Environ. Sci. Techno/. 1995, 29, 1336- 1345
Uncertainties in Incremental Reactivities of Volatile Organic YUEH-JIUN Y A N G , + W I L L I A M R . S T O C K W E L L , * AND J A N A B . MILFORD*,§ Environmental Research Institute, Department of Civil Engineering, University of Connecticut, Storrs, Connecticut 06269, Fraunhofer Institute for Atmospheric Environmental Research (IFU), 82467 Garmisch-Partenkirchen, Germany, Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309
Uncertainties in the rate parameters of a gas-phase chemical mechanism have been propagated through simulations of urban ozone formation to estimate uncertainties in calculated incremental reactivities of selected organic compounds. Incremental reactivities were defined as the sensitivity of the predicted ozone concentration to the initial concentration of each organic compound in a mixture. Uncertainties (la)in the reactivities ranged across compounds from about 30% to about 70% of mean estimates. Uncertainties in the rate constants of the reactions NO 03; NO2, 03, and HCHO photolysis; O’D H20; “03 formation; and PAN chemistry were found to be influential. For the reactivities of most compounds, rate constants of their primary oxidation steps were also influential. Because rate parameter uncertainties have directionally similar effects on the reactivities of most compounds, the significance of the uncertainties could be minimized by using reactivities in a relative sense.
+
+
Introduction The fact that individual organic compounds differ in the degree to which they contribute to photochemical air pollution has long been recognized (1). Nevertheless, until recently emissions of reactive organic gases (ROG) have been regulated in the United States on the basis of total mass (excluding methane), ignoring the composition of the emissions. This situation is changing due to interest in reformulated gasoline and alternative fuels that could reduce the “reactivity” of ROG emissions from motor vehicles (2). However, accounting for reactivity requires a more detailed understanding of atmospheric chemistrythan is needed for regulations based on total mass. As a step toward assessing whether the current understanding is adequate to support reactivity-based regulations, we have quantified the influence of uncertainties in chemical rate parameters on calculated reactivities. Specifically,we focus on “maximum incremental reactivities” as used by the California Air Resources Board (CARB) in their motor vehicle exhaust regulations. In 1990, CARB adopted regulations that included applying areactivity adjustment factor (RAF) to ROG emissions limits for vehicle exhaust. To calculate a RAF, the mass fraction of each organic compound in the exhaust associated with a particular fuellvehicle combination is weighted by its reactivity towards O3formation. The weighted emissions of the test fuel are then normalized by the reactivityweighted emissions of a baseline gasoline. As an example, the RAF for vehicles fueled with M85 (85%methanol and 15% gasoline) is 0.41 (3), so the emissions limit for ROG exhaust from M85-fueledvehicles is about 2.4 times greater (by mass) than the standard for vehicles fueled with conventional gasoline. Avariety of reactivity scaleshave been devised to quanUfy the degree to which different organic compounds affect ozone formation (4-6). The approach CARB has adopted follows the definition of the incremental reactivity of compound j (IRJ given by Carter and Atkinson (6): R(HCj
IRj = lim AH,*
+ AHC,) - R(HCj) (1)
AHCj
where RCHCj) is the maximum value of ([031 - [NO]) calculated in a base case simulation and R(HC, AHCj) is the maximum value of ([O,] - [NO])calculated in a second simulation in which AHCj, a small amount of organic compound j , has been added. IR calculations for CARB were performed with a single-cell trajectory model employing the SAPRC9O chemical mechanism (7). Previous studies of IR scales have shown that they depend on the conditions simulated as well as the reaction mechanism used in the calculations (8-13). Carter (13) has discussed a variety of approaches for defining generalized reactivity scales. The scales considered in this analysis are the maximum incremental reactivity (MIR)scale, which is calculated for conditions that maximize the overall
+
* Author to whom correspondence should be addressed. + University of Connecticut. + Fraunhofer Institute for Atmospheric Environmental Research. 4 University of Colorado.
1336 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 5,1995
0013-936)(/95/0929-1336$09.00/0
%, 1995 American Chemical Society
TABLE 1
Simulation Codiions for MIR and MOM Cases latitude declination time mixing height photolysis height
species NO2 (MIR) NO (MIR) HONO (MIR) NO2 (MOIR) NO (MOIR) HONO (MOIR) 03
co c02c
Hzo methaneC isoprene
36.22" N 16.5" 8 a m t o 6 pm 293-1823 m 640 m
initial 3.62 x 1.09 x 2-95 2.42 x 7.25 x 1.97 0 2.03 3.30 x 1.99 1.79 1.00
Initial and Aloft Concentrations (ppm) for Base Mixtureb aloft species
loT2 10-1 10-3 10-3
10+4 10-4
0 0 0 0 0 0 7.04 x 2.03 3.30 x 1.99 10+4 1.79 0
296-305" K 15.38 mmol m-2 day-' 3.84 mmol m-2 day-' 2.57 mmol m-2 day-'
temp total HCa total NO,(for MIRP total NO,(for MOIRP
a-pinene Ethene HCHO CCHOd RCHOe benzaldehyde unknown AAR1' AAR2' AARBf
OLElg OLE2g
initial 1.00 1.01 x 6.48 3.90 2-30 1-34 1.00 4.10 x 4.33 x 1.68 x 8.85 1.14 x
10-4 10-2
10-3 10-3 10-3 10-4 10-4 10-2
10-3
aloft
0 4.67 x 2.25 3.23 0 0 0 3.69 x 1.16 1.08 x 8.09 x 1.09 x
10-4 10-3 10-4
10-3 10-3 10-4 10-5 10-4
a Initial concentrations plus total emissions. For incremental reactivity calculations, initial concentrations equal to 4.76 x ppm are added for each of 26 explicit organic compounds or classes. Constant concentration species. dAcetaldehyde. * Propionaldehyde and higher aldehydes. Lumped clasess of alkanes and aromatics. g Lumped classes of alkenes.
