Kinetics of Supercritical Water Oxidation of Methanol Studied in a

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Ind. Eng. Chem. Res. 2001, 40, 3861-3868

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Kinetics of Supercritical Water Oxidation of Methanol Studied in a CSTR by Means of Raman Spectroscopy Seiichiro Koda,* Nozomu Kanno, and Hideo Fujiwara Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan

A newly devised continuous flow stirred tank reactor (CSTR) was employed for the study of kinetics of supercritical water oxidation (SCWO) of methanol near the critical point (390-430 °C, 24.7 MPa), where the reaction progress was analyzed by means of Raman spectroscopy. The production of CH2O, CO, and CO2 through the oxidation reaction was directly detected. Methanol conversion as a function of residence time could be analyzed on the basis of a simple first-order CSTR reaction model including phenomenological induction time. The overall reaction rate thus obtained was well-reproduced through simulation by a detailed chemical kinetics model, which supports the belief that the radical chain reaction mechanism is responsible for methanol SCWO even near the critical point. Introduction Supercritical water oxidation (SCWO) technology is now going to be practically applied for decomposing organic hazardous materials and/or for energy recovery from low-quality fuels such as biomass.1-3 SCWO has been so far supposed to be achieved at a relatively high temperature such as 500-600 °C at the pressure not so far from the critical pressure (22.4 MPa) where the state is considerably gaslike and the oxidation reactions under such conditions are naturally expected to be consisted of radical chain reactions. Indeed, several detailed chemical kinetic models derived as an extension from combustion reaction models have been applied with considerable success to the analysis of the reaction progress of SCWO of simple organic compounds such as methanol.4-9 The water molecules seem not to play any substantial role as solvent which interacts with the relevant species. However, the reaction mechanism and the solvent effect of water are not fully studied in the neighborhood of the critical point where the medium is not so much gaslike. It is important to study whether SCWO proceeds along radical chain reactions under such lower temperatures as those close to the critical temperature. The reaction progress of SCWO has been studied thus far using a batch reactor, mainly for final product analysis, and/or a flow tube reactor, ideally a plug flow reactor (PFR), for obtaining the reaction rate. The continuous flow stirred tank reactor (CSTR), however, has been employed very little for the study of SCWO except for our own short report4 and a computational model calculation.10 Performing a study using a CSTR may be worthwhile on the basis of the following points. First, experiments very frequently suffer from difficulties inherent in the adopted method. In the experiments involving flow reactors, for example, which have been commonly adopted in the kinetic analysis of SCWO, wall effects, such as catalytic effects, are not completely neglected. In a CSTR such wall effects are expected to * To whom correspondence should be addressed. Tel.: +81-3-5841-7327. Fax: +81-3-5841-7255. E-mail: koda@ chemsys.t.u-tokyo.ac.jp.

be fewer, if any, because of the much smaller surfaceto-volume ratio. Performing experiments using different kinds of reactors is thus crucial for establishing the reaction mechanism and kinetics. Second, intermediate species are expected to be more easily measured in a CSTR compared to the case of a PFR because the total mixture in a CSTR is well-mixed and we need not worry about the distribution of species in the reactor. The Raman spectroscopic method should be valuable as an in situ measurement, which the CSTR can be equipped with. Third, it is expected that the kinetics are different between a PFR and CSTR, in particular, for the complex reactions composed of many elementary reactions. We have once simulated the reaction progress of methanol SCWO by means of a detailed chemical kinetics model both in a PFR and CSTR5 and have shown that the conversion in a CSTR increases much more rapidly with an increase in the residence time than that in a PFR. Correspondingly, the induction time, whose presence supports a radical chain reaction mechanism, is much shorter in the CSTR. In the present work, we have devised for the first time a CSTR-type cell combined with a Raman spectroscopic method and wish to demonstrate the applicability of a CSTR for the reaction analysis. As far as we know, the present work is the first direct observation of SCWO progress in a CSTR, though Rice et al.11 once analyzed the kinetics in a PFR by means of a Raman spectroscopic method. We have selected methanol as the reactant because of its easy handling and also because a detailed chemical kinetics model is available for methanol. The reaction temperature adopted is not so far from the critical temperature. SCWO of methanol is known to be fairly well-described by such a detailed chemical kinetics model as far as the reactions in a certain high-temperature range (500-600 °C) are concerned.6 Experimental Section The experimental setup is shown in Figure 1, which consists of a reaction cell and flow systems. The reaction cell, the details of which are shown in Figure 2, is made of Hasteloy C-276 and has 6-mm inner diameter and

