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Waste tyre pyrolysis: Modelling of a moving bed reactor
Waste Management 30 (2010) 2530–2536
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Waste tyre pyrolysis: Modelling of a moving bed reactor E. Aylón, A. Fernández-Colino, R. Murillo *, G. Grasa, M.V. Navarro, T. García, A.M. Mastral Instituto de Carboquímica, CSIC, M Luesma Castan 4, 50018 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Received 9 March 2010 Accepted 16 April 2010 Available online 26 May 2010
a b s t r a c t This paper describes the development of a new model for waste tyre pyrolysis in a moving bed reactor. This model comprises three different sub-models: a kinetic sub-model that predicts solid conversion in terms of reaction time and temperature, a heat transfer sub-model that calculates the temperature profile inside the particle and the energy flux from the surroundings to the tyre particles and, finally, a hydrodynamic model that predicts the solid flow pattern inside the reactor. These three sub-models have been integrated in order to develop a comprehensive reactor model. Experimental results were obtained in a continuous moving bed reactor and used to validate model predictions, with good approximation achieved between the experimental and simulated results. In addition, a parametric study of the model was carried out, which showed that tyre particle heating is clearly faster than average particle residence time inside the reactor. Therefore, this fast particle heating together with fast reaction kinetics enables total solid conversion to be achieved in this system in accordance with the predictive model. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction At the end of their useful life, tyres are considered a waste product. The massive disposal of tyres poses a major environmental problem. Since tyres are designed to withstand very difficult conditions, used tyres are almost indestructible. At the same time, their disposal in landfills can be seen as a waste of raw material and natural resources but even several operating problems for the management of landfill. Moreover, new legislative constraints mainly outlaw this practice in developed countries. Therefore, the management and treatment of used tyres should be addressed in a careful way so as to make the best use of them. Tyres are composed of a metal part, which can be easily removed by electromagnetic separators, and rubber with great potential for energy generation or the production of chemicals. Different strategies have been introduced to minimise the environmental impact of waste tyres that focus on lowering the number of tyres requiring disposal. For example, improvements in materials and manufacturing have made it possible to reduce the weight of tyres and to extend their life cycle. Despite the success of these practices, it is still necessary to find ways of reusing many waste tyres. Waste tyres have been used as physical barriers for roads and quays, and in the manufacture of different paving materials. However, given that these measures are not capable of dealing with the massive numbers of waste tyres being produced, thermal valorisation is emerging as a possible solution for reprocessing huge amounts of this material. The three main technologies * Corresponding author. Tel.: +34 976 733977; fax: +34 976 733318. E-mail address: [email protected] (R. Murillo). 0956-053X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2010.04.018
for thermal valorisation are pyrolysis, gasification and combustion. Pyrolysis is a thermochemical process performed under inert atmosphere, while gasification and combustion are performed under mild and severe oxidative conditions, respectively. Tyre pyrolysis is designed to recover valuable fractions clean and efficiently while minimising energy valorisation, as highlighted in the laws governing waste treatment. Several studies have been carried out in order to study the applicability of different reactor technologies to this process. The use of a thermobalance has been reported (Aylon et al., 2005; Chen and Qian, 2003; Leung and Wang, 1998; Senneca et al., 1999) in order to obtain kinetic information. Fluidised bed reactors (Conesa et al., 1996; Araki et al., 1979; Shu-Yii et al., 1997), batch reactors (Laresgoiti et al., 2004) and many configurations based on fixed bed reactors have also been reported (Gonzalez et al., 2001; Diez et al., 2005; Napoli et al., 1997; Aylón et al., 2008). However, there are few works regarding waste tyre processing in continuous reactors. Diez et al. (2005) used a moving bed reactor with a batch feeding system. The aim of the process was to perform total tyre combustion in a supplementary reactor where the gas and solid fractions were burnt together. Serrano et al. (2001) developed a laboratory scale reactor for polymer degradation, but it can be operated only up to 100 g/h. In all these references, different configurations and reactor designs are shown and report many experimental results. However, none of these papers develop a mathematical model to describe how the system behaves. The aim of this work is to develop a model to describe the performance of a moving bed reactor for waste tyre pyrolysis. A very important part of this work is to determine the solid flow pattern inside the reactor. For this purpose, digital image analysis has been
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Nomenclature ci cp C CA C0 C(t) D D/uL E(t) Eai f(X) FA F(t) H hcondk hconv hrad I Imax Imin koi ks L m m0 N ni
rubber component i concentration (%) solid heat capacity (J/(kg K)) tracer concentration in the calibration equation (%) reactant concentration (mol/m3) tracer concentration in the inlet flow (kg/(m3 s)) tracer concentration in the outlet flow (kg/(m3 s)) effective dispersion coefficient (m2/s) dispersion module exit age distribution function (s1) activation energy for component i (kJ/mol) overall reaction rate for N components (s1) reactant molar flow (mol/s) dimensionless tracer concentration output effective heat transfer coefficient (W/(m2 K)) conduction heat transfer coefficient (W/(m2 K)) convection heat transfer coefficient (W/(m2 K)) radiation heat transfer coefficient (W/(m2 K)) mean value in the grey scale luminance of a dark/coloured rubber mixture mean grey scale value of the coloured rubber mean grey scale value of the darkest solid (rubber tyre) frequency factor for component i (s1) thermal conductivity (W/(m K)) reactor length (m) tracer mass introduced in the reactor (kg) rubber mass inside the reactor (kg) nodes inside the particle to solve the heat transfer model order of reaction for component i
used. This technique is used in different fields of knowledge such as medicine, astronomy, geology and engineering (Domingo, 1994). The main advantage of digital images is that it is possible to submit them to mathematical analysis by means of a matrix of numbers that can be used in any kind of arithmetic calculation. A typical system for image analysis comprises a system to acquire images, a system to process images and a system to represent images. For example, image analysis of bulk powder has been used in the study of macroscopic mixing dynamics in vessels (Wightman et al., 1996; Chester et al., 1999) or fluidised beds (Lim et al., 1993; Grasa et al., 2004). In this paper, the treatment of digital images has been applied to moving bed reactor technology in order to study the distribution of solid residence times. A modification of an image analysis first proposed by Lim et al. (1993) and developed by Grasa et al. (2004) has been applied to calibrate the images and relate them to the solid concentration. 2. Experimental 2.1. Feedstock characteristics The raw material used for the pyrolysis experiments was a sample of tyre rubber shreds supplied by Prosum Plus S.L., a Spanish waste tyre recycling company. These shreds were a mixture produced from truck, tractor and car tyres. The average particle size was 2 mm. The ultimate and proximate analyses of the waste tyre sample are compiled in Table 1. 2.2. Pilot plant The pilot plant comprises four main parts: the feeding system, the reactor (moving bed reactor), the solid collecting system and the condensing system. These parts have been described in detail
