Kinetic Model Comparison for Waste Tire Char Reaction with CO2

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Ind. Eng. Chem. Res. 2004, 43, 7768-7773

Kinetic Model Comparison for Waste Tire Char Reaction with CO2 Ramo´ n Murillo, Marı´a V. Navarro, Jose´ M. Lo´ pez, Elvira Aylo´ n, Marı´a S. Calle´ n, Toma´ s Garcı´a, and Ana M. Mastral* Instituto de Carboquı´mica, CSIC, M Luesma Castan 4, 50018 Zaragoza, Spain

Pyrolysis has proven to be a useful recycling process for waste tires, and pyrolytic char is ∼40% of initial sample weight. To valorize this solid, the activated carbon production has been studied for the last years from a generation point of view. However, there are only few studies about the kinetics of the reaction. In this paper, four gas-solid models have been applied to CO2 activation of tire char: volume model, modified volume model, changing grain size model, and random pore model. The reactions were performed in a thermobalance with a structural and analytically characterized tire char obtained by pyrolysis in a fixed-bed reactor at a temperature of 1000 °C for 3 h. Experimental conditions were optimized to minimize internal and external mass-transfer phenomena performing experiments with different particle sizes, at different flow rates and initial weights. Finally, to obtain the intrinsic kinetic parameters, several experiments were carried out at different partial pressures of CO2 and temperatures, concluding that the random pore model is the most appropriate model to describe the reaction. The tire char activation was found to be a first-order reaction with respect to CO2. The kinetic results reported in this paper can be useful for tire char activation scaling-up and the process engineering design, so that knowledge of the activation energy and the preexponential factor of the chemical reaction is fundamental to perform the chemical reactor design and the optimization of process parameters. Introduction Nowadays, more than 6 million tonnes per year of waste tires are being produced around the world.1 This waste material generation produces a growing concern related to the economic and environmental problem associated with this nonbiodegradable residue.2 The authorities at different levels have developed legislation in order to ensure the appropriate management of these waste tires. In this way, the strategy set by the European Commission on waste prevention and recycling has the next priorities: waste prevention, reuse, recycling, and energy recovery.3 Waste tires are constituted of natural and synthetic rubber (styrene-butadiene rubber and polybutadiene), carbon black, and an inorganic part mainly composed of zinc oxide4 and SiO2. Concerning the proximate analysis of waste tire, it is remarkable the low moisture and ashes in comparison to other solid fuels such as coal.5 With respect to its ultimate analysis, it contains a high carbon content, the main component of carbon black and rubber, and hydrogen with the presence of sulfur introduced into the tire during the vulcanization process. Different uses have been developed in order to manage scrap tire production. Waste tires can be used in civil engineering applications as substitutes for soil, sand, or aggregate in road bases. Tires can be involved in products such as mats, recreational surfaces, or drainage systems. Waste tires can also be used for energy recovery by means of combustion since the calorific value of this waste material is very high,6 ∼2837 MJ/kg. However, significant investments and operat* To whom correspondence should be addressed. Phone: 34 976 733977. Fax: 34 976 733318. E-mail: amastral@ carbon.icb.csic.es.

ing costs are required for efficient tire combustion due to the sophisticated incinerator designs7 and the environmental problems associated to tire combustion.2 Pyrolysis is one potential solution to waste tire management. In this process, tire-derived fuels, gas and oil, can be obtained in different percentages but, generally, 40% of the initial weight remains as a solid, mainly composed of carbon black with a high carbon content and low ash content. Therefore, this material could be susceptible to being activated in order to obtain high value-added products. Currently, several studies have been done in order to assess the possibility of using the solid residue obtained in tire pyrolysis to produce activated carbon by activation at high temperatures with steam or CO2.8-14 Concerning SBET results, values can be found ranging from 431 m2/g10 using a process of flame pyrolysis, 607 m2/g with a stream of N2 with 40% steam and a final percentage of activation of 60%,11 640 m2/g with a 65% activation in fixed bed with streams of steam or CO2,12 to even 1260 m2/g for an activation percentage of 91% with a process of thermal decomposition using steam13 as gasifying agent. Although there are several studies about activation of tire char as the referred above, the kinetics of the process, as a gas-solid reaction, have been addressed in few works. However, this is an important concept, to know the activation energy and the preexponential factor of the process, which gives basis to the development of chemical reactor designs and optimization of process parameters. Regarding the kinetics of activation reactions, several models have been developed especially for coal gasification that can be used to describe the kinetic behavior of tire char activation.15 Lee and Kim7 used the shrinking core model,16 the volumetric model,17 and the modified volumetric model7 to analyze the results

