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Kinetics of the oxidation of diesel soot
FuelVol. 76, No. 12, pp. 1129-1136,1997 © 1997ElsevierScienceLtd. All rightsreserved Printed in Great Britain 0016-2361/97$17.00+0.00
Plh S0016-2361(97)00119-1
ELSEVIER
Kinetics of the oxidation of diesel soot John P. A. Neeft, T. Xander Nijhuis, Erik Smakman, Michiel Makkee and Jacob A. Moulijn Industrial Catalysis, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands (Received 30 August 1996) The kinetics of the uncatalysed oxidation of a flame soot and diesel soot were studied, Oxidation of the flame soot could be described by an nth-order model, with an order in carbon of 0.7. The order in molecular oxygen concentration was found to be 1 for the flame soot and slightly lower than 1 for the diesel soot. This order in oxygen concentration was also found to be a function of conversion. Water caused a significant increase in oxidation rate of the flame soot, which was accompanied by an increase in reaction order in carbon and a much higher CO2/CO ratio, whereas the activation energy did not change. The oxidation rate of the diesel soot was not significantly influenced by the addition of water. Experimental results were more reproducible for the oxidation of the flame soot than for the oxidation of diesel soot, and the flame soot appeared to be a good model for diesel soot in oxidation studies. Therefore it is recommended to use a model soot in (kinetic) studies of soot oxidation. © 1997 Elsevier Science Ltd.
(Keywords: soot; diesel emissions; oxidation kinetics)
The emission of particulates from diesel engines has led to serious concern about possible health effects. Emission standards for particulates from diesel engines have been introduced, and much research towards strategies for reduction of such emissions has been performed over the last two decades 1. Oxidation of the soot plus hydrocarbon fraction of the particulates is one of the solutions proposed for the reduction of diesel particulate emissions. Although much research has been performed on noncatalytic and catalytic soot oxidation, the detailed kinetics of soot oxidation have hardly_ been studied. Only the studies of Ahlstr6m and Odenbrand,2 D u e t al. 34 • , Gilot et al. 5 and Otto et al. 6 provide some relevant data. The oxidation of carbons and graphite has been studied to a much greater extent 7- ~9. It was concluded 2° that more detailed insight in the kinetics and mechanism of soot oxidation might help in developing more active or selective soot oxidation catalysts. This paper reports on the kinetics of non-catalytic soot oxidation; a second paper will report on the mechanism (the elementary reaction steps) of non-catalytic oxidation of soot and other carbonaceous materials. Results of a study of the kinetics and mechanism of the catalysed oxidation of soot will be published later. Kinetic models that have often been used to describe the reaction rates of carbonaceous materials have the general form: r = N t . k ( T ) f ( P 0 2 ,pH20 .... )
(1)
where r is the reaction rate, Nt is the total number of active sites, k(T) is a temperature-dependent reaction rate constant, and J~oz,PH20,.-.) is a function which describes the
dependence of the reaction rate on the partial pressures of the various reactants and gas-phase components. The total number of active sites N t is often described by: N t = X.Sa
(2)
where X is the surface concentration of active sites and Sa the specific surface area. The proportionality between Nt (and thus reaction rate) and specific surface area S, has been discussed extensively 7-1°, and it is clear that this picture of direct proportionality is too simple. A linear proportionality might hold for the active surface area (ASA), or at least for part of this ASA in the form of the occupied or unoccupied fraction 7'8"1°. However, as long as ASA cannot be properly measured or predicted, eqn (2) is most convenient for deriving kinetic models. As it is generally accepted that the specific surface area S, is a function of the conversion ~ (the fraction of carbon that is oxidized), kinetic models describe the dependence of Nt as a function of conversion. A simple approach is to use an nth order of (l-G): Sa ---~Sa,0.( 1 _ ~)n~
(3)
where Sa,o is the initial surface area (at ~ = 0) and n~ is the reaction order in carbon. With increasing conversion this model predicts a decrease in Nt and therefore in reaction rate. However, for highly porous carbons such as soots and activated carbons, Sa can actually increase as a function of conversion, due to pore growth and opening of occluded pore space. Many models have been proposed to account for these phenomena. The model of Bhatia and Perlmutter 21, for instance, is based on the growth of pores with random pore size distribution,
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
and yields the following expression: Sa = Sa,0.(1 -- ~).V/1 - ¢ In(1 - ~)
(4)
where ¢ is a structural factor that describes the initial pore structure. For ¢ > 2, the model predicts that the total surface area initially increases and goes through a maximum at a conversion ~ between 0 and 0.393, depending on the value of ¢. The temperature dependence of the reaction rate is usually described by the Arrhenius equation:
k(T) = k0-exp( - Ea/RT)
(5)
where T is the absolute temperature, k0 the pre-exponential factor, R the molar gas constant and Ea the activation energy. Finally, the function that describes the influence of the partial pressures of the gas-phase components on the reaction rate is usually limited to the influence of the oxygen partial pressure, described by an nth order expression: f(Po2,PH20 .... ) ----p o2n°2
(6)
where Po2 is the partial pressure of oxygen and no2 is the order in oxygen partial pressure. This leads to the following two equations for the observed reaction rate: r = c.(1 - ~)"~.exp( - Ea/RT).p~~
(7)
for the nth-order model (with the shrinking-core model as a specific case, N~ = 0.67), and r = c.(1 - ~).X/1 - ¢ ln(1 - ~).exp( - Ea/RT).p~2
(8)
for the pore growth model of Bhatia and Perlmutter; c is a constant and is equal to X'Sa.o'ko. At a constant oxygen partial pressure and conversion, eqn (7) can be rewritten as: r = k'0.exp( - Ea/RT)
(9)
with ko' representing an overall pre-exponential factor: k0' = c.(1 ~)n~ .p~)~2. The aim of this kinetic study is to provide insight into the parameters that influence the uncatalysed oxidation of soot. Temperature and the concentrations of oxygen and water in the feed gas are the parameters of interest. In addition, CO2/ CO ratios are determined, which can provide information on the mechanism of soot oxidation. -
soot are presented elsewhere 2°. The soots were milled before use; this milling step did not affect the reaction rate, but it facilitated sample preparation. Milled Printex-U or diesel soot was mixed with silicon carbide in a weight ratio of 1/10 so as to reduce the pressure drop over the sample bed as well as to limit temperature rises in the sample due to the exothermic oxidation of soot. In this way, temperature rises registered by the thermocouple inside the sample bed amounted to < 2 K and were observed only in the first hour of the experiment. Experiments were performed under isothermal conditions. The sample of typically 20 mg soot was heated to the reaction temperature under inert (At) gas flow. At time zero, the gas flow was switched to an O2-Ar mixture. A flow rate of 500 mL min -~ (s.t.p.) was used in each reactor. For the longest experiments a lower flow rate (200 or 100 mL min -1) was chosen. Experiments lasted for typically 4 to 100 h. Near the end of each experiment the temperature of the reactor tubes was increased at a rate of 1 or 2 K min -~ so as to oxidise the remaining soot. Reaction rates were calculated from the total gas flow rate and the CO and CO2 concentrations as measured by a nondispersive infrared detector. Reaction rates are expressed in (p.g C)(gCinitial)-ls -1 throughout this paper. The carbon mass balance was obtained by numerical integration of the reaction rates in (/~g C)s -1 and was always in the range 90120% of the amount of soot placed in the reactor tubes. A more accurate mass balance was not aimed at. The reaction rates were divided by the total quantity of carbon measured by the NDIR detector as CO and CO2. The reaction rates expressed in (#g C)(g Cinitial)-~s-~ were therefore essentially unaffected by a small error in the mass balance. RESULTS
Reaction order in carbon, and influence of water on reaction rate and order in carbon Typical results of the oxidation of diesel soot and Printex-U are shown in Figure I. The curve of reaction rate versus time for Printex-U shows an exponential-like behaviour; that for diesel soot shows a plateau in the conversion range 0.25-0.5. This plateau is visible in all combustion curves of diesel soot, though often less pronounced than in Figure 1, e.g. as can be seen in Figure 3. In Figures 2-5, a number of similar curves are plotted as a function of carbon conversion, in both the absence (Figures 2 and 3) and presence of water (Figures 4
EXPERIMENTAL Experiments were performed with the six-flow reactor equipment described in detail elsewhere 2°. Five experiments could be performed simultaneously; the sixth reactor was used as a blank to correct for background CO and CO2 from the technical-grade argon, which contained typically 10-20 ppmv CO2 and a few ppmv CO. The temperature within each reactor was recorded by a thermocouple, which was placed in the soot bed. It was verified that this thermocouple had no effect on the soot oxidation rate. The temperature could be controlled with an accuracy better than 1 K, the reproducibility between the different reactors being slightly less accurate (1-2 K). Printex-U, a flame soot obtained from Degussa AG, was used as a model for diesel soot. A number of experiments were performed with diesel soot from a single-cylinder Yanmar diesel engine. This soot was collected at an engine load of 3 kW. Properties of both Printex-U and the diesel
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Fuel 1997 Volume 76 Number 12
Reaction rate (~g giaitia1-1 S"t) 0.30
0.20 0. i0 0.00 0
6000
12000 18000 Reaction time (s)
Figure 1 Typical results for Printex-U ( ) and diesel soot ( - - - ) combustion in 10 vol.% 02 in Ar (794 K, 500 mL min -L s.t.p., 20 mg sample)
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et
Reaction rate (tag ginitial "1 S "1) 250
Reaction rate (~tg ginitia1-1 S-l)
"° I \
\ 794 K
200
~\ "X.. 778K f. \, \ . . 774 K 150 •.',,. ~'-\ 768 K ~ k ~ ' ' " " ' " ' - "'X.. \ 758 K 100 \,.x,.......~ .... " - . . " \ 738 K -- ....
