2540
I n d . E n g . Chem. Res. 1994,33, 2540-2553
Validation and Updating of Detailed Kinetic Mechanisms: The Case of Ethane Oxidation Renato Rota,' Francesca Bonini, Albert0 ServidaJ Massimo Morbidelli, and Sergio CarrA Politecnico di Milano, Dip. di Chimica Fisica Applicata, via Mancinelli 7, 20131 Milano, Italy
We have investigated experimentally the oxidation of ethane in a perfectly stirred reactor in the temperature range 870-1080 K and for fuel-air stoichiometric ratio ranging from 0.25 to 1.27. The concentrations of the main molecular species have been measured by probe sampling and GC analysis. These experimental results have been compared with predictions of three popular detailed kinetic mechanisms previously presented in the literature. A reasonable agreement between the experimental results and the model predictions has been found for almost all the species and the mechanisms. The only relevant exception is acetylene, which is greatly overpredicted by one of the mechanisms for all the investigated conditions. Parametric sensitivity analysis has been used for updating such a mechanism in order to improve the agreement with our experimental observations.
+fuel+N,
Introduction Detailed kinetic models, based on complex mechanisms involving only elementary reactions, are increasingly used to simulate combustion processes. The main advantage of this approach versus the simpler empirical mechanisms is its wider operating window (Westbrook and Dryer, 1984). In other words, while the empirical mechanisms can be used only inside the range of operating parameters (temperature, pressure, inert concentration, and stoichiometric ratio) investigated for their tuning, the detailed ones attempt to describe the kinetics of combustion processes almost everywhere. Moreover, only detailed models provide an estimate of concentrations of the radical species involved in the combustion processes. These are needed to simulate the kinetics of the oxidation reactions to whom molecules not directly involved in combustion may take part. Examples include Nz, "3, NO, and others, which are of interest in environmental studies. Thus, detailed kinetic modeling represents an important tool for the analysis and design of combustion and related systems (Miller and Fisk, 1987). In practice, a detailed kinetic scheme consists of all possible elementary reactions between the various chemical species which arise during the oxidation process of a given fuel. Typically, a detailed kinetic scheme involves a few hundred elementary reactions, and thus, several hundred kinetic parameters. This is true not only for complex fuels, but also for the simple case of light hydrocarbon combustion. The large number of model parameters on one side, and the limited amount of experimental available observations on the other side, prevent a statistically robust evaluation of the kinetic parameters. The estimation of all the involved parameters cannot be achieved by a mere fitting of the available experimental data because such a procedure would lead to infinite solutions (Edelson and Allara, 1973). Experimental as well as theoretical procedures capable of estimating the kinetic parameters for a single elementary reaction are known, but they are rather
* To whom correspondence should be addressed. E-mail:
[email protected]. + Current address: Universita degli Stud di Genova, Istituto di Chimica Industriale, corso Europa 30, 16132 Genova, Italy. 0888-5885/94/2633-2540$04.50/0
capillary tube
air diluting N2
coil
injector
nozzle
probe port
Figure 1. Sketch of the perfectly stirred reactor (PSR).
expensive and time consuming. Thus, in the detailed models reported in literature, the kinetic parameters of many reactions are estimated on the basis of known parameters for similar reactions or even guessed in order t o reproduce the main experimental findings in different operating conditions (Miller and Bowman, 1989). It is worth pointing out that the validation of a detailed mechanism cannot be based only on the comparison with a single set of experiments, because different reactions may prevail when different operating conditions are applied. Consequently, each reaction scheme should be reexamined whenever new experimental or theoretical results become available (Dagaut et al., 1991). In principle, this procedure would eventually lead to the different detailed oxidation schemes, available for a specific fuel, to collapse in a single and comprehensive detailed kinetic model (Ranzi et al., 1993). For this, it would be very helpful to use experimental measurements of the reacting mixtures in terms not only of the molecular but also of the radical species. However, the in situ measurement of radical concentra-
0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2541 fuel air NZ
Figure 2. Schematic of the experimental apparatus.
