Oxidation of Carbon Particles in Supercritical Water - American

Oxidation of a carbon particle in supercritical water was studied in a flow-type reaction cell by directly observing the change in the size and shape ...
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Oxidation of Carbon Particles in Supercritical Water: Rate and Mechanism Masakazu Sugiyama,‡ Masahiko Kataoka,† Hisao Ohmura,§ Hideo Fujiwara,† and Seiichiro Koda*,| Departments of Chemical System Engineering and Electronic Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, Joint Research Center For Supercritical Fluids, Japan Chemical Innovation Institute, 4-2-1 Nigatake, Miyagino-ku, Sendai 983-8551, Japan, and Department of Chemistry, Faculty of Science and Technology, Sophia University, Kioi-cho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan

Oxidation of a carbon particle in supercritical water was studied in a flow-type reaction cell by directly observing the change in the size and shape of the particle through a sapphire window attached to the cell. Three types of carbon were investigated: activated carbon, synthetic graphite, and highly oriented pyrolytic graphite (HOPG). The reaction was observed at a pressure of 2330 MPa and a temperature of 673-873 K. The spherical particles (3-4 mm in diameter) of both the activated carbon and the synthetic graphite became smaller while maintaining their shape, indicating that the reaction occurred nearly at the surface of the sphere. The reaction was first order with respect to O2 concentration. The rate of the decrease in the radius was in the order of µm s-1 for the activated carbon, and the rate was about an order of magnitude slower for the synthetic graphite. The rate of O2 mass transfer was estimated by computational fluid dynamics (CFD) calculations, showing good agreement with the reaction rate of the activated carbon. Calculated surface temperature of the particle was higher than the fluid temperature by 200 K at its highest due to the heat of the surface reaction, C+O2 f CO2. This temperature difference caused density distribution in the fluid, and led to significant natural convection above the particle. The observed shadowgraph around the particle showed a texture corresponding to the above calculated flow field. This phenomenon was also taken into account in the CFD calculation of O2 mass transfer rate. Thus, the external mass transfer of O2 to the particle surface limited the reaction rate of the activated carbon. On the other hand, the reaction rate of the synthetic graphite was limited by the surface reaction. Oxidation rate of HOPG was so slow that no reduction in size or weight was observed. The activation energy for the oxidation rate of the synthetic graphite under surface-reaction-limited kinetics, 127 ( 10 kJ mol-1, was smaller than the values reported for the graphite combustion rates at ordinary pressures. The discrepancy can be partly due to characteristic reactions in supercritical water oxidation. Introduction Supercritical water oxidation (SCWO) technology is now going to be practically applied for decomposing organic hazardous materials and for energy recovery from low-quality fuels such as biomass and coals.1-3 For practical application, models for process design are indispensable. Kinetics of homogeneous reactions of SCWO have been intensively researched. Indeed, several detailed chemical kinetic models derived as an extension from combustion reaction models have been applied with considerable success to the analysis of SCWO of simple organic compounds such as methanol4-8 and benzene.9 However, the kinetics study of solids in SCWO is very limited. The SCWO of solids includes mass transport and heterogeneous reactions as well as * To whom correspondence should be addressed. Tel: +813-3238-3377. Fax: +81-3-3238-3361 (at Chemistry Office). E-mail: [email protected]. † Department of Chemical System Engineering, The University of Tokyo. ‡ Department of Electronic Engineering, The University of Tokyo. § Japan Chemical Innovation Institute. | Sophia University.

homogeneous reactions. Despite this complexity, comprehensive analysis of the SCWO of solids is to be pursued considering the practical importance of the process. The complexity coming from combined mass and heat transfer, homogeneous, and heterogeneous reactions has already been encountered in combustion science. To minimize such complexity, a system consisting of simple flow and chemistry is necessary. For this purpose, oxidation of carbon has been a target of intensive research in combustion science. Two configurations have been commonly used: graphite particles in a hot oxidizing environment10-13 and heated graphite surfaces placed in an oxidizer stream forming a stagnation-point flow field.14-18 Such experimental and numerical analyses have contributed to the understanding of heterogeneous combustion systems. These types of well-defined experiments, which will also promote the understanding of the SCWO of solid substances, however, have been lacking in the study of SCWO. Therefore, we have attempted direct observation of the progress of the SCWO of a spherical carbon particle as continuous shadowgraph images using a flow-type reaction cell equipped with sapphire windows, and the preliminary results have been reported.19 Spherical

