- Email: [email protected]
Kinetic model of the pyrolysis of polyethylene in a fluidized bed reactor
JOURNALol ANALYTlCALnd APPLIED PYROLYSIS
Journal of Analytical and Applied Pyrolysis 30 (1994) 101-120
ELSEVIER
Kinetic model of the pyrolysis of polyethylene fluidized bed reactor
in a
Juan A. Conesa *, Antonio Marcilla, Rafael Font Departmeni
of Chemical Engineering,
University
of Alicante, Apartado
99, Alicante,
Spain
Received 29 March 1994; accepted 28 April 1994
Abstract A kinetic study of the pyrolysis of polyethylene (HDPE) in a fluidized sand bed reactor was carried out. The HDPE particles were discharged onto the fluidized bed; in the upper part of the reactor, the volatiles evolved from primary reactions underwent secondary cracking reactions. A correlation model was applied to simulate the primary and secondary reactions, as well as the heat transfer process. The experimental yields of the total gases obtained in 41 runs performed at 500, 600, 700, 800 and 900°C fitted satisfactorily with the proposed model. The values of the kinetic parameters of the secondary reactions and the heat transfer coefficient from the bed to the sample were optimized. Keywords:
Fluidized bed reactor; Kinetic model; Polyethylene; Pyrolysis
1. Iotroduction The yields of the products obtained from a pyrolysis process are evolved from the raw material decomposition (primary reactions) and the reactions suffered by the primary volatiles (secondary reactions). The extension of the secondary reactions depends on the experimental equipment as well as on the operating conditions. It is well known that high residence times and high temperatures favor the secondary reactions.
* Corresponding
author. E-mail: [email protected].
0165-2370/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0165-2370(94)00806-C
102
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
The gas yield obtained from the primary reactions only is low, and the following decomposition of tars and waxes formed in these reactions by means of secondary reactions leads to the production of a great quantity of gases. There is not a lot of information in the literature about the kinetics of tar decomposition from lignocellulosic products. The most representative works on the thermal cracking of lignocellulosic tars are those presented by Antal [ 11, Diebold [2], Font et al. [3], Garcia [4], Liden et al. [5] and Boroson et al. [6]. No information about the cracking of tars and waxes from polyethylene has been found. The thermal decomposition of polyethylene is somewhat different from that of lignocellulosic materials, because the polyethylene melts before its decomposition, and the reaction can be treated as the decomposition of a liquid. From the polyethylene pyrolysis, the yields obtained at SOO”C, when the wax cracking takes place extensively, are the following: Total gas: 99.72% Ethane: 3.56% Propane: 0.40% Acetylene: 0.07% Butane: 0.32% Benzene: 5.84% Xylenes: 0.04%
Methane: 10.04% Ethylene: 25.30% Propylene: 15.61% Butylene: 6.54% Pentane: 5.05% Toluene: 2.19% Styrene: 0.04%
More details of the yields can be found elsewhere [7] and will be published in another paper. The thermal decomposition of polyethylene in a thermobalance was analyzed [7]. The heating rates used were 5, 25, 50 and lOO”C/min. The fitting of the experimental data of the four curves was very good using two different models. Three reaction scheme: k,
IfT
aG1+bA, P* p
a’G, + b’Az
In accordance with experimental results obtained in TG runds, reaction ( 1) and (3) are considered superficial, whilst reaction (2) is considered to occur in the bulk mass. Zero-order
PE 5
kinetic:
aGp+bAp
These models are discussed in the following sections. The aim of this paper is to develop and apply a kinetic model from the HDPE pyrolysis data obtained in a fluidized sand bed reactor. In the proposed model, primary and secondary reactions, the surface of the melted particles, and heat transfer between hot sand bed and sample have been considered.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
103
2. Experimental
Pyrolysis was carried out in a cylindrical 18/8 stainless steel reactor. The inert fluidized bed was sand of 0.105-0.210 mm particle size, calcinated at 900°C and washed by an acid solution of HCl. The inert gas used was helium at 99.999% purity. Heating was achieved by means of a refractory oven. The bed surface temperature was controlled automatically at five different temperatures: 500, 600, 700, 800 and 900°C. The reactor was not isothermal, showing a temperature gradient from the sand bed to the top of the reactor. Two chromel-alumel thermocouples were used to control and measure the temperature profile.
3. Results Data from 41 experiments of HDPE pyrolysis in a fluidized bed reactor at five different sand bed temperatures (500, 600, 700, 800 and 900°C) were used to calculate the kinetic parameters. The mass of sand and the weight of polyethylene discharged onto the hot bed were modified in each experiment. The mean residence time depended on the mass of volatiles produced and the volume of the upper part of the reactor. Fig. 1 shows the experimental yields of gases obtained vs. the magnitude V/m (volume of the upper part of the reactor, without sand/mass of the HDPE discharged onto the bed). When V is constant, the greater the value of m, the smaller the residence time. When m is constant, the greater the value of V, the greater the residence time. Note that although V/m is not directly proportional to the residence time of the volatiles in the non-isothermal upper part of the reactor, there is some relation between the ratio V/m and the residence time. In the experiments carried out at 500°C the principal product is a degraded HDPE, obtained in the solid state. The molecular weight of those HDPE waxes (analyzed by GPC) is around 300.
4. Kinetic study In the reactor used in this work two zones can be considered: (a) the fluidized sand bed where the sample is discharged and at the top of which the primary reactions take place; (b) a hot zone in the upper part of the reactor where the tars formed are cracked. The correlation model used to calculate the secondary kinetic parameters is similar to that presented by Font et al. [ 31 in their study of the pyrolysis of almond shells in a fluidized bed reactor. Nevertheless, some modifications in both the data treatment and the reaction scheme have been carried out on the new material used. The kinetic model is based on the following assumptions.
104
J.A. Conesa et al. I J. Anal. Appl. Pyrolysis
500’1:
%W(pS
100
30 (1994) 101-120
0
60
0 ___---0
0
40
20
0
200040006000aOw v/m Wg) 700%
wO%wp 0
lA 80
.
,,:”
_-+ 0
.i
0 20.
O0
20004aOOaooo8000
vhn Wg)
,
0’ 0
2000
4000 Vh (cc/e)
MOO
8000
Fig. 1. Variation ratio V/m.
of yield of total gas vs.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
105
30 (1994) 101-120
(1) As a consequence of the primary reaction undergone by the polyethylene sample discharged onto the bed, a small amount of volatiles (Al’,) is generated in a small interval (At,). The AV, formed is pushed by the helium flux through the hot zone above the fluidized bed. In this zone, the volatiles are cracked as a consequence of the secondary reactions, and the mixture expands. Over the next time interval (A&), another amount of volatiles (AV,) is generated. This is also pushed by the helium flux to the top of the reactor. AV, continues rising as its volatiles are pushed upwards by the helium flux and by the new volatiles increment AL’,. The distance of any volume element to the top of the sand bed is calculated taking into account the volume occupied by the elements under it, and this changes with time as a consequence of helium flow and the expansion of all the volumes due to the secondary reactions. This process continues until the total sample decomposition and 99.9% of volatiles evolved have left the reactor. Fig. 2 shows the steps considered. (2) In order to develop the mathematical model, both kinetic and heat transfer phenomena have been considered. The aspect that have been taken into account, as well as the basic expressions used in the model, are shown below: 4.2. I. Primary kinetic law The overall primary decomposition
reaction of HDPE can be represented by:
PE+aGp+bAp
.. u ...<. :: :.+Q jj::: I’
1H* t=o 0,
I t= At b
t=2
C
I He
He At
:t=3
At
d
Fig. 2. Steps in the pyrolysis process of HDPE in the fluidiid
t=Q At
e’ bed reactor.
