J . Phys. Chem. 1994,98, 80G809
800
Oxidation of Hydrogen and Carbon Monoxide in Sub- and Supercritical Water: Reaction Kinetics, Pathways, and Water-Density Effects. 1. Experimental Results H. Richard Holgatet and Jefferson W. Tester' Department of Chemical Engineering and Energy Laboratory, Massachusetts Institute of Technology, Room E40-455. 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 Received: May 27, 1993; In Final Form: November 1 1 , 1993"
Water under supercritical conditions (T > 374 OC, P > 221 bar) is an attractive medium for the efficient oxidation of wastes. Oxidation of carbon monoxide and hydrogen in supercritical water was studied at 550-570 OC and 118-263 bar in an isothermal, isobaric, tubular flow reactor. Carbon monoxide oxidation experiments a t 246 bar and 550 and 560 OC confirmed an oxygen dependence seen earlier and revealed an induction time of approximately 2 sin the oxidation reaction. Hydrogen formation during C O oxidation was strongly dependent on the fuel equivalence ratio, with fuel-rich conditions favoring its formation. Hydrogen formation occurs very slowly in the complete absence of oxygen. In the pressure range 118-263 bar, oxidation of both hydrogen and carbon monoxide is strongly pressure (water density) dependent, with higher densities favoring higher oxidation rates. At 550 and 570 OC, respectively, the rates of hydrogen and carbon monoxide oxidation increased by a factor of 3-5 when the operating pressure was increased from 118 to 263 bar. Limited studies of hydrogen and carbon monoxide oxidation in a packed reactor showed that the additional surface area inhibits oxidation, although the magnitude of the effect implies that high-temperature results from the tubular reactor may be treated as homogeneous.
Introduction Oxidation in a supercritical water environment is an innovative technology for the rapid destruction of hazardous organic and metabolic wastes without formation of harmful byproducts.14 Pure water is considered supercritical if its temperature and pressure both exceed the critical values of 374.2 OC and 221 bar, respectively. At or above the critical point, the density of water is a strong function of both temperature and pressure, as are its solvation properties.5 Under the conditions of the oxidation process, at temperatures above 400 OC and pressures between 230 and 260 bar, supercritical water acts as a dense gas, with the solvation characteristics of a nonpolar organic+ organics and gases are completely miscible with supercritical water, yet inorganic salts have very limited ~olubility.~These unique properties of supercritical water allow oxygen and organics to be contacted in a single phase, in which oxidation of the organics raises the mixture temperature to 550-650 OC, where waste destruction proceeds rapidly and completely. Conversions of 99.99% or greater can be achieved with reactor residence times of 1 min or less. Heteroatoms are converted to acids which can be neutralized and precipitated from the mixture as salts by adding a suitable base (such as sodium hydroxide) to the feed.* While supercritical water oxidation was first proposed 14 years ago, kinetic data for the oxidation of model compounds in supercritical water have become available only in recent years. Furthermore, the fundamental kinetics and mechanisms of oxidation in supercritical water remain poorly understood relative to those of more mature waste-treatment technologies such as incineration. Experimental data for the oxidation of simple compounds such as hydrogen and carbon monoxide are important, because their oxidation mechanisms are relatively simple and have been well characterized in the gas phase. Carbon monoxide is also often a major intermediatein the oxidation of more complex species. Hydrogen oxidation in supercritical water has been studied previously, at 246 bar and 495-600 OC.9 In that study, the f
Present address: The MITRE Corp., 7525 Colshire Drive, McLean, VA
22102.
* To whom correspondence should be addressed.
e
Abstract published in Aduance ACS Absrracrs, December 15, 1993.
0022-3654/94/2098-0800$04.50/0
experimental data were well described by the global rate form -d[H,]/dt = 1022.8f2.2 exp(-372 f 34/RT)[H2]
(1)
where the concentration is in mol/cm3, the rate in mol/(cm3 s), and the activation energy in W/mol; regression errors are 95% confidence estimates. Over the range of conditions studied, including fuel-lean and fuel-rich feed ratios, the kinetics were independent of oxygen concentrationand first order in hydrogen. The reaction also demonstrated a pronounced induction time, indicating a free-radical mechanism. Carbon monoxide oxidation in supercritical water was first studied in our laboratory by Helling and Testerlo and later reexamined by Holgate et al.,I1 at 246 bar and roughly 400-600 OC. Thelatter study confirmed earlier observationsof dual, global, empirical reaction pathways for carbon monoxide: the watergas shift, CO + HzO COZ+ Hz, and direct CO oxidation, CO + I/202 COZ. These "pathways" are convenient engineering representations of what is likely a coupled elementary reaction network and should not be interpreted as observed molecular reactions. For experiments in which oxygen was excluded from the reactor, as reported by Holgate et al., we regressed a rate expression to data for the water-gas shift pathway:
-
-
-d[CO]/dt = 107.0*0.4exp(-95 f 3/RT)[C0]0.71f0.08 (2) where the units are as in eq 1. Holgate et al." also developed a rate expression for the direct-oxidation pathway, which incorporated experimental data from the earlier study10 as well as newer data:
with the units as in eq 2. The first-order dependence on CO had been observed in the earlier study, but the fractional-order dependence on oxygen was new. In the present experimentalstudy, oxidation of hydrogen and carbon monoxide was examined over a wide range of sub- and supercritical pressures, to determine the effect of pressure (or water density) on the oxidation kinetics. In addition, carbon 0 1994 American Chemical Society
Sub- and Supercritical Water. 1
The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 801 (150-250 rm) Inconel 625 beads. The tubular and packed reactors are completely interchangeablewithout any additional modifications to the system. Carbon Monoxide Oxidation in Supercritical Water
L -l
Figure 1. Isothermal, isobaric, plug-flow reactor apparatus.
monoxide oxidation at 246 bar was studied in greater depth to reveal more detailed kinetic information. Finally, experiments were conducted to evaluate the influence of reactor surface on observed kinetics.
