ARTICLE pubs.acs.org/EF
Theoretical Model of Heating Patterns during Carbonization of Green Carbon Blocks Can Zhang,† Gui-Min Lu,*,‡ Ze Sun,*,† and Jian-Guo Yu†,‡ †
State Key Laboratory of Chemical Engineering, ‡National Engineering Research Center for Integrated Utilization of Salt Lake Resources, East China University of Science and Technology, Shanghai, China ABSTRACT: The potential to damage synthetic graphite is high during the pyrolysis of pitch/coke composite material in processing of carbon/carbon components. Exact modeling of heating patterns could optimize the preparation conditions in order to obtain high quality products. A capillarycell model was built to evaluate the internal pressure resulting from volatile matter in green carbon blocks during carbonization. The theoretical model for heating patterns was proposed by considering the influence of heating rates on the internal pressure and the thermal stress during the heat-treatment procedure. The results showed that the theoretical heating rates were mainly controlled by mass transfer in the range 467850 K and by heat transfer in other temperature ranges. The values calculated by the developed model were compared with the industrial results, and the validity of the proposed method for the prediction of heating patterns is evaluated.
1. INTRODUCTION Synthetic graphite has a wide range of applications from the manufacture of electrodes in the magnesium and steel industries to high-technology applications in fuel cells and lithium ion batteries.1 The graphite production process involves the selection of carbon materials (precursors) and the baking process. As is well-known, the world reserves of coal for consumption are large enough for 215 years, as opposed to 39 years for petroleum;2 many scholars synthesized graphite using anthracites as potential precursor materials, and the effects of the different mineral matter contents on the properties of graphite were researched.38 Carbonization plays an important role in the preparation of graphite. Not only the properties but also the economical efficacy of graphite are critically dependent on a careful control of its carbonization process, because carbonization is one of the most time- and energy-consuming steps in the full fabrication process of graphite. Therefore, the simplest way to reduce the manufacturing cost of graphite is to increase the carbonization rate, which is usually very low. However, carbonization is primarily a process of the pyrolysis of the hydrocarbons of a carbon precursor. To minimize the unfavorable effects, such as shrinkage, cracking, and thermal stresses, which may occur during carbonization, the lower carbonization/heating rates are usually required.9,10 The bulk density of artifacts is required to increase because high bulk density results in high-quality graphite.1113 However, with the bulk density increasing, the artifacts usually become more susceptible to fracture during carbonization. Increasing the sizes of industrial products is also required. However, the heating patterns previously used limit the dimensions. Considering the fact that the existing heating patterns are established empirically, it is desirable to determine the heating patterns that are suitable for each product, on the basis of theoretical considerations. According to work by the Henning group14 about the study on the mechanical behavior of an extruded mixture during carbonization, the specimen exhibited viscoelastic behavior at temperatures r 2011 American Chemical Society
below the resolidification temperature of binder pitch (∼770 K) and ideal elastic behavior at temperatures above it. It is generally accepted that the porosity that developed below 673 K is mostly due to an important release of volatile matter from the fluid, but highly impervious binder pitch tends to increase the internal pressure inside the green body.15 In that respect, the formation of porosity depends basically on kinetic considerations; that is, the rate of formation of volatiles must be comparable to or lower than the rate of their diffusion outside the green body.1618 It was analyzed that the internal pressure and the thermal stress were main factors that limit heating rates, and the result showed that both the gas pressure and the stress from the gas pressure increase approximately in proportion to specimen diameter and square root of heating rate. Born et al.19 researched the heating conditions in carbonization procedures and obtained the permissible heating rate by the calculation of mass transfer, but the result was qualitative and did not immediately lead to practically applicable heating diagrams, because a large number of simplifications in that model were made. Fukai et al.20 focused on heat stress and evaluated the heating program suitable for the cold isostatic pressing specimens with the bulk density of 1230 kg/m3, and they pointed out that the suitable heating rate had to be reduced at the elastic stage after 770 K. Regardless of the internal pressure of the green body during carbonization, the heating patterns did not conform to other carbon artifacts very well. The various heating rates used for the pyrolysis of the blocks are defined as the heating rates with which the expansion and brittle fractures of carbon materials can be avoided during carbonization. Therefore, there are critical heating rates for blocks during carbonization at different temperatures. The real heating rates should be no more than these critical heating
Received: July 19, 2011 Revised: September 20, 2011 Published: September 21, 2011 5353
dx.doi.org/10.1021/ef201055r | Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
where ε is the porosity; Rm is the mean capillary diameter (m); and n is the number of the mean capillary in unit area (m2). The porosity of carbon material also can be given by ε ¼ 1 Fapp =Ftr
where Ftr is the true density (kg/m3) and Fapp is the bulk density (kg/m3). Considering the weight of pitch and the change of volume in the heating-treatment procedures, Fapp can be defined as follows:
Figure 1. Vertical section of the capillarycell model.
