Ind. Eng. Chem. Res. 2008, 47, 4029–4033
4029
APPLIED CHEMISTRY Waste Tire Pyrolysis: Comparison between Fixed Bed Reactor and Moving Bed Reactor E. Aylo´n, A. Ferna´ndez-Colino, M. V. Navarro, R. Murillo,* T. Garcı´a, and A. M. Mastral Instituto de Carboquı´mica, CSIC, M Luesma Castan 4, 50018-Zaragoza, Spain
Waste tire pyrolysis has been performed in a fixed bed and a moving bed reactor, in order to know the influence of the reactor type on the yields and product characteristics. Typical pyrolysis conditions have been used in both reactors (600 °C and inert atmosphere). The moving bed reactor operates in continuous mode, and it is designed to process up to 15 kg/h of waste tire. An excellent process reproducibility and stability was observed. Moreover, when results obtained in the fixed bed and moving bed reactors are compared, it can be appreciated that total rubber conversion is achieved in both systems although solid residence time in the fixed bed is clearly longer than that in the moving bed reactor. In addition, a more severe cracking of the primary pyrolysis products occurs in the moving bed reactor due to the faster heating rate and the longer gas residence time. Regarding the pyrolysis products, the solid fraction is mostly constituted of carbon black, the liquid phase is a complex hydrocarbon mixture and the gas phase is a mixture of light hydrocarbons, carbon dioxide, carbon monoxide, hydrogen sulfide, and hydrogen. Introduction In spite of the efforts, the disposal of products at the end of their life still remains as an important environmental problem. In fact, this is a challenging problem for waste tires which represent over 2% of total solid waste. In only the European Union, it is estimated that around 250 million car and truck tires are discarded each year which is about 2.6 million tones of tire. Worldwide generation of waste tires is estimated to be 1 billion tires.1 The need to deal with this problem has been highlighted by the European Union that has attempted to control the management of tires through two European Commission Directives: The Waste Landfill Directive (1999)2 which bans the landfilling of tires by 2006 and The End of Life Vehicle Directive (2000)3 which stipulates the selective collection of tires from vehicle dismantlers and encourages the recycling of them. These two directives will have a great impact on the management of tires throughout the European Union. Up to now, the current main routes for the management of waste tires in Europe have been landfilling (40%), energy recovery (20%), material recycling (18%), rethreading (11%), and exportation (11%). Considering that The Waste Landfill Directive is now enforced, it is urgent to develop alternative technologies for recycling at least the 40% waste tires that are dumped in landfills. These technologies must ensure the tire transformation into usable products or into energy while being environmentally friendly. Tire material has high volatile and fixed carbon contents with heating values greater than that of coal and biomass. These properties make it an ideal raw material for thermochemical processes.4 Pyrolysis can be an alternative for waste tire management. After tire pyrolysis, three phases are obtained: gas, liquid, and solid. While solid and liquid products are recovered, stored, and possibly commercialized, the gas fraction can be * To whom correspondence should be addressed. Phone: 34 976 733977. Fax: 34 976 733318. E-mail:
[email protected].