tions is rather difficult, and thus, this information is still lacking in the literature. In this work, the kinetics of ethane combustion is investigated. Ethane has been chosen as it is frequently found as an oxidation intermediate of both higher hydrocarbons and methane (Dagaut et al., 1991). Thus, due to the hierarchic structure of the hydrocarbon oxidation kinetic mechanisms (Warnatz, 19831, the knowledge of the reaction mechanism of ethane is essential for any hydrocarbon oxidation study. The main aim of this work is to compare the predictions of three detailed kinetic schemes proposed in the literature (Miller and Bowman, 1989; Dagaut et al., 1991; Kilpinen et al., 1992) in the light of the new experimental runs we have performed in a perfectly stirred reactor (PSR). We have investigated a wide range of temperature (from 870 K up to 1080 K) and stoichiometric ratios (0.25 < < 1.271, keeping an atmospheric pressure and very diluted conditions ( Y N ~ > 97%). The new experimental data were compared with the predictions of a PSR model using the three kinetic mechanisms mentioned above.
Experimental Apparatus Various laboratory set ups have been developed for kinetic studies of combustion systems. The PSR configuration is often preferred since it provides direct measurements of the rate of formation or depletion of the involved chemical species. These data are not affected by fluid dynamics, provided that the characteristic time for mixing is smaller than that of chemical reactions (Miller and Fisk, 1987). In this work, a PSR similar to that developed by Dagaut et al. (1986) was designed and built. The reactor, depicted in Figure 1, is a 40 mm diameter sphere, made of silica t o minimize wall catalytic reactions. Fast mixing was achieved by introducing the reactants through four nozzles 1mm in diameter lying on the equatorial plane. In Figure 1the arrows indicate the directions of the four high-momentum jets coming from such nozzles which provide the desired mixing of gases inside the reactor. Preliminary tests confirmed the results discussed by Dagaut et al. (1986),indicating that macromixing and micromixing are good for our experimental conditions. As shown in Figure 2, the reactor was located inside an oven, which maintained the reaction temperature at the desired value. Due to the high dilution conditions adopted, the heat released by the combustion reaction was in fact negligible. The diluting gas (nitrogen) was fed through a preheating coil where it was heated at the desired reaction temperature before entering the reactor (see Figure 1). The fuel, properly diluted with
Table 1. Preliminary Experimental Runs for Assessing the Reliability of the Experimental Apparatus run
TIKI
rt,
TI T"
885
15
923
1.5
T3 T4 T5
975
1.5
1028
15 1.5
1080
IC~H~llppmvJ 1570 1570 1570 I570 I570
IOzllppmvl
3600 360U
3600 3tioo :jtioo
cold nitrogen, was fed through a capillary tube in order to reduce its residence time In the hot zone outside the reactor, thus minimizing the fuel pyrolysis. For the same reason, the capillary tube was jacketed by the admission tube of the cold air, as shown in Figure 1. Reactants and diluting nitrogen were mixed at the entrance ofthe injectors, whose residence time, r,",, w a s negliqble with respect to the residence time inside the Also, the fuel flow rate in the reactor, T (r8& = capillary was a small fraction ofthe global feed flow rate so that the temperature of the stream entering the reactor was rather close to the desired reacting temperature. Exhausts left the reactor through four holes in the upper part of the sphere. The entire experimental apparatus, illustrated in F i p r e 2, consisted of three main sections. In the first one, the flow rates of the reactants (ethane, air, and diluting nitrogen, were measured and regulated thrnugh mass-flow controllers, which allow for various mixture compositions to be prepared. The second section contained the well-stirred reactor enclosed in the oven, as described earlier. The temperature of the gases inside the reactor was measured by a chromel-alumel thermocouple. Since the temperature of the surroundings is higher than that inside the reactor, the measurements were corrected for radiant heat exchange effects (Hayhurst and Kittelson, 1977). The third and last section of the apparatus was devoted to sampling and analyzing of the products of the reaction. Small amounts of the gases inside the reactor were sampled by a sonic quartz probe jacketed with cooling water, as shown in Figure 2. Sonic conditions at the orifice of the probe (about 40 pm in diameter, were maintained by a leak-free membrane vacuum pump. The residual pressure in the probe was about 10 mbar. Such a low pressure, along with the fast cooling rates of the gases provlded by the external jacket, is able to freeze the composition of the sampled gases (Malte and Kramlic, 1980; Bertacchi et al., 1990,. These were fed, through a sampling valve, to a single column (Carbosieve S-11, gas chromatograph. equipped with TCD and FID connected in series. Helium was used as a carrier gas. This analytical device was able to separate and measure the main stable chemical molecular species involved in the ethane combustion, that is 0 2 , CO, C02, Hz, CHI, CzHz, G H I , and CzHs. We have estimated an error upper bound
il*ou
2542 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 1500
0
.
n
1
,a
s? 500
8
0
1000
800
1200
50
20 10
0 800
1000
1200
800
loo0
1200
T (K)
*
800 -
0
0
n
h
2 V
0,
400200 -
01
800
>
* .
