Reduced Gas-Phase Kinetic Mechanism for Atmospheric Plume

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Environ. Sci. Technol. 1998, 32, 1709-1720

Reduced Gas-Phase Kinetic Mechanism for Atmospheric Plume Chemistry PRAKASH KARAMCHANDANI, ANNIE KOO, AND CHRISTIAN SEIGNEUR* Atmospheric and Environmental Research, Inc., 2682 Bishop Drive, Suite 120, San Ramon, California 94583

FIGURE 1. Schematic description of the evolution of plume chemistry with dispersion.

The subgrid-scale simulation of plume chemistry in threedimensional air quality models can be computationally demanding. To minimize this computational burden, a reduced kinetic mechanism for the gas-phase chemistry of power plant plumes is developed and validated against a full chemical kinetic mechanism. This reduced mechanism simulates plume chemistry according to three stages of the plume evolution: (1) A first stage where plume radical concentrations are negligible and plume chemistry is limited to four major reactions during the day and two at night. (2) A second stage where plume concentrations of OH and NO3 radicals are sufficiently high to lead to significant formation of HNO3 and H2SO4 and which can be simulated with 30 reactions (or, alternatively, two different sets of 19 and 18 reactions for daytime and nighttime, respectively). (3) A third and final stage where VOC oxidation and O3 formation become important, and the full chemical mechanism is required. For 10% accuracy in simulated plume concentrations, the reduced mechanism led to reductions in computational time of up to a factor of 3.

1. Introduction Three-dimensional urban and regional air quality models are widely used in the regulatory process to estimate the effect of emission controls on ambient concentrations of pollutants such as ozone and particulate matter. These models employ an Eulerian grid system, with horizontal resolutions ranging from a few kilometers to several tens of kilometers depending upon the application. Thus, they are unable to resolve small-scale features, such as the strong concentration gradients created by plumes emitted from large point sources. In the basic formulation of Eulerian air quality models, emissions from such sources are immediately mixed into the grid cell containing the source, i.e., the plume dimensions are assumed to be comparable to the grid cell dimensions. However, a typical point source plume (e.g., from a power plant or a smelter) does not expand to the size of a grid cell until it has traveled several kilometers downwind. Near the source, the volume occupied by the plume is generally much smaller than the volume of the grid cell, so that air quality models typically overestimate the mixing rate of fresh emissions with the background air. (We define background air as the air outside of the plume.) This overestimation can significantly affect the chemistry calculations performed by the model. To address this issue, it is necessary to incorporate a subgrid-scale treatment of plumes in three-dimensional air * To whom correspondence should be addressed. Phone: (925)244-7121; fax: (925)244-7129; e-mail: [email protected]. S0013-936X(97)00707-4 CCC: $15.00 Published on Web 04/21/1998

 1998 American Chemical Society

quality models. A number of approaches to simulate plume chemistry at subgrid scales have been developed and implemented in operational air quality models (1, 2). However, significant computational resources tend to be associated with such models if a large number of plumes must be simulated at subgrid scales. To minimize the computational burden associated with the simulation of multiple puffs imbedded in a threedimensional grid model, it is necessary to develop an optimal representation of chemical reactions in the plume by specifying the lowest number of reactions needed to achieve a prespecified level of accuracy for reaction products such as ozone, nitrogen dioxide, sulfuric acid, and nitric acid with respect to a comprehensive reaction scheme, such as the Carbon-Bond Mechanism IV (CBM-IV) (3) or lumped molecules mechanisms (4, 5). Kumar and Russell (2) have simulated plume chemistry within a three-dimensional framework using three different chemical mechanisms: (a) a simple three-reaction mechanism of NO/NO2/O3 chemistry, (b) an extended inorganic chemical mechanism, and (c) a comprehensive mechanism with both inorganic and organic chemistry. Significant differences in the model results were observed between the simple and extended inorganic mechanisms. The differences were smaller between the extended inorganic mechanism and the comprehensive mechanism. The reactions that are important in plume chemistry will vary from a few reactions near the stack to a large set of reactions between organic and inorganic species when the plume is well mixed with background air. This behavior suggests that an optimal chemical mechanism for plume chemistry should evolve as the plume becomes increasingly mixed with background air. We describe here the development of such a reduced mechanism that can simulate the chemistry of plumes during the various stages of their evolution. We compare this reduced mechanism against a comprehensive mechanism for a wide range of conditions to test the validity of this multistage approach.

