.18

600 800 1.84 0.17 2.48 18.0 0.09 0.18

600 800 1.84 0.14 2.46 22.0 0.09 0.18

600 1000 1.58 0.15 2.66 22.0 0.09 0.18

600 1000 1.58 0.18 2.66 17.0 0.09 0.18


3. Theoretical model 3.1.1. Kinetic mechanism The model developed is based on a free radicals mechanism. The initiation step is a random and homolitic scission, in which hydrocarbons are consumed and primary radicals are generated [3,4]. Propagation reactions of two types are distinguished, bscission and hydrogen transfer. The b-scission is one of the main reactions of this step and of the pyrolysis process as a whole. It consists of the rupture of a radical to generate another primary radical and a hydrocarbon. If the b-scission of a primary radical takes place, ethylene, which is one of the main compounds of the gas fraction in the pyrolysis process, will be generated. Secondary radicals can generate alkenes and other primary radicals by b-scission, either alkenes or dialkenes. The production of dialkenes can be explained by means of the bscission of secondary radicals with an insaturation in terminal positions. Two different steps can be distinguished in the hydrogen transfer reactions. At low temperatures (400–450 8C), the intramolecular hydrogen transfer of the primary radicals occurs (backbiting), generating more stable secondary radicals. This type of reaction takes place by means of 1–4, 1–5 and 1–6 isomerizations, through intermediate cyclical structures. The reaction mechanism by means of 1–5 transfer is favoured, and occurs through an intermediate cycle of six carbon atoms, but 1.4 and 1.6 transfers are also possible [9]. The secondary radicals formed in the intramolecular transfer reactions can undergo a b-scission or isomerize again, although the probability of this route decreases in subsequent isomerizations. Hydrogen transfer reactions are favoured at low temperatures, whilst b-scission is more significant at high temperatures. This will lead to a greater amount of small molecules, increasing the yield to the gas fraction. At high temperatures the number of scissions occurring in the polymeric chain is greater, generating high concentrations of primary radicals, less stable than the secondary radicals. This will favour the reactions of intermolecular hydrogen transfer, and thus the formation of alkanes. The importance of these reactions will also increase when increasing the residence time in the reaction system. Despite the increase in the relative importance of intermolecular hydrogen transfer in these conditions, b-scission and intramolecular transfer continue to dominate the decomposition mechanism. The termination of the chain reaction takes place through the recombination of radicals and disproportion reactions. The above-mentioned reactions allow the prediction of the generation of olefins, paraffins and diolefins in the oil + wax fraction, as well as that of light gases. In order to predict the formation of simple aromatics or polyaromatics, it is necessary to consider some additional secondary reactions. Several mechanisms have been suggested to explain the formation of aromatic compounds [10]. In most of these an initial stage (corresponding to the formation of the first aromatic ring), and a

429

secondary stage (in which polyaromatic formation takes place) are distinguished. Although most of these mechanisms have been developed for combustion conditions and flames, they also include the phenomena occurring in the reduction zones of the flame and can therefore be applied to pyrolysis systems [11]. Numerous works have been carried out to determine the elementary reactions that originate the first aromatic ring [10,12–14]. The various studies indicate that the routes including radicals in the benzene formation stages are more significant than the mechanisms taking place through stable species. Cole et al. [12] found that the much slower Diels–Alder additions to butadiene could not explain the experimentally measured aromatic formation rates. The final conclusion of the different studies carried out is that more than one mechanism is required to explain the formation of the aromatic ring. One of the most widely accepted routes in the mechanism of aromatic formation is the recombination of two propargil radicals C3H3[13]: C3 H3 þ C3 H3 ! C6 H5 þ H

(1)

C3 H3 þ H3 CCHCCH ! C6 H5 CH2 H

(2)

Other important routes are the reactions of acetylene addition: nC4 H5 C2 H2 ! C6 H6 þ H

nC4 H3 þ C2 H2 ! C6 H5

(3) (4)

Other authors have studied the potential role of other species (such as C5) in the formation of benzene. An interesting path is that including cyclopentadiene (reaction (5)), since it is also an intermediate in the formation of heavier compounds, such as naphthalene and other polyaromatic compounds: C2 H4 þ c-C5 H6 ! benzene þ H þ CH3