Figure 1 shows the isothermal, isobaric, plug-flow reactor apparatus used in these studies. Experimental procedures and techniques have been described in detail el~ewhere.~J~ Briefly, dilute aqueous feed solutions of hydrogen or carbon monoxide and oxygen were prepared by dissolving the gases in purified water in two high-pressure 3-L saturators. The feed solutions weredelivered separatelyto the reactor by a duplex high-pressure feed pump. The reactor was 4.7 1 m of 0.635-cm 0.d. X 0.17 1-cm i.d. Inconel 625 tubing contained in a fluidized sand bath. The feeds were preheated separately to reaction temperature in two 2.8-m lengths of 0.1 59-cm 0.d. X 0.108-cm i.d. Hastelloy C276 tubing (denoted "preheating tubing" in Figure 1) contained in the reactor sand bath. Additional preheating was provided by a second sand bath during experiments with hydrogen in which no reaction during feed heating was possible. The preheated feeds met and mixed at the reactor inlet, where the oxidation reaction was initiated. Reactor temperature was taken as the average of the mixing and exit fluid temperatures. Upon exiting the reactor, the reaction mixture was quenched to ambient temperature in a countercurrent shell-and-tubeheat exchanger, and the pressure was reduced to ambient upon passing through the back-pressure regulator. The resulting gas and liquid phases were disengaged in a gas-liquid separator and the flow rate of each phase was measured. Pressuremeasurements upstream and downstream of the reactor confirmed that the system was isobaric within 3-4 bar. Compositional analysis of the effluent gas phase was accomplished by gas chromatography using a thermal conductivity detector. High sensitivity for H2 was obtained by performing duplicate sample analyses in a second GC using N2 as the carrier gas. A packed reactor is also available for studying the effect of increased reactor surface area. The packed reactor consists of a 61.67-cm length of 9.12-mm (0.359-in.) i.d. X 1.43-cm (9/1,4n.) 0.d. Inconel 625 tubing packed with -60+100 mesh
Subsequent to carbon monoxide oxidation experimentswhich were used to determine global rate expressions for the empirical direct-oxidationand water-gas-shiftpathways,' additional carbon monoxideoxidation experiments were conducted to obtain species concentrationsprofiles of the type obtained earlier for hydrogen oxidation? These profiles were of interest becauseof the induction times observed for hydrogen oxidation; similar induction times were considered likely to be present in CO oxidation, but their existence could only be ascertained from concentration profile data. Furthermore, concentrationprofiles provide a much more rigorous and detailed test of elementary reaction model predictions than mere conversion data, because concentration decay (or growth) rates may be directly compared. Four sets of experiments were conducted, one at 550 OC and three at 560 OC. Experimental temperatures were somewhat constrained by the need to resolve kinetic features over the range of accessible residence times (roughly 3.4-1 1 s), which were in turn constrained by the maximum pump flow rate and the desire to maintain turbulent flow within the reactor. As noted earlier, residence times in the current experimental system (at constant temperature and pressure) must be varied by varying the flow rate through the reactor. The two temperatures examined, 550 and 560 O C , were found to give oxidation rates of a magnitude that allowed species profiles to be spread over a moderately large range of residence times while still providing a broad range of conversions (species concentrations). All concentration profile data were obtained at a constant pressure of 246 bar, consistent with the earlier CO oxidation experiments.'' Carbon and oxygen balances on the four sets of data showed excellent closure, typically within about 3%. Reaction of carbon monoxide by the global water-gas-shift pathway during preheating was neglected, in accordance with the conclusions of Holgate et a1.l' The initial set of experiments was conducted at 550 OC with nominally stoichiometricconcentrationsof CO and 0 2 (1.02 X 1 W and 0.50 X 1od mol/cm3, respectively). The results are shown in Figure 2. The carbon monoxide, oxygen, and carbon dioxide profiles suggest that, like hydrogen oxidation, CO oxidation proceeds after a pronounced induction time. Also notable in Figure 2 is the H2 concentration, which increases continuously with residence time. This behavior suggests that H2 continues to be formed while CO is being oxidized, and thus, under these conditions, the rate of formation of H2 in the presence of COoxidationis larger than the rateat which Hzcan beoxidized. The magnitudes of the H2 concentrations show that H2 is effectively a trace component, present at levels about 30 times lower than that of the major product, C02. Figure 3 shows the results of a similar set of experiments, but with the temperature raised 10 OC to 560 OC. Initial concentrations of carbon monoxide and oxygen were maintained at the same stoichiometricvalues. Note that CO disappears markedly faster, even though the temperatureincreasewas relativelymodest. Again, the major species profiles suggest a pronounced induction time. Interestingly, the H2 concentrationseems to have peaked at approximately 2 X mol/cm3 at 4-s residence time. At longer residence times the H2 concentrationdecreases, indicating that hydrogen oxidation becomes faster than H2 formation at CO conversions greater than about 80%. These observations are completely consistent with the profiles in Figure 2; the faster rates at the higher temperature enable us to observe the higherconversion behavior of the H2 profile. The profiles in Figures 2 and 3 thus indicatean initial rise in H2concentration (net hydrogen formation) at low CO conversions, followed by a decrease (net hydrogen oxidation) at higher CO conversions.
Holgate and Tester
802 The Journal of Physical Chemistry, Vol. 98, No. 3, 1994
1.ox10.6
t
I
Carbon Dioxide
8.0~10-~
Ipr"
6 . 0 ~ 1 0 .-~ CI
E
3
c
1
Carbon Monoxide
2.0x10.6
4
Carbon Dioxide
+
0
E 4.0~10.~
i
._
'b'
4+
2 2 . 0 ~ 1 0-~ C
4-8-
s
+
'b'
Carbon Monoxide
4
5.0~10-
Hydrogen
00
1
0
2
3
4 5 6 Residence Time, s
7
8
9
10
Figure 4. Major species profiles for fuel-rich (6= 1.89) CO oxidation at 560 3 OC. [CO]o = (2.08 0.03) X 10-6 mol/cm3, [ O ~ =O(0.55 f 0.01) X 1 P mol/cm3, [H20] = (4.16 f 0.14) X l P 3 mol/cm3.
*
0 0
1
2
3
4 5 6 Residence Time, s
7
8
9
II 12x106
Figure 2. Major speciesprofilesfor stoichiometric (6= 1.04) CO oxidation at 550 2 OC. [CO]o = (1.04 0.02) X 10-6 mol/cm3, [02]0 = (0.50 f 0.01) X 10-6 mol/cm3, [H20] = (4.25 f 0.08) X l P 3 mol/cm3.
*
*
1.2x106
1 ' ' " I ' ' '
1.ox1 0 6
2
i
+
8.0~107
I " " l " " I ' " ' " ' ' " " ' ' I " ' ' I " ' '
Carbon Dioxide
Carbon Dioxide
6.0~10-~
1.ox10 6 0
E
2 0
E. 4 . 0 ~ 1 0 ~
8.0~107
c
-fi
.-
P
6.0~10~
**
CI
E
9
-e
4.0~10-7
*
e
._
E
2.0x107
s
Y)
._
p
Carbon Monoxide
20x10~
g'
0.0
1.ox1 0
0
8
I *
i
5 . 0 ~ 1 0 .: ~
2x1 0 8 1x108
0
1
2
3
4 5 6 Residence Time, s
7
8
9
10
Figure3. Major species profilesfor stoichiom&ic (6= 1.02) CO oxidation at 560 2 OC. [COIO= (1.02 0.02) X 10-6 mol/cm3, [ 0 2 ] 0 = (0.50
*
*
0.01) X l e mol/cm3. IH701 = (4.16
* 0.07)
X 10-3 mol/cm3.