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Figure 1. Experimental setup: 1, syringe pump (H2O2 + H2O); 1′, syringe pump (CH3OH + H2O); 2, magnetic stirrer; 3, heater; 4, pressure regulator. T indicates thermocouple.

Figure 2. Reaction cell: 1, sapphire window; 2, feed inlet; 3, thermocouple; 4, impeller blade; 5, outlet; 6, magnetic spinning bar.

7-mm height, whose uncertainties are (0.05 mm at most. The cell volume is thus 0.198 ( 0.005 cm3. The cell volume may also change with the rise in temperature, which will give us an underestimation of the cell volume of ≈4% at 400 °C. However, the cell volume at room temperature was used for the calculation of residence time. The inside of the cell can be seen through a sapphire window of 5-mm thickness whose crystal c axis is perpendicular to the window surface. For the purpose of mixing, a tiny impeller of a flat disk blade made of Hasteloy C-276 is rotated, which is connected via an axis rod to a magnetic spinning bar in a separate room where the bar is rotated by a magnetic stirrer from the outside. On the cylindrical wall Hastelloy C-276 tubings of 0.5-mm inner diameter are equipped for feeding the methanol/water mixture (tubing length, 30 cm) and O2/water mixture (tubing length 2 m) at the confronting side, respectively. The system was fed with two syringe pumps (ISCO 260D). The methanol/water and O2/water solutions entered from the confronting feed lines. The methanol/ water mixture had been, in advance, degassed by feeding N2 for 2 h, which resulted in decreasing O2 content below 2.2 × 10-5 mol %. The flow rates of individual feeds (typically from 0.02 to 1.0 mL min-1 with a precision of 0.002 mL min-1) were controlled to yield the desired residence time from 0.7 to 31 s. The exit fluid flowed along the rotating axis rod for the impeller and went out from the cell system. The

methanol/water flow was heated in advance in the preheating line by the surrounding heaters, whose temperatures were adequately maintained to not decompose methanol to any appreciable amount before the flow entered the cell. This was evidenced using Raman spectroscopic analysis without adding any oxidants. The O2/water flow was also heated by surrounding heating wires. The latter feed line was long enough to decompose the precursor H2O2 completely and stoichiometrically to yield a desired amount of O2. The 100% decomposition of H2O2 was supported by the Raman spectroscopic measurements of the O2 peak. At the same time, the decomposition of more than 99% of H2O2 was supported at any adopted experimental condition from the conversion calculation using the kinetic data by Croiset et al.12 for the H2O2 decomposition. The cell fluid temperature was measured using the thermocouple being protected by a SUS-316 cover tubing which is inserted to the inner part of the cell and directly touched to the fluid. The inside cell pressure was controlled using a back-pressure regulator (JASCO 880-81) with a precision of (2%. The reagent-grade methanol, hydrogen peroxide (30%), and doubly distilled water were commercially obtained and used without further purification. Through the sapphire window, a continuous wave Ar+ ion laser beam at 488 nm of 0.5 W was focused into the cell using a 5.5-cm focal length lens. The backscattered light was led inversely through an optical fiber to a spectrometer (JASCO NRS-2000) and analyzed for its Raman shifts. The typical bandwidth was 4 cm-1, and the wavelength was calibrated using neon-lamp lines within a precision of 2 cm-1. In the determination of the relative concentration of methanol from the Raman spectra, the Raman intensities due to water were at first subtracted from the original Raman intensities in the C-H stretching region of methanol. Then, the remaining intensities in the C-H region were averaged using a least-squares-fit procedure for canceling the influence of the fluctuation of the CCD detector of the Raman spectrometer. Then, the obtained intensity in the C-H region was corrected for the influence of the pollution of the sapphire window which proceeded with the repetition of the experimental runs by dividing the value in the C-H region by the intensities for the O-H stretching of water obtained in the same experiment as an internal standard. The cause of the pollution of the sapphire windows is not clear, but it may be the deposition of some polymeric species such as those derived from the intermediate formaldehyde. Simulation Procedure Detailed chemical kinetics models for the oxidation of methanol in supercritical water have been reported by Brock and Savage,7 Dagaut et al.,8 and Brock et al.9 In this paper we adopted the model of a full set of elementary reactions. The model consists of 22 species, 139 reversible and 24 irreversible reactions; the rate parameters of these reactions are faithfully referred to in the original papers.7,9 For the reversible reactions, the rate constant of the backward reaction was calculated from the forward rate constant divided by the equilibrium constant which could be obtained from the Gibbs free energy of the reaction. The thermodynamic information of each compound in this model is included in the CHEMKIN II package13 used for the simulation, though the values of the heat of formation were partly revised according to recent literature.9