10.1021/ie040026p CCC: $27.50 © 2004 American Chemical Society Published on Web 11/02/2004

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7769 Table 1. Samples Proximate and Ultimate Analysis sample

tire

tire char

% moisture (ar) % ash (ar) % fixed carbon (ar) %volatiles (ar) % C (daf) % N (daf) % S (db) % H (daf)

0 5.3 30.0 64.7 88.3

0.1 8.4 90.8 0.7 98.7 0.2 1.2 0.3

1.9 7.7

obtained in the CO2 activation of waste tires in a thermobalance. They found good agreement between experimental and theoretical data using the modified volumetric model, finding a rate expression in terms of temperature, CO2 partial pressure, and solid conversion. However, an important point in the activated carbon production is to know the structural evolution of the solid. This has been studied for gas-solid reaction with models such as changing grain size model (CGSM)18 and random pore model (RPM).19,20 With these models, a prediction of final solid properties can be done in terms of initial solid properties and reaction conditions. In this paper, for the first time these two models are used in tire char activation with carbon dioxide. In this paper, an in-depth study of tire char-CO2 reaction kinetics is done by using a thermobalance and by applying different kinetic models to have a better knowledge of solid evolution. Experimental Section For CO2 activation reactions, a tire char obtained by carbonization in a stainless steel fixed-bed reactor was used. This solid was produced in several batch reactions of 300 g of shredded waste rubber tires, each one at 1000 °C for 3 h with a heating rate of 8 °C/min and a solid yield of 40%. The main properties of the solid product are listed in a previous work.21 In this section, results of proximate and ultimate analysis of tire and tire char samples used are compiled in Table 1. The study of the activation process by CO2 was performed in a thermobalance SETARAM TGDTA-92, described elsewhere,21 registering the sample weight loss in terms of the reaction time. Different initial sample weights ranging between 2.5 and 10 mg were tested to optimize variables and in this way to ensure a reaction regime of intrinsic kinetic control. The influence of the particle size was also studied ranging from 0.1 to 2 mm. Different flow rates were also tested (4.3-7.1 cm/s) until no influence of these variables on the conversion was achieved. In this way, a weight of 2.5 mg, a particle size of 0.15 mm, and a flow rate of 4.3 cm/s have been found to be optimum to avoid any possible effect of external and internal transport phenomena. The reaction order was determined by modifying the CO2 inlet concentration from 20 to 40%. One more set of samples was performed at different temperatures (850, 900, 950, and 1000 °C) in order to determine the activation energy and preexponential factor, both basic intrinsic kinetic parameters of the activation process for the different kinetic models. The experimental conversion (Xexp) was calculated according to eq 1 where w0 is the initial sample weight,

Xexp )

w0 - wi w0 - wash

(1)

wi is the sample weight at any time, and wash is the ash weight (the stable weight after reaction). Kinetic Models. Different models, which take into account structural changes during the reaction, have been proposed to describe the char reaction with CO2 1. Volume Reaction Model (VRM). The VRM22 is the simplest one, supposes uniform gas diffusion in the entire particle, and simplifies the heterogeneous gassolid reaction of carbonaceous material with carbon dioxide by assuming that the gas is reacting homogeneously with char. The kinetic expression for reaction rate is

dX/dt ) kV(1 - X)

(2)

