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Mechanistic Study Of Air Pollution

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Mechanistic Study Of Air Pollution

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Content This dissertation has been microfilmed exactly as received 70-8522 ERNEST, T erry Eugene, 1941- MECHANISTIC STUDY OF AIR POLLUTION. University of Southern California, Ph.D ., 1969 Engineering, chemical University Microfilms, Inc., Ann Arbor, Michigan Q COPYRIGHT BY TERRY EUGEIIE ERMEST 1970 MECHANISTIC STUDY OP AIR POLLUTION by Terry Eugene Ernest A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy (Chemical Engineering) August 1969 UNIVERSITY O F SO U T H E R N CALIFORNIA T H E G RADUATE S C H O O L U N IV ERSITY PARK LO S A N G EL ES, C A L IFO R N IA 9 0 0 0 7 This dissertation, w ritten by under the direction of h ^ 3 .... D issertation C o m m ittee, an d a p p ro v e d by all its m em bers, has been presen ted to and a ccep ted by T h e G ra d u ate School, in partia l fu lfillm ent of require ments of the d egree of D O C T O R O F P F I I L O S O P H Y D a te... DISSERTATION COMMITTEE * ylA^t^x - Chairman ACKNOWLEDGMENTS The author would like to express his appreciation to the following people and organizations for their aid and encouragement: Dr. L. G. Wayne— for his guidance and encouragement during the period of this research; The members of the Dissertation Committee: Dr. J. M. Lenoir, Dr. C. J. Rebert and Dr. G. V. Chilingar; Mrs. Ruth Toyama— for her preparation of the final draft; The National Institute of Health— for their finan cial support of this project; California Air Resources Board— for their guidance and for supplying the experimental data used in this dissertation; The Systems Simulation Laboratory of the University of Southern California— for providing the use of both analog and digital computers; The Union Oil Company of California— for providing access to high speed digital computers; and ii My wife, Mary Kay— for preparation of the rough draft of this manuscript and her help and understanding through the graduate study period. iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ...................................... ii LIST OF TABLES ....................................... vi LIST OF FIGURES ....................................... viii CHAPTER I. INTRODUCTION ................................. 1 II. EXISTING DATA................................ 7 III. EXISTING MECHANISM FOR AIR POLLUTION PRODUCTION................................... 12 IV. METHOD OF ATTACK............................ 20 A. Choice of Programs ...................... 20 B. Test of Steady State Assumption .......... 21 V. PRELIMINARY PROPOSED MECHANISM A ............ 24 A. Description of Reactions ................ 24 B. Comparison of Predicted vs. Experimental Results .................................. 28 C. Effect of Variation of Estimated Rate Constants ................................ 31 VI. PROPOSED MECHANISM B .................... 38 A. Description of Reactions ................ 38 B. Comparison of Predicted and Experimental Results .................................. 45 iv Page C. Effect of Varying Estimated Rate Constants ................................ 49 D. Varying of Initial Conditions ........... 54 VII. CONCLUSIONS .................................. 63 REFERENCES ........................................... 65 APPENDICES ........................................... 68 A. COMPUTER PROGRAMS ........................ 69 B. DATA FROM TEST OF PSEUDO-STEADY STATE ASSUMPTION............................... 91 C. ESTIMATION OF RATE CONSTANTS ............ 92 V LIST OF TABLES Table Page II-l Error Criteria in the Propylene Experimental Data ......................................... 10 III-l Mechanism Proposed by Saltzman .............. 13 III-2 Mechanism Proposed by Leighton .............. 15 III-3 Mechanism I Suggested by Wayne .............. 17 III-4 Mechanism II Suggested by Wayne ............. 18 V-l Reactions for Mechanism A .................... 25 V-2 Reaction Rates Used for Mechanism A ......... 27 V-3 Comparison of Results of Mechanism A and Experimental Data ........................... 30 VI-1 Reactions in Mechanism B ..................... 39 VI-2 Reaction Rate Constants for Mechanism B ..... 41 VI-3 Comparison of Results of Mechanism B and Experimental Data ........................... 46 VI-4 Effect of Initial Conditions in Mechanism B . 61 (In Appendices) A-l Input Program................................ 70 A-2 Output Program............................... 71 A-3 Derivative Calculation Program .............. 72 A-4 Hamming's Modified Predictor-Corrector Program...................................... 74 vi Table Page A-5 Sample Input ................................. 87 A-6 Sample Output ................................ 90 C-l Estimated Thermodynamic Properties of Mechanism B .................................. 98 vii LIST OP FIGURES Figure Page 1-1 Reactant and Product Profiles in Smog Reaction ...................................... 5 V-l Comparison of Predicted Results from Mechanism A and Experimental Data............ 29 V-2 Effect of Change in K Value for Mechanism A, Reactions 6 or 8 by Factor of 10“1 ....... 32 V-3 Effect of Change in K Value for Mechanism A, Reaction 7 by Factor of 10 ................ 34 V—4 Effect of Change in K Value for Mechanism A, Reaction 10 by Factor of 10 ............... 35 V-5 Effect of Change in K Value for Mechanism A, Reaction 11 by Factor of 10 ............... 37 VI-1 Comparison of Mechanism B Predicted Results and Experimental Data ........................ 47 VI-2 Variation of Rate Constant for Reaction Producing PAN ................................. 55 VI-3 Variation of Initial Concentration of N02 in Mechanism B .................... 56 VI-4 Variation of Light Intensity in Mechanism B .. 57 VI-5 Variation of Initial Concentration of NO in Mechanism B ................................... 59 VI-6 Variation of Initial Concentration of Propylene in Mechanism B ............. 