\ I / United States Environmental Protection Agency Atmospheric Sciences Research Laboratory Research Triangle Park NC 27711 - Research and Development EPA/600/S3-85/012 Apr. 1985 SERA Project Summary Methods for Simulating Gas Phase S02 Oxidation in Atmospheric Models James F. Meagher and Kenneth J. Olszyna Two different approaches are presented for simulating gas phase sulfur dioxide oxidation in at- mospheric models. The first approach was to develop an empirical relation- ship based on rate data collected at four coal-fired power plants during 11 separate studies. Cosine functions were used to simulate annual and diurnal variations in the oxidation rate constant. The time variant rate con- stant was superimposed on a con- stant rate coefficient of 0.002 h'1 used for nonsunlight hours. The model predicts a maximum (solar noon) rate constant of 0.0285 h'1 for mid-July. The second approach was to develop a kinetic model based on data obtained from smog chamber ex- periments using mixtures of sulfur dioxide propene, butane, nitrogen ox- ides, and water vapor. Sulfur dioxide oxidation in the gas phase was found to occur by two mechanisms. At low HC/NOX values hydroxyl radical addi- tion to sulfur dioxide predominates. At high HC/NOX values, oxidation via reaction with products of the ozone- olefin reaction dominates. The chamber data suggest that the HO- SO2 reaction leads mainly to the pro- duction of hydroperoxyl radical and sulfuric acid. A previously proposed mechanism for the reaction of sulfur dioxide with Criegee intermediates was found to provide an excellent fit to the data at the high HC/NOX values. This Project Summary was developed by EPA's Atmospheric Sciences Research Laboratory, Research Triangle Park, NC, to an- nounce key findings of the research project that is fully documented in a separate report of the same title (see Project Report ordering information at back). Introduction In the past decade there has been an intensive effort to determine the rate and the mechanism of sulfur dioxide (S02) ox- idation in the atmosphere. Although the oxidation is believed to be a composite of gas and liquid phase reactions, the majori- ty of data available are applicable to the gas phase only. Studies of droplet oxida- tion have only just begun and the infor- mation for chemical processes in cloud systems is sparse. The mechanism and models discussed in this report deal ex- clusively with the gas phase oxidation of SO2. Mathematical models that simulate S02 to sulfate conversion in the atmosphere fall into two general classes. The first, empirical models, are based on ex- perimental data with statistical averaging to remove the inherent variability found in field measurements. The rate is usually assumed to be first order in S02. The sec- ond, kinetic models, are based on a chemical mechanism developed to describe S02 oxidation in terms of elementary reactions. Laboratory measured rates of reactions are used in mathematical expressions that describe the time dependence of the major species. Empirical models represent average conditions and thus can be expected to fail in an event calculation. Kinetic schemes borrow heavily from the ------- smog/ozone models developed for urban areas. The scheme may contain 50 to 150 individual reactions and might be ex- pected to perform better for event calculations. The price for this capability is considerable. Model input requirements can be staggering. A set of simultaneous differential equations, one for each species, must be solved at each time step. In this report various empirical and kinetic schemes will be discussed. Al- ternative schemes will be described. These alternatives have been developed using recent field and laboratory data, much of which was not available to previous modelers. Empirical Model A wide variety of schemes for the parameterization of the S02 oxidation rate constant has been developed in recent years. Techniques vary from the use of time invariant values for the rate constant to ones that are allowed to vary diurnally and seasonally. These procedures are based loosely on field data and often represent best fits to monitoring data. Field studies funded by the U.S. En- vironmental Protection Agency (EPA) be- tween 1974 and 1979 have provided data useful in developing parametric equations relating S02 gas-phase oxidation and meteorological variables. Wilson (1981), for example, has analyzed the data from 12 power plant and smelter studies and obtained a linear fit to the data (excluding the VISTTA data from the Navajo Power Plant): SP/ST % = 3.66 (average solar radia- tion, KW/m2 (time, h ) - 0.84 where the left-hand side of the equation represents the percentage sulfur in paniculate form. This relationship is only useful if reliable solar intensity data are available or can be predicted. A more elaborate scheme was proposed by Gillani ef al. (1981) for dry conditions. Based on analysis of two sets of field measurements taken in 1976, the authors obtained the following relationship: (k,)d = (0.03 ± 0.01)(R.H.