rates (theoretical heating rates), in order to obtain high quality products. The objective of the present paper is to investigate the internal pressure and the thermal stress during the carbonization of green carbon blocks and establish a theoretical model of heating patterns on the basis of both mass transfer and heat transfer.
2. THEORETICAL MODEL DERIVATION It is necessary to know the magnitudes of internal pressure and thermal stress of green carbon blocks during carbonization to obtain the applicable heating diagrams for the graphite synthesis. Before resolidification, the yield stress has a significant effect on the specimen. If the magnitude of the internal stress due to gas pressure distribution is greater than the yield stress, the materials expand obviously. After resolidification, the formation of volatiles nearly comes to one end. The maximum-principal-stress theory is used to judge the fractures of carbon materials during the elastic stage. According to this theory, when the magnitude of the thermal stress is greater than the tensile strength σt, carbon materials will fracture. It is assumed that the total stress results mainly from the gas pressure before resolidification and from the thermal stress after resolidification. This assumption is acceptable, because it is found that expansion occurs before resolidification and brittle fractures form after resolidification.2022
Fapp, T ¼
quantitatively, it is necessary to know the magnitude of the internal pressure. However, it is very difficult to calculate, since the microscopic structures of the specimen are very complex. The specimen is modeled as a viscoelastic plate with finite thickness and infinite area on a right angle coordinate, the origin being at the center of the body. The model assumes that parallel isometric capillaries traverse the plate along the direction of the thickness; the capillaries are connected with cells, as shown in Figure 1; the capillaries and the cells are distributed uniformly in the specimen; the pyrolysis gas of pitch during carbonization is stored in the cells and leaves the body through the capillaries; the volume of the cells is in proportion to that of the capillaries, and the proportionality constant is k. When the porosity increases, the diameters of the capillaries and the cells increases; the specimen expands and shrinks at the same proportion in all directions. In the model, the length of the capillaries (the thickness of the model) may be determined by ð1Þ
where b0 is the thickness of the green specimen (m); b is the length of the capillaries (m); τ ≈ 2 is the tortuosity factor;19 and βT is the volume expansivity. The porosity is defined as follows: ε ¼ nπRm2 ð1 þ kÞ
ð2Þ
1 ζð1 wp, T Þ Fapp, T 0 1 þ βT
ð4Þ
where wp,T is the weight of binder pitch; ζ is the content of pitch in the green specimen; and subscript T0 refers to the initial temperature. The effective porosity ε0 , used for mass transfer, is defined as ε0 ¼ nπRm2
ð5Þ
According to eqs 25, ε0 T also can be calculated by " # 1 ζð1 wp, T Þ Fapp, T0 1 0 1 εT ¼ 1 þ k Ftr, T 1 þ βT
ð6Þ
According to eqs 5 and 6, in the heat-treatment procedures, the relative effective porosity χT = ε0 T/ε0 T0 and the mean capillary diameter can be given by χT ¼