50
.
I
250 f
........ _--.,... ",%'..,,
772 K
\7,7
'"'.'.'~-.~'~ ~
150 l" lOO
"----... ,..-.. ,,.
-
al.
f "'..'."
......
--'2-:-::::~
50
778K
~..?-~."~. ~
774K 768 K
0
0.0
0.5 1.0 Conversion (-)
Figure 2 Oxidation rate of Printex-U versus conversion as a function of temperature (10 vol.% 02 in Ar)
100
150
\ \ "', 768 K ~ "-. "-., 758K ~ k "'" ...... "'-':":"~ 738 K
100
'~
"%N.~.
"~..
787 K 779 K
" ?'"-. 729K
50
50 .......
0.0
787 K 777 K ",~ 768 K
",,~
',, 787 K \ ',. 777 K \ ~
Figure 4 Influence of water on oxidation rate of Printex-U as a function of temperature. - - - , 10vol.% oxygen in Ar; , 10 vol.% oxygen + 10 vol.% water in Ar
200
', 794 K
150
0.5 1.0 Conversion (-)
Reaction rate (lag ginitial I S -1)
Reaction rate (lag ginitia1-1 S -1) 200
0.0
-
. . , ~
0.5 1.0 Conversion (-)
Figure 3 Oxidation rate of diesel soot versus conversion as a function of temperature (10 vol.% 02 in Ar)
and 5). For both Printex-U and diesel soot the reaction rates in the initial 10-20% conversion are always relatively high. This is attributed to oxidation of more reactive parts in the soot (e.g. adsorbed hydrocarbons) during the initial stage of the experiment. The influence of H20 on the soot oxidation rate is different for Printex-U and diesel soot. For Printex-U (Figure 4), water increases the oxidation rate, whereas for diesel soot (Figure 5) it does not significantly influence the oxidation rate. The oxidation rate increase for Printex-U is observed at a number of water concentrations in the range 4 - 1 0 vol.%. However, no statistically significant correlation between water concentration and reaction rate increase can be given, due to the rather poor reproducibility. The reaction order in carbon was determined by fitting combustion curves as shown in Figures 2-5 with the nthorder model by applying eqn (7) in a linearised form. Figures 6 and 7 give the results for Printex-U and diesel soot, respectively. The nth-order model fits well the single combustion curves of Printex-U in O 2 - A r in the conversion range 0.2-0.9. The standard deviations of the determined reaction orders are small (the poorest fit shown in Figure 6 yields n~ = 0.741, with a standard deviation of 0.001).
0.0
0.5 1.0 Conversion (-)
Figure 5 Influence of water on oxidation rate of diesel soot as a function of temperature, symbols as Figure 4
However, the reaction order in carbon varies between different experiments; for Printex-U oxidation in the absence of water, the reaction order in carbon is in the range 0.65-0.80. This variation does not correlate with temperature. No explanation has been found for this varying reaction order in carbon for different experiments. Reaction order in carbon is more difficult to determine for the diesel soot. At low conversions the nth-order model is a poor fit to the experimental curves for diesel soot. Only in relatively narrow conversion intervals (~ = 0.5-0.95, log(1-~) = -1.3 to -0.3) is the nth-order model sometimes found to result in a reasonable fit, in both the presence and absence of water, as illustrated in Figure 7. The order in carbon is then 0.56 ( ___ 0.07) in the absence of water, and 0.69 ( ___ 0.05) in its presence. In the absence of water the curves, which show a more pronounced 'plateau' of reaction rate versus conversion, yield a poor fit, even in this narrow conversion range. An attempt was also made to fit the higher reaction rate at low conversions and the apparent plateau in reaction rate by the 'random pore model' (eqn (8)), but this model also did not result in an appropriate fit. Water influences the reaction order in carbon, as shown in Figure 6 for Printex-U and in Figure 7 for diesel soot. In
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
both cases, a higher reaction order is found than in the absence of water. Data on the reaction order are shown in Table 1. These data are averages plus standard deviations of reaction orders found in typically 10 experiments in the absence of water, and typically five experiments in the presence of water. In all cases the standard deviations of fits on individual curves are much smaller than those of averaged reaction orders as indicated in Table 1.
log(reaction rate; ~tg ginitial "1 g-l) 2.5 [ T = 778 K
Reaction order in oxygen The influence of oxygen partial pressure on the soot oxidation rate was studied in the range 5-15 vol.% 02, which is typical of diesel exhaust gas concentrations. The results are shown in Figures 8 and 9 for Printex-U and diesel soot respectively, at carbon conversions of 0.2, 0.4, 0.6 and 0.8. Fitting (by least-squares optimisation) of log(reaction rate) versus log(oxygen concentration) at nine conversion levels shows that the order in oxygen concentration, no2 (eqn (6)), depends on the conversion level. Results for Printex-U and diesel soot are listed in Table 2 at carbon conversions of 0.2, 0.5 and 0.8. The fits are shown by the solid lines in Figures 8 and 9. As can be concluded from the
2.0 Table 1 Reaction orders in carbon of non-catalytic diesel soot and Printex-U combustion
1.5
1.0 I
2.5 2.0 1.5 1.0
I
= 787 K
T
I
10 vol.% 02 10 vol.% O2 + 10 vol.% H20
Printex-U
Diesel soot
0.73 +__0.04 0.87 _ 0.03
0.56 _+ 0.07 0.69 +_ 0.05
o*** Reaction rate (pg
ginitid -1 S -l)
250 200 150
I
I
-1.5
-1.0
I
I
-0.5 0.0 log(1 - conversion)
Figure 6 Fit of reaction order in carbon (Printex-U). ©, 10 vol.% oxygen in Ar; °, 10vol% oxygen + 10vol.% water in Ar; , fitted curves
100 50 ,
0 log(reaction rate; ~tg giniti.l "1 2.5 T = 778 K
,
i
,
,
,
i
,
,
,
i
,
,
,
J
4 8 12 16 Oxygen concentration (vol%)
8 "1)
Figure 8 Printex-U oxidation rate as a function of oxygen concentration (793 K) at carbon conversions: o, 0.2; A, 0.4; V, 0.6; O, 0.8
O
e
2.0
,
1.5
Reaction rate (pg ginitial "1 S "1) 150
1.0 O0
2.5
T = 787 K
100
o
2.0 50 1.5 0
1.0
Figure 7
I
I
-1.5
-1.0
I
-0.5 0.0 log(1 - conversion)
Fit of reaction order in carbon (diesel soot), symbols as
Figure 6
1132
I
Fuel 1997 V o l u m e 76 N u m b e r 12
,
0
,
,
i
4
,
,
,
i
8
,
,
,
i
12
,
,
,
i
16
Oxygen concentration (vol%) Figure 9 Diesel soot oxidation rates as a function of oxygen concentration (793 K) at carbon conversions: o, 0.2; A, 0.4; V, 0.6; ©, 0.8
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al. 95% confidence intervals shown in Table 2, the order in oxygen concentration does not differ significantly from 1 for Printex-U, and is significantly lower than 1 for diesel soot. For Printex-U, the dependence of the individual CO and CO2 production rates on the oxygen concentration was also determined. The CO2 production rate has an average order of 0.92 in oxygen concentration over the conversion range studied. This order decreases (from 0.97 to 0.87) with increasing conversion (from 0.2 to 0.8). The CO production rate has a lower average order in oxygen concentration, 0.85, which also decreases (from 0.90 to 0.81) with increasing conversion in the same range. For these data the 95% confidence levels are large, and it is concluded that the orders are not significantly lower than 1.