[03]0 where (k,)d = dry atmospheric rate con- stant (% h'1) R = solar radiation (kW/m2) H = mixing height (m) [03] = background ozone con- centration (ppm) The parameterization is based on a very limited data base and requires more input parameters than other techniques. Perhaps the most obvious feature of field measurements for S02 oxidation rate constants is the variability of the data. Measured rate constants range from 0.0 to greater than 0.1 h"1, sometimes at the same location within a period of a few days. There are, however, several features of the data that provide reason for op- timism. The most striking of these are the diurnal and seasonal trends. Diurnal Variations The diurnal variation in the measured S02 rate constant has been reported by Husar et al. (1978), Forrest ef al. (1981), Gillani et al. (op. cit. 1981), and Bailey et al. (1982). The maximum rate constant (0.02 - 0.08 rr1) was observed for measurements made near solar noon. Nighttime values are generally less than 0.005 h'1 with intermediate values in the morning and late afternoon. All of the studies cited above occurred during the summertime and early fall. There is a limited data base for wintertime studies. Meagher et al. (1978) reported no systematic change (diurnal trend) in a Tennessee Valley Authority (TVA) study during the winter of 1975-76. This marked difference between summer and winter measurements leads to a discussion of seasonal trends. Seasonal Variations Altshuller (1979) used model estimates of clean tropospheric hydroxyl (HO), hydroperoxyl (H02), and methylperoxyl (CH302) radical concentrations to calculate the seasonal dependence of the homogeneous S02 oxidation rate. The bulk of the oxidation was due to the hydroxyl radical reaction. Meagher, et al. (1983) used data col- lected during eight plume studies at four coal-fired power plants to demonstrate similar annual trends. The average rates calculated varied from a winter low of 1.5 x 10~3 h"1 to a summer high of 1.3 x 10"2 h'1; this variation was similar to that predicted by Altshuller's model. Model Description Conceptual development. An alternative parameterization scheme for estimating the atmospheric S02 oxidation rate is presented here. It is intended that this technique complement those described previously and be used when the amount of reliable input data are limited. The model developed is based loosely on the diurnal and annual variation in clear-sky, solar intensity. The basic assumption is that the rate constant can be separated into a constant value and a component that is allowed to vary diurnal- ly and annually. t,i) = k0 fA(i) where k(t,i) = diurnally and annually vary- ing rate constant t = time of day (solar) i = Julian date k0 = time invariant component of the rate constant km* = maximum value the time variant portion of the rate constant may attain fA (12 + 0.5 Td) For a time dependent rate constant the average value (k) during any period of the solar day (tj --- > t2) is given by t2 * = (t2 - t,)-1 J k(t,)dt t, Substituting the proposed functionality for k(t)i and integrating we obtain a rela- tionship between k~ and sine functions of Td, t2, and t, . This equation is of the form i ------- R = ko + Mmax) • g(t,,t2). Values for g(t,,t2) have been calculated for each of the plume measurement data bases. Estimates of Mi)™* have been obtained for each study by plotting R against g(t,,t2) and performing a least squares fit while forcing the line through 0.002 h'1 at g(ti,tz) = 0. The objective of the model is to reproduce average situations rather than events; thus, a single outlier was removed from each data set to prevent it from unduly biasing the fit. Annual function If All The annual variation in the daily maximum rate constant, kCOmax, was determined from the expres- sion M1U, = 0.5 [cos (2* (\ - inv»)/365) + 1] where im>x occurs Julian date on which kn The seasonal trend previously described by Meagher ef al. (op. tit. 