Energy & Fuels 2006, 20, 2627-2631
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Modeling of Activated Carbon Production from Lignite M. V. Navarro, R. Murillo, J. M. Lo´pez, T. Garcı´a, M. S. Calle´n, and A. M. Mastral* Instituto de Carboquı´mica, CSIC, M Luesma Castan 4, 50018-Zaragoza, Spain ReceiVed March 7, 2006. ReVised Manuscript ReceiVed August 10, 2006
In the current work, a model has been successfully developed to describe the production of activated carbons from lignite char by physical activation. The mathematical model is based on the random pore model for the partial gasification undergone in a solid composed of spherical char particles placed in a fixed bed. To provide the necessary experimental input to test the model, three sets of samples have been produced by activation with carbon dioxide at different temperatures and a sequence of times. Data for the adsorption of nitrogen were obtained and analyzed to study the experimental development of the solid porosity in different ranges of pore size. With the initial textural characteristics of the char and only one previously fitted parameter from thermogravimetric analysis, the kinetic constant, the model predicts accurately not only the conversion rate but also the porosity development of the solid to an extent of 60% activation.
1. Introduction Activated carbons, being highly porous carbon materials, can be produced from a variety of carbonaceous source materials such as coals, lignite, agricultural waste, or waste synthetic polymers.1 Possible applications of these materials include processes of separation, purification, concentration, and catalyzed reactions which have different needs of mean pore size, pore size distribution, or pore volume. To produce these porous solids with optimum properties for each different process, it is necessary to understand the mechanisms involved in the porosity development of the solids. Even in conventional processes, such as the activation of char, the pore structure of the product has a strong dependence on operating conditions.2 A modeling process would relate the operating conditions to the properties of the reaction, like the structure development of the solid, allowing the identification of the optimal process parameters without actually producing and characterizing a large number of candidate structures. A large proportion of the porosity in activated carbons is developed in physical activation during the partial gasification of the char by gases, e.g., air, steam, or carbon dioxide. The experimental physical activation of various types of char has been extensively studied.3 There are several works focusing on the nanostructure, particularly concerning its morphology and pore wall structure development. In these works, different models of porosity are proposed:4 the network of homogeneous cylindrical pores, the crumpled paper morphology, the slitlike pore approach mainly used in simulation, and the basic structural unit definition with squared or spherical stacked layers. However, in a general approach to gasification of coal, the nanostructure of the solid is simplified and processes of inter- and intraparticle diffusion are added to the system. * To whom correspondence should be addressed. Phone: 34 976 733977. Fax: 34 976 733318. E-mail:
[email protected]. (1) Nishiyama, N.; Zheng, T.; Yamane, Y.; Egashira, Y.; Ueyama, K. Carbon 2005, 43, 269-274. (2) Bhatia, S. K.; Gupta, J. S. ReV. Chem. Eng. 1992, 8, 177-258. (3) Feng, B.; Bhatia, S. K. Carbon 2003, 41, 507-523. (4) Py, X.; Guillot, S.; Cagnon, B. Carbon 2004, 42, 1743-1754.
The most commonly used mathematical models for gas-solid reactions involving porous solids are the volume reaction model,5 the grain model,6 and the random pore model.7 These models differ primarily in terms of the assumed structural representation of the solid, as well as assumed overlapping or nonoverlapping populations of grains or pores of arbitrary size distribution.2 Among the structural models, the random pore model, accounting for the effects of pore growth and coalescence, has often shown satisfactory agreement between theory and experiment.3 The purpose of this paper is to report on the validation of a model developed for activated carbon production through porosity development monitoring. First, activated carbons were prepared by physical activation with carbon dioxide, at different temperatures and a sequence of times. In a second stage, the samples were characterized and the effects of time and temperature on the textural parameters were determined. Finally, experimental and calculated results were compared, both according to the reaction rate and porosity development. 2. Model Description Gasification, the main chemical reaction during the physical activation of a char, can be described as follows:
Agas + Bchar S Cproduct gas
(1)
The mathematical model of the isothermal activation of lignite char with carbon dioxide in a fixed bed is based on the reactor mass balance, the particle mass balance, the kinetic equation, and boundary and initial conditions. Model assumptions are that the system is isothermal and there is plug flow throughout the reactor. According to these assumptions, the model equations are as follows: (5) Kasaoka, S.; Sakata, Y.; Tong, C. Int. Chem. Eng. 1985, 25, 160175. (6) Georgakis, C. D.; Chang, W.; Szeckely, J. Chem. Eng. Sci. 1979, 34, 1072-1705. (7) Bhatia, S. K.; Permultter, D. D. AIChE J. 1980, 26, 379-386.