106
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) IOI-I.?0
where PE, Gp and Ap refer to the polyethylene, primary gases and primary tars and waxes respectively. In the mathematical expressions, PE, Gp and A, are the mass fractions of the corresponding material PE (polyethylene), Gp (primary gas) and Ap (primary waxes and tars); the values a and b are the yield coefficients, i.e. product formed (kg) /PE reacted (kg). Obviously a+b=l
(2)
a = G,,,
(3)
b = A,,,,
(4)
and
where Gp_ and A,,, are weight fractions that can be formed when all the sample is decomposed (at time infinity). It is evident that a(P&
- PE) = G,
(5)
b(PE, - PE) = A,
(6)
Consequently,
at any time
AJG,, = b/a
(7)
PE,=l=PE+G,+A,
(8)
and -GF+
dPE dt
(9)
dPE 7 = -Awn
dPE dt
(10)
dPE
%_
dt --adt= dA
P=_b
dt
For the volume of gases formed by the primary reaction (G,), it can be written that
dVGp -=dt where V, and V~p,m For the conditions,
v
dPE GP.~ 7
(11)
is the volume of gases formed at any moment for a given temperature, is the maximum value of V, (at time infinity). tars and waxes formed (in the gaseous state at the experimental and as liquids .or solids at room temperature), it can be written that
dVA~ -=dt
v
dPE AP,~ dt
where VA, is the volume of tars formed and V,,,, time infinity) at a given temperature.
(12) is the maximum value of VAp (at
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
107
If Vvr is the total volume of volatiles (gases + primary tars and waxes), it can be written that (13)
v,, = VIZ,+ Y4r VVP,00
-
v,,,
+
(14)
vAp,m
From Eqs. (1 l), (12), (13), and (14), it can be deduced that -= dt
__v
dVVP
.-dPE V&‘,m dt
(15)
Eq. (15) is the one considered in the model, and applies to polyethylene decomposition. For the primary pyrolysis, two different models have been considered [7]: (a) Three reaction scheme: aG, + bA, k, LP*Ta’Gl+b’A, kz No difference in behavior is considered between gases Gi and GZ, and tars A, and A, as well as in their yields, directly from either P or P*. In this scheme
A, +&=A, G, +
(16)
G2 = G,
and
MdP=-kS1 ’
dt
p
(p + p*> -
k2PMo
0x=
(17)
P*
M dP* +k2J’Mo
-
k3S
cp
+
p*j
where S is the surface exposed to the surrounding atmosphere, MO is the initial mass of the sample, and the kinetic constants (k,, k2, k3) vary with the absolute temperature by the Arrhenius equation: ki = k, exp( - Ei /RT)
i=l,
2, 3
The overall equation for the polyethylene dPE -=k,x dt
(18) decomposition
can be written as
(1%
M,&+k3&&z
where PE is the amount of polyethylene (P + P*) present at any time. The constants obtained from TG experiments were the following [7]: ko, = 2.892 x 1019 s-’ me2 kg-’
E, = 171.1 (kJ/mol)
k 02 = 2 . 830 x 1013 s-i
E2 = 234.6 (kJ/mol)
ko3 = 2.349 x 16O s-l me2 kg-’
E3 = 195.8 (kJ/mol)
J.A. Conesa et al. /J. Anal. Appl. Pyrolysis
108
30 (1994) 101-120
(b) Zero order kinetic: kl PE aGp+bAp in which -d!+,;
(20) 0
and klo = 8.543 x 1018 s-r mm2 kg-’
E, = 164.3 kJ/mol
Note that in a TG apparatus the surface exposed to decomposition is known. Nevertheless, when the polyethylene sample is discharged onto the hot sand bed, the polyethylene melts prior to its decomposition and the surface exposed is not known. To account for this, the parameter exterior surface/initial mass of a particle (S/M,& is introduced into the model. This parameter has also been optimized. The TG results indicate that there is no great difference between the two models at the heating rates mentioned. Nevertheless, in this paper the two models have been tested, due to the fact that reaction (2) becomes more important at high heating rates. 4.2.2. Heat transfer between the. sand bed and the sample Heat transfer processes between the hot sand bed and the sample have been modeled taking into account the possible differences between bed temperature and sample temperature. A heat transfer coefficient (U,) has been included in the model to estimate the actual temperature of the primary decomposition. The expression used is as follows:
dTp dt
u,S
-c,
(21)
(T,,-T,)=H,!$(T,,-TJ P
where Tb is the temperature of the fluidized bed, Tp is the actual temperature of the sample at time t, and S is the external surface of the polyethylene. Owing to difficulties in modeling (especially for S), HP = U, S/M, C, is considered as a fitting parameter. Although the value of 17, can vary as a function of time, it has been considered constant throughout the process. The parameter HP, therefore, represents a simplification to calculate the heat transfer coefficient. 4.2.3. Secondary reaction G, (secondary gases) bAp :” < ” S, (solids, waxes and heavy tars)
(22)
According to the suggested model, it is considered that during a small time interval, a certain amount of primary gases and tars ( Vcr,o and VAp,o, respectively) is
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
109
generated as a consequence of primary reactions. These compounds are entrained by the helium flow to the exit of the reactor, undergoing cracking inside the reactor as a consequence of the secondary reaction. If the primary tar decomposition is given by Eq. (22), it can be written that 1 dAA, _ --_ AV, dz
(23)
where AV, is the volume reaction element considered, which rises throughout the reactor, containing: (a) a constant quantity of primary gases AG,,; (b) a quantity of untracked tars AA,; (c) a quantity of secondary gases AG, generated as a consequence of tar cracking; (d) a quantity of helium (function of the flux and the time interval considered). This volume element will vary as a consequence of the volatile expansion due to secondary reactions. If the evolution of this volume is known, the situation can be determined and its temperature, therefore, is obtained from the previously determined temperature profile. The integration limits of Eq. (23) are AA,, = AA,,,, when r = 0 (the volume element has been
generated as a consequence of the primary reaction) and AA, = AA,,,
when z = z, (the volume element leaves the reactor)
Eq. (23) can be written as
dAAP _ - +,I + kz) AA, dr
-
The quantity of untracked primary tars can be expressed as a function of the tenerated tars (AA,,) and of the reaction extension (X,): AA, = AA&
1 - X,)
(25)
From Eqs. (24) and (25):
2 =(k, + kd(
1 - X,)
Eq. (26) defines the kinetics of the secondary reaction as a function of the extent of reaction of the tars. If AV,, is the total volume of gases (primary + secondary) that are within a volume AVR considered, it can be written that AV,, = AVGp,o + AV,, + AV,,
(27)
and also AV~,_~_AA&l--s) PAP
(28) PAP
where pAp is the density of the primary tars.