2. Approach The following approach was taken to develop the reduced plume chemical mechanism. First, we used existing knowledge about plume chemistry (6-12) to define different stages of plume chemistry, where within each stage a given set of chemical reactions governs the plume chemistry. As depicted in Figure 1, three distinct stages were defined. Stage 1. Early plume dispersion where NOx concentrations are sufficiently high that the photostationary state applies for NO/NO2/O3 and radical concentrations within the plume are negligible. Stage 2. Midrange plume dispersion where radical concentrations within the plume start to be sufficiently large VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Reduced Kinetic Mechanisms for Plume Chemistrya reactionb O2

(1) 2NO 98 2NO2 (2) NO + O3 f NO2 + O2 (3) NO2 + hν f NO + O(3P) O2, M

daytime

stage 1 nighttime

X

X

X

X

daytime

X

stage 2 nighttime day/night transition

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X X

X X

X

X

X X

X X

(4) O(3P) 98 O3 (5) O3 + hν f O(3P) + O2 (6) O3 + hν f O(1D) + O2 M

(7) O(1D) 98 O(3P) (8) O(1D) + H2O f 2OH (9) HONO + hν f NO + OH (10) H2O2 + hν f 2OH O2

(11) HCHO + hν 98 CO + 2HO2 (12) HCHO + hν f CO (13) ALD2 + hν f HCHO + XO2 + 2HO2 + CO (14) PAN f C2O3 + NO2 (15) C2O3 + NO2 f PAN (16) C2O3 + NO f HCHO + XO2 + HO2 + NO2 (17) NO + HO2 f NO2 + OH (18) NO + OH f HONO M

(19) NO2 + OH 98 HNO3 O2, H2O

(20) SO2 + OH 98 H2SO4 + HO2 (21) NO2 + O3 f NO3 + O2 (22) NO + NO3 f 2NO2 (23) NO2 + NO3 f NO2 + NO + O2 M

(24) NO2 + NO3 98 N2O5 M

(25) N2O5 98 NO2 + NO3 (26) N2O5 + H2O f 2HNO3 (27) NO + XO2 f NO2 (28) XO2 + XO2 f products (29) HO2 + HO2 f H2O2 + O2 (30) HO2 + HO2 + H2O f H2O2 + H2O + O2 (31) NO3 + hν f 0.89NO2 + 0.89O(3P) + 0.11NO

X

X

X

X

X

X

X

X

X

X

X

X

X X

X X

X X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X X

a Rate parameters are from Gery et al. (3) with updates as given in CBM-4.1, U.S. Environmental Protection Agency Technology Transfer Network. b In the CBM-4.1 notation, ALD2 represents the carbonyl group of acetaldehyde and higher aldehydes, C2O3 represents peroxyacyl radicals, and XO2 represents peroxyalkyl radicals.

to lead to some significant formation of secondary acids (e.g., HNO3 and H2SO4). Stage 3. Long-range plume dispersion where sufficient mixing of the plume with the background air has taken place such that the same reactions are important in the plume as in the background air (e.g., O3 formation, VOC oxidation), although to different extents.

Chemical kinetic mechanisms were developed for stages 1 and 2 based on the characteristics defined above for the chemistry of each stage (the stage 3 mechanism is identical to the background mechanism, i.e., the full mechanism, by definition). Knowledge available from previous comprehensive sensitivity analyses of photochemical smog chemistry (13) was used in this initial selection of reactions.

The Carbon-Bond Mechanism IV was used to represent the full chemistry (3). However, our methodology is independent of the mechanism used to simulate the full chemistry. Therefore, the results presented here can be readily adapted to other chemical mechanisms such as those of Carter (4) and Stockwell et al. (5).

Then, reactions that were included in these initial mechanisms were discarded, one at a time, to assess whether all reactions of the initial selection set were necessary. Next, reactions (or groups of reactions) that were not included in the original set of reactions were added one at a time to (a) confirm that such reactions were not needed and (b) help

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develop the rationale for the reasons why such reactions were not needed. The measures used to assess whether a reaction was needed or not consisted of the differences between the concentrations calculated with the full and reduced mechanisms for the following major plume species: NO, NO2, O3, SO2, HNO3, and H2SO4. The concentration of total VOC (weighted by their OH reactivity) was also used in this comparison. We used an error of 10% in those species concentrations as the tolerance limit to decide the importance of reactions. The reduced chemical kinetic mechanisms developed for each stage are presented and discussed below. Note that some reactions are more important during the day than during the night and vice versa. Thus, we distinguish between daytime and nighttime plume chemistry.