2. Modified Volume Reaction Model (MVRM). This model, proposed by Kasoaka et al.,17 is based in the previous one, but the apparent constant rate changes with solid conversion as the gasification reaction proceeds. The reaction rate can be expressed by the following equation:

dX/dt ) kMV(X)(1 - X)

(3)

where kMV(X), kinetic reaction constant, can be calculated by using the equation

kMV(X) ) R1/ββ[- ln(1 - X)](β-1/β)

(4)

This expression can be integrated to obtain an average rate constant, as an index of reactivity, which is used to obtain the kinetic parameters of a reaction rate general expression useful to be compared with the other model expressions:

kM )

0.99 kMV(X) dx ∫0.01

(5)

3. Changing Grain Size Model (CGSM). This model was developed by Georgakis18 and considers the char composed by idealized shaped particles that are also composed by uniformly sized grains of some idealized shape. The most usual case is to assume sphericalshaped particles and grains. These grains follow the unreacted core model under kinetic control; therefore, the reaction rate expression is

dX/dt ) (3/τ)(1 - X)2/3

(6)

τ ) rg/bvBkCGSMCn

(7)

rg ) 3/SBETFt

(8)

here τ is the model characteristic parameter, comprising (see eq 7) the constant rate, some solid characteristics, and the gas concentration. This model uses initial grain radius, rg, calculated from solid surface area and supposing the solid is composed of initially equal spheres (see eq 8). 4. Random Pore Model. This model was developed simultaneously by Bhatia and Perlmutter19 and Gavalas,20 which allows for arbitrary pore size distributions in the reacting solid and considers the random overlapping of pores’ surfaces during reaction changing the area available for gasification. The expression developed with all these physical assumptions for tire gasification under chemical control is eq 9 with the structural parameter

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Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 n dX kRPMC S0 (1 - X)x1 - ψ ln(1 - X) ) dt (1 - 0)FM

ψ ) 4πL0(1 - 0)/S02

(9) (10)

Ψ characteristic of this model (eq 10). To characterize pore structure by means of Ψ, the required information (eq 10) on porosity, 0, surface area, S0, and pore length, L0 of the solid porous system can be determined from pore volume distribution data by using the following relationships:23

0 )

∫0∞V0(r) dr ∫0∞

S0 ) 2 L0 )

V0(r) dr r

∫0∞

1 π

V0(r) r2

dr

(11) (12)

Figure 1. Conversion data based on volume model for different temperatures (950 °C, 4.3 cm/s, and 0.15-mm particle size).

(13)

In general, for experiments carried out at different temperatures, the Arrhenius equation can be applied in order to obtain a kinetic expression independent of temperature. The general form of this equation is as follows:

k ) k0e-(E/RT)

(14)

In the case of the volume and modified volume models, a modification can also be introduced into eq 7 to obtain, in this way, a gas reactant concentration influence (eq 15).

kM ) kM0e-(E/RT)CCO2n

(15)

This parameter, in the CGSM and RPM, was taken into account in the kinetic expression of the general model.

Figure 2. Conversion data based on modified volume model for different CO2 concentrations (20% CO2, 4.3 cm/s, and 0.15-mm particle size). Table 2. Textural Parameters Needed To Apply the Changing Grain Size Model SBET, m2/g

Results and Discussion

63

For VRM, a linear expression can be used for chemical reaction rate:

-ln(1 - X) ) kVt

(16)

Data obtained from reactions carried out at different temperatures were fitted to 0.8 conversion with this expression (see Figure 1), with a regression coefficient value greater than 0.96 in all the cases. By applying the Arrhenius eq 15 to the constant values obtained from runs at different temperatures and CO2 concentrations, the expression for tire char reaction with carbon dioxide using volume reaction model is

dX/dt ) 6426.1e- 191790/8.314TC0.7231(1 - X) (17) In the case of the MVRM, conversion is expressed by eq 18:

X ) 1 - e-Rtβ

(18)