600-
:
O;
'
1000
1
1
1200
T (K)
V
: i m
0
800
loo0
.
1200
T (K)
Figure 3. Comparison between the results of experiments performed in the same conditions (reported in Table 1): (0)this work
(*)
Dagaut et al. (1991).
for the concentration measurements of about 3% for all the species. In order t o assess the reliability of the experimental apparatus, few experiments performed previously by Dagaut et al. (1991) were repeated using the same operating conditions, as reported in Table 1. The results of this comparison are summarized in Figure 3 where the concentrations of the measured species are shown as a function of temperature. The agreement between the two sets of experimental data provides an indication of the level of reproducibility which can be achieved for this type of experiments in different laboratories. It is worth noting that, for all these runs, as well as for all the others discussed in the following, the overall atomic balance of the carbon has been found accurate within 8%. We have also checked the reproducibility of a typical experimental run and found that the changes in the composition of the outlet stream are again within 5%.
The experimental runs performed in this work, covering a wide range of stoichiometric ratio and temperature values, are summarized in Table 2. All the experiments have been performed with a residence time in the reactor o f t = 0.1 s, while maintaining constant the concentration of ethane in the feed and equal to about 2100 ppmv. A small amount of C02 (about 100 ppm) was also present in the feed as an impurity. The same
table reports the results of all the experiments in terms of the concentration values of the measured species in the outlet stream. It is worth noting that, since we have worked in diluted conditions, the rate of production for the measured species (i.e., i = H2, CO, C02, CH4, C2H2, C2H4, C2H6, and 0 2 ) can be obtained from the concentration values, yi, reported in Table 2 as follows:
Data of this type, which constitute direct measurements of the rate of production, are the most convenient ones for validating kinetic models.
Mathematical Modeling The reactor model is constituted of the usual steadystate material balances for each chemical species. The energy balance equation has been disregarded because all the experiments have been carried out isothermally. In particular, we have used the computer code PSR (Glarborg et al., 19901, based on the CHEMKIN subroutine library (Kee et al., 1989), to solve the system of N , nonlinear algebraic equations:
QCi - Q°Cio- riV = 0 (2) Three different reaction schemes have been investi-
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2543 Table 2. Experimental Results and Operating Conditions
Table 4. Percentage Errors between Experimental Data and Model Predictionso
concentration (ppmv) r ~ n
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
T(K) Hz
1.27 873 925 978 1030 1079 1.00 873 925 978 1030 1079 0.75 873 925 978 1030 1079 0.52 873 925 978 1030 1079 0.25 873 925 978 1030 1079
0 0 368 1002 1562 0 0 405 1054 1208 0 0 403 868 461 0 0 334 454 284 0 0 220 235 0
0 2
CO
COS CHd CzHz CzHr CZH6
6019 6088 5941 5272 4283 7548 7550 7318 6563 4539 9978 10223 9799 8114 5296 14554 14711 14215 11319 9077 29923 29831 28948 26183 23372
0 0 95 684 1641 0 0 151 998 2017 0 0 246 1356 1312 0 0 320 1411 1246 0 0 721 1516 1445
42 0 65 0 56 23 95 94 253 170 78 1 82 1 166 27 157 107 613 132 56 2 73 1 104 34 357 94 1907 54 47 0 81 1 70 35 1261 51 2421 43 104 0 83 0 228 38 1492 45 2642 25
0 0 0 15 43 0 0 2 15 29 0 0 2 13 15 1 0 2 6 9 0 0 2 2 4
0 0 559 1018 913 3 32 579 955 637 0 45 659 718 381 0 28 670 478 302 1 9 560 377 126
2194 2208 1598 817 345 2150 2163 1519 695 238 2096 2052 1357 488 148 2182 2158 1415 319 111 2097 2096 1057 169 25
species H2 0 2 CO COZ CH4 CzH2 CZ% CzH6 av DCB 37 8 36 51 47 3 42 32 32 MB 52 26 94 147 79 77 61 57 74 31 14 32 62 65 1898 51 KGH 36 273 modifiedKGH 39 15 39 64 44 398 65 37 87 mechanism
z
For the ith species, cl = EfZ[ylerpfk - ealcpkl/y:rpC x 100/Nm, (only for ylexPht 0). Average error, e = El=l e,/N,.