10.1021/ef060103o CCC: $33.50 © 2006 American Chemical Society Published on Web 09/26/2006
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Mass Balance on a Swept Fixed Bed. If the flow rate is constant and the effect of axial dispersion is neglected, the mass balance on a portion of bed is given by the following:
u
∂C ∂C + r pF B + B )0 ∂z ∂t
(2)
Where, the particle reaction rate is rp, calculated as follows:
rp(t) )
dX dt
(3)
with the initial conditions of X ) 0 for t ) 0 and z g 0 and where the concentration at the reactor inlet is equal to the bulk concentration. Due to the changes in weight in the particles during reaction, the bed density will change with time. This parameter is calculated as follows:
FB ) FM[1 - (t)](1 - B)
(3)
Mass Balance on a Spherical Particle. The equation that describes the mass balance for the gaseous reactant on the particle is the following:
∂C 1 ∂ ∂C ) D r2 - (r)s ∂t r2 r e ∂r
(
)
(4)
Where, the intrinsic reaction rate in the particle is (r)s, calculated as follows:
(r)s ) FM
dX dt
(5)
with the boundary condition of De ∂C/∂r ) kg(CB - CN) when r ) R0 and t g 0, the condition of symmetry in the particle expressed as ∂C/∂r ) 0 when r ) 0 and t g 0, and the quasisteady-state condition of ∂C/∂t ) 0. Kinetic Model. In this work, the random pore model has been used, seeing the kinetic expression described by Bhatia and Perlmutter7 as follows: -Ea/RT n C S0 dX k0e ) (1 - X)x1 - ψ ln(1 - X) dt (1 - 0)FM
(6)
based on the structural factor ψ ) 4πL0(1 - 0)/S02. This model is able to describe the local porosity variation as follows:8
) 0 + (1 - 0)X
(7)
The properties in this model have been calculated assuming that the particles are spherical and the reactor is composed of homogeneous cylinders. All the parameters were calculated from expressions proposed in the literature8-10 apart from the kinetic constant which was fitted elsewhere.11 In this previous work, studies in thermobalance were carried out to reach the following final expression: (8) Bhatia, S. K.; Perlmutter, D. D. AIChE J. 1981, 27, 247-254. (9) McCabe, W. L.; Smith, J.; Harriott, P. Unit operations of Chemical Engineering; McGraw-Hill: Mexico, 1996. (10) Smith, J. M. Chemical Engineering Kinetics; McGraw-Hill: New York, 1986. (11) Murillo, R.; Navarro, M. V.; Lo´pez, J. M.; Garcı´a, T.; Calle´n, M. S.; Aylo´n, E.; Mastral, A. M. Energy Fuels 2006, 20, 11-16.
dX 42824e-210.25/8.314T5.95‚104C ) ‚ dt 1.42 6 ‚10 (1 - 0.19) 12 (1 - X)x1 - 4.98 ln(1 - X) (8)
(
)
Program Algorithm. A computer program was developed to apply the model explained above to the production of activated carbon by carbon dioxide partial gasification in a fixed bed reactor. The numerical method used was the finite difference method with the upward finite difference explicit scheme. Equations 2, 4, and 8 were simultaneously solved taking into account all the initial and boundary conditions. The data obtained with this method were compared with the experimental data to find a very good agreement. 3. Experimental Section For CO2 activation reactions, a lignite char obtained by carbonization in a stainless steel swept fixed bed reactor was used. This system, which was also subsequently used for the activation experiments themselves, has been described in detail elsewhere.12 The char was produced in several batch reactions of 60 g of lignite with a particle size of 0.2-0.5 mm, each reaction being carried out at 900 °C for 3 h with a heating rate of 8 °C/min. The average solid yield obtained with this method was 49%. Ultimate and proximate analyses for both solids, the raw material, and the char obtained, are shown in Table 1. To obtain the activated carbon samples, as mentioned above, a swept fixed bed reactor was used. The experiments were performed with a fixed sample particle diameter between 0.2 and 0.5 mm, a char weight of 5 g, a bed height of 10 cm (ceramic rings were used as inerts), and a heating rate of 8 °C/min. A stream of N2 was used to reach the reaction temperature that was changed to a mixture of 9% CO2-91% N2 to carry out the activation. Once the reaction had finished, the stream was changed again to N2 to let the sample cool gradually. The different sets of samples were obtained at 675, 725, and 775 °C and with reaction times between 0.25 and 12 h. Burnoff of samples was defined as follows: m0(mvf) - mf Burnoff ) 100‚ m0Cf
(9)
The samples obtained were characterized by N2 adsorption at -196 °C, using a quantachrome AUTOSORB 1 apparatus. The experimental error due to sample heterogeneity was around 5% depending on the sample. The BET surface area, SBET, total pore volume, VT, and total micropore volume, Vmic, were obtained from experimental N2 isotherms. VT was calculated at a relative N2 pressure of 0.95, and Vmic was calculated using the Dubinin-Radushkevich (DR) equation. The mesopore volume, Vmeso, was calculated by subtracting the micropore volume from the total pore volume. Samples were identified using AXXXYY where A comes from activated, the XXX is related to the activation temperature, and YY is the burnoff. Thus, the sample A72509 was activated at 725 °C with 9% burnoff.