tracer volumetric flow rate (m3/s) heat absorbed by the volatiles leaving the particle (W/ m2) r particle radial coordinate (m) (rA)dV disappearance of A by reaction (mol/s) R ideal gas law constant (8.314 J/mol K) Rp radius of particle (m) RTD residence time distribution S reactor section (m2) t reaction time (s) tm mean solid residence time (s) T reaction temperature (K) Tb bulk phase temperature (K) T0 initial particle temperature (K) particle temperature (K) Tp Ts particle surface temperature (K) u superficial velocity (m/s) wash weight of inorganic material present in the rubber material (kg) wf weight of converted solid (kg) wfixed carbon weight of carbon black in the sample (kg) weight of tyre fed to the system (kg) w0 X calculated conversion (%) Xexp experimental conversion (%) Xi conversion for sample component i (%) a thermal diffusivity (m2/s) r standard deviation q solid density (kg/m3)
q Q
elsewhere (Aylón et al., 2008). The feeding system has a total capacity of approximately 10 kg and allows the process to be carried out continuously under inert atmosphere using nitrogen as the carrier gas. The reactor is a moving bed reactor able to operate continuously and designed to process up to 15 kg/h of waste tyre. The tyre shreds move through the heated reactor to decompose into a gaseous product and a solid residue. The solid residue leaves the reactor by gravity, falling into a solid collecting system, and the gas reaches the condensing system by natural convection, helped by the carrier gas. The non-condensed pyrolysis gas is eventually conducted to a burner before it reaches the atmosphere. Four series of experiments were carried out in order to study the main operation variables: solid residence time, reaction temperature, mass flow rate and inert gas flow. Although, the product distribution and characteristics were studied thoroughly (Aylon et al., 2010) only the total conversion after the reaction are used in this paper to validate the developed model. The pyrolysis conditions for these experiments are given in Table 2. The experimental conversion (Xexp) was calculated according to Eq. (1), where w0 is the weight of tyre fed to the system, wf is the weight of the converted solid collected after reaction, wash is the weight of inorganic
Table 1 Ultimate and proximate analyses of the rubber tyre (as received). C (wt%) H (wt%) S (wt%) N (wt%)
81.72 6.54 1.87 0.55
% % % %
6.64 0.71 62.58 30.07
Ash Moisture Volatile matter Fixed carbon
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Table 2 Pyrolysis conditions used in the pilot plant and in the simulations. Experiment
T (K)
Solid residence time (min)
Mass flow rate (kg/h)
T 873 T 973 T 1073
873 973 1073
3.7 3.7 3.7
3.5 3.5 3.5
11.4 11.4 11.4
873 873 873 873 873
5.3 3.7 2.5 1.9 1.5
3.5 3.5 3.5 3.5 3.5
11.4 11.4 11.4 11.4 11.4
MFR 1 MFR 2 MFR 3
873 873 873
3.7 3.7 3.7
3.5 6 8
11.4 11.4 11.4
INERT 1 INERT 2 INERT 3
873 873 873
3.7 3.7 3.7
3.5 3.5 3.5
11.4 68.4 144.0
SRT SRT SRT SRT SRT
1 2 3 4 5
Inert gas flow (l N/h)
material accompanying the rubber material and wfixed carbon is the weight of carbon black in the sample (both values obtained from the proximate analysis).
X exp ¼
w0 wf w0 wash wfixed
ð1Þ carbon
2.3. Residence time distribution (RTD) A common practice to determine RTD is to carry out stimulus– response experiments in the system by means of inert tracers. Coloured tracers were used in this work to determine RTD of solids. Coloured tracers have been used in the past to measure solid flux,
0% Coloured rubber
40% Coloured rubber
or solid mixing patterns and its concentration has been measured trough image analysis in cold experiments. To adapt this image analysis technique to a given system, it is necessary to obtain a calibration equation to relate a property of the image with the tracer concentration. Among the different properties of the digital images, the grey scale value has been used by several authors in the literature (Lim et al., 1993; Grasa et al., 2004), and it was also chosen to construct the calibration equation in this work. Eight different proportions of raw rubber/coloured rubber (ranging from 0 to 1) were prepared and five photographs were taken of each mixture. To minimise any external influence during the analysis of the images (e.g. light and dust) two portions of raw rubber and coloured rubber were included together with the mixture in the photo (not shown in the photo). Fig. 1 shows an example of photos taken for different proportions of raw rubber/coloured rubber. The mean grey scale value was extracted from the mixtures, and from the individual portion of raw and coloured rubber in every photo. Eq. (2), previously used in other works (Lim et al., 1993; Grasa et al., 2004), is the calibration equation used to represent the experimental data in this work.
C¼
I Imin Imax Imin
ð2Þ
where C is the tracer concentration (%), I is the mean value in the grey scale luminance of the mixture, Imin is the mean grey scale value of the darkest solid (raw rubber) and Imax is the mean grey scale value of the coloured rubber. Four different cold experiments were carried out by varying the speed of the reactor screw (4.5, 5.7, 8.4 and 14 rpm) and maintaining the mass flow feed to the reactor. The tyre feeding rate was 3.5 kg/h, and the system ran until steady state was achieved. At that point, 1 kg of coloured rubber was introduced and the exit of the solids was controlled to determine the starting point for tak-
15% Coloured rubber
70% Coloured rubber
Fig. 1. Images of different proportions black rubber/coloured rubber used to determine RTD.
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1.2
ing samples at homogeneous intervals (in terms of time). Photos were taken of the solid samples collected at different times and the tracer concentration in the outlet flow (C(t)) was calculated by applying Eq. (2).
0.8
F(t)
3. Results and discussion
3.1.1. Flow sub-model The development of a flow sub-model is necessary to calculate the solid residence time inside the reactor. When the reactor behaviour is close to an ideal reactor (a plug flow reactor taking into account the geometry of the real system) the residence time for all the solid particles will be the same and the plug flow reactor design equation might be used. However, if the radial or longitudinal dispersion is not negligible, the assumption of plug flow will not be valid and it would be necessary to develop a more complex model. The dispersion module (D/uL) is the magnitude that determines the proximity to ideal reactor behaviour, where D is the effective dispersion module (m2/s), u is the superficial gas velocity (m/s) and L is the reactor length (m) (Levenspiel, 1999). Dispersion modules (D/uL) higher than 0.002 indicate that the ideal plug flow model is not valid, and that more complex models need to be implemented. This parameter can be calculated from the solid residence time distribution (RTD) inside the reactor, determined in this work by digital image analysis using coloured tracers. Step signal experiments have been chosen to determine solid RTD. F(t) curve (Eq. (3)) represents the non-dimensional tracer concentration (C(t)/C0) in the outlet flow versus time. This curve can be found by having the tracer concentration rise from zero to unity.
ð3Þ
where C0 is the tracer concentration in the inlet flow, q is the tracer volumetric flow and m is the tracer mass introduced to the system. The area over the F(t) curve represents tm, the particle mean residence time. The E(t) curve (exit age distribution) can be obtained by differentiating the F(t) curve (see Eq. (4)). Both curves are shown in Fig. 2.
dFðtÞ dt
EðtÞ ¼
ð4Þ
The variance (r2) of the E(t) curve is used to indicate the width or dispersion of the distribution:
r2 ¼
Z
1
2
ðt t m Þ EðtÞdt
ð5Þ
0
After determining r2, the dispersion module (D/uL) can be calculated from this parameter (Levenspiel, 1999). The results are shown in Table 3. It was found that the dispersion module depends on the solid linear velocity. It is observed that when the solid linear velocity increases, the dispersion module also increases and, therefore, the reactor flow model is not so similar to plug flow hypoth-
0.2 0
0
4
1
2
3
4
5
6
3
4
5
6
t (min)
4.7 rpm 5.7 rpm 8.4 rpm 14 rpm
3.5 3 2.5
E(t)
The aim of the mathematical model is to determine the particle conversion and the gas and solid residence time inside the reactor. The first stage in the development of the reactor model is to determine the solid flow pattern inside the reactor (flow sub-model). In addition, it would be necessary to have detailed information about the reaction kinetics (kinetic sub-model) and finally to develop a heat transfer model to estimate the particle temperature in terms of time (heat transfer sub-model). Eventually, all the information obtained from these sub-models, described below, needs to be integrated.
