Ind. Eng. Chem. Res. 2002, 41, 3081-3086
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A Novel Cyclic Reaction System Involving CaS and CaSO4 for Converting Sulfur Dioxide to Elemental Sulfur without Generating Secondary Pollutants. 1. Determination of Process Feasibility Hong Yong Sohn* and Byung-Su Kim† Department of Metallurgical Engineering, University of Utah, 135 S 1460 E RM 412, Salt Lake City, Utah 84112-0114
A new process for converting SO2 to elemental sulfur by a cyclic process involving CaS and CaSO4 has been developed. In this process, the raw material CaSO4 is reduced to produce CaS, which is used to reduce SO2 to elemental sulfur and produce CaSO4. The latter is then reduced to regenerate CaS. Experimentally, about 75% of CaS powder was converted to CaSO4 in 20 min at 1153 K under 25.8 kPa of SO2 partial pressure. About 95% of nickel-catalyzed CaSO4 powder was reduced to CaS in 20 min at 1123 K under 86.1 kPa of hydrogen partial pressure. The reactivities of the powders remained relatively unchanged after 10 cycles of reactions and regenerations. Sulfur dioxide containing streams from certain sources contain higher partial pressures of SO2, in which case the SO2-CaS reaction will be proportionally faster than that reported here. Detailed kinetics of the two-component reactions are described in the accompanying parts of this series. 1. Introduction Gas streams containing high levels of sulfur dioxide are generated from nonferrous metal smelters, coalburning power plants, and integrated gasification combined cycle desulfurization units.1-4 The sulfur dioxide in the flue gas from the power plant is scrubbed, generating wastes that need to be disposed of.5,6 The scrubbing byproduct calcium sulfate has been used in the manufacture of cement, sheet, and tiles, but the supply is quickly overcoming the demand, and billions of tons of it are being stockpiled. Its disposal usually poses an expensive environmental problem. Nonferrous smelters convert sulfur dioxide to sulfuric acid. However, there are often few attractive markets for sulfuric acid, and thus its production is to fix the pollutant byproduct sulfur dioxide rather than to make a marketable commodity.7-9 The current trend in the sulfide smelting industry is to utilize increasingly high oxygen enrichment in the process gas to reduce the heavy energy load to heat nitrogen to the process temperature and reduce the volume of the process gas.3 As a consequence, the modern sulfide smelting technologies produce high-strength sulfur dioxide gas streams. As an example, the new Kennecott copper-converting process in Utah generates a steady stream of off-gas containing 35-45% sulfur dioxide.3,10,11 For conversion to sulfuric acid, however, this stream must be diluted to 10-14% sulfur dioxide concentration.2,9,12 Therefore, it would be highly desirable to develop an alternative process to treat sulfur dioxide streams. Technology exists to condense sulfur dioxide gas to liquid, but the market for liquid sulfur dioxide is even more limited than that for sulfuric acid. Furthermore, liquid sulfur dioxide is not easily stored because of its * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: 801-581-5491. Fax: 801-5814937. † Present address: Korea Institute of Geoscience & Mineral Resources, Daejeon, Korea 305-350.
high volatility. Conversion to elemental sulfur would have many advantages because it is highly inert as a solid and its long-distance transportability is excellent. For this reason, hydrogen sulfide contained in natural gas is currently converted to elemental sulfur. Sulfur dioxide gas, however, is much more difficult to convert to elemental sulfur than hydrogen sulfide gas. A number of processes for converting sulfur dioxide directly to elemental sulfur have been suggested and developed previously. There are two categories of technologies for this: dry (gas-phase) reduction4,13-15 and wet (liquidphase) reduction.4,16,17 All of these processes have either been discontinued or never been commercialized because of their complexities and/or costliness. The reader is referred to the cited references for further details on these processes. The present research is concerned with developing a new process for converting sulfur dioxide gas to elemental sulfur that is relatively simple, fast, and without secondary environmental problems. The proposed scheme involves a cyclic process of the reduction of sulfur dioxide by calcium sulfide and the regeneration of calcium sulfide by the reduction of the product calcium sulfate with a suitable reducing agent such as hydrogen. The overall process would begin with calcium sulfate as the starting material. 2. Choice of the Reaction System The following two types of processes would satisfy the requirements stated above for a new process for converting sulfur dioxide to elemental sulfur without secondary environmental problems: (1) A process in which the reaction of sulfur dioxide produces a gas-phase product containing essentially pure sulfur. The solid product in this case must be reusable in the process, because it is undesirable to generate large amounts of waste solids that require disposal. (2) A process in which the reaction of sulfur dioxide produces a solid product containing excess sulfur which
10.1021/ie010993p CCC: $22.00 © 2002 American Chemical Society Published on Web 05/23/2002
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Figure 1. Equilibrium composition for the reaction of FeS (2 mol) and C (1 mol) with SO2 (1 mol) and 0.2 mol of N2 at a total pressure of 1 atm.