Ind. Eng. Chem. Res., Vol. 40, No. 18, 2001 3863 Table 1. Characteristic Mixing Times turbulent

Figure 3. Mixing experiments: methanol fraction vs rotational speed at 24 °C, 24.6 MPa. Residence time ) 12 s. O, upper location; 4, center location; 0, lower location.

laminar

1 rcNqfgn

macro

=

meso

d02 = 0.1 {ηj(λm/4)4}1/3

3 = d0 c

micro

ν3/2 = 0.1 1/2  D

= 0.5

The calculation was performed using the CHEMKIN II package which was originally developed by Sandia National Laboratory.13 To simulate the reactions in a CSTR, the FORTRAN codes of the “PSR” in the package were used. It should be noticed that, in the calculation, we input a pressure that was higher than the experimental pressure so that the CHEMKIN II would calculate the correct experimental density and species concentrations from the ideal gas law. Results and Discussion Establishment of the Cell as a CSTR. Mixing Measurements. To estimate whether the present cell could be regarded as a well-mixed reactor, the degree of mixing was estimated, which was reached when a 50 wt % methanol/water mixture and pure water were introduced through the confronting feed lines with changing of the rotational speed of the impeller. For our purposes, the relative concentration of methanol was measured as a peak intensity of the C-H bond at 2953 and 2846 cm-1 in the Raman spectrum, changing the focal point of the excitation laser beam from an upper, center, and lower location inside the cell. Figure 3 was obtained at 24 °C, 24.6 MPa and at the residence time of 12 s. The relative concentrations coincided at and above the rotational speed of 8 s-1, which implies that almost complete mixing is realized. Figure 4 shows the results obtained at 410 °C, 24.6 MPa and at the residence time of 8.4 s. Though the data scatter along the change of the residence time, the three data points obtained at different individual locations coincided with each other within the error limits of the peak measurements independent of the rotational speed, that is, 0, 8, and 25 s-1. Thus, the mixing is considered to be almost complete even without stirring at the present

( ) Npfg c2

1/3

Sc1/3

d02/3 j1/3

high-temperature conditions above the critical temperature of water. Analysis of the Mixing Time. Whether the flow in the cell is laminar or turbulent can be determined on the basis of the Reynolds number, Re, which is given by

Re ) Fnd2/µ

Figure 4. Mixing experiments: methanol fraction vs rotational speed at 410 °C, 24.6 MPa. Residence time ) 8.4 s. O, upper location; 4, center location; 0, lower location.