ð1 þ βT ÞFtr, T ½1 ζð1 wp, T ÞFapp, T0 Ftr, T0 ð1 þ βT ÞFtr, T Ftr, T0 Fapp, T0 ð7Þ
Rm, T ¼ χT 1=2 Rm, T0
2.1. Theoretical Model Derivation on the Basis of Mass Transfer. To assess the expansion of green carbon blocks
b ¼ τð1 þ βT Þ1=3 b0
ð3Þ
ð8Þ
The HagenPoiseuille law can be written as Vx =t ¼
r 4 π dp 8μ dl
ð9Þ
According to the mass transfer theory and the Hagen Poiseuille law, the internal pressure of green carbon blocks produced by pyrolysis gas can be calculated by eq 10. The I.C. (initial conditions) and B.C. (boundary conditions) are given by eq 11. ! ∂ ε ∂ nπRm4 ∂p p ¼ p ð10Þ þ WRg ∂t T ∂l 8μg T ∂l I:C:
p ¼ p0 ;
B:C:
p ¼ p0
∂p ¼ 0; ∂l
T ¼ T0
at t ¼ 0 at l ¼ b=2
ð11Þ
where μg refers to the gas viscosity (Pa s); Rg is the gas constant [Pa m3/(mol K)]; p is the internal pressure of the specimen (Pa); and p 0 is the external pressure of the specimen (Pa). The gas releasing rate per unit volume of the specimen W [mol/(m3 s)] is given by ζFapp, T0 dwp B0 ð12Þ W ¼ ð1 þ βT ÞτMg dT T T where Mg is the mean molecular weight of pyrolysis gases 5354
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
Table 1. Characterization of Based Coal-Tar Needle Coke ultimate analysis (wt %) C
H
atomic ratio H/C
ash (wt %)
volatile content (wt %)
real density (g/cm)
specific resistance (μΩ m)
97.02
1.55
0.192
0.03
0.33
2.141
508
Table 2. Characterization of Coal Tar Pitch ultimate analysis (wt %)
a
composition (wt %)
C
H
atomic ratio H/C
ash (wt %)
softening point (°C)
TSa
QS-TIb (β-resin)
QIc
94.25
4.42
0.562
0.20
109.4
71.99
19.56
8.45
Toluene-soluble. b Toluene-insoluble/quinoline-soluble. c Quinoline-insoluble.
Figure 2. Variation curves of the tensile strength (a), true density (b) and volume expansivity (c) for the green body with a 5 K/h heating rate.
(kg/mol) and B0 T = (dT/dt)T is the heating rate based on mass transfer (K/s). eq 10 is solved with the initial conditions and the boundary condition (eq 11), when the asymmetric temperature distribution is ignored in the steady state. The P = f(T) curves nearly overlapped with each other when the asymmetric temperature distribution was considered, and the steady-state curve could be used to predict the internal pressure of specimens.21 The solution is well-known as P ¼ ½1 þ Γð1 R 2 Þ1=2
ð13Þ
Setting R = 0 in eq 13 gives Pmax ¼ ð1 þ ΓÞ1=2
the nondimensional half thickness. The nondimensional gas releasing rate Γ is given by Γ¼
ζFapp, T0
4 2 nπRm, T p0 ð1 þ βT ÞτMg
dwp dT
B0T
ð15Þ
T
Materials expand obviously when Pmax exceeds the nondimensional critical pressure. It denotes that the maximum value of Pmax is equivalent to the nondimensional critical pressure, which does not result in expansion and breakage. According to the Tresca yield criterion, a suitable heating rate satisfies the following equation: Pmax ðB0T Þ e ðσ T =p0 þ 1Þ
ð14Þ
where P = p/p0 is the nondimensional pressure and R = 2 L/b is
2μg b2 Rg T
ð16Þ
where σT is the tensile strength (Pa). 5355
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
Figure 5. Heating patterns based on mass transfer (b0 = 0.02 m). Figure 3. Thermogavimetrivc analysis for a binder coal-tar pitch at a 10 K/min heating rate in nitrogen.