CðtÞ q CðtÞ ¼ C0 m
0.6 0.4
3.1. Model development
FðtÞ ¼
4.7 rpm 5.7 rpm 8.4 rpm 14 rpm
1
2 1.5 1 0.5 0
0
1
2
t (min)
Fig. 2. F(t) and E(t) curves for different reactor rates.
Table 3 Dispersion module for different solid linear velocity. rpm
r2 D/uL
4.7 0.706 0.00036
5.7 0.705 0.00040
8.4 0.700 0.00065
14 0.698 0.00235
esis. However, the results show that all the values found are below or close to 0.002. Since this value is the upper dispersion module value used to consider ideal plug flow behaviour, it can be concluded that our reactor could be reasonably modelled according to this flow pattern. 3.1.2. Kinetic sub-model The kinetic sub-model that will be integrated in the reactor model has been previously developed and described in detailed elsewhere (Aylon et al., 2005). This model considers that rubber tyre is comprised of four components that can be separately but simultaneously reacting. These components are: additives (nonpolymeric material added during the manufacturing process including oils, plasticizers, etc.), a first polymeric material (probably polybutadiene or styrene butadiene rubber), a second polymer (usually natural rubber) and the solid residue (the carbon black and mineral matter added as reinforcing material and filler). The general kinetic law for each single reaction is: Eai dX i ¼ koi e RT ð1 X i Þni dt
ð6Þ
where Xi is the solid fractional conversion for sample component i calculated according to Eq. (1), t is the reaction time, R is the gas universal constant, T is the reaction temperature, koi is the frequency factor for component i, Eai is the activation energy and ni is the reaction order for component i. It is assumed that the sample components decompose independently. Therefore, the overall pyrolysis rate for N reactions occurring in parallel can be described by the following equation:
E. Aylón et al. / Waste Management 30 (2010) 2530–2536
f ðXÞ ¼
X N N X Eai dX i ¼ ci ci koi e RT ð1 X i Þni dt i¼1 i¼1
ð7Þ
where ci is a coefficient that expresses the contribution of each single reaction to the mass total loss. Table 4 shows the kinetic parameters obtained from the model resolution described elsewhere (Aylon et al., 2005). 3.1.3. Heat transfer model The heat transfer model was developed in order to know the heating rate and the temperature particle profile. This temperature profile will be integrated into the reactor model at a later time and an average particle temperature will be used to evaluate the reaction rate inside the reactor. When a rubber particle enters the reactor, it heats up by means of three different mechanisms: conduction, convection and radiation transmission. However, the heating inside the particle takes place only by means of the conduction mechanism. Therefore, if a spherical shape is assumed for the rubber particles, the equation that regulates the process is:
@T p 1 @ @T p r2 a ¼ 2 r @r @t @r
a¼
ð8Þ
ks
ð9Þ
q cp
where Tp is the particle temperature (K), t is the time (s), r is the particle radial coordinate (m), a is the thermal diffusivity (m2/s), ks is the thermal conductivity (W/(m K)), q is the solid density (kg/m3) and cp is the solid heat capacity (J/(kg K)). The initial and boundary conditions for Eq. (8) are as follows, where Eq. (10) is the initial condition, Eq. (11) states that heat transferred to the outer particle surface is conducted into the material and Eq. (12) states that the particle is symmetric around the centre:
T p ðr; 0Þ ¼ T 0 ks
ð10Þ
@T p ¼ hðT b T s Þ Q @r r¼Rp
ð11Þ
@T p ¼0 @r r¼0
ð12Þ
where Rp is the particle radius (m), h is the heat transfer coefficient (W/(m2 K)), Tb is the bulk phase temperature (K), Ts is the particle surface temperature (K) and Q is the heat absorbed by the volatiles (W/m2) that leave the particle. The algorithm developed to solve the differential equation is based on the regressive differences method where the particle is divided into concentric sections or nodes. If the particle has been divided into N nodes, the resulting system of linear equations will be of the same order. Finally, an iterative method (SOR method (Burden and Faires, 1993)) was used for the resolution of the linear equations system. A sensitivity analysis was performed to determine the parameters that have a relevant influence on the heat transfer mechanism. The influence of particle diameter, solid physical properties and heat transfer coefficient were specifically studied.
Fig. 3 shows the evolution of the internal temperature at four different radial coordinates (N5, N10, N20 and N30) for particles of different diameters (2, 5 and 10 mm). It can be observed that for the particle diameter that will be used in the pilot plant, 2 mm, no radial temperature profile can be found inside it. Therefore, in the following simulations it would be possible to consider an average particle temperature. In the same way, similar results were found in all the simulations carried out modifying the physical properties of the solid (density, heat capacity and thermal conductivity). Fig. 4 shows the simulations considering that the particles are rubber, char and a mixture of both. It can be observed that it is possible to consider that the solid properties remain constant throughout the reaction and that an average value between the raw solid and the char can be used. Finally, the heat transfer coefficient h, represents the effective coefficient that includes the three possible heat transfer mechanisms (conduction, convection and radiation):
h ¼ hcond þ hconv þ hrad
ð13Þ
Simulations were carried out with values between 20 and 80 W/ (m2 K) for the effective heat transfer coefficient according to previous results by Larsen et al. (2006). Fig. 4 shows that the higher the coefficient the faster the particle heating; however the particle heating time in all of the studied range is much lower than the solid residence time (1.5 min was the minimum residence time for the rubber particles), including the case with a lower heat transfer coefficient. Therefore, a conservative value for this parameter of 20 W/(m2 K) was used in the following simulations. After this sensitivity study it can be concluded that it is possible to consider a uniform particle internal temperature, average solid properties between raw rubber and char and a heat transfer coefficient of 20 W/(m2 K). Therefore, these values will be used in the following simulations. Finally, taking into account the results obtained from the sensitivity analysis, the heating rates in the reactor were calculated for the working temperatures tested in the pilot plant (873, 973 and 1073 K). These heating rates will be used to evaluate the reaction kinetics. Hence, Fig. 5 shows the evolution of particle temperature with time where it can be observed that the heating rate is not a constant value and it would be necessary to introduce these profiles in the reactor model. 3.1.4. Reactor model The reactor model integrates all the process variables previously obtained with the sub-models. The model includes the reactor variables (length, diameter, characteristic screw dimensions, screw speed, reaction temperature and heating rate), the rubber
900 800 700
T (K)
2534
600
2 mm (N30, N20, N10, N5) 5 mm N30 5 mm N20 5 mm N10 5 mm N5 10 mm N30 10 mm N20 10 mm N10 10 mm N5
500 400 300
Table 4 Kinetic parameters for the rubber tyre devolatilization reaction.