can easily be decomposed in a separate step to yield pure sulfur gas and a reusable solid residue. In this case, the off-gas from the reaction step should only contain species that can be vented directly or with a minimum amount of treatment such as afterburning. With this in mind, a number of possible reaction systems were examined based on thermodynamic analysis. Equilibrium compositions at various temperatures were calculated to find the most suitable reaction system for converting sulfur dioxide to elemental sulfur without generating secondary pollutants. The thermodynamic analysis was performed by the use of HSC chemical software developed by Outokumpu Research Oy, which is based on the principle of the Gibbs free energy minimization. Some selected examples of the calculated results will be discussed below, followed by the result for the most promising system of SO2-CaS that was investigated in detail. Fe-SO2 System. At temperatures higher than 1500 K, this reaction will yield S2 gas and iron oxides plus some FeS. The iron oxides could be reduced by carbon or reformed natural gas to iron in a separate reactor and recycled. This would satisfy the first condition stated above. However, this reaction accompanies relatively low sulfur yields and requires a high temperature and a large amount of energy, and the FeS present in the product iron oxide may be troublesome by generating sulfur-containing gases during reduction. FeS-SO2 System. The equilibrium product of this reaction contains FeS2 and iron oxides at temperatures lower than 800 K, but at higher temperatures, where the reaction rates may be adequate, the conversion of sulfur dioxide is low. FeS-C-SO2 System. Figure 1 shows the calculated equilibrium composition against temperature for the FeS-C-SO2 system from a starting mixture of 1 mol of SO2, 2 mol of FeS, and 1 mol of C. Because complete conversion of SO2 is the objective, an excess amount of FeS was used. Below about 1100 K, the solid product is FeS2, and the gaseous products are S2 and CO2, together with small amounts of CO and COS that may have to be burned after the sulfur is recovered by condensation. Because solid carbon is completely oxidized under this condition, this process may be operated by maintaining a bed of FeS/FeS2 through which an SO2 stream mixed with CO or carbon powder is fed.
Figure 2. Equilibrium composition for the reaction of 1 mol of CaS with 1 mol of SO2 at a total pressure of 1 atm.
CaS-SO2 System. In this system, the following reactions are possible:
CaS(s) + 2SO2(g) ) CaSO4(s) + S2(g)
(1)
CaS(s) + 1/2SO2(g) ) CaO(s) + 3/4S2(g)
(2)
CaS(s) + 3CaSO4(s) ) 4CaO(s) + 4SO2(g)
(3)
3
/2CaS(s) + 1/2CaSO4(s) ) 2CaO(s) + S2(g)
(4)
CaSO4(s) ) CaO(s) + SO3(g)
(5)
CaSO4(s) ) CaO(s) + SO2(g) + 1/2O2(g)
(6)
However, reactions (2)-(6) all have positive ∆G° values around 1000 K. The calculated equilibrium compositions for the CaSSO2 system, from a starting mixture of 1 mol of CaS and 1 mol of SO2, are shown in Figure 2. The amounts of all other species considered in reactions (1)-(6) as well as other sulfur species S3-S8 were negligible. It is seen that when sulfur dioxide gas is reacted with an excess amount of calcium sulfide, the solid product will be calcium sulfate, and the gaseous product will be essentially pure sulfur up to a temperature of about 1150 K. The product calcium sulfate can be reduced to calcium sulfide without any other environmental problems, as will be explained later. This system presented the greatest potential as the candidate for a new process for converting sulfur dioxide to elemental sulfur and thus was investigated further by carrying out experimental work. Some sulfur dioxide streams may contain low levels of hydrogen. Thus, an additional calculation was performed with the above feed with an additional 0.1 mol of hydrogen, as shown in Figure 3. It is seen that the hydrogen is consumed to reduce SO2 to produce water vapor but also generates a small amount of hydrogen sulfide. After sulfur is separated by condensation, the remaining gas that might also contain unreacted SO2 could be recycled to the feed stream, scrubbed, or fed to a sulfuric acid plant, if one is available nearby. Any
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Figure 3. Equilibrium composition for the reaction of 1 mol of CaS, 1 mol of SO2, and 0.1 mol of H2 at a total pressure of 1 atm.