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shape is useful for simplifying the flow field around the particle as has been attempted in combustion analysis. Carbon was used as a model material because a lot of knowledge has been accumulated on the combustion of carbon under ordinary pressures,10-18,20-22 and thus the characteristics of SCWO will be clarified through comparison with such studies. We expected that different kinds of carbon material would lead to different kinetics of SCWO. Therefore, in this study, synthetic graphite and highly oriented pyrolytic graphite (HOPG), the latter of which consists of highly ordered crystal grains of graphite, were employed, as well as the activated carbon as discussed in the preliminary report.19 In addition, a mechanism was newly devised in the experimental apparatus for the transfer of the sample into a supercritical condition and was used to accurately define the start of the reaction: the sample was initially held in the cold part of the cell and was transferred to the hot zone after stabilizing the experimental condition. The outline of this paper is as follows. After describing the experimental and modeling procedure, the SCWO progress of three kinds of carbon materials will be reported. Significant difference in the oxidation rate is observed and thus different rate-limiting steps are deduced: external mass transfer of O2 for the activated carbon and surface reaction for the synthetic graphite. For the SCWO of the activated carbon, mass transfer rates will be estimated by computational fluid dynamics (CFD) calculations and they will be compared with observed reaction rates of the activated carbon. For the SCWO of the synthetic graphite, observed reaction rates, which seem to be intrinsic surface reaction rates of the graphite, will be compared with values estimated using the experimental relations for the reaction rates of graphite combustion under ordinary pressures. The discrepancy between observed SCWO rates and extrapolated rates from combustion conditions will suggest characteristic phenomena in SCWO. Experimental and Computational Method Experimental Setup. The experimental setup is shown in Figure 1, and consists of the reaction cell and flow systems. Two different cells were used. One is the cell made of a Hasteloy block with a sample-transfer mechanism, which will be called the “sample-transfer cell” hereafter. Inside of the cell is the vertical cylinder (8 mm in diameter), with the cross equipped with four sapphire windows at the position where the particle is observed. The cell is controlled to be at supercritical temperatures using four rod-heaters and a thermocouple embedded in the Hasteloy block. The cell is connected to the other cylinder through the ceramic insulator and the cooling fins, owing to which the temperature of the lower cylinder is kept below 373 K. The particle is clamped to a Hasteloy rod (1.6 mm in diameter), the other end of which is attached to a magnet. The magnet is coupled with the other magnet outside of the cell for moving the rod. The distance between the fluid inlet and the center of the cell where the particle is observed is 20 mm. The flow exits upward. Although this cell is desirable for accurately defining the start of the reaction as described below, another cell is also used with the sample particle always fixed on the observation position. This cell, which was already used in the previous report,19 will be called the “fixed-sample cell.” The carbon particle is supported on a spiral wire. For both cells, the decreasing rate of the

Figure 1. Schematic diagram of the reaction cells and flow system. The reaction progress of a particle was observed in the flow-type cells through the sapphire windows. Two types of reaction cells were employed. In the “fixed-sample cell” a particle is supported by a spiral wire holder from the beginning of the experiment. In the “sample-transfer cell” a particle is initially held in the cold zone and is transferred to the hot zone after the reaction condition is stabilized.

radius was nearly identical under the same experimental condition within experimental errors. Two syringe pumps (ISCO 100DM) supply water and aqueous solution of H2O2, respectively. H2O2 is decomposed to O2 and H2O completely and stoichiometrically in the preheater,22 the temperature of which is the same as that of the hot zone of the cell. Therefore, the O2 fraction in the supercritical fluid can be calculated from the H2O2 concentration in the syringe pump, assuming its complete and stoichiometric decomposition. The outlet of the preheater flows into the cell through the Hasteloy tube (1.6 mm diameter and about 500 mm long) surrounded by glass wool, and the temperature of the fluid at the inlet of the cell should be somewhat lower than that of the cell. The fluid was introduced to the cylinder through the narrow inlet (1 mm diameter). The pressure inside the cell was controlled by the backpressure regulator (JASCO SCF-Bpg). Three kinds of carbon particles were employed: activated carbon, synthetic graphite, and HOPG. The particle of the activated carbon (Wako Chemical Co.) was made nearly spherical with the diameter of approximately 4 mm. The density of the activated carbon