Influence of temperature The influence of temperature on reaction rates was determined in the range 715-800K. In Figure 10, for Printex-U, reaction rates are shown at carbon conversion levels of 0.2, 0.4, 0.6 and 0.8. It is clear that the activation energy is independent on the conversion level. As a result, values of activation energy and pre-exponential factor can be fitted from the whole data set of seven conversion levels using eqn (9), resulting in an activation energy of 168 kJ mo1-1 (Table 3). The result of this fit is shown in Figure 10 by the solid lines. The same fitting procedure was followed for the data on Printex-U oxidized in 10 vol% 02 + 10 vol% H20 in Ar. Results of this fit are also shown in Table 3. In the presence of water there is a large scatter of the data points, which causes the large standard deviation of the activation energy and pre-exponential factor. For diesel soot, the activation energy was not determined, because the data were too scattered. It can be concluded
Table 2 Reaction orders in oxygen concentration for non-catalytic oxidation of Printex-U and diesel soot Conversion level Printex-U
0.2 0.5 0.8 0.2 0.5 0.8
Diesel soot
Reaction order ( _+ standard deviation) 0.94 0.88 0.85 0.76 0.78 0.80
( ( ( ( ( (
95% confidence interval
_+ 0.06) + 0.07) _+ 0.09) _+ 0.03) --- 0.03) _+ 0.07)
0.74-1.13 0.65-1.11 0.58-1.13 0.61-0.90 0.63-0.92 0.50-1.11
from Figures 2 and 3, however, that the rates of oxidation of diesel soot and Printex-U are similar. Moreover, these figures show that for these two materials the increases in reaction rate with increasing temperature are of the same order of magnitude, which means that the activation energies must be of the same order of magnitude.
CO:/CO ratio The CO2/CO ratio depends on temperature and on the presence of water, as is shown in Figure 11 for Printex-U oxidation in O2-Ar and in O2-HzO-Ar. The addition of water to the feed gas causes a marked increase in the CO2/CO ratio, by a factor of - 2 . The C O J C O ratios for diesel soot show a large scatter in both the absence and presence of water and are therefore not shown in Figure 11. The range of these ratios for diesel soot is typically 1.4-1.9. The influence of 02 concentration on the CO2/CO ratio is small; at the lowest 02 concentration of 5 vol.% somewhat lower ratios are measured for both Printex-U and diesel soot.
The temperature dependence of the C O J C O ratio was fitted using the temperature dependence of the watergas shift equilibrium. Data for this equilibrium constant Kp ( = [CO2]'[H2]'[CO]-I'[H20]-1) were taken from the li terature Jl . Assuming the H20 and the H2 concentrations to be constant, the CO2/CO ratio is proportional to Kp. The two solid lines shown in Figure 11 fulfil this correlation. DISCUSSION
Kinetic models The oxidation of carbonaceous materials in the absence
Table 3 Activationenergies and pre-exponential factors for noncatalytic combustion of Printex-U" Pre-exponential factor b (107 s -I) 10 vol.% 02 10vol.% O2 + 10vol.% H20
Activation energy (kJ mol -])
1.26 ( _+ 0.02) 1.87(_+0.21)
168 ( ___ 1) 169(___ 16)
"95% confidence intervals in parentheses 6k0' at ~ = 0.5 (eqn (9))
CO2/CO ratio
lnl r e a c t i o n rate in /ag g-t s-l) 5.0
2.2 2.0 1.8
4.0
1.6 1.4
3.0
1.2 1.0
2.0
0.8
1.0
i 760
1.25
1.30 1.36 1.41 1 0 0 0 / T e m p e r a t u r e (K -])
Figure 10 Arrhenius plots for uncatalysed oxidation of Printex-U at carbon conversions: °, 0.2; A, 0.4; !?, 0.6; ©, 0.8
,
i °,°1 770
,
iu~
780 790 Temperature (K)
Figure 11 CO2/COratios (4 = 0.5) of Printex-U oxidation versus temperature. ©, 10 vol.% oxygen in Ar;., l0 vol.% oxygen + I0 vol.% water in Ar
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
(or, better, without the extra addition) of catalytic materials has been studied both for carbons 3'7-9'=3 and for soots 2'3'5'22. The oxidation rates of these materials are known to depend on the active surface area (ASA), rather than on the total surface area (TSA) or the total mass of the carbonaceous material. It is not obvious that ASA is proportional to TSA, but ASA is often found to increase as TSA increases 7'9. The concept of ASA provides an explanation for the shape of the combustion curves of diesel soot as shown in Figure 3. The opening of occluded micropores, being the result of either desorption of hydrocarbons or partial oxidation of the carbon, is thought to occur up to a considerable carbon conversion. The opening of occluded micropores enlarges the total surface area at increasing conversions, as found experimentally 6'14'22. An increase in TSA is likely to result in an increase in ASA also, resulting in an increase in reaction rate per unit mass of residual carbon. From these considerations it is obvious that the reaction rate cannot simply be fitted by eqn (7), as the conversion is a poor indicator of TSA or ASA and therefore of reactivity. Moreover, eqn (8) poorly describes the oxidation rate as a function of conversion. This is not surprising, bearing in mind that the main cause of the increase in surface area is probably not the widening of pores, for which the model described by eqn (8) was derived, but the opening of occluded pore volume. Instead of ASA, a better parameter would be the accessible ASA. The difference between the combustion curves of diesel soot and Printex-U might be a result of different amounts of adsorbed hydrocarbons. Diesel soot contains large amounts ( - 2 5 wt%) of adsorbed hydrocarbons 2°, whereas Printex-U contains only - 6 wt%. Apparently, the latter amount of adsorbed hydrocarbons is sufficiently low that the increase in TSA and ASA as a function of conversion plays a less important role in the oxidation of Printex-U than in that of diesel soot. This explains why for Printex-U, eqn (7) describes the combustion pattern quite reasonably, with the order in carbon n~ being -0.73. This order of 0.73 ( - 0.04) has a 95% confidence interval which encompasses the order of 0.67 that is expected for the shrinking-core model ==. In this model, the particles are considered as spheres with decreasing radius as the oxidation, taking place at the surface, proceeds. However, such a picture is probably a poor description of the processes taking place in oxidation of Printex-U or diesel soot. In the literature, the oxidation of individual soot particles (with a size of - 3 0 nm ='2°'22) is reported to take place not merely on the surface but throughout the entire particle, resulting in increased porosity and only a small decrease in particle diameter with increasing conversion 22. It is difficult, if not impossible, to predict the dependence of TSA (and certainly ASA) on the conversion if the oxidation is not limited to the outer surface of the elementary particles of the soot. Percolation models have been applied, but in the present case such models do not fit the experimental observations. Concerning the dependence of the soot oxidation rate on the oxygen partial pressure, published data are not consistent. Although several authors report a relation that is first-order in oxygen partial pressure for soot oxidation 5'6'23, carbon oxidation 12'13"15 and graphite oxidation 16, other reaction orders have also been reported. D u e t al. 4 found an order of 0.83 when oxidising a flame soot, Ahlstr6m and Odenbrand 2 reported an order in oxygen
1134
Fuel 1997 Volume 76 Number 12
concentration of 0.65 for the oxidation of diesel soot, and Silva and Lobo 17 reported an order in oxygen of 0.66 for the oxidation of a charcoal. The reaction orders in a large number of carbon oxidation studies have been critically reviewed by Smith z4 and Essenhigh 25, who concluded that the order in oxygen fluctuates between 0 and 1. The order in oxygen concentration is always 1 or close to 1 in studies performed at relatively low temperatures. It seems however that this order tends to be somewhat lower than 1 (range 0.61.0) in a significant number of these studies. An explanation will be given in a future publication on the mechanism of soot oxidation 26.