oxygen that might be contained in the feed stream would oxidize calcium sulfide to calcium sulfate. 3. Thermodynamics of the Reduction of Calcium Sulfate to Calcium Sulfide The reaction of calcium sulfate with hydrogen is of interest as a means of regenerating calcium sulfide from calcium sulfate in the proposed process as well as producing sulfur from gypsum and anhydrite. The equilibrium constant for the reaction
CaSO4(s) + 4H2(g) ) CaS(s) + 4H2O(g)
(7)
is about 108 in the temperature range of 973-1173 K. This indicates that the reduction of calcium sulfate to calcium sulfide would be highly feasible thermodynamically. On the other hand, the side reactions such as
CaSO4(s) + H2(g) ) CaO(s) + SO2(g) + H2O(g) (8) CaSO4(s) + H2(g) ) CaO(s) + H2S(g) + 3/2O2(g) (9) will not be thermodynamically feasible because of the positive ∆G° values of these reactions. Equilibrium calculations for the overall H2-CaSO4 system at various temperatures were performed using the HSC software. The calculated data presented in Figure 4 indicate that CaS by reaction (7) is the main product and the side reactions that produce CaO and H2S do not occur to appreciable extents below about 1150 K. 4. Experimental Work Experiments were carried out in a horizontal tube furnace to determine the products from CaS-SO2 and CaSO4-H2 reaction systems, and a thermogravimetric analysis (TGA) unit18 was used to measure the reaction rate. In the former experiment, a weighed amount of solid reactant was placed in an alumina boat (1.2 cm diameter and 8.0 cm length), which was pushed into the central hot zone of an alumina reaction tube of 4 cm diameter and 150 cm length that was maintained at a desired temperature. The reactor system was made oxygen-free with a nitrogen gas flow inside the reactor before the reactant gas was introduced at a controlled
Figure 4. Equilibrium composition for the reaction of CaSO4 (1 mol) with H2 (3 mol) at a total pressure of 1 atm.
rate. The cooled residual solid was weighed, and this solid as well as the solid condensed from the gaseous product was analyzed by X-ray diffraction (XRD). The TGA apparatus consisted of a reactor and a gasdelivery system together with a Cahn electrobalance (model 1000) that continuously recorded the weight changes taking place during the reaction. The reactor was an Inconel tube of 5.1 cm i.d. and 66 cm length. During the experiments, the balance chamber was purged with nitrogen to prevent the intrusion of reactant gas and heat into it. Powder samples weighing 100-200 mg placed in a shallow holder were used in the TGA experiments. Sulfur dioxide gas (99.9%) was supplied by Union Carbide Co., and hydrogen (99.9%) and nitrogen (99.9%) gases were purchased from Air Products Co. The calcium sulfide powder, manufactured by Alfa AESAR Co., was 99.9 wt % pure, and the anhydrous calcium sulfate powder (99.5%) was obtained from Aldrich Chemical Co. Both materials were of -44 µm size as determined by sieving. In preliminary experiments, it was determined that the rate of reduction of plain calcium sulfate was quite slow and a nickel catalyst increased the rate considerably. Thus, all of the subsequent study was done with powders that contain the nickel catalyst. The calcium sulfate powder was impregnated with nickel by mixing 5 g of it for 24 h in 100 mL of a 5 wt % nickel nitrate solution prepared with reagent-grade Ni(NO3)2‚6H2O manufactured by Alfa AESAR Co. The use of nickel nitrate solutions of higher concentrations did not increase the catalytic effect on the reduction of calcium sulfate. The impregnated powder was then dried at 443 K for 3 h in an oven and reduced to calcium sulfide by hydrogen at 1153 K for 1 h in a horizontal furnace. 5. Results and Discussion 5.1. Reaction Products. For the CaS-SO2 reaction, a gas mixture containing nitrogen and sulfur dioxide at a partial pressure of 8.7 kPa was passed over the calcium sulfide held in an alumina boat for various reaction times at 1073 K. Figure 5 shows the X-ray pattern of the final solid phase. It is seen that the solid contains only calcium sulfate and unreacted calcium sulfide. The XRD pattern of the solid collected by cooling the product gas revealed only sulfur, as shown in Figure
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Figure 5. X-ray pattern of intermediate product solid from the CaS-SO2 reaction.