60 viii CHAPTER I INTRODUCTION Over the last two decades, air pollution has been an ever increasing problem of the metropolitan and urban areas. Air pollution is generally felt to be responsible for reduction of visibility, irritation of the lungs and eyes of humans and animals, and damage to plant life. The analysis of air pollution in different parts of the world has led to the formulation of two basic types of air pol lution. These are illustrated by the type of air pollution found in the Los Angeles area and the type found in the London area. Air pollution found in the London area generally occurs in the presence of fog and at low atmospheric tem peratures (1)*. The London pollution is of a chemically reducing nature and contains relatively high concentrations of sulfur compounds. In comparison, the Los Angeles pol lution generally occurs with clear skies and in a *Numbers in parenthesis refer to numbered items in the References. 1 2 temperature range of 70 to 100 degrees Fahrenheit. Fur thermore, chemically it is an oxidizing type pollution with relatively low concentrations of sulfur compounds. Both types of air pollution result in reduced visibility. Rela tive to the reactions of humans to air pollution, the Lon<- don type results in severe bronchial congestion, whereas the Los Angeles type primarily causes eye irritation. Over the years it has been shown that the Los Ange les type of air pollution results from photochemical reac tions of certain contaminants in the atmosphere. The work of Haagen-Smit (2) in the early fifties demonstrated that ozone was produced by reactions of hydrocarbons with nitric oxide when the system was subjected to irradiation. Others (3) established the link between this type of irradiated system and eye irritation. This dissertation will concern itself only with the Los Angeles Basin type of smog system. Analyses of this type of system have led to the following generally accepted conclusions: 1. A hydrocarbon is consumed in the reaction with the ultimate formation of oxygenated products, generally of a lower carbon number. 3 2. The nitric oxide is consumed and converted mostly to nitrogen dioxide. 3. The nitrogen dioxide is subsequently converted to various organic and inorganic nitrogen com pounds . 4. Upon the disappearance of the nitric oxide, oxidants (predominantly ozone) accumulate in the system. 5. Upon the disappearance of nitric oxide, a ni trated organic compound, probably peroxyacetyl nitrate (PAN), begins to accumulate in the sys tem. 6. Olefins disappear in the smog system faster than do saturated hydrocarbons. 7. Eye irritation increases as the smog reaction proceeds. Leighton (1) has concluded that the smog system re actions can probably be explained by a series of chain re action steps. This conclusion is based partly on the observation that the olefin in general disappears at a rate greater than can be explained by its reaction with atomic oxygen and ozone. Also, the rate of disappearance 4 of the olefin is further increased if other saturated hydrocarbons exist in the system (7). These conclusions on the smog reaction have lead to numerous possible mechanisms being proposed. Most of these mechanisms involve the formation of intermediate free radicals which are involved in chain reaction steps. Figure 1-1 depicts, in general, the change in con centration of some of the important products and reactants of the smog system. The purpose of this research was threefold: 1. To explore existing postulated mechanisms of smog production. This exploration was accom plished by assigning reasonable estimated rate constants to each reaction step and comparing the predicted results with experimental evi dence. 2. To postulate a new mechanism for the production of smog. This mechanism included all of the major reactions known or suspected to be in volved in the smog system. Rate constants for the various reaction steps were either obtained from the literature or estimated. The predicted Concentration (pphm) 100 4 Aldehyde p . PAN 0 50 150 100 Elapsed Time (minutes) Figure 1-1 Reactant and Product Profiles in Smog Reaction in 6 results of this mechanism were again compared with existing experimental data. 3. As a large number of the rate constants were by necessity estimated, an investigation as to the effect of changing any one rate constant in the mechanism on the predicted results was investi gated . Through these investigations it was felt that new insight into what really happens in the smog reaction could be gained and be used by future investigators to guide the direction of their research. The insight thus gained might also point the way towards the ultimate solution of the smog problem. CHAPTER II EXISTING DATA The data used in this paper were collected by the California Department of Public Health's Vehicle Pollution Laboratory. Their study (7) was performed in test chambers located in Los Angeles, California. The chambers were built of glass and aluminum to reduce possible surface re actions. The volume of the chamber was large (1140 cubic feet), to reduce possible Errors caused by leakage. Ir radiation of the chamber was accomplished by numerous in ternal and external ultraviolet sources such that the acti- o nic irradiation (3600A) was approximately equal to that received at the earth's surface on a clear summer day at noon. The chamber was maintained at approximately room temperature with a slight temperature increase with time due to the heat generated by the light sources. The three hydrocarbon systems used in the tests were: SYSTEM 1 100% Propylene 7 8 SYSTEM 2 5% Isobutylene 10% Propylene 30% Ethylene 55% Gasoline SYSTEM 3 100% Automobile exhaust Their tests of these systems were run at two concentra tion ranges. The low range was from 0 to 2 ppm and the high range from 2 ppm to 8 ppm. The nitric oxide concen tration ranges were 0 to 1 ppm and 1 to 4 ppm. For each set of initial conditions the experiment was repeated four times. The chamber was filled with filtered air and then the hydrocarbon and nitric oxide were introduced. After the lights were turned on, the concentration