Influence of water and C02/C0 ratio In this study, the addition of 10 vol.% H20 to the reactant gas caused an increase in the oxidation rate of Printex-U (Figure 4), whereas the oxidation rate of diesel soot was not affected or hardly so (Figure 5). An increase in reaction rate of diesel soot on adding water (2-10 vol.%) to an O2-N2 gas mixture was also reported by Ahlstr6m and Odenbrand 2. They gave two possible explanations: (1) a rapid reaction of carbon with water which is accelerated by removal of adsorbed hydrogen atoms by oxygen, and (2) a more pronounced increase in surface area due to gasification of carbon with H20. Neither of these explains the change in reaction order as observed in this study. In explanation (1) the cause of the increase in the reaction rate has no effect on the reaction order in carbon. Explanation (2) would result in a more pronounced 'plateau' as observed in the diesel soot oxidation experiments in the absence of water (Figure 5), as the surface area would increase to an even greater extent. It is believed that an explanation for the increase in Printex-U reaction rate and the change in reaction order for diesel soot and Printex-U on addition of water to the reactant gas can be based on changes in the carbon surface. In this respect, an important observation is that the CO2/CO ratio increases on adding water to the feed gas. It is unlikely that this increase is explained by the occurrence of the water-gas shift (WGS) reaction in the gas phase. However, the occurrence of the WGS reaction on the carbon surface might well be possible. The increase in CO2/CO ratio can be attributed to an influence of water on reactions on the carbon surface in which CO and CO2 are involved. Apart from the heterogeneous WGS reaction, two possible influences of water on such reactions can be postulated. In the first place, water can react directly with the carbon, giving rise to a different CO2/CO ratio than that for the C-O2 reaction. Although the C-H20 reaction is orders of magnitude slower than the C-O2 reaction 18, in the C-O2H20 system the reactions of 02 and H20 might differ from the sum for the two single components, since for instance the surface of the carbon is very different in the C-O2 and the C-H20 reactions. A second explanation is the influence of water on the stability of surface oxygen complexes, which are thought to play an important role in carbon oxidation, as will be discussed in detail in a future publication 26. From this discussion it may be clear that the picture of carbon oxidation in the absence or presence of water is far from complete. One interesting question is whether the correlation between the temperature dependence of the CO2/CO ratio and the temperature dependence of the WGS reaction is only coincidence, or whether the WGS reaction is at equilibrium during carbon oxidation. It should be noted that empirically determined temperature dependences for the CO 2/CO ratio that have been reported in the literature 3'12
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
are also very similar to that for the WGS reaction presented in Figure 11. Activation energy In the determination of the activation energy, the weight factor (magnitude of estimated errors in the data points) influences the results of the fit of the Arrhenius equation and therefore the magnitude of the determined activation energy. A weight factor proportional to In(reaction rate) resulted in the activation energy of 168 kJ mo1-1. Another fit was performed with a weight factor proportional to the reaction rate, which resulted in a poor fit for the lowtemperature points and which ~ave a slightly lower activation energy of 158 kJ m o l - . Because the error in the measured reaction rates cannot be properly assessed, a weight factor proportional to In(reaction rate) was chosen, resulting in the activation energy of 168 kJ mol -~ for the oxidation of Printex-U. This activation energy is in accordance with data reported in the literature: 142 kJ mo1-1 for soot oxidation 6'24, a range of 116-459 kJ mol -~ for the oxidation of coals, chars, activated carbons and graphitised carbons j3'~7'19"24"25,and a range of 105-524 kJ mol -~ for graphite oxidation 16"24'25. Due to surface heterogeneity and structural changes between different types of carbon, a 'true' activation energy for carbonaceous materials does not exist. It is generally agreed that the activation energy increases if the structure of the carbon becomes more ordered, i.e., in the sequence: soot ---* activated carbon ---, carbons and chars graphitized carbons and chars ---* graphite. Water does not seem to have an influence on the activation energy. The scatter of the data and their relatively small temperature range do not exclude a small change (of 40 kJ mol-1 at most) in activation energy. Checking for mass transfer limitations It has been verified that the activation energies are not affected by mass transfer limitations. Calculations of Thiele moduli and effectiveness factors (according to Smith 27) show that soot particles are much smaller than the sizes at which mass transfer limitations start to play a role under the conditions of this study. This has been verified for (1) masstransfer limitations in the macroporosity of the soot particulates (the voidage between the 30 nm carbon spheres) and (2) mass transfer limitations in the micropores of the individual carbon spheres. Moreover, the depletion of oxygen has been calculated to be small: at most 1 vol.% of the oxygen available at the highest reaction rates observed in this study. In accord with the conclusion that the experiments were performed far from conditions of mass transfer limitation is the value of activation energy found for the oxidation of Printex-U of --170 kJ mo1-1. If the measurements had been performed under conditions of pore diffusion control, then the true activation energy would have been twice this value, i.e. 3 4 0 k J m o l -l, which is unrealistically high 6'24. Printex-U as a model substance for diesel soot From the experimental results of this and a previous study 2°, it is concluded that Printex-U is a good model substance for diesel soot. The arguments are: (1) the activation energy of Printex-U is in the range of published values for diesel soot; (2) the absolute reaction rates of Printex-U and diesel soot correspond within a factor of two
in the temperature range used; and (3) Printex-U as well as soot consists of coagulated elementary carbon spheres of 20-30 nm, made up of parallel crystallites of graphitic carbon 20,22. The availability of a good model substance for diesel soot is important for two reasons. The first is that in the development of oxidation catalysts, the use of diesel soot might easily give rise to scatter in experimental data, because the composition of diesel soot is not very constant (as a function of time and as a function of batch produced). The second reason is that the kinetics of soot oxidation are important when numerical simulations are to be carried out, for instance when batchwise soot oxidation in filters in the exhaust of diesel engines is modelled. This study shows that the kinetics of the oxidation of Printex-U can be determined more accurately than the kinetics of the oxidation of diesel soot. Because the reaction rates of these two soots do not differ to a large extent, it is recommend that a model soot such as Printex-U be used in kinetic and catalyst screening studies.
CONCLUSIONS From the present study it is concluded that Printex-U is a good model substance for diesel soot. The oxidation rates of these two soots do not differ by more than a factor of two over the temperature range considered, and the kinetics are similar. The oxidation rates of Printex-U oxidation as a function of conversion can be described by an nth-order model, the order in carbon being -0.73, which is close to the order 0.67 applicable for the shrinking-core model. For the oxidation of diesel soot, this model is less appropriate, which may be due to a change in surface area of the soot with increasing conversion. The order of reaction rate in 02 concentration is close to 1. Values for Printex-U are not significantly lower than 1, but for diesel soot this order in 02 is significantly below 1 (values of 0.76-0.80 in the conversion range ~ = 0.2-0.8). The CO2/CO ratio decreases with increasing temperature. The addition of 10 vol.% water to the feed gas significantly increases the observed CO2/CO ratio. Water also increases the reaction rate of Printex-U but has less influence on the reaction rate of diesel soot. The reaction order in carbon increases on addition of water to the feed gas. The activation energy of Printex-U oxidation is 168 kJ mol -~. No change in activation energy occurs on addition of 10 vol.% water to the reactant gases. The kinetics of the oxidation of Printex-U are expressed by the equation: [molC] (1 - ~)0.73 r = 5.2 × 106 [molCinitial'S] × e x p ( - 168 × 103/8.314T)
p~0 [mol O2'm - 3]
where T is in kelvins. For diesel soot, this equation yields an estimate of the reaction rate that can be used in reactor design studies, for example. If more accurate data are needed, it is recommended that the reaction rate be measured. A similar equation for diesel soot has not been determined, since adsorbed hydrocarbons complicate the accurate determination of such an equation.
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
REFERENCES 1 2 3
4 5 6 7 8 9 10 11 12
1136
Neeft, J. P. A., Makkee, M. and Moulijn, J. A., Fuel Processing Technology, 1996, 47, 1. Ahlstr6m, A. F. and Odenbrand, C. U. I., Carbon, 1989, 27, 475. Du, Z., Sarofim, A. F., Longwell, J. P. and Tognotti, L. In Fundamental Issues in Control of Carbon Gasification Reactivity, ed. J. Lahaye and P. Ehrburger. Kluwer, Dordrecht, 1991, p. 91. Du, Z., Sarofim, A. F., Longwell, J. P. and Mims, C. A., Energy and Fuels, 1991, 5, 214. Gilot, P., Bonnefoy, F., Marcuccilli, F. and Prado, G., Combustion and Flame, 1993, 95, 87. Otto, K., Sieg, M. H., Zinbo, M. and Bartosiewicz, L., SAE Paper 800336, 1980. Laine, N. R., Vastola, F. J. and Walker, P. L. Jr, Journal of Physical Chemistry, 1963, 67, 2030. Walker, P. L. Jr, Taylor, R. L. and Ranish, J. M., Carbon, 1991, 29, 411. Lizzio, A. A. and Radovic, L. R., in Nineteenth Biennial Conference on Carbon. American Carbon Society, 1989, p. 586. Calo, J. M., Suuberg, E. M. and Wojtowicz, M., in Proceedings, Carbon '88. 1988, p. 319. Kapteijn, F. and Moulijn, J. A., in Carbon and Coal Gasification, ed. J. L. Figueiredo and J. A. Moulijn. Martinus Nijhoff, Dordrecht, 1986, p. 291. Phillips, R., Vastola, F. J. and Walker, P. L. Jr, Carbon, 1970, 8, 205.
Fuel 1997 Volume 76 Number 12
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Floess, J. K., Longwell, J. P. and Sarofim, A. F., Energy and Fuels, 1988, 2, 18. Zhuang, Q.-L., Kyotani, T. and Tomita, A., Energy and Fuels, 1994, 8, 714. Phillips, R., Vastola, F. J. and Walker, P. L. Jr, Carbon, 1969, 7, 479. Rakszawski, J. F. and Parker, W. E., Carbon, 1964, 2, 53. Silva, I. F. and Lobo, L. S., Journal of Catalysis, 1990, 126, 489. Walker, P. L. Jr, Rusinko, F. Jr and Austin, L. G., Advances in Catalysis, 1959, 11, 133. Cheng, A. and Harriot, P., Carbon, 1986, 24, 143. Neeft, J. P. A., Ph.D. thesis, Delft University of Technology, 1995. Bhatia, S. K. and Perlmutter, D. D., AIChE Journal, 1980, 26, 379. Ishiguro, T., Suzuki, N., Fujitani, Y. and Morimoto, H., Combustion and Flame, 1991, 85, 1. Miyamoto, N., Hou, Z. and Ogawa, H., SAE Paper 881224, 1988. Smith, I. W., Fuel, 1978, 57, 409. Essenhigh, R. H., in Chemistry of Coal Utilization, Second Supplementary Volume, ed. M. A. Elliott. WileyInterscience, New York, 1981, p. 1153. Neeft, J. P. A., Kapteijn, F. and Moulijn, J. A. (in preparation). Smith, J. M., Chemical Engineering Kinetics. McGraw-Hill, New York, 1956.