(5)

Although several important mechanisms in benzene formation have been identified, it can be concluded that the global mechanism in the formation of the first aromatic ring has not yet been found [10]. Similarly, numerous works have been carried out to determine the growth of polyaromatic compounds, considered to be soot precursors in combustion processes [15–17]. Further studies have also been put forward showing that the processes of formation of polyaromatics under pyrolytic and oxidative conditions are similar. Several mechanisms have been studied [16], and it has been concluded that the main one is that of hydrogen abstraction and acetylene addition, also called the HACA mechanism. The influence of the fuel type on the relative importance of the mechanism has also been studied [16]. Although the fuel type can affect the mechanism in the initial stages, when the residence time increases the formation paths always tend to a HACA type mechanism. One of the main difficulties in the development of this type of mechanism is the uncertainty in the kinetic and thermodynamic data of heavy polyaromatics. Moreover, few studies have investigated the influence of the molecule growth. This is one of the possible causes of the underestimation of the production predicted by the models. The existence of additional

430


paths in the formation of polyaromatics that have not yet been evaluated could also be the cause of disagreements [10]. 3.2. System description The reactors described in the theoretical study correspond to those shown in Section 2. They are tubular quartz reactors connected in series. Their characteristics and dimensions are:

Reactor 1: Dimensions: f = 17 mm, L = 500 mm. Volume: 0.09 l. Reactor 2: Dimensions: f = 17 mm, L = 1000 mm. Volume: 0.18 l.

The reactors are simulated assuming ideal plug flow behaviour. A one-dimensional model is suggested, in which constant concentration and temperature are assumed along the radius. Constant temperature along the reactor axis was verified experimentally. 3.3. Heating of polyethylene particles throughout the reactor An important issue to consider in the modelling of processes of thermal degradation of solid fuels in free fall reactors is the determination of the relation between the heating and decomposition rates of the particles and their speed of falling. The relationship between these parameters will allow the determination of the process controlling step. A system of continuous fluid was considered, taking a falling particle that, due to its small diameter, does not present wall effects. The calculations indicate that the necessary distance for the terminal speed of the particle (100 mm) is shorter than the distance from the hopper exit to the reactor entrance. Therefore, the speed of the particles within the reactor will be the sum of the terminal speed and the speed of the control volume (equal to the gas speed). In addition, radiation heating is assumed. In order to estimate the heating time of the polyethylene entering the reactor an input flow rate of about 0.2 g/min is assumed. From the values of radiant heat flow and particle speed the heating times are calculated, obtaining values two orders of magnitude lower than the feeding characteristic time, so the heating of the particle can be considered instantaneous. The relationship between the heating rate and chemical decomposition rate will allow us to determine the decomposition regime in the experimental system. The controlling step can be determined from the characteristic times of internal (tc) and external (tw) heat transfer and of chemical reaction (treac) [18]. The possible decomposition regimes are shown in Table 3. The physicochemical parameters used in the calculations are shown in Table 2. The chemical parameters are taken from Di Blasi [19] (k0 = 6,19 104 s1, Ea = 71 kJ/mol), average temperature of 700 8C and mass flow density of 1.12 kg/m3. Calculating the dimensionless numbers, Bi = 5.5 1 and

Table 2 HDPE and N2 properties Parameter

Value

Units

HDPE rHDPE cp l t

950 2090 0.33 225

kg/m3 J/kg K W/m K mm

N2 rN2 (600/800 8C) mN2 (600/800 8C)

