Elementary Reactions and Intermediate Species Formed during the

Ind. Eng. Chem. Res. 2004, 43, 3097-3104

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APPLIED CHEMISTRY Elementary Reactions and Intermediate Species Formed during the Oxidative Regeneration of Spent Fluid Catalytic Cracking Catalysts J.-O. Barth, A. Jentys, and J. A. Lercher* Lehrstuhl II fu¨ r Technische Chemie, Technische Universita¨ t Mu¨ nchen, 85747 Garching bei Mu¨ nchen, Germany

The surface chemistry of coke precursors on spent fluid catalytic cracking catalysts during the oxidative regeneration process was investigated by temperature-programmed desorption and temperature-programmed oxidation experiments and IR spectroscopy. NH3 and HCN are formed via cracking and hydrolysis reaction of coke above 350 °C. The amount of NH3 released depends on the concentration of water in the samples. In contrast to water-free conditions, in the presence of 5% water, significantly lower amounts of coke N (40% vs 74%) were converted to NOx during the regeneration process. Temperature-programmed oxidation experiments indicated that polyaromatic nitrogen compounds are cracked to CO and HCN, which are subsequently oxidized in part to NO. The addition of Pt-based CO combustion promoters enhances the oxidation of reduced nitrogen intermediates and leads to an increase of NO emissions. Isotope-labeling experiments indicate that NO reacts to N2 with CO generated during the regeneration and HCN/ NH3 formed during pyrolysis of the coke species. 1. Introduction Fluid catalytic cracking (FCC) is a key process in modern refineries.1 Worldwide approximately 300 FCC units are operated, converting vacuum gas oil and high boiling residues into lighter fuel products and petrochemical feedstocks. Because of the central function of the FCC process, a range of technological improvements have been implemented to increase its economical benefits.2 In addition to investments concerning the process design, new catalysts and additives have been developed to fulfill the economic demands of the market and to obtain the desired products.3 However, refiners are bound to invest also in ecoefficient technologies for the production of fuels and petrochemicals with significantly reduced emissions of environmental pollutants. This is imposed by various national and international regulations addressing emissions from a range of refinery processes and especially FCC regenerators, such as NO, SOx, CO, and CO2 emissions from regenerator flue gases.1 Approximately 2000 tons of NOx/year are released from a typical refinery, among which the FCC units contribute approximately 50%. The concentrations of the NOx emissions from regenerator flue gases vary between 50 and 500 ppm depending on the nature of the feed, the operating conditions of the FCC unit, and the amount of CO promoter added.4,5 In the FCC process, nitrogen-containing species in the feedstock are cracked in the riser reactor to lighter molecules and a fraction is deposited in the coke on the spent catalyst. During oxidative regeneration of the * To whom correspondence should be addressed. Fax: +49/89/28913544. E-mail: [email protected].

catalyst, approximately 90% of the coke-bound nitrogen is converted to molecular nitrogen (N2), while the remaining part is released in the form of NO.4,6 Sources of nitrogen leading to NOx formation are mainly the FCC feedstock (“fuel NOx”), while only minor amounts ( 600 °C of FCC catalysts coked with various