Results for a fuel-rich ( 2 0 - 0 2 mixture at 560 'C are shown in Figure 4; initial concentrations were 2.08 X 10-6 and 0.53 X 10-6 mol/cm3 for CO and 0 2 , respectively, corresponding to a fuel equivalence ratio (4 = [C0]0/2[02]0) of 1.89. The concentration profiles for these fuel-rich conditions are markedly different from those for the stoichiometric conditions in Figure 3. First, the oxygen becomes completely depleted at a residence time of about 6 s; reaction at subsequent residence times is therefore oxygen-limited. However, note the high H2 concentrations, even prior to the oxygen depletion: H2 concentrations in the presence of 0 2 are a factor of 5 higher than for the comparable stoichiometric experiment (Figure 3), rising to an order of magnitude higher by the time 0 2 has been depleted. This
Oxygen
@
. ) .
e+
Carbon Monoxide
+-++
The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 803
Sub- and Supercritical Water. 1 1.000
0.0 -0.5
3 0.100 0 r,
4-P
.,*
-1 .o
-1.5
sx s
r_
F C
B
5: 0.010 I
-2.0 -2.5
: 0 560 "C,6 = 1.02
A 56OoC,6=1.69 0 560 "C,6 = 0.53 I
0.001
I
~ " " " " ' ~ ' ' " " " ' ~ ' ' ' " " ' " " " ' ' ' ' ' ~ " " ' ~ ~
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.6
0.9
1
CO Conversion
0
1
2
3
4
5
6
7
6
9
10
Residence Time, s
Figure 6. Variation in H2 yield with CO conversion. Initial conditions as in Figures 2-5.
Figure 7. Normalized CO profiles demonstrating effective induction times and dccay constants. Experimental conditions as in Figures 2-5. Lines are linear fits to data.
to CO oxidation, the short-residence-timedata in Figure 4 indicate that Hz formation had been occurring at a significant rate prior to 0 2 depletion. Once 0 2 has been depleted, however, H2 formation appears to cease completely, suggesting that it is facilitated in the presence of oxygen. Finally, a set of experiments was conducted at 560 OC for fuel-lean conditions, with nominally the same initial concentration of 1 X 1od mol/cm3 for both CO and 0 2 , or a fuel equivalence ratio of about 0.5. The results are shown in Figure 5. Under these conditions, CO is oxidized virtually to completion within about 8 s. The H2 concentrationdecreases steadily for all residence times, indicating its formation occurred within the first 3 s, and there is net oxidation of hydrogen for longer residence times. The extremelylow concentrations of H2 present at the longer residence times (-2 X 10-9 mol/cm3) are over 2 orders of magnitude lower than the H2 concentrations under fuel-rich concentrations. The dependence of hydrogen concentration on fuel equivalence ratio is very strong; fuel-rich conditions favor H2 formation to a much greater extent than fuel-lean conditions. Observed H2 concentrations thus decrease significantly with increasing 0 2 concentration, although oxygen-free conditions tend to dramatically decrease the rate of Hz formation. A similar effect of fuel equivalence ratio on hydrogen formation was seen in a gas-phase study of formaldehyde oxidation,14in which low fuel equivalence ratios suppressed hydrogen formation. Figure 6 shows the evolution of H2 yield with CO conversion, for the conditions of Figures 2-5. For stoichiometric conditions, the H2 yield decreases steadily for CO conversions greater than about 15%, indicating that all formation of H2 occurs at low CO conversions; at higher conversions, the yield decreases as COz formationincreases. For the fuel-rich condition,HZyield increases steadily up to the point of oxygen depletion. At the fuel-lean condition, the H2 yield decreases sharply (by an order of magnitude) as the last 20% of the CO is oxidized, demonstrating that Hz oxidation dominates as consumption of CO nears completion. The strong dependence of H2 formation on equivalence ratio, combined with the apparently very slow reaction in the absence of 0 2 , raises the possibility that previously measured rates of the water-gas-shift pathwaylOJ1did not truly reflect the rate of the reaction in an oxygen-free environment. For example, all watergas-shift data obtained by Holgate et al.11 exhibited lower H2 yields than CO2 yields, indicating that oxygen was present in the reactor in all of the experiments. Thus the "water-gas-shift" results may be more accurately characterized as an "oxidative pyrolysis," that is, oxidation at very high fuel equivalenceratios.14
Experimental limitations prevented the attainment of a strictly oxygen-free environment in the reactor for the earlier water-gas shift experiments.loJ1 Future experiments under fuel-rich conditions, at higher temperatures and/or longer residence times, could provide a direct measurement of the water-gas-shift rate by allowing observationof the rate of reaction of CO under oxygendepleted conditions (e.g., the long-residence-time behavior in Figure 4). The data of Figures 2-5 have been recast in Figure 7 in the form of CO profiles normalized by the initial concentrations; the normalized profiles are plotted logarithmically with straight-line fits to the data. There are four distinct profiles in Figure 7; thus the CO decay constants,k', defined by the slopes of the logarithmic profiles (k' = -d In [CO]/dt), are different for each of the sets of data. The linear curve fits, when extrapolated back to the initial concentration, indicate an apparent induction time of approximately 2 s in all the profiles. Figure 7 thus permits the determination of decay constants and induction times for the CO profiles. Although the fuel-rich profile is shown without a curve fit because the data deviate from a smooth decay when oxygen becomes depleted, an approximate decay constant and induction time