3. Chemical Mechanisms 3.1. Stage 1 Chemistry. Daytime. Stage 1 corresponds to the conditions near the stack and during the early stages of plume dispersion, when NO concentrations are large. During the day, the dominant reactions in this stage include four reactions among five species. This reduced mechanism is shown in Table 1. This reaction set consists of the three reactions of the photostationary state between NO, NO2, and O3 and the termolecular oxidation of NO by O2. This latter reaction (reaction 1) is important very near the stack where NO concentrations are very high (i.e., above about 1 ppm). At NO concentrations of about 1 ppm, the rate of destruction of NO by reaction 1 is about 1%/h. Farther downwind, the oxidation of NO by O2 becomes negligible, because its rate is proportional to the square of the NO concentration and, therefore, decreases rapidly. Nighttime. At night, the photolysis of NO2 does not take place, and only the first two reactions involving four species need to be taken into account (see Table 1). Therefore, NO gets depleted and converted irreversibly to NO2. As discussed above for the daytime chemistry, the importance of reaction 1 decreases rapidly, so that when NO concentrations drop below 1 ppm, reaction 2 is the only important one. 3.2. Stage 2 Chemistry. Daytime. In stage 2, the midrange plume dispersion stage, we consider other reactions that form the radicals that lead to the formation of sulfuric and nitric acids. These radicals also lead to some ozone formation. However, at this stage, NOx concentrations in the plume are significantly larger than VOC concentrations, so that ozone concentrations within the plume are still lower than in the background air. Table 1 shows the set of 19 reactions among 20 species that dominates during stage 2 during the day. These reactions can be grouped according to the following major categories: (a) The three photostationary state reactions (reactions 2-4) among NO, NO2, and O3. Note that the termolecular oxidation of NO by oxygen (reaction 1) can be neglected in stage 2 once plume NO concentrations are low enough (i.e., less than about 1 ppm) that the O3 oxidation of NO dominates. For example, the rate of destruction of NO by O2 is about 1% of the rate of destruction of NO by O3 for NO ) 1 ppm and O3 ) 1 ppb. (b) Seven photolytic reactions and the two reactions of O(1D) that lead to the formation of free radicals and, directly or indirectly, formation of OH and HO2 radicals (reactions 5-13). (c) Three reactions (reactions 14-16) corresponding to PAN chemistry and the production of radicals through PAN thermal decomposition. In the presence of high NO concentrations, PAN can be an important source of radicals.

(d) The reaction of NO with HO2 to form NO2 and OH, thereby converting HO2 radicals to OH radicals and oxidizing NO to NO2 without O3 consumption (reaction 17). (e) The oxidation of NO, NO2, and SO2 to HNO2, HNO3, and H2SO4, respectively (reactions 18-20). The differences between the daytime stage 1 and stage 2 mechanisms reside, therefore, in the fact that the chemistry of OH radicals is included in the Stage 2 mechanism, thereby allowing for secondary acid formation. Note that, in the above set of reactions, concentrations of species such as H2O2, HCHO, ALD2, and PAN correspond to background conditions (i.e., concentrations outside the plume), while concentrations of NO, NO2, O3, and SO2 are plume values. At this point of plume chemistry, reactions leading to O3 formation are not important. This is apparent when comparing the rates of the oxidation reaction of NO to NO2 by O3 and HO2. Ozone formation takes place when the latter reaction proceeds at a nonnegligible rate, thereby producing NO2 (which by photolysis leads to O3 formation) without consuming O3. In the 7 a.m. plume simulation that is discussed later, the ratio of the relative rates of the reaction of NO with O3 and NO with HO2 at the plume centerline is 1400, 900, and 400 after 100, 200, and 300 min of simulation, respectively. Therefore, in stage 2, the reaction of NO with HO2 is essential because it converts HO2 to OH, but not because of its role in NO to NO2 conversion. The potential importance of other inorganic reactions was assessed by conducting the simulation with and without these reactions. No significant changes in the model results were obtained; therefore, no additional inorganic reactions needed to be added. Besides the photolytic reactions of aldehydes, which lead to a net production of radicals, we investigated the potential importance of the thermal oxidation of VOC by OH, O3, O, and NO3 in stage 2. None of these groups of reactions led to significant differences in simulation results. It is interesting to note that the reactions of VOC with OH contribute significantly to the consumption of OH radicals in the plume. For example, in the 7 a.m. simulation discussed later, the consumption of OH by VOC amounts to 40% of the total OH consumption reactions after 100 min of simulation (the reactions leading to secondary acid formation account for most of the remainder with 60%). Therefore, it may seem that VOC reactions with OH should be important. However, this is not the case because the VOC/OH reactions lead to HO2 radicals that are rapidly converted back to OH radicals by reaction with NO. This conversion occurs without significantly affecting the NO/NO2/O3 concentrations since these concentrations are primarily governed in stage 2 by the photostationary state reactions, as discussed above. Moreover, the oxidation of VOC in the plume is sufficiently slower than in the background atmosphere so that it can be neglected without significantly affecting the VOC concentrations. Nighttime. At night, the photolysis reactions can be neglected. However, additional reactions are required to represent the formation of NO3 radicals and N2O5 and the formation of nitric acid by hydrolysis of N2O5. The set of reactions for stage 2 for nighttime consists of 18 reactions among 15 species as shown in Table 1. These reactions can be grouped according to the following major categories: (a) The oxidation of NO by O3 to form NO2 (reaction 2). (b) The five reactions that determine NO3 radical concentrations (reactions 21-25) (c) The formation of HNO3 through N2O5 hydrolysis (reaction 26). VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Criteria for Switching Stages in Plume Chemistry simulation

daytime

nighttime and day/night transition

stage 1 to stage 2

[OH]a g 1 × 10-9 ppm at 298K

[OH]a g 1 × 10-9 ppm at 298K or [O3] g 3.5 × 10-4 ppm and [NO3]b g 10-8 ppm

stage 2 to stage 3

[HO2]/[O3] g 2.2 × 10-6 and [O3] g 0.001 ppm

[HO2]/[O3] g 2.2 × 10-6 and [O3] g 0.001 ppm or ∑ki[VOCi]c/k24[NO2] g 0.01 and [NO3] g 10-8 ppm

a

[OH] )