Eai (kJ/mol) koi (s1) ni
200
Additives
Polymer 1
Polymer 2
70 1.00E + 04 2.8
212 8.20E + 14 1.4
265 3.20E + 17 1.9
0
20
40
60
80
100
t (s) Fig. 3. Evolution of the internal temperature for particles of different diameters at different nodes (N5, N10, N20, N30) dividing the particle.
2535
1000
1000
900
900
800
800
700
700
T (K)
T (K)
E. Aylón et al. / Waste Management 30 (2010) 2530–2536
600 500
600 500
400
400
Average density Rubber density Char density
300
Heat Capacity average Rubber Heat Capacity Char Heat Capacity
300 200
200 0
10
20
30
40
50
60
0
10
20
1000
1000
900
900
800
800
700
700
T (K)
T (K)
30
40
50
60
t (s)
t (s)
600 500
600 20 W/m2/K
500
400 300
40 W/m2/K
400
ks media ks neumático ks char
60 W/m2/K
300
200
80 W/m2/K
200 0
10
20
30
40
50
60
0
10
20
t (s)
30
40
50
60
t (s)
Fig. 4. Particle temperature evolution in terms of physical properties of the solid (density, heat capacity and thermal conductivity) and heat transfer coefficient.
that depends on the conversion (initially it corresponds to the rubber density and when it is completely converted, it coincides with char density (kg/m3)) and f(X) is the reaction rate, the sum of the decomposition rates for each one of the tyre components according to Eq. (7). A Runge–Kutta method was used to solve the differential equation. This method was applied first to the resolution of the kinetic equation obtaining f(X) and later to solve the reactor design equation. In addition, it was necessary to apply an interpolation method (Neville algorithm) when solving the kinetic equation, to evaluate f(X) in the specific values generated by the Runge–Kutta method applied to the reactor design equation.
1100 1000 900 700 600 500 400
Tb = 873 K Tb = 973 K Tb = 1073 K
300 200 0
10
20
30
40
50
60
70
80
t (s)
3.3. Model validation
Fig. 5. Evolution of particle temperature inside the reactor for different final reaction temperatures.
and char physical properties (density, heat capacity and thermal conductivity) and the kinetic parameters. According to the previous RTD results, the reactor behaviour is close to an ideal plug flow reactor. Therefore, the initial equation used is the design equation of a plug flow reactor adapted for this case. This equation is obtained from the mass balance carried out in steady state to a differential volume element:
F A ðF A þ dF A Þ ðr A ÞdV ¼ dV
dC A ¼0 dt
ð14Þ
The mass balance can be transformed into the following equation:
dX LS qðXÞ f ðXÞ ¼ dt tm m0
ð15Þ
Several simulations were performed by varying the main operation variables (temperature, solid residence time, mass flow rate and inert gas flow) in order to know their influence over the solid conversion. The experimental conditions used in the simulations
1
Conversion
T (K)
800
0.8 0.6
5.3 min 3.7 min 2.5 min 1.9 min 1.5 min
0.4 0.2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Length (m)
where L is the reactor length (m), S is the reactor section (m2), tm is the solid residence time inside the reactor, q(X) is the solid density
Fig. 6. Solid conversion evolution along the reactor for different solid residence time.
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Table 5 Comparison between experimental and simulated conversion. Experiment
Experimental conversion (%)
Calculated conversion (%)
T 873 T 973 T 1073
97.3 98.8 99.2
97.6 98.5 99.0
SRT SRT SRT SRT SRT
97.5 97.3 97.5 96.9 94.7
97.8 97.6 97.2 96.5 93.9
MFR 1 MFR 2 MFR 3
97.3 97.8 97.4
97.6 97.7 97.8
INERT 1 INERT 2 INERT 3
97.3 98.1 98.0
97.6 97.6 97.6
1 2 3 4 5
are shown in Table 2 and are the same conditions used in the pilot plant experiment, so it would be possible to validate the capacity of the model to predict the solid conversion. The evolution of conversion in terms of reactor length was obtained in all the simulations performed. As an example, Fig. 6 shows the conversion evolution of the waste tyre for the different solid residence times tested. For the entire range studied, the conversion reached at the end of the reactor is approximately complete, except for the lowest residence time (SRT 5, 1.5 min). In this case, the final conversion is lower owing to a faster advance of the solid inside the reactor. The final conversions obtained from the simulations were also compared with the experimental conversions calculated according to Eq. (1). Table 5 shows the calculated and experimental conversions when the process variables are modified. Good agreement is observed between the experimental results and those calculated in all the experiments performed. As an example, it is observed that the model can predict the conversion decrease produced at the lowest residence time (experiment SRT 5). 4. Conclusions The determination of the RTD inside the moving bed reactor by means of digital image analysis has demonstrated that the behaviour of the system is close to an ideal plug flow reactor. Therefore, the design equation of a plug flow reactor can be used to develop the mathematical model that predicts the solid conversion inside the reactor. It has been proven that this model, which integrates hydrodynamics, kinetics and heat transfer, is able to predict the final solid conversion at different experimental conditions and that it could be a valuable tool for scaling up the system.
Acknowledgment Authors would like to thank to the Spanish Ministry of Science and Innovation for their financial support (Project PET2008_0103). References Araki, T., Niikawa, H., Hosoda, H., Nishizaki, H., Mitsui, S., Endoh, K., Yoshida, K., 1979. Development of fluidized-bed pyrolysis of waste tyres. Resources, Conservation and Recycling 3, 155–164. Aylon, E., Callen, M.S., Lopez, J.M., Mastral, A.M., Murillo, R., Navarro, M.V., Stelmach, S., 2005. Assessment of tyre devolatilization kinetics. Journal of Analytical of Applied Pyrolysis 74, 259–264. Aylón, E., Fernández-Colino, A., Navarro, M.V., Murillo, R., García, T., Mastral, A.M., 2008. Waste tire pyrolysis: comparison between fixed bed reactor and moving bed reactor. Industrial Engineering Chemistry Research 47 (12), 4029–4033. Aylon, E., Fernández-Colino, A., Murillo, R., Navarro, M.V., García, T., Mastral, A.M., 2010. Valorisation of waste tyre by pyrolysis in a moving bed reactor. Waste Management 30, 1220–1224. Burden, R.L., Faires, J.D., 1993. Numerical Analysis. PWS Kent Publishing, Boston. Chen, F., Qian, J., 2003. Studies of the thermal degradation of waste rubber. Waste Management 23, 463–467. Chester, A.W., Kowalski, J.A., Coles, M.E., 1999. Mixing dynamics in catalyst impregnation in double-cone blenders. Powder Technology 102, 85–94. Conesa, J., Font, R., Marcilla, A., 1996. Gas from the pyrolysis of scrap tyres in a fluidized bed reactor. Energy and Fuels 10, 134–140. Diez, C., Sanchez, M.E., Haxaire, P., Martinez, O., Moran, A., 2005. Pyrolysis of tyres: a comparison of the results from a fixed-bed laboratory reactor and a pilot plant (rotary reactor). Journal of Analytical of Applied Pyrolysis 74, 254–258. Domingo, A., 1994. Tratamiento de imágenes, Ed. Anaya Multimedia. Gonzalez, J.F., Encinar, J.M., Canito, J.L., Rodriguez, J.J., 2001. Pyrolysis of automobile tyre waste. Influence of operating variables and kinetics study. Journal of Analytical of Applied Pyrolysis 58–59, 667–683. Grasa, G., Abanades, J.C., Oakey, J., 2004. Investigation of the solid flow between two fluidized beds connected by an orifice. Chemical Engineering Science 59, 5869– 5872. Laresgoiti, M.F., Caballero, B.M., de Marco, I., Torres, A., Cabrero, M.A., Chomon, M.J., 2004. Characterization of the liquid products obtained in tyre pyrolysis. Journal of Analytical of Applied Pyrolysis 71 (2), 917–934. Larsen, M.B., Schultz, L., Glarborg, P., Skaarup-Jensen, L., Dam-Johansen, K., Frandsen, F., Henriksen, U., 2006. Devolatilization characteristics of large particles of tyre rubber under