can be derived for the fuel-rich conditions using only the first four data points. Table 1 summarizes the kinetic decay constants and apparent induction times for the four data sets, as derived from both the CO and 0 2 profiles; quoted errors are 1 standard deviation. Analysis of kineticdata using k'eliminates the confounding effect of induction time by recognizing that measurable reactant depletion does not occur during the entire reactor residence time. The experimental apparatus did not allow direct measurement of induction-period chemistry, and induction times can only be inferred. These apparent induction times are probably not true kinetic induction times, owing to the sensitivity of induction chemistry to effectssuch as surface reactions and radical formation during feed preheating. Note that only stoichiometric conditions in Table 1 give the same decay constants and induction times for both the CO and the 0 2 profiles; for off-stoichiometricconditions,the two profiles yield different values. Table 1 shows that the CO decay constant more than doubles for stoichiometric conditions when the temperature is raised from 550 to 560 OC, reflecting a strong temperature dependence. For these two conditions, the activation energy for the CO decay constant is approximately 488 kJ/mol, which is much higher than the activation energy regressed for CO oxidation in eq 3, 134 & 32 kJ/mol (at a 95% confidence level). On the other hand, the induction time in Table 1 remains
804
The Journal of Physical Chemistry, Vol. 98, No. 3, 1994
Holgate and Tester
TABLE 1: Apparent Induction Times and Decay Constants for Carbon Monoxide Oxidation at 246 bar
initial conditions, 10-6 mol/cm3 550 f 2 "C [CO]o = 1.04 f 0.02 [ 0 2 ] 0 = 0.50 f 0.01 560 f 2 "C [COIO = 1.02 f 0.02 [ 0 2 ] 0 = 0.50 f 0.01 560 f 3 OC [CO]o = 2.08 f 0.03 [02]0 = 0.55 f 0.01 560 f 2 OC [CO]o = 1.03 0.04 [02]0 0.97 f 0.04
*
k', s-] (CO)
k',
0.17 f 0.01
0.17 f 0.01
2.0 f 0.3
1.9 f 0.3
0.40 f 0.03
0.42 f 0.03
2.1 f 0.3
2.3 f 0.3
0.21 f 0.01
0.86 f 0.03
1.3 f 0.1
2.2 f 0.1
0.71 f 0.05
0.13 f 0.03
1.9 f 0.3
0.3 f 0.4
essentially constant (within estimation error) at approximately 2 s as temperature is raised from 550 to 560 O C . Accurate estimation of the decay constant and induction time for the fuelrich profile at 560 O C is difficult because oxygen becomes depleted; however, the decay constant under fuel-rich conditions clearly decreases relative to that under stoichiometric conditions at the same temperature. The fuel-rich induction time may be somewhat shorter but remains roughly 2 s. The fuel-lean profile at 560 O C exhibits a decay constant significantly higher than the corresponding stoichiometric profile; the three profiles at 560 O C thus suggest a dependenceon oxygen of CO disappearance, consistent with the global rate expression (eq 3). The fuel-lean induction time is also about 2 s, so that the induction time is independent of both fuelequivalence ratioand temperature for theseconditions, suggesting that the induction period may be influenced by effects other than simple homogeneous kinetics. A dependence of CO disappearance on oxygen is consistent with earlier, gas-phase, global rate expressions,"J2 but is in constrast to the more recent gas-phase results at 1030 K (757 "C) of Yetter et al.,I5 who observed an independence of oxygen of CO disappearance. Comparison of the values in Table 1 for CO oxidation with the corresponding values for H2 oxidation9J2reveals several interesting trends. First, for identical conditions of temperature (550 "C) and stoichiometric concentrations, the decay constant for CO (0.17 s-I) is less than half the decay constant for H2 (0.44 s-l). The ratio of these two decay constants is very close to the ratio of the rate constants of the primary oxidizing elementary reactions, i.e.
"e)
~CO+OH-CO~+H(~~~
~H,+OH-H,O+H
(550 " C )
= 0.45 (4)
where the rate constants for the CO and H2 oxidizing reactions have been taken from pressure-dependent calculationsI2 and Michael and Sutherland,16 respectively. Under the same conditions at 550 OC, then, hydrogen oxidation in supercritical water proceeds more rapidly than carbon monoxide oxidation. At 560 OC, the decay constant for stoichiometric CO oxidation (0.40 s-l) is approximately the same as that for H2 oxidation at 550 OC (a decay constant for H2 oxidation at 560 O C was not measured). This observation is consistent with the global kinetic behavior predicted by eqs 1 and 3. On the other hand, the observed induction times of both CO oxidation and H2 oxidation at 550 O C are approximately 2 s. The apparent induction time is thus roughly independent of the particular fuel for these conditions. An analysis12of the oxygen dependence of the concentration decays in Figure 7 revealed an approximate global order of carbon monoxide oxidation with respect to oxygen of 0.5. This derived order is in good agreement with theorder obtained in the regression of earlier CO oxidation data (eq 3), 0.34 f 0.24. The two sets of data are thus consistent with regard to the global oxygen dependence.
s-'
(02)
Ti&,
s (CO)
rind, s ( 0 2 )
Fluid Density, g/cm3 0.01
0.6
I
0.0'2 0.03 0.04 0.05 0.06 0.070.080.090.10 I
I
I
I
I
I
I
I
I
J
First-Order Rate Constant, IC
0 Kinetic Decay Constant, k'
- c
-I
0.4
0
I
m
5
5-- O3 t
2
0.2
0.1
0 0
50
100
150 200 250 Operating Pressure, bar
300
350
Figure 8. Effects of operating pressure (fluid density) on apparent firstorder rate constant, k*,and kinetic decay constant, k', for H2 oxidation at 550 OC. Experimentalconditions: 550 f 2 OC, [Hz]o = (1.06 i 0.02) X 10-6 mol/cm', [ 0 2 ] 0 = (0.53 f 0.01) X 10-6 mol/cm3.