used in situ to provide the energy requirements of the process, contributing to design a cost-effective and thermally integrated process. Different experimental systems have been used to perform waste tire pyrolysis. The use of a thermobalance has been reported5–8 in order to obtain kinetic information, fluidized bed reactors,9–11 batch reactors,12 and many configurations based on fixed bed reactors have also been reported.13–15 However, there are few works regarding waste tire processing in continuous reactors. Dı´ez et al.14 used a moving bed reactor with a batch feeding system. In addition, the aim of the process was to perform total tire combustion in a supplementary reactor where the gas and solid fractions were burnt together. Serrano et al.16 have developed a reactor for polymer degradation, but it can be operated only up to 100 g/h. The main objective of this work is to show the technical viability of a continuous pyrolysis pilot plant and compare the results with the ones obtained in a fixed bed reactor in terms of yields and product characteristics. 2. Experimental Details 2.1. Feedstock Characteristics. The raw material used for the pyrolysis experiments was a sample of tire rubber shreds supplied by Negrell Residus S.L., a Spanish waste tire recycling company. These tire shreds were a mixture of tires from trucks, tractors, and cars. The average particle size was 2 mm. The ultimate and proximate analyses of the waste tire sample are compiled in Table 1. 2.2. Fixed Bed Pyrolysis Reactor. The swept fixed bed reactor was 30 cm long and had an internal diameter of 2.54 cm. The reactor was constructed in stainless steel and was heated by an external electrical furnace. It was purged continuously with nitrogen at a flow rate of 2 L N/min to sweep the evolved gases from the reaction zone. Approximately 65 g of tire sample was placed on a support in the center of the hot zone of the reactor, heated at a controlled rate of 5 °C/min to a final temperature of 600 °C, and held for 10 min. The liquid products
10.1021/ie071573o CCC: $40.75 2008 American Chemical Society Published on Web 05/14/2008
4030 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 Table 1. Proximate and Ultimate Analyses of the Rubber Tire and the Char Obtained in Waste Tire Pyrolysis (as received basis)
C (%w) H (%w) S (%w) N (%w) % ash % moisture % volatile matter
rubber tire
fixed bed
moving bed
81.72 6.54 1.87 0.55 6.64 0.71 62.58
81.57 0.84 2.95 0.33 13.82 0.26 2.51
82.10 0.97 3.41 0.35 13.17 1.24 3.50
were condensed in a cold trap which was weighed at the end of the experiments to determine the mass of the condensed liquid products. After completion of the pyrolysis, the reactor was allowed to cool down and the solid material was recovered and weighed. Finally, noncondensable gases were sampled and analyzed by gas chromatography. The noncondensable gas yield was calculated by difference. Five experiments were performed under identical conditions in order to determine the reproducibility of the experimental procedure that turned out to be 2.6 wt % for char, 1.8 wt % for oil, and 5.3 wt % for gas. 2.3. Moving Bed Pyrolysis Reactor. A schematic diagram of the reactor is shown in Figure 1. Four main parts can be observed: the feeding system, the reactor, the solid collecting system, and the condensing system. The feeding system (1) consists of two hoppers coupled by a butterfly valve with a total capacity of 10 kg of tire shreds approximately. This system allows carrying out the process continously under inert atmosphere by using nitrogen as carrier gas. The shredded tire is fed to the reactor (3) by a screw (2). This screw allows selecting the feed mass flux introduced in the reactor. The reactor is also a screw but is surrounded by an electric heater (4) in order to supply the required energy to perform the endothermic reaction. This heating system is divided in three areas provided with a K-type thermocouple in order to achieve an optimum control of the reactor temperature. The tire shreds move through the reactor, and at the same time, they decompose into a gaseous product and a solid residue. The solid residue leaves the reactor by gravity falling into a solid collecting system (5). It is important to highlight that the solid can be recovered during the experiment. The gas from the reactor reaches the condenser by natural convection and helped by the carrier gas. The condensing system (6) consists of a shell-and-tube counter current flow condenser with