nitrogen-containing precursor molecules (pyrrole, pyridine, and aniline). The TPD experiments on the coked catalysts demonstrate the strong influence of water on the formation of NH3 during coke pyrolysis. We have shown earlier by MALDI/LD-TOF-MS and elemental analysis that the main fraction of the nitrogen bound in coke exists in the form of (poly)aromatic alkylcarbazole (pyrrole) and quinoline (pyridine) derivatives.10,12 During pyrolysis, HCN and NH3 can be formed by cracking and/or hydrolysis of such polyaromatic species (cf. Figure 5). Cracking of nitrogen-containing precursor molecules leads to HCN, which can be subsequently oxidized to NO and N2O.13 In addition, at temperatures above 700 °C, HCN is hydrolyzed to NH3.13,14 This reaction is favored over (basic) oxides,14 such as clays and binder materials (e.g., kaolin), which are present in the matrix of cracking catalysts.1,2 A second route to the formation of NH3 is the hydrolysis of isocyanate (NCO) intermediates generated during the degradation of polycyclic nitrogencontaining aromatic molecules. In the FCC regenerator, approximately 1-7% water is present. Under these conditions, Al2O3 present in the FCC catalyst matrix will catalyze the hydrolysis of pyridine derivatives to NH3 via adsorbed isocyanate intermediates, as illustrated in Figure 5. The reaction of isocyanates with water leads to the formation of NH3 and CO2. Note that in the temperature region between 750 and 850 °C a distinct maximum for CO2 (m/e ) 44) is observed during TPD, parallel to the maximum/shoulder for NH3 at ∼820 °C (cf. Figure 2). IR spectra recorded during oxidative regeneration of coked FCC catalysts only show isocyanate intermediates if the experiment is performed with thermally activated samples (i.e., in the absence of water), whereas with nonactivated samples such species were not detected. This observation can be explained with an instantaneous hydrolysis of the intermediate species on the surface of the FCC catalyst, leading to NH3 and CO2. Our observations are supported by experiments of Ha¨ma¨la¨inen and Martti,15 who reported for coal combustion that the HCN/NH3 ratio in the pyrolysis gases decreases with an increasing fuelO/fuel-N ratio. This effect was attributed to the presence of phenolic OH groups (in the coal molecules), which are precursors for water and OH radicals favoring the formation of NH3. Nitrogen-containing coal species belong to the same class of compounds as the coke compounds (NOx precursor) found on deactivated FCC catalysts. 3.2. Generation of N2 and NO during Regeneration of Spent FCC Catalysts. 3.2.1. TPO of Coked FCC Catalysts and the Effect of Pt-Based Combustion Promoters. TPO experiments carried out with samples of a coked FCC catalyst in the presence and absence of a CO combustion promoter are shown in Figure 6. Carbon- and nitrogen-containing species were burnt sequentially; therefore, the maximum of NO formation (653 °C) occurred at significantly higher temperatures compared to that of CO and CO2 (570 °C, not shown). In the absence of a Pt-based CO combustion promoter, the maximum of NO emission was observed at higher temperatures than that of HCN (653 vs 622 °C). Note that NO2 was generated at lower temperatures (570 °C) together with the maximum of CO2 formation, while NH3 was not detected in the presence of oxygen. After the addition of a 1 wt % commercial CO combustion additive, remarkably higher amounts of NO and

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Figure 5. Pathways to the formation of nitrogen intermediates (HCN and NH3) in the FCC regenerator.

Figure 6. TPO of a coked FCC catalyst (5% O2): effect of Pt-based CO combustion promoters.

Figure 7. TPO of a coked FCC catalyst: effect of water. Full symbols: activation of the sample at 300 °C, 3 h, oxidation with 5% O2, absence of H2O. Open symbols: no activation, oxidation with 5% O2 in the presence of 5% H2O.

NO2 were formed and the maximum of desorption was shifted to lower temperatures [611 vs 653 °C (NO) and 558 vs 570 °C (NO2)]. The addition of the promoter led to an almost complete removal of HCN and a simultaneous increase of NO and NO2 concentrations. 3.2.2. TPO of Coked FCC Catalysts and the Effect of Water on the Formation of NOx and Reduced Nitrogen-Containing Species. Figure 7 shows an analysis of NO/NO2 emissions during TPO of

a spent FCC catalyst in a tubular fixed-bed reactor. To investigate the effect of water on the formation of NOx, the experiment was carried out in the presence or absence of 5% H2O. Under water-free conditions, significantly larger amounts of NO (1.2 µmol/100 mg of coked catalyst) were released during oxidative regeneration of the catalyst. The formation of NO showed a distinct maximum at T ) 680 °C and a shoulder at 390-550 °C. A total of 74% of the coke nitrogen was converted into NO and NO2. If the same experiment was performed in the presence of 5% H2O, only 0.7 µmol of NO and NO2 (∼40% coke nitrogen) was released during combustion of the carbonaceous deposits. Interestingly, in the TPO experiment in the presence of H2O, the characteristic shoulder in the NO emission (390-550 °C) was not observed. 3.2.3. TPO of Spent FCC Catalysts Isotope Labeled with 15N-Coke Species. To elucidate the formation of molecular nitrogen in the FCC regenerator, TPO experiments were performed using FCC catalysts deactivated with 15N-aniline as the coke precursor. Figure 8 demonstrates the formation of HC15N (m/e ) 28, superimposed by the CO desorption curve) and 15NH3 (m/e ) 18, superimposed by the H2O desorption curve) during oxidative regeneration of the isotope-labeled FCC catalyst. Both intermediates showed a desorption maximum at ∼760 °C, whereas CO formation led to a maximum at 675 °C. Molecular nitrogen (15N15N; m/e ) 30) was formed from 15N-nitrogen-containing coke

