The 5th ISFR (October 11-14, 2009, Chengdu, China)

CATALYTIC DEGRADATION OF HIGH DENSITYPOLYETHYLENE AND ASSOCIATED MODEL
Sandeep Sarathy, Michael D. Wallis, Suresh K. Bhatia*
Division of Chemical Engineering, The University of Queensland, Brisbane,
QLD 4072, Australia
Email: s.bhatia@uq.edu.auAbstract: Catalytic degradation of high density polyethylene (HDPE) using silica-alumina
has been investigated in a thermogravimetric analyser, and the degradation kinetics
determined using a population balance model recently published by our laboratory. An earliermodel used [1]considered only a single catalytic mechanism, and consequently under
predicted the amount of gaseous products at high temperatures. The new model accounts forboth thermal and catalytic modes of degradation acting in parallel, with the latter influenced
by molecular size-dependent surface adsorption, yielding activation energies of about 256
kJ/mol and 174 kJ/mol respectively. This new model agrees better with experimental data
than single mechanism models. Whilst catalytic cracking was predominant for most polymer
chain sizes, this model shows that thermal cracking is responsible for the over cracking ofmolecules after desorption from the catalyst, leading to the formation of excessive gaseousproducts.
This model can predict product distributions while varying temperature and catalytic
loading.
1. Introduction
The knowledge of the kinetics of catalytic degradation of high density polyethylene isimportant in many applications, including recycling. The breaking of the β bond, known as
β-scission, is the most common method of cracking [2,3]. This paper reports the experiments
performed, and new model developed, to determine the kinetic parameters.
2. Experimental Methods
The thermogravimetric (TGA) experiments were performed on a NETZSCH STA 409C,
using silica-alumina (Si/Al ratio of 4.9) from Sigma Aldrich as the catalyst, and HDPE
supplied by Qenos (polyethylene fluff). Experimental runs at loadings of 0% (thermal), 0.25%,0.5%, 0.75%, 1%, 1.5% and 2% were performed using a heating rates of 1, 14 and 20 K/min
until a constant temperature of 748 K was attained.

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3. ModelOur model uses population balances to track the mass loss by evaporation as the cracking
proceeds. The derivation of the model is beyond the scope of this short note, further details
are provided in Sarathy et al[4].
There were two specific models used: the first assumed a single catalytic mechanism,
while the second accounted for thermal and catalytic mechanisms occurring in parallel (Eq.
(1). The former occurs by setting Athermal = 0. Both are developed from that proposed by
Wallis and Bhatia[5], but are improved with the incorporation of a term accounting for size
dependent multisite adsorption of the molecules on the catalyst.
¥¶N(x,t)2= ò Athermal e¶t total ymin y- Ethermal
RTy N(y,t)dy - Athermal ep- Ethermal
RTx p N(x,t)- Ecat- Ecatææ
72 - ~x ö θ(y,t)
72 - ~x ö θ(x,t)
2 z v -1( 1 - z)v -1+ òAcat e RT ç y - ~ min ÷dy - Acat e RT ç x - ~ min ÷ççyB(v,v)x avg ÷ø υ(y)x avg ÷ø υ(x)y minè
è¥where x ³(1)72 - ~xmin
and ymin refers to the smallest molecule still in liquid form which is~
xavg

found from the following correlation derived by using a cubic line of best fit of the boilingpoints of n-paraffins[6].
x = 1.0673 ´ 10 -7 T 3 - 6.1439 ´ 10 -5 T 2 + 0.0339T - 2.5855(2)

The terms are defined as follows: N(x,t) is the number density of the polymer at any
dimensionless size x where x is defined as:~
(3)
x -~
x
x = ~ minx
avg

The mass of the molecules in g/mol is defined by ~x, ~xmin is the mass of the smallest
carbon chain (methane at 16 g/mol), whilst ~x is the number average molecular weight ofavg

the polymer chains (5218.46 g/mol). Athermal, Acat, Ethermal, and Ecat refer to the pre exponential
factors and activation energies of the thermal and catalytic portions, R is the universal gas
constant and B(v,v) is the beta function[7]. The parameter v[8,9] determines the width of theproduct distribution and was fixed at 4.54 which produced the best fit to experimental data inprevious experiments[10].The value p was fixed equal 1, which assumes that breakage islinearly proportional to size. The number of catalytic sites a molecule of size x occupies isgiven by:u ( x) = N Ck(4)where NC is the number of carbons, and k was set equal to 2/3 – reflecting the relation
between the molecular surface area and volume. A further assumption made is that after a sizeof 100 carbons, all molecules occupy the same number of sites