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
110
30 (1994) 101-120
For each interval considered, at any temperature,
A&2%
it can be written that
(29) PGs
PGs
where pGs is the density of the secondary gases, and the ratio ksl /(k,, + ks2) represents secondary gases formed (kg)/primary tar formed (kg). Combining Eqs. (27) -( 29) :
AV,,,==AVG,,o+hAp30(1
-‘I+ PGs
PAP
AAp3o =
AvGp.0
(30)
+
Bearing in mind that AA,, A VA,, = d
(31)
PAP
and AGpo
(32)
AL,‘,,0 =A
PGP
Eq. (31) can be written as
( )k,
-A+AA,
o
AAp,o
k,, + ks2
PGs
AVW =
(AVGP,O
+
AVA,o)
1 +
-&
PAp AG,o d+d PGp
(33)
AA,, PAp
Since
AV,,, = AV,,,o+ AV,,,o
(34)
and defining
AA, ------+ cI=
o PGs
PAP AGP,O PGp
( AAP.0 PAp
(35)
J.A. Conesa et al. /J. Anal. Appl. Pyrolysis
Eq. (33) can be transformed AVv, = AJ&,(l+
30 (1994) 101-120
111
to
mx,)
(36)
Eq. (36) defines the expansion of total volatiles (primary plus secondary) as a consequence of the cracking of tars in the secondary reaction. Bearing in mind that by the primary reaction AG,,,o= (0)
A-%,,
(37)
and taking into account the molecular weights of the tars, primary gases and secondary-gases (MAP, MGp , Mos respectively), Eq. (35) can be rewritten as:
(38)
4.2.4. Heat transfer between the volatiles and the reactor wall The volatiles flow through the reactor from the bed to the top of the reactor. The temperature profile along the reactor was measured when only the inert gas flowed through it. This profile is a consequence of the heat transfer between the walls of the reactor and the gas which is flowing. The profile can be modified in the presence of volatiles. Bearing these aspects in mind a correction factor has been introduced for any volume:
where Tj is the real temperature of the volume considered, and TR is the reactor temperature according to the temperature profile measured at the position of the volume of volatiles.
5. Correlation of experimental data The experimental data of the total gas yield for 41 runs [7] were correlated by the suggested models. The objective function considered was
0.F. = i
(Yexpj- L&2
j=l
where the experimental yield was calculated as gas analyzed (g) sample (g)
yexpj = polyethylene
(41)
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
112
30 (1994) 101-120
The gases analyzed were methane, ethane, ethylene, propane, propylene, acetylene, butane, butylene, pentane, benzene, toluene, xylenes and styrene. The calculated yields according to the simulation program were obtained by the following equation:
Yca,cj = : A%, + i=l
I?A~p,cpsi
(42)
i=l
where the sum comprises all the intervals considered (i), and where AG,,,i and AY&~ are the quantities (g) of gases and primary tars generated in the “i” interval per gram of polyethylene discharged, respectively. The sum considers 150 intervals (it has been proved that the same result is obtained with a number of intervals greater than 150). The second part of the sum in Eq. (42) represents the quantity of gases generated from the primary tars:
and consequently
However, the mean volatile residence time can be defined as
where Vvp,i is the volume of total primary volatiles in the i interval, and I’,, = 5 i=l
Avv,i
(46)
In Eq. (25), ri is the time required by the element i to flow through the empty part of the reactor from its generation. Note that Z refers to the mean residence time of volatiles in the upper part of the reactor, where cracking takes place. This mean residence time of volatiles is different from the total mean residence time, which also includes the period of time from the discharge of the material to the generation of the different elements by the primary reactions. Eqs. (41) and (42) have been used to calculate the value of the objective function. The optimized variables were the following: - modulus HP, referring to the heat transfer sample-sand bed; - correction fractor H, of the temperature in the upper part of the reactor; - activation energy of the two secondary reactions (E,,IR and Es2/R); - secondary kinetic constants at 1000 K (k,,,,,, and ks2,iW0& (since interrelation between activation energy and kinetic constant at 1000 K is lower than inter-relation between the activation energy and the pre-exponential factor); - ratio between the surface and the initial mass of a particle (S/M,,,). The optimization method was the Flexible Simplex [8].
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
30 (1994) 101-120
113
In order to carry out the calculations, the following data were considered in each experiment. (1) Volume of primary gases and tars generated at the temperature of the sand bed. These values were estimated from the data obtained in the Pyroprobe 1000. The quantity of heavy tars was calculated by difference, because the TG data provide values of the primary kinetic constants but not information about the amounts of tars and gases. An average molecular weight of tars of 320 kg kmol-’ was considered from an analysis of waxes obtained in the 500°C experiments. (2) Experimental total yield of gases. (3) Temperature of the fluidized sand bed. (4) Temperature profile in the upper part of the reactor. (5) Flux of helium and section of the reactor. (6) Weight of polyethylene discharged. (7) Average molecular weight of the gases analyzed. (8) Average molecular weight of the secondary gases, obtained from total gases analyzed in the fluidized bed reactor and the primary gases in the Pyroprobe 1000. (9) Value of the coefficients a and b of the primary reaction (Eq. l), calculated as G,,, and A,,,. The mean value of the coefficient a (where b = 1 - a), the average molecular weight of the gases analyzed, and the average molecular weight of the primary gases, were correlated with temperature. Figs. 3-5 show these variations. The correlations obtained were used in the simulation program.
a coefficient 0.4
0.3 -
0.2 -
0.1 -
0 400
500
600
700
800
900
11
Temperature CC)
Fig. 3. Variation of coefficient a with temperature.
114
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
Mean molecular weight of analyzed gases 60
50-
.
401
\
.
.
30
.
20 -
10 -
0’ 400
500
600
700
800
900
Ii00
Temperature CC) Fig. 4. Variation reactor.
of average
molecular
weight
with temperature
of analyzed
gases in the fluidized
bed
lean molecular weigM of primary gases 50
40
30
20
10
OL
400
500
600
700
800
900
1000
Temperature (%) Fig. 5. Variation 1000.
of average
molecular
weight
with temperature
of primary
gases
in the Pyroprobe
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
115
6. Analysis of the calculated parameters Table 1 shows the results of the correlations for the two models used. Table 1 also shows the objective function (OX) and the variation coefficient (V.C.), defined as
V.C. (%) =
J
O.F.
IZ experimenr-n
parameters x 1OO (47)
=P
where FeXpis the mean value of the experimental yields of total gases that were considered in the fitting (n experiments = 41). For the spherical particle used of 5 mm diameter with a density of 940 kg/m3, the value of the ratio S/A+ is 1.27 m*/kg. In the model, the parameter obtained varied between 6.01 and 6.32 m*/kg (depending on the model). It is observed that the value S/M,, obtained in the correlation is greater than the value S/MpO for the solid particle. This difference could be due to the fact that the polyethylene particles melt prior to their decomposition, and the ratio SM,,,, is therefore greater than in the solid state. The value of the modulus HP is, 5.2 x IO-* SK’ or 8.3 x lo-* s-i, depending on the model used. Considering a 5 mm average diameter particle (that has not melted), a density of 940 kg rne3, a value of C, of 3762 J/kg “C, values of U, = 153 and 244 J/s m* K can be obtained from models 1 and 2 respectively. The value of H, is 2.8 or 3.1 SK’ depending on the model. This value is high enough to rule out any significant differences between the temperature prior to and after the discharge of the sample. Fig. 6 shows the kinetic constants for some materials at different temperatures. The values represented correspond to those obtained by Antal [l] for tar cracking from cellulose, Diebold [2] for wood pyrolysis, Liden et al. [5] for biomass, Font et al. [3] for almond shells, and the present work. As can be seen in Fig. 6, the activation energies are similar to those obtained by Antal for the cracking of cellulose tars, assuming also two parallel reactions for the cracking of tars. Table 1 Values of optimum parameters and objective function Case
1 (three reactions)
S/M,, (m2/k) HP (s-l) Hs (s-l)
6.32 5.29 x 10-Z 3.01
k s*.1mK1 ‘s-:’ k;S.;m$g1
9.93 3.09
-J&/R (K) O.F.