incremental reactivity of the base ROG mixture, and the maximum ozone incrementalreactivity (MOIR)scale, which is calculated for conditions that yield the maximum possible O3 concentration with the base ROG mixture. One question that has been raised about the use of IRs is whether the chemistry of organic compounds in polluted atmospheres is understood well enough to predict their relative air quality impacts. Errors in measured rate parameters and product yields lead to uncertainties in chemical mechanisms. More importantly, parameters of many reactions employed in chemical mechanisms have never been directly measured. Numerous reactions are included in mechanisms by analogywith known reactions. For many organic compounds, the rate constant for reaction with the HO radical is known much better than product yields and subsequent secondary chemistry. Additional uncertainties are introduced in the process of eliminating or combining reactions or chemical species to "condense" mechanisms for inclusion in photochemical models. Due to the potential significance of IRs, uncertainties in these values are of great interest. This paper Focuses on uncertainties in MIRs and MOIRs due to rate parameters in the SAPRC9O mechanism, quantifylng the uncertainties and identifyingthe rate parameters that contribute the most to them. Uncertainties in product yields and uncertainties associatedwith condensingmechanisms are not considered here, although the former are being evaluated in ongoing work. The effect on R A F S of uncertainties in rate parameters and in the composition of exhaust emissions from various fuelhehicle combinations is discussed in a separate paper (14).
Methodology The analysis of the innuence of rate parameter uncertainties on IRs employed two steps: using first-order uncertainty analysis to identify the most influential parameters and then treating these parameters as random variables in a Monte Carlo analysis. In the first-order analysis, local estimates of the sensitivity of key output species to each
parameter were calculated, and the resulting sensitivity coefficients combined with estimates of the uncertainty in the parameter values (15). For the Monte Carlo analysis, Latin hypercube sampling (16)was used to generate sets of rate parameter values, which were propagated through the IR calculations to produce probability distribution functions for the MIRs and MOIRs. The methods used are described in more detail below, following a description of the simulationconditions for which the IRs were calculated. California's regulations used average MIR values from 39 simulations, representing high-ozone cases in cities across the United States (13). For each case, MIR conditions were defined by first adjusting the amount of NO, input to the simulation to maximize the overall incremental reactivity of a base ROG mixture. It would have been computationally prohibitive to perform Monte Carlo calculations if we followed the fullIR calculation procedure for 39 sets of simulation conditions. Consequently, two approximations were made: first, IRs were estimated from a single set of simulation conditions (13) developed to yield results close to the average from the original 39 simulations. Second, IR values for all compounds were calculated from the same simulation, as the local sensitivity of the 0 3 concentration to the initial concentration of each organic compound in a mixture. The local sensitivity coefficients were calculated using the direct decoupled method (DDM; 17,181. The simulation conditions used in the analysis are shown in Table 1. The input ROGNO, ratios for the MIR and MOIR simulations were 5.8:1 and 8.0:1, respectively. On the basis of the first-order Taylor series expansion and assumingthe parameters are independent, an estimate of the contribution of uncertainty in the value of parameter pj to uncertainty in the predicted concentration of a product species is
where yi is the concentration of species i, and a,] represents VOL. 29, NO. 5, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
= 1337
the input parameter uncertainty. Ranking values of V, provides an indication ofwhich parameters contribute most to the overall uncertainty in the outputs. In this study, the DDM was used both to calculate sensitivities of key output species to rate parameters for the first-order uncertainty analysis and to estimate IRs as sensitivities to the initial concentrations of the organic compounds. On the basis of the first-order analysis and using the uncertainty estimates discussed below, 73 (out of 203 rate parameters in the mechanism) were identified as influential and then treated as random variables in the Monte Carlo analysis. Rate constants associated with the initial oxidation steps for all of the organic compounds of interest in the study were included in this set. For the MIR simulation conditions, these 7 3 rate parameters accounted for more than 98% of the total variance of the output concentrations of 0 3 , PAN, HCHO, HO, and H202. To reduce computational requirements in the Monte Carlo calculations, Latin hypercube sampling (LHS;16')was used to sample from the probability distributions of rate parameters. The optimal size of an LHS sample depends on balancing the cost of additional model runs against the accuracyrequired in the output distributions (19). With 73 rate parameters treated as random variables, we tested sample sizes of 100, 200, and 300 for convergence of the means and standard deviations of output probability distribution functions (20). The results presented below are for a sample size of 100. A LHS option that minimizes rank correlations between parameters was used to ensure that spurious pairwise correlationswould not be introduced. In order to identify the rate constants that have the most influence on incremental reactivities, linear multivariate regression analysis was performed on the IR values generated in the Monte Carlo calculations. This approach is valid because the responses to rate parameter variations are approximately linear within the range of variation. The equation
IR,
- = Boj
IRj
+ 1=1
ki1 By k,
(3)
where IR, is the IR value for compound j generated in simulation i; IR, is the nominal IR value of compoundj; Bo, is a constant coefficient; By is the regression coefficient corresponding to the Zth uncertain rate constant; kil is the value of the Zth rate constant used in simulation i; and kl is the nominal value of the Zth rate constant was fit to the Monte Carlo results using a least squares criterion. By replacing the sensitivitycoefficients in eq 2 with normalized regression coefficients, uncertainty contributions were estimated from the Monte Carlo results.