0.391/0.318 4.0 105/4.6 105

kg/m3 kg/m s

Th = 0.0043 1. The controlling regime in the system therefore corresponds to case b1, shown shaded in Table 3. This kinetic control can be explained taking into account the fast external heat transfer and the small particle size (225 mm) that favours internal heat transfer. These results allow some simplifications to be made concerning the heat transfer phenomena. 4. Model description Different groups of compounds are considered in the model: alkanes (Pn), olefins (On), diolefins (Dn), aromatic compounds (Arn), (classified by the number of rings) and the corresponding radicals, generated during the decomposition process. The probability of generation of each intermediate species is considered, according to the model described by Faravelli et al. [9]. A pseudostationary state is not assumed, so the concentration of each radical can be calculated, although this implies longer calculation time. The expressions used in the balance for the different species for each of the reactions considered are explained in the following paragraphs. The initial scission or initiation of the chain reaction takes place through a homolitic scission in which free radicals form and hydrocarbons are consumed. The model allows this step to occur in the three hydrocarbon groups: alkanes, olefins and diolefins: kpp

Pn !RPm þRPðnmÞ kpp

On !ROm þRPðnmÞ kpp RPm þRDðnmÞ

Dn !ROm þROðnmÞ It seems a reasonable assumption that the scission of any C–C bond has the same probability and an initial scission rate which is proportional to the number of bonds that can be broken. For example, (n 1) for paraffins:

(9)

Thus, the consumption rate of an alkane Pn is given by r Ppp ¼ kpp ðn 1ÞPn

(10)


and for olefins On and diolefins Dn: r Opp ¼ ðn 2Þkpp On

(11)

r Opp ¼ ðn 3Þkpp Dn

(12)

As has been previously mentioned, the rupture of any bond has the same probability of occurring. On the other hand, it is obvious that a radical RPn will only be obtained from alkanes, olefins and diolefins with a number of carbon atoms greater than n, which will depend on the reaction and scission type as follows: 8 < RP1 þRPðn1Þ (13) Pn ! RPm þRPðnmÞ to obtain # : RPðn1Þ þRP1 From an alkane of n carbon atoms, duplicated alkane radicals of up to (n 1) carbon atoms are obtained. Thus, for the obtention of a RPn radical from an alkane, it must have at least n + 1 atoms: 8 < RP1 þROðn1Þ (14) On ! ROm þRPðnmÞ to obtain # : RPðn2Þ þRO2 Thus, from an olefin of n carbon atoms, alkane radicals of one to n 2 atoms will be obtained, and olefin radicals of 2 to n 1 atoms. For the abstention of a radical RPn from an olefin, it must have at least n + 2 carbon atoms. And for diolefins: 8 < RP1 þRDðn1Þ RPm þRDðnmÞ and to obtain # Dn ! ROm þROðnmÞ : RPðn3Þ þRD3

The propagation steps of the chain reaction include hydrogen abstraction and b-scission reactions. 4.1. Hydrogen abstraction In these reactions, hydrogen transfer between radicals and hydrocarbons takes place generating new hydrocarbons and more stable radicals. Hydrogen abstraction reactions can be outlined as follows: kf

RZx þ Yn !Zx þ RYn kf

RZn þ Yx !Zn þ RYx

Oj

þ

j¼nþ1

r RD pp ¼ kpp

M AX X

2 Dj 3 j¼nþ1

AX X 2M Dj 3 j¼nþ2

(20)

where x and n are the number of carbon atoms and Z = Y = P, O, D. For example, an alkane Pn is consumed when reacting with any radical (RP, RO, RD), and similarly, it will be formed in the reaction of a RPn radical with any hydrocarbon, paraffin, olefin or diolefin. Taking this into account, and similarly for olefins, diolefins and radicals, the global balances for the hydrocarbons are as follows: X r Pf þ r Pr ¼ ðkf þ kr Þ RPn ½hydrocarbons

X Pn ½radicals

r Of þ r Or ¼ ðkf þ kr Þ On

X

r Df þ r Dr ¼ ðkf þ kr Þ

X ½hydrocarbons

½radicals

RDn

(22)

X ½hydrocarbons

X Dn ½radicals

(23)

and for the corresponding radicals: r RP f þ r RO r

X ðradicalsÞ ¼ ðkf þ kr Þ Pn X RPn ½hydrocarbons

(24)

X ðradicalsÞ ¼ ðkf þ kr Þ On X ROn ½hydrocarbons

(25)

r RO f þ r RO r (18)

ROn

(17)

(21)

(15)

(16) M AX X

(19)