V.C. (%)
23745 28397 0.141 10.67
2 (zero order) 6.01 8.28 x lo-* 2.79 11.17 2.85 23616 27935 0.094 8.72
116
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
,ooo KS(l/S) 1
fy&Qfp SXX
100
l
IO1 0. 0.1
~ ~ ~ ~ . 0.
oooxxx l
.
0.01
l
*.
0.001
-di& 0
X 0
.
.
0.0001
O.OOOQ1~” 0.8
”
”
”
0.9
”
”
I
.
”
”
1.2
1.1
1
0
X
0
0
.
.
X 0
.
1”” 1.3
”
1.4
1000/T (1000/K) l
Antal + Diebold
n Font
* Liden
X Present work reaction 1 0 Present work reaction 2
Fig. 6. Kinetic constants for tar decomposition.
Nevertheless, the ranges of the kinetic constant ksl and k,, are close to those proposed by Diebold [2], Liden et al. [ 51 and Font et al. [3], in the decomposition temperature range. Fig. 7 shows very good agreement between the yields calculated by model 2 vs. the experimental ones. Fig. 8 represents the calculated and experimental yields, together with the Pyroprobe results, vs. the calculated residence time. If this Figure is compared with Fig. 1, it can be seen that the V/m value is not totally proportional to the residence time. Fig. 7 shows less dispersion than that in Fig. 1. Nevertheless, this residence time is not representative of the tar cracking because the reactor is not isothermal. Similar results are obtained for model 1. In accordance with the proposed model and taking into account the optimized parameters, the variation of temperature and the extent of the primary reaction vs. time were simulated. Fig. 9 and 10 show the ratio total gas flow/helium flow, and
0
20
40
80
80
loo
Experimental yield
Fig. 7. Calculated vs. experimental yields of total gases.
117
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120 T profile: 300-500 =‘C
%Wgrrs
100
0
2
4
8 8 10 12 Residence time (s)
14
T profile: 300-600 “c
16
T profile: 300-700 “c loo%lotal@=
T profile: 30O-K10 “c 100%totalP
lo
60
0 80.
0
i”,
111 0
60
40
20
20
0
0
2
4
6 Resiince
‘11 0
8
10
12
14
OL 0
16
4
4
6
. 0
IO
12
14
’
16
Flesidence time (s)
time (a)
2
’
2
, , 6 8 10 12 Residence time (s) I
14
1 16
Fig. 8. Calculated and experimental yields, together with the Pyroprobe results, vs. calculated residence time.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
118
30 (1994) 101-120
T(K) 800
x (%) 100
800 80 - 700 80 40 20 -
/
0 15
20
25
30
35
40
time (s) Fig. 9. Temperature
and extent
of primary
reaction
vs. time of reaction.
251 20 .-
IO 5-
/
0 15
20
25
30
35
40
time (s) Fig. 10. Total
gas flow/helium
flow ratio vs. time of reaction.
the temperature evolution of a particle and extension of primary reaction, for run no. 26 (T = 7OO”C, 300 g sand and 1.487 g PE) with model 2. As can be seen from Fig. 10, the production of gases increases as the temperature increases, until all the PE is decomposed. This is due to the primary reaction, in which the gas production increases continuously with temperature, independent of the mass of the sample.
7. Conclusions On considering the kinetic law corresponding to the primary decomposition, obtained in TG runs, the experimental results obtained in the fluidized bed reactor with cracking in the upper part of the reactor fit satisfactorily to a model with two
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
119
parallel reactions: Secondary gases Primary tars and waxes :” < ” Solids, waxes and heavy tars The activation energies are around 196.3 and 232.2 kJ/mol for reactions 1 and 2 respectively. The values of the kinetic constant at 1000 K are around k sl,lmK = 9.93-11.17 s-l k s2,1mK = 3.09-2.85 s-r
depending on the kinetic model used. Acknowledgments
Support for this work was provided by CYCIT-Spain, Research project AMB931209. List of symbols
primary gases (kg)/HDPE decomposed (kg) mass fraction of primary tars and waxes formed mass fraction of tars and waxes that can be formed at time infinity primary tars and waxes (kg) /HDPE decomposed (kg) calorific capacity of polyethylene (J/kg “C) activation energy of the primary reaction i (kJ/mol) activation energy for the secondary reactions 1 and 2, respectively (kJ/mol) mass fraction of primary gases formed mass fraction of gases that can be formed at time infinity volume element of secondary gases formed in the reaction volume AVR(m3) optimized parameter related to the heat transfer to the particle (s-l) optimized parameter related to the heat transfer to the volatiles (s-l) kinetic constant of the primary reaction i (s-l) pre-exponential factor of the kinetic constant of the reaction i
GP G
AX
4 k,
(s-9
k,, 9 ks, k sl,lOOOK~
k s2,lOOO
K
kinetic constant for the secondary reactions 1 and 2, respectively (s-r) kinetic constant at 1000 K for the secondary reactions 1 and 2, respectively (s - ‘) molecular weight of primary tars (kg/kmol)
120
MGP MGS MPO
O.F. PE s Ati u, V.C. Vim VAP VAp,m VGP VGPm
AVi AV, A VW
J.A. Conesa ef al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
molecular weight of primary gases (kg/kmol) molecular weight of secondary gases (kg/kmol) initial mass of a particle (kg) objective function mass fraction of polyethylene not decomposed by primary reaction surface of PE exposed to the surrounding atmosphere (m’) time interval (s) heat transfer coefficient for the primary reaction (J/s m2 K) variation coefficient volume of the upper part of the reactor/mass of polyethylene discharged onto the bed (cm’/g) volume of tars and waxes formed at a given temperature (m’) volume of tars and waxes formed at a given temperature and at time infinity (m3) volume of gases formed at a given temperature (m3) volume of gases formed at a given temperature and at time infinity ( m3) volatiles generated by the primary in the time interval Ati (m’) volume of reaction element considered (m3) total volume of gases (primary + secondary) in a volume AVR Cm’)
VVP VVP,rn x,
YCdC j yexpj
volume of volatiles (gases + tars + waxes) (m3) volume of volatiles (gases + tars + waxes) at time infinity (m3) extent of secondary reaction calculated yield in experiment j experimental yield in experiment j
Greek letters PAP PGS z
density of primary tars and waxes (kg/m3) density of secondary gases (kg/m3) residence time (s)
References [l] M.J. Antal, Jr., Ind. Eng. Chem., Prod. Res. Dev., 22 (1983) 366-375. [2] J. Diebold, The Cracking Kinetics of Depolymerized Biomass Vapors in a Continuous Tubular Reactor, Ph.D. Thesis, School of Mines, Golden, CO, 1985. [3] R. Font, A. Marcilla, E. Verdu and J. Devesa, J. Anal. Appl. Pyrolysis, 27 (1993) 221. [4] A.N. Garcia, Estudio Termoquimico y Cinttico de la Pirolisis de Residuos Solidos Urbanos, Ph.D. Thesis, University of Alicante, Spain, 1993. [5] A.G. Liden, F. Berruti and D.S. Scott, Chem. Eng. Commun., 65 (1988) 207-221. [6] M.L. Boroson, J.B. Howard, J.P. Longwell and W.A. Peters, AIChE J., 35 (1989) 120-128. [7j J.A. Conesa, Estudio cinttico de la pirolisis de polietileno, Master’s Thesis, University of Alicante, Spain, 1994. [8] D.M. Himmelblau, Process Analysis Statistical Methods, Wiley, New York, 1968.