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Figure 8. TPO (2% O2) of a FCC catalyst deactivated with

15N-aniline

Figure 9. TPO (2% O2 and 2000 ppm of 14NO) of a FCC catalyst deactivated with 15N-aniline as the coke precursor.

species at 718 °C. The maximum of 15NO (m/e ) 31) desorption was shifted to higher temperatures (732 °C). The TPO of the catalyst after regeneration in the presence of 2% O2 and 2000 ppm of 14NO is shown in Figure 9. In the temperature range between 350 and 800 °C, 14NO was consumed during the regeneration experiment with a distinct minimum of the 14NO concentration at 660-750 °C. Only minor formation of 14NO (m/e ) 46) by oxidation of 14NO was observed in 2 this experiment (not shown); therefore, the formation 14NO cannot account for the consumption of 14NO 2 observed. The reduction of 14NO can be tentatively divided into two reactions: (i) reduction of 14NO below T ) 670 °C (reduction zone I) and (ii) reduction at T ) 670-800 °C (reduction zone II). The first decrease of the 14NO concentration followed the formation of CO in the regeneration experiment. The second minimum (maximum of the NO reduction) occurred at the same temperature as that of the maximum formation of 15NH and HC15N. Note that parallel to the consumption 3 of 14NO isotopically scrambled molecular nitrogen (14N15N; m/e ) 29) was formed with a maximum at ∼720 °C. For 14N14N, a distinct maximum could not be unambiguously attributed because the desorption was superimposed by the generation of relatively large amounts of CO and HC15N (m/e ) 28). The experiments carried out suggest that for the generation of N2 and NO during regeneration of spent FCC catalysts several effects are important, i.e., (i) enhancement of NOx emissions by the use of noble metal containing CO combustion promoters, (ii) the influence of water on the formation of nitrogen intermediates and

as the coke precursor.

NOx, and (iii) reaction of NOx with such intermediates and nitrogen-containing coke species. The simultaneous formation of HCN and NH3 (maximum: 760 °C) was conclusively shown to occur even under oxidizing conditions using TPO of deactivated FCC catalysts containing 15N-coke compounds (cf. Figure 8). Under oxidative conditions, the intermediate NH3 was only observed if the catalyst was loaded with relatively high concentrations of nitrogen-containing coke (0.51 wt % N). The addition of a Pt-based CO combustion promoter to the FCC catalyst leads to a total suppression of NH3 and an almost complete oxidation of HCN, while NO and NO2 concentrations increase simultaneously. This observation is in agreement with the reports of Yaluris and Peters7,8 and is tentatively explained by a Pt-catalyzed oxidation of the nitrogen intermediates to NO and NO2 analogous to the Ostwaldt process (eqs 1 and 2).

4HCN + 7O2 f 4NO + 4CO2 + 2H2O

(1)

2NH3 + 2.5O2 f 2NO + 3H2O

(2)

HCN and NH3 may not only be oxidized to NO but also directly to N2 (eqs 3 and 4).

4HCN + 5O2 f 2N2 + 4CO2 + 2H2O

(3)

2NH3 + 1.5O2 f N2 + 3H2O

(4)

HCN + H2O f NH3 + CO

(5)

H2O has a remarkable influence on the concentration of NOx emitted during oxidative regeneration. In an earlier study, we showed that in the presence of water the concentration of HCN formed during oxidative regeneration was significantly lower than that formed during water-free conditions.10 The difference is attributed to the hydrolysis of HCN (eq 5) and NCO intermediates (see Figure 5) in analogy to the chemistry occurring during coal combustion.14,15 Note that in Figure 7 the NO emission started at temperatures around 350 °C, which is in agreement with the temperature of the formation of NCO and HCN intermediates observed by TPD, TPO, and IR experiments. In the presence of water (significantly lower NO emissions), both NOx precursors are easily converted to NH3. Such transformations lead to a higher concentration of NH3 in the regenerator, which can act as an in situ reductant

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Figure 10. Formation of N2 in the FCC regenerator by the direct reaction of NO+ with nitrogen-containing coke species.