Plh S0016-2361(97)00119-1
ELSEVIER
Kinetics of the oxidation of diesel soot John P. A. Neeft, T. Xander Nijhuis, Erik Smakman, Michiel Makkee and Jacob A. Moulijn Industrial Catalysis, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands (Received 30 August 1996) The kinetics of the uncatalysed oxidation of a flame soot and diesel soot were studied, Oxidation of the flame soot could be described by an nth-order model, with an order in carbon of 0.7. The order in molecular oxygen concentration was found to be 1 for the flame soot and slightly lower than 1 for the diesel soot. This order in oxygen concentration was also found to be a function of conversion. Water caused a significant increase in oxidation rate of the flame soot, which was accompanied by an increase in reaction order in carbon and a much higher CO2/CO ratio, whereas the activation energy did not change. The oxidation rate of the diesel soot was not significantly influenced by the addition of water. Experimental results were more reproducible for the oxidation of the flame soot than for the oxidation of diesel soot, and the flame soot appeared to be a good model for diesel soot in oxidation studies. Therefore it is recommended to use a model soot in (kinetic) studies of soot oxidation. © 1997 Elsevier Science Ltd.
(Keywords: soot; diesel emissions; oxidation kinetics)
The emission of particulates from diesel engines has led to serious concern about possible health effects. Emission standards for particulates from diesel engines have been introduced, and much research towards strategies for reduction of such emissions has been performed over the last two decades 1. Oxidation of the soot plus hydrocarbon fraction of the particulates is one of the solutions proposed for the reduction of diesel particulate emissions. Although much research has been performed on noncatalytic and catalytic soot oxidation, the detailed kinetics of soot oxidation have hardly_ been studied. Only the studies of Ahlstr6m and Odenbrand,2 D u e t al. 34 • , Gilot et al. 5 and Otto et al. 6 provide some relevant data. The oxidation of carbons and graphite has been studied to a much greater extent 7- ~9. It was concluded 2° that more detailed insight in the kinetics and mechanism of soot oxidation might help in developing more active or selective soot oxidation catalysts. This paper reports on the kinetics of non-catalytic soot oxidation; a second paper will report on the mechanism (the elementary reaction steps) of non-catalytic oxidation of soot and other carbonaceous materials. Results of a study of the kinetics and mechanism of the catalysed oxidation of soot will be published later. Kinetic models that have often been used to describe the reaction rates of carbonaceous materials have the general form: r = N t . k ( T ) f ( P 0 2 ,pH20 .... )
(1)
where r is the reaction rate, Nt is the total number of active sites, k(T) is a temperature-dependent reaction rate constant, and J~oz,PH20,.-.) is a function which describes the
dependence of the reaction rate on the partial pressures of the various reactants and gas-phase components. The total number of active sites N t is often described by: N t = X.Sa
(2)
where X is the surface concentration of active sites and Sa the specific surface area. The proportionality between Nt (and thus reaction rate) and specific surface area S, has been discussed extensively 7-1°, and it is clear that this picture of direct proportionality is too simple. A linear proportionality might hold for the active surface area (ASA), or at least for part of this ASA in the form of the occupied or unoccupied fraction 7'8"1°. However, as long as ASA cannot be properly measured or predicted, eqn (2) is most convenient for deriving kinetic models. As it is generally accepted that the specific surface area S, is a function of the conversion ~ (the fraction of carbon that is oxidized), kinetic models describe the dependence of Nt as a function of conversion. A simple approach is to use an nth order of (l-G): Sa ---~Sa,0.( 1 _ ~)n~
(3)
where Sa,o is the initial surface area (at ~ = 0) and n~ is the reaction order in carbon. With increasing conversion this model predicts a decrease in Nt and therefore in reaction rate. However, for highly porous carbons such as soots and activated carbons, Sa can actually increase as a function of conversion, due to pore growth and opening of occluded pore space. Many models have been proposed to account for these phenomena. The model of Bhatia and Perlmutter 21, for instance, is based on the growth of pores with random pore size distribution,
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
and yields the following expression: Sa = Sa,0.(1 -- ~).V/1 - ¢ In(1 - ~)
(4)
where ¢ is a structural factor that describes the initial pore structure. For ¢ > 2, the model predicts that the total surface area initially increases and goes through a maximum at a conversion ~ between 0 and 0.393, depending on the value of ¢. The temperature dependence of the reaction rate is usually described by the Arrhenius equation:
k(T) = k0-exp( - Ea/RT)
(5)
where T is the absolute temperature, k0 the pre-exponential factor, R the molar gas constant and Ea the activation energy. Finally, the function that describes the influence of the partial pressures of the gas-phase components on the reaction rate is usually limited to the influence of the oxygen partial pressure, described by an nth order expression: f(Po2,PH20 .... ) ----p o2n°2
(6)
where Po2 is the partial pressure of oxygen and no2 is the order in oxygen partial pressure. This leads to the following two equations for the observed reaction rate: r = c.(1 - ~)"~.exp( - Ea/RT).p~~
(7)
for the nth-order model (with the shrinking-core model as a specific case, N~ = 0.67), and r = c.(1 - ~).X/1 - ¢ ln(1 - ~).exp( - Ea/RT).p~2
(8)
for the pore growth model of Bhatia and Perlmutter; c is a constant and is equal to X'Sa.o'ko. At a constant oxygen partial pressure and conversion, eqn (7) can be rewritten as: r = k'0.exp( - Ea/RT)
(9)
with ko' representing an overall pre-exponential factor: k0' = c.(1 ~)n~ .p~)~2. The aim of this kinetic study is to provide insight into the parameters that influence the uncatalysed oxidation of soot. Temperature and the concentrations of oxygen and water in the feed gas are the parameters of interest. In addition, CO2/ CO ratios are determined, which can provide information on the mechanism of soot oxidation. -
soot are presented elsewhere 2°. The soots were milled before use; this milling step did not affect the reaction rate, but it facilitated sample preparation. Milled Printex-U or diesel soot was mixed with silicon carbide in a weight ratio of 1/10 so as to reduce the pressure drop over the sample bed as well as to limit temperature rises in the sample due to the exothermic oxidation of soot. In this way, temperature rises registered by the thermocouple inside the sample bed amounted to < 2 K and were observed only in the first hour of the experiment. Experiments were performed under isothermal conditions. The sample of typically 20 mg soot was heated to the reaction temperature under inert (At) gas flow. At time zero, the gas flow was switched to an O2-Ar mixture. A flow rate of 500 mL min -~ (s.t.p.) was used in each reactor. For the longest experiments a lower flow rate (200 or 100 mL min -1) was chosen. Experiments lasted for typically 4 to 100 h. Near the end of each experiment the temperature of the reactor tubes was increased at a rate of 1 or 2 K min -~ so as to oxidise the remaining soot. Reaction rates were calculated from the total gas flow rate and the CO and CO2 concentrations as measured by a nondispersive infrared detector. Reaction rates are expressed in (p.g C)(gCinitial)-ls -1 throughout this paper. The carbon mass balance was obtained by numerical integration of the reaction rates in (/~g C)s -1 and was always in the range 90120% of the amount of soot placed in the reactor tubes. A more accurate mass balance was not aimed at. The reaction rates were divided by the total quantity of carbon measured by the NDIR detector as CO and CO2. The reaction rates expressed in (#g C)(g Cinitial)-~s-~ were therefore essentially unaffected by a small error in the mass balance. RESULTS
Reaction order in carbon, and influence of water on reaction rate and order in carbon Typical results of the oxidation of diesel soot and Printex-U are shown in Figure I. The curve of reaction rate versus time for Printex-U shows an exponential-like behaviour; that for diesel soot shows a plateau in the conversion range 0.25-0.5. This plateau is visible in all combustion curves of diesel soot, though often less pronounced than in Figure 1, e.g. as can be seen in Figure 3. In Figures 2-5, a number of similar curves are plotted as a function of carbon conversion, in both the absence (Figures 2 and 3) and presence of water (Figures 4
EXPERIMENTAL Experiments were performed with the six-flow reactor equipment described in detail elsewhere 2°. Five experiments could be performed simultaneously; the sixth reactor was used as a blank to correct for background CO and CO2 from the technical-grade argon, which contained typically 10-20 ppmv CO2 and a few ppmv CO. The temperature within each reactor was recorded by a thermocouple, which was placed in the soot bed. It was verified that this thermocouple had no effect on the soot oxidation rate. The temperature could be controlled with an accuracy better than 1 K, the reproducibility between the different reactors being slightly less accurate (1-2 K). Printex-U, a flame soot obtained from Degussa AG, was used as a model for diesel soot. A number of experiments were performed with diesel soot from a single-cylinder Yanmar diesel engine. This soot was collected at an engine load of 3 kW. Properties of both Printex-U and the diesel
1130
Fuel 1997 Volume 76 Number 12
Reaction rate (~g giaitia1-1 S"t) 0.30
0.20 0. i0 0.00 0
6000
12000 18000 Reaction time (s)
Figure 1 Typical results for Printex-U ( ) and diesel soot ( - - - ) combustion in 10 vol.% 02 in Ar (794 K, 500 mL min -L s.t.p., 20 mg sample)
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et
Reaction rate (tag ginitial "1 S "1) 250
Reaction rate (~tg ginitia1-1 S-l)
"° I \
\ 794 K
200
~\ "X.. 778K f. \, \ . . 774 K 150 •.',,. ~'-\ 768 K ~ k ~ ' ' " " ' " ' - "'X.. \ 758 K 100 \,.x,.......~ .... " - . . " \ 738 K -- ....