To fit experimental data, the last expression is modified to obtain eq 19. In Figure 2 the fitting results for

ln(-ln(1 - X)) ) lnR + β ln t

(19)

Fp, g/cm3 0.86

Ft, g/cm3 1.69

rg, m

 0.49

2.8 ×

M, g/mol

10-8

12

experiments carried out at 950 °C with 20, 30, and 40% CO2 in the gas stream are compiled. An excellent agreement between experimental and calculated values is observed. With values obtained of average rate constants for experiments at several CO2 concentrations and temperatures and by applying the Arrhenius eq 15, the expression for tire char reaction with carbon dioxide using MVRM is

dX/dt ) 9164.8e-191395/8.314TC0.5362(1 - X)

(20)

The next model of gas-solid reaction to be examined is CGSM. To obtain τ data, a linealized version of eq 6 (see eq 21) can be used in order to fit experimental results. With the obtained results, specific textural solid parameter (see Table 2), and by applying eq 8, values of the rate constant are calculated. These values are compiled in Table 3.

1 - (1 - X)1/3 ) t/τ

(21)

τ values obtained at different CO2 concentrations are plotted versus concentration in Figure 3a, to evaluate the reaction order. The linear behavior exhibited in

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7771 Table 3. Char Activation Constant Rates for the Different Kinetic Models temp % CO2 (°C) vol 850 900 950 950 950 1000

20 20 20 30 40 20

kv

kvm

kcgsm

krpm (m/s)

1.73 × 10-5 3.47 × 10-5 7.80 × 10-5 7.44 × 10-5 9.51 × 10-5 1.83 × 10-4

1.61 × 10-5 3.32 × 10-5 6.72 × 10-5 7.79 × 10-5 9.83 × 10-5 1.89 × 10-4

7.99 × 10-9 1.70 × 10-8 3.73 × 10-8 3.20 × 10-8 3.01 × 10-8 9.90 × 10-8

1.04 × 10-8 2.30 × 10-8 4.93 × 10-8 4.17 × 10-8 3.91 × 10-8 1.30 × 10-7

Figure 3a, in agreement with the τ definition (eq 7), is indicative of a chemical reaction of first order with respect to CO2. Once the reaction order has been deduced, the rate constants can be calculated at several temperatures. These constants are presented on Arrhenius coordinates in Figure 3b. In this case, the linear behavior shown confirms that the experimental conditions are optimum to work in the chemical reaction regime, free of transport or diffusional limitation24 over the temperature range. At the same time, from these fitting values, preexponential factor, and activation energy are obtained. The expression for tire char activation with CO2 fitting data to CGSM, with separated influence of temperature and concentration is

dX 3 × 1 × 12 × 11.31e-197450/8.314T C(1 - X)2/3 ) dt 2.8 × 10-8 × 1690 (22) To fit experimental data to the last model studied, the RPM, the general reaction rate expression is used (Equation 9). To ensure the best fitting, a computer program was developed using the Nelder and Mead optimization algorithm, obtaining, in all the runs, regression coefficients values between experimental and theoretical conversions up to 0.99. The intrinsic reaction rate equation with RPM was calculated in a previous work21 and equal to

dX 15.33 × 2.67 × 107e-197700/8.314‚T × ) dt 1.69 (1 - 0.49) × 106 12

(

)

C(1 - X)x1 - 6.26 ln(1 - X) (23) To calculate this expression, several pore size distributions were tried in order to find the one that achieved the best fitting of the experimental results. According to the range of pore size where the distribution is focused, from micro- to macropores, distributions used were obtained by the Medek model,25 density functional

Table 4. Char Activation Energy and Order for Kinetic Models Studied volume model modified volume model changing grain size model random pore model