combustion conditions. Fuel 85, 1335–1345. Leung, D.Y.C., Wang, C.L., 1998. Kinetic study of scrap pyrolysis and combustion. Journal of Analytical of Applied Pyrolysis 45, 153–169. Levenspiel, O., 1999. Chemical Reaction Engineering, third ed. John Wiley and Sons. Lim, K.S., Gururajan, V.S., Agarwal, P.K., 1993. Mixing of homogenous solids in bubbling fluidized beds: theoretical modelling and experimental investigation using digital image analysis. Chemical Engineering Science 48 (12), 2251–2265. Napoli, A., Soudais, Y., Lecomte, D., Castillo, S., 1997. Scrap tyre pyrolysis: are the effluents valuable products? Journal of Analytical of Applied Pyrolysis 40–41, 373–382. Senneca, O., Salatino, P., Chirone, R., 1999. A fast heating-rate thermogravimetric study of the pyrolysis of scrap tyres. Fuel 78, 1575–1581. Serrano, D.P., Aguado, J., Escola, J.M., Garagorri, E., 2001. Conversion of low density polyethylene into petrochemical feedstocks using a continuous screw kiln reactor. Journal of Analytical of Applied Pyrolysis 58–59, 789–801. Shu-Yii, W., Mao-Feng, S., Baeyens, J., 1997. The fluidized bed pyrolysis of shredded tyres: the influence of carbon particles, humidity and temperature on the hydrodynamics. Powder and Technology 93, 283–290. Wightman, C., Muzzio, F., Wilder, J., 1996. A quantitative image analysis method for characterising mixtures of granular materials. Powder Technology 89, 165–176.
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Waste Management journal homepage: www.elsevier.com/locate/wasman
Waste tyre pyrolysis: Modelling of a moving bed reactor E. Aylón, A. Fernández-Colino, R. Murillo *, G. Grasa, M.V. Navarro, T. García, A.M. Mastral Instituto de Carboquímica, CSIC, M Luesma Castan 4, 50018 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Received 9 March 2010 Accepted 16 April 2010 Available online 26 May 2010
a b s t r a c t This paper describes the development of a new model for waste tyre pyrolysis in a moving bed reactor. This model comprises three different sub-models: a kinetic sub-model that predicts solid conversion in terms of reaction time and temperature, a heat transfer sub-model that calculates the temperature profile inside the particle and the energy flux from the surroundings to the tyre particles and, finally, a hydrodynamic model that predicts the solid flow pattern inside the reactor. These three sub-models have been integrated in order to develop a comprehensive reactor model. Experimental results were obtained in a continuous moving bed reactor and used to validate model predictions, with good approximation achieved between the experimental and simulated results. In addition, a parametric study of the model was carried out, which showed that tyre particle heating is clearly faster than average particle residence time inside the reactor. Therefore, this fast particle heating together with fast reaction kinetics enables total solid conversion to be achieved in this system in accordance with the predictive model. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction At the end of their useful life, tyres are considered a waste product. The massive disposal of tyres poses a major environmental problem. Since tyres are designed to withstand very difficult conditions, used tyres are almost indestructible. At the same time, their disposal in landfills can be seen as a waste of raw material and natural resources but even several operating problems for the management of landfill. Moreover, new legislative constraints mainly outlaw this practice in developed countries. Therefore, the management and treatment of used tyres should be addressed in a careful way so as to make the best use of them. Tyres are composed of a metal part, which can be easily removed by electromagnetic separators, and rubber with great potential for energy generation or the production of chemicals. Different strategies have been introduced to minimise the environmental impact of waste tyres that focus on lowering the number of tyres requiring disposal. For example, improvements in materials and manufacturing have made it possible to reduce the weight of tyres and to extend their life cycle. Despite the success of these practices, it is still necessary to find ways of reusing many waste tyres. Waste tyres have been used as physical barriers for roads and quays, and in the manufacture of different paving materials. However, given that these measures are not capable of dealing with the massive numbers of waste tyres being produced, thermal valorisation is emerging as a possible solution for reprocessing huge amounts of this material. The three main technologies * Corresponding author. Tel.: +34 976 733977; fax: +34 976 733318. E-mail address: [email protected] (R. Murillo). 0956-053X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2010.04.018
for thermal valorisation are pyrolysis, gasification and combustion. Pyrolysis is a thermochemical process performed under inert atmosphere, while gasification and combustion are performed under mild and severe oxidative conditions, respectively. Tyre pyrolysis is designed to recover valuable fractions clean and efficiently while minimising energy valorisation, as highlighted in the laws governing waste treatment. Several studies have been carried out in order to study the applicability of different reactor technologies to this process. The use of a thermobalance has been reported (Aylon et al., 2005; Chen and Qian, 2003; Leung and Wang, 1998; Senneca et al., 1999) in order to obtain kinetic information. Fluidised bed reactors (Conesa et al., 1996; Araki et al., 1979; Shu-Yii et al., 1997), batch reactors (Laresgoiti et al., 2004) and many configurations based on fixed bed reactors have also been reported (Gonzalez et al., 2001; Diez et al., 2005; Napoli et al., 1997; Aylón et al., 2008). However, there are few works regarding waste tyre processing in continuous reactors. Diez et al. (2005) used a moving bed reactor with a batch feeding system. The aim of the process was to perform total tyre combustion in a supplementary reactor where the gas and solid fractions were burnt together. Serrano et al. (2001) developed a laboratory scale reactor for polymer degradation, but it can be operated only up to 100 g/h. In all these references, different configurations and reactor designs are shown and report many experimental results. However, none of these papers develop a mathematical model to describe how the system behaves. The aim of this work is to develop a model to describe the performance of a moving bed reactor for waste tyre pyrolysis. A very important part of this work is to determine the solid flow pattern inside the reactor. For this purpose, digital image analysis has been
E. Aylón et al. / Waste Management 30 (2010) 2530–2536
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Nomenclature ci cp C CA C0 C(t) D D/uL E(t) Eai f(X) FA F(t) H hcondk hconv hrad I Imax Imin koi ks L m m0 N ni
rubber component i concentration (%) solid heat capacity (J/(kg K)) tracer concentration in the calibration equation (%) reactant concentration (mol/m3) tracer concentration in the inlet flow (kg/(m3 s)) tracer concentration in the outlet flow (kg/(m3 s)) effective dispersion coefficient (m2/s) dispersion module exit age distribution function (s1) activation energy for component i (kJ/mol) overall reaction rate for N components (s1) reactant molar flow (mol/s) dimensionless tracer concentration output effective heat transfer coefficient (W/(m2 K)) conduction heat transfer coefficient (W/(m2 K)) convection heat transfer coefficient (W/(m2 K)) radiation heat transfer coefficient (W/(m2 K)) mean value in the grey scale luminance of a dark/coloured rubber mixture mean grey scale value of the coloured rubber mean grey scale value of the darkest solid (rubber tyre) frequency factor for component i (s1) thermal conductivity (W/(m K)) reactor length (m) tracer mass introduced in the reactor (kg) rubber mass inside the reactor (kg) nodes inside the particle to solve the heat transfer model order of reaction for component i