Journal of Analytical and Applied Pyrolysis 30 (1994) 101-120
ELSEVIER
Kinetic model of the pyrolysis of polyethylene fluidized bed reactor
in a
Juan A. Conesa *, Antonio Marcilla, Rafael Font Departmeni
of Chemical Engineering,
University
of Alicante, Apartado
99, Alicante,
Spain
Received 29 March 1994; accepted 28 April 1994
Abstract A kinetic study of the pyrolysis of polyethylene (HDPE) in a fluidized sand bed reactor was carried out. The HDPE particles were discharged onto the fluidized bed; in the upper part of the reactor, the volatiles evolved from primary reactions underwent secondary cracking reactions. A correlation model was applied to simulate the primary and secondary reactions, as well as the heat transfer process. The experimental yields of the total gases obtained in 41 runs performed at 500, 600, 700, 800 and 900°C fitted satisfactorily with the proposed model. The values of the kinetic parameters of the secondary reactions and the heat transfer coefficient from the bed to the sample were optimized. Keywords:
Fluidized bed reactor; Kinetic model; Polyethylene; Pyrolysis
1. Iotroduction The yields of the products obtained from a pyrolysis process are evolved from the raw material decomposition (primary reactions) and the reactions suffered by the primary volatiles (secondary reactions). The extension of the secondary reactions depends on the experimental equipment as well as on the operating conditions. It is well known that high residence times and high temperatures favor the secondary reactions.
* Corresponding
author. E-mail: [email protected].
0165-2370/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0165-2370(94)00806-C
102
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
The gas yield obtained from the primary reactions only is low, and the following decomposition of tars and waxes formed in these reactions by means of secondary reactions leads to the production of a great quantity of gases. There is not a lot of information in the literature about the kinetics of tar decomposition from lignocellulosic products. The most representative works on the thermal cracking of lignocellulosic tars are those presented by Antal [ 11, Diebold [2], Font et al. [3], Garcia [4], Liden et al. [5] and Boroson et al. [6]. No information about the cracking of tars and waxes from polyethylene has been found. The thermal decomposition of polyethylene is somewhat different from that of lignocellulosic materials, because the polyethylene melts before its decomposition, and the reaction can be treated as the decomposition of a liquid. From the polyethylene pyrolysis, the yields obtained at SOO”C, when the wax cracking takes place extensively, are the following: Total gas: 99.72% Ethane: 3.56% Propane: 0.40% Acetylene: 0.07% Butane: 0.32% Benzene: 5.84% Xylenes: 0.04%
Methane: 10.04% Ethylene: 25.30% Propylene: 15.61% Butylene: 6.54% Pentane: 5.05% Toluene: 2.19% Styrene: 0.04%
More details of the yields can be found elsewhere [7] and will be published in another paper. The thermal decomposition of polyethylene in a thermobalance was analyzed [7]. The heating rates used were 5, 25, 50 and lOO”C/min. The fitting of the experimental data of the four curves was very good using two different models. Three reaction scheme: k,
IfT
aG1+bA, P* p
a’G, + b’Az
In accordance with experimental results obtained in TG runds, reaction ( 1) and (3) are considered superficial, whilst reaction (2) is considered to occur in the bulk mass. Zero-order
PE 5
kinetic:
aGp+bAp
These models are discussed in the following sections. The aim of this paper is to develop and apply a kinetic model from the HDPE pyrolysis data obtained in a fluidized sand bed reactor. In the proposed model, primary and secondary reactions, the surface of the melted particles, and heat transfer between hot sand bed and sample have been considered.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
103
2. Experimental
Pyrolysis was carried out in a cylindrical 18/8 stainless steel reactor. The inert fluidized bed was sand of 0.105-0.210 mm particle size, calcinated at 900°C and washed by an acid solution of HCl. The inert gas used was helium at 99.999% purity. Heating was achieved by means of a refractory oven. The bed surface temperature was controlled automatically at five different temperatures: 500, 600, 700, 800 and 900°C. The reactor was not isothermal, showing a temperature gradient from the sand bed to the top of the reactor. Two chromel-alumel thermocouples were used to control and measure the temperature profile.
3. Results Data from 41 experiments of HDPE pyrolysis in a fluidized bed reactor at five different sand bed temperatures (500, 600, 700, 800 and 900°C) were used to calculate the kinetic parameters. The mass of sand and the weight of polyethylene discharged onto the hot bed were modified in each experiment. The mean residence time depended on the mass of volatiles produced and the volume of the upper part of the reactor. Fig. 1 shows the experimental yields of gases obtained vs. the magnitude V/m (volume of the upper part of the reactor, without sand/mass of the HDPE discharged onto the bed). When V is constant, the greater the value of m, the smaller the residence time. When m is constant, the greater the value of V, the greater the residence time. Note that although V/m is not directly proportional to the residence time of the volatiles in the non-isothermal upper part of the reactor, there is some relation between the ratio V/m and the residence time. In the experiments carried out at 500°C the principal product is a degraded HDPE, obtained in the solid state. The molecular weight of those HDPE waxes (analyzed by GPC) is around 300.
4. Kinetic study In the reactor used in this work two zones can be considered: (a) the fluidized sand bed where the sample is discharged and at the top of which the primary reactions take place; (b) a hot zone in the upper part of the reactor where the tars formed are cracked. The correlation model used to calculate the secondary kinetic parameters is similar to that presented by Font et al. [ 31 in their study of the pyrolysis of almond shells in a fluidized bed reactor. Nevertheless, some modifications in both the data treatment and the reaction scheme have been carried out on the new material used. The kinetic model is based on the following assumptions.
104
J.A. Conesa et al. I J. Anal. Appl. Pyrolysis
500’1:
%W(pS
100
30 (1994) 101-120
0
60
0 ___---0
0
40
20
0
200040006000aOw v/m Wg) 700%
wO%wp 0
lA 80
.
,,:”
_-+ 0
.i
0 20.
O0
20004aOOaooo8000
vhn Wg)
,
0’ 0
2000
4000 Vh (cc/e)
MOO
8000
Fig. 1. Variation ratio V/m.
of yield of total gas vs.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
105
30 (1994) 101-120
(1) As a consequence of the primary reaction undergone by the polyethylene sample discharged onto the bed, a small amount of volatiles (Al’,) is generated in a small interval (At,). The AV, formed is pushed by the helium flux through the hot zone above the fluidized bed. In this zone, the volatiles are cracked as a consequence of the secondary reactions, and the mixture expands. Over the next time interval (A&), another amount of volatiles (AV,) is generated. This is also pushed by the helium flux to the top of the reactor. AV, continues rising as its volatiles are pushed upwards by the helium flux and by the new volatiles increment AL’,. The distance of any volume element to the top of the sand bed is calculated taking into account the volume occupied by the elements under it, and this changes with time as a consequence of helium flow and the expansion of all the volumes due to the secondary reactions. This process continues until the total sample decomposition and 99.9% of volatiles evolved have left the reactor. Fig. 2 shows the steps considered. (2) In order to develop the mathematical model, both kinetic and heat transfer phenomena have been considered. The aspect that have been taken into account, as well as the basic expressions used in the model, are shown below: 4.2. I. Primary kinetic law The overall primary decomposition
reaction of HDPE can be represented by:
PE+aGp+bAp
.. u ...<. :: :.+Q jj::: I’
1H* t=o 0,
I t= At b
t=2
C
I He
He At
:t=3
At
d
Fig. 2. Steps in the pyrolysis process of HDPE in the fluidiid
t=Q At
e’ bed reactor.