Estimates of Uncertainty in SAPRC Parameters Both the first-order and Monte Carlo analyses required uncertainty estimates for rate parameters in the SAPRC9O mechanism. These estimates were compiled by Stockwell et al. (15) from panel reviews published by NASA (21)and IUPAC (22), supplemented with additional reviews and some original estimates. From this compilation, estimates were made of the standard deviations for each rate constant at the simulation conditions used in the IR calculations. In most cases, the published uncertainty factors represent the subjective judgment of the reviewers rather than statistical 1338 ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, NO. 5. 1995
analysis of experimental results. The NASA and IUPAC panel estimates were interpreted as corresponding to & lo. However, in some of the independent reviews the definition of the uncertainties was not clear, so our subjective judgment was added to that of the reviewers. Where different sources were in conflict or definitions were unclear, we conservatively used the interpretation or assignment that would give the largest uncertainty. Finally, as a simplifyingassumption, all rate constants were treated as independent. The rate parameters listed in Table 2 were treated as log-normally distributed random variables in the Monte Carlo simulations. For the photolysis rates in the SAPRCSO mechanism, only uncertainties in the action spectra were considered, with actinic fluxes viewed as given. For the action spectra, uncertainties given by NASA were adopted as multiplicative factors, which were assumed to apply uniformly across wavelengths. NASA panel uncertainty factorswere available for most ofthe inorganic species,formaldehyde,and organic peroxide. For the more complex organic compounds, original assignments were made. Among all of the photolysis rates, the estimated uncertainties were lowest for 0 3 and NO2 and greatest for the unknown aromatic products (AFG1 and AFG2). For rate constants of second-order reactions, the NASA panels gave uncertainty factors at 298 K (f(298)) and estimates of uncertainty in the Arrhenius temperature coefficients (AB. From these values, the uncertainty of a second-order rate constant can be estimated as a function of temperature:
fln =A2981 expi-(AE 1 R T
-)I
1
298
(4)
where R is the ideal gas constant, The (lo)uncertainty of a thermal rate constant was estimated as:
If both NASA and IUPAC uncertainty estimates were available, they were compared after converting the IUPAC estimates to the NASA format, and the larger uncertainty estimate was adopted. For parameters of several thermal reactions for which NASA and IUPAC have not reported uncertainty estimates, other reviews (23-26) were used. For reactions determined by analogy, the uncertainty estimates of the root reactions were assigned. Of note, the uncertainty estimates assigned to parameters of the secondary chemistry of aromatics oxidation are highly subjective. The secondary reactions of aromatics are poorly understood. In practice, aromatic mechanisms have been developed as parameterizations of environmental chamber experiments. Since the resulting parameterizations are very sensitive to the aromatic rate parameters and fit the chamber data reasonably well, an operational view might suggest a lower level of uncertainty than indicated by the status of basic understanding. However, the chamber experiments have substantial limitations, so a good fit does not rule out the possibility of an invalid parameterization. For recombination (Troe) reactions, the NASA panel provides uncertainty estimates at 300 K for the lower pressure rate constant, k,,; for the high pressure rate constant, k,; and for the temperature dependence factors. Apparent second-order rate constants between the high
TABLE 2
Rate Constants Treated as Random Variables reaction
k (300K)'
Thermal Reactions 2.76 x IO+' 3.23 10+5 4.29 10+4 1.66 10+4 3.52 x 1.21 10+4 2.54 x 10+3 1.34 x lo-' 1.13 10+4 1.13 x 7.19 10+3 3.08 10+4 2.30 10+4 2.89 10+4 1.46 x 7.19 10+3 1.60 10+4 1.46 x 1.23 x 7.19 x 1.60 10+4 CzCO-02 ROz PPN 2.97 x HCHO HO 1-43 10+4 A A R l HO 2.76 10+3 AAR2 HO 8.80 10+3 9-67 10+4 1,3-butadiene HO 8.80 10+4 2-rn-I-butene HO 2-rn-2-butene HO 1.26 x I O f 5 3-rn-cyclopentene HO 9.62 10+4 1.46 10+5 isoprene HO benzene HO 1.89 x 8-67 10+3 toluene HO 1.04 x ethylbenzene HO 1,2,4-TMB HO 4.77 x 10+4 2.86 10+4 m p x y l e n e HO 2.01 10+4 o-xylene HO 1.70 10+3 MEK HO methanol HO 1.38 x 4.81 10+3 ethanol HO
+ NOO'D + H20 O'D + M HO + N02HO+COHOz + N O HOz + HOz HOz + HOz + Hz0 ROz + NOR02R + NO R02R + H02 NO2 + CRES CCHO + HO RCHO + HO CCO-02 + NO CCO-02 + HOz CCO-02 + RO2 CzCO-02 + NO C2CO-02 + NO2 CzCO-02 + HOz 0 3
+
4
+
4
4
4
4
+
-+ + + + + + + + + + + + + + + + + -
a
5.18 x 7.60 1.01 4.53 9.58 x 2-86 9.02 x 4.74 x 8.55 x 8.55 5.48 2.35 8-15 1.02 x 1.10 5-48 1.21 1.10 x 9.52 5.55 x 1.21 x 2.04 x 3.40 x 5.13 x 3.04 1.79 1.62 2.33 x 1.78 x 2.72 5.08 x 1.62 x 3.22 x 1.47 x 8.86 x 4.56 4.60 x 6.64 x 2.30
k (300K)'
reaction
la
IOo 10+4 10+4 10+3
lo+'
10+3 10-2 10+3 10+3 10+3 10+4 10+3 10+4 10+4 10+3 10'4 10+4 10+3 10+3 10+4 10+3 10+3 10+4 10+4 10+4 10+4 10+4 IOf2 10+3 10+4 10+3
lot2 10+3
---+ + + -. + + -
Thermal Reactions MTBE HO 4.17 x 10+3 ETBE HO 1.10 10+4 4.02 x ethane HO 3.76 10+3 butane HO 8.31 x 2-rnethylpentane HO 1.19 x 10+4 rn-cyclopentane HO 2,2,4-TMB HO 5.46 x 10+3 1-24 10+4 ethene HO 3.82 10+4 propene HO PAN 4.04 x ethene 03 2.75 x lo-' propene 0 3 1.74 x 2.20 x 10-2 isoprene 03 1,3-butadiene 0 3 1.16 x 2-rn-I-butene 03 1.85 x 2-rn-2-butene 0 3 6.33 x I O - ' 3.93 x lo-' 3-rn-cyclopentene 0 3
+ + + +
-+ + + + + + + +
- -.