1983), is based on morning rate measurements. The mean solar time for each of these is 8.4 ± 0.9 a.m. The rate constant was calculated for each of the five diurnal studies. The annual maximum time variant rate constant at solar noon Ik™*) and the date of that maximum (inuJ were adjusted to obtain the best fit to the data. The best fit was obtained for k,™, = 0.0265 rr1 and imax = 192.5. Therefore, the maximum rate constant of 0.0285 rr1 is predicted for mid-July, 20 days after the summer solstice. Model results. A combination of the diur- nal and seasonal functions provides the following equation for the pseudo first order rate constant. k(i,t,Td) = 0.002 + 0.006625 [cos (2 T (\ - 192.5)7365)+ 1] . [cos(2 T (t - 12)/Td) + 1] where k(i,t,Td) is in units of Ir1 A linear regression analysis of all 1.03 in- dividual measurements from the data base indicates that this simple model accounts for 56% of the observed variation. Model Limitations The model proposed is intended to represent average situations. It should not be expected to exhibit significant skill in reproducing individual events such as daily values. All the field measurements of S02 oxidation have been made in rural areas; past experience has shown that ur- ban areas with their local emissions can significantly alter the observed rate con- tent. Thus, extrapolation of these data to urban conditions must be done with cau- tion. Kinetic Models Many of the limitations inherent in em- pirical models can be avoided through the use of detailed kinetic schemes. As the name implies, this approach presupposes an understanding of the operative mechanisms and requires rate data for all elementary and composite reactions mak- ing up the mechanisms. Calvert and Stockwell (1984) reviewed available data on, gas phase oxidation of S02 in the atmosphere. They concluded that hydroxyl radical addition was the most important reaction in the oxidation process. At higher HC/NOX values and pollutant concentrations another mechanism becomes equally important. This mechanism is poorly understood but involves the products of the ozone-alkene reaction. Models that are used for rural assessment could probably ignore the contribution of the ozone-alkene mechanism without significantly affecting the predictions of atmospheric sulfate pro- duction. However, in an urban environ- ment, both mechanisms should be included. HO + S02. Most modelers have assumed that S02 is an HO chain terminator and have summarized the oxidation by S02 + HO H2S04 If the reaction is chain terminating, then model calculations predict a high degree of nonlinearity between S02 and sulfate concentrations. Also, this assumption leads modelers to conclude that a reduc- tion in S02 would lead to an increase in nitrate concentrations. Recently, the S02 + HO reaction has been studied by photolyzing mixtures of nitrous acid (HONO) in the presence of S02, NO, N02, H20, and CO. Extrapola- tion of the data to atmospheric conditions leads one to conclude the reaction can be summarized in one equation thusly: HO + S02 + (02, H20) ---- > H2S04 + H02 and is, therefore, not chain terminating. TVA conducted smog chamber ex- periments to evaluate the mechanistic op- tions for S02 oxidation. Chamber runs were performed at constant initial NOX and hydrocarbon concentrations with variable amounts of S02 (0 to 6.4 ppm). Runs were conducted at low and moderate humidities (5% and 40% at 25°C). The overall effect of S02 on the NO to N02 conversion and the formation of ozone was to slightly accelerate the conversion process and to increase the 03 peak concentration. The HO steady state concentration decreased during the runs. Comparison between the dry and wet ex- periments reconfirms the observation of other investigators that water vapor enhances the photochemical activity in these systems. The HO concentrations for each experi- ment were used to calculate the sulfate formation rate using the rate coefficient recommended by Atkinson and Lloyd (1984) (1.39 x 103 ppm-1 min'' at 350°K, 1 atm). These values were compared with values calculated by monitoring the rate of aerosol volume increase. The agree- ment between the two methods indicates that under these conditions, HO addition to S02 can account for all measured sulfate. Discussion Two extreme mechanistic approaches have been used to explain sulfate produc- tion following HO addition to S02. The first mechanism tested in this study was the simple HO chain termination. The reduction in HO steady-state