106
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) IOI-I.?0
where PE, Gp and Ap refer to the polyethylene, primary gases and primary tars and waxes respectively. In the mathematical expressions, PE, Gp and A, are the mass fractions of the corresponding material PE (polyethylene), Gp (primary gas) and Ap (primary waxes and tars); the values a and b are the yield coefficients, i.e. product formed (kg) /PE reacted (kg). Obviously a+b=l
(2)
a = G,,,
(3)
b = A,,,,
(4)
and
where Gp_ and A,,, are weight fractions that can be formed when all the sample is decomposed (at time infinity). It is evident that a(P&
- PE) = G,
(5)
b(PE, - PE) = A,
(6)
Consequently,
at any time
AJG,, = b/a
(7)
PE,=l=PE+G,+A,
(8)
and -GF+
dPE dt
(9)
dPE 7 = -Awn
dPE dt
(10)
dPE
%_
dt --adt= dA
P=_b
dt
For the volume of gases formed by the primary reaction (G,), it can be written that
dVGp -=dt where V, and V~p,m For the conditions,
v
dPE GP.~ 7
(11)
is the volume of gases formed at any moment for a given temperature, is the maximum value of V, (at time infinity). tars and waxes formed (in the gaseous state at the experimental and as liquids .or solids at room temperature), it can be written that
dVA~ -=dt
v
dPE AP,~ dt
where VA, is the volume of tars formed and V,,,, time infinity) at a given temperature.
(12) is the maximum value of VAp (at
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
107
If Vvr is the total volume of volatiles (gases + primary tars and waxes), it can be written that (13)
v,, = VIZ,+ Y4r VVP,00
-
v,,,
+
(14)
vAp,m
From Eqs. (1 l), (12), (13), and (14), it can be deduced that -= dt
__v
dVVP
.-dPE V&‘,m dt
(15)
Eq. (15) is the one considered in the model, and applies to polyethylene decomposition. For the primary pyrolysis, two different models have been considered [7]: (a) Three reaction scheme: aG, + bA, k, LP*Ta’Gl+b’A, kz No difference in behavior is considered between gases Gi and GZ, and tars A, and A, as well as in their yields, directly from either P or P*. In this scheme
A, +&=A, G, +
(16)
G2 = G,
and
MdP=-kS1 ’
dt
p
(p + p*> -
k2PMo
0x=
(17)
P*
M dP* +k2J’Mo
-
k3S
cp
+
p*j
where S is the surface exposed to the surrounding atmosphere, MO is the initial mass of the sample, and the kinetic constants (k,, k2, k3) vary with the absolute temperature by the Arrhenius equation: ki = k, exp( - Ei /RT)
i=l,
2, 3
The overall equation for the polyethylene dPE -=k,x dt
(18) decomposition
can be written as
(1%
M,&+k3&&z
where PE is the amount of polyethylene (P + P*) present at any time. The constants obtained from TG experiments were the following [7]: ko, = 2.892 x 1019 s-’ me2 kg-’
E, = 171.1 (kJ/mol)
k 02 = 2 . 830 x 1013 s-i
E2 = 234.6 (kJ/mol)
ko3 = 2.349 x 16O s-l me2 kg-’
E3 = 195.8 (kJ/mol)
J.A. Conesa et al. /J. Anal. Appl. Pyrolysis
108
30 (1994) 101-120
(b) Zero order kinetic: kl PE aGp+bAp in which -d!+,;
(20) 0
and klo = 8.543 x 1018 s-r mm2 kg-’
E, = 164.3 kJ/mol
Note that in a TG apparatus the surface exposed to decomposition is known. Nevertheless, when the polyethylene sample is discharged onto the hot sand bed, the polyethylene melts prior to its decomposition and the surface exposed is not known. To account for this, the parameter exterior surface/initial mass of a particle (S/M,& is introduced into the model. This parameter has also been optimized. The TG results indicate that there is no great difference between the two models at the heating rates mentioned. Nevertheless, in this paper the two models have been tested, due to the fact that reaction (2) becomes more important at high heating rates. 4.2.2. Heat transfer between the. sand bed and the sample Heat transfer processes between the hot sand bed and the sample have been modeled taking into account the possible differences between bed temperature and sample temperature. A heat transfer coefficient (U,) has been included in the model to estimate the actual temperature of the primary decomposition. The expression used is as follows:
dTp dt
u,S
-c,
(21)
(T,,-T,)=H,!$(T,,-TJ P
where Tb is the temperature of the fluidized bed, Tp is the actual temperature of the sample at time t, and S is the external surface of the polyethylene. Owing to difficulties in modeling (especially for S), HP = U, S/M, C, is considered as a fitting parameter. Although the value of 17, can vary as a function of time, it has been considered constant throughout the process. The parameter HP, therefore, represents a simplification to calculate the heat transfer coefficient. 4.2.3. Secondary reaction G, (secondary gases) bAp :” < ” S, (solids, waxes and heavy tars)
(22)
According to the suggested model, it is considered that during a small time interval, a certain amount of primary gases and tars ( Vcr,o and VAp,o, respectively) is
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
109
generated as a consequence of primary reactions. These compounds are entrained by the helium flow to the exit of the reactor, undergoing cracking inside the reactor as a consequence of the secondary reaction. If the primary tar decomposition is given by Eq. (22), it can be written that 1 dAA, _ --_ AV, dz
(23)
where AV, is the volume reaction element considered, which rises throughout the reactor, containing: (a) a constant quantity of primary gases AG,,; (b) a quantity of untracked tars AA,; (c) a quantity of secondary gases AG, generated as a consequence of tar cracking; (d) a quantity of helium (function of the flux and the time interval considered). This volume element will vary as a consequence of the volatile expansion due to secondary reactions. If the evolution of this volume is known, the situation can be determined and its temperature, therefore, is obtained from the previously determined temperature profile. The integration limits of Eq. (23) are AA,, = AA,,,, when r = 0 (the volume element has been
generated as a consequence of the primary reaction) and AA, = AA,,,
when z = z, (the volume element leaves the reactor)
Eq. (23) can be written as
dAAP _ - +,I + kz) AA, dr
-
The quantity of untracked primary tars can be expressed as a function of the tenerated tars (AA,,) and of the reaction extension (X,): AA, = AA&
1 - X,)
(25)
From Eqs. (24) and (25):
2 =(k, + kd(
1 - X,)
Eq. (26) defines the kinetics of the secondary reaction as a function of the extent of reaction of the tars. If AV,, is the total volume of gases (primary + secondary) that are within a volume AVR considered, it can be written that AV,, = AVGp,o + AV,, + AV,,
(27)
and also AV~,_~_AA&l--s) PAP
(28) PAP
where pAp is the density of the primary tars.