of the various reactants and products were determined by instrumentation of the type used in monitoring the atmospheric pollution. The concentrations of nitric oxide, nitrogen dioxide, pro pylene, formaldehyde and ozone were determined throughout the run. The data chosen to be used in this dissertation was 9 that of System 1, with Propylene as the hydrocarbon. Due to the repetition of each run, it was possible to analyze the data for systematic error. The correlation coefficients and the coefficients of variation are given in Table II-1. The average standard error was around 20%. f This error was considered to be small enough to allow the data to be used as a test for proposed mechanisms of smog production. The tests on propylene differ to some extent from what happens during atmospheric smog generation. Firstly, in the atmosphere there exists a great mixture of hydrocar bons. These hydrocarbons are of the aromatic, olefinic and saturated types. Also, in the atmosphere the hydrocarbon concentration is constantly being replenished from auto exhaust and other sources, whereas in the chamber experi ments the hydrocarbon was introduced at the start of the run. The wind currents, amount of sunlight and other fac tors also affect atmospheric smog generation. The tests on propylene, however, are believed to be indicative of the type of data that would be gathered, if it were possible, by experiments on the atmosphere. As such, they offer a basis of experimental data on which mechanisms for smog 10 TABLE II-l Error Criteria in the Propylene Experimental Data (7) Correlation Coefficient Coefficient of Variations Peak HCHO .96 21.3 Corrected Oxidant .92 7.4 NO2 maximum .98 10.8 N02 half-life .82 43.2 NO half-life 00 • 40.1 C3H6 half-life • 00 H 24.7 (a) Standard deviation of error as percent of ihean. 11 generation can be based. Initially, to model a system of mixed hydrocarbons would cloud the issue as to which type of reaction is important. The basic types of reactions important to smog generation can be tested using the pro pylene data. Once these basic reactions are understood, extensions to more complicated systems can be attempted. CHAPTER III EXISTING MECHANISMS FOR AIR POLLUTION PRODUCTION Most of the mechanisms published to date for smog production involve free radical chain paths. To date,,the literature does not contain a proposal for a comprehensive mechanism of smog production. Several simplified schemes, however, have been published. Saltzman (4) has proposed the smog production mechanism shown in Table III-l. This mechanism attempts to account for the olefin disappearance by an increase in the ozone production rate over that expected from the nitric oxide-nitrogen dioxide interaction. To accomplish this end, his reaction 11 shows the formation of ozone from a free radical reacting with oxygen. The olefin dis appearance rate, however, is only a function of the ozone. No account of the possible reactions of the olefin with atomic oxygen or free radicals is given, except for the hydrogen abstraction reactions. The production of ozone appears to have no link to the olefin; thus, one would 12 13 TABLE III-l Mechanism Proposed by Saltzman (4) 1 NC>2 + h V ------NO + 0 2 0 + O2 O3 3 2N0 + 02---^ 2N02 4 03 + NO--- >» 02 + N02 5 O3 + 2N02------N20cj + 02 6 0 + H20----- 20H* 7 O3 + olefins ^ products 8 0 + RH---- >R- + OH- 9 OH- + RH-->R* + H2O 10 R* + 02---> R02* 11 ®2 ^ R0- + O3 12 R0- + RH ROH + R* 13 R02- + RH--- >• ROOH + R- 14 2R02->»2R0- + 02 15 2R0* y aldehyde + alcohol 16 R0- + NO >R0N0 17 R02- + NO---> R02N0 14 expect the presence of olefin to reduce the rate of produc tion of nitrogen dioxide via the route of reaction 5. An alysis of this mechanism (5) predicts that the saturated hydrocarbons would disappear more rapidly than the olefin. This appears to be in violation of the experimental evi dence showing the olefin disappearance rate to be greater than that of the saturated hydrocarbon. Thus, other reac tions of olefins must be added to this mechanism to account for the experimental findings. Leighton (1) has proposed the simplified mechanism shown in Table III-2. This mechanism allows for the reac tion of atomic oxygen with the olefin, but does not include any reaction between ozone and the olefin. In addition, the mechanism allows the reaction of the olefin with OH* and H02* but does not consider the reaction of the olefin with organic free radicals, which might be expected to ex plain the increase in rate caused by the addition of satu rated hydrocarbons to the system. Also, no outlet for the nitrogen dioxide except the photo-induced decomposition is allowed. This is not sufficient to explain the decrease in nitrogen dioxide encountered late in the reaction. Also no provision is made for the production of PAN which is 15 TABUS III-2 Mechanism Proposed by Leighton (1) 1 N02 + bV--b NO + 0 2 02 + 0 + M — ■*- 03 + M 3 03 + NO---»- 0>2 + N02 4 0 + C4H8-- ch3- + c3h50- 5 ch3. + o2— ^-ch302- 6 CH300* + 02 — -b CH30- + 03 7 ch3o- + no --*- ch3ono 8 ch3ono + W — J-CH30-* + NO 9 ch3o-* + o2 ——> “H2C0 + H00- 10 H02 • + — >-h2co + (ch3)2 11 H* + 02 --»- H02- 12 H02* + NO — b■ OH- + N02 13 OH- + C4Hg--b (CH3)2 CO + CH 14 2H02- --b H20 2 + °2 15 2OH- --bH + 16 experimentally noted. The mechanism proposed by Wayne (5), as shown in Table III-3, contains steps to attempt to model the short comings of the previous mechanisms. It allows atomic oxy gen, ozone and oxygenated free radicals to react with the olefin and also accounts for the formation of PAN. It does not, however, allow for the disappearance of nitric oxide to any stable compound except nitrogen dioxide. Ap plication of reasonable rate constants to this mechanism does not result in the expected rapid decrease in nitric oxide concentration that occurs in experiments. A second mechanism proposed by Wayne (6) (Table III-4), although severely oversimplified, does seem to give results as would be expected from experimental evidence (7). This mechanism predicts a too rapid disappearance of nitric oxide and as a result, the nitrogen