water circulating in the shell side as the cold fluid. The liquid fraction goes down the tubes by gravity and it is recovered in a liquid collector situated at the bottom of the condenser. Eventually, the noncondensed pyrolysis gas is conducted to a burner (7) before it reaches the atmosphere. Five experiments were carried out under the same conditions to determine the plant reproducibility. A constant mass flow of 6 kg/h was fed to the reactor for 4 h. The pyrolysis was performed at 600 °C with a solid residence time of 3.7 min and an inert gas flow of 1.2 L N/min. From this series of experiments, it was found that the standard deviation for the solid yield was 2.4 and 2.9 wt % for the liquid yield and 5.8 wt % for the gas yield. In addition, a longer experiment was performed (8 h) in order to study the process stability and possible deviations from the steady state parameters. The pyrolysis conditions were the same as in the other experiments, except the tire mass flow, 3.5 kg/h in this case. Samples of the three fractions (solid, liquid, and gas) were taken at timed intervals throughout the experiment. 2.4. Product Analysis. Permanent gases were analyzed in a Varian 3800 CP gas chromatograph equipped with a thermal
conductivity detector (TCD) and HAYESEP Q and Mole Sieve HP-Al/KCl columns. Hydrogen was analyzed in a HewlettPackard 5890 series II model, equipped TCD detector and a Mole Sieve column with Ar as carrier gas. For C1-C4 compounds, a split/splitless injector, flame ionization detection (FID), and a wide bore capillary Supelco KCl/Al2O3 column system was employed. The gross calorific values of the gases were calculated from their individual gross calorific values and their fraction present in the total gas volume. The ultimate liquid composition was determined using a Carlo Erba analyzer model EA1108. In addition, the tire oil was analyzed by GC-FID in a Varian Star 3400 model in order to find the boiling point range according to the simulated distillation method described in ASTM D2887-04. Finally, thin layer chromatography (TLC) with an FID (IATROSCAN MK-5) was performed to determine the saturate, aromatic, and polar compound content in the sample. 3. Results and Discussion 3.1. Product Yield. The char yield obtained is similar in both reactors, about 38% of the raw material. According to previous results obtained in thermobalance,6 the raw material has been completely devolatilized in both reactors. This percentage corresponds to the inorganic material and the carbon black present in the sample. Total rubber conversion is achieved in both systems, although solid residence time in the fixed bed (30 min) is clearly longer than in the moving bed reactor (3.7 min). A considerable production of liquid has been obtained, over the 50% in the fixed bed reactor. It can be observed that the liquid and gas yields are different depending on the installation. In this way, the liquid yield decreases (from 54.6% to 43.2%) and the gas yield increases (from 7.5% to 17.1%) when the pyrolysis is performed in the moving bed instead of in the fixed bed reactor. This fact can be attributed to the faster heating rate and the longer gas residence time in the moving bed reactor where a more severe cracking of the pyrolysis products occurs. Regarding to the moving bed reactor, it is important to point out that the experiment has been completed satisfactorily, and no problem was detected working during such a long time (8 h). Although the amount of tire pyrolyzed (28 kg) and the products obtained is very high (11.1 kg of solids and 12.1 kg of liquids), the feeding of the raw material and the extraction of the products has been carried out continuously during the experiment without altering the conditions and the inert atmosphere inside the reactor. This fact confirms the appropriate design of such a complex installation. 3.2. Characterization of the Pyrolysis Fractions. Gas Fraction. Table 2 shows the gas composition for the samples taken during the experiment performed in the moving bed reactor. It is shown that the pyrolysis gas is mainly composed of light hydrocarbons, CO, CO2, H2, and H2S, corresponding to the highest concentration to CH4 and H2. It is important to highlight that H2 percentage in the gas produced in the moving bed reactor is close to 40% in volume. The COx components must be mostly derived from the oxygenated organic compounds present in tires, such as stearic acid, extender oils, etc. On the other hand, the presence of H2S comes from the decomposition of the sulfur links of the vulcanized rubber structure. Concerning hydrocarbons, C4 compounds represent a significant percentage of the gas sample, mainly the isobutylene, which is probably formed in the polyisoprene depolymerisation, one of the main components of the rubber tire. All the samples taken during