true density); (5) the volume expansivity; and (6) the ratio of the volume of cells to that of capillaries. On the basis of the experimental data, Figure 2 shows the values of the tensile strength σT(MPa), the true density Ftr (kg/m3), and the volume expansivity β at different temperatures. 8 > 5, T < 373 K > > < 62:8 0:336T þ 7:13 104 T 2 σT ¼ 7:52 107 T 3 þ 3:96 1010 T 4 > > > : 8:22 1014 T 5 , T < 373 K ð18Þ ( Ftr ¼
1865, 1573 þ 0:721T 2:543 104 T 2 ,
T < 500 K T g 500 K ð19Þ
Figure 4. Composition of major hydrocarbon gases generated during the carbonization of pitch. βT ¼ 9:5 0:075T þ ð2:05 104 ÞT 2
According to eqs 216, the heating rate based on mass transfer is given by Mg χT 2 ð1 þ βT Þ εT0 R 2 ðσ 2 þ 2σ T p0 Þ B0T e dwp 2Rg Tμg Fapp, T0 τb02 ð1 þ kÞ m, T0 T ζ dT T
ð17Þ The theoretical heating rate, based on mass transfer, to be evaluated is the maximum value of B0 T that satisfies eq 17. 2.2. Calculation for Heating Patterns on the Basis of Mass Transfer. A pitch-coke paste with a binder content of 23% by weight was obtained by mixing at 428 K, and green carbon blocks were obtained by molding at 408 K. The bulk density of the specimens was 1750 kg/m3. The coal-based needle coke used in this study was produced by Shanghai Hongte Chemical Co., Inc. The ultimate analysis, as well as some other characteristics of this material, is presented in Table 1. The coal-tar pitch used in the study was produced by Shanghai Hongte Chemical Co., Inc. The analytical data of the pitch are summarized in Table 2. For the theoretical heating rate on the basis of mass transfer, eq 17 includes the following factors: (1) the amount of binder and pyrolysis rate of binder pitch; (2) the mean pore radius and porosity of the green specimen; (3) the physical properties of pyrolysis gases (the viscosity and the mean molecular weight); (4) the physical properties of the specimen (tensile strength and
ð2:38 107 ÞT 3 þ ð1:2 1010 ÞT 4 ð2:22 1013 ÞT 5
ð20Þ From thermogravimetric measurements on the modified pitch with a softening point at 382.6 K, the weight wp,T and the derivative weight (dwp/dT)T can be described as shown in Figure 3. The pyrolysis products were characterized by thermovolumetric measurements with subsequent analysis of the gas compositions. The gases were mainly composed of H2, CH4, and C2H6, as shown in Figure 4,19 and the molecule weight Mm and the gas viscosity μm could be calculated by the composition of the pyrolysis gas.23 The green mean pore radius Rm,T0 was 2.0 μm.19 The calculation was performed for the specimen with 0.02 m height, 1750 kg/m3 green bulk density, 23% pitch content, and 2.0 μm green mean capillary radius. The values τ = 2, T0 = 373 K, Tmax = 1100 K (heat-treatment temperature), and p0 = 0.101 MPa (external pressure) were determined. Substituting eqs 1822 into eq 17, B0 T was obtained as a function of the temperature and the ratio of the volume of cells to that of capillaries, as shown in Figure 5. Figure 5 shows that B0 T has to be reduced in the range 450 850 K and the heating patterns during carbonization of the molded mixtures are similar to industrial heating patterns. However, except in the range 450850 K, the heating rates are unreasonable for the enormous calculated values. It cannot describe the fractures that mainly appeared at the elastic stage. 5356
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
Figure 7. Experimental setup: (a) specimen; (b) granular mixture of 90% river sand and 10% met coke; (c) mullite sagger; and (d) thermocouple.
Figure 6. Heating patterns based on heat transfer (b0 = 0.02 m).