2k8[O1D][H2O] + k9[HONO] + k17[HO2][NO] + 2k10[H2O2]

k18[NO] + k19[NO2] + k20[SO2]

where [O1D] ) where

k6[O3] k7 + k8[H2O]

a ) 2{k29 + k30 [H2O]};

{

b ) k17[NO] 1 -

; [HO2] )

-b + xb2 - 4ac 2a

}

k20[SO2]

k18[NO] + k19[NO2] + k20[SO2]

;

c ) -2{k11[HCHO] + k13[ALD2]} - k16[C2O3][NO] -

k20[SO2]{k9[HONO] + 2k10[H2O2] + 2k8[O1D][H2O]} ; k18[NO] + k19[NO2] + k20[SO2]

and [C2O3] )

k14[PAN]

k15[NO2] + k16[NO] Concentrations of NO, NO2, SO2, and O3 are plume concentrations; concentrations of HONO, H2O2, HCHO, ALD2, and PAN are background concentrations. Reaction rate constants correspond to the 30-reaction mechanism presented in Table 1. k21[O3][NO2] b All concentrations are plume concentrations. c ki is the rate parameter for oxidation of [NO3] ) k24k25[NO2] k31 + k22[NO] + [k23 + k24][NO2] k25 + k26[H2O] VOCi by NO3.

(d) The five reactions of nocturnal PAN chemistry that lead to OH formation by reaction of NO with peroxy radicals (reactions 14-17 and reaction 27). (e) The formation of HNO2, HNO3, and H2SO4 by reaction of NO, NO2, and SO2, respectively, with OH (reactions 1820). (f) The radical chain termination reactions for regions of the plume where all NO has been consumed by reaction with O3 (reactions 28-30). The differences between daytime and nighttime chemistry can be summarized as follows: (a) The lack of NO2 photolysis leads to titration of NO with O3, which will result in zero NO concentrations at the edges of the plume, and, possibly, zero O3 concentrations at the plume core, particularly near the stack. (b) The chemistry of NO3 is important at night (NO3 radicals are photolyzed rapidly during the day) and can lead to significant HNO3 formation. (c) In cases where background PAN concentrations are high (i.e., several ppb), its thermal decomposition in the presence of high NO concentrations leads to significant OH concentrations that are generated through the reaction of NO with peroxy radicals (i.e., CH3COO2, CH3O2, and HO2). Consequently, nitrous, nitric, and sulfuric acid formation will take place by OH oxidation of NO, NO2, and SO2, respectively. However, the OH concentrations are lower during nighttime than daytime since the photolytic reactions that generate radicals do not occur at night. As for the daytime chemistry, we verified the potential importance of other inorganic and organic reactions by conducting the simulations with and without these reactions (or groups of reactions). Therefore, the mechanism presented 1712

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above represents the optimal set of reactions for nighttime stage 2 chemistry, based on the tolerance criteria defined above. Day/Night Transitions. For situations involving day/night transitions, it may be necessary to combine the daytime and nighttime mechanisms in stage 2. As shown in Table 1, this results in a set of 30 reactions among 22 species that includes a reaction for NO3 photolysis (reaction 31). This mechanism can be used to simulate both daytime and nighttime chemistry. It includes 11 and 12 more reactions than the individual daytime and nighttime mechanisms, respectively. However, it reduces to the 18 reaction nighttime mechanisms when the photolytic reactions get turned off. The additional computational burden is therefore carried only during daytime. 3.3. Stage 3 Chemistry. For dispersion of the plume at long distances where mixing with the background air has become significant, the chemistry of VOC oxidation becomes important. To simulate plume chemistry in stage 3, the full chemical mechanism (i.e., here, CBM-IV, which includes 82 reactions among 36 species) is used.

4. Implementation in a Reactive Plume Model The mechanisms discussed above were implemented into a reactive plume model, the Reactive and Optics Model of Emissions (ROME), that includes state-of-the-science formulations of plume rise and dispersion using second-order closure algorithms, aerosol dynamics, and atmospheric chemistry (14). The model uses a Lagrangian approach to describe the dispersion of a plume emitted from a stack and advected by the mean flow and simulates the chemical reactions that occur as the plume mixes with the background

FIGURE 2. Comparison of HNO3 plume centerline concentrations from full and reduced mechanisms as a function of travel time for a summer daytime simulation beginning at 7 a.m. (a) Base criteria used for reduced mechanism; (b) tight criteria used for reduced mechanism; (c) relaxed criteria used for reduced mechanism. air. The model consists of a two-dimensional array of contiguous cells that are perpendicular to the wind direction. The cells can expand horizontally according to a normal distribution for inert species. The vertical depths of the cells remain constant during a given simulation. Reactive chemical species undergo chemical reactions within each cell and diffuse between contiguous cells and between the cells and the background according to a Fickian diffusion algorithm. For the study described here, we used ROME in its gas-phase chemistry mode. The gas-phase chemistry module in ROME was modified to include the three mechanisms for the three stages discussed above. For stage 2, we used the combined day/ night 30-reaction mechanism for the simulations presented here. However, for simulations that did not involve day/ night or night/day transitions, the results obtained with the