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4031
Figure 1. Moving bed reactor pilot plant. Table 2. Composition of Gases Produced in the Pyrolysis of Waste Tire (percent volume)
Table 3. Ultimate and TLC-FID Analyses of Oils from Waste Tire Pyrolysis
moving bed reactor t (h)
1.5
3.0
4.5
6.0
7.5
H2 36.9 39.0 38.7 37.0 40.1 CO2 2.3 2.3 2.4 2.2 2.4 CO 1.9 2.0 1.8 1.5 1.9 H2S 2.2 2.1 2.2 2.1 2.3 methane 20.0 19.1 19.4 19.9 19.4 ethane 5.5 5.2 5.3 5.4 5.4 ethene 5.7 5.5 5.7 5.7 5.7 propane 2.8 2.4 2.4 2.5 2.4 propene 1.6 1.3 1.4 1.4 1.3 iso-butane 0.6 0.5 0.5 0.5 0.5 butane 0.3 0.2 0.2 0.2 0.2 trans-2-butene 0.4 0.4 0.4 0.3 0.3 1 butane 0.2 0.2 0.2 0.2 0.2 isobutene 4.4 4.3 4.3 4.2 4.2 c2-butene 0.3 0.3 0.3 0.3 0.3 1,3,butadiene 0.7 0.6 0.7 0.7 0.7 total 85.7 85.4 85.9 84.2 87.6
moving bed reactor average fixed bed reactor 38.3 2.3 1.8 2.2 19.6 5.4 5.7 2.5 1.4 0.5 0.2 0.4 0.2 4.3 0.3 0.7 85.8
30.4 2.9 2.38 1.55 23.27 6.20 4.45 5.17 2.48 1.24 0.2 0.72 0.10 7.55 0.52 0.41 89.5
the experiment show a very similar composition. This fact reveals a good stability of the process. The different gas compositions from tire pyrolysis found in the literature indicate that, unlike the liquid and solid fraction, the composition of the gases is not only affected by the reaction temperature but also by the experimental installation and even the raw material. The results shown in Table 2 reflect the influence of the experimental system on the gas composition. Some differences can be observed between the results obtained from the fixed bed reactor and the moving bed reactor. In the case of the moving bed reactor, the percentage corresponding to the lightest compounds is higher than in the fixed bed reactor. This fact was also observed by Dı´ez et al.14 carrying out the pyrolysis in fixed bed and in a batch moving bed pilot plant. The more severe cracking of the products in the moving bed reactor can be attributed to the faster heating rate and longer gas residence time in this reactor. A slow heating rate allows a gradual degradation of the different polymers that constitute the
T (h)
2.0
3.5
5.0
6.5
C (% w) H (% w) N (% w) S (% w) saturate (%) aromatic (%) polar (%)
84.35 10.3 0.91 0.99 4.9 69.8 25.3
85.44 10.33 1.01 1.00 7.1 65.1 27.8
85.44 10.42 1.09 0.99 7.4 61.9 30.7
85.84 10.36 1.04 0.98 7.1 65.6 27.3
average fixed bed reactor 85.27 10.35 1.01 0.99 6.7 65.6 27.8
83.45 10.31 1.05 0.99 10.9 62.1 27.0
rubber. Thus, the new molecules formed leave the reactor before suffering more cracking reactions and the percentage corresponding to the lightest compounds is lower. Other authors17 have also pointed out the influence of the heating rate on the amount and composition of pyrolysis gas. This gas composition confers them a high calorific value (around 29 MJ/N m3) that could satisfy the process energy requirement.18 However, it would be necessary a previous gas cleaning in order to remove the hydrogen sulfide present in the gas fraction according to restrictive technical and environmental requirements. The presence of H2S in the gas would damage the downstream equipments due to the corrosive nature of this gas. In fact, only those gas streams with a H2S amount lower than 500 ppmv can be burnt in commercial alternative engines. Besides, the SO2 emitted after the gas stream combustion should meet with the strict legislation about residues incineration.19Liquid Fraction. Table 3 shows the ultimate analysis of the oils derived from the pyrolysis process in both reactors. It is observed that regardless the reactor used, similar results are found. The analysis performed by TLC-FID reveals that the oil is mainly comprised of aromatic hydrocarbons with a significant percentage of polar compounds. The aromatic content is due, on the one hand, to the aromatic nature of the source rubber material and, on the other hand, to the cyclation of primary pyrolysis products followed by dehydrogenation reactions or even to the tendency of small radicals to stabilize
4032 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
Figure 2. Comparison between distillation data of waste tire pyrolysis liquids, a commercial diesel oil, and a gasoline.