Sc x‚τ

(1)

where F is the fluid density, n, the rotational speed of the impeller, and d, the diameter of the impeller. When Re > 1000, the fluid is in a turbulent region. At the temperature of 24 °C, Re is 0-440 for n of 0-25 s-1. On the other hand, at the temperature of 410 °C and the pressure of 24.6 MPa, Re becomes larger than 1000 when n goes over 13 s-1. In the latter calculation, the fluid density was taken from a steam table14 and the viscosity was estimated from the equation given in the article15 assuming that the mixture behaved similarly to pure water. We have tried to estimate the degree of mixing using the correlation equations described in chemical engineering standard textbooks, noting that we must not overemphasize the propriety of their usage because of the relatively large different geometries and experimental conditions between the present reactor and usual CSTR reactors in chemical engineering. There are three mixing times, that is, macro-, meso- and micromixing time. When a flow containing a reactant is introduced at some point into the reactor, such as done in the present case, the mixing of that flow with the reactor contents may be critical. This process is mesomixing. In a turbulent flow, mesomixing is faster than macromixing, but it is generally slower than micromixing. We have estimated the above mixing times under the conditions relevant to the present mixing experiments according to the procedure described in a standard text.16 The adopted equations for the estimation are summarized in Table 1, consulting the text description. Briefly, the diffusion coefficient in the supercritical region was estimated according to the equation obtained in the literature,17 that is,

D[cm2/s] × F[g/cm3] ) 2.24 × 10-6 × (T[K])0.763 (2) The Schmidt number, Sc, was calculated from the diffusion coefficient and kinematic viscosity. In these calculations, the fluid was assumed to behave as pure water at the given temperature and pressure as stated before. The very important concept relevant to turbulence is the mean specific power dissipation per unit of fluid, j, which is estimated as

j ) Npfgn3d2

(3)

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Figure 5. Calculated mixing times as a function of rotational speed at 24 °C, 24.6 MPa. Bold line, mesomixing time (tme); dashed line, micromixing time (tmi)

where the power number Np is calculated according to Nagata.18

Np )

(

) ()

0.66 p

3

A 10 + 1.2Re +B Re 103 + 3.2Re0.66

×

ht dt

(0.35+b/dt)

(sin θ)1/2 (4)

where

A ) 14 + (b/dt) × {670(d/dt - 0.6)2 + 185} B ) 10{1.3-4(b/dt-0.5) -1.14(b/dt)} 2

p ) 1.1 + 4(b/dt) - 2.5(d/dt - 0.5)2 - 7(b/dt)4 The values concerning the cell (as the CSTR tank) geometry and impeller size are selected as follows. They are ht (height of the fluid in the tank) ) 7.0 × 10-3 m, dt (diameter of the cylindrical tank) ) 6.0 × 10-3 m, b (width of the impeller blade) ) 1.5 × 10-3 m, and d (diameter of the impeller) ) 4.0 × 10-3 m. And θ, the angle of the blade, is in the present case 90°. The ratio between the local and mean specific power dissipation η () /j) was selected as 0.1. The mean specific power dissipation in the laminar region was estimated as

j ) Npfgνn2

(5)

where ν is the kinematic viscosity. The geometric factor, fg, is calculated as,

fg )

4d3 πdt2ht

(6)

both for laminar and turbulent regions from the cell geometry. Other parameters which should be evaluated for the estimation of individual mixing times were selected as follows. The integral length scale λm was equated to the width of the impeller blade. rcNq was arbitrarily set to 2.0. The constant c which appears in the laminar region equations was equated to 0.4. Comparison of Mixing Times, Residence Time, and Characteristic Reaction Time. The individual mixing times calculated according to the above procedure are drawn as a function of the rotational speed for the adopted two experimental conditions in Figures 5 and 6, respectively. Under the ambient temperature and pressure, the fluid is in the laminar region independent

Figure 6. Calculated mixing times as a function of rotational speed at 410 °C, 24.6 MPa. Bold line, macromixing time (tma); dashed line, mesomixing time (tme); chain line, micromixing time (tmi). The arrow indicates the transition between the laminar and turbulent region.