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was 0.75 g cm-3, and the BET specific surface area was 1.0 × 103 m2 g-1. The characteristic size of the pore diameter was approximately 5 Å. The nearly spherical graphite particle with a diameter of approximately 3 mm was made of the synthetic graphite rod (Nilaco Co.). The density of the rod was 1.8 g cm-3, and the BET specific surface area was 0.78 m2 g-1. For a spherical particle of this synthetic graphite with the diameter of 3 mm, the ratio of the actual surface area to the outer surface area of the sphere is about 700. The corresponding value for a spherical activated carbon is about 4 × 105. Therefore, we should note that the surface of the synthetic graphite is actually porous but it is much less porous than the activated carbon. The fragment of HOPG disk (NT-MDT Co.) was also investigated. The density of the HOPG was 2.2 g cm-3. The fragment size was approximately 1.7 mm in width and height, and 1.5 mm in thickness. The experimental procedure with the sample-transfer cell was as follows. First, the cell was filled with water to a desired pressure with water flow. Then the cell and the preheater were heated. After the temperature was stabilized, the aqueous solution of H2O2 was supplied. After a sufficient period for stabilizing the O2 concentration in the cell, the particle was transferred into the cell and its shadow image was observed by a video camera. When using the fixed-sample cell, the sample was placed in the cell, being supported with a spiral wire. Then the cell was filled with water, pressurized and heated to an experimental condition, and finally the aqueous solution of H2O2 was supplied. In this case, the start of the reaction was not precisely determined because the arrival of O2 at the cell inlet was delayed due to the passage through the tube and the preheater. The delay amounted to around 15 min depending on the pressure, temperature, and flow rate.19 The ranges of experimental conditions were 23-30 MPa in total pressure, 673873 K in temperature, 3.0-21 wt % in H2O2 fraction in the syringe pump corresponding to 1.4-10 wt % in O2 fraction at the cell inlet, and 0.5-5.0 cm3 min-1 in total flow rate at normal pressure and room temperature. CFD Calculation. To estimate the flow field and the transfer of mass and heat, we executed CFD calculations with FLUENT version 6.23 This is effective to estimate the mass flux of O2 reaching the particle surface which determines the oxidation rate of the particle under mass-transfer-limited kinetics. The calculation used the geometry of the fixed-sample cell corresponding to experimental data. The particle was modeled as a sphere of 4-mm diameter. The holder of the particle was omitted because of its complex shape, which may yield a slight difference from experimental flow field. Equations for the conservation of mass, momentum, energy, and species were solved numerically using a finite volume method. The cell was divided into about 47 000 unstructured hexagonal and tetragonal meshes. For simulating the mass transport around the particle, the mesh was densely divided in the vicinity of the particle surface. As the values of density, specific heat, viscosity, and thermal conductivity of the mixture fluid which mainly consists of H2O, O2, and CO2, the values of pure water24,25 were employed as an approximation. In the cell, although the variation of pressure seems negligible, the distribution of temperature can be significant due to both the heat evolution from the surface reaction and the relatively low inlet temperature. Thus, the fluid

properties were set as the function of temperature. The temperature of the fluid at the inlet was not measured but tentatively set to 573 K. The temperature at the inner wall of the cell was fixed to the temperature of the Hasteloy block, and the heat flux from the particle surface to the center of the particle was set to zero, providing that the particle was thermally in steady state. This assumption is justified by considering the time, τ, required to stabilize the particle temperature: τ ≈ R2/(2R), where R is the particle radius and R is the thermal diffusivity. For the activated carbon, τ ≈ 3 s, which is smaller than the time scale of the size decrease of the particle. Using the averaged velocity (9.2 mm s-1 at 30 MPa, 723 K and 5.0 cm3 min-1 in the flow rate) in the cell, the Reynolds number, Re, was about 130, which was in the range of laminar flow. However, the narrow inlet of the cell (1-mm diameter) might derive a large local velocity (920 mm s-1 at the maximum) resulting in Re ≈ 13 000, which might cause turbulence. Thus, the k- model was employed. Because the Grashof number was approximately 108, the effect of buoyancy was also taken into account in the simulation. To estimate the mass-transfer rate of O2 at the surface of the particle, the overall surface reaction of carbon oxidation was considered as C+O2 f CO2. The reaction rate was assumed to be first order with respect to O2 concentration, and the reaction probability of O2 at the surface was set to be unity. Heat of the surface reaction (387 kJ mol-1 at 773 K) was taken into account and the temperature of the particle increased because of this reaction heat. The binary diffusion coefficient of O2 in supercritical water was approximated by the selfdiffusion coefficient of supercritical water26 because trustable data for the binary diffusion coefficient are not available at this stage. Although the simulation assumed steady state, the flow pattern obtained under the same boundary conditions varied depending on the method of conversion when buoyancy was considered. This may be due to the instability of the solution associated with turbulence and buoyancy. However, the calculated mass-transfer rate of O2 to the surface was nearly invariant if the boundary conditions were the same. Results SCWO Progress of Carbon Particles. The shadowgraph of the particle of activated carbon during SCWO changed as shown in Figure 2. In the images, the shadows of the spiral wire for holding the particle and the opposite window are also seen in addition to the particle. Corresponding to the images, the time evolution of the radius of the activated carbon is shown in Figure 3, which was measured in the same experimental run as Figure 2. The radius in the figure is the average of the maximum and the minimum radius because the shape of the particle was not a perfect sphere. After the insertion of the particle into the center of the cell, the size decreased. However, a certain induction time of about 30 s can be observed before the radius started to decrease, as shown in Figure 3. As discussed in the Experimental Section, it takes about 3 s for the particle temperature to be equilibrated at the temperature of the hot zone. This is somewhat shorter than the observed induction time, suggesting that an unobservable process had proceeded before the radius started

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Figure 4. Time evolution of the particle radius for three types of carbon: the activated carbon (b), the synthetic graphite (0) and the highly oriented pyrolytic graphite (HOPG) (2). The fixedsample cell was used at 30 MPa, 0.50 cm3 min-1 flow rate, and 10 wt % in O2 fraction, at either 773 K (activated carbon) or 873 K (graphite and HOPG). The lines for the activated carbon and the synthetic graphite are drawn as a visual aid.