dioxide peak is obtained too early. However, the decomposition of the ole fin into two non-differential parts severely limits the mechanism. Also, no method of directly disposing of ni tric oxide was included and no attempt was made to model a reaction between free radicals and the olefins. This mechanism did, however, show that by the free radical 17 TABLE III-3 Mechanism I Suggested by Wayne (5) 1 N02 + h V --->-N0 + 0 2 0 + 02 + M >-03 + M 3 03 + NO -N02 + 02 4 01 (olefin) + 0 — 010* 5 010* + 0--->- 0103* 6 01 + 03 0103* 7 OIO3* -aldehyde + RO- + RCO- 8 RO- + 02 + NO >"R02’ + N02 9 RCO- + 02---V-RC03- 10 RC03- + NO V-RO- + N02 11 R02- + NO->-R0- + N02 12 RC02* + NO----►" RCO • + N02 13 01 + R02* --->-010* + RO- 14 01 + RC02------- 010* + RCO- 15 aldehyde + RO- — »- RCO- + ROH 16 RO- + N02--->-R0N02 17 RC03- + N02---*-RC03 N02 18 RO + RCO- >-ketene + alcohol 18 TABLE II1-4 Mechanism II Suggested by Wayne ( 6 ) 1 N02 + --*-N0 + 0 2 0 + 02 + M >“ 03 + M 3 03 + NO >- N02 + 02 4 0 + olef — >- A* + AO* 5 O3 + olef BO* + B02- 6 B02* + NO ► — BO* + N02 7 A* + 02 (+M) V- A02» 8 AO* + 02 (+M) AO3 * 9 A02* + NO >- AO* + N02 10 A03* + NO--->~A02* + N02 11 2A02*----- A 2 02 + 02 12 2A0 • (+M)----»- A2 02 13 A02* + AO* v-A20 + 02 14 A02* + N02 — * - A02 N02 15 A03* + N02 »*-A03 N02 is no2 + o3 — >— no3 + o2 17 H03 + U02 — ^-H2 05 19 path, experimental results can be roughly reproduced. CHAPTER IV METHOD OP ATTACK The evaluation of the proposed mechanisms were per formed with the aid of a digital computer. (IBM 360 MOD 65). The use of a computer was necessary due to the high complexity involved in solving the system of non-linear simultaneous differential equations resulting from the proposed mechanisms. A. Choice of Programs Commercially available subprograms for solving non linear simultaneous differential equations were evaluated relative to speed and accuracy. It was found that an IBM supplied program of Hamming's modified predictor-corrector method (27) was the best suited to our type of system, both in speed and in accuracy. Hamming's modified pre- dictor-correctQr method is used to obtain approximate solu tions of a general non-linear system of first order differ ential equations with a given set of initial conditions. This is a fourth order stepwise procedure for solving dif ferential equations that requires fewer iterations per step 20 21 than other methods, far example Runge-Kutta. Also, this method estimates the truncation error of each step which is used to choose the optimum stepsize. To avoid problems of round-off error, double precision (16 decimal charac ters) was used for all computations. Using the steady state assumption, interface pro grams were written for input and output of data to IBM's Hamming's modified predictor-corrector method program. These interface programs were written in such a way as to allow changes in the reaction system to be handled as input data, instead of requiring programming changes for each re action scheme. These programs are presented in Appendix A. Also presented is sample input and output showing the method of use of the program. B. Test of Steady State Assumption It was found early in the investigations, that sys tems containing more than ten differential equations were highly prone toward divergent solutions. This necessitated the use of a very small time increment for the execution of the program, on the order of 10“8 minutes per iteration. Intervals of this size resulted in excessively long compu tation time, on the order of six hours per problem case. 22 In order to shorten computing times, the different systems of equations were tested to see if all of the free radical components could be considered to be at pseudo-steady state. Pseudo-steady state was based on the assumption that the concentration of the free radicals did not change greatly with time. The pseudo-steady state concentration was derived by assuming that the rate of appearance of each free radical was equal to its rate of disappearance at any point in time. This assumption greatly reduced the number of pertinent differential equations and thus, the computa tion time. Appendix B presents the data obtained in the test of the steady state assumption. Two computer runs were executed to perform this test. The first contained all of the differential equations for the products, react ants and free radicals. The second contained only the differential equations of the products and reactants. The concentration of the free radicals was calculated at each step in time by the pseudo-steady state assumption. The concentration of the free radicals calculated as a func tion of time under both systems were compared. The pseudo steady state assumption concentration varied from the base case containing all of the differential equations by an 23 average error of one to two percent. Under the steady -4 state assumption the time increment was increased to 10 minutes which resulted in a compute time per case of approximately twenty minutes. Due to the savings in com puter time and the low error introduced by the steady-state assumption, the pseudo-steady state assumption was used in all subsequent tests of reaction mechanisms. CHAPTER V PRELIMINARY PROPOSED MECHANISM A A greatly simplified reaction scheme, a modifica tion of the existing schemes, discussed in Chapter III, was adopted for the first part of this study. This scheme, as shown in Table V-l, incorporates a free radical chain mechanism to explain the typical disappearance of the ole fin and the increase in nitrogen dioxide concentrations encountered in the photochemical smog reaction. The pro posed reactions were greatly simplified for use in screen ing tests to determine if the free radical route yielded results close to available experimental data. A. Description of Reactions The first three reactions of Mechanism A were de rived from the reactions commonly associated with irradi ated systems of nitrogen oxides and oxygen. Reaction 4 was postulated as a possible overall reaction between the olefin considered in this study, propylene, and atomic