50
.
I
250 f
........ _--.,... ",%'..,,
772 K
\7,7
'"'.'.'~-.~'~ ~
150 l" lOO
"----... ,..-.. ,,.
-
al.
f "'..'."
......
--'2-:-::::~
50
778K
~..?-~."~. ~
774K 768 K
0
0.0
0.5 1.0 Conversion (-)
Figure 2 Oxidation rate of Printex-U versus conversion as a function of temperature (10 vol.% 02 in Ar)
100
150
\ \ "', 768 K ~ "-. "-., 758K ~ k "'" ...... "'-':":"~ 738 K
100
'~
"%N.~.
"~..
787 K 779 K
" ?'"-. 729K
50
50 .......
0.0
787 K 777 K ",~ 768 K
",,~
',, 787 K \ ',. 777 K \ ~
Figure 4 Influence of water on oxidation rate of Printex-U as a function of temperature. - - - , 10vol.% oxygen in Ar; , 10 vol.% oxygen + 10 vol.% water in Ar
200
', 794 K
150
0.5 1.0 Conversion (-)
Reaction rate (lag ginitial I S -1)
Reaction rate (lag ginitia1-1 S -1) 200
0.0
-
. . , ~
0.5 1.0 Conversion (-)
Figure 3 Oxidation rate of diesel soot versus conversion as a function of temperature (10 vol.% 02 in Ar)
and 5). For both Printex-U and diesel soot the reaction rates in the initial 10-20% conversion are always relatively high. This is attributed to oxidation of more reactive parts in the soot (e.g. adsorbed hydrocarbons) during the initial stage of the experiment. The influence of H20 on the soot oxidation rate is different for Printex-U and diesel soot. For Printex-U (Figure 4), water increases the oxidation rate, whereas for diesel soot (Figure 5) it does not significantly influence the oxidation rate. The oxidation rate increase for Printex-U is observed at a number of water concentrations in the range 4 - 1 0 vol.%. However, no statistically significant correlation between water concentration and reaction rate increase can be given, due to the rather poor reproducibility. The reaction order in carbon was determined by fitting combustion curves as shown in Figures 2-5 with the nthorder model by applying eqn (7) in a linearised form. Figures 6 and 7 give the results for Printex-U and diesel soot, respectively. The nth-order model fits well the single combustion curves of Printex-U in O 2 - A r in the conversion range 0.2-0.9. The standard deviations of the determined reaction orders are small (the poorest fit shown in Figure 6 yields n~ = 0.741, with a standard deviation of 0.001).
0.0
0.5 1.0 Conversion (-)
Figure 5 Influence of water on oxidation rate of diesel soot as a function of temperature, symbols as Figure 4
However, the reaction order in carbon varies between different experiments; for Printex-U oxidation in the absence of water, the reaction order in carbon is in the range 0.65-0.80. This variation does not correlate with temperature. No explanation has been found for this varying reaction order in carbon for different experiments. Reaction order in carbon is more difficult to determine for the diesel soot. At low conversions the nth-order model is a poor fit to the experimental curves for diesel soot. Only in relatively narrow conversion intervals (~ = 0.5-0.95, log(1-~) = -1.3 to -0.3) is the nth-order model sometimes found to result in a reasonable fit, in both the presence and absence of water, as illustrated in Figure 7. The order in carbon is then 0.56 ( ___ 0.07) in the absence of water, and 0.69 ( ___ 0.05) in its presence. In the absence of water the curves, which show a more pronounced 'plateau' of reaction rate versus conversion, yield a poor fit, even in this narrow conversion range. An attempt was also made to fit the higher reaction rate at low conversions and the apparent plateau in reaction rate by the 'random pore model' (eqn (8)), but this model also did not result in an appropriate fit. Water influences the reaction order in carbon, as shown in Figure 6 for Printex-U and in Figure 7 for diesel soot. In
Fuel 1997 Volume 76 Number 12 1131
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
both cases, a higher reaction order is found than in the absence of water. Data on the reaction order are shown in Table 1. These data are averages plus standard deviations of reaction orders found in typically 10 experiments in the absence of water, and typically five experiments in the presence of water. In all cases the standard deviations of fits on individual curves are much smaller than those of averaged reaction orders as indicated in Table 1.
log(reaction rate; ~tg ginitial "1 g-l) 2.5 [ T = 778 K
Reaction order in oxygen The influence of oxygen partial pressure on the soot oxidation rate was studied in the range 5-15 vol.% 02, which is typical of diesel exhaust gas concentrations. The results are shown in Figures 8 and 9 for Printex-U and diesel soot respectively, at carbon conversions of 0.2, 0.4, 0.6 and 0.8. Fitting (by least-squares optimisation) of log(reaction rate) versus log(oxygen concentration) at nine conversion levels shows that the order in oxygen concentration, no2 (eqn (6)), depends on the conversion level. Results for Printex-U and diesel soot are listed in Table 2 at carbon conversions of 0.2, 0.5 and 0.8. The fits are shown by the solid lines in Figures 8 and 9. As can be concluded from the
2.0 Table 1 Reaction orders in carbon of non-catalytic diesel soot and Printex-U combustion
1.5
1.0 I
2.5 2.0 1.5 1.0
I
= 787 K
T
I
10 vol.% 02 10 vol.% O2 + 10 vol.% H20
Printex-U
Diesel soot
0.73 +__0.04 0.87 _ 0.03
0.56 _+ 0.07 0.69 +_ 0.05
o*** Reaction rate (pg
ginitid -1 S -l)
250 200 150
I
I
-1.5
-1.0
I
I
-0.5 0.0 log(1 - conversion)
Figure 6 Fit of reaction order in carbon (Printex-U). ©, 10 vol.% oxygen in Ar; °, 10vol% oxygen + 10vol.% water in Ar; , fitted curves
100 50 ,
0 log(reaction rate; ~tg giniti.l "1 2.5 T = 778 K
,
i
,
,
,
i
,
,
,
i
,
,
,
J
4 8 12 16 Oxygen concentration (vol%)
8 "1)
Figure 8 Printex-U oxidation rate as a function of oxygen concentration (793 K) at carbon conversions: o, 0.2; A, 0.4; V, 0.6; O, 0.8
O
e
2.0
,
1.5
Reaction rate (pg ginitial "1 S "1) 150
1.0 O0
2.5
T = 787 K
100
o
2.0 50 1.5 0
1.0
Figure 7
I
I
-1.5
-1.0
I
-0.5 0.0 log(1 - conversion)
Fit of reaction order in carbon (diesel soot), symbols as
Figure 6
1132
I
Fuel 1997 V o l u m e 76 N u m b e r 12
,
0
,
,
i
4
,
,
,
i
8
,
,
,
i
12
,
,
,
i
16
Oxygen concentration (vol%) Figure 9 Diesel soot oxidation rates as a function of oxygen concentration (793 K) at carbon conversions: o, 0.2; A, 0.4; V, 0.6; ©, 0.8
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al. 95% confidence intervals shown in Table 2, the order in oxygen concentration does not differ significantly from 1 for Printex-U, and is significantly lower than 1 for diesel soot. For Printex-U, the dependence of the individual CO and CO2 production rates on the oxygen concentration was also determined. The CO2 production rate has an average order of 0.92 in oxygen concentration over the conversion range studied. This order decreases (from 0.97 to 0.87) with increasing conversion (from 0.2 to 0.8). The CO production rate has a lower average order in oxygen concentration, 0.85, which also decreases (from 0.90 to 0.81) with increasing conversion in the same range. For these data the 95% confidence levels are large, and it is concluded that the orders are not significantly lower than 1.