q ( x, t ) is calculated from the following implicit equation- 97 -

The 5th ISFR (October 11-14, 2009, Chengdu, China)( N c - 5) K 0e

-DH 0
RT ( t )(5)q ( x, t )=N ckæ
ö
ç1 - ò q ( x¢, t )dx¢ ÷ç÷è 0ø
¥X ( x, t )X(x,t) is the mole fraction of molecules of size x, K 0 and DH 0 represent theequilibrium parameters of adsorption, the factor ( N C - 5) represents the number of carbon
numbers adsorbed.
To solve the above population balance model we discretise using the fixed pivot
method[11] to obtain a set of ordinary differential equations which are solved usingMATLAB.
For the single catalytic mechanism, Athermal was set to 0, and Eq. (1) was fitted to data.
For both methods simultaneously, it was necessary to find the thermal parameters, Athermal , andEthermal . This was done by fitting Eq. (1), with Acat set to 0, to thermal experiments. Once

known, they were substituted into Eq. (1) and fitted onto experimental data. The fitting
parameters for both ways were Acat , Ecat , K 0 and DH 0 .
4. Results and Discussion
Fig. 1 depicts the experimental data and model fits at 20 K/min, showing excellent
agreement between the model and experimental values for all cases. The quality of fit
between the model and the experimental data was quantitively measured by the sum ofsquared residuals. The total sum of squared errors was 0.7381 (single catalytic mechanism)and 0.5408 (thermal and catalytic). Whilst it is clear that the separation of thermal andcatalytic rates is more successful, both methods show considerable improvement over ourrecent model1 which yielded a total sum of squared error of 1.3457 for data obtained here.
Fig. 2 compares a typical fit with the current model (thermal and catalytic rates separated)
and the previous model (0.25% catalyst, 20 K/min). It can be seen that the previous model
underestimated the rate of cracking at large time, causing it to have a larger error than thecurrent model. The values of parameters are shown in Tab. 1.
Tab. 1 Parameters for catalytic kinetics used in model fit
parameter

Catalytic parameters andmechanism considering
catalytic and thermal rates

Mechanism assumed purely
catalytic

E (kJ/mol)

173.95185.95-DH

7.884

7.873

2.089 x 10-4

2.089 x 10-40K 0 (-)- 98 -(kJ/mol)

1.2

1.2

1.0

1.0

0.8

0.8

0.6
0.4
0.2
0.0

mass (%)

mass (%)

PARTⅠ PYROLYSIS

measured, 0.25%
measured, 0.5%
measured, 0.75%
model, 0.25%
model, 0.5%
model, 0.75%

0.6experimental
initial model
new model

0.4
0.2
0.0

-0.2

-0.2

1000

1200

1400

1600

0500

1000

time (s)

1500

2000

2500

time (s)Fig. 1. Experimental data and model fits,
for a model [1]Heat in rate of 20 K/minand catalyst loadings of 0.25%,

Fig. 2. Comparison between
previous and new model.
Heating rate = 20 K/min.

Thus the novel consideration of the multisite adsorption in the current model yields
considerable improvement over the conventional homogenous model such as that adopted
earlier[1].
The overall activation energy with the kinetics represented by a mechanism with a single
rate constant, was found to be 185.95 kJ/mol, comparing favourably with Hara et al[12] who
calculated 188 kJ/mole for β scission (catalytic cracking). The thermal activation energy wasfound to be 256.44 kJ/mole, in excellent agreement with published data by Lin et al[13] of256.11 kJ/mole when calculated by the Ozawa[14] method. When subsequently isolating thecatalytic rate constant while considering both the thermal and catalytic mechanisms as
simultaneously operative, it was found that the activation energy of the catalytic reaction is173.95 kJ/mol.
The ratio of the thermal rate to the overall rate was plotted against conversion for a rangeof molecular sizes and catalytic loadings. Fig. (3) shows that C5 is predominately formed bythermal cracking, half the C12 is formed thermally, and a large portion of C16 forms
catalytically. Hence it is surmised that a two step process naturally occurs: initially thecatalyst cracks the polymer, producing mainly liquid products which then desorb; then theseproducts crack further, by a thermal process, into lighter liquids and gaseous products. Thisfinding has major implications for reactor and process design if a specific size range (i.e.
petrol, diesel) is to be created.
1.2

thermal/overall

1.0C5C12C160.80.60.4
0.2
0.0
0.0

0.2

0.4

0.6

0.8

1.0

1.2

conversion

Fig. 3 Ratio of thermal rate / overall rate for 2% catalytic loading- 99 -The 5th ISFR (October 11-14, 2009, Chengdu, China)
5. Conclusion
Our strategy of incorporating multisite adsorption in the model greatly enhanced the fit
and was successful in determining the kinetic parameters, with the activation energy values
determined (Esingle = 185.95 kJ/mol) being more consistent with published data than a previous
model that overlooks adsorption-desorption effects. Further, the strategy of separating thethermal and catalytic contributions led to a better fit than the traditional method of assuming asingle catalytic mechanism. It is proposed that a two step process occurs with the initialcatalytic cracking to liquid (Ecat = 173.95 kJ/mol) followed by thermal cracking (Ethermal =256.44 kJ/mol) to a gas.
Acknowledgments
The authors acknowledge the support of this research by the Australian ResearchCouncil. We also thank Qenos Ltd for the supply of HDPE.
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