CCO-02 NO2 AAR3 HO OLEl HO OLE2 HO OLEl 02OLE2 02
+ + + + +
--
Troe Reactions 1.23 3.59 3.19 x 9.69 1.72 x 2.34 x
10+4 10+4 10+4
IO-'
la 1.47 x 3.90 7.42 x 6.96 x 1.89 3.18 1.01 x 1.75 x 5.39 2.76 x 4.25 x 6.03 7.63 x 4.89 x 6.40 2.65 x 1.65 x
10+3 10+3
lo+'
10+3 10+3 10+3 10+3 10+3 10-3 10-3 10-3 10-3
lo-' IO-'
9.52 10+3 9.63 10+3 5.89 10+4 1.79 x 3.20 10-3 4.35 x 10-2
Photolysis Reactionsb
+ hv+ hv-NO2 + 0 0 3 + hv-O'D + 02 HCHO + hv 2H02 + 0 2 HCHO + h v - H2 + CO CCHO + hv RCHO + hv MEK + hv MGLY + hv AFGl + h v AFG2 + hv NO2 NO3
4
1.3 2.0 1.4 1.4 1.4 1.4 1.4 1.5 1.6 3.0 3.0
Nominal values of random variables, ppm min units as appropriate for the order of each reaction. bAction spectra uncertainty factors.
and low pressure limits are estimated using the Troe expression:
lt-
k,
To estimate uncertainties for IR simulation conditions, uncertainties for k 0 ( n and were estimated from the NASA formula, and then Monte Carlo calculations were performed to propagate uncertainties through the Troe expression. Independent log-normal distributions were assumed for the random variables gooand and normal distributions were assumed for n and m.
k(n
coo,
PAN and its analogs were all treated similarly. IUPAC evaluations were used to estimate the PAN formation and decomposition reaction uncertainties because they were not included in the NASA evaluation (21).A rather high uncertainty was assigned to the temperature dependence. Similar to the procedure for the inorganic Troe reactions, Monte Carlo calculations were performed to calculate the apparent second-order rate constant distribution for each k,,-k, pair.
Finally, uncertainty estimates were compiled for rate parameters of the primary reactions of 26 organic compoundsfor which IRs were to be estimated. The compounds selected included alkanes, alkenes, aromatics, and oxygenated species. Uncertainties for the reactions of HO radicals with most of the selected organics were based on the review of Atkinson (23),supplemented with original evaluations for several compounds. The AE assignments were chosen to be consistent with the uncertainties in similar reactions. Uncertainty assignmentsfor 03-alkenereactionswere taken from Atkinson and Carter (25). Original estimates of the uncertainty in AEvalues for these reactions were made for this study (15).
-
Overall, the most uncertain parameters (withol k 0.75 or greater at 300 K) in the SAPRC mechanism are estimated to be those associated with the reactions of the carbonyl products of aromatics oxidation (AFG1andAFG21, reactions between peroxy radicals, peroxy radical reactions with NO and NOa, and organic nitrate decomposition. Among the organic compounds of interest, relatively high uncertainties (olk 0.35-0.50) were assigned for the rate constants of the HO radical reactions of oxygenates (acetaldehyde, propionaldehyde, methanol, ethanol, ETBE, and MTBE)
-
VOL. 29, NO. 5, 1995 I ENVIRONMENTAL SCIENCE &TECHNOLOGY 1 1339
-
0.25
s
MIRcase
T
T
8
9
0.20
.B g
0.15
. YI
I
b
g
0.10,
s
8
0.05 ’
0.00 0
1
2
3
4
5
6
7
10
Time (hours) FIGURE 1. Concentration profiles of predicted ozone under MIR and MOIR conditions.
and for the reactions of alkenes (other than ethene) with 03.The remainder of the paper shows the effects of the rate parameter uncertainties on IR values.