used. This technique is used in different fields of knowledge such as medicine, astronomy, geology and engineering (Domingo, 1994). The main advantage of digital images is that it is possible to submit them to mathematical analysis by means of a matrix of numbers that can be used in any kind of arithmetic calculation. A typical system for image analysis comprises a system to acquire images, a system to process images and a system to represent images. For example, image analysis of bulk powder has been used in the study of macroscopic mixing dynamics in vessels (Wightman et al., 1996; Chester et al., 1999) or fluidised beds (Lim et al., 1993; Grasa et al., 2004). In this paper, the treatment of digital images has been applied to moving bed reactor technology in order to study the distribution of solid residence times. A modification of an image analysis first proposed by Lim et al. (1993) and developed by Grasa et al. (2004) has been applied to calibrate the images and relate them to the solid concentration. 2. Experimental 2.1. Feedstock characteristics The raw material used for the pyrolysis experiments was a sample of tyre rubber shreds supplied by Prosum Plus S.L., a Spanish waste tyre recycling company. These shreds were a mixture produced from truck, tractor and car tyres. The average particle size was 2 mm. The ultimate and proximate analyses of the waste tyre sample are compiled in Table 1. 2.2. Pilot plant The pilot plant comprises four main parts: the feeding system, the reactor (moving bed reactor), the solid collecting system and the condensing system. These parts have been described in detail
tracer volumetric flow rate (m3/s) heat absorbed by the volatiles leaving the particle (W/ m2) r particle radial coordinate (m) (rA)dV disappearance of A by reaction (mol/s) R ideal gas law constant (8.314 J/mol K) Rp radius of particle (m) RTD residence time distribution S reactor section (m2) t reaction time (s) tm mean solid residence time (s) T reaction temperature (K) Tb bulk phase temperature (K) T0 initial particle temperature (K) particle temperature (K) Tp Ts particle surface temperature (K) u superficial velocity (m/s) wash weight of inorganic material present in the rubber material (kg) wf weight of converted solid (kg) wfixed carbon weight of carbon black in the sample (kg) weight of tyre fed to the system (kg) w0 X calculated conversion (%) Xexp experimental conversion (%) Xi conversion for sample component i (%) a thermal diffusivity (m2/s) r standard deviation q solid density (kg/m3)
q Q
elsewhere (Aylón et al., 2008). The feeding system has a total capacity of approximately 10 kg and allows the process to be carried out continuously under inert atmosphere using nitrogen as the carrier gas. The reactor is a moving bed reactor able to operate continuously and designed to process up to 15 kg/h of waste tyre. The tyre shreds move through the heated reactor to decompose into a gaseous product and a solid residue. The solid residue leaves the reactor by gravity, falling into a solid collecting system, and the gas reaches the condensing system by natural convection, helped by the carrier gas. The non-condensed pyrolysis gas is eventually conducted to a burner before it reaches the atmosphere. Four series of experiments were carried out in order to study the main operation variables: solid residence time, reaction temperature, mass flow rate and inert gas flow. Although, the product distribution and characteristics were studied thoroughly (Aylon et al., 2010) only the total conversion after the reaction are used in this paper to validate the developed model. The pyrolysis conditions for these experiments are given in Table 2. The experimental conversion (Xexp) was calculated according to Eq. (1), where w0 is the weight of tyre fed to the system, wf is the weight of the converted solid collected after reaction, wash is the weight of inorganic
Table 1 Ultimate and proximate analyses of the rubber tyre (as received). C (wt%) H (wt%) S (wt%) N (wt%)
81.72 6.54 1.87 0.55
% % % %
6.64 0.71 62.58 30.07
Ash Moisture Volatile matter Fixed carbon
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Table 2 Pyrolysis conditions used in the pilot plant and in the simulations. Experiment
T (K)
Solid residence time (min)
Mass flow rate (kg/h)
T 873 T 973 T 1073
873 973 1073
3.7 3.7 3.7
3.5 3.5 3.5
11.4 11.4 11.4
873 873 873 873 873
5.3 3.7 2.5 1.9 1.5
3.5 3.5 3.5 3.5 3.5
11.4 11.4 11.4 11.4 11.4
MFR 1 MFR 2 MFR 3
873 873 873
3.7 3.7 3.7
3.5 6 8
11.4 11.4 11.4
INERT 1 INERT 2 INERT 3
873 873 873
3.7 3.7 3.7
3.5 3.5 3.5
11.4 68.4 144.0
SRT SRT SRT SRT SRT
1 2 3 4 5
Inert gas flow (l N/h)
material accompanying the rubber material and wfixed carbon is the weight of carbon black in the sample (both values obtained from the proximate analysis).
X exp ¼
w0 wf w0 wash wfixed
ð1Þ carbon
2.3. Residence time distribution (RTD) A common practice to determine RTD is to carry out stimulus– response experiments in the system by means of inert tracers. Coloured tracers were used in this work to determine RTD of solids. Coloured tracers have been used in the past to measure solid flux,
0% Coloured rubber
40% Coloured rubber
or solid mixing patterns and its concentration has been measured trough image analysis in cold experiments. To adapt this image analysis technique to a given system, it is necessary to obtain a calibration equation to relate a property of the image with the tracer concentration. Among the different properties of the digital images, the grey scale value has been used by several authors in the literature (Lim et al., 1993; Grasa et al., 2004), and it was also chosen to construct the calibration equation in this work. Eight different proportions of raw rubber/coloured rubber (ranging from 0 to 1) were prepared and five photographs were taken of each mixture. To minimise any external influence during the analysis of the images (e.g. light and dust) two portions of raw rubber and coloured rubber were included together with the mixture in the photo (not shown in the photo). Fig. 1 shows an example of photos taken for different proportions of raw rubber/coloured rubber. The mean grey scale value was extracted from the mixtures, and from the individual portion of raw and coloured rubber in every photo. Eq. (2), previously used in other works (Lim et al., 1993; Grasa et al., 2004), is the calibration equation used to represent the experimental data in this work.
C¼
I Imin Imax Imin
ð2Þ
where C is the tracer concentration (%), I is the mean value in the grey scale luminance of the mixture, Imin is the mean grey scale value of the darkest solid (raw rubber) and Imax is the mean grey scale value of the coloured rubber. Four different cold experiments were carried out by varying the speed of the reactor screw (4.5, 5.7, 8.4 and 14 rpm) and maintaining the mass flow feed to the reactor. The tyre feeding rate was 3.5 kg/h, and the system ran until steady state was achieved. At that point, 1 kg of coloured rubber was introduced and the exit of the solids was controlled to determine the starting point for tak-
15% Coloured rubber
70% Coloured rubber
Fig. 1. Images of different proportions black rubber/coloured rubber used to determine RTD.
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E. Aylón et al. / Waste Management 30 (2010) 2530–2536
1.2
ing samples at homogeneous intervals (in terms of time). Photos were taken of the solid samples collected at different times and the tracer concentration in the outlet flow (C(t)) was calculated by applying Eq. (2).