oxygen. As possible explanations for the apparent increase 24 25 TABLE V-l Reactions for Mechanism A 1 N02 + hV — * - NO + 0 2 0 + 02 + M 03 + M 3 03 + NO — »- 02 + N02 4 0 + C3Hg y- 2CH3* + CO 5 CH3* + 02--CH300» 6 CH300* + c3h6 — >- C2H40 + CH3* + ch2o 7 CH300* + NO CH30v + N02 8 ch3°* + c3H6 ^ C3H6° + CH3* 9 03 + C3H6 >- C2H40 + H2C02 10 no2 + ch3o« — >~ch3ono2 11 NO + CH30* -->- CH30N0 in the rate of disappearance of olefin above that which can be explained by its reaction with atomic oxygen and ozone (1), reactions 6 and 8 were inserted into the mecha nism. For possible chain propagating steps, reactions 5 and 7 were proposed. Also, reaction 7 gives a possible route for the rapid conversion of nitric oxide to nitrogen dioxide. Reaction 9 was inserted as a possible reaction between ozone and propylene. As chain termination steps, reactions 10 and 11 were proposed. Values for the rate constants were either estimated or obtained from the literature (see Table V-2). Appendix C contains a discussion on the method used to estimate the rate constants. Also contained therein is a discussion on the accuracy of the rate constants obtained from the liter ature. Because most of the rate constants were estimated, numerous computer studies were performed to determine the effect that the variation of these estimated constants over limited ranges had on the resultant time vs. concen tration curves. This study was performed on a digital computer using the programs developed and the assumption that all free radicals were in pseudo-steady state. The ranges of the different rate constants studied are pre sented in Table V-2. 27 Reaction No. TABLE V-2 Reaction Rates Used for Mechanism A Rate . . Range of Constant'3' Constants Used Units Reference 1 1. 0.32— 1.0 c 2 0.14 x 107 c (8) 3 0.5 b (9) 4 70. b (10) 5 1.0 x 106 c est. 6 1.0 x 102 102— 103 b est. 7 1.0 x 104 104— 106 b est. 8 1.0 x 103 102— 104 b est. 9 1.5 x 10“4 b (11) 10 1.0 x 102 10---104 b est. 11 1.0 x 102 1. — 103 b est. a) In all reactions 02 was assumed to be at a constant 7 concentration of 2.0 x 10 pphm. b) pphnT^min"’1 c) min-1 28 The rate constants for reactions 2, 3, 4 and 9 were obtained from the literature and therefore not varied. Due to the similarity of reaction 5 to reaction 2, it was as sumed to have the same rate constant. B. Comparison of Predicted vs. Experimental Results Comparison of the experimental results (7) and the prediction of Mechanism A are given in Figure V-l and Table V-3. The general shape of the predicted curves agrees roughly with the experimental for the initial part of the reaction. The predicted results late in the reac tion, however, are considerably different from the experi mental. The rates of disappearance of both nitric oxide and propylene were much too rapid in the predicted results. Also, the decrease in nitrogen dioxide concentration after its peak was approximately ten percent of the peak con centration, whereas experimental data shows a decrease of from fifty to seventy percent. The lack of decrease in nitrogen dioxide was felt to be responsible for the low ozone buildup. Also, the nitric oxide concentration de creased to only 20 pphm, where data shows a decrease to less than 10 pphm. The fit of the predicted values to the Concentration (pphm) Experimental Predicted 100 100 50 150 0 Elapsed Time (minutes) Figure V-l Comparison of Predicted Results from Mechanism A and Experimental Data to vo 30 TABLE V-3 Comparison of Results of Mechanism A* and Experimental Data DATA (7> PREDICTION pphm min pphm min 03 max 37 10 CH20 max 48 N02 max 85 70 NO half-life 40 20 C3H6 half-life 115 10 N02 half-life 100 N02 peak drop 70% 5% *At initial conditions of: N02 10 pphm NO 100 pphm C3Hg 100 pphm Reaction Ik' = k Dvr'll = 1.0 31 experimental data could not be improved, even with large changes in the estimated rates of reaction. The variation of rate constants in some cases did have large effects on the predicted results as will be shown later. The reac tion rates given in Table V-2, in the column labeled rate constant, represent the optimum values to result in the minimum error of prediction. The failure of Mechanism A to accurately reflect experimental data appeared to be the too rapid disappear ance of the olefin source of free radicals, caused by the inaccuracy of the mechanism. When the olefin concentration was low, a pseudo-equilibrium appeared to exist between nitric oxide, nitrogen dioxide and ozone, with the result that their concentrations did not change with time. The pseudo-equilibrium concentrations appeared to be governed by the first three reactions of Mechanism A. This over simplified mechanism did, however, display that the free radical path of reaction did produce results resembling those obtained in chamber experiments. C. Effect of Variation of Estimated Rate Constants As shown in Figure V-2, the reduction of the rate constant of either reaction 6 or 8 caused a resultant Concentration (pphm) 100. Base — Effect of Change A N02 50 100 Elapsed Time (minutes) 150 Figure V-2 Effect of Change in K Value for Mechanism A , Reactions. 6 or 8 by Factor of 10*"1 OJ JO 33 reduction in the rate of propylene disappearance. Also, the height of the nitrogen dioxide peak was reduced to approximately half of the base case value. The rate of disappearance of the nitric oxide concentration was also reduced. The cause of these changes can be related direct ly to the rate constant change which caused a reduction in free radical concentration, thus slowing the overall reac tion. The increase of the rate constant for reaction 7 by a factor of ten resulted in a change to the rate of nitro gen dioxide production of a factor of two (Figure V-3). The low rate increase for nitrogen dioxide production can be explained by noting that the methoxyl radical is also formed in reaction 7. Higher concentration of this radi cal would increase the rates of reactions 10 and 11, thus removing nitrogen dioxide from the system at a faster rate. The increasing of the rate constant of reaction 10 by a factor of 10 (termination