Furthermore, the model parameter k needs to be confirmed by experiments. 2.3. Heating Patterns on the Basis of Heat Transfer. In order to assess the fractures of specimens quantitatively, it is necessary to know the magnitudes of thermal stress in the specimens at the elastic stage. According to the maximum-principalstress theory, fracture occurs in elastic materials when the maximum principal stress σ1 (Pa) exceeds the tensile strength σt (Pa). It denotes that the maximum value of σ1 is equivalent to σt, which does not result in fracture. A suitable heating rate satisfies the following equation: σ1 ðB00T Þ σt e ð21Þ E E max According to the previous research on the maximum thermal stress,20 (σ1/E)max is approximated by σ1 jαjB00T b02 ¼ ð22Þ E max 32ð1 ηÞkef f Substituting eq 22 into eq 21, B00 T can be calculated by 32ð1 ηÞkef f σ t B00T e jαjb02 E
ð23Þ
where B00 T is the heating rate based on heat transfer (K/s); keff = λeff/(FappCP,app) is the effective thermal diffusivity; E is the Young’s modulus (Pa); and η is the Poisson’s ratio. The linear expansion coefficient α (1/K) can be calculated as follows: α ¼ d½ð1 þ βT Þ1=3 =dT
ð24Þ
The theoretical heating rate evaluated is the maximum value of B00 T that satisfies eq 23. Based on the experimental data, CP,app [ J/(kg K) ], λeff [W/(m K)], are given by ( 1250, T < 600 K CP, app ¼ ð25Þ 1250 þ 1:25ðT 600Þ, T g 600 K λef f ¼ expð 0:660 ð4:53 103 ÞT þ ð5:12 106 ÞT 2 Þ
ð26Þ
Little information is available on Young’s modulus E and Poisson’s ratio η of the artifacts during carbonization. The results are therefore represented by the normalized quantity σt /E. The values σt /E = 1.1 102 at T e 770 K and 3.3 103 at
Figure 8. Profiles of the specimen surfaces after baking (a) 0.20 K/s; (b) 0.25 K/s; (c) 0.30 K/s; and (d) 0.35 K/s.
T > 770 K are selected. The value η = 0.2 is obtained from experiments with coke pieces.20 Substituting eqs 2426 into eq 23, and selecting b0 = 0.02 m, B00 T is obtained as a function of temperature, as shown in Figure 6. Figure 6 shows the estimated heating patterns based on heat transfer. It is predicted that high heating rates can be used in the range 300400 K; with 600800 K, and out of the range, heating rates should be reduced. By comparing Figure 2c with Figure 6, it is concluded that the first peak of the heating rate is due to the contraction peak P1 in Figure 2c, and the other peak is due to the expansion peak P2.
3. EXPERIMENT AND DISCUSSION For the measurement of the model parameter k, green carbon blocks with a thickness of 0.02 m, a length of 0.16 m, and a width of 0.08 m were prepared. To eliminate the temperature difference, green carbon blocks were pyrolyzed in a shaft furnace with pentahedral heating. The experiment was designed as shown in Figure 7. The samples were pyrolyzed at a constant heating rate from 298 K to the final temperature, which was in all cases equal to 923 K; then, they were isothermally treated for an hour. After that, the samples were cooled to room temperature naturally. The visible cracks, convexity, and other distortions of the treated samples were examined, as shown in Figure 8. During the experiments, with the specimens with the thickness of 0.02 m, the critical heating rate Bcr was 0.20 K/s. When the heating rate was higher than 0.20 K/s, convexity appeared in the specimens. Even when the heating rate was 0.35 K/s, visible cracks did not appear in the specimen. On the basis of the heating patterns due to heat transfer shown in Figure 6, the theoretical minimum heating rate was 3.85 K/s. The heating rate 0.35 K/s was greater than the minimum of B0 T, while it was less than the minimum value of B00 T. On the basis of the above-mentioned analysis, it was concluded that the critical heating rate 0.20 K/s was the minimum value of B0 T. According to the minimum heating rates based on mass 5357
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
new product, using the above method, the heating pattern can be evaluated.