Figure 6. X-ray pattern of a condensed vapor-phase product from the CaS-SO2 reaction.
6. These results indicate that sulfur gas can be produced by the reaction between calcium sulfide and sulfur dioxide without any appreciable side reactions. For the CaSO4-H2 reaction, hydrogen at a partial pressure of 8.7 kPa was passed over the calcium sulfate powder at 1073 K for various lengths of time. The result of X-ray analysis of the solid product showed only calcium sulfide, and the gaseous product was water. 5.2. Rates of the CaS-SO2 Reaction. The rates of the CaS-SO2 reaction were measured using a TGA unit. Experiments were continued until the sample showed no noticeable further mass change. The conversion at a particular time was determined by dividing the mass change of the solid sample at the time by the theoretical maximum total mass change. External mass-transfer and interparticle diffusional effects were eliminated by using a sufficiently large gas flow rate and a sufficiently small bed height.19-21 Shown in Figure 7 are the conversion vs time relationships for the reaction at 1073 K under a sulfur dioxide partial pressure of 25.8 kPa of a calcium sulfide powder prepared by the hydrogen reduction of a fresh nickel-catalyzed calcium sulfate powder as well as calcium sulfide regenerated from calcium sulfate produced in the subsequent cycles. It is noted that all of the curves represent continuous TGA outputs, and the
Figure 7. Conversion of CaS by SO2 at various cycles (1073 K, 25.8 kPa of SO2 pressure). All curves represent continuous TGA outputs; symbols are used just to distinguish different run conditions.
Figure 8. Scanning electron micrographs of CaS particles from the H2 reduction of the CaSO4 powder.
symbols on the lines are used just to distinguish different run conditions. Also shown for reference is the result for a fresh calcium sulfide powder, although calcium sulfate produced from the reaction of this fresh calcium sulfide was not used in the subsequent cycles. Conversion of the fresh calcium sulfide powder was around 48% in 1 h. After the same amount of time, the conversion of the calcium sulfide powder reduced from the fresh nickel-catalyzed calcium sulfate powder (the first preparation from the starting material) was about 68%. These curves were reproducible within (3.0%. The increased reactivity can be explained by the fact that the volume of CaS formed from the reduction of calcium sulfate is just 55% of that of CaSO4 based on the Pilling-Bedworth coefficient.22 This makes calcium sulfide particles regenerated from nickel-catalyzed calcium sulfate particles very porous and high in specific surface area, as verified by a scanning electron micrograph shown in Figure 8. The unreacted fresh calcium sulfide particles were relatively dense. It is also seen that after 10 cycles of reaction with sulfur dioxide and regeneration from the resultant calcium sulfate, calcium sulfide remains reactive. This is important because the solids must be reusable for repeated cycles, as mentioned earlier.
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Figure 9. Effect of temperature on the CaS-SO2 reaction. All curves represent continuous TGA outputs; symbols are used just to distinguish different run conditions.
Figure 10. Conversion of CaSO4 by H2 at various cycles (1073 K, 86.1 kPa of H2 pressure). All curves represent continuous TGA outputs; symbols are used just to distinguish different run conditions.