30-reaction mechanism are virtually identical to the results obtained with the day-only or night-only mechanisms discussed above. In addition, we also included the termolecular oxidation of NO by O2 in stage 2 even though it can be neglected once NO concentrations are lower than about 1 ppm as discussed earlier. The reason for including this reaction in stage 2 is that in some of our simulations, as described later, the switch to stage 2 from stage 1 occurred almost instantaneously depending upon the ambient VOC and PAN concentrations. Because the oxidation of NO by O2 is important near the stack, this reaction could not be ignored for these situations. As part of the implementation, we developed criteria for switching from stage 1 to stage 2 and from stage 2 to stage 3. The transition from one stage to another in a plume grid cell is assumed to occur as soon as one of the criteria for that VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Comparison of O3 plume centerline concentrations from full and reduced mechanisms as a function of travel time for a summer daytime simulation beginning at 7 a.m. (a) Base criteria used for reduced mechanism; (b) tight criteria used for reduced mechanism; (c) relaxed criteria used for reduced mechanism. transition is met. This means that at a given time step, some cells may be in stage 1 and others may be in stage 2 or stage 3. The criteria for switching from one stage to the next are determined from the chemical conditions in the plume and the background air. These criteria were initially developed based on our understanding of the dominant chemistry in the three stages. They were later refined after performing simulations for a large number of conditions. In the following section, we describe the criteria and discuss our rationale for selecting them. Table 2 summarizes the final criteria that were used in the results presented here. Note that these criteria are based on plume concentrations of NO, NO2, SO2, and O3 and background (i.e., outside the plume) concentrations of species such as aldehydes and PAN. Thus, the information required to switch from one stage to the next one is always available. 4.1. Selection of Switching Criteria. Stage 1 to Stage 2 Criteria. By definition, stage 2 begins when the formation of acids becomes important. For most situations, the 1714

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absolute rate of formation of HNO3 is much larger than that of H2SO4. Thus, we assume that the plume switches to stage 2 when plume OH concentrations are such that the rate of oxidation of NO2 to nitric acid by OH in the plume is 0.1%/h or more. As shown in Table 2, plume OH concentrations are estimated from plume O3, NOx, and SO2 concentrations and background concentrations of radical precursors such as aldehydes, PAN, etc. The above criterion is used during both day and night, although it is most likely to be satisfied during the day because OH concentrations are usually very small at night. During the night or in situations involving day/night transitions, an additional criterion is required to address nitric acid formation by hydrolysis of N2O5. This process is initiated by the formation of the NO3 radical through the oxidation of NO2 by O3. Thus, in addition to the OH criterion, we specify the onset of stage 2 to occur when the rate of oxidation of NO2 to the NO3 radical by O3 in the plume is 0.1%/h or more and plume NO3 radical concentrations are 10-8 ppm or more.

TABLE 3. Stage Durations (Minutes from Simulation Start) stage 1

stage 2

stage 3

simulation

start

end

start

end

start

end

7 a.m. base case 7 a.m. O3 × 2 7 a.m. VOC × 5 7 a.m. VOC × 10 7 a.m. dispersion × 2 7 a.m. N2O5 rate × 10 7 a.m. PAN ) 10 ppb noon base case noon O3 × 2 noon VOC × 5 noon VOC × 10 noon dispersion × 2 noon N2O5 rate × 10 noon PAN ) 10 ppb 5 p.m. base case 5 p.m. O3 × 2 5 p.m. VOC × 5 5 p.m. VOC × 10 5 p.m. dispersion × 2 9 p.m. base case 9 p.m. O3 × 2 9 p.m. PAN ) 10 ppb 9 p.m. N2O5 × 10 midnight base case midnight O3 × 2 midnight PAN ) 10 ppb 3 a.m. base case 3 a.m. O3 × 2 3 a.m. PAN ) 10 ppb

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

23 25 6 1 23 24 0 14 14 0 0 13 14 0 204 250 17 6 198 331 247 99 331 331 247 99 289 239 99

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 80 0 0 0 80 0 0 80 0 0

268 185 6 1 246 268 0 270 183 0 0 247 270 0 386 557 331 330 359 383 371 383 381 383 371 383 320 239 240

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 189 3 8 3 189 3 8 189 3 8

600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 490 490 490 490 490 490 490 490 490 490