R2

n

>0.97 >0.99 >0.99 >0.99

0.7231 0.5362 1 1

Ea, kJ/mol 191.79 191.40 197.45 197.70

k0 6426.1 9164.8 11.31 15.33

theory model,26 Barret, Joyner and Halenda model,27 and mercury porosimetry,28 finding the best fitting values with the pore distribution obtained by mercury porosimetry. This fact can be explained because tire char has porosity mainly in the range of meso- and macropores.4,12,13,21 In Table 3 are compiled all the values obtained for rate constants of different experiments according to the model used in each case. First, the strong difference in rate constant values between the volume models, normal and modified, and the structural models should be pointed out. For structural models, conversely to the volume ones, the kinetic expression takes into account not only a solid conversion dependence of reaction rate but also solid structural information that influences the constant rate values obtained. There are two different trends in rate constants regarding the temperature and CO2 concentration. As was expected, the same trend with temperature was found in all the models; constant values increase with temperature. However, the trend of the rate constant with CO2 concentration differs with the model. On the other hand, nonstructural model rate constants increase with CO2 concentration, but on the other hand, for CGSM and RPM, much more similar values are calculated (11.5 and 12.2% RSD, respectively, due to experimental error) since there is a concentration factor in the kinetic expression that controls this influence. With the four models used, high values of activation energy have been calculated (see Table 4), in the range of 191.40-197.70 kJ/mol, which confirms that experiments have been performed under kinetic control and there is no influence of CO2 diffusion, neither in the film nor in the particle. Lee and Kim7 obtained a value for activation energy of 238 kJ/mol for the reaction of tire char with CO2 by applying the modified volume model. There is a great variety in activation energy in the literature.29 Using RPM in pyrolyzed wood gasification modeling, Struis et al.30 found results between 196 and 222 kJ/mol. Other authors,17,29 working with chars from several coal types, have obtained values between 79 and 309 kJ/mol, probably due to the use of different coals, different kinetic models, or different instrument configurations.

Figure 3. Order and Arrhenius plot fitting with data based in changing grain size model.

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Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004

Figure 4. Experimental and calculated conversion in tire char model comparison (20% CO2, 4.3 cm/s, and 0.15-mm particle size).

In regard to the reaction order, in the case of the one obtained with the modified volume model, from the slope of ln-ln plot of km and CO2 partial pressure, the reaction order is found to be 0.54 for partial CO2 pressures between 0.2 and 0.4 atm at 950 °C. Lee and Kim7 obtained a higher value of 0.68 in a different range of pressures, from 0.3 to 1 atm. With structural models, CGSM and RPM, a first-order reaction has been used by most of the authors with solid-gas reactions under chemical control.17,20,24,31 Different authors17,22,32 have reported different reaction orders depending on the pressure range studied, from zero order assumed by Dutta and Wen22 at high CO2 pressures (15 atm), to first order reported by Dutta and Wen22 and Kwon et al.32 at atmospheric or lower pressure of CO2. Figure 4 shows that the four models produce good agreement between experimental and theoretical data; therefore, it is necessary to look for other kinetic factors to choose the most appropriate model for tire char activation kinetics. One singularity of tire char activation with CO2 is that a maximum in reaction rate of ∼40% of solid conversion can appear. This fact can be explained because the configuration of the char used could be described as composed by sheets of condensed aromatic units, which are stacked in randomly crosslinked, irregular, nonpolar layers12 together with disorganized carbon and tarry material.12 During the initial stage of activation, the disorganized carbon is burnt off preferentially and the tarry material is lost, opening up previously blocked porosity. During the second stage of activation, carbon from the aromatic ring system is burnt off, widening the previously opened pores.12 This evolution of porosity during activation, explained mainly by RPM, is related to reaction rate producing a maximum on it. In Figure 5, reaction rate versus solid conversion, experimental and theoretical data obtained with the four models, are plotted. It is shown that VRM and CGSM cannot describe this maximum observed in tire activation rate with CO2 since they describe a continuously decreasing rate.33 In the first case, the VRM supposes that the reaction rate is proportional to the solid unreacted, that is homogeneously decreasing each time.22 For CGSM, the reaction rate is proportional to the grain radius, which decreases as the reaction proceeds.18 About models able to origin a maximum in reaction rate, MRVM could be discarded due to the absence of a