Effects of Water Density on Kinetics
The potential advantages of operation of the SCWO process at lower, even subcritical, pressures have recently been outlined by Hang" and include reduced construction costs, decreased corrosion, and more favorable phase behavior of salts. The effect of reduced operating pressure on the oxidation kinetics, however, is not well-known. Furthermore, a systematic variation of the fluid density or water concentration, with all other conditions (reactant concentrations, temperature) held constant, can help elucidate the role of water in the oxidation mechanism. Hydrogen Oxidation. Subsequent to the experiments described by Holgateand Tester,9a series of hydrogen oxidation experiments was conducted in which the operating pressure (and hence the water density) was varied from approximately 120 to 260 bar, at a constant nominal temperature of 550 O C and nominal stoichiometric reactant concentrations: [H& = 1 X 1od mol/ cm3, [0210 = 0.5 X 1V mol/cm3. These conditions were chosen to allow observation of significant changes in H2 conversion (either increasing or decreasing) as operating pressure was varied. Maximum reactant concentrations were constrained by saturator solubilities, and the chosen concentrations were the highest attainable for an operating pressure of 100 bar. The maximum operating pressure, 263 bar, was set by the ratings of pressurerelief equipment (rupture disks) in the experimental system. Results of the variable-pressure experiments are shown in Figure 8. Data were obtained for pressures from 118 to 263 bar, with observed hydrogen conversions ranging from 9 to 87%. An additional experiment at 97.5 bar and a 2.3-s residence time gave no observable conversion of H2. Mass-balance closures for these
The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 805
Sub- and Supercritical Water. 1 experimentswere at worst within 1 1%and most often within 3%. The examined range of pressures spans the critical region, from well above the critical pressure (221 bar) to well below, and corresponds to water densities of 0.033 to 0.083 g/cm3 (reduced densities, p / p c , of 0.10-0.26), or nearly a factor of 3 variation in density. The density of water varies smoothly with pressure at 550 OC; at pressures below 221 bar, the reaction medium is essentially a high-pressure gas phase. Figure 8 clearly shows that the apparent first-order rate constant, k*, increases significantly with increasing operating pressure (water density); at 263 bar, k* is almost an order of magnitude higher than at 118 bar. The large errors bars at the lower pressures result from the higher proportional uncertainty in the lower measured hydrogen conversion. The dramatic increase in k* with pressure in Figure 8 is somewhat overemphasized by the hidden effect of varying residence time. All other things being equal, k* increases with increasing residence time owing to the presence of an induction time in the oxidation reaction. Since k* in general increases with increasing residence time, and longer residence times tend to fall at higher pressures in Figure 8, the pressure dependence of k* is somewhat exaggerated. The limitations of using k* to describe kinetic behavior have been discussed earlier;9J2however, when only a single measurement (at one residence time) is available for a set of conditions, k* is the only measurable kinetic quantity. Figure 8 eliminates residence time as a confounding variable by showing the decay constant K as a function of residence time for the various operating pressures studied. A value of k’could be derived only for the five pressures at which data were available for multiple residence times. Although there is considerable uncertainty in thevalues of k’, Figure 8 suggests that the pressure dependence of k’ is similar to that of k*, such that the disappearance of HZoccurs significantly more quickly at higher pressures. Over the range of pressures examined, k’increases by about a factor of 5 . Our observation of increasing oxidation rate with increasing pressurecan be examined in the context of the explosion behavior for hydrogen-oxygen mixtures. An explosion boundary for stoichiometric H2-02 mixtures is an S-shaped curve in (T,P) space delineating the boundary between the slow reaction of hydrogen with oxygen (by a chain-propagatingmechanism) and theexplosively fast reaction (by a chain-branchingmechanism).ls For pressures and temperatures to the left (lower-temperature side) of the curve, hydrogen and oxygen react slowly; to the right of the curve, the reaction rate becomes very fast. The explosion boundary can be divided into three branches or limits.lS The first limit correspondsto the quenching of chain-carryingspecies by vessel walls. At pressures above the first limit (>-0.01 bar), homogeneous reactions become important and homogeneous chain-branching steps overcome the heterogeneous chain termination at the walls. At pressures well above the first limit, an upper explosion limit (the second limit) is encountered. In the explosive region between the first and second limits, chain branching occurs via the reaction
H
+ 0, + O H + 0
(5)
At and above the second limit, the alternate reaction
H
+ 0,+ M
+
HO,
+M
(6)
which depends on pressure via the third-body concentration [MI, competessuccessfully witheq5. Since theHOzradicalisrelatively unreactive at temperatures and pressures just above the second limit, eq 6 moderates the overall reaction rate and prevents explosive chain-branching from occurring.lS Increasing the pressure above the second limit results in steadily increasingreaction rates, sincethe rate of eq 6 continues to increase with pressure. Furthermore, as eq 6 becomes faster, reactions of H02 become important, including
HO,
+ HO,
HO, + H,
-
H,O, + 0,
-.
+H
-
H,O,
+ OH
+
+
H,O,
(7)
At high water concentrations, H02 may also react via
HO,
+H20
(9) By themselves, eqs 7-9 are either chain-terminating (eq 7) or chain-propagating (eqs 8 and 9). However, Hz02 formed in eqs 7-9 can dissociate in a pressure-dependent step to form OH radicals:
+
H20, M +OH OH M (10) As eq 10 becomes fast at higher pressures, the sequences of eqs 6-8-10 and 6-9-10 become chain-branching and result in rapid production of OH radicals; eventually (above the third limit) this sequence can become explosive.ls The “extended” second limit has recently been studied comp u t a t i ~ n a l l yand ~ ~ ~experimentally.2’ ~~ This limit appears to represent the conditions under which the branching by eq 5 is replaced by propagation (by eq 6), with a corresponding decrease in reaction rate. At temperatures and pressures above the extended second limit, eq 6 can initiate the branching sequences of eqs 8 and 9 with eq 10. However, the branching nature of eqs 6-8-10 and 6-9-10 is largely overwhelmed by the propagating nature of eqs 6-7-10; hence branching is less extensive than by eq 5 alone. The reaction rate thus increases with pressure both above and below the extended second limit, but relatively more slowly above the limit than below. The pressures and temperatures of experiments in this laboratory (400-600 O C , 118-263 bar) suggest that our operating regimelies between the extended second and third limits. In no case was an explosively fast reaction observed, however; instead, the oxidation reaction occurred on time scales of seconds, and increased smoothly with increasing pressure. In reality, the third limit is most likely not a well-defined boundary between slow and fast (explosive) reaction. The computational studies of Dougherty and RabitzZ2and Maas and WarnatzZ3suggest that the third limit is an explosion boundary only for pure or concentrated H2-02 mixtures or for adiabatic conditions, where the exothermicityof the reaction serves to heat the reaction mixture to temperatures at which explosion (rapid chain branching) is unavoidable. In the presence of a large quantity of diluent (like supercritical water) and/or under isothermal conditions (the operating regime in this study), the reaction rate does not become explosively fast but rather increases steadily with increasing p r e ~ s u r e . ~Hence ~ ~ * ~the third limit is a thermal limit rather than a kinetic limit; as long as concentrated, adiabatic conditions are avoided, the third limit is merely a region of steady reaction. The present experimental observations are thus consistent with the chain-propagating mechanism of eqs 6, 7, and 10, corresponding to the pressure-moderated reaction between the extended second and third limits. Carbon Monoxide Oxidation. An additionalset of experiments was conducted to evaluate the effect of operating pressure or water density on the rate of carbon monoxide oxidation. The same approach was taken in these experiments as was used to study pressure (density) effects in hydrogen oxidation. That is, experiments were performed at a constant temperature, 570 O C , and constant,stoichiometricreactant concentrationsof nominally 1 X 10-6 mol/cm3 for carbon monoxide and 0.5 X 10-6 mol/cm3 for oxygen, such that the only effect of changing the operating pressure was a change in the concentration (density) of water in the reactor. As in the hydrogen experiments, these conditions were chosen to allow observation of significant changes in conversion with operating pressure. Furthermore, recognition of the complicatingeffect of residence time in the results for hydrogen oxidation at varying pressure led us to maintain a constant
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Figure 9. Effects of operating pressure (fluid density) on apparent firstorder rate constant, k*, and kinetic decay constant, k', for CO oxidation at 570 OC. Experimental conditions: 570 f 2 O C , [CO]o = (1.03 f 0.01) X 10-6 mol/cm3, [02]0 = (0.51 i 0.01) X 106 mol/cm3. Values of k* for two residence times (3.4, 4.1 s) are shown.