for NO.16-18 Concerning the role of water in the FCC unit, it has to be mentioned that, in a typical commercial reactor, steam stripping of occluded hydrocarbons from the catalyst surface is performed at 480-540 °C. Higher temperatures (600-750 °C) are encountered in the regenerator, where steam rarely exceeds the 10% limit. The concentration of water in the FCC regenerator is determined by the C/H ratio of the coke. The above-described observations strongly imply that at temperatures below 670 °C NO is mainly reduced by CO (eq 6), whereas at higher temperatures the reaction between 14NO and intermediates such as 15NH3 and HC15N (eqs 7 and 8) becomes the dominant effect, leading to isotopically scrambled molecular nitrogen species.

2NO + 2CO f N2 + 2CO2

(6)

3NO + 2NH3 f 2.5N2 + 3H2O

(7)

2HCN + 5NO f 3.5N2 + 2CO2 + H2O

(8)

Under the conditions of the FCC unit, isocyanates can be generated by oxidation of HCN (eq 9).

HCN + 0.5O2 f HNCO

(9)

NCO- species react with NO to form N2O and N2 (eqs 10 and 11). The reaction of 14NO with CO present in the regenerator in considerable amounts (∼5%) also leads to 14NCO intermediates adsorbed on the FCC catalyst, which subsequently react with 14NO or 15NO to form 14N14N (m/e ) 28) and 14N15N (m/e ) 29) and CO2. It has to be pointed out that in the investigated temperature region 14N15NO (m/e ) 45) and 15N15NO (m/e ) 46) were observed in the TPO measurements. Under the relevant operating conditions, N2O decomposes on the oxide matrix of the FCC catalyst to N2 (eq 12).

2HNCO + 2NO + 0.5O2 f 2N2O + 2CO + H2O (10) 2HNCO + 2NO + 0.5O2 f 2N2 + 2CO2 + H2O (11) N2O f N2 + 0.5O2

(12)

While only 100-500 ppm of NO is present in the regenerator, significant concentrations (7-10%) of CO exist under these conditions, thus favoring the formation of NCO. Isocyanate species adsorbed on the silicaalumina support of the FCC catalyst were observed by IR spectroscopy (cf. Figure 4) up to temperatures of 500-600 °C. At temperatures >600 °C, HCN hydrolysis (eq 5) becomes the dominant reaction. This transformation is well studied over (basic) oxide compounds such as (CaO, CaCO3, etc.) under the conditions of coal

combustion.14 Note that such hydrolysis reactions may easily occur over oxide phases in the matrix (clays, mixed aluminum oxides, etc.) of the FCC catalyst. In addition, a direct reaction between 14NO present in the regenerator and 15N-nitrogen-containing aromatic coke species leading to isotopically scrambled N2 cannot be ruled out. Such a reaction appears possible because electrophilic substitutions between NO+ species and organic amine/imino groups lead to well-known diazonium compounds that immediately decompose to N2 and CxHy fragments in the relevant temperature region (Figure 10). NO+ species are readily formed by the reaction of NO with NO2 and water on the acidic cracking catalyst. The pathways of nitrogen observed in our experiments and elementary reactions leading to N2 and NO in the FCC regenerator can be summarized as follows: having passed the stripping section, the deactivated cracking catalyst enters the bottom of the regeneration unit at a temperature of ∼550 °C. The dense phase of the regenerator typically has a temperature of 680-700 °C. In this region the degradation of large nitrogen-containing polycyclic aromatic hydrocarbons to carbazole- and quinoline-type species was observed.10 Moreover, the concentration of CO reaches a maximum in this temperature range.5 The conditions in the dense phase can best be compared with reduction zone I (cf. Figure 9) in the TPO experiments, in which the reduction of NO with CO dominates. The upper part of the regeneration unit (T ) 720-760 °C) is characterized by the diluted phase of the fluidized bed. In this temperature zone, we have observed maxima of HCN and NH3 emissions. Both species can be oxidized to NO or can act as a reducing agent (reduction zone II), depending on whether they are present in the oxygen-rich zone (the dense phase near the air grid: 2-5% O2) or in the oxygen-depleted zone (the dense phase and parts of the diluted phase: ∼0.5% O2). Under reaction conditions typical of the diluted phase, the hydrolysis of HCN to NH3 will take place over oxidic phases in the FCC catalyst. Emission data from FCC units operating under partial burn conditions (no excess O2) show that up to 600 ppm of NH3 and HCN are released with the flue gases of the regenerator, whereas with increasing oxygen concentrations (full burn mode; 1-2% excess oxygen), a nearly complete removal of these intermediates was observed.19 The diluted phase of a cocurrent FCC regenerator (such as Exxon Flexicrackers) is the region of highest temperature in the regenerator (700-750 °C). Our TPD and TPO measurements suggest that the actual “nitrogen chemistry” (i.e., formation of HCN, NH3, NO, and N2) is observed in this temperature region. Although the actual concentration of the catalyst in this region is low, the formation of nitrogen compounds takes place in this part of the regenerator, whereas the majority of carbon compounds are removed in the dense phase (550-650 °C). In countercurrent regenerators (the coked