Influence of temperature The influence of temperature on reaction rates was determined in the range 715-800K. In Figure 10, for Printex-U, reaction rates are shown at carbon conversion levels of 0.2, 0.4, 0.6 and 0.8. It is clear that the activation energy is independent on the conversion level. As a result, values of activation energy and pre-exponential factor can be fitted from the whole data set of seven conversion levels using eqn (9), resulting in an activation energy of 168 kJ mo1-1 (Table 3). The result of this fit is shown in Figure 10 by the solid lines. The same fitting procedure was followed for the data on Printex-U oxidized in 10 vol% 02 + 10 vol% H20 in Ar. Results of this fit are also shown in Table 3. In the presence of water there is a large scatter of the data points, which causes the large standard deviation of the activation energy and pre-exponential factor. For diesel soot, the activation energy was not determined, because the data were too scattered. It can be concluded
Table 2 Reaction orders in oxygen concentration for non-catalytic oxidation of Printex-U and diesel soot Conversion level Printex-U
0.2 0.5 0.8 0.2 0.5 0.8
Diesel soot
Reaction order ( _+ standard deviation) 0.94 0.88 0.85 0.76 0.78 0.80
( ( ( ( ( (
95% confidence interval
_+ 0.06) + 0.07) _+ 0.09) _+ 0.03) --- 0.03) _+ 0.07)
0.74-1.13 0.65-1.11 0.58-1.13 0.61-0.90 0.63-0.92 0.50-1.11
from Figures 2 and 3, however, that the rates of oxidation of diesel soot and Printex-U are similar. Moreover, these figures show that for these two materials the increases in reaction rate with increasing temperature are of the same order of magnitude, which means that the activation energies must be of the same order of magnitude.
CO:/CO ratio The CO2/CO ratio depends on temperature and on the presence of water, as is shown in Figure 11 for Printex-U oxidation in O2-Ar and in O2-HzO-Ar. The addition of water to the feed gas causes a marked increase in the CO2/CO ratio, by a factor of - 2 . The C O J C O ratios for diesel soot show a large scatter in both the absence and presence of water and are therefore not shown in Figure 11. The range of these ratios for diesel soot is typically 1.4-1.9. The influence of 02 concentration on the CO2/CO ratio is small; at the lowest 02 concentration of 5 vol.% somewhat lower ratios are measured for both Printex-U and diesel soot.
The temperature dependence of the C O J C O ratio was fitted using the temperature dependence of the watergas shift equilibrium. Data for this equilibrium constant Kp ( = [CO2]'[H2]'[CO]-I'[H20]-1) were taken from the li terature Jl . Assuming the H20 and the H2 concentrations to be constant, the CO2/CO ratio is proportional to Kp. The two solid lines shown in Figure 11 fulfil this correlation. DISCUSSION
Kinetic models The oxidation of carbonaceous materials in the absence
Table 3 Activationenergies and pre-exponential factors for noncatalytic combustion of Printex-U" Pre-exponential factor b (107 s -I) 10 vol.% 02 10vol.% O2 + 10vol.% H20
Activation energy (kJ mol -])
1.26 ( _+ 0.02) 1.87(_+0.21)
168 ( ___ 1) 169(___ 16)
"95% confidence intervals in parentheses 6k0' at ~ = 0.5 (eqn (9))
CO2/CO ratio
lnl r e a c t i o n rate in /ag g-t s-l) 5.0
2.2 2.0 1.8
4.0
1.6 1.4
3.0
1.2 1.0
2.0
0.8
1.0
i 760
1.25
1.30 1.36 1.41 1 0 0 0 / T e m p e r a t u r e (K -])
Figure 10 Arrhenius plots for uncatalysed oxidation of Printex-U at carbon conversions: °, 0.2; A, 0.4; !?, 0.6; ©, 0.8
,
i °,°1 770
,
iu~
780 790 Temperature (K)
Figure 11 CO2/COratios (4 = 0.5) of Printex-U oxidation versus temperature. ©, 10 vol.% oxygen in Ar;., l0 vol.% oxygen + I0 vol.% water in Ar
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
(or, better, without the extra addition) of catalytic materials has been studied both for carbons 3'7-9'=3 and for soots 2'3'5'22. The oxidation rates of these materials are known to depend on the active surface area (ASA), rather than on the total surface area (TSA) or the total mass of the carbonaceous material. It is not obvious that ASA is proportional to TSA, but ASA is often found to increase as TSA increases 7'9. The concept of ASA provides an explanation for the shape of the combustion curves of diesel soot as shown in Figure 3. The opening of occluded micropores, being the result of either desorption of hydrocarbons or partial oxidation of the carbon, is thought to occur up to a considerable carbon conversion. The opening of occluded micropores enlarges the total surface area at increasing conversions, as found experimentally 6'14'22. An increase in TSA is likely to result in an increase in ASA also, resulting in an increase in reaction rate per unit mass of residual carbon. From these considerations it is obvious that the reaction rate cannot simply be fitted by eqn (7), as the conversion is a poor indicator of TSA or ASA and therefore of reactivity. Moreover, eqn (8) poorly describes the oxidation rate as a function of conversion. This is not surprising, bearing in mind that the main cause of the increase in surface area is probably not the widening of pores, for which the model described by eqn (8) was derived, but the opening of occluded pore volume. Instead of ASA, a better parameter would be the accessible ASA. The difference between the combustion curves of diesel soot and Printex-U might be a result of different amounts of adsorbed hydrocarbons. Diesel soot contains large amounts ( - 2 5 wt%) of adsorbed hydrocarbons 2°, whereas Printex-U contains only - 6 wt%. Apparently, the latter amount of adsorbed hydrocarbons is sufficiently low that the increase in TSA and ASA as a function of conversion plays a less important role in the oxidation of Printex-U than in that of diesel soot. This explains why for Printex-U, eqn (7) describes the combustion pattern quite reasonably, with the order in carbon n~ being -0.73. This order of 0.73 ( - 0.04) has a 95% confidence interval which encompasses the order of 0.67 that is expected for the shrinking-core model ==. In this model, the particles are considered as spheres with decreasing radius as the oxidation, taking place at the surface, proceeds. However, such a picture is probably a poor description of the processes taking place in oxidation of Printex-U or diesel soot. In the literature, the oxidation of individual soot particles (with a size of - 3 0 nm ='2°'22) is reported to take place not merely on the surface but throughout the entire particle, resulting in increased porosity and only a small decrease in particle diameter with increasing conversion 22. It is difficult, if not impossible, to predict the dependence of TSA (and certainly ASA) on the conversion if the oxidation is not limited to the outer surface of the elementary particles of the soot. Percolation models have been applied, but in the present case such models do not fit the experimental observations. Concerning the dependence of the soot oxidation rate on the oxygen partial pressure, published data are not consistent. Although several authors report a relation that is first-order in oxygen partial pressure for soot oxidation 5'6'23, carbon oxidation 12'13"15 and graphite oxidation 16, other reaction orders have also been reported. D u e t al. 4 found an order of 0.83 when oxidising a flame soot, Ahlstr6m and Odenbrand 2 reported an order in oxygen
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concentration of 0.65 for the oxidation of diesel soot, and Silva and Lobo 17 reported an order in oxygen of 0.66 for the oxidation of a charcoal. The reaction orders in a large number of carbon oxidation studies have been critically reviewed by Smith z4 and Essenhigh 25, who concluded that the order in oxygen fluctuates between 0 and 1. The order in oxygen concentration is always 1 or close to 1 in studies performed at relatively low temperatures. It seems however that this order tends to be somewhat lower than 1 (range 0.61.0) in a significant number of these studies. An explanation will be given in a future publication on the mechanism of soot oxidation 26.