residence over the range of pressures investigated. At a fixed reaction temperature, for pressures ranging from 118 to 263 bar in one set of experiments, it was possible to maintain a constant residence time of 4.1 s. When possible, experiments were also conducted for each pressure at a residence time of 3.4 s. Results of the variable-pressure results are shown in Figure 9, where the apparent first-order rate constant, k*, is shown as a function of operating pressure (water density). Observed carbon monoxide conversions ranged from about 30% to 80%. Carbon and oxygen balances closed in all experiments within 6% and typically within 2%. Adatum point for 263 bar and 3.4-sresidence time was not obtainable owing to feed-pump flow limitations. Note that k* is consistently higher for the 4.1-s results than for the 3.44 results, the result of the induction time identified earlier. Figure 9 shows unambiguously that the rate of carbon monoxide oxidation increases uniformly (and almost linearly) with operating pressure or water density, from subcritical to supercritical pressures. Over the range of pressures studied, from 118 to 263 bar, the apparent first-order rate constant for CO oxidation increases by a factor of more than 3. The availability of data at two residence times at the same operating pressure permits the derivation of a decay constant k'at each pressure. Values of k' shown in Figure 9 range from 0.16 s-* at 118 bar to 0.66s-I at 246 bar, about a 4-fold increase in k'with increasing pressure. If the decay constant k'is assumed to depend on pressure (water concentration) in a power-law fashion, i.e. k' = ftqH,O]" where f' is the "water-free" decay constant, then the data in Figure 9, when regressed linearly as In k'vs In [H20], exhibit an order with respect to water of approximately 1.7. This water dependence is much stronger than the 0.5-order dependence observed in many gas-phase studies of moist carbon monoxide oxidation,2428 although those studies were conducted under conditions far from those of the present experiments. Figure 10 shows the conversion of CO and the H2 yield as functions of operating pressure for a constant residence time of 4.1 s. The CO conversion increases steadily with pressure. The ratio of H2 to C02 (the yield of hydrogen) remains constant at about 0.04 from 118 to 201 bar and increases slightly to about 0.07 at 263 bar. The increasein H2 yield at higher CO conversions is contrary to the isobaric results for stoichiometricCO oxidation,
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in which H2 yield decreased at high conversions (Figure 6). The results in Figure 10 suggest that increasing operating pressures (water densities) favor increased hydrogen formation. The strong dependence of the oxidation rate on water concentration seen here cannot be extrapolated to gas-phase conditions,just as the gas-phase 0.5-order dependencecannot be extrapolated to supercritical water conditions. Gas-phase studies of moist CO o x i d a t i ~ nat~ temperatures ~,~~ similar to the present investigation (570 "C) observed an oxidation rate of similar magnitude to the rates observed in the high-pressuresupercritical water phase. For the oxidation rates in the two environmentsto be similar, yet with rates in the two environments dependent on water concentration, there must exist a region, between the lowdensity gas phase and the high-density supercritical-water phase, where increasing water concentration decreases the oxidation rate. Clearly this region exists somewhere between 1 and 120 bar. The existenceof such a "negative water dependence" region is consistent with the theory of the extended second explosion limit for hydrogen oxidation, as described by Yetter et al.'9920In that concept, water enhances oxidation rates at low pressures by improving the production of OH radicals. At higher pressures or water concentrations, formation of more slowly reacting H02 radicals becomes favored, chain branching is reduced, and the reaction rate decreases. At still higher pressures, different chainbranching mechanisms (e.g., eqs 8 and 9 with eq 10) become important and the reaction rate again increases with increasing pressure (water concentration). The implications of the pressure (water-density) dependence of carbon monoxide oxidation for the commercialSCWO process are clear: operation at lower water concentrationsentails a penalty in terms of oxidation rate. However, the relationship between water concentration and operating pressure is less direct in the process than it is in these experiments, because water is a much less dominant component in the process stream. For a concentrated, high-heating-value waste with air as the oxidant, water may account for less than 30wt %of the reactor fluid. A decrease in operating pressure at these lower water contents will have a much less dramatic effect on the water concentration than if water were the dominant component, as in our experimental system. The strong decrease in oxidation rate with decreasing pressure seen in Figure 9 is thus likely an overestimate of the effect of decreasing operating pressure in the SCWO process. Results for carbon monoxide oxidation under practical process conditions (595 to 600 "C, 160-260 bar), as reported by Hong,17
The Journal of Physical Chemistry, Vol. 98, No. 3, I994 807
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showed a much less pronounced effect of the operating pressure on the oxidation rate. Operation of the SCWO process at reduced pressures appears to entail a kinetic penalty, but a relatively small one that may well be compensated by improvements in process operability.