Figure 9. Theoretical heating rates of industrial specimen with a 0.4 m thickness.
4. CONCLUSIONS The capillarycell model was built to evaluate the internal pressure resulting from volatile matter in the green carbon blocks during carbonization, and the constant ratio of the volume of cells to the volume of capillaries equalled 210. Combining the pyrolysis gas transfer kinetics on the basis of the capillarycell model, with the maximum thermal stress produced by the asymmetric temperature distribution in the specimen, the theoretical model of heating patterns was proposed. The theoretical heating rates could be calculated with the physicochemical properties of green carbon blocks. The results showed that the theoretical heating rates were mainly controlled by mass transfer in the range 467850 K and by heat transfer out of that range. Comparing the calculated values of the new model with the industrial results, the validity of the proposed method is proved. ’ AUTHOR INFORMATION Corresponding Author
*Fax: +86-21-64252826. Tel.: +86-21-64252065. E-mail: gmlu@ ecust.edu.cn (G.L.). E-mail:
[email protected] (Z.S.).
Figure 10. Optimum heating rates of industrial specimen with a 0.4 m thickness.
transfer, k was approximately calculated by k ¼ min½ð1 þ kÞB0T =Bcr 1
ð27Þ
On the basis of Figure 5 and eq 27, the model factor k equalled 210. To verify the new model reasonably, the heating patterns of industrial specimens of 0.4 m thickness and with the other parameters remaining the same, as previously mentioned, were calculated, as shown in Figure 9. Figure 9 shows that the estimated heating rates based on heat transfer are higher than those based on mass transfer when the temperature is within the range 467850 K, but out of the region, the trend is opposite. Based on the minimal values of the two curves, the theoretical heating patterns are given. In industry, the heating process is divided into N sections. A constant heating rate is assumed in each temperature range. An optimum heating rate (Bk)opt (K/h) in the range Tk1 e T e Tk (k = 1 N) satisfies the following equations: ðBk Þopt e BT Tk1 e T e Tk
ð28Þ
BT ¼ minðB0T , B00T Þ
ð29Þ
where BT (K/h) is the theoretical heating rate. The value N = 4 is selected. Figure 10 shows the optimum heating rates of industrial specimens with a 0.4 m thickness. The model predicts that (Bk)opt is 1.8 K/h in the range 500700 K and 2.5 K/h in the range 700900 K, which is agreement with the industrial results.24 This demonstrates the validity of the proposed method. For a
’ ACKNOWLEDGMENT We thank Professor Ping Li for her useful advice for our manuscript. We acknowledge financial support by the National Natural Science Foundation of China (Grant No. 50874048), National High-Tech R&D Program (863 Projects) of China (No. 2009AA06Z102), the Fundamental Research Funds for the Central Universities, and State Key Laboratory of Exploration Fund of China. ’ REFERENCES (1) Pierson, H. O. Handbook of Carbon, Graphite, Diamond and Fullerene; Noyes: Park Ridge, NJ, 1993; pp 87121. (2) Schobert, H. H.; Song, C. Chemicals and materials from coal in the 21st century. Fuel 2002, 81, 15–32. (3) Atria, J. V.; Rusinko, F., Jr.; Schobert, H. H. Structural ordering of Pennsylvania anthracites on heat treatment to 20002900°C. Energy Fuels 2002, 16, 1343–1347. (4) Gonzalez, D.; Montes-Moran, M. A.; Garcia, A. B. Graphite materials prepared from an anthracite: a structural characterization. Energy Fuels 2003, 17, 