was incorporated in the scheme since it plays an important role in the methane oxidation process. The nitrogen chemistry was described through a subset of 79 reactions involving 18 nitrogen compounds. In particular, the HCN mechanism was developed from HCN doped hydrogen flames, while the subset of reactions representing the conversion of NH, to NO and N2 was deduced from ammonia flame experiments. Moreover, the MB and the KGH mechanisms have been compared with experimental data concerning ignition and oxidation of methane, as well as a number of NO abatement techniques (Thermal DeNOx, RapreNOx, and Reburning processes). Finally, note that for all the kinetic models examined, the forward reaction rate constants have been computed through the modified Arrhenius expression:
Table 3. Number of Elementary Reactions and Chemical Species Considered in Each Detailed Kinetic Model mechanism MB DCB KGH
reactions 235 200 225
species 51 42 50
gated: (1) the mechanism proposed by Miller and Bowman (1989) (MB mechanism), (2) the one proposed by Dagaut et al. (1991) (DCB mechanism), and (3) the scheme by Kilpinen et al. (1992) (KGH mechanism). These detailed kinetic mechanisms involve few hundreds of reactions and several chemical species, as reported in detail in Table 3. The DCB mechanism was originally validated by comparison with experimental data obtained in a PSR operated at high dilution conditions. These included the combustion of methane (2' = 900-1300 K P = 1-10 atm; CP = 0.1-1.5) and ethane (7'= 800-1200 K P = 1-10 atm; CP = 0.1-1.5). Moreover, measurements of the ignition delay time behind a reflected shock wave of the mixture CzHdOdAr (7'= 1200-1700 K, P = 2-10 atm; CP = 0.5-2) and of the concentrations of H and 0 radicals behind a reflected shock wave of the same mixture (7'= 1430-1755 K, P = 2 atm; 10 ppm Of CzH6 and 2000 ppm of 0 2 ) were also used to validate this kinetic model. For a few reactions, not only the temperature but also the pressure dependence of the kinetic parameters was provided. In this kinetic model the nitrogen chemistry is not considered. Both the MB and the KGH mechanisms are updated versions of the same kinetic model originally developed by Glarborg et al. (1986). In particular, the more recent KGH mechanism includes many of the improvements proposed earlier in the MB scheme. The original mechanism (Glarborg et al., 1986), involving 213 reactions and 45 species was largely based on previous work of Miller and co-workers. The oxidation mechanism of methane was derived mainly from experiments involving acetylene and methane flames. The C2 chemistry
(3) The backward reaction rate constants have been computed from the forward ones using the equilibrium constant values obtained from the thermodynamic data base CHEMKIN (Kee et al., 1990),or from Burcat (1984) for species not included in this data base.
Results and Discussion
A comparison between the three detailed kinetic models discussed above and the experimental data obtained in this work is shown in Figures 4-8. The data are reported in terms of the outlet concentration of each examined chemical species, as a function of temperature, for five different values of the fuel-air stoichiometric ratio, CP. Due to the complexity of the combustion kinetics, a qualitative agreement between the experimental findings and the model predictions is an indication that the proposed mechanism is representative of the system, at least in the range of operating conditions considered. Thus, we first compare the results of the detailed kinetic models with the experimental data in terms of qualitative trends. From this point of view, it can be seen that while the computations made with the DCB scheme always agree with the experimental trends, the MB mechanism predicts a wrong behavior for a few species. For instance, it predicts for fuel-rich mixtures a maximum for the H2 and CH4 concentrations as a function of temperature, at about 1000 K. This behavior, which is instead characteristic of lean mixtures, is exhibited neither by the experiments nor by the other two models. About the KGH model: we may note that this reproduces rather well the experimental trends for all chemical species, except for C2H2. For all the fuel-air stoichiometric ratios here investigated, the model predictions are in fact rather far from the experimental observations for this species. This seems to suggest a lack in a welldefined portion of the KGH model, which is indeed
2544 Ind. Eng. Chem. Res., Vol. 33,No. 11,1994
600
900
la00
1100
T e)
T e,
'' ,, :
:
I
I
mL-Li 800
900
1000
,
200
100
, 0
...... .