Figure 2. Shadow photographs of the carbon particle in the sample-transfer cell: (a) 0 s, (b) 180 s, and (c) 300 s after the particle was transferred to the hot-zone of the cell at 30 MPa, 723 K, 2 cm3 min-1 flow rate, and 3.6 wt % in O2 fraction. The clamp supporting the particle is seen. The shadow at the left side in the window is the edge of the opposite window.

Figure 3. Radius of the nearly spherical particle of the activated carbon as a function of the time after the sample was transferred to the hot-zone of the cell for the same experiment as in Figure 2. The radius is the average between the maximum and minimum value.

to decrease. After the induction time, the size decreased and the edge of the initial particle was removed, while keeping the shape nearly unchanged as shown in Figure 2(b). Between 50 and 300 s, the radius decreased linearly with time, preserving the shape. The weight of

the particle when its radius was 80% of the initial value was about a half of the initial weight, which is roughly 80%.3 Therefore, the density of the particle was unchanged during the SCWO. Therefore, it seems that the reaction of the particle proceeded nearly at the surface of the particle. After 300 s, the radius decreased more rapidly and the surface became somewhat rough. As the reaction proceeded further, the decrease in size accelerated with the surface more roughened. Finally, the particle became so small that it dropped out of the holder upon the small fluctuation of the flow. At this final stage, the particle surface seemed irregular and the reaction seemed no more limited to the vicinity of the outer surface. It is possible that the kinetics of the reaction also changed as the size of the particle decreased. SCWO progress of three kinds of carbon materials significantly differed as shown in Figure 4. Note that the size-reduction rate of the activated carbon was much faster than the others, although the temperature for the activated carbon was 100 K lower than for the others. On the other hand, the size of the synthetic graphite particle decreased after a long induction period of about 1200 s. The decrease was mostly linear with time and the shape was nearly preserved, as was the case with the activated carbon. The rate of decrease for the synthetic graphite was about 1 order of magnitude smaller than that for the activated carbon. The HOPG showed no decrease in size, and no weight loss was observed after a long exposure to the reaction condition. Effect of Experimental Conditions on the Oxidation Rate. To discuss the dependence of the oxidation rate on experimental conditions, we focus on the initial stage of the oxidation in which the particle radius decreased linearly with time for both the activated carbon and the synthetic graphite. In this period, because the shape of the particles was nearly preserved, the reaction seemed to proceed neatly at the surface. Therefore, for simplicity of the analysis, it was assumed that the particle was a rigid sphere and the reaction occurred at its surface. By defining the surface reaction rate, r, based on the outer surface area, the decrease in the radius, dR, in an infinitesimal period, dt, is related to r as

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Figure 5. Effect of O2 fraction on the decreasing rate of the particle radius (dR/dt) for the activated carbon (b) and the synthetic graphite (0). The fixed-sample cell was used at 30 MPa, 0.50 cm3 min-1 flow rate, at either 773 K (activated carbon) or 873 K (graphite). Regression lines show the reaction order of 1.17 for the activated carbon and 0.98 for the synthetic graphite, respectively. Error bars are regression errors when dR/dt were estimated from the relations between the radius and time as in Figure 3.

4πR2dR ) 4πR2rdt/FP

(1)

dR/dt ) (1/FP)r

(2)

where Fp is the particle density. Hereafter, dR/dt, which is proportional to r, is used as a measure of the reaction rate. Figure 5 shows the effect of the O2 fraction on dR/dt. For both the activated carbon and the synthetic graphite, the reaction rate was nearly first order with respect to the O2 fraction. The reaction order for the activated carbon was somewhat larger than 1 even if the range of experimental errors is considered. Figure 6 shows the effect of total flow rate, cell temperature, and total pressure on the reaction rate of the activated carbon. The reaction rate increased with the total flow rate, whereas the cell temperature and total pressure had little effect on the reaction rate. Figure 7 shows the comparison between the temperature dependence of the reaction rate of both the activated carbon and the synthetic graphite in the form of an Arrhenius plot. The reaction rate of the activated carbon showed little temperature dependence, as can be seen in Figure 6(b), and the dependence is not Arrhenius-type. On the other hand, the reaction rate of the synthetic graphite showed Arrhenius-type dependence with the activation energy of 127 ( 10 kJ mol-1. At the same time, the induction time, which is observed in Figure 4, showed significant temperature dependence. The Arrhenius plot of the reciprocal induction time showed good linearity with the activation energy of 139 ( 8 kJ mol-1, as plotted in Figure 8, which is nearly identical with the activation energy for the size decrease. O2 Mass Transfer Rate as Estimated by CFD Calculations. The mass flux of O2 to the particle surface was estimated by CFD calculations, and is equal to the reaction rate per external surface area, r, under mass-transfer-limited kinetics. Equation 2 was used to convert the mass flux to dR/dt under mass-transferlimited kinetics. The estimated mass-transfer rates are shown in Figure 6 in addition to the observed reaction rates for the activated carbon. The mass-transfer rates are comparable to the reaction rates of the activated