0.8
F(t)
3. Results and discussion
3.1.1. Flow sub-model The development of a flow sub-model is necessary to calculate the solid residence time inside the reactor. When the reactor behaviour is close to an ideal reactor (a plug flow reactor taking into account the geometry of the real system) the residence time for all the solid particles will be the same and the plug flow reactor design equation might be used. However, if the radial or longitudinal dispersion is not negligible, the assumption of plug flow will not be valid and it would be necessary to develop a more complex model. The dispersion module (D/uL) is the magnitude that determines the proximity to ideal reactor behaviour, where D is the effective dispersion module (m2/s), u is the superficial gas velocity (m/s) and L is the reactor length (m) (Levenspiel, 1999). Dispersion modules (D/uL) higher than 0.002 indicate that the ideal plug flow model is not valid, and that more complex models need to be implemented. This parameter can be calculated from the solid residence time distribution (RTD) inside the reactor, determined in this work by digital image analysis using coloured tracers. Step signal experiments have been chosen to determine solid RTD. F(t) curve (Eq. (3)) represents the non-dimensional tracer concentration (C(t)/C0) in the outlet flow versus time. This curve can be found by having the tracer concentration rise from zero to unity.
ð3Þ
where C0 is the tracer concentration in the inlet flow, q is the tracer volumetric flow and m is the tracer mass introduced to the system. The area over the F(t) curve represents tm, the particle mean residence time. The E(t) curve (exit age distribution) can be obtained by differentiating the F(t) curve (see Eq. (4)). Both curves are shown in Fig. 2.
dFðtÞ dt
EðtÞ ¼
ð4Þ
The variance (r2) of the E(t) curve is used to indicate the width or dispersion of the distribution:
r2 ¼
Z
1
2
ðt t m Þ EðtÞdt
ð5Þ
0
After determining r2, the dispersion module (D/uL) can be calculated from this parameter (Levenspiel, 1999). The results are shown in Table 3. It was found that the dispersion module depends on the solid linear velocity. It is observed that when the solid linear velocity increases, the dispersion module also increases and, therefore, the reactor flow model is not so similar to plug flow hypoth-
0.2 0
0
4
1
2
3
4
5
6
3
4
5
6
t (min)
4.7 rpm 5.7 rpm 8.4 rpm 14 rpm
3.5 3 2.5
E(t)
The aim of the mathematical model is to determine the particle conversion and the gas and solid residence time inside the reactor. The first stage in the development of the reactor model is to determine the solid flow pattern inside the reactor (flow sub-model). In addition, it would be necessary to have detailed information about the reaction kinetics (kinetic sub-model) and finally to develop a heat transfer model to estimate the particle temperature in terms of time (heat transfer sub-model). Eventually, all the information obtained from these sub-models, described below, needs to be integrated.
CðtÞ q CðtÞ ¼ C0 m
0.6 0.4
3.1. Model development
FðtÞ ¼
4.7 rpm 5.7 rpm 8.4 rpm 14 rpm
1
2 1.5 1 0.5 0
0
1
2
t (min)
Fig. 2. F(t) and E(t) curves for different reactor rates.
Table 3 Dispersion module for different solid linear velocity. rpm
r2 D/uL
4.7 0.706 0.00036
5.7 0.705 0.00040
8.4 0.700 0.00065
14 0.698 0.00235
esis. However, the results show that all the values found are below or close to 0.002. Since this value is the upper dispersion module value used to consider ideal plug flow behaviour, it can be concluded that our reactor could be reasonably modelled according to this flow pattern. 3.1.2. Kinetic sub-model The kinetic sub-model that will be integrated in the reactor model has been previously developed and described in detailed elsewhere (Aylon et al., 2005). This model considers that rubber tyre is comprised of four components that can be separately but simultaneously reacting. These components are: additives (nonpolymeric material added during the manufacturing process including oils, plasticizers, etc.), a first polymeric material (probably polybutadiene or styrene butadiene rubber), a second polymer (usually natural rubber) and the solid residue (the carbon black and mineral matter added as reinforcing material and filler). The general kinetic law for each single reaction is: Eai dX i ¼ koi e RT ð1 X i Þni dt
ð6Þ
where Xi is the solid fractional conversion for sample component i calculated according to Eq. (1), t is the reaction time, R is the gas universal constant, T is the reaction temperature, koi is the frequency factor for component i, Eai is the activation energy and ni is the reaction order for component i. It is assumed that the sample components decompose independently. Therefore, the overall pyrolysis rate for N reactions occurring in parallel can be described by the following equation:
E. Aylón et al. / Waste Management 30 (2010) 2530–2536
f ðXÞ ¼
X N N X Eai dX i ¼ ci ci koi e RT ð1 X i Þni dt i¼1 i¼1
ð7Þ
where ci is a coefficient that expresses the contribution of each single reaction to the mass total loss. Table 4 shows the kinetic parameters obtained from the model resolution described elsewhere (Aylon et al., 2005). 3.1.3. Heat transfer model The heat transfer model was developed in order to know the heating rate and the temperature particle profile. This temperature profile will be integrated into the reactor model at a later time and an average particle temperature will be used to evaluate the reaction rate inside the reactor. When a rubber particle enters the reactor, it heats up by means of three different mechanisms: conduction, convection and radiation transmission. However, the heating inside the particle takes place only by means of the conduction mechanism. Therefore, if a spherical shape is assumed for the rubber particles, the equation that regulates the process is:
@T p 1 @ @T p r2 a ¼ 2 r @r @t @r
a¼
ð8Þ
ks
ð9Þ
q cp
where Tp is the particle temperature (K), t is the time (s), r is the particle radial coordinate (m), a is the thermal diffusivity (m2/s), ks is the thermal conductivity (W/(m K)), q is the solid density (kg/m3) and cp is the solid heat capacity (J/(kg K)). The initial and boundary conditions for Eq. (8) are as follows, where Eq. (10) is the initial condition, Eq. (11) states that heat transferred to the outer particle surface is conducted into the material and Eq. (12) states that the particle is symmetric around the centre:
T p ðr; 0Þ ¼ T 0 ks
ð10Þ
@T p ¼ hðT b T s Þ Q @r r¼Rp
ð11Þ
@T p ¼0 @r r¼0
ð12Þ
where Rp is the particle radius (m), h is the heat transfer coefficient (W/(m2 K)), Tb is the bulk phase temperature (K), Ts is the particle surface temperature (K) and Q is the heat absorbed by the volatiles (W/m2) that leave the particle. The algorithm developed to solve the differential equation is based on the regressive differences method where the particle is divided into concentric sections or nodes. If the particle has been divided into N nodes, the resulting system of linear equations will be of the same order. Finally, an iterative method (SOR method (Burden and Faires, 1993)) was used for the resolution of the linear equations system. A sensitivity analysis was performed to determine the parameters that have a relevant influence on the heat transfer mechanism. The influence of particle diameter, solid physical properties and heat transfer coefficient were specifically studied.