concentra- tion predicted by this mechanism severely inhibited photochemical reactivity resulting in an extreme underestimation of ozone formation and very slow NO to N02 conversion. In this study, reaction with S02 represents a significant sink for HO radicals (about 35% using 1.5 ppm S02). Atkinson ef al. (1982) had successfully modeled Miller's experiments using the termination mechanism because, in that case, the S02 + HO > H2S04 reaction represented only a 2% loss of HO radicals. A better agreement between ex- perimental data and model results was ob- tained when a simplified version of the reaction HO + SO2 > H2SO« + H02 (1) proposed by Calvert and Stockwell was used. This model qualitatively predicts the main chemical changes observed, i.e., ac- celerated NO to N02 conversion, en- hanced O3 formation, and the depression of the HO steady state concentration with added S02. The experimental data show that at the beginning of the experiment the HO concentration is insensitive to ad- ded S02 probably because H02 produced in the above reaction probably regener- ates HO by reacting with NO. The model predicts this observation. Near the end of the experiment the lack of NO inhibits the H02 to HO conversion and the HO ------- steady-state concentration decreases. This mechanism, however, does overestimate the ozone formation increase caused by S02 addition. It is apparent that the assumption of an HO chain propagation mechanism is a better approximation to the experimental data than that provided by termination. However, the data suggest addition ter- mination routes are needed. Several reac- tions, which may occur in this system, were proposed: S02 + HO > HS03 (2) AH = - 37 kcal • moM HS03 + 02 > HS05 (3) AH = - 16 kcal • mol'1 HS05 + NO > HSO, + N02(4) AH = -25 kcal • mol'1 HS04 + H02 > H2S04 + 02 (5) AH = - 61 kcal • mol'1 It was assumed that reactions (3) and (4) are very fast (k3 and kj are greater than 1 x 10* ppnr1 min"1). The rate coef- ficient ks was estimated to be in the range of 103 - 106 pprrr1 min"1. The addition of these reactions to the model enhanced the fit to the 03 data in the early stages of the experiments, but little improvement was noted in the prediction of the 03 maximum. The overestimation of the 03 maximum suggests the presence of additional reac- tion(s) that consume 03 or its precursors. A simple reaction that satisfies this re- quirement is HSO« + 03 > HS05 + 02 (6) AH = - 23 kcal > mor1 By adjusting the ratios k,/k2 and kg/kg, good agreement was obtained between model prediction and experimental data. All rate coefficients used for the simula- tions are listed in the Project Report. Because this project was intended to develop the capability to predict ambient sulfate levels, it is of interest to compare model predictions with observed values. The data also allow a comparison be- tween the wet and dry experiments, i.e., high and low relative humidity. At low S02 concentrations (< 1.0 ppm) when the consumption of HO by S02 is small (<10%) the approximation of linearity (perfect hydroxyl propagation} between S02 and sulfate formation is valid. As the S02 concentration increased to about 5 ppm, significant deviation (factors of 2 to 3) from linearity were observed. The chemical mechanism proposed in this report indicates that 98.5% of the time the H0-S02 reaction leads to H02 formation. This is consistent with the conclusions of Calvert and Stockwell (op. cit. 1984) that S02 termination of the HO radical may not be important in the free atmosphere. It must be emphasized that, although the observed HO termination is a small fraction of the total reaction, it significantly affects the temporal behavior and maximum levels of secondary pollutants. Alkene + O3 + SO* Although the S02 + OH addition reac- tion can explain the bulk of the field measurements of S02 oxidation rate, the mechanism cannot explain nighttime S02 oxidation, the very high rates observed near urban areas, or the formation of organosulfur compounds. An additional pathway to sulfate forma- tion that has been suggested by several authors involves S02 oxidation in the presence of ozone and olefinic hydrocar- bons. The mechanism of this reaction is not well understood at all. The general opinion is that the S02 oxidation occurs via reaction with a product from the ozone-olefin reaction. A reasonable mechanism proposed by Calvert et al. (1978) to explain the observed S02 oxida- tion in this system is R'HC = CHR + 03 > Molozonide (7) Molozonide > R'CHO + [RHCOO]* (8) [RHCOO]* > Products (9) [RHCOO]* + M > RHCOO + (10) M Thermalized Criegee intermediate The thermalized Criegee intermediate can then react with S02 to produce S03 which hydrolyzes to H2S04 or with H2O to undergo rearrangement to a carboxylic acid. RHCOO + S02 > (11) H20 RCHO + S03 > H2SO, RHCOO + H20 > (12) RCOOH + H20 The Criegee intermediate can also react with other atmospheric constituents as follows: RHCOO + NO >RCHO + N02 (13) RHCOO+ NO2 >RCHO + NO2 (14) RHCOO + CO > Products (15) RHCOO + RCHO >0zonides (16) Martinez and Herron (1981) also pro- posed an addition reaction between S02 and the Criegee intermediate to produce an organosulfur intermediate collisionally stabilized to a heterocyclic organosulfur species. M RHCOO + S02 --- > (17) 0 — -S = 0 This species can then react with water to produce sulfuric acid: 0-0 RCH RCHO+H2SO« (18) To simplify the kinetic treatment of aerosol production in these systems, we propose an empirical representation of the formation process thusly: X0 Ox (19) RCH 0 S = 0 > S(IV) aerosol A steady-state treatment -of the in- termediates in this mechanism yields the following rate law for S02 oxidation: -d[S02]/dt = k7[03][HC].A.B (I) where k7 = rate coefficient for the ozone- alkene reaction A = MMl/kg + k10tM]; frac- tional yield of the thermal- ized Criegee intermediate B = k17[S02]/k,7[S02] + k,2[H20] + k,3[NO] + k,4[N02]; frac- tion of Criegee intermediates that react with S02 The rate law for sulfuric acid formation becomes: d[H2S04]/dt = k7[O3][HC]A.B-C (II) where k;, A and B are defined above and C = k18[H20]/(kie[H20] + k,9); fraction of the S02-Criegee adduct intermediates that are hydrolyzed to H2S04. Conversely, the production of the S(IV) aerosols can be described by d[S(IV)]/dt = k7[03][HC]A • B • D (III) where D = ki9/(ki8 [H2O] = ki9); fraction of the S02-Criegee adduct intermediates that produce S(IV) aerosol The equation for H2S04 production rate states that the S02 oxidation to sulfuric acid is a function of six terms. The im- portance of this nonhydroxyl pathway is ( ------- difficult to assess due to the paucity of experimental data. The results of chamber runs conducted at TVA indicated that all of the S02- Criegee adduct intermediates hydrolized to sulfuric acid. Under dry conditions (~ 5% RH) the results were in qualitative agreement with Equations I and II. The competition between H20 and paniculate formation for the adduct species (term D in Equation III) predicts an increase in S(IV) aerosol formation. The dry experi- ment was repeated with measurements for total aerosol volume and analysis of the aerosols produced for both total sulfur content and sulfate content. The sulfate is found to be approximately 25 to 50% of the total sulfur. The results suggest that both sulfate and nonsulfate aerosols are produced in an S02-NO-alkene system. Laboratory experiments during this study confirmed an earlier observation by Eatough et al. (1981) that S(IV) aerosols formed in an 03-alkene-S02 system spon- taneously convert to S(VI) aerosols over a period of days or weeks. Since most am- bient air filter samples are usually not analyzed for several weeks after being taken, one would not expect to observe S(IV) aerosols in these samples. Kinetic Mechanism-SO2 Oxidation A summary of the mechanism and a listing of the rate parameter requirements for modeling SO2 oxidation are presented in the Project Report. The entire chemical mechanism, which draws extensively on the work of Atkinson et al. (op. cit. 1982) is also listed there. The mechanism in- volves 33 individual species and 69 reac- tions and is obviously too large to be in- cluded here. The reactions and rate data presented must be combined with a free radical photochemical scheme describing atmospheric HC-NOX reactions. Several such schemes are available (see reference list in Project Report) and can be modified to accommodate this mechanism. The mechanism is suitable for both rural and urban situations because it has been tested over a broad HC/NOX range. The hydroxyl radical mechanism will dominate at low values of HC/NOX with the Criegee mechanism becoming more important at the higher values. From modeling and chamber data we conclude that, although the relative importance of the two mechanisms shifts dramatically as the HC concentrations inprease from 0.5 (to 3.0 ppm C, the effect on sulfate pro- duction is small. Conclusions and Recommendations Two options are provided in the Project Report for simulating