reaction) resulted in a lowering of the nitrogen dioxide peak by one-fourth and the elapsed time to this peak was double (Figure V-4). The disappearance rates of nitric oxide and olefin were reduced by a factor of approximately two. This result was Concentration (pphm) Base Effect of Change 100 0 50 100 150 Elapsed Time (minutes) Figure V-3 Effect of Change in K Value for Mechanism A, Reaction 7 by Factor of 10 to Concentration (pphm) ------ Base ■ — — Effect of Change 100 0 100 50 150 Elapsed Time (minutes) Figure V-4 Effect of Change in K Value for Mechanism A, Reaction 10 by Factor of 10 u U1 36 caused by removing free radicals and nitrogen dioxide from the system at a faster rate, thus ultimately lowering the atomic oxygen concentration and slowing the rate of conver sion of the olefin. Increasing the rate of reaction 11 by a factor of 10 had a similar effect, except that the rate of olefin disappearance was reduced by a factor of three (Figure V-5). Concentration (pphm) Base Effect of Change 100 0 50 100 150 Elapsed Time (minutes) Figure V-5 Effect of Change in K Value for Mechanism A, Reaction 11 by Factor of 10 u> CHAPTER VI PROPOSED MECHANISM B Due to the limited success of Mechanism A, it was used only as a concept for the postulation of a new mecha nism. This new Mechanism B, Table VI-1, was formulated with the goal of eliminating all of the assumptions inher ent in the oversimplified reactions of Mechanism A, and thus being closer to reality. Mechanism B contains all of the major reactions known or suspected of being important in the smog reaction. A. Description of Reactions The first seven reactions in Mechanism B (Table VI-1), relating the interaction of a system of nitrogen oxides and oxygen, were suggested as being important by Bufalini (12). For all of these reactions the rate con stants have been experimentally determined (Table VI-2). Reactions 9 through 17 were included as possible models for the interaction between organic free radicals and the nitrogen oxides. Reactions of this type have been suggested in the literature by Avery (22) and Leighton 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 39 TABLE VI-1 Reactions In Mechanism B N02 + hZ'-*- NO + 0 0 + 02 + M »-03 + M 03 + NO *- N02 + 0 2N0---+ 02-> “ 2N02 no2 + 03 -J — no3 + o2 no3 + N02 n2o5 N03 + NO » “ 2N02 NO + H02* -->“ N02 + OH* C2h3°3 * + NO )-C2H302* + N02 C2h3°2* + NO »- C2H30* + N02 CH30* + NO >-CH3* + N02 CH303* + NO )-CH302* + N02 CH302* + NO — CH30* + NOg C2h4°2 + NO *- CH3CHO + N02 ch3o* + 02 + NO h- ch3o2* + no2 CH3* + N02-->-CH30* + NO CH302* + N02-->- NO + 03 + CH3* 0 + c3h6 >-CH3* + C2H30* 03 + C3H6 »- HCHO + C2H402 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 40 TABLE VI-1 (con't.) ch3o- + c3h6 2CH3 * + c2h3o* ch3o2- + c3h6 — >-ch3- + ch3o* + c2h3o- c2h3°2 HCHO + CHO- ^■2^3^* ®2--C2H3O3 • CH3- + 02 + M >-CH302* + M C2H30* + 0H» >-CH3CH0 + 0 ch3o2• + o2 — o3 + ch3o* 0 + HCHO * — OH* + CHO* 0 + CHO* >- CO + OH- OH- + CHO CO + H20 ch3cho + OH---- V- ch3co- + H20 2CH3C0- -->- CH3CHO + c2h2o ch3o- + o2— ch3o3- CH30- + 02 HCHO + H02- H* + 02 -->- H02* CO + OH* H- + C02 20H* -->- 0 + H20 ch3o- + N02 — v-ch3ono2 C2H3°3* + N02— ->“ c2H303n02 (pAN* CH3* + NO 2-->-CH30N0 CH3 • + NO »- CH3NO 41 TABLE VI-2 Reaction Rate Constants for Mechanism B Reaction No. Rate Constant Range of Constants Used Units Reference 1 0.5 0.25— 1.0 b 2 1.4 x 106 - b (8) 3 0.5 - c (9) 4 3.0 x 10“6 - c (13,14) 5 1 x 10-3 - c (15) 6 8.5 - c (16) 7 245. - c (17) 8 10. - c est. 9 1000. 100— 10000 c est. 10 50. 10— 100 c est. 11 5 .1— 10 c est. 12 1000. .1— 1000 c est. 13 100 - c est. 14 100 10— 100 c est. a) In all reactions O2 was assumed to be at a constant concentration of 2 x 10^ pphm. b) min-* c) pphm"* min"* 42 Reaction No. TABLE Rate . Constant VI-2 (con't.) Range of Constants Used Units Referei 15 10 1— 10 b est. 16 80 - c (18) 17 1 - c est. 18 70. - c (10) 19 .0001 - c (11) 20 1. .1— 10 c est. 21 1. .1— 10 c est. 22 1000. 100— 1000 b est. 23 1000. 500— 1000 b est. 24 1.4 x 106 - b est. from 25 1. - c est. 26 .002 - c est. 27 50. .1— 50 c est. 28 .1 x 104 - c est. 29 .1 x 105 - c est. 30 1 .1— 1 c est. 31 1 .1— 1 c est. 32 .01 - b est. 33 10 1— 10 b est. 43 TABLE VI-2 (con't.) Reaction Rate Range of No. Constant Constants Used 34 2. x 10° - 35 1.0 - 36 40 - 37 10 1— 100 38 1 1— 10 39 40 - 40 12 Units Reference c est. from RX2 c (19) c (19,20) c est. c est. c (18) c (21) 44 (23). These reactions allow for both the free radical con version of nitric oxide to nitrogen dioxide and nitrogen dioxide to nitric oxide. Reaction 18 was included to model the attack of atomic oxygen on propylene. Cvetanovic (24) notes that the attack of atomic oxygen on propylene would probably occur at the single bond. The result of this attack would prob ably be the formation of a methyl free radical as was assumed in reaction 18. Altshuller (25) notes that in the reaction of ozone with olefins the attack would be on the double bond. This information led to the formulation of reaction 19 for the attack of ozone on the double bond of propylene, forming formaldehyde and a reactive intermediate. Reactions 20 and 21 represent an attempt to model the abnormally high rate of olefin disappearance suggested by Leighton (1). This high rate of disappearance was noted to be above that which could be explained by the re action of atomic oxygen and ozone with the olefin. Chain propagating reactions 22 through 36 were postulated to allow for interchange of oxygen between the free radicals and to allow for the formation of the 45 aldehyde products found in the photochemical reaction. Reaction 26 was suggested by Hanst (26) and reactions 30 and 31 by Avery (22). Chain termination reactions 37 through 40 were de rived from suggestions of Leighton (1). These reactions were considered to be the most important termination reac tions because of the high concentrations of the nitrogen oxide reactants. They serve both to diminish the free radical concentrations and as a route for the disappearance of the nitrogen oxides. Reaction 38 served as the route for the