Fig. 3 shows the evolution of the internal temperature at four different radial coordinates (N5, N10, N20 and N30) for particles of different diameters (2, 5 and 10 mm). It can be observed that for the particle diameter that will be used in the pilot plant, 2 mm, no radial temperature profile can be found inside it. Therefore, in the following simulations it would be possible to consider an average particle temperature. In the same way, similar results were found in all the simulations carried out modifying the physical properties of the solid (density, heat capacity and thermal conductivity). Fig. 4 shows the simulations considering that the particles are rubber, char and a mixture of both. It can be observed that it is possible to consider that the solid properties remain constant throughout the reaction and that an average value between the raw solid and the char can be used. Finally, the heat transfer coefficient h, represents the effective coefficient that includes the three possible heat transfer mechanisms (conduction, convection and radiation):
h ¼ hcond þ hconv þ hrad
ð13Þ
Simulations were carried out with values between 20 and 80 W/ (m2 K) for the effective heat transfer coefficient according to previous results by Larsen et al. (2006). Fig. 4 shows that the higher the coefficient the faster the particle heating; however the particle heating time in all of the studied range is much lower than the solid residence time (1.5 min was the minimum residence time for the rubber particles), including the case with a lower heat transfer coefficient. Therefore, a conservative value for this parameter of 20 W/(m2 K) was used in the following simulations. After this sensitivity study it can be concluded that it is possible to consider a uniform particle internal temperature, average solid properties between raw rubber and char and a heat transfer coefficient of 20 W/(m2 K). Therefore, these values will be used in the following simulations. Finally, taking into account the results obtained from the sensitivity analysis, the heating rates in the reactor were calculated for the working temperatures tested in the pilot plant (873, 973 and 1073 K). These heating rates will be used to evaluate the reaction kinetics. Hence, Fig. 5 shows the evolution of particle temperature with time where it can be observed that the heating rate is not a constant value and it would be necessary to introduce these profiles in the reactor model. 3.1.4. Reactor model The reactor model integrates all the process variables previously obtained with the sub-models. The model includes the reactor variables (length, diameter, characteristic screw dimensions, screw speed, reaction temperature and heating rate), the rubber
900 800 700
T (K)
2534
600
2 mm (N30, N20, N10, N5) 5 mm N30 5 mm N20 5 mm N10 5 mm N5 10 mm N30 10 mm N20 10 mm N10 10 mm N5
500 400 300
Table 4 Kinetic parameters for the rubber tyre devolatilization reaction.
Eai (kJ/mol) koi (s1) ni
200
Additives
Polymer 1
Polymer 2
70 1.00E + 04 2.8
212 8.20E + 14 1.4
265 3.20E + 17 1.9
0
20
40
60
80
100
t (s) Fig. 3. Evolution of the internal temperature for particles of different diameters at different nodes (N5, N10, N20, N30) dividing the particle.
2535
1000
1000
900
900
800
800
700
700
T (K)
T (K)
E. Aylón et al. / Waste Management 30 (2010) 2530–2536
600 500
600 500
400
400
Average density Rubber density Char density
300
Heat Capacity average Rubber Heat Capacity Char Heat Capacity
300 200
200 0
10
20
30
40
50
60
0
10
20
1000
1000
900
900
800
800
700
700
T (K)
T (K)
30
40
50
60
t (s)
t (s)
600 500
600 20 W/m2/K
500
400 300
40 W/m2/K
400
ks media ks neumático ks char
60 W/m2/K
300
200
80 W/m2/K
200 0
10
20
30
40
50
60
0
10
20
t (s)
30
40
50
60
t (s)
Fig. 4. Particle temperature evolution in terms of physical properties of the solid (density, heat capacity and thermal conductivity) and heat transfer coefficient.
that depends on the conversion (initially it corresponds to the rubber density and when it is completely converted, it coincides with char density (kg/m3)) and f(X) is the reaction rate, the sum of the decomposition rates for each one of the tyre components according to Eq. (7). A Runge–Kutta method was used to solve the differential equation. This method was applied first to the resolution of the kinetic equation obtaining f(X) and later to solve the reactor design equation. In addition, it was necessary to apply an interpolation method (Neville algorithm) when solving the kinetic equation, to evaluate f(X) in the specific values generated by the Runge–Kutta method applied to the reactor design equation.
1100 1000 900 700 600 500 400
Tb = 873 K Tb = 973 K Tb = 1073 K
300 200 0
10
20
30
40
50
60
70
80
t (s)
3.3. Model validation
Fig. 5. Evolution of particle temperature inside the reactor for different final reaction temperatures.
and char physical properties (density, heat capacity and thermal conductivity) and the kinetic parameters. According to the previous RTD results, the reactor behaviour is close to an ideal plug flow reactor. Therefore, the initial equation used is the design equation of a plug flow reactor adapted for this case. This equation is obtained from the mass balance carried out in steady state to a differential volume element:
F A ðF A þ dF A Þ ðr A ÞdV ¼ dV
dC A ¼0 dt
ð14Þ
The mass balance can be transformed into the following equation:
dX LS qðXÞ f ðXÞ ¼ dt tm m0
ð15Þ
Several simulations were performed by varying the main operation variables (temperature, solid residence time, mass flow rate and inert gas flow) in order to know their influence over the solid conversion. The experimental conditions used in the simulations
1
Conversion
T (K)
800
0.8 0.6
5.3 min 3.7 min 2.5 min 1.9 min 1.5 min
0.4 0.2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Length (m)
where L is the reactor length (m), S is the reactor section (m2), tm is the solid residence time inside the reactor, q(X) is the solid density
Fig. 6. Solid conversion evolution along the reactor for different solid residence time.
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E. Aylón et al. / Waste Management 30 (2010) 2530–2536
Table 5 Comparison between experimental and simulated conversion. Experiment
Experimental conversion (%)
Calculated conversion (%)
T 873 T 973 T 1073
97.3 98.8 99.2
97.6 98.5 99.0
SRT SRT SRT SRT SRT
97.5 97.3 97.5 96.9 94.7
97.8 97.6 97.2 96.5 93.9
MFR 1 MFR 2 MFR 3
97.3 97.8 97.4
97.6 97.7 97.8
INERT 1 INERT 2 INERT 3
97.3 98.1 98.0
97.6 97.6 97.6
1 2 3 4 5
are shown in Table 2 and are the same conditions used in the pilot plant experiment, so it would be possible to validate the capacity of the model to predict the solid conversion. The evolution of conversion in terms of reactor length was obtained in all the simulations performed. As an example, Fig. 6 shows the conversion evolution of the waste tyre for the different solid residence times tested. For the entire range studied, the conversion reached at the end of the reactor is approximately complete, except for the lowest residence time (SRT 5, 1.5 min). In this case, the final conversion is lower owing to a faster advance of the solid inside the reactor. The final conversions obtained from the simulations were also compared with the experimental conversions calculated according to Eq. (1). Table 5 shows the calculated and experimental conversions when the process variables are modified. Good agreement is observed between the experimental results and those calculated in all the experiments performed. As an example, it is observed that the model can predict the conversion decrease produced at the lowest residence time (experiment SRT 5). 4. Conclusions The determination of the RTD inside the moving bed reactor by means of digital image analysis has demonstrated that the behaviour of the system is close to an ideal plug flow reactor. Therefore, the design equation of a plug flow reactor can be used to develop the mathematical model that predicts the solid conversion inside the reactor. It has been proven that this model, which integrates hydrodynamics, kinetics and heat transfer, is able to predict the final solid conversion at different experimental conditions and that it could be a valuable tool for scaling up the system.
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