RO2 þROðn2Þ # ROðn2Þ þRO2

From a diolefin of n carbon atoms, alkane radicals of one to n 3 carbon atoms and diolefin radicals of 2 to n 2 atoms will be obtained. For the obtention of a RPn radical from a diolefin, it must have at least n + 3 carbon atoms. Moreover, an alkane of n atoms can undergo n 1 possible scissions, in which a given radical appears twice. Thus, the probability of obtaining an alkane radical from an alkane is 2/ (n 1). From an olefin, the number of scissions is 2(n 2), and each radical appears twice, so its probability is 1/(n 2), while from a diolefin the possible scission are 3 (n 3) (three competitive and scission reactions with the same probability), the probability being 2/3(n 3). Taking this into account, the formation rates of alkane, olefin and double olefin radicals from the initiation reaction will be: MAX X X 2 MAX X MAX r RP pp ¼ kpp 2 Pj þ Oj þ Dj 3 j¼nþ3 j¼nþ1 j¼nþ2

r RO pp ¼ kpp

431

432


r RD f þ r RD r ¼ ðkf þ kr Þ

Dn

X ðradicalsÞ

X RDn ½hydrocarbons

(26)

4.2. b-Scission In this reaction scission of paraffin, olefin and diolefin radicals generates olefins or diolefins, along with a new radical: kb

kb

(27)

D j þ RPðn jÞ O j þ ROðn jÞ

(28)

It is considered that the probability of these two considered reactions is the same, i.e. 1/2: kb

RDn !

D j þ ROðn jÞ O j þ RDðn jÞ

MAX X

1 RO j 2ð j 3Þ j¼nþ1

þ

MAX X

1 RD j 2ð j 4Þ j¼nþ2

kb

RPn !O j þ RPðn jÞ RPn !Oðn jÞ þ RP j

The radical formation rate includes the term of consumption of the radicals by the reaction: M M AX AX X X 1 1 r RP b ¼ k b RP j þ RO j ð j 2Þ 2ð j 3Þ j¼nþ2 j¼nþ3 RP j (34)

(29)

The option of scission of a diolefin radical generating a paraffin radical and a hydrocarbon with three double bonds is not considered, since this type of compound is not obtained experimentally. This fact can be explained taking into account that in the two options considered, the unpaired electron can be stabilized in the conjugated system, whereas in this last option this possibility does not appear. As with the homolitic scission, the corresponding radical can suffer rupture at different places, with (n i) possibilities, these being i: 2, 3, 4 for paraffin radicals, olefin and diolefin, respectively. Thus an olefin On, can only be generated from a paraffin radical with a minimum size of n + 1 carbon atoms. The same probability is assumed for any rupture of the (n i) available, this possibility being 1/(n 1). However, for the scission of a given bond two different results can be obtained:

kb

r Db ¼ kb

(33)

RPn !O j þ RPðn jÞ ROn !

The formation rates of the hydrocarbon species corresponding to the reactions of b scission are given by M M AX AX X X 1 1 RP j þ RO j r Ob ¼ kb ð j 2Þ 2ð j 3Þ j¼nþ1 j¼nþ2 MAX X 1 RD j þ (32) 2ð j 4Þ j¼nþ3

r RO b ¼ k b

M AX X

ROn r RD b ¼ k b

1 RO j 2ð j 3Þ j¼nþ2

þ

M AX X


(35)

M AX X


RDn

(31)

The probability of obtaining a given Oj will be 1/2(n i). On the other hand, Oj can be generated not only by this reaction, but also in the scission of the bond symmetric to that considered above (and with the same probability), so that global probability is 1/(n i). Similarly, by the b-scission of ROn and RDn radicals olefins from n 2 to 2 and n 3 to 2 will be generated, respectively, due to the minimum lengths of olefin and diolefin compounds (and their radicals). The two possible competitive routes of b-scission of olefin and diolefin radicals previously mentioned must also be included (factor 1/2 appearing in the corresponding terms).