of the rotational speed. According to Figure 5, the mesomixing time coincides with the residence time of the present experiment (12 s) at the rotational speed of ≈10 s-1. It is reasonable to consider that the present experiment using the Raman spectral intensity roughly corresponds to the mesomixing. We are not sure whether the complete macromixing is achieved in the present experiment; however, almost complete meso- and micromixing within the residence time are expected to be realized when n is larger than 10 s-1. In the case at 410 °C and 24.6 MPa, the fluid condition changes from laminar to turbulent at n ≈13 s-1. Independent of the rotational speed of the impeller, the meso- and micromixings are achieved within the experimental residence time of 8.4 s of the present experiment, comparing the experimental and simulated results. When the rotational speed is over 13 s-1, the three mixing times are much shorter than the residence time of the present mixing experiments. The efficient mixing found without any rotation of the impeller may be attained as a result of the agitation caused by the introduction of the feeds. Anyhow, we have employed n over 20 s-1 in any experiments for obtaining the reaction kinetics. The other problem is whether the characteristic reaction time is shorter than the mixing times or not. This is a very difficult problem. As will be described later, the simulated induction time is on the order of 1 s. The characteristic reaction time is thus expected to be longer than the macromixing time of ≈0.1 s. The other mixing times are much shorter than the macromixing time, and we consider that the chemical reaction is not appreciably affected by any incomplete mixing. We will support this conclusion later by checking the effect of the rotational speed on the reaction progress itself. Observation of Raman Spectra during SCWO. Raman SpectrasGeneral Observation. In the following experiments and also simulations, the properties of the reaction mixtures have been assumed to be equal to those of pure water, considering that the fractions of the reactants and products are rather small. Oxygen is of the highest fraction, whose fraction is still less than 5 mol %. The effect of this assumption will be discussed later. Figure 7 shows typical Raman spectra at two different residence times, that is, 0.8 and 8.4 s. In the former spectra, we only notice the existence of methanol due to its two C-H stretching vibrations at 2953 and 2846 cm-1 and O2 at 1555 cm-1 other than the strong O-H stretching due to water. At the longer residence time

Ind. Eng. Chem. Res., Vol. 40, No. 18, 2001 3865 Table 3. Summary of Methanol Oxidation Experiments

Figure 7. Raman spectra observed at 410 °C, 24.6 MPa. Initial concentrations are as follows: [CH3OH]0 ) 2.52 mol %; [O2]0 ) 4.86 mol %. (a) Residence time ) 0.8 s; (b) residence time ) 8.4 s. Table 2. Assignment of Raman Peaks (cm-1) species

assignmenta

CH3OH

2δs(CH3) νs(C-H) ν(O-O) νa(C-H) νs(C-H) ν(C-O) (1110)-(0110) (1000)-(0000) (0200)-(0000) (0310)-(0110)

O2 CH2O CO CO2

present work

in SCW

2953 2846 1555

2944b 2843b 1571b

2795 2141 1412 1389 1289 1268

2780b 2165b 1411c 1389,c 1389b 1285c 1263c

gas phase 2844d 1556.379e 2843.4f 2766.4f 2143.237g 1409.4756h 1388.1847h 1285.4087h 1265.0901h