Figure 5. Experimental and calculated reaction rate vs conversion in tire char model comparison. (20% CO2, 4.3 cm/s, and 0.15mm particle size).

physics base that explained this maximum, conversely to the RPM. In addition, the first one cannot be used to assess the textural properties of the resulting solid. This last model, used in previous works of gasification by Bhatia and Perlmutter19,34 and Gavalas,20 is based on the pore system growing, which produces an internal solid surface increment with reaction until the pores overlap. The model takes into account that the intersection of pores produces their collapse, a destruction of surface, and a reduction in reaction rate. Similar results were found by Bhatia amd Perlmutter,19 concluding that the maximum in reaction rate arises from two opposite effects: the growth of reaction surfaces associated with the pores and the loss of these surfaces as they progressively collapse by intersection. In Figure 5, it is observed that both reaction rate curves, experimental and RPM theoretical, have maxima in the conversion interval between 0.2 and 0.4. Due to its physical base, RPM is able to describe not only the reaction rate during reaction but also the porosity evolution from the initial structural parameters of solid. If the objective of the activation process is to produce activated carbons, high char conversions should be avoided because the final product has not a high surface area but, in addition, the developed surface on the first stages is destroyed, decreasing the value of the product obtained. Lin and Teng,35 working in the activation of tire char with steam at 900 °C, observed that there is a maximum in surface area for activated carbons at a burnoff of 43%, decreasing at higher conversions, which coincides with the results obtained given above for reaction rate development. Acknowledgment This work has been partially supported by the Spanish Environmental Ministry (AMB2000-168), by the General Council of Arago´n, D.G.A., Spain (Pre-Doctoral Grants of T.G. and J.M.L.), and the Spanish Science and Technology Ministry for the (R.M. and M.S.C.) Ramo´n y Cajal Program. Nomenclature C ) gasifying agent concentration (mol‚m-3) b ) solid stequiometric coefficient Ea ) activation energy (kJ‚mol-1) k ) generic intrinsic constant rate in Ahrrenius equation

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7773 kRPM ) intrinsic constant rate of RPM molc/s‚m2‚(m3/ molCO2)n kCGSM ) intrinsic constant rate of CGSM molc/s‚m2‚(m3/ molCO2)n kv ) intrinsic constant rate of volume model (s-1) kMV(X) ) intrinsic constant rate of modified volume model (s-1) kM ) intrinsic constant rate of modified volume model (s-1) kMo ) preexponential factor in Ahrrenius equation for modified volume model (m‚s-1) k0 ) preexponential factor in Ahrrenius equation (m‚s-1) L0 ) length of a system that is made by the random overlapping of cylindrical surfaces whose size distribution is V0(r) (cm‚cm-3) n ) reaction order PCO2 ) partial pressure of CO2 (Pa) R ) universal gas constant (8.314 J‚mol-1‚K-1) r ) particle radius (m) rg ) grain radius (m) S0 ) surface area of a system that is made by the random overlapping of cylindrical surfaces whose size distribution is V0(r) (cm2‚cm-3) SBET ) surface area obtained by applying the BET equation to the N2 adsorption isotherm (m2‚g-1) t ) time (s) T ) temperature (K) V0(r) ) pore volume distribution wash ) sample ash weight (mg) wi ) sample weight at any time (mg) w0 ) sample initial weight (mg) XCalc ) solid fractional conversion XExp ) solid functional conversion Greek symbols R ) modified volume model parameter β ) modified volume model parameter FM ) molar density of the reactant solid (mol‚m-3) Ft ) intrinsic density of the reactant solid (kg‚m-3) Ψ ) Bathia and Perlmuter structural parameter 0 ) total volume of a system that is made by the random overlapping of cylindrical surfaces whose size distribution is V0(r) νB ) molar volume of solid reactant, (m3‚mol-1) τ ) characteristic parameter of CGSM, s

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Received for review January 20, 2004 Revised manuscript received June 15, 2004 Accepted July 1, 2004 IE040026P