production of the peroxyacetyl nitrate (PAN) found in experimental data. No attempt was made to model all of the possible reactions in the smog system. Reactions were screened and only those believed important were used in Mechanism B. A discussion of the methods used to estimate the rate constant for the reactions is given in Appendix C. B. Comparison of Predicted and Experimental Results A comparison of the predicted results of Mechanism B and the experimental data is given in Table VI-3 and Figure VI-1. The predicted decay rate of the propylene almost exactly matches the experimental data. The 46 TABLE VI-3 Comparison of Results of Mechanism B* and Experimental Data DATA ^7 ^ PREDICTION pphm min pphm min O3 max 37 35 CH20 max 48 44 N02 max 85 79 NO half-life 40 30 C3H6 half-life 115 115 N02 peah drop 70% 62% *At initial conditions of: N02 10 pphm NO 100 pphm C3Hg 100 pphm CO 100 pphm Reaction 1 lc' = 3c [h^O =0.5 t Concentration (pphm) Experimental 100 Predicted 4 Aldehydes 50 100 0 150 Elapsed Time (minutes) Figure VI-1 Comparison of Mechanism B Predicted Results and Experimental Data 48 prediction of the ozone concentration was closely matched with the data until after the nitrogen dioxide concentra tion peak. At this point the prediction started to devi ate from the data. The maximum difference between the two curves was less than 6%. The maximum formaldehyde con centration prediction varied from the data by about 10%. In the case of both ozone and formaldehyde the predicted results were lower than the experimental data. The predicted rate of disappearance of the nitric oxide was too high by about 30%. The nitric oxide concen tration did, however, decline to a value of about four parts per hundred million as was expected. The high pre dicted rate resulted in an error in the concentration of approximately 20%. The nitrogen dioxide accumulation rate was predicted to be only about 82% of the observed rate. This resulted in an error in the elapsed time to the peak concentration of approximately 9%. Also, an error of 7% occurred in the calculation of the peak concentration. This prediction error relative to nitrogen dioxide is directly related to the too rapid disappearance of nitric oxide. The average deviation of the predicted results from 49 the experimental data was approximately 10%. This devia tion, however, lies within the estimated error of the ex perimental data of 20%. A test of the correlation between the data and the predictions resulted in a correlation co efficient of 0.96. For the chosen initial conditions, therefore, there is no significant difference between the experimental data and the predicted results. C. Effect of Varying Estimated Rate Constants The rate constant assigned to reaction 9 had no effect on the predicted values of Mechanism B when it was varied over a range of three orders of magnitude. This was the result of the slow production of the CgH-jOg* radical in reaction 23. Also, reaction 38 competed for the use of this radical. The varying of the rate constant of reac tion 23 also did not affect the predicted results of the mechanism. It did, however, affect the production of PAN by reaction 38. If the rate constant for reaction 23 was reduced, the production rate of PAN was also reduced by roughly the same factor. If the rate of reaction 23 was increased, the production rate of PAN did not greatly change. This was due to the more rapid consumption of the radical by reaction 9. The increase of the rate of reaction 10 by a factor of ten had varying effects on the system. The resultant nitrogen dioxide peak was slightly (5%) higher and the ozone peak was increased. The increase in the ozone peak can be directly related to the increase in the nitrogen dioxide production rate and thus, via reactions 1 and 2 an increase in the ozone rate of accumulation. This reac tion does, however, greatly affect the elapsed time to the nitrogen dioxide peak. The increase in the rate constant by a factor of ten caused the peak to be reached about one- third faster. Thus, reaction 10 has little effect on the resultant concentrations of the products, but does severe ly affect the time scale of the nitrogen oxides concentra tion curves. The increase in the rate of reaction 11 also has little effect on the peak concentrations of nitrogen di oxide and ozone. The rate of this reaction did, however, like reaction 10 severely affect the time scale of the re sultant concentration curves. Reactions 10 and 11 seemed to be the most important reactions relative to the deter mination of the elapsed time to the nitrogen dioxide and ozone peak. 51 Changes In the rate constants of reactions 12 through 15 had very little effect on the nitrogen dioxide or ozone curves. If any one of the reactions was assumed not to take place, however, the effect on the predictions of Mechanism B was great. The concentration of the free radicals involved in these reactions changed little (10.0%) with variation of the rates of the reactions. The lack of any one reaction shifted the production of the respective free radical to another reaction. This, in general, caused a lowering of the free radical concentration and a result ant lowering of the nitrogen dioxide peak. Also, reaction 14 is one of the sources of acetaldehyde. When this reac tion rate was set to zero, there was no outlet for the C2H4O2 intermediate, implying that the intermediate is stable. This is one inadequacy of Mechanism B. The possi bility of rearrangement of this intermediate to acetic acid was considered, but was felt to be too slow to be of any importance. Thus, the rates of reaction for this group of reactions was not important, as long as they were equal to some finite value. The results of the mechanism's predictions did not greatly depend on which one of the reactions, 20 or 21 52 was active. The best fit of the experimental data was ob tained by the use of both reactions. But, removing one of the reactions from consideration and doubling the rate of the other, produced results that were almost identical to those obtained when both