a ν and δ indicate stretching and deformation mode. The subscripts “s” and “a” mean symmetric and asymmetric, respectively. The assignments of CO2 lines are represented using three vibrational quantum numbers v and the quantum number of vibrational angular momentum to the degeneration mode l (v1v2lv3). b Rice, S. F.; Croiset, E. Oxidation of Simple Alcohols in Supercritical Water III. Formation of Intermediates from Ethanol. Ind. Eng. Chem. Res. 2001, 40, 86. c Brown, M. S.; Steeper, R. R. CO2-Based Thermometry of Supercritical Water Oxidation. Appl. Spectrosc. 1991, 45, 1733. The values were read from the figures in the literature. d Herzberg, G. Molecular Spectra and Molecular Structure II; Van Nostrand: New York, 1945. e Edwards, H. G. M.; Long, D. A.; Najm, K. A. B.; Thomsen, M. The VibrationRotation Raman Spectra of 18O2, 17O18O, 17O2, and 16O2. J. Raman Spectrosc. 1981, 10, 60. f Job, V. A.; Sethuraman, V.; Innes, K. K. The 3500 Å 1A2 - X1A1 Transition of Formaldehyde-h2, d2 and hd1. J. Mol. Spectrosc. 1969, 30, 365. g Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV; Van Nostrand: New York, 1979. h Rothman, L. S. Infrared Energy Levels and Intensities of Carbon Dioxide. Appl. Opt. 1986, 25, 1795. The values were calculated from the observed vibrational levels in the literature.

we find the decrease of the methanol and O2 peaks parallel to the appearance of CH2O at 2795 cm-1, CO at 2141 cm-1, and CO2 at 1268-1412 cm-1, though the products peaks suffered considerably from poor S/N ratio. In particular, the observed center frequency of CH2O may have suffered from large error (≈15 cm-1). The Raman shifts observed in the present work have been compared in Table 2 with those found by Rice and

reaction temp (°C)

methanol (mol %)

oxygen (mol %)

residence time (s)

methanol conversion

390 390 390 390 390 390 390 390 390 390 390 390 410 410 410 410 410 410 410 410 410 410 410 430 430 430 430 430 410 410 410 410

2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 0.43 0.43 0.43 0.43

4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 4.86 2.55 2.55 2.55 2.55

2.4 6.1 1.2 8.1 4.0 12.1 24.2 8.2 2.5 30.9 12.1 15.1 1.7 0.8 2.8 8.4 4.2 2.1 10.5 4.2 16.8 1.7 10.5 7.1 1.4 0.7 3.6 2.4 8.4 1.7 21.0 10.5

-0.01 0.21 -0.11 0.37 0.05 0.43 0.53 0.28 0.24 0.58 0.41 0.20 0.29 0.22 0.38 0.58 0.36 0.32 0.60 0.37 0.71 0.16 0.56 0.78 0.58 0.28 0.67 0.62 0.21 0.00 0.59 0.53

Croiset19 in SCW and/or gas-phase vibrational Raman shifts. In SCWO of methanol, the important carbon-containing intermediates are suggested to be CH2O and CO. The production of CH2O was indeed directly observed by Rice et al. using a Raman spectroscopic method coupled with a flow-type reactor.11 The observation of CH2O, though unfortunately somewhat unclear, is the second case of the direct Raman spectroscopic observation. The character of the successive reaction progress, that is, methanol f CH2O f CO f CO2, is expected to be similar to that at the higher temperature studied using tube-type reactors5,6 and correspondingly we Raman spectroscopically observed the CO and CO2 in the products. Disappearance Kinetics of Methanol under Oxidation Conditions. Though the qualitative information concerning the intermediates and products is obtained, their time profiles are not yet quantitatively obtained. Thus, our analysis will be limited to the disappearance kinetics of the methanol peak. In the kinetic analysis, the system is treated as a CSTR. In an analysis of the methanol conversion data, the first-order model of eq 7 is applied,

k(τ - tind) )

X 1-X

(7)

where k is the phenomenological first-order rate constant, τ, the residence time, tind, the apparent induction time, and X, the methanol conversion. For a single firstorder reaction, the relation should not contain any induction time. In the present SCWO, however, the induction time may appear phenomenologically. In the simulation, the same functional dependency between

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Figure 8. Relationship between X/(1 - X) vs residence time at 24.7 MPa with the initial concentrations of [CH3OH]0 ) 2.52 mol % and [O2]0 ) 4.86 mol % at three different temperatures, 390 °C (O, experiment; bold line, simulation), 410 °C (4, experiment; dashed line, simulation), and 430 °C (0, experiment; chain line, simulation). The bar corresponds to (1σ.