4. Results and Discussion 4.1. Activated Carbons Production. The aim of this study is to evaluate the model proposed for the activation step of the carbon dioxide activation of lignite char, and therefore, the physical properties of the raw char will provide the initial conditions for the model. The apparent surface area of the char was 278 m2/g with a total pore volume of 0.19 cm3/g and also a porosity of 0.19, measured by mercury intrusion porosimetry. (12) Murillo, R.; Navarro, M. V.; Lo´pez, J. M.; Garcı´a, T.; Calle´n, M. S.; Aylo´n, E.; Cruz, T. d. l.; Mastral, A. M. Ind. Eng. Chem. Res. 2005, 44, 7228-7233.
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Table 1. Ultimate and Proximate Analyses of Lignite and Lignite Char
% C (daf) % H (daf) % N (daf) % S (mf) % moisture (ar) % ash (ar) % volatiles (ar) % fixed carbon (ar)
lignite
char
68.9 4.8 0.8 6.3 21.9 3.3 35.1 39.7
92.59 0.87 1.17 1.07 0.40 6.84 7.51 85.25
Therefore, this solid is not macroporous, with similar values of total pore volume and porosity, and could be said to be mainly microporous with a total micropore volume of 0.14 cm3/g. 4.1.1. Influence of Temperature and Burnoff on the Reaction Rate. The influence of burnoff and temperature on the rate of reaction of the lignite char with carbon dioxide is shown in Figure 1. From the data obtained, it can be deduced that there is a direct correlation between temperature and reaction rate, as expected, so that the higher the temperature, the higher the conversion for the same reaction time. For the lowest temperature studied, with burnoff below 10%, the linear relationship between time and burnoff shows a constant reaction rate. However, in the case of the sets of samples produced at 725 and 775 °C, for the samples with the highest burnoff, the reaction slows down for burnoff higher than 60%. Therefore, although the reaction rate is constant at the beginning, it decreases for higher conversions. 4.1.2. Influence of Temperature and Burnoff on Porous Texture. The nitrogen adsorption isotherms of activated carbons obtained at 725 °C and different reaction times are shown in Figure 2. The total nitrogen adsorption capacity increases continuously with the extent of burnoff. The isotherms evolve with activation from type I IUPAC classification for char and samples with low burnoff to type II. The samples with isotherms of type II show an increasing H3 hysteresis loop with burnoff, indicating a probable increase of mesopore volume. Figure 3 shows the influence of activation temperature on the textural properties of the samples. For the four different textural properties studied in a range of temperatures between 675 and 775 °C, there are some slight differences in the values achieved. In Figure 3a, the trend for the apparent surface area evolution is shown to have a maximum for burnoff between 40 and 50%. With regards to the pore volume produced in different pore size ranges, plotted in Figure 3b-d, a similar trend is observed for micropore volumes as for surface area: this property reaches a maximum for burnoff around 40%. However, there is a different trend in the case of total and mesopore volume: the higher the activation, the higher the volume. Common to all the properties studied is the absence of any temperature influence, and therefore, the difference in the reaction rate that was observed in Figure 1 does not have any influence on the structure changes under the conditions used to carry out the activation reactions. This fact can be explained if the reaction takes place under chemical kinetic control. Activation reactions performed with chemical kinetic control should produce the same properties in the solids, no matter the installation design or working conditions, as long as they are still in the regime I defined by Levenspiel,13 since CO2 diffusion into the solid is favored. The slight differences observed in the textural properties of the samples obtained may be due to slight deviations in reaction conditions from those of regime I, sample heterogeneity, or experimental error. (13) Levenspiel, O. Chemical Reaction Engineering; Reverte´: Mexico, 1996.