,'
0
800
1100
900
la00
1100
T e) Figure 4. Runs 1-5 in Table 2 (0= 1.27). Experimental results (0) and model predictions: (- - -1 KGH mechanism.
related to the mechanism of production and consumption of acetylene. However, this is somehow surprising since both the KGH and the MB models are based on the kinetic mechanism proposed originally by Glarborg et al. (19861, and the MB does not exhibit this same deficiency. A quantitative comparison between modeling and experimental results is reported in Table 4, where the percentage errors between experimental data and model predictions are reported. These data refer only t o the concentration values in Table 2 not equal to zero for the three higher temperatures, since for the two lower values the production rates are negligible. The analysis of the results reported in Table 4 leads to conclusions similar t o those drawn earlier from the
(..*)
MB mechanism; (-) DCB mechanism;
qualitative comparison. A reasonable agreement between experimental results and model predictions is found for almost all the chemical species and the kinetic models. As it is also appearing from Figures 4 to 8, the DCB mechanism performs generally better than the other two. This is not surprising, since this is the only one which was developed by comparison with a set of experimental data which included the operating window investigated in this work. On the other hand, the MB model exhibits in general the largest percentage errors. The performance of the KGH model is comparable to that of the DCB model, except for the chemical species acetylene, whose concentration, as discussed above, is over predicted by about 1order of magnitude. However, this kinetic model has been originally validated by
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2645
800
900
loo0
1100
T (K)
:I
...-..-. ..
: .'I:
50
0 800
900
1000
.,
1100
800
900
loo0
1100
T (K)
800
900
loo0
1100
T (K) Figure 5. Runs 6-10 in Table 2 (a = 1.00). Legend as in Figure 4.
comparison with experiments covering a broader range of operating conditions than that used for the DCB model although not including those considered in this work. Therefore, it seems useful to further investigate this model in order to remove this anomalous behavior. For this, in the next section we the subset of elementary reactions in the KGH mechanism which is related to acetylene.
A Modified KGH Model There are two possible sources of error in the model which may justify the discrepancies between calculated and measured acetylene concentration values. The fist is related to some error in the values of the kinetic
parameters of one or more elementary reactions present in the KGH mechanism, which are important in determining the rate of production or consumption of acetylene, but not ofthe other involved chemic- species. The elementary reactions,which second is that one or strongly affect the acetylene concentration, are not included in the mechanism. The first possibility has been investigated by first identifying the elementary reactions in the KGH mechanism which are most important in determining the final concentration of acetylene. However, since the KGH n d e l Provides a good representation of all the other chemical species investigated, we should limit our analysis only to those reactions which do not affect the concentration of the
2546 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
600 400 200 800
900
lo00
1100
n3m1 B 2000 N
e_,l ,
lo00 0
800
1 0
.-' 900
1000
1100
100
60 40 .:..... .. \I8
20
800
900
lo00
1100
800
900
IO00
1100
T (K) Figure 6. Runs 11-15 in Table 2 (CJ= 0.72). Legend as in Figure 4. other species. For this we have used the parametric sensitivity analysis, which is a powerful tool for deriving this information in a systematic way (Frenklach, 1984). Among the various approaches to the sensitivity analysis (cf. Rabitz et al., 19831, we have used a firstorder local method. It is based on the evaluation of the relative sensitivity coefficients for the isothermal PSR model, which in general terms can be recast in the form:
F(qNa),d= 0
(4)
where F is the vector representing the mass balance of all the involved chemical species, q is the vector of the state variables (i.e., the concentrations of the chemical species, ~y = (CI, ..., CN.)T),and a is a set of parameters of the model (e.g., the pre-exponential factors, Aj). The
aforementioned PSR program (Glarborg et al., 1990) allows also for the evaluation of the first-order sensitivity coefficients: a l n q i - alnCi s..= -a l n aj a l n A j which represents the relative sensitivity of the outlet concentration of the ith species, Ci,to changes in the pre-exponential factor of the j t h reaction, Aj. In order to identify the subset of reactions which is most important in determining the CzH2 concentration, but not that of the other involved chemical species, a two-step procedure has been used. First, for each experimental run, the most important reactions have
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2547
1 -1.6 f
0.6
800
900
lo00
1100
T (K)
g: 2000
W
H
1000 800
900
lo00
1100
800
900
1000
1100
T 6) 100
l
o
o
m /I,,
40 860
O
k
I
l
40 20
8
I I
,
I
bo
\
:
20
900
loo0
1100
0
800
900
loo0
1100
800
900
lo00
1100
T (K) Figure 7. Runs 16-20 in Table 2 (0= 0.52). Legend as in Figure 4.