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
110
30 (1994) 101-120
For each interval considered, at any temperature,
A&2%
it can be written that
(29) PGs
PGs
where pGs is the density of the secondary gases, and the ratio ksl /(k,, + ks2) represents secondary gases formed (kg)/primary tar formed (kg). Combining Eqs. (27) -( 29) :
AV,,,==AVG,,o+hAp30(1
-‘I+ PGs
PAP
AAp3o =
AvGp.0
(30)
+
Bearing in mind that AA,, A VA,, = d
(31)
PAP
and AGpo
(32)
AL,‘,,0 =A
PGP
Eq. (31) can be written as
( )k,
-A+AA,
o
AAp,o
k,, + ks2
PGs
AVW =
(AVGP,O
+
AVA,o)
1 +
-&
PAp AG,o d+d PGp
(33)
AA,, PAp
Since
AV,,, = AV,,,o+ AV,,,o
(34)
and defining
AA, ------+ cI=
o PGs
PAP AGP,O PGp
( AAP.0 PAp
(35)
J.A. Conesa et al. /J. Anal. Appl. Pyrolysis
Eq. (33) can be transformed AVv, = AJ&,(l+
30 (1994) 101-120
111
to
mx,)
(36)
Eq. (36) defines the expansion of total volatiles (primary plus secondary) as a consequence of the cracking of tars in the secondary reaction. Bearing in mind that by the primary reaction AG,,,o= (0)
A-%,,
(37)
and taking into account the molecular weights of the tars, primary gases and secondary-gases (MAP, MGp , Mos respectively), Eq. (35) can be rewritten as:
(38)
4.2.4. Heat transfer between the volatiles and the reactor wall The volatiles flow through the reactor from the bed to the top of the reactor. The temperature profile along the reactor was measured when only the inert gas flowed through it. This profile is a consequence of the heat transfer between the walls of the reactor and the gas which is flowing. The profile can be modified in the presence of volatiles. Bearing these aspects in mind a correction factor has been introduced for any volume:
where Tj is the real temperature of the volume considered, and TR is the reactor temperature according to the temperature profile measured at the position of the volume of volatiles.
5. Correlation of experimental data The experimental data of the total gas yield for 41 runs [7] were correlated by the suggested models. The objective function considered was
0.F. = i
(Yexpj- L&2
j=l
where the experimental yield was calculated as gas analyzed (g) sample (g)
yexpj = polyethylene
(41)
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
112
30 (1994) 101-120
The gases analyzed were methane, ethane, ethylene, propane, propylene, acetylene, butane, butylene, pentane, benzene, toluene, xylenes and styrene. The calculated yields according to the simulation program were obtained by the following equation:
Yca,cj = : A%, + i=l
I?A~p,cpsi
(42)
i=l
where the sum comprises all the intervals considered (i), and where AG,,,i and AY&~ are the quantities (g) of gases and primary tars generated in the “i” interval per gram of polyethylene discharged, respectively. The sum considers 150 intervals (it has been proved that the same result is obtained with a number of intervals greater than 150). The second part of the sum in Eq. (42) represents the quantity of gases generated from the primary tars:
and consequently
However, the mean volatile residence time can be defined as
where Vvp,i is the volume of total primary volatiles in the i interval, and I’,, = 5 i=l
Avv,i
(46)
In Eq. (25), ri is the time required by the element i to flow through the empty part of the reactor from its generation. Note that Z refers to the mean residence time of volatiles in the upper part of the reactor, where cracking takes place. This mean residence time of volatiles is different from the total mean residence time, which also includes the period of time from the discharge of the material to the generation of the different elements by the primary reactions. Eqs. (41) and (42) have been used to calculate the value of the objective function. The optimized variables were the following: - modulus HP, referring to the heat transfer sample-sand bed; - correction fractor H, of the temperature in the upper part of the reactor; - activation energy of the two secondary reactions (E,,IR and Es2/R); - secondary kinetic constants at 1000 K (k,,,,,, and ks2,iW0& (since interrelation between activation energy and kinetic constant at 1000 K is lower than inter-relation between the activation energy and the pre-exponential factor); - ratio between the surface and the initial mass of a particle (S/M,,,). The optimization method was the Flexible Simplex [8].
J.A. Conesa et al. / J. Anal. Appl. Pyrolysis
30 (1994) 101-120
113
In order to carry out the calculations, the following data were considered in each experiment. (1) Volume of primary gases and tars generated at the temperature of the sand bed. These values were estimated from the data obtained in the Pyroprobe 1000. The quantity of heavy tars was calculated by difference, because the TG data provide values of the primary kinetic constants but not information about the amounts of tars and gases. An average molecular weight of tars of 320 kg kmol-’ was considered from an analysis of waxes obtained in the 500°C experiments. (2) Experimental total yield of gases. (3) Temperature of the fluidized sand bed. (4) Temperature profile in the upper part of the reactor. (5) Flux of helium and section of the reactor. (6) Weight of polyethylene discharged. (7) Average molecular weight of the gases analyzed. (8) Average molecular weight of the secondary gases, obtained from total gases analyzed in the fluidized bed reactor and the primary gases in the Pyroprobe 1000. (9) Value of the coefficients a and b of the primary reaction (Eq. l), calculated as G,,, and A,,,. The mean value of the coefficient a (where b = 1 - a), the average molecular weight of the gases analyzed, and the average molecular weight of the primary gases, were correlated with temperature. Figs. 3-5 show these variations. The correlations obtained were used in the simulation program.
a coefficient 0.4
0.3 -
0.2 -
0.1 -
0 400
500
600
700
800
900
11
Temperature CC)
Fig. 3. Variation of coefficient a with temperature.
114
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
Mean molecular weight of analyzed gases 60
50-
.
401
\
.
.
30
.
20 -
10 -
0’ 400
500
600
700
800
900
Ii00
Temperature CC) Fig. 4. Variation reactor.
of average
molecular
weight
with temperature
of analyzed
gases in the fluidized
bed
lean molecular weigM of primary gases 50
40
30
20
10
OL
400
500
600
700
800
900
1000
Temperature (%) Fig. 5. Variation 1000.
of average
molecular
weight
with temperature
of primary
gases
in the Pyroprobe
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
115
6. Analysis of the calculated parameters Table 1 shows the results of the correlations for the two models used. Table 1 also shows the objective function (OX) and the variation coefficient (V.C.), defined as
V.C. (%) =
J
O.F.
IZ experimenr-n
parameters x 1OO (47)
=P
where FeXpis the mean value of the experimental yields of total gases that were considered in the fitting (n experiments = 41). For the spherical particle used of 5 mm diameter with a density of 940 kg/m3, the value of the ratio S/A+ is 1.27 m*/kg. In the model, the parameter obtained varied between 6.01 and 6.32 m*/kg (depending on the model). It is observed that the value S/M,, obtained in the correlation is greater than the value S/MpO for the solid particle. This difference could be due to the fact that the polyethylene particles melt prior to their decomposition, and the ratio SM,,,, is therefore greater than in the solid state. The value of the modulus HP is, 5.2 x IO-* SK’ or 8.3 x lo-* s-i, depending on the model used. Considering a 5 mm average diameter particle (that has not melted), a density of 940 kg rne3, a value of C, of 3762 J/kg “C, values of U, = 153 and 244 J/s m* K can be obtained from models 1 and 2 respectively. The value of H, is 2.8 or 3.1 SK’ depending on the model. This value is high enough to rule out any significant differences between the temperature prior to and after the discharge of the sample. Fig. 6 shows the kinetic constants for some materials at different temperatures. The values represented correspond to those obtained by Antal [l] for tar cracking from cellulose, Diebold [2] for wood pyrolysis, Liden et al. [5] for biomass, Font et al. [3] for almond shells, and the present work. As can be seen in Fig. 6, the activation energies are similar to those obtained by Antal for the cracking of cellulose tars, assuming also two parallel reactions for the cracking of tars. Table 1 Values of optimum parameters and objective function Case
1 (three reactions)
S/M,, (m2/k) HP (s-l) Hs (s-l)
6.32 5.29 x 10-Z 3.01
k s*.1mK1 ‘s-:’ k;S.;m$g1
9.93 3.09
-J&/R (K) O.F.