Figure 9. Relationship between X/(1 - X) vs residence time at 410 °C, 24.7 MPa with two different sets of initial concentrations. One is [CH3OH]0 ) 2.52 mol % and [O2]0 ) 4.86 mol % (O, experiment; bold line, simulation), and the other is [CH3OH]0 ) 0.43 mol % and [O2]0 ) 2.55 mol % (), experiment; dashed line, simulation). The bar corresponds to (1σ. The dotted line shows the result of simulation for [CH3OH]0 ) 2.52 mol % and [O2]0 ) 4.86 mol % mixtures after correction for the density change due to the presence of O2. Table 4. Rate Constants and Induction Times from Experiments and Simulation conditions conc.a

experiments

simulation

(mol %)

temp (°C)

k (10-2 s-1)

tind (s-1)

k (10-2 s-1)

tind (s-1)

2.52 2.52 2.52 0.43

390 410 430 410

4.5 ( 1.7 13.2 ( 2.0 45.1 ( 14.9 7.9 ( 6.5

-0.1 ( 5.3 -0.9 ( 1.3 -1.0 ( 1.1 1.3 ( 4.9

4.5 18.5 54.5 11.7

5.0 2.2 0.9 4.6

a conc. means the initial concentration of methanol in the reactor.

the conversion and residence time is indeed obeyed, as will be described later in more detail. The experimental data are tabulated in Table 3. Figure 8 shows the experimental results at three different temperatures, and Figure 9 shows two different initial concentrations of methanol and O2. The relation obtained by simulation on the basis of a detailed chemical kinetics model for the same reaction conditions as the experiments are simultaneously drawn. The ranges of the data scattering ((1σ) are drawn in Figures 8 and 9. The experimental data scatter badly, mainly because of the poor S/N ratio of the peak intensity measurements. However, eq 7 is recognized as a model to be followed, at least as a first approximation. In Table 4, the first-order rate constants and induction times evaluated from the data in Figures 8 and 9 are tabulated, where the 95% confidence limits through the least-squares fit are also given. The induc-

Figure 10. Relationship between X/(1 - X) vs residence time at 430 °C, 24.7 MPa with the initial concentrations of [CH3OH]0 ) 0.95 mol % and [O2]0 ) 2.04% under different rotational speeds, n ) 0 (O), 12.5 (4), and 33.3 s-1 (0).

tion time could not be determined with any reliable precision. To check whether the mixing conditions affected the reaction progress, the reaction progress was pursued under different rotational speeds of the impeller, and the effect was indeed negligible as demonstrated in Figure 10. Any meaningful differences are not noticed over the data scattering among the experiments of different rotational speeds. Simulated Time Profiles of Methanol Conversion in a CSTR and Kinetic Features. The general features of the methanol SCWO based on the detailed chemical kinetics model has been discussed elsewhere.5 It has been shown that the first-order relation as eq 7 is followed satisfactorily. The presence of phenomenological induction time is simulated in a PFR as well as a CSTR. The experiments by Brock et al.6 evidenced the presence of induction time in methanol SCWO studied by a flow tube method (approximated as a PFR) though in a higher temperature region (>500 °C) than the present case. The induction time should imply that SCWO is a radical chain reaction that needs accumulation of branching agents and/or radical species before the reaction progresses appreciably. The induction time is shorter in a CSTR than in a PFR due to the fact that a CSTR is a kind of recycling reactor which can make use of the once-produced species in the later stages as the initiator. The simulation results obtained under the same conditions adopted in the experiments are simultaneously plotted in Figures 8 and 9 as curved lines. In the simulation, being different from the case of experiments, both the rate constants and induction times could be obtained from the plots. The rate constants and induction times thus obtained are tabulated in Table 4. Comparison of the Experimental Results and Simulation. The inspection of Figures 8 and 9 indicates that the experimental data are in satisfactory agreement with the simulated results. This is also true when we inspect the rate constants obtained experimentally, comparing with those obtained through simulation in Table 4. Before concluding, however, we must take into consideration the fact that the real reaction medium is not pure water. Thus, we have estimated the possible effects of the presence of O2 as the component of the highest concentration next to water. The equation of state due to Heilig and Frank (CSOF/SWPA EOS)20 was adopted for evaluating the density of the mixture of water-O2 (4.86 mol %), employing the parameters for the water-N2 mixtures due to the lack of those for water-O2 mixtures. The behavior of N2 and O2 is quite similar. Indeed, we checked that the critical curve for