been extracted by selecting, for a given species i, the reactions j for which:
IS,I
L
0.1 max(IS,l, f o r j = 1,N,)
(6)
In other words, for the given ith species, we select all reactions exhibiting a value of the sensitivity coefficient which is larger than a given fraction, say lo%, of the maximum one. By this procedure the most important reactions, with respect to each of the eight measured species, have been identified for each experimental run. The second step consists in the selection of the reactions influencing principally the CzH2 concentration. These reactions have been identified, for each experiment, by
the following condition:
IS,
2
Zj
I 2 2lS,I, f o r i * C,H,
(7)
that is, only the reactions with a sensitivity coefficient with respect to acetylene which is at least double of that related to any other species have been selected. It has been found that the developed procedure provides for each examined experimental run a similar set of critical reactions. This shows that the adopted extraction criterion is rather general and leads to results which do not depend on the operating conditions. The most important or critical reactions as extracted over the wide range of operating conditions investigated in
2548 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
2.2
-
1
800
3000
ii g 2000
900
1100
lo00
T (K)
o . ..# :
I
:, :.., , :, :4 :: ,, :
N
I
:,
1000
: I
:; $1
800
900
1000
0 800
1100
900
1000
1100
T cx)
7
lSO
20 10
800
-
800
900
1000
1100
2000
I
t,,
T 6) Figure 8. Runs 21-25 in Table 2 (@ = 0.25). Legend as in Figure 4.
this work are
O+OH-"0, C,H,
+ OH - CH,O + CH,
(8)
(9)
The kinetic parameters for reaction 8 are well-established, and the values reported by the NIST Chemical Kinetics Database (1993) are in good agreement with those used in the KGH mechanism. On the contrary, the kinetics of reaction 9 is as yet not well-known, as indicated by the kinetic data available in the literature which are scattered within a relatively wide range. This is clearly illustrated in Figure 9 where the values of the rate constant of reaction 9 as reported by various literature sources are shown as a function of tempera-
ture. Unfortunately, changing the value of this kinetic parameter within the uncertainty range indicated in Figure 9 does not lead to any significant improvement. Good predictions for the acetylene concentration could be obtained only for a much larger change of the kinetic parameters of reaction 9. However, this results in a worsening of the model predictions for ethylene. Thus, we can conclude that the desired improvement of the kinetic model KGH cannot be obtained by merely changing the value of the kinetic parameters of reaction 9. We have next considered the second possible source of error mentioned above, i.e., that some important elementary reaction was not included in the original kinetic model. For this we have investigated the
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2649
1014
I
1
I
I
1
1
I
I
1200
1300
I
lol i 1°'i
109 I 500
I
1
1
1
I
I
600
700
800
900
loo0
1100
1
I
1400
I 1500
Figure 9. Comparison among the rate constant values for reaction 9 reported by various literature sources as a function of temperature.
-
e..)