Figure 1. Burnoff versus time profile for char activation with CO2.
Figure 2. Experimental nitrogen adsorption isotherms at 77 K for some activated carbons prepared at different percentages of burnoff.
Figure 3 also shows the influence of burnoff on porous texture. Both the total pore and mesoporous volumes show a continuous increase with burnoff for the range of burnoff studied. However, the slope in the case of the total pore volume decreases slowly for the highest burnoff studied. This decrease in porosity development with burnoff could be explained by the maximum presented by the micropore volume at around 50% burnoff. These differences in trends result in an increase in the percentage of mesoporosity in the samples such that it dominates the porosity for burnoff higher than 50%. The type of porosity is mainly determined by the type of precursor employed. However, the activation method is another parameter which may affect the final pore size distribution.14 The physical activation has been described as a group of different processes of pore opening of previously inaccessible pores, creation of new pores by selective activation, and widening of the existing pores.15 In addition to these processes, processes of cleaning of constrictions16 and pore coalescence7 have also been described. Although all these processes could be occurring in the whole solid during the whole reaction, some of them will be favored in determined steps of the reaction depending on the pore size. From the continuous increase of the mesopore volume, the process of physical activation could be described mainly as a process of creation and widening of pores; nonetheless, micropore development appears to be a more complicated process. In this range of pore sizes, due to the high initial increase of pore volume compared to the mesopores, not only pore widening (14) Laine, J.; Yunes, S. Carbon 1992, 30, 601-604. (15) Rodriguez-Reinoso, F. Fundamental issues in control of carbon gasification reactiVity; Kluwer Academic Publishers: Netherlands, 1991. (16) Navarro, M. V.; Seaton, N. A.; Mastral, A. M.; Murillo, R. Carbon 2006, 44, 2281-2288.
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Figure 3. Apparent surface area and porosity profiles as a function of pore size for char activation with CO2. Table 2. Data for Different Temperature Simulations temperature (°C)
675
725
775
% vol CO2 Dm (m2/s) µN2 (Pa s) µCO2 (Pa s) µCO (Pa s) Q (N dm3/min)
9 1.33 × 10-4 3.99 × 10-5 4.40 × 10-5 4.28 × 10-5 1.94
9 1.44 × 10-4 4.13 × 10-5 4.62 × 10-5 4.48 × 10-5 1.84
9 1.59 × 10-4 4.27 × 10-5 4.85 × 10-5 4.68 × 10-5 1.75
takes place but also processes of pore opening and cleaning of constrictions should be taken into account. Microporosity reaches a maximum for burnoff around 50%, probably due to the nature of the precursor which experiences significant coalescence at this reaction point. The decrease in the micropore volume is directly related to the decrease observed in Figure 3a for the apparent surface area. 4.2. Production Modeling. The model proposed in this paper is tested by comparing the experimental and calculated activation data of the lignite char. The reaction rate and the porosity are used as the criteria to validate the model. 4.2.1. ActiVation Process. The data obtained for the dependence of activation on temperature, shown in Figure 1, were modeled with the program described previously and the data from Table 2. The results obtained theoretically are shown as lines in Figure 1, where the experimental data are shown as solid symbols. The description of the activation process could be considered as excellent for the set of samples obtained at 675 °C, as well as for the sets of samples produced at 725 and 775 °C up to 60% burnoff. Beyond this point, the model predicts a smaller reduction in the reaction rate than the experimental observations and overestimates the conversion data. To explain this burnoff overestimation, it should be considered that the reaction model used to fit the kinetics, the random pore model, assumes the porous solid to be composed of a system of cylindrical pores that grow continuously until part of
the contiguous pores is consumed and pore overlapping7 occurs. The kinetic model directly relates the surface area of these pores to the reaction rate and takes into account the fact that the surface area will decrease with pore coalescence so the reaction rate decreases. The larger reduction in reaction rate obtained experimentally in this case would be related to a higher destruction of surface area, hence a higher reduction of pores. In Figure 3, we observed a reduction in the BET surface related to a reduction in the microposity. Therefore, we can conclude that the process of coalescence in micropores is more complex than the one described by the random pore model and deviations of experimental results from simulated results will be found when microporosity dominates the surface area development process. 4.2.2. Porosity. The random pore model is a structural kinetic model able through eq 7 to evaluate the porosity development of the solid. The data for the pore volume calculated from nitrogen isotherms of the samples need to be converted into porosity data that can be compared with the results of porosity development simulated in the program. The conversion is carried out using the following equation:
i )
Vi Vi + V s
(10)
The simulated porosity evolution of reactions at 675, 725, and 775 °C was compared with the experimental results depending on the pore size range. Agreement was only observed with the development of the total pore volume up to 2 h, overpredicting on a general basis. However, when the study focused on the changes produced during the reaction, the pore volumes normalized by the initial value, the model is able to describe correctly the mesoporosity development. Results obtained from the three sets of samples produced at different temperatures are
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Energy & Fuels, Vol. 20, No. 6, 2006 2631
studied. Therefore, the contribution of micropores to the total porosity decreases for burnoff above 40%. On the other hand, the model described provides the possibility of modeling the reaction from initial textural parameters of the char and the kinetic constant. The experimental data for the reaction rate and the calculated data were found to correlate successfully up to 60% burnoff. In addition, the description of the normalized mesoporosity development was also possible with a very good agreement between experimental and calculated data. Finally, due to the physical basis of the random pore model and the best fitting of the model to development of mesopores, it can also be concluded that pores other than mesopores undergo different widening processes that still need to be studied. Figure 4. Normalized mesoporosity-time profile for char activation with CO2.