Figure 6. Effects of total flow rate (a), cell temperature (b), and total pressure (c) on the decreasing rate of the particle radius (dR/dt) for the activated carbon oxidized in the fixed-sample cell. The observed decreasing rate (b) and the rate derived from the mass transfer rate of O2 to the particle surface that was estimated by the computational fluid dynamics simulation (- - -). Fixed experimental conditions: (a) 30 MPa, 773 K, and 3.6 wt % in O2 fraction; (b) 30 MPa, 0.50 cm3 min-1 flow rate, and 3.6 wt % in O2 fraction; (c) 723 K, 2.0 cm3 min-1 flow rate, and 3.6 wt % in O2 fraction.

carbon, though they are always larger than the reaction rates. The dependence of the mass-transfer rate on the experimental conditions is similar to that of the reaction rate of the activated carbon, but the dependence on the total flow rate is somewhat stronger than that of the observed reaction rate. Surface Temperature of the Particle and Flow Pattern. The CFD calculations also estimated the temperature of the particle and the flow pattern inside

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Figure 7. Arrhenius plot of the decreasing rate of the particle radius (dR/dt) for the activated carbon (b) and the synthetic graphite (0). The fixed-sample cell was used at 30 MPa, 0.50 cm3 min-1 flow rate, and either 3.6 wt % (activated carbon) or 10 wt % in O2 fraction (synthetic graphite). For the synthetic graphite, the regression line (- - -) shows the activation energy of 127 ( 10 kJ mol-1.

Figure 8. Arrhenius plot of the reciprocal induction time for the size decrease of the synthetic graphite particle. The fixed-sample cell was used at 30 MPa, 0.50 cm3 min-1 flow rate, and 10 wt % in O2 fraction. The regression line shows the activation energy of 139 ( 8 kJ mol-1.

the cell. As shown in Figure 9(a), the estimated temperature of the particle is distinctively higher than the cell temperature (773 K in Figure 9(a)). The particle temperature is determined by the balance between the heat release due to the reaction progress at the particle surface and the heat transfer from the particle surface to the surrounding fluid. For faster reaction, if the heat transfer rate is the same, the particle temperature becomes higher. Therefore, such temperature difference between the particle temperature and the cell temperature should not be significant in the case of the synthetic graphite because of its slow reaction rate. In the calculation, the high temperature of the particle causes strong buoyancy-driven flow from the top of the particle as shown in Figure 9(b). The buoyancy-driven flow around the particle significantly enhances the mass transfer of O2 to the surface. On the other hand, the flow below the particles is relatively weak. This is because the effect of buoyancy cancels the upward flow at the inlet because the inlet temperature of the fluid is lower than the cell temperature.

Figure 9. Temperature contour (a) and typical flow pattern (b) on the cross sectional plane of the fixed-sample cell as obtained by the computational fluid dynamics simulation, corresponding to 30 MPa, 773 K, 2.0 cm3 min-1 flow rate, and 3.6 wt % in O2 fraction. Brighter color in the panel (a) represents higher temperature as shown in the index. The arrows in the panel (b) represent local flow directions with their lengths corresponding to local velocity magnitude. The circles in the middle are the carbon particles. The holders supporting particles were omitted in the simulations because of the complexity of their shape.

Corresponding to the temperature difference, density distribution is also formed. A possible indication of such density distribution was indeed observed in the shadowgraphs. In some experiments, the picture corresponding to the calculated high-temperature zone above the particle (Figure 9(a)) was observed distinctively as shown in Figure 10. Discussions Different Reactivity of Carbon Materials. The rate of the progress of SCWO considerably depended on the carbon materials. The major reason for the high reaction rate of activated carbon is its porosity. Although the reaction rate was defined per external surface area, the reaction proceeded at the inner surface of the pores. Hence, the reaction rate per external surface area becomes much larger than the intrinsic surface reaction rate, although the reaction seemed to proceed only in the vicinity of the surface, that is, the effectiveness factor seemed to be small.

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Table 1. Peak Position of the Raman Spectra in Figure 11 and the Area Ratio of Two Peaks a b c d e

activated carbon before oxidation activated carbon after oxidation synthetic graphite before oxidation synthetic graphite after oxidation HOPG before oxidation

peak 1 position (cm-1)

peak 2 position (cm-1)

area ratio peak 1/peak 2

1358 1363 1361 1362

1604 1607 1583 1577 1584

1.3 1.0 0.51 0.19

Figure 10. Texture in the shadowgraph corresponding to the flow pattern in Figure 9. The contrast of the photograph was exaggerated to clarify the flow pattern.

Figure 11. Raman spectra of the particle surface: (a) the activated carbon before oxidation; (b) the activated carbon after 510 s oxidation at 30 MPa, 773 K, 2.0 cm3 min-1 flow rate, and 1.4 wt % in O2 fraction; (c) the synthetic graphite before oxidation; (d) the synthetic graphite after 7200 s oxidation at 30 MPa, 773 K, 0.5 cm3 min-1 flow rate, and 10 wt % in O2 fraction; and (e) HOPG before oxidation.