V.C. (%)
23745 28397 0.141 10.67
2 (zero order) 6.01 8.28 x lo-* 2.79 11.17 2.85 23616 27935 0.094 8.72
116
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
,ooo KS(l/S) 1
fy&Qfp SXX
100
l
IO1 0. 0.1
~ ~ ~ ~ . 0.
oooxxx l
.
0.01
l
*.
0.001
-di& 0
X 0
.
.
0.0001
O.OOOQ1~” 0.8
”
”
”
0.9
”
”
I
.
”
”
1.2
1.1
1
0
X
0
0
.
.
X 0
.
1”” 1.3
”
1.4
1000/T (1000/K) l
Antal + Diebold
n Font
* Liden
X Present work reaction 1 0 Present work reaction 2
Fig. 6. Kinetic constants for tar decomposition.
Nevertheless, the ranges of the kinetic constant ksl and k,, are close to those proposed by Diebold [2], Liden et al. [ 51 and Font et al. [3], in the decomposition temperature range. Fig. 7 shows very good agreement between the yields calculated by model 2 vs. the experimental ones. Fig. 8 represents the calculated and experimental yields, together with the Pyroprobe results, vs. the calculated residence time. If this Figure is compared with Fig. 1, it can be seen that the V/m value is not totally proportional to the residence time. Fig. 7 shows less dispersion than that in Fig. 1. Nevertheless, this residence time is not representative of the tar cracking because the reactor is not isothermal. Similar results are obtained for model 1. In accordance with the proposed model and taking into account the optimized parameters, the variation of temperature and the extent of the primary reaction vs. time were simulated. Fig. 9 and 10 show the ratio total gas flow/helium flow, and
0
20
40
80
80
loo
Experimental yield
Fig. 7. Calculated vs. experimental yields of total gases.
117
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120 T profile: 300-500 =‘C
%Wgrrs
100
0
2
4
8 8 10 12 Residence time (s)
14
T profile: 300-600 “c
16
T profile: 300-700 “c loo%lotal@=
T profile: 30O-K10 “c 100%totalP
lo
60
0 80.
0
i”,
111 0
60
40
20
20
0
0
2
4
6 Resiince
‘11 0
8
10
12
14
OL 0
16
4
4
6
. 0
IO
12
14
’
16
Flesidence time (s)
time (a)
2
’
2
, , 6 8 10 12 Residence time (s) I
14
1 16
Fig. 8. Calculated and experimental yields, together with the Pyroprobe results, vs. calculated residence time.
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
118
30 (1994) 101-120
T(K) 800
x (%) 100
800 80 - 700 80 40 20 -
/
0 15
20
25
30
35
40
time (s) Fig. 9. Temperature
and extent
of primary
reaction
vs. time of reaction.
251 20 .-
IO 5-
/
0 15
20
25
30
35
40
time (s) Fig. 10. Total
gas flow/helium
flow ratio vs. time of reaction.
the temperature evolution of a particle and extension of primary reaction, for run no. 26 (T = 7OO”C, 300 g sand and 1.487 g PE) with model 2. As can be seen from Fig. 10, the production of gases increases as the temperature increases, until all the PE is decomposed. This is due to the primary reaction, in which the gas production increases continuously with temperature, independent of the mass of the sample.
7. Conclusions On considering the kinetic law corresponding to the primary decomposition, obtained in TG runs, the experimental results obtained in the fluidized bed reactor with cracking in the upper part of the reactor fit satisfactorily to a model with two
J.A. Conesa et al. 1 J. Anal. Appl. Pyrolysis
30 (1994) 101-120
119
parallel reactions: Secondary gases Primary tars and waxes :” < ” Solids, waxes and heavy tars The activation energies are around 196.3 and 232.2 kJ/mol for reactions 1 and 2 respectively. The values of the kinetic constant at 1000 K are around k sl,lmK = 9.93-11.17 s-l k s2,1mK = 3.09-2.85 s-r
depending on the kinetic model used. Acknowledgments
Support for this work was provided by CYCIT-Spain, Research project AMB931209. List of symbols
primary gases (kg)/HDPE decomposed (kg) mass fraction of primary tars and waxes formed mass fraction of tars and waxes that can be formed at time infinity primary tars and waxes (kg) /HDPE decomposed (kg) calorific capacity of polyethylene (J/kg “C) activation energy of the primary reaction i (kJ/mol) activation energy for the secondary reactions 1 and 2, respectively (kJ/mol) mass fraction of primary gases formed mass fraction of gases that can be formed at time infinity volume element of secondary gases formed in the reaction volume AVR(m3) optimized parameter related to the heat transfer to the particle (s-l) optimized parameter related to the heat transfer to the volatiles (s-l) kinetic constant of the primary reaction i (s-l) pre-exponential factor of the kinetic constant of the reaction i
GP G
AX
4 k,
(s-9
k,, 9 ks, k sl,lOOOK~
k s2,lOOO
K
kinetic constant for the secondary reactions 1 and 2, respectively (s-r) kinetic constant at 1000 K for the secondary reactions 1 and 2, respectively (s - ‘) molecular weight of primary tars (kg/kmol)
120
MGP MGS MPO
O.F. PE s Ati u, V.C. Vim VAP VAp,m VGP VGPm
AVi AV, A VW
J.A. Conesa ef al. 1 J. Anal. Appl. Pyrolysis 30 (1994) 101-120
molecular weight of primary gases (kg/kmol) molecular weight of secondary gases (kg/kmol) initial mass of a particle (kg) objective function mass fraction of polyethylene not decomposed by primary reaction surface of PE exposed to the surrounding atmosphere (m’) time interval (s) heat transfer coefficient for the primary reaction (J/s m2 K) variation coefficient volume of the upper part of the reactor/mass of polyethylene discharged onto the bed (cm’/g) volume of tars and waxes formed at a given temperature (m’) volume of tars and waxes formed at a given temperature and at time infinity (m3) volume of gases formed at a given temperature (m3) volume of gases formed at a given temperature and at time infinity ( m3) volatiles generated by the primary in the time interval Ati (m’) volume of reaction element considered (m3) total volume of gases (primary + secondary) in a volume AVR Cm’)
VVP VVP,rn x,
YCdC j yexpj
volume of volatiles (gases + tars + waxes) (m3) volume of volatiles (gases + tars + waxes) at time infinity (m3) extent of secondary reaction calculated yield in experiment j experimental yield in experiment j
Greek letters PAP PGS z
density of primary tars and waxes (kg/m3) density of secondary gases (kg/m3) residence time (s)
References [l] M.J. Antal, Jr., Ind. Eng. Chem., Prod. Res. Dev., 22 (1983) 366-375. [2] J. Diebold, The Cracking Kinetics of Depolymerized Biomass Vapors in a Continuous Tubular Reactor, Ph.D. Thesis, School of Mines, Golden, CO, 1985. [3] R. Font, A. Marcilla, E. Verdu and J. Devesa, J. Anal. Appl. Pyrolysis, 27 (1993) 221. [4] A.N. Garcia, Estudio Termoquimico y Cinttico de la Pirolisis de Residuos Solidos Urbanos, Ph.D. Thesis, University of Alicante, Spain, 1993. [5] A.G. Liden, F. Berruti and D.S. Scott, Chem. Eng. Commun., 65 (1988) 207-221. [6] M.L. Boroson, J.B. Howard, J.P. Longwell and W.A. Peters, AIChE J., 35 (1989) 120-128. [7j J.A. Conesa, Estudio cinttico de la pirolisis de polietileno, Master’s Thesis, University of Alicante, Spain, 1994. [8] D.M. Himmelblau, Process Analysis Statistical Methods, Wiley, New York, 1968.