S02 chemistry in at- mospheric models. Both are intended for gas-phase oxidation and do not address cloud or precipitation chemistry. The op- tion selected depends, to a large extent, on available input data. The empirical model provides a simple alternative to the complex kinetic models. The S02 rate coefficient predictions are based on field measurements solely. This model is intended to represent the average situation. It should not be ex- pected to reproduce individual events. The kinetic model provides much more insight into the complex chemical reac- tions governing SO2 oxidation in the at- mosphere. When coupled with a com- prehensive free radical photochemical model, the recommended scheme should reproduce observed sulfate formation over a wide range of NOX and HC concentra- tions. This scheme is more appropriate to assessments requiring estimates for fine temporal and spatial scales. References 1. Altshuller, A. P. Model predictions of the rates of homogeneous oxidation of sulfur dioxide to sulfate in the at- mosphere. Atmos. Environ. 13, 1653-1661 (1979). 2. Atkinson, R., and A. C. Lloyd. Evaluation of kinetic and mechanistic data for modeling of photochemical smog. J. Phys. Chem. Ref. Data (in press) (1984). 3. Atkinson, R., A. C. Lloyd, and L. Winges. An updated chemical mechanism for hydrocar- bons/NOX/S02 photooxidation suit- able for inclusion in atmospheric sim- ulation models. Atmos. Environ. 16, 1341-1355 (1982). 4. Bailey, E. M., R. W. Garber, J. F. Meagher, R. J. Bonanno, and L. Stockburger. Atmospheric oxidation of flue gases from a partially sulfur dioxide-scrubbed power plant: Study II. TVA Report No. ONR/ARP-82/4 (1982). 5. Calvert, J. G., F. Su, J. W. Bot- tenheim, and 0. P. Strausz. Mechanism of homogeneous oxida- tion of sulfur dioxide in the troposphere. Atmos. Environ. 12, 197-226 (1978). 6. Calvert, J. G. and J. R. Stockwell. Mechanism and rates of gas-phase oxidations of sulfur dioxide and nitrogen oxides in the atmosphere. In: Acid Precipitation Series—Volume 3, S02, NO, and NO2 Oxidation Mechanisms: Atmospheric Considera- tions. John I. Teasley, Series Editor, Ann Arbor Press (1984). 7. Eatough, D. J., M. L. Lee, D. W. Later, B. E. Richter, N. L. Eatough, and L. D. Hansen. Dimethyl sulfate in paniculate matter from coal- and oil- fired power plants. Environ. Sci. Tech. 15, 1502-1510 (1981). 8. Forrest, J., R. W. Garber, and L. Newman. Conversion rates in power plant plumes based on filter pack data: The coal-fired Cumberland plume. Atmos. Environ. 15, 2273-2282 (1981). 9. Gillani, N. V., S. Kohli, and W. E. Wilson, Jr. Gas to particle conversion of sulfur in power plant plumes—I. Parameterization of the conversion rate for dry, moderately polluted am- bient conditions. Atmos. Environ. 15, 2293-2313 (1981). 10. Husar, R. B., D. E. Patterson, J. D. Husar, N. V. Gillani, and W. E. Wilson, Jr. Sulfur budget of a power plant plume. Atmos. Environ. 12, 549-568 (1978). 11. Martinez, R. I. and J. T. Herron. Gas phase reaction of S02 with a Criegee intermediate in the presence of water vapor. J. Environ. Sci. Health, A16(6), 623-636 (1981). 12. Meagher, J. F., E. M. Bailey, and M. Luria. The seasonal variation of the atmospheric S0a to SOf conversion rate. J. Geophys. Res. 88, 1525-1527 (1983). 13. Meagher, J. F., L. Stockburger, E. M. Bailey, and 0. Huff. The oxidation of sulfur dioxide to sulfate aerosols in the plume of a coal-fired power plant. Atmos. Environ. 12, 2197-2203 (1978). 14. Wilson, W. E., Jr. Sulfate formation in point source plumes: A review of recent field studies. Atmos. Environ. 15, 2573-2581 (1981). *U.S.Government Printing Office: 1985 — 559-111/10823 ------- James F. Meagher and Kenneth J. Olszyna are with the Tennessee Valley Authority, Muscle Shoals, AL 35660. H. M. Barnes is the EPA Project Officer (see below). The complete report, entitled "Methods for Simuilating Gas Phase SOz Oxidation in A tmospheric Models," (Order No. PB 85-173 110/AS; Cost: $11.50. subject to change) will be available only from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 Telephone: 703-487-4650 The EPA Project Officer can be contacted at: Atmospheric Sciences Research Laboratory U.S. Environmental Protection Agency Research Triangle Park, NC 27711 United States Environmental Protection Agency Center for Environmental Research Information Cincinnati OH 45268 Official Business Penalty for Private Use $300 0000329 PS U S ENVJR PROTECTION AGENCY REGION 5 LI8RARY 230 S DEARB6RN STREET CHICAGO IL ------- |