Considering that different combustion rates for different kinds of graphite were reported in the previous combustion study,17 the reactivity may also depend on the crystallographic nature of the surface. Therefore, the origin of the differences in reactivity was investigated by observing the microscopic Raman spectra of the particle surface before and after the SCWO as shown in Figure 11. The positions of the observed peaks are listed in Table 1. Because the excitation light is focused by microscopic lenses, the spectra include the information on chemical bonds within about 1 µm from the surface. For both the activated carbon and the synthetic graphite, two kinds of peaks were observed (noted as peak 1 and peak 2 in Table 1) as shown in the spectrum (a) and spectrum (c). The peak 1 at lower wavenumbers (∼1360 cm-1) corresponds to a less crystalline structure.27 On the other hand, the peak 2 at higher wavenumbers (∼1605 cm-1 for the activated carbon and ∼1580 cm-1 for the synthetic graphite) corresponds to a more crystalline structure.27 For both the activated carbon and the synthetic graphite after the SCWO (spectra (b) and (d), respectively), the positions of the two peaks did not change, but the area of the peak 1 decreased compared to the area of peak 2: the area ratio

(peak 1/peak 2) in Table 1 decreased after the oxidation. This change suggests that the less crystalline part of the surface was selectively oxidized. For the surface of HOPG, only the peak 2 was observed as shown in spectrum (e), indicating that the HOPG consisted of highly crystalline graphite that is difficult to oxidize. This is consistent with the result that HOPG showed no change after the SCWO. Therefore, the difference of the reaction rate between the synthetic graphite and HOPG would be due to the degree of crystallinity as well as the difference in the effective surface area. Reaction Order with Respect to O2 Concentration. The reaction rate was nearly first order with respect to the O2 fraction. However, when discussing the reaction order with respect to O2 “concentration”, it should be taken into account that the density of a water-O2 mixture is lower than pure water in supercritical conditions. The existence of 10 wt % O2 in supercritical water reduces the fluid density by 7.0% at 773 K and 3.5% at 873 K, as calculated using the equation of state by Heilig and Frank (CSOF/SWPA EOS)28 employing the parameters for water-N2 mixtures because of the lack of those for water-O2 mixtures. Considering this effect, the reaction order for the activated carbon is still larger than unity. In the case of the activated carbon, CFD calculations suggested that the temperature of the particle was higher than the cell temperature due to the heat evolution from the surface reaction. The surface temperature is higher for faster reaction, which will lead to a positive feedback of the reaction rate under surface-reaction-limited kinetics. Higher surface temperature will enhance the mass transfer of O2 to the particle by enhancing natural convection, which also will lead to a positive feedback of the reaction rate. The increase in the particle temperature due to heat evolution from the surface reaction seems to be a reason the reaction order for the activated carbon was somewhat larger than unity. Rate-Limiting Step. Considering that the reaction seemed to proceed at the surface of the particle, the ratelimiting step can be either external mass transfer of O2 to the particle surface or surface reaction. If the limiting step is the surface reaction, the reaction rate will generally increase with temperature with Arrheniustype dependence. Such temperature dependence was observed for the oxidation of the synthetic graphite, suggesting that the reaction rate of the synthetic graphite was limited by the surface reaction. On the other hand, if the limiting step is the mass transfer, the rate will be nearly independent of temperature, and a high flow rate will increase the mass transfer rate and thus the reaction rate. The diffusion coefficient is inversely proportional to density. Because large density both increases O2 concentration and decreases the diffusion coefficient, the rate will be independent of pressure. These characteristics of masstransfer-limited kinetics were indeed demonstrated by the results of CFD calculations in Figure 6. Comparing the above trends with the experimental results, the reaction rate of the active carbon seems to be limited