TABLE 3
Uncertainty Apportionment of Average Ozone Concentrations
Results
reaction
As stated previously, 73 influential rate constants, identified by the first-order uncertainty analysis, were treated as random variables in Monte Carlo simulations. Figure 1 shows the resulting uncertainties (la) in time-varying O3 concentrations predicted for the MIR and MOIR conditions. Somewhat higher uncertainty in predicted O3 is seen for the MIR scenario than for the MOIR scenario, which end with respective uncertainties of 30%and 20% compared to the means from the two sets of simulations. Ozone exhibits higher sensitivityto the perturbation of most rate constants at the lower ROG/NO, ratio, as shown by the results of a regression analysis. The regression coefficients shown in Table 3 can be interpreted as the normalized sensitivities of O3 to the rate constants. Table 3 includes the rate constants that contribute most to the uncertainty in the time-averaged O3concentrations. The dominant contribution to the uncertaintyis associatedwith the rate constant for the “ 0 3 formation reaction, which is a major sink for NO,. Rate constants for photolysis of O3 and NOe, the reaction O3 NO, PAN chemistry, and the reaction OID H20,which produces HO to initiate radical chain reactions, also strongly influence the uncertainty. Because the calculation procedures used here only approximated those used previously, MIRs and MOIRs calculated for this study were compared to those of Carter (13) before proceeding with the uncertainty analysis. As shown in Figure 2, the average difference for MIR values is less than 5%. For MOIRs, the values calculated for this study average about 10% higher than those given by Carter (13). The discrepancies arise because we calculated IRs as sensitivities to initial concentrations, whereas Carter estimated IRs as the sensitivities to the compounds when they are added in part to the initial conditions and in part as emissions during the simulations. A further discrepancy is introduced by use of results from the single average
+
+
1340 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 5, 1995
u/k+
reg coeff
MIR Case ( R z= 0.97; constant coeff = 0.41) HO N 0 z 0.28 -0.54 NO2 h v 0.28 0.36 O3+hv0.35 0.23 PAN 0.69 0.10 HCHO hv- 2H02 CO 0.34 0.18 0 3 NO0.19 -0.31 CCO-02 NOz 0.64 -0.083 CCO-02 NO 0.70 0.073 OID M 0.23 -0.22 O’D Hz0 0.24 -0.21
+
+
+
-+
+
-
+
+
+ + MOM Case ( R z= 0.98, constant coeff = 0.70) HO + N020.28 -0.40 +
+ hv-
-+ +
NO2
PAN
CCO-02 NO 03 NOCCO-02 NO2 03 hvAFGl/AFG2 hv CzCO-02: NOz O’D HzO
+
+
+
+
4
+
0.28 0.69 0.70 0.19 0.64 0.35 1.26 0.82 0.24
0.34 0.084 0.082 -0.31 -0.087 0.13 0.033 -0.045 0.14
UCb (%) 36.28 15.56 10.28 8.24 5.65 5.57 4.58 4.23 4.16 4.12 32.57 22.49 8.73 8.66 8.66 7.97 5.29 4.54 3.44 3.10
Normalized uncertainty of rate constant defined as odk, where uk is tu uncertainty of the rate constant, k. Uncertainty contribution defined as [(odk)(reg coeff)l*/d x 100%, where o is lo uncertainty of average ozone concentration for the Monte Carlo simulations. a
scenario as opposed to averaging IRvalues from 39 separate scenarios (13). Uncertainties (la)in the MIRs of 26 organic compounds, calculated with Monte Carlo simulations, are shown in Figure 3. The uncertainties range from 27% of the mean estimate for 2-methyl-1-butene to 68% of the mean for ethanol. Relatively unreactive compounds tend to have higher uncertainties than more reactive compounds. This is because the latter react completely over the 10-h simulation period, so their impact on O3 is not affected by modest changesin their primary oxidation rates. The inputs of NO, for the MIR case were set specifically to maximize
5.0
d;
0
%'
E a \a 4.0
0" faa
.-.M .-.+
e
3.0
0
MIR (Carter,1994)
A
MIR (this study)
0
MOIR (Carter,1994)
V
MOIR (this study)
Y
Y
8
2.0
p! I
(d *
E
8c
6
P
9
1.0
Y
0.0
FIGURE 2. Comparisons of MIR and MOIR values calculated by DDM with those of Carter (13).
6.0 5 .o 4.0
3 .O
T
2.0 1.o
0.0
FIGURE 3. Mean values and l a uncertainties of MlRs from the Monte Carlo simulations.
the incremental reactivity of a base mixture, given nominal rate parameter values (13). This N0,value was not adjusted from one Monte Carlo simulation to another. As a result, the system moves away from the condition of maximum
reactivity as rate constants are assigned values different than their nominal values, and the average MIRs shown in Figure 3 are lower than the values calculated using nominal rate constants. VOL. 29, NO. 5,1995 /ENVIRONMENTAL SCIENCE &TECHNOLOGY