Reactor Surface Effects The gas-phase oxidation of hydrogen has long been known to be profoundly affected by the nature and the extent of the interactions between the reacting species and the surface of the r e a c t i o n ~ e s s e l .Most ~ ~ ~frequently, ~ the (noncatalytic) effect of the reactor surface is to inhibit the oxidation reaction by acting as a site for termination of free radicals.I8 Surface inhibitory effects are usually most pronounced at low pressures (((1 bar), where molecular mean free paths are large and radical collisions with the wall are relatively frequent. At higher pressures, the homogeneous collisional frequency is higher, and homogeneous reactions increase in importance at the expense of any heterogeneous reactions. In the present experimental system, the nominal surface areato-volume ratio of the tubular reactor is rather high (253 cm2/ 10.82 cm3, 23.4 cm-I) owing to the small diameter of the reactor; thus heterogeneouscontributionsto theoverall reaction ratecannot be ruled out a priori. In previous studies in the present experimental system, using the packed-bed reactor, Webley et a1.33J4 found a pronounced catalytic effect of the reactor material (Inconel 625) on the oxidation of ammonia. Limited experiments in the packed reactor for methane, methanol, and carbon monoxide oxidation did not reveal a distinct effect of the additional surface on the observed oxidation rate, but those conclusions must be regarded as preliminary. The present experimental results for hydrogen and carbon monoxide oxidation can only be used for elementary reaction modeling purposes if heterogeneous contributionsare small or absent, or at least well defined. We therefore sought to perform a definitive set of experiments to identify the effect of the reactor surface on observed kinetics. Hydrogen Oxidation. A series of experiments was conducted in the packed reactor with the experimental conditions T = 550 f 2 OC, [H2]0 = (1.04 f 0.01) X 10-6 mol/cm3, [ 0 2 ] 0 = (0.55 f 0.01) X 1 W mol/cm3. The results are shown in Figure 11, where they are compared to experimental results for the same conditions in the tubular reactor, shown originally by Holgate and Tester.g The range of accessibleresidence times in the packed reactor is shifted to somewhat longer times because of the greater
void volume in the packed reactor (16.00 cm3,vs 11.1 1 cm3 for the tubular reactor). Figure 11 clearly shows that the added surface area in the packed reactor inhibits the oxidation reaction. The kinetic decay constant k'for the H2 profile in the packed reactor is 0.074 s-1, compared to the value of 0.44 s-l obtained in the open tubular r e a ~ t o r . The ~ added surface area thus decreases the rate of disappearance of H2 by a factor of about 6. Considering that the surface area-to-volume ratio in the packed reactor is 20.5 times that of the tubular reactor (480 vs 23.4 cm2/cm3),the reduction in rate is less than directly proportional to the increase in surface area. If the observed decay constant is assumed to vary linearly with the surfacearea-to-volume ratioin the reactor, extrapolation of the decay constant to the limit of zero surface area gives a value for k'of 0.46 s-l, which is very close to that observed in the tubular reactor and well within the experimental error and the estimation error for k'. This crude approximation implies that the role of the reactor surface is sufficiently small in the tubular reactor experiments that heterogeneous reaction effects can be neglected. The measured kinetics are therefore assumed to reflect the true homogeneous rate of hydrogen oxidation. The exponential fits to the experimental data in Figure 11 reveal an interesting trend in the tubular and packed reactor results. The extrapolated exponential curves for the packed reactor intersect the extrapolated curves for the tubular system at concentrations corresponding approximately to the feed concentrations. Similarly, both points of intersection occur at the same residence time (-2.0 s), which corresponds to the induction time observed in the tubular reactor. Taken together, these results suggest that the induction time in the packed reactor is almost identical to that in the tubular reactor. This behavior is unexpected, since the inhibitory effect of the additional surface would presumably tend to lengthen appreciably the chemical induction time. Instead, the experimental evidenceindicates that the heterogeneous reactions do not affect the kinetic behavior until the decay of hydrogen begins. This lag in heterogeneous influence is conceivable if the surface reactions are relatively slow. During the induction period, when radical concentrations are low and rising, the rate of heterogeneous termination may be small relative to homogeneous branching. When the radicals reach their maximum or steady-state levels, the heterogeneous rates may be sufficiently fast that they perturb (decrease) these ultimate radical concentrations. In this scenario, the induction period would be relatively unaffected by added surface area, yet the decay constant would be decreased by the reduced steadystate radical pool. The conclusion regarding the importance of surface reactions is strictly valid only for the conditions of the packed-reactor experimentsand may not necessarily be valid under all conditions. For example, gas-phase studies of H2 o x i d a t i ~ n ~ ~found * ~ ~that J$ surface reactions became important for temperatures below about 520-550 OC, as evidenced by a pronounced changein theactivation energy for the overall reaction. No change in activation energy was found in the present study, indicating that the role of surface reactions (or lack thereof) was most likely constant over the conditions of this study. Carbon Monoxide Oxidation. A limited series of experiments was conducted to evaluatethe potential influenceof reactor surface on observed kinetics. In these experiments,a stoichiometricCO0 2 mixture, with nominal initial concentrations of 1 X 1 W and 0.5 X 10-6 mol/cm3, respectively, was reacted at 560 OC in the packed reactor, which had a greater than 20-fold higher surfaceto-volume ratio than the open tubular reactor. Conditions were thus essentially identical to those used in Figure 3 in the tubular reactor, with the exception that longer residencetimes were studied owing to the larger volume of the packed reactor. Results of the experiments are shown in Figure 12, where the major species
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The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 1.2x10-6
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profiles from the packed reactor are compared to the profiles from the comparable tubular reactor experiments. Figure 12 indicates that theoxidation of CO, like the oxidation of Hz, is significantlyinhibited in the presenceof additional Inconel surface area. All four of the major species profiles are extended to longer times (the CO2 profiles have been omitted from Figure 12 for clarity). In particular, the hydrogen profile, which peaks slightly at 4 s and then decreases steadily, has not reached its peakconcentration for a residence time of over 10 s in the packed reactor. The magnitudes of the two hydrogen profiles are in good agreement, indicating that the formation of H2 is not preferentiallyinhibited (or catalyzed) in the presence of additional reactor surface. Figure 12 shows exponential fits to the CO and 0 2 profiles for the two reactors. The kinetic decay contant k'for the CO profile in the packed reactor, 0.057 s-l, is markedly smaller than the decay constant in the tubular reactor, 0.40 s-I. However, if the observed decay constant is assumed to be linearly proportional to the surface area-to-volume ratio in the reactor, extrapolation of the decay constant to the limit of zero