The effect of temperature on this reaction is shown in Figure 9 for the reaction under a sulfur dioxide partial pressure of 25.8 kPa of calcium sulfide powder samples reduced from the fresh nickel-catalyzed calcium sulfate powder (the first preparation in Figure 7). It is seen that the reaction rate substantially increases with temperature. For example, at 1153 K the conversion is about 75% in 20 min. A comprehensive kinetics analysis on this reaction including the effects of sulfur dioxide partial pressure and temperature is presented in part 2 of this series.23 5.3. Regeneration of Calcium Sulfide by the Hydrogen Reduction of the Produced Calcium Sulfate. In Figure 10, the conversion vs time relationships for the hydrogen reduction of fresh and nickelcatalyzed and regenerated nickel-catalyzed calcium sulfate powders are compared at 1073 K under a hydrogen partial pressure of 86.1 kPa (atmospheric pressure at Salt Lake City). About 60% of the fresh calcium sulfate powder and over 95% of the fresh nickelcatalyzed and regenerated nickel-catalyzed calcium sulfate powders, respectively, were converted to calcium sulfide in 1 h. These curves were also reproducible within (3.0%. As shown in Figure 10, the conversion rate of nickel-catalyzed calcium sulfate was substantially higher than that of uncatalyzed calcium sulfate. The increase may be explained by the fact that nickel
Figure 11. Effect of temperature on the hydrogen reduction of CaSO4.
is a strong hydrogen adsorbent. Hydrogen molecules dissociate on the nickel surface to produce atomic hydrogen with a much greater reactivity. The regenerated calcium sulfate still contained some unreacted calcium sulfide (as indicated by the “fractional conversion” at zero time), because the reaction of calcium sulfide and sulfur dioxide became slow after a certain conversion value, as can be seen in Figure 9. It is noted, however, that the regenerated nickel-catalyzed calcium sulfate portion remained as reactive as the fresh nickelcatalyzed sample. This reactivity remained intact even after 10 reaction cycles, much like that of calcium sulfide, shown above. Again, this is important because the solids must be reusable for repeated cycles, as mentioned earlier. The effect of temperature on the reduction of the fresh nickel-catalyzed calcium sulfate powder by hydrogen is shown in Figure 11. It is seen that at 1123 K more than 95% reduction is achieved in only 20 min. A comprehensive kinetics analysis on this reaction including the effects of hydrogen partial pressure and temperature is presented in part 3 of this series.24 6. Concluding Remarks Thermodynamic analyses showed calcium sulfide to be suitable for converting sulfur dioxide to elemental sulfur. This reaction scheme is attractive because the solid product calcium sulfate can be reduced to regenerate calcium sulfide without generating any solid waste. The rates of the two component reactions were determined to be reasonably fast. For example, at 1153 K and under the sulfur dioxide partial pressure of 25.8 kPa, about 60% of the calcium sulfide powder was converted to calcium sulfate in 10 min, reducing the corresponding amount of sulfur dioxide to elemental sulfur. In addition, more than 95% of nickel-catalyzed calcium sulfate powders was reduced to calcium sulfide in 20 min at 1123 K under a hydrogen partial pressure of 86.1 kPa. Furthermore, the reactivities of the two solids remain largely intact over 10 cycles of regeneration and reaction. Thus, the proposed reaction scheme, which uses inexpensive calcium sulfate as the starting raw material, has been shown to be suitable for converting sulfur dioxide to elemental sulfur without generating a solid waste.
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Acknowledgment This work was supported in part by a Faculty Research Grant from the University of Utah Research Committee. Literature Cited (1) Dalton, S. M. Flue Gas Desulfurization Design in the U.S.: Additives and Materials of Construction. In Symposium Series on Desulfurization 3; Kyte, W. S., Ed.; Chameleon Press: London, 1993; pp 67-77. (2) Friedman, L. J. Production of liquid SO2, sulfur and sulfuric acid from high strength SO2 gases. In Sulfur Dioxide Control in Pyrometallurgy; Chatwin, T. D., Kikumoto, N., Eds.; TMS: Warrendale, PA, 1981; pp 205-220. (3) Asteljoki, J. A.; Bailey, L. K.; George, D. B.; Rodolff, D. W. Flash Converting - Continuous Converting of Copper Mattes. J. Met. 1985, 37 (5), 20-23. (4) Kwong, V.; Meissner, R. E. Rounding up Sulfur. Chem. Eng. 1995, 102, 74-83. (5) Levendis, Y. A.; Zhu, W.; Wise, D. L. Effectiveness of Calcium Magnesium Acetate as an SOX Sorbent in Coal Combustion. AIChE J. 1993, 39, 761-773. (6) Dennis, R. A.; Ford, N. W. J.; Cooke, M. J. A guide to flue gas desulfurization for the industrial plant manager. In Symposium Series on Desulfurization 3; Kyte, W. S., Ed.; Chameleon Press: London, 1993; pp 119-137. (7) Weisenberg, I. J.; Winkler, F. M.; Burckle, J. O. Weak SO2 Stream Control from Copper Smelter. In Sulfur Dioxide Control in Pyrometallurgy; Chatwin, T. D., Kikumoto, N., Eds.; TMS: Warrendale, PA, 1981; pp 33-53. (8) Burckle, J. O.; Worrell, A. C. Comparison of Environmental Aspects of Selected Nonferrous Metals Production Technologies. In Sulfur Dioxide Control in Pyrometallurgy; Chatwin, T. D., Kikumoto, N., Eds.; TMS: Warrendale, PA, 1981; pp 55-65. (9) Agarwal, J. C.; Loreth, M. J. Preliminary Economic Analysis of SO2 Abatement Technologies. In Sulfur Dioxide Control in Pyrometallurgy; Chatwin, T. D., Kikumoto, N., Eds.; TMS: Warrendale, PA, 1981; pp 67-89. (10) Bouillon, D. F. Developments in Emission Control Technologies/Strategies: A Case Study. In Restoration and Recovery of an Industrial Region; Gunn, J. M., Ed.; Springer-Verlag: New York, 1995; pp 275-285.