(- - -) Coffee, 1984; Westbrook and Dryer, 1984; (-) Glarborg et al., 1986 (- -) Thorne et al., 1986 (- 0 -) Basevich, 1987; (- * -) Dagaut et al., 1988a; (- + -1 Kilpinen et al., 1992; (***) this work.
differences between the reaction subsets affecting the acetylene concentration in the three different kinetic schemes (MB, DCB, and KGH). Dagaut et al. (1991) found that in the framework of the DCB model, and for experimental conditions close to those investigated here, the formation and consumption of acetylene is mainly due to the following reactions:
+H C,H, + 0 -.CH, + CO C,H, + 0 HCCO + H C,H, + 0, - HCCO + OH C,H3 + 0, - CH,O + HCO CzH3
-+
CZH,
+
(10) (11) (12)
(13) (14)
The first three reactions above are also included in the KGH model, but with different values of the kinetic parameters. However, the values used in the KGH model lead to acetylene consumption rates equal to or larger than those computed using the DCB parameter values. Thus, these differences cannot account for the wrong behavior of the KGH model which, as discussed above, always overestimates the acetylene concentration in the reactor outlet. Reactions 13 and 14 are not included in the KGH mechanism, even though they were considered in both the original compilation by Glarborg et al. (1986) and in the MB model. Through some model simulations, we have seen that, at least in the range of operating conditions considered in this work, the effect of reaction 13 is rather small, while the introduction of reaction
14 is able to modify significantly the KGH model predictions. This latter result is not really surprising, since the oxidation reaction of the radical C2& has been shown to play a significant role in many different circumstances (cf. Thorne et al., 1986; Dagaut et al., 1988b; Dagaut et al., 1991). In our case, reaction 14 has a strong effect on the product rate of acetylene because it competes with reaction 10, which is one of the main sources of acetylene. We are now in the position of proposing a modified version of the KGH model (hereafter referred to as modified KGH mechanism, MKGH), which provides an improved interpretation of the experimental data discussed above. This is identical to the original KGH model with the exception of reactions 9 and 14. While for the second reaction the kinetic parameters reported by Slagle et al. (1984) were used (i.e., A = 3.2 x lo1, cm3/mol s, ,8 = 0, E = -350 cal/mol), for the first one the following kinetic parameters were found to give the best results: A = 2.5 x 1013cm3/mol s, ,8 = 0.0, and E = 1500 cal/mol. Note that these values are rather close to those reported by Coffee (1984) and lay inside the range of uncertainty as shown in Figure 9. From the comparison reported in Figure 10, it is seen that the agreement between the experimental outlet acetylene concentration values and those calculated through the MKGH model is definitely improved. Moreover, the predictions of the MKGH model for the other species are substantially the same as those of the original KGH model, as it can be seen from the percentage error values summarized in Table 4. Also, the performance of the MKGH model is similar t o that of the DCB one for these species. It may be noted that the percentage error for acetyl-
2650 Ind. Eng. Chem. Res., Vol. 33,No. 11, 1994 0 =1.00
1 :,A
60 8 1
J
40
1
, ,
20
,
I
#
0 800
0
900
1000
'0
1100
T (K) 150
0 4.25
T (K) Figure 10. Comparison between the values of the outlet acetylene concentration measured experimentally (O), and those predicted by the KGH (- - -) and the modified KGH (-1 model.
ene exhibited by the MKGH model, as shown in Table 4, remains much larger than that exhibited by the DCB, or the MB, model. This is a somehow fictitious result, which arises because the experimental C2H2 concentration values are lower than those of all the other species, and often are rather close to zero. Thus, small absolute differences between experimental and calculated values of the C2H2 concentration can lead to a large percentage error, defined as N,,
In particular, this is true when the predicted values are larger than those measured experimentally, as it is the case for the MKGH model. On the other hand, since the DCB and MB models underpredict the C2H2 concentration values, the corresponding percentage errors are upper bounded by loo%, regardless of the absolute value of the experimental measurements. This leads to percentage errors much lower for these models than for the MKGH model. Finally, we tested the MKGH model by comparison with experimental data obtained in conditions similar
to those where the original KGH model was tuned, which differ significantly from those developed in this work. In particular, we considered two sets of experimental data: the first one by Chen and Malte (1984) for the species NO, HCN, and NH3 produced from the combustion of methane doped with 5000 ppm of NO in a jet stirred reactor. The operating conditions were z = 9.0 ms, T = 1800 K, and P = 1 atm. The second set of experimental data was obtained by Singh et al. (1979) and involves the species CO, COz, and H20, producec' from the combustionof methane in a jet stirred. In tim case, the operating conditions investigated were as follows: z = 3 ms, T = 1879 K, and P = 0.92 atm. The main differences between the operating conditions of these two sets of data and those used in this work refer both to the temperature (1800-1900 against 900-1100 K) and to the concentration of the diluting gas (no dilution for these data, more than 97% of Nz in this work). In Figures 11and 12 the predictions of the KGH and MKGH models are compared with the two sets of experimental data, respectively. It appears that for these conditions the original and the modified KGH models exhibit rather similar performances. No substantial differences have been found between the two models. Thus, the modified KGH model may be used
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2551
4500 4000 3500
' 5 d
3000
2500
0
.r( c.)