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catalyst is added on the top of the catalyst bed), higher CO concentrations are encountered even in the upper part of the regenerator. Such higher levels of the reductant CO lead to significantly lower NO emissions in the case of countercurrent regenerators. 4. Conclusions HCN and NH3 are formed during the FCC regeneration process via pyrolysis of nitrogen-containing carbonaceous deposits. The intermediates are generated by cracking and hydrolysis of polycyclic aromatic coke molecules. Higher water concentrations favor the formation of NH3 via the hydrolysis of isocyanate intermediates adsorbed on the alumina support of the FCC catalyst. At temperatures above 700 °C, HCN can be directly converted into NH3 and CO via hydrolysis over oxide phases present in the FCC inventory. Both intermediates can be oxidized to NO at temperatures above 550 °C. This reaction is favored if Pt-based CO combustion promoters are added to the FCC catalyst. Under oxidizing conditions, the concentration of HCN decreases significantly, while the presence of the CO promoter leads to an increase of NO emissions. In the presence of 5% H2O, significantly lower amounts of HCN, NO, and NO2 are released during oxidation of the coked FCC catalyst. Higher water concentrations promote the hydrolysis of HCN and NCO species and thus provide increasing amounts of NH3, which can act as a reductant for NO (NO can be reduced in situ with CO or NH3/HCN). Removal of NO present in the regeneration unit starts at ∼400 °C is parallel to the formation of increased concentrations of CO. NO reduction with CO proceeds via the generation of isocyanate intermediates, which subsequently react with NO to form N2 or N2O. Under the conditions of the FCC regenerator, N2O decomposes to N2 on the oxide matrix of the FCC catalyst. As shown by TPO experiments using carbonaceous deposits labeled with 15N compounds, NO reacts at 650-800 °C predominantly with reduced nitrogen intermediates generated during the pyrolysis of the coke species. NO can react as well directly with nitrogencontaining coke species. The reaction with such polycyclic aromatic hydrocarbons of the carbazole and quinoline type should lead via NO+ species to diazonium compounds, which immediately decompose into N2, CxHy, and CO species. The formation of nitrogen intermediates represents the final stage of the FCC regeneration process. The coke oxidation starts at 550-580 °C with a gradual decomposition of large polycyclic aromatic hydrocarbons to carbazole and quinoline derivatives in the dense phase of the regenerator, where the highest concentrations of the reducing agent CO are typically found. The diluted phase of the fluidized-bed regenerator represents the zone of highest temperatures (720-750 °C) and low oxygen concentrations. In this temperature range, maxima of HCN and NH3 formation are observed. The generation of N2 and NO reaches a maximum in the high-temperature regime (diluted phase) of the FCC regenerator. Acknowledgment Financial support of the European Union (Project G1RD-CT99-0065-“DENOXPRO”) is gratefully acknowledged. Special thanks go to Prof. I. A. Vasalos and Dr. E. Efthimiadis (Chemical Process Engineering Research Institute (CPERI), Thessaloniki, Greece) for the elemen-