(11) George, D. B. Continuous Copper ConvertingsA Perspective and View of the Future. In Sulfide Smelting 2002; Stephens, R. L., Sohn, H. Y., Eds.; TMS: Warrendale, PA, 2002; pp 3-13. (12) Puricelli, S. M.; Grendel, R. W.; Fries, R. M. Pollution to Power: A Case Study of the Kennecott Sulfuric Acid Plant. In Sulfide Smelting ’98: Current and Future Practices; Asteljoki, J. A., Stephens, R. L., Eds.; TMS: Warrendale, PA, 1998; pp 451462. (13) Sander, U. H. F.; Fischer, H.; Rothe, U.; Kola, R. Sulphur, Sulphur Dioxide and Sulphuric Acid; The British Sulphur Corporation Ltd.: London, 1984; pp 90-95. (14) Katz, M.; Cole, R. J. Recovery of Sulfur Compounds from Atmospheric Contaminants. Ind. Eng. Chem. 1950, 42, 22582269. (15) Nelson, S. G. Elemental Sulfur production from SO2-Rich Gases. In Processing and Utilization of High-Sulfur Coals; Parekh, V. B. K.; Groppo, J. G., Eds.; Elsevier: New York, 1993; pp 543553. (16) Semrau, K. Controlling the Industrial Process Sources of Sulfur Oxides. In Sulfur Removal and Recovery from Industrial Processes; Advances in Chemistry Series 139; Pfeiffer, J. B., Ed.; American Chemical Society: Washington, DC, 1975; pp 1-22. (17) Korosy, L.; Gewanter, H. L.; Chalmers, F. S.; Vasan, S. Sulfur Dioxide Absorption and Conversion to Sulfur by the Citrate Process. In Sulfur Removal and Recovery from Industrial Processes; Advances in Chemistry Series 139; Pfeiffer, J. B., Ed.; American Chemical Society: Washington, DC, 1975; pp 192-211. (18) Szekely, J.; Evans, J. W.; Sohn, H. Y. Gas-Solid Reactions; Academic Press: New York, 1976; pp 209-213. (19) Kim, B.-S.; Sohn, H. Y. The Reduction of Sulfur Dioxide by Calcium Sulfide. In EPD Congress 1999; Mishra, B., Ed.; TMS: Warrendale, PA, 1999; pp 181-188. (20) Kim, B.-S.; Sohn, H. Y. The Reduction of Calcium Sulfate by Hydrogen to Produce Calcium Sulfide as a Reductant of Sulfur Dioxide to elemental Sulfur. In EPD Congress 1999; Mishra, B., Ed.; TMS: Warrendale, PA, 1999; pp 11-16. (21) Kim, B.-S. Reduction of Sulfur Dioxide to Elemental Sulfur by a Cyclic Process Involving Calcium Sulfide and Sulfate. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1999. (22) Jones, D. A. Principles and Prevention of Corrosion; Prentice-Hall: Englewood Cliffs, NJ, 1996; pp 418-420. (23) Same as ref 2 in part 3. (24) Same as ref 2 in part 2.
Received for review December 7, 2001 Revised manuscript received April 8, 2002 Accepted April 10, 2002 IE010993P