as six carbon aromatic structures. However, the polar percentage could be attributed to the presence of hydrocarbons with heteroatom such as sulfur as shows the ultimate analysis. This sulfur content is slightly over the legislated limit value according to the Spanish Royal Decree about gasoline, gas oil, and fuel oil specifications20 where it is established that the sulfur content in commercial fuel oils should be lower than 1 wt %. Although the analyses of the oils obtained are very similar, a slight difference in the aromatic and saturate percentages is observed. The lower percentage observed in the fixed bed reactor could be attributed to the fast removal of the pyrolysis products from the reaction zone preventing secondary reactions. Figure 2 shows the distribution boiling points of the tire pyrolysis oils compared with commercial automotive diesel oil and gasoline. The distillation range of the tire pyrolysis oils reflects the fact that the oils are unrefined and consequently have a wide range of boiling points. It can be observed that about 45% of the oil distillates under 200 °C, which corresponds to the limit boiling point of gasoline fraction and about 35% distillates between 210 and 360 °C, which corresponds to the diesel fraction. Tire pyrolysis oils were analyzed by GC/MS, and it was observed that the most abundant products are the BTX fraction, other substituted monoaromatic compounds with two or more short aliphatic chains and limonene. All of them can be considered as valuable products. Other authors12,21 have reported the presence of polycyclic aromatic compounds such as naphthalene, phenanthrene, fluorene, etc. in the pyrolysis oil. However, these hydrocarbons have not been detected in the present analysis, probably due to the low reaction temperature, short gas residence time, and the type of reactor. Finally, it is worth mentioning that the gross calorific value is rather high (41.8 MJ/kg), similar to a light fuel oil and reflects the potential of the oils to be used as synthetic liquid fuels.Solid Fraction. The results of the ultimate and proximate analyses of the initial tire sample and the solid fraction are reported in Table 1. The low volatile matter present in the solid residue indicates that the devolatilization has been completed satisfactorily in both reactors. According to these results, there is no influence of the experimental system on the solid characteristics because total conversion is achieved in both devices due to the inert character of carbon black under pyrolysis conditions.22,23 The solid residue after reaction is comprised of the initial mineral matter, the carbon black used in tire manufacturing, and some repolymerization products formed as a consequence of the process severity. The ash content has increased as the result of the polymeric material devolatilization. The ash percentage found in the char is high and similar to that reported
by other authors24 where the ash percentage ranges from 9% to 15% depending on the characteristics of the tire feed. Consequently, the pyrolytic char is not suitable for tire manufacturing due to this high ash content, which substantially decreased the carbon black reinforcing ability, unlike commercial carbon black that presents a maximum ash percentage around 1-2%. The sulfur content of the solid residue is high, even higher than 3%. This is probably due to the formation of metal sulfides, mostly zinc sulfide in the form of sphalerite,4 during the pyrolysis reaction. This high sulfur percentage in the solid residue implies that although solid residue yield is close to 40%, the 64% of the initial rubber tire sulfur concentrates in this fraction. In addition, according to the previous analysis of the liquid and gas fractions, approximately 23% of the initial sulfur remains in the liquid and only 13% in the gas fraction. These percentages are too high in order to meet with legislation, and it would be necessary to include some cleaning stages in the global process. 3.3. Process Scaling up. This work completes previous studies performed in a thermobalance reactor,5 demonstrating that scaling up the waste tire pyrolysis process is feasible. Total depolymerization has been achieved regardless the experimental device used and the amount of waste tire processed. Hence, milligrams, grams, and kilograms of waste tire are respectively pyrolyzed in the thermobalance, fixed bed reactor, and moving bed reactor. Therefore, it could be expected a satisfactory scaling up to an industrial reactor able to pyrolyze even tonnes of waste material. On the other hand, differences have been found regarding to product distribution and characteristics depending on the experimental device. Probably, these changes are due to the different heating rate and gas residence time used in both reactors. Obviously, both parameters clearly depend on the reactor geometry. This fact should be taken into account in order to perform an industrial design that could maximize the production of the most valuable fraction. Acknowledgment The authors would like to thank Negrell Residus S.L. for the tire sample supply and the Spanish Science and Education Ministry for the FPU Pre-Doc grant (E.A.) and the Ramo´n y Cajal Program contract (T.G.). Literature Cited (1) European Tyre Recycling Association. http://www.etra-eu.org/ (accessed Jan 2008). (2) European Commission. Landfill of Waste DirectiVe; Council Directive 1999/31/EC, European Commission: Brussels, Belgium, 1999. (3) European Commission. End of life Vehicle DirectiVe; Council Directive 2000/53/EC, European Commission: Brussels, Belgium, 1999. (4) Murillo, R.; Aylo´n, E.; Navarro, M. V.; Calle´n, M. S.; Aranda, A.; Mastral, A. M. The application of thermal processes to valorise waste tyre. Fuel Proc. Tech. 2006, 87 (2), 143–147. (5) Aylo´n, E.; Calle´n, M. S.; Lo´pez, J. M.; Mastral, A. M.; Murillo, R.; Navarro, M. V.; Stelmach, S. Assessment of tyre devolatilization kinetics. J. Anal. Appl. Pyrol. 2005, 74, 259–264. (6) Chen, F.; Qian, J. Studies of the thermal degradation of waste rubber. Waste Manage. 2003, 23, 463–467. (7) Leung, D. Y. C.; Wang, C. L. Kinetic study of scrap pyrolysis and combustion. J. Anal. Appl. Pyrol. 1998, 45, 153–169. (8) Senneca, O.; Salatino, P.; Chirone, R. A fast heating-rate thermogravimetric study of the pyrolysis of scrap tyres. Fuel 1999, 78, 1575– 1581. (9) Conesa, J.; Font, R.; Marcilla, A. Gas from the Pyrolysis of Scrap Tyres in a Fluidized Bed Reactor. Energy Fuels 1996, 10, 134–140. (10) Araki, T.; Niikawa, H.; Hosoda, H.; Nishizaki, H.; Mitsui, S.; Endoh, K.; Yoshida, K. Development of fluidized-bed pyrolysis of waste tires. Resour. ConserV. Recycl. 1979, 3, 155–164.