tal analysis of coked catalysts. We thank Dr. K. Seshan and Prof. L. Lefferts (Twente University) for supplying the catalyst coked with aniline, pyrrole, and pyridine. The authors further thank Dr. R. Harding, Dr. J. Nee, and Dr. G. McElhiney (Grace Davison) and Dr. H. Rhemann (OMV) for helpful discussions concerning FCC deNOx technologies. Literature Cited (1) Harding, R. H.; Peters, A. W.; Nee, J. R. D. New developments in FCC catalyst technology. Appl. Catal. A 2001, 221, 389. (2) Mann, R. Fluid catalytic cracking: some recent developments in catalyst particle design and unit hardware. Catal. Today 1993, 18, 509. (3) Cheng, W. C.; Kim, G.; Peters, A. W.; Zhao, X.; Rajagopalan, K.; Ziebarth, M. S.; Pereira, C. J. Environmental Fluid Catalytic Cracking Technology. Catal. Rev.sSci. Eng. 1998, 40, 39. (4) Zhao, X.; Peters, A. W.; Weatherbee, G. W. Nitrogen chemistry and NOx control in a FCC regenerator. Ind. Eng. Chem. Res. 1997, 36, 4535. (5) Peters, A. W.; Yaluris, G.; Weatherbee, G. W.; Zhao, X. Origin and control of NOx in the FCCU regenerator. Fluid Cracking Catal. 1998, 259. (6) Dishman, K. L.; Doolin, P. K.; Tullock, L. D. NOx Emissions in Fluid Catalytic Cracking Regeneration. Ind. Eng. Chem. Res. 1998, 37, 4631. (7) Yaluris, G.; Peters, A. W. Realistic evaluation of the performance of FCCU regenerator additives in the laboratory. 2nd International Conference on Refining Processes, AICHE Spring National Meeting, Houston, TX, 1999. (8) Yaluris, G.; Peters, A. W. Studying the chemistry of the FCCU regenerator in the laboratory under realistic conditions. In Designing transportation fuels for a cleaner environment; Reynolds, J. G., Khan, M. R., Eds.; Taylor & Francis: Philadelphia, 1999; p 151. (9) Iliopoulou, E. F.; Efthimiadis, E. A.; Vasalos, I. A.; Barth, J.-O.; Lercher, J. A. Effect of Rh-based additives on NO and CO formed during regeneration of spent FCC catalysts. Appl. Catal. B 2004, 47, 165. (10) (a) Barth, J.-O.; Jentys, A.; Lercher, J. A. Towards understanding the genesis and removal of NOx in FCC regenerators. Proceedings of the 17th World Petroleum Congress, Rio de Janeiro, Brazil, 2003; Institute of Petroleum (IP): London, Vol. 3, p 445; ISBN 0 85293 366 5. (b) Barth, J.-O.; Jentys, A.; Lercher, J. A. On the Nature of Nitrogen-Containing Carbonaceous Deposits on Coked Fluid Catalytic Cracking Catalysts. Ind. Eng. Chem. Res. 2004, 43, 2368. (11) Hadjiivanov, K. I. Identification of neutral and charged NxOy surface species by IR spectroscopy. Catal. Rev.sSci. Eng. 2000, 42, 71. (12) Qian, K.; Tomczak, D. C.; Rakiewicz, E. F.; Harding, R. H.; Yaluris, G.; Cheng, W. C.; Zhao, X.; Peters, A. W. Coke Formation in the Fluid Catalytic Cracking Process by Combined Analytical Techniques. Energy Fuels 1997, 11, 596. (13) Wo´jtowicz, M. A.; Pels, J. R.; Moulijn, J. A. Combustion of coal as a source of N2O emission. Fuel Process. Technol. 1993, 34, 1. (14) Scha¨fer, S.; Bonn, B. Die Hydrolyse von HCN als Zwischenschritt bei der Stickoxidbildung. Chem. Ing. Tech. 1999, 71, 613. (15) Ha¨ma¨la¨inen, J. P.; Martti, J. A. Effect of fuel composition on the conversion of volatile solid fuel-N to N2O and NO. Fuel 1995, 74, 1922. (16) Armor, J. N. Catalytic removal of nitrogen oxides: where are the opportunities? Catal. Today 1995, 26, 99. (17) Bradford, M.; Grover, R.; Paul, P. Controlling NOx Emissions, Part 1. Chem. Eng. Prog. 2002, 42. (18) Bradford, M.; Grover, R.; Paul, P. Controlling NOx Emissions, Part 2. Chem. Eng. Prog. 2002, 38. (19) Vasalos, I. A. Personal communication.

Received for review December 10, 2003 Revised manuscript received March 25, 2004 Accepted April 8, 2004 IE034300B