(36)

In the termination reactions two radicals react to generate a hydrocarbon molecule, paraffin, olefin or diolefin. The possible reactions are as follows: kt

RPn þ RPm !Pnþm

(37)

kt

RPn þ ROm !Onþm

(38)

kt

RPn þ RDm !Dnþm

(39)

kt

(30)

ROn þ ROm !Dnþm

(40)

Termination reactions of types RO–RD or RD–RD are not considered, since they would lead to triolefins and tetraolefins. In the termination process hydrocarbons of n carbon atoms will form when the reaction between the corresponding radicals takes place (RP, RO, RD). The terms of the formation rates of Pn, On and Dn due to the termination reaction are as follows: r Pt ¼ kt

n1 X

RP j RPðn jÞ

(41)

j¼1

r Ot ¼ kt

n2 X RP j ROðn jÞ

(42)

j¼1

r Dt ¼ kt

n3 n2 X X RP j RDðn jÞ þ RO j ROðn jÞ j¼1

j¼2

(43)


433

An additional consideration must be included in the radical consumption rate in the termination reactions. The length of the molecules formed must not exceed the maximum length considered in the model, and the minimum lengths of olefin and diolefin radicals will be 2 and 3, respectively. The coefficient 2 in the alkane and olefin terms can be explained taking into account the stoichiometry of the reactions considered, since two radicals of the same type are consumed for each hydrocarbon formed so that global consumption rate is doubled:

Alkanes react to form aromatics: X aromatics r P2ar ¼ k2ar P2 RD4 þ 2

r RD 3ar ¼ k1ar RD3 ½2 þ RD4

(54)

MAXn MAXn MAXn X X X r RP t ¼ kt RPn 2 RP j þ RO j þ RD j

r RD 4ar ¼ k1ar RD3 RD4 þ k2ar RD4 ½P2 þ O2

(55)

j¼1

j¼2

j¼3

(44) r RO t ¼ kt ROn

MAXn MAXn X X RP j þ 2 RO j j¼1

r RD t ¼ kt RDn

(45)

j¼2

MAXn X RP j

(46)

j¼1

Finally, the formation reactions of aromatics and polyaromatics are included. For the aromatic production the following routes have been considered: C3 H3 þ C3 H3 ! C6 H5 þ H

(47)

C3 H3 þ H3 CCHCCH ! C6 H5 CH2 þ H

(48)

nC4 H5 þ C2 H2 ! C6 H6 þ H

(49)

Whilst a mechanism of successive acetylene additions for the formation of polyaromatics (PAHs) is suggested [15,16]. In these reactions aromatics, polyaromatics and acetylene are consumed to form more complex PAHs. In the formation process of the first radical ring, a diolefin of three or four carbon atoms reacts with acetylene. Although acetylene is not a species included in the present model, the experimental results show that at the highest temperatures (conditions in which the acetylene addition is more important) the predominant species of two carbon atoms is acetylene. It is assumed that the addition reaction takes place between a diolefin radical of four carbon atoms (or an aromatic compound) and a hydrocarbon of two carbon atoms, P2 and O2. Therefore, the sum of the concentrations of these species is considered as the ‘‘hypothetical’’ acetylene concentration. The formation rate of aromatics of one ring is given by r Ar1 ¼ k1ar RD3 ½1 þ RD4 þ k2ar RD4 ½P2 þ O2 k2ar Arð1Þ½P2 þ O2

(50)

The first aromatic ring takes part in the formation of polyaromatics through the addition of acetylene. Polyaromatics also react to generate polyaromatics of higher molecular weight, so their rate can be formulated as follows: r Arn ¼ k2ar ½P2 þ O2 ½Arn1 Arn

(51)

(52)

Olefins:

X r O2ar ¼ k2ar O2 RD4 þ 2 aromatics

(53)