g8
8
2000 1500 1000 500
0 StoichiometricRatio Figure 11. Comparison between experimental results and model predictions. Experimental data: (0) NO, (*) HCN, (+) NH3 (Chen and Malte, 1984);(-1 KGH kinetic model; (- - -) MKGH kinetic model.
-I
+
3
$
+
+
0.18
0.120.1 -
Q)
&
3
0.08-
*
*
*
StoichiometricRatio Figure 12. Comparison between experimental results and model predictions. Experimental data: (0) CO, (*) COz, (+) HzO (Singh et al., 1979); (-) KGH kinetic model; (- -) MKGH kinetic model.
-
with confidence for all the operating conditions where the original KGH can be used and, in addition, provides
a better representation of the acetylene formation in the operating conditions investigated in this work.
2552 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
Conclusions The oxidation of ethane has been investigated experimentally in a perfectly stirred reactor, operated at highly diluted conditions, in a wide range of temperature and fuel-air stoichiometric ratio values. The concentrations of the main molecular species in the outlet stream have been measured by probe sampling and GC analysis. The reliability of the experimental apparatus has been assessed by performing several preliminary tests for mixing and by comparing the results with experimental data available in the literature for similar conditions. The experimental results obtained in this work have been used to confirm the predictions of three detailed kinetic models (MB, DCB, and KGH) previously presented in the literature. A reasonable agreement between the experimental results and the model predictions has been found for almost all the species and the models. However, some inaccuracy in representing the experimental trends has been evidenced for the MB model. This leads to the conclusion that the DCB and the KGH models provide a better interpretation of the obtained experimental data. The only relevant exception is the acetylene concentration, which is greatly overpredicted by the KGH mechanism for all the operating conditions investigated. The parametric sensitivity analysis, and a comparison with other detailed mechanisms, suggested the introduction of a new reaction, accounting for the direct oxidation of the radical C2H3, and a small change in the kinetic parameters of another reaction in the original KGH mechanism. The modified mechanism has been able to reproduce reasonably well the C2Hz concentration, without worsening the predictions of all the other species. We have also verified that the changes introduced in the KGH model do not affect their predictions within the operating window used for tuning the original model. Thus, the developed modified KGH model provides a tool for simulating the ethane oxidation process in a rather wide range of operating conditions. In this regard this model is superior to the DCB model, which provides similar performances in the range of experimental conditions investigated in this work but cannot be applied to situations involving for example the nitrogen oxides formation (e.g., the data by Chen and Malte, 19821, where instead the MKGH model provides equally good predictions.
Acknowledgment This study has been supported by CRTN-ENEL, Pisa, Italy (Contract No. U117). Nomenclature A = pre-exponential factor, cm3,mol, s, K C = concentration, mol/cm3 E = activation energy, cal/mol F = generic function K = reaction rate constant, cm3, mol, s N,= number of reaction N,= number of chemical species N,, = number of experiments Q = volumetric flowrate entering the reactor, cm3/s r = production rate, mol/cm3s or ppmv/s R = ideal gas constant S i = first order sensitivity coefficient T = temperature, K V = reactor volume, cm3 y = mole fraction, ppmv or %
Greek Letters
a = parameter vector 8, = temperature exponent = percentage error CP = stoichiometric ratio, (Fuel/Oz)/(FueYOz)stoi,h )t = state variable vector t = residence time, s E
Subscripts and Superscripts
calc = calculated exp = experimental i = species inj = injector j = reaction k = experiment o = inlet
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Received for review March 31, 1994 Accepted August 1, 1994@ @
Abstract published in Advance ACS Abstracts, October 1,
1994.