The plume NO3 concentration is calculated from the plume NO, NO2, and O3 concentrations (see Table 2). Stage 2 to Stage 3 Criteria. During the day, the transition from stage 2 to stage 3 is defined to occur when there is net formation of plume O3. We use the ratio of the rate of consumption of plume NO by HO2 radicals to the rate of consumption of plume NO by plume O3 as an indicator for triggering the switch to stage 3 in the plume (see Table 2). The former reaction leads to some net ozone formation, whereas the latter reaction leads to no net ozone formation. Therefore, the ratio of these reaction rates is a measure of the potential for net ozone formation within the plume. Switching from stage 2 to stage 3 is assumed to occur when the ratio exceeds 0.1% and O3 concentrations are 1 ppb or more. During the night or for day/night transition situations, an additional criterion is used to determine if it is necessary to switch to the full mechanism. This criterion is based on the relative rates of consumption of plume NO3 by organic compounds and by NO2 (see Table 2). As NO2 concentrations decrease in the plume through dilution, the former reactions become important, and it is necessary to incorporate them to ensure that nitric acid formation via N2O5 hydrolysis is not overestimated. Thus, switching to stage 3 is assumed to occur when either (a) the daytime criterion above is met or (b) the ratio of the total rate of consumption of plume NO3 by VOCs to the rate of consumption of NO3 by NO2 is 1% or more and plume NO3 radical concentrations are 10-8 ppm or more. 4.2. Effect of Changes in the Switching Criteria. As discussed previously, we arrived at the above criteria by performing numerous simulations for varying conditions and using different values for the criteria. The values described above represent the best compromise between computational accuracy and computational efficiency of the multistage chemical mechanism. When we used the above criteria, concentration differences between the complete and multistage mechanisms were less than 10% for all the species of

interest for all the case studies examined. Furthermore, switching between the various stages occurred at reasonably large intervals for many of the case studies. Relaxing the criteria resulted in later switching to the more complex mechanisms, but this gain in efficiency was at the cost of a severe degradation in performance in some cases. Conversely, tightening the criteria caused a quicker switching to the complex mechanisms, but the resultant gain in accuracy was not enough to justify the shortened durations of the simpler mechanisms. To illustrate the effects of relaxing and tightening the criteria for a simulation, we present results from a simulation beginning at 7 a.m. on a summer day and continuing for a period of about 10 h. Emission rates of NOx and SO2 were 88 and 161 ton/day, respectively. Ambient VOC concentrations were specified at ∼50 ppb C, and ambient ozone and PAN concentrations were specified to be 34 and 0.2 ppb, respectively. The ambient concentrations of sulfuric and nitric acids were specified to be 0.5 ppb, corresponding to clean conditions. The mean wind speed was 2.4 m/s, relative humidity was 36%, and the temperature was about 20 °C, varying with height. Figure 2 shows the nitric acid concentrations at the plume centerline as a function of travel time. In Figure 2a, the results from the full mechanism are compared with results from the multistage modified mechanism described in section 3 using the base criteria discussed in section 4.1. In Figure 2b, the criteria are tightened by a factor of 10 (i.e., switching from stage 1 to stage 2 occurs when the rate of oxidation of NO2 to nitric acid by OH in the plume is 0.01%/h or more, and switching from stage 2 to stage 3 occurs when the ratio of the rate of consumption of plume NO by HO2 radicals to the rate of consumption of plume NO by plume O3 is 0.01%). In Figure 2c, the criteria are relaxed by a factor of 10. The figures also show the duration of each stage of the multistage mechanism for the three different sets of criteria. As seen in Figure 2a, when the base criteria are used, results from the full mechanism and multistage mechanism are comparable for the entire duration of the simulation and always within 10% of each other. The duration of stage 1 is relatively brief (about 23 min), while the duration of stage 2 is approximately 4 h. The entire plume shifts to stage 3 after about 268 min. When the criteria are tightened (Figure 2b), the two simulations are virtually identical since the model switches to stage 2 (acid formation regime) instantaneously and to the full mechanism after less than 40 min. Finally, when the criteria are relaxed (Figure 2c), the durations of both stage 1 and stage 2 are larger (approximately 2 and 6 h, respectively), but most of the early production of nitric acid in the plume in the first 2 h is missed in the multistage mechanism, and the nitric acid concentrations in the plume from the multistage mechanism are much lower than those from the full mechanism for the entire duration of the simulation. Qualitatively similar results were obtained for sulfuric acid. The corresponding results for plume centerline ozone concentrations are shown in Figure 3. Again, Figure 3a shows that the results with the modified mechanism using the base criteria are almost identical to those from the full mechanism, and Figure 3b shows that tightening the criteria results in a highly accurate simulation at the loss of computer efficiency. In contrast to the HNO3 results, Figure 3c shows that the delay in the transition to stage 2 caused by relaxing the criteria does not significantly affect the O3 results in the first 2 h of the simulation, because ozone formation does not become important until about 4 h into the simulation. However, the delay in the transition from stage 2 to stage 3 (after 8 h using the relaxed criteria versus 268 min using the base criteria) does result in poor performance of the modified mechanism. The deviation between the full and modified mechanisms VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Relative differences between H2SO4, HNO3, and O3 concentrations from full and reduced mechanisms as a function of travel time for the summer base case simulation beginning at 7 a.m. (a) Plume centerline concentrations; (b) cross-sectionally averaged concentrations at plume height. for plume centerline ozone concentrations begins after about 4 h when the relaxed criteria are used and becomes progressively larger until the transition to stage 3 chemistry occurs.