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by mass transfer of O2 to the particle. When the external mass transfer of the oxidizer limits the rate of the decrease in the particle size, R2 is linear with t because the reaction rate r in eq 2 is proportional to the externalmass-transfer rate that is inversely proportional to R. We confirmed that R2 is linear with t for the oxidation of the activated carbon during which its initial shape was nearly unchanged. However, because we focused on the initial stage of the decrease in the particle size, both R and R2 seem to be linear with t within experimental error. The calculated mass-transfer rate largely agreed with the reaction rate of the activated carbon. The fact that the calculated mass-transfer rate is somewhat larger than the observed reaction rate of the activated carbon implies two possibilities: (1) the accuracy of CFD calculations is insufficient because of the assumptions included, and/or (2) the reaction was actually in the intermediate between the mass-transfer-limited and surface-reaction-limited kinetics. Effect of the Reactor Geometry on the Mass Transfer Rate of O2. Some assumptions were employed in the CFD calculation and we should first examine their effect on the calculated results. The particle diameter was fixed to be 4 mm in the calculation, which corresponds to the initial stage of the reaction. This seems reasonable because we considered the reaction rate at the initial stage when considering the effect of the reaction conditions. The temperature of the fluid at the inlet was set to 573 K. In the calculation, the mass transfer rate of O2 to the particle was insensitive to the inlet temperature: the inlet temperatures of 473, 573, and 673 K yielded the same mass transfer rate within an accuracy of 3%. The spiral wire particle holder was omitted in the calculation. Since the flow under the particle was rather weak due to the buoyancy-driven flow that was induced by the low inlet temperature, we expect that the existence of the sample holder would not affect so much the flow pattern, and thus the mass transfer rate of O2 to the particle will be insensitive to the existence of the holder. The heat generated on the particle surface can dissipate through the particle holder. The heat generated on the total surface area was calculated to be 5.5 W at 30 MPa, 723 K cell temperature, 2.0 cm3 min-1 total flow rate, and 3.6 wt % in the O2 fraction. In the calculation, because we assumed that the particle was in steady state, i.e., heat flux from the particle surface to its center was zero, this heat dissipated by conductive and convective heat transfer around the particle and the surface temperature amounted to 998 K. If the Hasteloy rod of 1-mm diameter and 10-mm length is connected to the particle without any thermal resistance and the other end of the rod is connected to the inner wall of the cell, the heat dissipated from the particle to the wall is about 0.4 W. The actual heat dissipation through the sample holder seems to be lower than that value because thermal resistance between the particle and the holder is usually large. Therefore, the existence of the particle holder will not significantly affect the calculated temperature of the particle. The geometry of the reaction cell can affect the flow field inside the cell and thus the mass transfer rate of O2 to the particle will be dependent on the geometry. The most apparent factor is the inner diameter of the cell. If the inner diameter is larger, the line velocity of the fluid is smaller and the flow field will change

Figure 12. Arrhenius plot of the graphite oxidation rate observed in supercritical oxidation conditions and the estimated value using the proposed experimental relations obtained for graphite combustion at ordinary pressures by Makino et al.,15 Bradley et al.,12 and Bews et al.11 The activation energies are also shown.

because the buoyancy-driven flow is dependent on both the temperature difference and the distance between the particle and the inner wall. The calculated flow field in Figure 9(b) was also affected by the diameter of the outlet. The narrow outlet enhanced the circular flow around the buoyancy-driven upward flow from the particle. Therefore, if the mass transfer limits the reaction rate, the reactor geometry should be carefully examined in order to control the reaction rate. SCWO Rate of the Synthetic Graphite as Compared with the Combustion Rate under Ordinary Pressures. Because the oxidation of the synthetic graphite particle seemed to be limited by the surface reaction, the observed reaction rate corresponds to the intrinsic surface reaction rate of the graphite under the SCWO conditions. The oxidation of graphite under ordinary pressure was intensively researched and some relations for the reaction rate were deduced on the basis of the experimental analysis.11,12,15 It is interesting to extrapolate those relations to the SCWO conditions and see whether the extrapolated rates agree with the observed rates of SCWO. Strictly speaking, the comparison cannot reveal any information because the accuracy of such extrapolated values were not ensured by experiments and also we did not use the same graphite as those used in the literature. Nonetheless, we expect that the comparison will reveal some perspective on the characteristics of the SCWO of graphite. Figure 12 shows the comparison between the rate of SCWO of the synthetic graphite in this work and three extrapolated reaction rates based on the experimental relations for the graphite oxidation rates under ordinary pressures. The three relations are for the reaction C + 1/ O f CO. Bews et al. employed graphite particles of 2 2 around 115-µm diameter and measured their oxidation rate in a fluidized bed with silica sand at 973-1173 K and O2 partial pressure of less than 0.7 atm. They concluded that the reaction order with respect to O2 concentration was 1/2. Bradley et al. employed graphite

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particles smaller than 4.3-µm diameter and measured their oxidation rate in methane-air flame at 0.142 atm.12 The particle temperature was above 1200 K. According to their relation, the reaction rate is independent of the O2 concentration when their formula is applied to the SCWO conditions in this work, although the relation shows linearity with O2 concentration when O2 is dilute. Makino et al. observed the reaction rate of a graphite rod of 10-mm diameter in a hot oxidizing stream of either air, O2, or CO2 at a surface temperature of 1000-2000 K and pressure up to 0.8 MPa.15 In contrast to Bews and Bradley, the graphite they used was reported to be porous with a density of 1.82 g cm-3, which is similar to the value of the synthetic graphite in this study. They assumed that the reaction was first order with respect to O2 concentration. The relation they postulated represents the reaction rate per the external surface area, i.e., the effect of the porosity is included in their reaction rate, which is the same situation as in our study. Concerning the absolute value of the reaction rate, the formulas of Bews et al. and Bradley et al. resulted in SCWO rates that were about 4 orders of magnitude smaller than the observed SCWO rate of the synthetic graphite in the present study. Admitting that the actual surface area of the synthetic graphite was about 700 times larger than the outer surface area of a sphere, the reaction rate we observed seems somewhat larger than the extrapolated value based on the relations of Bews and Bradley. The value based on the formula by Makino is smaller than our data within an order of magnitude, but the porosity of the material makes strict comparison difficult. The activation energy for the present SCWO of the synthetic graphite seems to be somewhat lower than that for the combustion under ordinary pressures. This difference can be a characteristic of the SCWO of the graphite. In the combustion under ordinary pressures, the radicals such as O and OH participate at higher temperatures above 1300 K.14 In homogeneous SCWO systems, radicals such as OH and HO2 are formed and they participate in the oxidation of the solutes even below 800 K, as expected by the detailed chemical kinetics model.4-6 It is possible that an appreciable amount of OH and HO2 exist on the surface and/or in the homogeneous phase and that they can participate in the surface reaction of carbon, leading to lower activation energy than expected by the extrapolation of the reactions under ordinary pressures. In homogeneous systems, the source of H atoms in radical species is reactant molecules. In the SCWO of carbon, the reactant does not contain H atom. However, it is possible that a surface reaction between an oxygen atom chemisorbed on the carbon surface (or adsorbed COx species) and a water molecule adsorbed on the surface can react to generate a radical species containing H atom, which leads to an appreciable concentration of OH and HO2 on the surface and/or in the homogeneous phase through chain reactions. It is also possible that the activation energy for the reaction between the carbon surface and O2 is lowered by the presence of water. The reaction order with respect to O2 concentration is also interesting. When applying the experimental relations by both Bews and Bradley, the reaction order for the SCWO conditions is less than unity. On the other hand, for the SCWO of the synthetic graphite, the