Influence of water and C02/C0 ratio In this study, the addition of 10 vol.% H20 to the reactant gas caused an increase in the oxidation rate of Printex-U (Figure 4), whereas the oxidation rate of diesel soot was not affected or hardly so (Figure 5). An increase in reaction rate of diesel soot on adding water (2-10 vol.%) to an O2-N2 gas mixture was also reported by Ahlstr6m and Odenbrand 2. They gave two possible explanations: (1) a rapid reaction of carbon with water which is accelerated by removal of adsorbed hydrogen atoms by oxygen, and (2) a more pronounced increase in surface area due to gasification of carbon with H20. Neither of these explains the change in reaction order as observed in this study. In explanation (1) the cause of the increase in the reaction rate has no effect on the reaction order in carbon. Explanation (2) would result in a more pronounced 'plateau' as observed in the diesel soot oxidation experiments in the absence of water (Figure 5), as the surface area would increase to an even greater extent. It is believed that an explanation for the increase in Printex-U reaction rate and the change in reaction order for diesel soot and Printex-U on addition of water to the reactant gas can be based on changes in the carbon surface. In this respect, an important observation is that the CO2/CO ratio increases on adding water to the feed gas. It is unlikely that this increase is explained by the occurrence of the water-gas shift (WGS) reaction in the gas phase. However, the occurrence of the WGS reaction on the carbon surface might well be possible. The increase in CO2/CO ratio can be attributed to an influence of water on reactions on the carbon surface in which CO and CO2 are involved. Apart from the heterogeneous WGS reaction, two possible influences of water on such reactions can be postulated. In the first place, water can react directly with the carbon, giving rise to a different CO2/CO ratio than that for the C-O2 reaction. Although the C-H20 reaction is orders of magnitude slower than the C-O2 reaction 18, in the C-O2H20 system the reactions of 02 and H20 might differ from the sum for the two single components, since for instance the surface of the carbon is very different in the C-O2 and the C-H20 reactions. A second explanation is the influence of water on the stability of surface oxygen complexes, which are thought to play an important role in carbon oxidation, as will be discussed in detail in a future publication 26. From this discussion it may be clear that the picture of carbon oxidation in the absence or presence of water is far from complete. One interesting question is whether the correlation between the temperature dependence of the CO2/CO ratio and the temperature dependence of the WGS reaction is only coincidence, or whether the WGS reaction is at equilibrium during carbon oxidation. It should be noted that empirically determined temperature dependences for the CO 2/CO ratio that have been reported in the literature 3'12
Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
are also very similar to that for the WGS reaction presented in Figure 11. Activation energy In the determination of the activation energy, the weight factor (magnitude of estimated errors in the data points) influences the results of the fit of the Arrhenius equation and therefore the magnitude of the determined activation energy. A weight factor proportional to In(reaction rate) resulted in the activation energy of 168 kJ mo1-1. Another fit was performed with a weight factor proportional to the reaction rate, which resulted in a poor fit for the lowtemperature points and which ~ave a slightly lower activation energy of 158 kJ m o l - . Because the error in the measured reaction rates cannot be properly assessed, a weight factor proportional to In(reaction rate) was chosen, resulting in the activation energy of 168 kJ mol -~ for the oxidation of Printex-U. This activation energy is in accordance with data reported in the literature: 142 kJ mo1-1 for soot oxidation 6'24, a range of 116-459 kJ mol -~ for the oxidation of coals, chars, activated carbons and graphitised carbons j3'~7'19"24"25,and a range of 105-524 kJ mol -~ for graphite oxidation 16"24'25. Due to surface heterogeneity and structural changes between different types of carbon, a 'true' activation energy for carbonaceous materials does not exist. It is generally agreed that the activation energy increases if the structure of the carbon becomes more ordered, i.e., in the sequence: soot ---* activated carbon ---, carbons and chars graphitized carbons and chars ---* graphite. Water does not seem to have an influence on the activation energy. The scatter of the data and their relatively small temperature range do not exclude a small change (of 40 kJ mol-1 at most) in activation energy. Checking for mass transfer limitations It has been verified that the activation energies are not affected by mass transfer limitations. Calculations of Thiele moduli and effectiveness factors (according to Smith 27) show that soot particles are much smaller than the sizes at which mass transfer limitations start to play a role under the conditions of this study. This has been verified for (1) masstransfer limitations in the macroporosity of the soot particulates (the voidage between the 30 nm carbon spheres) and (2) mass transfer limitations in the micropores of the individual carbon spheres. Moreover, the depletion of oxygen has been calculated to be small: at most 1 vol.% of the oxygen available at the highest reaction rates observed in this study. In accord with the conclusion that the experiments were performed far from conditions of mass transfer limitation is the value of activation energy found for the oxidation of Printex-U of --170 kJ mo1-1. If the measurements had been performed under conditions of pore diffusion control, then the true activation energy would have been twice this value, i.e. 3 4 0 k J m o l -l, which is unrealistically high 6'24. Printex-U as a model substance for diesel soot From the experimental results of this and a previous study 2°, it is concluded that Printex-U is a good model substance for diesel soot. The arguments are: (1) the activation energy of Printex-U is in the range of published values for diesel soot; (2) the absolute reaction rates of Printex-U and diesel soot correspond within a factor of two
in the temperature range used; and (3) Printex-U as well as soot consists of coagulated elementary carbon spheres of 20-30 nm, made up of parallel crystallites of graphitic carbon 20,22. The availability of a good model substance for diesel soot is important for two reasons. The first is that in the development of oxidation catalysts, the use of diesel soot might easily give rise to scatter in experimental data, because the composition of diesel soot is not very constant (as a function of time and as a function of batch produced). The second reason is that the kinetics of soot oxidation are important when numerical simulations are to be carried out, for instance when batchwise soot oxidation in filters in the exhaust of diesel engines is modelled. This study shows that the kinetics of the oxidation of Printex-U can be determined more accurately than the kinetics of the oxidation of diesel soot. Because the reaction rates of these two soots do not differ to a large extent, it is recommend that a model soot such as Printex-U be used in kinetic and catalyst screening studies.
CONCLUSIONS From the present study it is concluded that Printex-U is a good model substance for diesel soot. The oxidation rates of these two soots do not differ by more than a factor of two over the temperature range considered, and the kinetics are similar. The oxidation rates of Printex-U oxidation as a function of conversion can be described by an nth-order model, the order in carbon being -0.73, which is close to the order 0.67 applicable for the shrinking-core model. For the oxidation of diesel soot, this model is less appropriate, which may be due to a change in surface area of the soot with increasing conversion. The order of reaction rate in 02 concentration is close to 1. Values for Printex-U are not significantly lower than 1, but for diesel soot this order in 02 is significantly below 1 (values of 0.76-0.80 in the conversion range ~ = 0.2-0.8). The CO2/CO ratio decreases with increasing temperature. The addition of 10 vol.% water to the feed gas significantly increases the observed CO2/CO ratio. Water also increases the reaction rate of Printex-U but has less influence on the reaction rate of diesel soot. The reaction order in carbon increases on addition of water to the feed gas. The activation energy of Printex-U oxidation is 168 kJ mol -~. No change in activation energy occurs on addition of 10 vol.% water to the reactant gases. The kinetics of the oxidation of Printex-U are expressed by the equation: [molC] (1 - ~)0.73 r = 5.2 × 106 [molCinitial'S] × e x p ( - 168 × 103/8.314T)
p~0 [mol O2'm - 3]
where T is in kelvins. For diesel soot, this equation yields an estimate of the reaction rate that can be used in reactor design studies, for example. If more accurate data are needed, it is recommended that the reaction rate be measured. A similar equation for diesel soot has not been determined, since adsorbed hydrocarbons complicate the accurate determination of such an equation.
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Kinetics of the oxidation of diesel soot: J. P. A. Neeft et al.
REFERENCES 1 2 3
4 5 6 7 8 9 10 11 12
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Neeft, J. P. A., Makkee, M. and Moulijn, J. A., Fuel Processing Technology, 1996, 47, 1. Ahlstr6m, A. F. and Odenbrand, C. U. I., Carbon, 1989, 27, 475. Du, Z., Sarofim, A. F., Longwell, J. P. and Tognotti, L. In Fundamental Issues in Control of Carbon Gasification Reactivity, ed. J. Lahaye and P. Ehrburger. Kluwer, Dordrecht, 1991, p. 91. Du, Z., Sarofim, A. F., Longwell, J. P. and Mims, C. A., Energy and Fuels, 1991, 5, 214. Gilot, P., Bonnefoy, F., Marcuccilli, F. and Prado, G., Combustion and Flame, 1993, 95, 87. Otto, K., Sieg, M. H., Zinbo, M. and Bartosiewicz, L., SAE Paper 800336, 1980. Laine, N. R., Vastola, F. J. and Walker, P. L. Jr, Journal of Physical Chemistry, 1963, 67, 2030. Walker, P. L. Jr, Taylor, R. L. and Ranish, J. M., Carbon, 1991, 29, 411. Lizzio, A. A. and Radovic, L. R., in Nineteenth Biennial Conference on Carbon. American Carbon Society, 1989, p. 586. Calo, J. M., Suuberg, E. M. and Wojtowicz, M., in Proceedings, Carbon '88. 1988, p. 319. Kapteijn, F. and Moulijn, J. A., in Carbon and Coal Gasification, ed. J. L. Figueiredo and J. A. Moulijn. Martinus Nijhoff, Dordrecht, 1986, p. 291. Phillips, R., Vastola, F. J. and Walker, P. L. Jr, Carbon, 1970, 8, 205.
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13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Floess, J. K., Longwell, J. P. and Sarofim, A. F., Energy and Fuels, 1988, 2, 18. Zhuang, Q.-L., Kyotani, T. and Tomita, A., Energy and Fuels, 1994, 8, 714. Phillips, R., Vastola, F. J. and Walker, P. L. Jr, Carbon, 1969, 7, 479. Rakszawski, J. F. and Parker, W. E., Carbon, 1964, 2, 53. Silva, I. F. and Lobo, L. S., Journal of Catalysis, 1990, 126, 489. Walker, P. L. Jr, Rusinko, F. Jr and Austin, L. G., Advances in Catalysis, 1959, 11, 133. Cheng, A. and Harriot, P., Carbon, 1986, 24, 143. Neeft, J. P. A., Ph.D. thesis, Delft University of Technology, 1995. Bhatia, S. K. and Perlmutter, D. D., AIChE Journal, 1980, 26, 379. Ishiguro, T., Suzuki, N., Fujitani, Y. and Morimoto, H., Combustion and Flame, 1991, 85, 1. Miyamoto, N., Hou, Z. and Ogawa, H., SAE Paper 881224, 1988. Smith, I. W., Fuel, 1978, 57, 409. Essenhigh, R. H., in Chemistry of Coal Utilization, Second Supplementary Volume, ed. M. A. Elliott. WileyInterscience, New York, 1981, p. 1153. Neeft, J. P. A., Kapteijn, F. and Moulijn, J. A. (in preparation). Smith, J. M., Chemical Engineering Kinetics. McGraw-Hill, New York, 1956.