5. Testing of the Multistage Reduced Mechanism In this section, we present selected results from the large number of simulations that were conducted to test the multistage chemical mechanism described above. The following section provides a description of the simulations that were performed. 5.1. Description of Simulations. We conducted daytime and nighttime simulations as well as simulations involving day/night and night/day transitions. The daytime and day/ night transition simulations were performed for summer conditions, while the nighttime and night/day transition simulations were performed for winter conditions, to test a 1716

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wide range of conditions for key variables such as photolytic flux and temperature. Winter temperatures were about 20 °C lower than summer temperatures. The summer simulations were performed for plume travel times of 10 h with starting times of 7 a.m., noon, and 5 p.m. Sunset occurred at about 7 p.m., so that the 7 a.m. simulation was for daytime alone, while the noon and 5 p.m. simulations involved a day/night transition. Similarly, the winter simulations were performed for plume travel times of about 8 h with starting times of 9 p.m., midnight, and 3 a.m. Since sunrise occurred at about 7 a.m., the 9 p.m. simulation was for night alone, while the other two winter simulations involved night/day transitions. The emission rates of NOx and SO2 were kept constant for all simulations at 88 and 161 ton/day, respectively. For each starting time, a base case was defined. In addition to the base case, we performed sensitivity studies to examine the effect of changes in ambient concentrations, dispersion, and

FIGURE 5. Comparison of plume centerline concentrations from full and reduced mechanisms as a function of travel time for the summer base case simulation beginning at 5 p.m. (a) H2SO4 concentrations; (b) HNO3 concentrations; (c) O3 concentrations. N2O5 hydrolysis rates on the performance of the modified mechanism as well as to understand the chemistry of the plume. Ambient concentrations for the base case simulations were specified as follows. Ambient VOC concentrations were specified at ∼50 ppb C, and ambient ozone and PAN concentrations were specified to be 34 and 0.2 ppb, respectively. Ambient concentrations of sulfuric and nitric acids were specified to be 0.5 ppb, corresponding to clean conditions. The sensitivity studies that were performed include the following: (a) ambient ozone concentrations increased by a factor of 2, (b) ambient VOC (including aldehydes) concentrations increased by factors of 5 and 10, (c) ambient PAN concentrations increased to 10 ppb, (d) horizontal and vertical dispersion coefficients increased by a factor of 2, and (e) N2O5 hydrolysis rate increased by a factor of 10. Table 3 summarizes the simulations that were performed.

5.2. Discussion of Simulation Results. Stages of Plume Chemistry. It is useful to discuss first how the model shifts from one stage to another for the various simulations that were performed. This provides some insight into the chemistry of the plume and how the model can be expected to react for different conditions. Table 3 provides a summary of the durations of each stage of the multistage mechanism for all the simulations. The duration consists of the start time and end time for that stage. As discussed previously, each plume cell switches from one stage to another as soon as it meets one of the criteria for the transition. Thus, a cell at the edge of the plume will shift more rapidly to the next stage than a cell at the center of the plume. In many cases, the cell at the plume edge will shift to stages 2 and 3 instantaneously. Thus, the start time given in Table 3 corresponds to the first cell that shifts to that stage, while the end time corresponds to the last cell that shifts to the stage. VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 6. Comparison of plume centerline concentrations from full and reduced mechanisms as a function of travel time for the winter base case simulation beginning at 9 p.m. (a) H2SO4 concentrations; (b) HNO3 concentrations; (c) O3 concentrations. For the early morning and noon simulations, stage 1 is relatively briefsthe duration does not exceed 0.5 h for any of the simulations. For the high VOC and PAN simulations, the switch to stages 2 and 3 occurs almost instantaneously throughout the plume. The higher VOC and PAN concentrations lead to a more rapid buildup of OH levels in these simulations, causing the quick transition to the acid and ozone formation regimes in the plume. For the 5 p.m. simulations, the duration of stage 1 is larger than for the morning and noon simulations due to significantly lower photochemical activity in the 5 p.m. simulation (the transition to nocturnal chemistry occurs about 2 h into the 5 p.m. simulation). The duration of stage 2 is larger than that for stage 1 for the morning and noon simulations except for the high VOC and PAN sensitivity studies, when the duration is close to zero, again due to the higher radical concentrations for these 1718

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cases. For the other morning and noon simulations, the duration of stage 2 ranges from 3 to 4.5 h. For the 5 p.m. simulations, the duration of stage 2 ranges from 5.5 h for the high VOC cases to more than 9 h for the high ozone case. Increasing the ambient ozone concentrations by a factor of 2 has compensating effects on the durations of stages 1 and 2 because on one hand ozone is a source of radicals, primarily through its photolysis, and on the other hand, it competes with HO2 for the oxidation of NO. During the day, an increase in O3 leads to more reactivity in the plume and, therefore, a shorter period for stage 2. In the evening, however, the latter pathway tends to dominate, thereby limiting the ability of the plume material to form additional ozone. Increasing the dispersion coefficients by a factor of 2 shows some effect on the transition to stage 3 as enhanced mixing