compared with the experimental results for normalized mesopore volume in Figure 4. A very good agreement is observed for the trend of porosity development in all the cases. For the set produced at 725 °C, some discrepancies are observed with overestimation of porosity for reaction times higher than 8 h, which corresponds to 60% burnoff. As explained above, the random pore model assumes the porous solid to be composed of a system of cylindrical pores that grow continuously until part of the contiguous pores is consumed and they overlap.7 From the main results achieved in this study, it can be concluded that this process of porosity development applies in the mesoporous range. In the case of the development of porosity within the micropores, the process seems to be more complex and produces a greater reduction of pore volume than the one described by the model. When this process dominates the pore development, some discrepancies will appear between theoretical and experimental results. The simulations indicate that comparisons of overall carbon conversion, porosity development, and operating bed temperature with experimental data are accurate to an extent of 60% burnoff. Taking into account the fact that commercial applications rarely exceed this degree of activation, the part of the process with industrial interest is described by the model. 5. Conclusions The model developed to describe the production of activated carbons by physical activation has been shown to be valid for describing the activation process and porosity development. On one hand, from the experimental activation of lignite char with carbon dioxide, it can be concluded that the relationship between the reaction rate and temperature is as expected: the higher the temperature, the higher the reaction rate. In addition, the textural properties of the activated carbons depend on the burnoff, regardless of the experimental conditions used to carry out the reaction, as long as it is performed under the kinetic regime. With regards to the development of the different range of pore sizes, different trends can be observed. The microporosity reaches a maximum for 40% burnoff while the mesoporosity and total porosity increase continuously for the conversion
Acknowledgment. This work has been partially supported by the Spanish Science and Technology Ministry with the PPQ-4145 project and the Ramo´n y Cajal Program (R.M. contract).
Nomenclature C ) gas concentration (mol/m3) CB ) bulk concentration (mol/m3) Cf ) fraction of fixed carbon in the char CN ) gas concentration in the outer particle surface (mol/m3) De ) effective diffusion coefficient (m2/s) Dm ) molecular diffusion coefficient (m2/s) Ea ) activation energy (J/mol) k0 ) kinetic constant (mols ms3/s ms2 molg) kg ) mass transfer coefficient (m/s) L0 ) initial length of overlapped porous system (m/m3) m0 ) initial weight of sample (kg) m0(mvf) ) moisture, volatile free initial weight of sample (kg) mf ) final weight of sample (kg) n ) reaction order (dimensionless) Q ) gas flow (N dm3/min) r ) inner particle radius (m) R ) ideal gas constant, 8.314 (J/mol K) R0 ) particle radius (m) (r)s ) inner reaction rate in the particle (mol C/m3 s) rp ) particle reaction rate S0 ) initial reaction surface of overlapped pores T ) temperature (K) t ) time (s) u ) superficial velocity (m/s) Vi ) porous volume in different ranges of pore sizes (cm3/g) Vs ) solid volume (cm3/g) X ) solid conversion (dimensionless) z ) longitudinal coordinate (m) Greek Symbols 0 ) initial porosity B ) bed porosity i ) porosity in different ranges of pore sizes (dimensionless) µ ) viscosity (Pa s) FB ) bed density (mol/m3) FM ) solid molar density (mol/m3) ψ ) structural parameter EF060103O