Diolefin radicals:

where Arn represents an aromatic compound with n rings. 4.3. Solution of the model As has been explained in the previous section, the degradation process is described through the mass balance to the different species in the system. The mass balance equations of the different groups of compounds are expressed as dPn ¼ r Ppp þ r Pf þ r Pr þ r Pt r P2ar (56) dt dOn ¼ r Opp þ r Of þ r Or þ r Ob þ r Ot r O2ar (57) dt dDn ¼ r Dpp þ r Df þ r Dr þ r Db þ r Dt (58) dt dRPn ¼ r Rp pp þ r Rp f þ r Rp r þ r RP b r Rp t (59) dt dROn ¼ r RO pp þ r RO f þ r RO r þ r RO b r RO t (60) dt dRDn ¼ r RD pp þ r RD f þ r RD r þ r RD b r RD t r RD 3ar r RD 4ar dt (61) dArn ¼ r Ar1 þ r Arn dt

(62)

The simulation of the degradation process requires the numerical integration of systems of ordinary differential equations. A second order Runge–Kutta method for the solution of the system has been selected. By means of this type of method an acceptable degree of precision is obtained, with an error of the order h3, where h represents the time increase used in the solution (Dt). 4.4. Kinetic study of the pyrolysis of polyethylene A review of the literature on the kinetics of the chemical reactions included in the model was carried out and is shown in Table 4. It should be noted that only a few detailed kinetic data relative to polymer pyrolysis exist. For this reason they have been compared with the values obtained for hydrocarbon pyrolysis. In the case of the kinetics of PAHs formation, the kinetic constant of acetylene addition has been assumed to be that corresponding to the formation of the first ring, kar2. The subsequent fit was carried out varying the activation energy and preexponential factor values of each of the reactions considered within certain ranges.

434


The evaluation of the errors was made using the sum of the squares of the differences of the different fractions considered. 4.5. Sensitivity analysis: influence of the maximum number of carbon atoms The maximum number of carbon atoms of a molecule affects the calculation time (and thus the computational cost), since an increase considerably increases the number of calculations in the mass balances. As an initial approach, residence time, temperature and kinetic constants have been kept constant and the maximum size of the sample has been varied. Since the maximum number of carbon atoms per molecule allowed by the system is 16000 (the limit of elements of a vector to carry out the calculation), seven tests with 10,000, 5000, 2000, 1000, 500, 200 and 100 carbon atoms were carried out, maintaining the other the variables constant. As can be observed in Fig. 1, the error obtained for the cases with molecules of 1000 carbon atoms and higher is very small (0.4% maximum). On the other hand it can be seen that from 2000 carbon atoms the calculation time increases considerably. For example, from 2000 to 5000 carbon atoms, the calculation time increases almost six times, whereas the error decreases by only 0.13%.

When increasing the termination rate, the formation of olefins decreases and that of diolefins and paraffins increases. The cracking intensity decreases, since the overall concentration of radicals diminishes. The aromatization reactions depend strongly on the temperature, becoming more important at 800 8C and above. They also depend on the concentration of smaller aromatic species, so that generation is relatively slow. The first adjustment tests indicated that the initial decomposition at low temperatures was much slower than that obtained experimentally, although there was an adequate fit at temperatures higher than 700 8C. For this reason two independent zones were considered, a low temperature (500– 600 8C) and a high temperatures zone (700 8C and above). Another interesting result of the fit was a better correlation when diminishing the b-scission rate. This decreases the control of this reaction, which is related to the olefin production and the shape of the cracking curve. After the literature had been reviewed the termination rate was assumed to be independent of the temperature, the values obtained being within the range observed in previous works. The optimal kinetic parameters obtained were:

5. Model results The kinetic mechanism theoretically studied is formed by a set of competitive reactions in series. Initiation and termination reactions will mark the global concentration of the radicals. Furthermore, b-scission, hydrogen transfer and termination reactions compete in the consumption of the radicals implicated in the decomposition process. The relative importance of the rates of the different reactions will mark the selectivity of the process: A fast b-scission increases the cracking process and generates an important amount of olefins and diolefins (mainly olefins). On the other hand, inter and intramolecular hydrogen transfer reactions influence the distribution towards paraffins and diolefins.

Fig. 1. Relative error and calculation time vs. maximum number of atoms of C.