FIGURE 7. Comparison of plume centerline concentrations from full and reduced mechanisms as a function of travel time for the winter base case simulation beginning at 3 a.m. (a) H2SO4 concentrations; (b) HNO3 concentrations; (c) O3 concentrations. with background air accelerates the maturity of plume chemistry. Increasing the N2O5 hydrolysis rate by a factor of 10 shows an effect on the onsets of stages 2 and 3 only for the nighttime simulations since N2O5 is not a major pathway for HNO3 formation during daytime. The wintertime night and night/day transition simulations have generally longer durations of the reduced chemistry stages than the summer daytime simulations, because of lower radical concentrations at night. Performance of the Mechanism. The multistage reduced mechanism reproduced chemical concentrations within 10% of the full mechanism values for all the simulations conducted. Differences between the full and multistage mechanisms were negligible for NO, SO2, and H2O2 and almost negligible for NO2. The largest differences were seen for

sulfuric acid, nitric acid, and ozone for the daytime simulations. We present here results for O3, H2SO4, and HNO3 for the 7 a.m., 5 p.m., 9 p.m., and 3 a.m. base case studies. Other studies are omitted from the discussion because either the durations of the reduced chemistry stages for these studies are brief (e.g., the high VOC and PAN cases) or their results are qualitatively similar to the studies that are discussed here. Some results from the 7 a.m. base case study have already been presented above in our discussion of the selection of criteria from switching from one stage to another (see Figures 2 and 3). Figure 4a shows the relative differences between the multistage mechanism and the full mechanism estimates of plume centerline concentrations of H2SO4, HNO3, and O3 as a function of travel time for the 7 a.m. base case study. Figure 4b shows the corresponding errors for concentrations averaged across the cross-section at plume height. The VOL. 32, NO. 11, 1998 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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figures also show the last transition to each stage. As seen in Figure 4, the largest differences between the two mechanisms are for the nitric acid concentrations. Errors for the plume centerline concentrations for all species are generally higher than for the cross-sectional averages by about a factor of 2. This is due to the fact that cells at the edge of the plume have shifted faster to the complex chemical mechanisms than cells at the plume centerline. As expected, the relative errors typically peak near the times of transition to stages 2 and 3. The cross-sectional average peak errors occur a few minutes before the plume centerline concentration peak errors because, in the former case, some cells at the plume edge have already shifted before the last transition occurs. Figure 5 shows the H2SO4, HNO3, and O3 plume centerline concentrations, respectively, for the 5 p.m. base case simulation. Errors in the modified mechanism results are less than 6% for all three species. Because this simulation starts late in the day, OH concentrations are low and there is very little sulfuric acid production for the entire simulation. On the other hand, we see pronounced nitric acid formation after sunset, due primarily to the NO3/N2O5 pathway. Ozone concentrations at the plume centerline are zero after sunset and until about 320 min, as the ozone is initially scavenged by excess NO in the plume. Figure 6 shows the results for the 9 p.m. wintertime base case study. The results from the two mechanisms are virtually identical for all three species. There is negligible production of H2SO4 in this simulation because of the low OH levels. For the same reason, there is no formation of HNO3 until about 5.5 h into the simulation (at the same time as the last transition to stage 2). At this point, NO3 levels are high enough for production of HNO3 by N2O5 hydrolysis. Plume ozone concentrations are zero for the first 5.5 h due to scavenging by plume NO. Finally, Figure 7 shows the results for the 3 a.m. wintertime base case study. This simulation involves a transition to daytime at approximately 7 a.m., about 4 h into the simulation. The last transition to stage 2 occurs approximately 45 min after sunrise, and we see a slight production of H2SO4 at this point. Significant HNO3 production also begins only after the last transition to stage 2 occurs. There is negligible production of HNO3 from the NO3/N2O5 pathway in this simulation since plume NO3 concentrations are small initially because of the scavenging of O3 by NO, and after sunrise NO3 is rapidly photolyzed.

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Ozone concentrations begin to build up after sunrise due to mixing of ambient ozone as well as some daytime production. The reduction in computational time varies among the simulations depending on how rapidly the mechanism switches to stages 2 and 3. Reductions in computational time for the chemistry calculations during the periods when the reduced mechanisms (stages 1 and 2) are active can be as much as a factor of 3.

Acknowledgments This work was conducted under Contract WO 9031-12/WO 4501-02 with EPRI. The authors thank the EPRI Project Managers, Drs. Pradeep Saxena and Alan Hansen, for suggesting this study and for useful discussions during the course of the study.

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Received for review August 7, 1997. Revised manuscript received March 12, 1998. Accepted March 12, 1998. ES970707U