1341
TABLE 4
Uncertainty Apportimment for MRs by Reg~ressionAnalysis reaction
-
a/&
reg coeff
UCb (%)
Formaldehyde( R 2 = 0.91; constant coeff = 0.63) HCHO hv 2H02 CO 0.34 0.50 CCO-02 N O 2 4 0.64 -0.89 CCO-02 NO 0.70 0.075 HCHO+ h v - H z + C O 0.34 -0.13 HO+CO0.29 0.15 NO2 h v 0.27 0.15 R02R HOz0.87 -0.044
48.43 5.50 4.64 3.14 2.95 2.68 2.46
m,pXylene ( R 2 = 0.93; constant coeff = 0.80) AFGl/AFG2 hv 1.26 0.084 cc0-02 + NO‘ 0.70 0.13 HO N020.28 -0.32 MP-XYL HO 0.31 0.27 CCO-02 NOz0.64 -0.13 NO2 hv 0.27 0.30 PAN 0.69 0.1 1
16.58 12.46 12.00 10.60 10.10 10.04 9.27
Methanol ( R = 0.99, constant coeff = 0.25) MEOH HO 0.48 0.79 HO NOz0.28 -0.57 NO2 hv0.27 0.44 HCHO h v - H2 CO 0.34 0.33 03 hv 0.35 0.26 CCO-02 NO 0.70 0.13 CCO-02 NO?0.64 -0.13
55.85 9.94 5.65 4.85 3.20 3.04 2.72
+ + +
+
-
+
+
-
+
+
+ +
- -
+
+
+
+ + + -
+ +
a
-
-
+
-
ulk”
reaction
reg c o d
Propene ( R = 0.92; constant coeff = 0.78) CCO-02 NOz0.64 -0.18 CCO-02 NO 0.70 0.16 HO N O 2 4 0.28 -0.29 NO2 h v 0.27 0.28 PAN 0.69 0.11 HCHO hv Hz CO 0.34 0.20 03 NO0.19 -0.36
+ +
+ +
-
-+ +
+
--
MEK ( R 2 = 0.93; constant coeff = -0.21) MEK hv 0.44 0.37 cc0-02 + NO 0.70 0.22
+
+
CCO-02 N O 2 4 MEK HO NO2 h v PAN HO N O 2 4
+
+ +
-
0.64 0.27 0.27 0.69 0.28
-0.24 0.51 0.40 0.15 -0.35
Butane ( R z = 0.95 constant coeff = -0.67) HO NO20.28 -0.67 CCO-02 N 0 2 0.64 -0.24 CCO-02 NO 0.70 0.19 NO2 hv0.27 0.48 BUTANE HO 0.18 0.69 PAN 0.69 0.18 O3+hv0.35 0.30
+
+
-
+
+ +
-
-
UC’ ( O h ) 21.19 18.08 9.88 9.12 9.02 7.17 7.13 17.87 16.26 15.59 12.20 8.03 7.38 6.27 20.81 13.89 10.81 10.53 9.73 9.59 6.98
Uncertainty contribution defined as [(odk)(regcoeff)12/dx loo%, where o is l o uncertainty of the reactivity. l o uncertainty in rate constant
a t 303 K.
The rate constants that have the most influence on calculated MIRs were identified through regression analysis. Results for the MIRs of selected compounds are presented in Table 4. The uncertainty attribution results indicate that rate constants that are influential for predicting O3 concentrations are also influential for MIRs. In addition, the rate constant for its primary oxidation step is influential for most compounds, except for the alkenes. The alkenes react completely, so their reactivities are less sensitive to their primary oxidation rate constants. Compounds with relatively slow HO reaction rates also exhibit high sensitivity to uncertainties in the rate of HO production, through the rates of O3 photolysis and O’D reactions. Rate constants for the reactions of stable oxidation products are also influential for most compounds. For example, the MIRs for alcohols and olefins are sensitive to uncertainties in the associated aldehyde photolysis rates and those of aromatics are sensitive to uncertainties in AFGl and AFG2 photolysis rates. Uncertainties (lo)of MOIRs calculated with Monte Carlo simulations are presented in Figure 4. Uncertainties in MOIRs are larger than those in MIRs for most compounds and range from 28% of the mean value for methane to 75% for ethylbenzene. Relatively high uncertainties of 50% or greater were also found for the MOIRs of aldehydes, aromatics, and alcohols. Table 5 shows the uncertainty apportionment results for MOIR values. Rate parameter uncertainties that were influential for MIRs, including those for O3 and NO2 photolysis, OID H20, “ 0 3 formation, and the chemistry of PAN and its analogues, are also important for MOIRs. However, for the rate constants that affect the supply of hydroxyl and peroxyl radicals in the simulations, the response of MOIRs is opposite to that of MIRs. Starting from nominal MOIR conditions, enhanced radical availability (e.g.,through increased 0 3 photolysis rates) leads to
+
1342 1 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 5,1995
lower sensitivity of peak 0 3 to added inputs of organic compounds. In contrast, under nominal MIR conditions, the main effect of increased radical availability on MIRs is positive in speeding up the rate of oxidation of the added organic compound or of its reaction intermediates so that more NO to NO2 conversions occur prior to the end of the simulations.