1324–1329. (5) Gonzalez, D.; Montes-Moran, M. A.; Garcia, A. B. Influence of inherent coal mineral matter on the structural characteristics of graphite materials prepared from anthracites. Energy Fuels 2005, 19, 263–269. (6) Cabielles, M.; Montes-Moran, M. A.; Garcia, A. B. Structural study of graphite materials prepared by HTT of unburned carbon concentrates from coal combustion fly ashes. Energy Fuels 2008, 22, 1239–1243. (7) Cabielles, M.; Rouzaud, J. N.; Garcia, A. B. High-resolution transmission electron microscopy studies of graphite materials prepared by high-temperature treatment of unburned carbon concentrates from combustion fly ashes. Energy Fuels 2009, 23 (2), 942–950. (8) Lu, Z.; Maroto-Valer, M. M.; Schobert, H. H. Catalytic effects of inorganic compounds on the development of surface areas of fly ash carbon during steam activation. Fuel 2010, 89, 3436–3441. (9) Ko, T. H.; Chen, P. C. Study of the pyrolysis of phenolic resin reinforced with two-dimensional plain-woven carbon fabric. J. Mater. Sci. Lett. 1991, 10, 301–303. 5358
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
Energy & Fuels
ARTICLE
(10) Chang, W. C.; Ma, C. C. M.; Tai, N. H.; Chen, C. B. Effect of processing methods and parameters on the mechanical properties and microstructure of carbon/carbon composites. J. Mater. Sci. 1994, 29, 5859–5867. (11) Lakin, R. J. Assessment techniques for graphite electrodes. Fuel 1978, 57, 151–154. (12) Song, Y. Z.; Qiu, H. P.; Guo, Q. G.; Zhai, G. T.; Song, J. R.; Liu, L. Effect of the electrical and thermal conductivity of bulk graphite. New Carbon Mater. 2002, 17 (2), 56–60. (13) Rubenstein, J.; Davis, B. Wear testing of inert anodes for magnesium electrolyzers. Metall. Mater. Trans. B 2007, 38 (2), 193–201. (14) Henning, K. D; Bongartz, W.; Knoblauch, K. Mechanical properties of pitch-coal extrudate during the carbonization process. Fuel 1987, 66 (11), 1516–1518. (15) Vohler, O. V.; Sturm, V.; Wege, E. Ullman’s Encyclopedia of Industrial Chemistry; John Wiley & Sons, Inc.: New York, 1986. (16) Ehrburger, P.; Sanseigne, E.; Tahon, B. Formation of porosity and change in binder pitch properties during thermal treatment of green carbon materials. Carbon 1996, 34 (12), 1493–1499. (17) Trick, K. A.; Saliba, T. E.; Sandhu, S. S. A kinetic model of the pyrolysis of phenolic resin in a carbon/phenolic composite. Carbon 1997, 35 (3), 393–401. (18) Ko, T. H.; Kuo, W. S.; Tzeng, S. S.; Chang, Y. H. The microstructural changes of carbon fiber pores in carboncarbon composites during pyrolysis. Compos. Sci. Technol. 2003, 63, 1965–1969. (19) Born, M. Pyrolysis and behavior in the baking of industrial carbons. Fuel 1974, 53, 198–203. (20) Fukai, J.; Orita, H.; Yu, X.; Isokawa, I.; Miyatake, O. Heating patterns during carbonization of formed mixtures of coke and pitch. Fuel 1996, 75 (7), 809–815. (21) Fukai, J.; Orita, H.; Yu, X.; Isokawa, I.; Miyatake, O. Modeling of heat transfer, gas flow, and stress in porous material with thermal decomposition. Kagaku Kogaku Ronbunshu 1995, 21 (2), 378–384. (22) Born, M.; Seichter, A.; Starke, S. Characterization of baking behaviour of carbonaceous materials by dilatation investigations. Carbon 1990, 28 (23), 281–285. (23) Sun, W.; Wang, J. Design Manual Throttling Device Flow Measurement; Chemical Industry Press: Beijing, 2000 (in Chinese). (24) Li, S. H. Graphite Electrode Manufacturing; Metallurgy Industry Press: Beijing, 1997 (in Chinese).
5359
dx.doi.org/10.1021/ef201055r |Energy Fuels 2011, 25, 5353–5359