H abstraction in primary radicals : kf ¼ 108:5 e½6000=T ðm3 =kmolÞ

(65)

H abstraction in secondary radicals : kr ¼ 108:5 e½6750=T ðm3 =kmolÞ b-scission : termination :

(66)

kb ¼ 1014:5 e½16800=T ðs1 Þ

(67)

kt ¼ 108:5 ðm3 =kmol sÞ

(68)

Table 3 Decomposition regimes for different values of the system parameters


435

Table 4 Kinetic data for the chemical reactions included in the model Reaction

Reference

Chain reaction initiation

[4] [20] [21] [22] [23] [24] [9]

ko (s1)

Ea (kJ/mol)

Additional data 15

1.7 10 5.3 1016 – 8 1015 1016 to 1017 5 1016 1014.9

251 364 251–293 301 356 343 343

Pyrolysis of C6 Polystyrene

108 to 6 108 1.5 108 108 to 10 9 108.5 108.5 108.5


1013.3 2.6 1012 1013 to 1014 1014.1


0.0 2.3 0.0 5.9

1.9 109 2.3 109 109.5 to 10 10 1010.4


[25] [11]

0 0

5 1012 3 109

[17] [25] [11]

42.3 66.9 22.6

Hydrogen abstraction

[20] [22] [23] [24] [9]

43.5–60.7 51.9 – 49.8–56.1 49.8 56.1

b-Scission

[20] [22] [23] [24]

111.8–120.8 95 120.1 126.4

Termination

[20] [22] [23] [9]

k1ar k2ar

A comparison between the predicted results and those obtained in the free fall experimental system using the first reactor are shown in Table 5 The comparison with the experimental results obtained with both reactors in series is shown in Table 6 and discussed later. 5.1. Series A simulation As can be observed in Table 5, although some quantitative differences appear, the model predicts acceptably the main

3.98 1013 5.0 1013 1.0 1013

trends discussed in the previous section. It is observed that at the lowest temperatures studied the main products are high molecular weight waxes, and that the production of gases increases when the temperature rises. Other observations to be noted are the minimum in the C5–C8 fraction, as a consequence of the greater formation of gaseous compounds, the maximum around C19–C32 and the cracking of the heaviest fractions. It can be observed in Fig. 2 that the greater discrepancies appear in the prediction of the cracking for low temperatures, and in the greater production of the gas fraction at 700 8C. The results obtained show that the controlling step in the cracking is b-scission. As has been explained previously, a fast b-scission generates more olefins, whereas the amount of paraffins obtained is smaller since they are generated in the hydrogen transfer and termination reactions. Therefore, the b-scission reaction provides the basis for an explanation of the evolution

Table 5 Comparison of experimental and predicted results for series A Series A

C1–C4 C5–C8 C9–C12 C13–C18 C19–C32 >C33 Aromatics

A-1

A-2

A-3

A-4

Theoretical

Experimental

Theoretical

Experimental

Theoretical

Experimental

Theoretical

Experimental

6.72 5.23 4.57 6.16 43.07 34.25 0.00

2.80 1.60 1.07 12.13 67.01 14.60 0.00

10.72 7.76 6.36 8.19 47.52 19.68 0.05

4.78 1.93 3.01 17.17 57.42 14.86 0.15

23.36 8.58 6.15 7.34 39.23 15.53 0.15

7.23 4.74 5.86 21.05 49.29 11.21 0.25

42.03 10.95 7.18 7.70 25.95 6.18 0.79

41.25 3.03 4.9 13.63 34.13 0.97 1.31

436


decrease curve from the heaviest to the lightest fractions, due to the progressive cracking of the heaviest fractions (still remaining in the sample) towards light compounds. When increasing the temperature and the residence time (so that the intensity of cracking increases), the form of the curve is reversed and an exponential decrease from light to heavy fractions is observed. For intermediate cracking levels the curve obtained shows a relatively high gas production (C1–C4), followed by a variation, with a minimum for C5–C12 and a maximum production for C19–C32, a result of the cracking of the intermediate fractions towards light compounds. Although it has been verified that b-scission is the fastest reaction in the cracking process, the importance of the other steps should be emphasized. Hydrogen abstraction play an important role in the evolution of paraffins and diolefinas, the initiation and termination reactions mark the global concentration of radicals and the aromatization reactions determine the evolution of this type of compounds. 5.2. Series B simulation