Discussion Reducing uncertainties in the rate parameters identified in Tables 3-5 would reduce overall uncertainties of incremental reactivities in organiccompounds. However, several of the most influential rate parameters (e.g., for O3 NO and HO NO*) are already well established, and uncertainties in other influential parameters have proven difficult to reduce (e.g., parameters associated with secondary aromatics chemistry). One step toward reduced uncertainty in MIRs and MOIRs that is already underway is revising the PAN chemistry and HCHO photolysis rates in the SAPRC mechanism to be consistent with recent measurements (26-31). In addition, measurements of the HO rate constants of oxygenated compounds and higher alkanes could help reduce uncertainty in their IRs. For example, if the uncertainty estimate (a/k) for the methanol HO rate constant is reduced from the conservative estimate of 48% (22) used above to the more recent estimate of 20% (21),the uncertainty in the MIR for methanol drops from 66% to 48%. Most reactive organic compounds are emitted in mixtures from a given source. Moreover, decisions in which reactivity is likely to be considered are apt to involve comparison of two or more alternative compounds or mixtures. Such applications include CARB’s RAFs and similar approaches that have been used in comparing reactivities of exhaust from alternative fueled vehicles (9, 10). Therefore, beyond calculation of uncertainties in
+
+
+
2.0
1.o
0.o
FIGURE 4. Mean values and la uncertainties of MOlRs from the Monte Carlo simulations. TABLE 5
Uncertainty Apportionment for MOlRs by Regression Analysis reaction u/k reg coeff uc (Yo) Formaldehyde ( R z = 0.96; constant coeff = 1.59) 0.35 -1.39 0.24 -1.44 0.28 1.01 0.23 0.95 1.26 -0.1 1 0.34 -0.40 0.44 -0.25 0.34 -0.29
+ hvO'D + H20HO + NOz' O'D + M'AFGl/AFG2 + hv RCHO + hv OLE1 + 0 3 HCHO + hv - 2H02 + CO 03
m,pXylene ( R z = 0.94; constant coeff = 1.75) 0.35 -0.97 0.24 -1.10 0.23 0.92 0.31 0.56 0.34 -0.40 0.28 0.49 1.26 0.10 0.28 0.45 NOz-
+ hvO'D + H20O'D + MMP-XYL + HO HCHO + hv - 2H02 + CO NO2 + hv AFGl/AFG2 + hv 03
HO
+
-
Methanol ( R 2 = 0.95; MEOH HO NO2 hv03 hvO'D HzOHO2 NOH02 H02HO N O 2 4
+ + + + + +
+
constant coeff = 1.68) 0.48 1.06 0.28 0.67 0.35 -0.50 0.24 -0.53 0.24 0.38 0.37 -0.22 0.28 -0.29
ulk
reaction
reg coeff
Propene ( R z = 0.96; constant coeff = 1.43) 0.35 -0.77 0.24 -0.77 0.23 0.50 0.69 0.17 0.28 0.38 0.70 0.15 0.58 -0.17 0.34 -0.28
+ hvO'D + H20O'D + MPAN NO2 + hv CCO-02 + NOCCO-02 + N02RCHO + hv -
43.20 22.28 14.33 8.97 3.66 3.22 2.21 1.77
03
29.64 18.35 11.78 7.57 4.74 4.64 4.03 3.91
03
uc (Yo) 34.62 16.44 6.57 6.11 5.21 5.09 4.75 4.18
MEK ( R z = 0.96; constant coeff = 0.22)
61.27 8.08 7.49 4.03 1.95 1.63 1.53
individual IRs, the degrees of uncertainty in reactivities of mixtures and in "relative" reactivities (i.e., ratios to the reactivity of a base compound or mixture) are also of interest. Rate parameter uncertainties have directionally similar effects on MIRs or MOIRs of many compounds. To quantlfy this similarity, pairwise correlations between.the MIRs of selected compounds have been calculated from the Monte Carlo results. Table 6 lists the correlation matrix
+ hvCCO-02 + NO+
-+
NO2 hvPAN CCO-02 N O 2 4 MEK HO MEK hv O'D HzO
+ +
+
-4
-+
0.35 0.70 0.28 0.69 0.58 0.27 0.44 0.24
-0.65 0.32 0.68 0.27 -0.31 0.59 0.34 -0.53
Butane ( R z = 0.96; constant coeff = 0.44) PAN 0.69 0.27 CCO-02 NO0.70 0.25 NO2 h,0.28 0.62 CCO-02 NOz0.58 -0.29 BUTANE HO 0.19 0.68 HO N020.28 -0.34 03 NO0.19 -0.44
+
+ +
+
+
-
15.80 15.23 10.73 10.53 9.58 7.79 6.74 4.98 18.30 16.69 15.50 14.96 8.53 4.92 3.80
for MIRs of 12 compounds, including aldehydes, alkenes, aromatics, and oxygenates. As shown, positive correlations ranging from 0.40 to 0.92 exist between the MIRs. The lowest correlations occur with the MIR of HCHO for which uncertainty stems primarily from the HCHO photolysis rate. The highest correlation is between the MIRs of propene and CCHO (acetyldehyde), a reaction intermediate of propene. The correlations suggest that uncertainties in VOL. 29, NO. 5, 1995 /ENVIRONMENTAL SCIENCE &TECHNOLOGY
1343
TABLE 6
Matrix of Correlations of MlRs between Compounds butane 224TMC5a propene 13BUTDb toluene rn,pXYL HCHO CCHOC MEOH ETOH MTBE MEK a
butane
224TMC5'
propene
13BUTDb
toluene
m,pXYL
HCHO
CCHOC
MEOH
ETOH
MTBE
MEK
1 0.84 0.83 0.74 0.81 0.77 0.45 0.73 0.55 0.71 0.73 0.78
1 0.73 0.86 0.77 0.70 0.40 0.61 0.50 0.58 0.66 0.76
1 0.81 0.78 0.77 0.71 0.92 0.58 0.77 0.65 0.81
1 0.72 0.7 1 0.62 0.71 0.50 0.60 0.56 0.77
1 0.86 0.40 0.67 0.50 0.64 0.65 0.7 1
1 0.42 0.68 0.49 0.65 0.56 0.70
1 0.59 0.45 0.48 0.40 0.50
1 0.46 0.72 0.49 0.76
1 0.41 0.51 0.46
1 0.50 0.65
1 0.59
1
2,2,4-Trirnethylpentane.
1,3-Butadiene. Acetaldehyde.
relative reactivities will be lower than those shown above for absolute IRs. A companion paper explores this comparison further in an analysis of uncertainties in RAFs (14).