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4033 (11) Shu-Yii, W.; Mao-Feng, S.; Baeyens, J. The fluidized bed pyrolysis of shredded tyres: the influence of carbon particles, humidity and temperature on the hydrodinamics. Powder Technol. 1997, 93, 283–290. (12) Laresgoiti, M. F.; Caballero, B. M.; de Marco, I.; Torres, A.; Cabrero, M. A.; Chomo´n, M. J. Characterization of the liquid products obtained in tyre pyrolysis. J. Anal. Appl. Pyrol. 2004, 71 (2), 917–934. (13) Gonza´lez, J. F.; Encinar, J. M.; Canito, J. L.; Rodrı´guez, J. J. Pyrolysis of automobile tyre waste. Influence of operating variables and kinetics study. J. Anal. Appl. Pyrol. 2001, 58-59, 667–683. (14) Dı´ez, C.; Sa´nchez, M. E.; Haxaire, P.; Martı´nez, O.; Mora´n, A. Pyrolysis of tyres: A comparison of the results from a fixed-bed laboratory reactor and a pilot plant (rotary reactor). J. Anal. Appl. Pyrol. 2005, 74 (1-2), 254–258. (15) Napoli, A.; Soudais, Y.; Lecomte, D.; Castillo, S. Scrap tyre pyrolysis: Are the effluents valuable products? J. Anal. Appl. Pyrol. 1997, 40-41, 373–382. (16) Serrano, D. P.; Aguado, J.; Escola, J. M.; Garagorri, E. Conversio´n of low density polyethylene into petrochemical feedstocks using a continuous screw kiln reactor. J. Anal. Appl. Pyrol. 2001, 58-59, 789–801. (17) Williams, P. T.; Besler, S.; Taylor, D. T. The pyrolysis of scrap automotive tyres. Fuel 1990, 69 (12), 1474–1482.
(18) Aylo´n, E.; Murillo, R.; Ferna´ndez-Colino, A.; Aranda, A.; Garcı´a, T.; Calle´n, M. S.; Mastral, A. M. Emissions from the combustion of gasphase products at tyre pyrolysis. J. Anal. Appl. Pyrol. 2007, 79 (1-2), 210– 214. (19) Spanish Royal Decree about Residues Incineration 653/2003, May 30th, 2003. (20) Spanish Royal Decree about gasolina, gas oil and fuel oil characteristics 61/2006, January 31th, 2006. (21) Cunliffe, A. M.; Williams, P. T. Composition of oils derived from the batch pyrolysis of tyres. J. Anal. Appl. Pyrol. 1998, 44, 131–152. (22) Murillo, R.; Navarro, M. V.; Lo´pez, J. M.; Garcı´a, T.; Calle´n, M. S.; Aylo´n, E.; Mastral, A. M. Activation of pyrolytic tyre char with CO2: kinetic study. J. Anal. Appl. Pyrol. 2004, 71 (2), 945–957. (23) Liu, Z.; Zondlo, J. W.; Dabyburjor, D. B. Tyre Liquefaction and its effect on coal-liquefaction. Energy Fuels 1994, 8 (3), 607–612. (24) Helleur, R.; Popovic, N.; Ikura, M.; Stanciulescu, M.; Liu, D. Characterization and potential applications of pyrolytic char from ablative pyrolysis of used tyres. J. Anal. Appl. Pyrol. 2001, 58-59, 813–824.
ReceiVed for reView November 20, 2007 ReVised manuscript receiVed February 7, 2008 Accepted March 19, 2008 IE071573O