Fig. 2. Comparison between simulated and experimental results for series A.

of the product distribution with the temperature and the residence time. At low temperatures (and thus, low cracking intensity), a product distribution is obtained that follows an exponential

In this experimental series the residence time of the products in the reaction zone increases due to the use of two reactors in series, and the temperature of the second zone is also higher (up to 1000 8C). In Table 6 it can be observed that the experimentally obtained trends are adequately predicted including the increase in the gas fraction as the temperature increases and the decrease in the heaviest fractions. It should also be noted that in all cases an olefin fraction greater than those of paraffins and double olefins has been obtained, in agreement with the experimental results. It is also observed that the model overestimates the influence of the residence time on the olefin fraction cracking. The experimental results show a small variation in the product distribution, whilst the theoretical results show significant cracking towards the gas fraction (almost reaching 30%). These variations are less significant at high temperatures. Given the small wax production, the gaseous compounds have been shown separately in Fig. 3. A good agreement is observed, with an important production of fractions C1 and C2, and a much lower production of C3 and C4, involved in the production of aromatics.

Table 6 Comparison of experimental and simulated results for series B Series B

C1–C4 C5–C8 C9–C12 C13–C18 C19–C32 >C33 Aromatics

B-1

B-2

B-3

Simulated

Experimental

Simulated

Experimental

Simulated

Experimental

29.66 16.47 10.79 11.51 25.68 5.34 0.56

7.65 5.17 4.23 21.40 45.53 15.18 0.13

44.19 16.04 9.41 9.09 16.48 2.05 2.75

46.10 1.90 3.94 8.71 21.50 9.30 7.50

50.48 0.70 0.20 0.00 0.00 0.00 49.23

36.4 1.30 1.60 5.20 4.70 0.35 50.43


437

agreement is obtained (Fig. 3). At 1000 8C, the model predicts the generation of mostly one-ring aromatics (almost 90%), whilst the experimentally obtained fraction is mainly composed of polyaromatics. This low yield to polyaromatics agrees with the results presented by several authors [10] who suggest the possible existence of other mechanisms of formation of these compounds, such as the direct reaction between polyaromatics, or the participation of other species in the growth of this fraction [26]. In the present case another possible reason is that a global kinetics of formation of aromatics has been considered instead of a more detailed mechanism. 6. Conclusions A mechanistic model has been developed that simulates the pyrolysis of polyethylene. The model qualitatively predicts the main trend: a greater cracking of the olefin fraction with the rise in temperature and the consequent increase in the gas fraction. It also shows an increase in the cracking (overestimated) and in the production of aromatics when the residence time is increased. The production of aromatics increases as the temperature rises. This is also observed experimentally, and a good agreement is obtained for high temperatures (when the production of this fraction is more significant). The present model could be improved by including alternative kinetic routes for the production of polyaromatics, which would improve the quantitative results of this fraction. The addition of some significant gaseous species and intermediate aromatic compounds could also be useful for the prediction of the evolution of these fractions. Acknowledgements The authors express their gratitude to C.I.C.Y.T. (Projects QUI 98-0669 and PPQ2002-01625) for providing financial support for this work. Fig. 3. Comparison between simulated and experimental results for series B.

References The overestimation of C1–C4 at high residence times and intermediate temperatures (experiment A-3 in Table 5) can be explained by the model definition, since isomerizations by intramolecular hydrogen transfer and the consequent ruptures by b-scission are considered to occur with the same probability. However, some authors [9] indicate that more favoured isomerizations exist, mainly generating gaseous products (C3–C5). This would explain why in order to obtain gaseous fractions similar to those experimentally obtained at low temperatures and residence times the cracking rate must be increased and that at intermediate temperatures (PCL-B3) and long residence times (PCL-C1) the predicted gas production is greater than the experimental. At high temperatures, the importance of this phenomenon is negligible, since the cracking takes place from fractions of smaller molecular weight. The production of aromatic compounds increases as the temperature rises, and although at low temperatures the production of aromatics is underestimated, an adequate

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