Conclusions and Summary This study has presented the results of an analysis of uncertainties in incremental reactivities calculated for a range of organic compounds. The only source of uncertainty considered was the kinetic parameters in the SAPRC mechanism used to calculate MIRs and MOIRs. Other sources of uncertainty, including product yields, mechanism formulation, and simulation conditions, were neglected and could also have a significant effect on incremental reactivityestimates. The uncertainties in individual rate parameters that were propagated through the analysis were subjectivelyestimated, in most cases based on reviews by NASA and IUPAC panels. Uncertainties were assumed to be log-normally distributed and independent across parameters. Uncertainties (la) in MIRs of the organic compounds studied ranged from 27% for 2-methyl-1-butane to 68%for ethanol; uncertainties in MOIRs ranged from 28% for methane to 75% for ethylbenzene. Uncertainties in the final O3 concentrations predicted for MIR and MOIR simulation conditions were 30% and 20%, respectively. Only a limited number of rate parameters contribute significantly to uncertainty in incremental reactivities. Some of them were also found to be influential for predicting 0 3 concentrations. Rate constants for the reactions of NO 03,NOz, 03,and HCHO photolysis, HN03 formation, and PAN chemistry were generally influential. The rate constants of their primaryH0 oxidation or photolysis reactions were influential for the IRs of most compounds, with the exception of the alkenes. The rate constants of the reactions of O'D Ha0 and 0 3 photolysis were found to have substantial influence on the MIRs of alkanes, aromatics,
+
+
ethers, and alcohols and on the MOIRs of most compounds.
The photolysis rate of the aromatics oxidation intermediates AFGl andAFG2 were influential for ozone as well as for the IRs of aromatics. It should be possible to reduce uncertainties in IRs somewhat by updating the PAN chemistry and HCHO photolysis rates in the SAPRC mechanism, and with new measurements of the HO rate constants of oxygenated compounds and higher alkanes. Improved understanding of aromatics oxidation mechanisms would also be valuable. In the meantime, the finding that rate parameter uncertainties have directionally similar effects on reactivities of 1344
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 29, NO. 5, 1995
many compounds suggests that a useful way of dealing with existinguncertainties is to apply IRs in a relative sense, as done with California's RAFs. In future work, we plan to refine the uncertainty estimates for IRs by incorporating correlations between rate parameters, accounting for uncertainties in product yields, and improving uncertainty estimates for some critical parameters. In particular, better uncertainty estimates are needed for photolysis parameters, for which uncertainties in actinic fluxes as well as action spectra should be considered, and for the rate parameters of the aromatics oxidation intermediates that have been estimated from smog chamber experiments and not measured directly.
Acknowledgments Support for this research was provided by the AutolOil Air Quality Improvement Research Program, under CRC Contract AQIRP-19-92. The views expressed in this paper are those of the authors and do not necessarily represent the views of the AQIRP. We thank W. P. L. Carter for providing the SAPRC9O mechanism and for reviewing our uncertainty estimates and calculation procedures and D. Gao and M. Das for valuable assistance with calculations.
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Carter's Detailed Mechanism.Auto/OilAir Qualityhprovement Research Program Report, Mar 1994. (16)Iman,R. L.; Shortencarier, M. J. A F O R T W 77 Program and User's Guidefor the Generation ofLatin Hypercubeand Random Samplesfor Use with ComputerModeki;NUREG/CR-3624; Sandia National Laboratories: Mar 1984. (17)Dunker, A. M. 1. Chem. Phys. 1984,81,2385-2395. (18)McCroskey, P. S.; McRae, G. J. Documentation for the Direct Decoupled Sensitivity Analysis Method-DDM. Report, Department of Chemical Engineering, Camegie Mellon University, Pittsburgh, PA, 1987. (19)Iman, R. L.; Helton, J. C. A Comparison of Sensitivity AnaZysis Techniques for Computer Modeki; NUREGICR-3904; Sandia National Laboratories: Mar 1985. (20)Yang, Y.-J.; Das, M.; Milford, J. B.; Bergin, M. S.; Russell, A. G.; Stockwell, W. R. Quantification of Organic Compound Reactivities and Effects of Uncertainties in Rate Parameters. Auto/ OilAir QualityImprovement Research Program Report,Aug 1994. (21)DeMore, W.B.; Sander, S . P.; Golden, D. M.; Molina, M. J.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. Chemical Kinetics Data for Use in Stratospheric Modeling, Evaluation No. 9; National Aeronautics and Space Administration, fet Propulsion Laboratory, California Institute of Technology: Pasadena, CA,1990. (22)Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A,; Troe, J. 1.Phys.Chem. Ref Data 1989,13,1259-1380.
(23)Atkinson, R. Chem. Rev. 1986, 86,69-201. (24)Atkinson, R. Amos. Environ. 1990,24A,1-41. (25)Atkinson, R.; Carter, W. P. L. Chem. Rev. 1984,84,437-470. (26)Atkinson, R.; Lloyd,A. C.1. Phys. Chem. Ref: Data 1984,13,315444. (27)Bridier, I.; Caralp, F.; Loirat, H.; Lesclaux, R.; Veyret, B.; Becker, K. H.; Reimer, A.; Zebel, F. 1.Phys. Chem. 1991,95,3594-3600. (28)Kirchner,F.;Zabel, F.;Becker, K. H. Ber. Bunsen-Ges. Phys. Chem. 1990,94, 1379-1382. (29)Tuazon, E. C.; Carter, W. P. L.; Atkinson R. 1.Phys. Chem. 1991, 95,2434-2437. (30)Moortgat, G.K.;Schneider, W. Unpublished data presented in Atkinson, R.; Baulch, D. L.; Cox, R. F.; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J.1.Phys. Chem. Ref: Data 1992,21,1125-1568. (31)Cantrell, C. A.; Davidson, J. A.; McDaniel, A. H.; Schetter, R. E.; Calvert, I. R. 1.. Phys. Chem. 1990,94,3902-3908. (32)Atkinson, R. 1.Phys. Chem. Ref: Data 1994,Monograph No. 2, 1-216.
Received for review August 29, 1994. Revised manuscript received January 11, 1995. Accepted January 26, 1995." ES940546J @
Abstract published in Advance ACS Abstracts, March 1, 1995.
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