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water-O2 mixtures21 could be well-reproduced by the above CSOF/SWPA EOS. As one example, the density of pure water at 410 °C and 24.7 MPa is 7.86 mol dm-3 and that for the water-O2 (4.86 mol %) mixture is calculated to be 6.40 mol dm-3 according to the CSOF/ SWPA EOS calculation. This difference in the density affects the estimation of the residence time. Thus, the experimentally obtained rate constant k should be multiplied by ≈1.20 ()7.86/6.40). We also repeated the simulation and found that the reaction progress is slightly slower, as shown by the dotted line in Figure 9. This is probably ascribed to the decreased concentrations of individual species under the lower density, which slows down the relevant bimolecular reactions. The other constituents of the reaction mixture, in particular methanol, may also affect the analysis of the experimental results through the density change, and the simulated results might be also affected to some extent. The evaluation of the total effects is, unfortunately, not possible. However, we consider the conclusion that the experiments and simulations are in satisfactory agreement is still true. It is interesting to note that the conversion data are affected by the difference in initial concentration of methanol and/or O2, both in experiments and simulation as shown in Figure 9. The effect of the different O2 concentrations is very small according to the previous simulation5 and experimental works.6 Thus, the difference is mostly caused by the different initial concentrations of methanol rather than the different initial O2 concentrations. This should not be so if the reaction is a single first-order reaction of methanol. This fact then supports the idea that the present SCWO system is very complex, even though the reaction appears as a single first-order reaction of methanol when the time evolution of methanol is pursued. Summary 1. A well-mixed reactor which could be monitored using a Raman spectroscopic method was constructed and its applicability to the analysis of SCWO reaction progress was demonstrated. 2. SCWO of methanol proceeds along a radical chain mechanism even near the critical point. 3. The time evolution, including pseudo-first-order rate constant and induction time, can be roughly predicted by a detailed chemical kinetics model. 4. The SCWO system behaves differently for PFR- and CSTR-type reactors. The design of the practical reactors should take into account not only the global reaction rate but also the kinetics behavior. Acknowledgment This work is supported by Research for the Future Program of the Japan Society for the Promotion of Science (96P00401), which is greatly appreciated. We are grateful to Prof. Yoshito Oshima of the University of Tokyo for his valuable comments and discussions. Nomenclature b ) width of the impeller blade (m) c ) constant d ) diameter of the impeller (m) d0 ) diameter of the inlet tube (m) dt ) diameter of the cylindrical tank (m) fg ) geometrical factor

ht ) height of the fluid in the tank (m) n ) rotational speed of the impeller (s-1) Np ) power number Nq ) pump number rc ) circulation ratio Re ) Reynolds number Sc ) Schmidt number tind ) induction time (s) tma ) macromixing time (s) tme ) mesomixing time (s) tmi ) micromixing time (s)  ) specific energy dissipation per unit fluid mass (W/kg) j ) average specific energy dissipation per unit fluid mass (W/kg) θ ) angle of the impeller blade (deg) η ) local relative specific energy dissipation F ) density (g/cm3) λm ) integral length scale (m) µ ) viscosity of the fluid ( kg m-1 s-1) ν ) kinematic viscosity (m2 s-1) τ ) mean residence time (s)

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Received for review February 2, 2001 Revised manuscript received May 25, 2001 Accepted June 18, 2001 IE0101083