reaction was observed to be first order. Considering that Makino modeled the combustion rate of the graphite as first order, the discrepancy seems mainly due to the different nature of the graphite surface. The graphite surface is reported to contain some kinds of surface sites with different reactivity and the reaction proceeds mainly via more reactive surface sites.20,21 When the fraction of the reactive surface sites is small, the reactive sites tend to be saturated with the adsorbates generated from O2 and thus the reaction rate will be insensitive to the increase in O2 concentration. In the SCWO of the synthetic graphite, it is possible that either radical species or H2O itself react with such adsorbates and make the reactive site unoccupied and ready to react with O2. Therefore, the reaction order of nearly unity observed for the synthetic graphite can be a manifestation of the characteristic reactions in SCWO. Conclusions The progress of the SCWO of three carbon materials, activated carbon, synthetic graphite, and HOPG, were studied by direct observation of the size reduction through the window of the reaction cell. The activated carbon was oxidized rapidly. Despite its porosity, the particle of activated carbon appeared to be oxidized nearly at its external surface at the initial stage of the reaction, suggesting that the effectiveness factor was small. The rate of size reduction for the synthetic graphite particle was smaller than that for the particle of activated carbon by about an order of magnitude. The reaction also seemed to proceed at the particle surface. The HOPG particle showed no decrease in either size or weight. The rate of size reduction differed because of two factors: (1) difference in the specific surface area and (2) the degree of the surface crystallinity. The mass transfer of O2 to the particle surface limited the reaction rate of the particle of activated carbon, as judged from the dependence of the reaction rate on the total flow rate, the cell temperature, and the total pressure. The CFD calculations estimated the rate of O2 mass transfer and the results showed good agreement with the reaction rate of the particle of activated carbon. The calculation suggested that the temperature of the particle was higher than the cell temperature by up to 200 K and this high temperature caused the upward buoyancy-driven flow from the particle, which enhanced the O2 mass transfer to the particle surface. If the reaction is in mass-transfer-limited kinetics as is the case of the activated carbon, the reaction rate will be affected by the geometry and temperature profile of the reactor through the flow pattern, including buoyancydriven flows, inside the reactor. The reaction of the synthetic graphite particle was limited by the surface reaction. The activation energy for the reaction rate at the initial stage of the size reduction was 127 ( 10 kJ mol-1. For the reaction of the synthetic graphite, an induction time of considerable length (103-104 s) was observed before the size of the particle started to decrease. The reciprocal induction time also showed Arrhenius-type dependence on the temperature with the activation energy of 139 ( 8 kJ mol-1, nearly the same value for the rate of size reduction, suggesting that some reaction proceeded at and/or near the particle surface before the particle size began to decrease. The rates of the graphite combustion under ordinary pressure were extrapolated using some experimental relations for the reaction rates. The

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activation energies for the graphite combustion under ordinary pressures are larger than the observed value for the SCWO in the present work. This might be due to either the solvent effect of the supercritical water or the heterogeneous radical reactions that seem to be more important at lower temperature in SCWO than in ordinary pressures. Acknowledgment The present study was supported in part by a grant provided by NEDO (via JCII) based on the project “Research & Development of Environmentally Friendly Technology Using SCF” of the Industrial Science Technolgy Frontier Program (METI), which is greatly appreciated. Nomenclature r ) Reaction rate based on the outer surface area (4πR2) [mol m-2 s-1] R ) Radius of the particle [m] Re ) Reynolds number ()F u dp/µ) [-] FP )Density of the particle [kg m-3]

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Received for review March 7, 2003 Revised manuscript received November 21, 2003 Accepted November 20, 2003 IE030222G