reactor surface area gives a value for k'of 0.42 s-l, which is very similar to the tubularreactor value. Using the logic presented for hydrogen oxidation, the similarity of the decay constants for the tubular reactor and the zero-surface-area case implies that the tubular reactor results, at least at 560 OC, may be treated as reflective of homogeneous reaction rates. This conclusion, however, is strictly true only for the higher temperatures examined, and heterogeneous reactions may increase in importance at lower temperatures. While there was no evidence of a corresponding change in activation energy for H2 oxidation, such a change cannot be completely ruled out for CO oxidation.l2 The importance of surface reactions in the low-temperature results for CO oxidation thus has not been conclusively eliminated, and further studies of heterogeneous effects under those conditions may be necessary to resolve the issue. More quantitative and conclusive information about the role of surface effectscould be obtained by performing experiments in a series of tubular reactors with varying diameters. Finally, note that the intersection of the decay curves for the tubular and packed reactors in Figure 13 occurs almost exactly
Studies of carbon monoxide oxidation in supercritical water showed that the reaction, like hydrogen oxidation, possesses an induction time. The induction time for carbon monoxide oxidation was the same or slightly shorter than that for hydrogen oxidation, about 2 s, and was independent of fuel equivalence ratio at 560 OC. Hydrogen formation during carbon monoxide oxidation is facilitated by the presence of oxygen and is very slow in the absence of oxygen. Hydrogen formation is strongly dependent on the fuel equivalence ratio, with fuel-rich conditions favoring its formation. The oxidation of hydrogen and carbon monoxide, at 550 and 570 OC, respectively, is strongly pressure (water-density) dependent over the range 118-263 bar, with higher pressures favoring higher oxidation rates. The effective order with respect to water for stoichiometriccarbon monoxide oxidation at 570 OC was 1.7. This dependence suggests that a slight kinetic penalty is incurred for operation of the supercritical water oxidation process at lower pressures or lower water concentrations. Higher water densities favor increased H2 formation, and the formation of H2 is expected to be less important under supercritical water oxidationprocess conditionswhere water concentrations arelower. Limited studies of hydrogen and carbon monoxide oxidation in a packed reactor showed that the additional Inconel 625 surface area tends to inhibit oxidation, most likely through termination of free radicals. Experimental evidence strongly suggests that the hydrogen and carbon monoxide oxidation reactions have a negligibly small heterogeneouscontributionin the tubular reactor. Data obtained in the tubular reactor at higher temperatures can therefore be treated as purely homogeneous, and elementary reaction models for these data need not incorporate surface reactions. Future experiments should, however, attempt to verify the unimportance of surface effects using variable-diameter reactors. Acknowledgment. The authors gratefully acknowledge the financial support of NASA/Johnson Space Center, the Army Research Office, and the Environmental Protection Agency. Invaluable experimental assistance was provided by Victor Antaramian, Jay Corbett, and Jerry Meyer. Profs. Jack Howard and Adel Sarofim of MIT and Drs. K. C. Swallow and Glenn Hong of MODAR, Inc. contributed thoughtful comments and suggestions. Experimental data presented herein are tabulated in numerical form in ref 12. The authors also very much appreciate the extensive and constructive commentsof one of the reviewers. References and Notes (1) Modell, M. In Standard Handbook of Hazardous Waste Treatment andDisposal; Freeman, H. M., Ed.; McGraw-Hill: New York, 1989;p 8.1 53. (2) Swallow, K. C.; Killilea, W. R.;Malinowski,K. C.;Staszak, C. Waste Management 1989, 9, 19. (3) Thomason, T. B.; Hong, G. T.; Swallow, K.C.; Killilea, W. R. In Innovative Hazardous Waste Treatment Technology Series. Thermal Processes, Freeman,H. M., Ed.;Technomichblishing: Lancaster,PA, 1990; Vol. 1, p 31. (4) Tester, J. W.; Holgate, H. R.;Armellini, F. J.; Webley,P. A.; Killilea, W. R.;Hong, G. T.; Barner, H. E. In Emerging Technologies in Hazardous WasteManagementIII;Tedder, D. W.,Pohland, F. G.,Eds.;ACSSymposium Series 518; American Chemical Society: Washington, DC, 1993; p 35. ( 5 ) Franck, E. U. Pure Appl. Chem. 1970, 24, 13. (6) Connolly, J. F. J. Chem. Eng. Data 1966, 2 2 , 13. (7) Martynova, 0. I. In High Temperature, High Pressure Electrochemistry in Aqueous Solutiom; Jones, D. de G., Staehle, R. W., Chairmen; National Association of Corrosion Engineers: Houston, TX, 1976; p 131. (8) Thomason, T. B.; Modell, M. Has. Waste 1984, 2 , 453. (9) Holgate, H. R.; Tester, J. W. Combust. Sci. Technol. 1993,88,369.
Sub- and Supercritical Water. 1 (10) Helling, R. K.;Tester, J. W. Energy Fuels 1987, 1, 417. (1 1) Holgate, H. R.; Webley, P. A.; Tester, J. W.; Helling, R. K.Energy Fuels 1992, 6, 586. (12) Holgate, H.R. Oxidation Chemistry and Kinetics in Supercritical Water: Hydrogen, Carbon Monoxide, and Glucose. Ph.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology,Cambridge, MA, 1993. (13) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R. Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; J . Phys. Chem. Re$ Dara 1985, 14, Suppl. No. 1. (14) Hochgreb,S.;Yetter,R. A.;Dryer, F. L.Proc.Symp. (Inr.)Combusr., 23rd 1990, 171. (15) Yetter, R. A.; Dryer, F. L.; Rabitz, H. Combust. Sci. Technol. 1991, 79, 129. (16) Michael, J. V.; Sutherland, J. W. J. Phys. Chem. 1988, 92, 3853. (17) Hong, G. T. Process for Oxidation of Materials in Water at Supercritical Temperatures and Subcritical Pressures. United States Patent 5,106,513, Apr 1992. (18) Lewis, B.; von Elbe, G. Combustion, Flames, and Deronarions of Gases, 3rd ed.; Academic Press, Inc.: Orlando, FL, 1987. (19) Yetter, R. A.; Dryer, F. L.;Golden, D. M. Pressure Effects on the Kinetics of High Speed Chemically Reacting Flows. Contribution to A Workshop on High Speed Combustion, Institute for Computer Applications in Science and Engineering, Newport News, VA, Oct 1989. (20) Yetter, R. A.; Rabitz, H.; Hedges, R. M. Inr. J. Chem. Kiner. 1991, 23, 251. (21) Vermeersch, M. L. A Variable Pressure Flow Reactor for Chemical Kinetic Studies: Hydrogen, Methane and Butane Oxidation at 1 to 10
The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 809 Atmospheres and 880 to 1,040 K. Ph.D. Thesis, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 1991. (22) Dougherty, E. P.; Rabitz, H. J. Chem. Phys. 1980, 72, 6571. (23) Maas, U.; Warnatz, J. Combust. Flame 1988, 74, 5 3 . (24) Kozlov, G. I. Proc. Symp. (Inr.) Combust., 7rh 1958, 142. (25) Hottel, H. C.; Williams, G. C.; Nerheim, N. M.; Schneider, G. R. Proc. Symp. (Int.) Combust., 10th 1965, 111. (26) Dryer, F. L.;Glassman, I. h o c . Symp. (Inr.) Combust., 14rh 1973, 987. (27) Howard, J. B.; Williams, G. C.; Fine, D. H. Proc. Symp. (Int.) Combusr., 14th 1973, 975. (28) Lyon, R. K.;Hardy, J. E.; Von Holt, W. Combusr. Flame 1985,61, 79. (29) Khitrin, L. N.; Solovyeva, L. S.Proc. Symp. (Inr.) Combust., 7th 1958,532. (30) von Elbe, G.; Lewis, B. J. Am. Chem. SOC.1937,59, 656. (31) von Elbe, G.; Lewis, B. J. Chem. Phys. 1942, 10, 366. (32) Kassel, L. S.Proc. Symp. (Int.) Combusr., 2nd 1937, 175. (33) Webley, P. A.; Holgate, H. R.; Stevenson, D. M.; Tester, J. W. SAE TechnicalPaper Series 901333,20th IntersocietyConferenceon Environmental Systems, Williamsburg, VA, July 1990. (34) Webley, P. A.; Tester, J. W.; Holgate, H. R. Ind. Eng. Chem. Res. 1991,30, 1745. (35) Gibson, C. H.; Hinshelwd, C. N. Proc. Royal Soc. London, A 1928,119, 591.