reactions were active. The ex perimental results could not be reproduced without the use of at least one of these reactions. This result tends to lend further credence to the theory that free radicals are necessary to explain the smog reaction. These reactions could also be part of the reaction path followed by satu rated hydrocarbons, thus helping to explain the increase in the rate of olefin disappearance when they are present. The concentrations of the reactants of reaction 25 are so low that its rate constant can be varied over a wide range without the reaction competing with reaction 14 for the production of acetaldehyde. Reaction 27 is an attempt to model the maximum in the concentration of formaldehyde that occurs during the smog reaction. At least one molecule of formaldehyde forms with the reaction of each molecule of propylene. This will either be by direct formation in the ozone reaction or by the decomposition of a free radical, or by the decomposi 53 tion of acetaldehyde. As a result, it would be expected that the maximum formaldehyde yield would be at least as great as the initial concentration of propylene. This assumption, however, as shown by experimental data was false. The maximum yield of formaldehye is about one-half of the initial propylene concentrations. Thus, the rate constant of reaction 27 can greatly change the formaldehyde maximum. Reactions 28 and 29 served as a route for termina tion of free radical chains and for the production of car bon monoxide and water. These reactions were assumed to occur rapidly. No study was performed on the effect their rate constants had upon the system. Reactions 30 and 31 were used to control the con centration of acetaldehyde. These reactions were assumed to be slow and the ultimate fitting of the concentration of acetaldehyde to experimental data resulted in the verifi cation of this assumption. The rate constants of reactions 37 and 38 severely affected the system. The rate constant of reaction 38 was adjusted to approximate the experimental data on the pro duction of PAN. Increasing this rate constant resulted in 54 a lowering of the nitrogen dioxide peak, as would be ex pected (Figure VI-2). Reaction 37 had a slightly more pro nounced effect than reaction 38 due to the higher concen tration of its reactant free radicals. D. Varying of Initial Conditions The variation of the initial conditions were stud ied as to their effect on the predicted results. The reduction of the nitrogen dioxide initial con centration had no effect on the system other than the re duction of the nitrogen dioxide peak concentration (Figure VI-3). For an initial condition change of 8 pphm the peak concentration was reduced by 9 pphm. The time curves of the reactants and products did not appear to change with changes in the nitrogen dioxide initial condition. Changing the rate of reaction 1 (or, in fact, vary ing the incident light intensity) resulted in a spreading of the reactant and product curves relative to time (Figure VI-4). The maxima encountered did not vary, but all of the rates appeared to change inversely with the change in the rate of reaction 1. For example, a change in the rate of reaction 1 from 0.5 to 0.43 minutes-1 resulted in the Concentration (pphm) Base Case Increasing Rate of PAN Production 100 ▲ NO, ▼ no' • 0 0 50 100 150 Elapsed Time (minutes) Figure VI-2 Variation of Rate Constant for Reaction Producing PAN U1 U1 Concentration (pphm) Base Case 100 Change 0 150 100 50 Elapsed Time (minutes) Figure VI-3 Variation of Initial Concentration of NO2 in Mechanism B Ul o> Concentration ipphm) Base Case k| = .5 — Change k-^ » . 1*3 ▲ N02 - y NO 100 0 50 100 150 Elapsed Time (minutes) Figure VI-4 Variation of Light Intensity in Mechanism B < J 1 ' j 58 elapsed time to the nitrogen dioxide and ozone peaks in creasing by approximately the inverse ratio of the rate change. Doubling the initial concentration of nitric oxide (Figure VI-5) caused greatly different predictions. The heights of the nitrogen dioxide peaks varied directly with the nitric oxide initial concentrations. The nitric oxide half-life was doubled. The half-life of the propylene varied with the square root of the nitric oxide initial concentration. The ozone and formaldehyde maxima varied with the inverse square root of the nitric oxide initial concentrat ion. Figure VI-6 presents the effect of doubling the pro pylene initial concentration. The nitrogen dioxide maximum remains relatively unchanged with the shift in propylene concentration. The formaldehyde maximum increased propor tionally to the propylene initial concentration increase. The propylene half-life was reduced inversely by the square root of the propylene initial concentration change. Table VI-4 presents a comparison of the predicted vs. experimental results on changing the initial concen tration of the various reactants. As shown, the experi- Concentration (pphm) 200 — Base Case Change ▲ NO, ▼ NO 100 50 0 100 150 Elapsed Time (minutes) Figure VI-5 Variation of Initial Concentration of NO in Mechanism B ui VO Concentration (pphm) 200 — Base Case — Change HO; HO 100 0 50 100 150 Elapsed Time (minutes) Figure VI-6 Variation of Initial Concentration of Propylene in Mechanism B CTv o TABLE VI-4 Effect of Initial Conditions in Mechanism B* Initial Cond. Maxima (pphm) Half-life (minutes) Component o3 ch30 no2 NO c3h6 Changed pphm pred. exp. pred. exp. pred. exp. pred. exp. pred. exp. no2 2 35 37 44 43 72 85 30 40 115 115 C3H6 200 42 45 35 80 79 80 25 30 90 95 NO 200 26 30 38 40 140 150 63 80 145 150 i c All components are column, "Component at base Changed initial I I conditions except those in NO 100 pphm N02 10 pphm C3H6 100 pphm i - * 62 mental data supports all of the findings outlined above. These results indicate that Mechanism B is in reality a good model for the simulation of the smog reaction system studied. CHAPTER VII CONCLUSIONS Mechanism B proposed in Chapter VI predicts within reasonable accuracy the reactant and product changes with time of the reaction of propylene in an irradiated system containing oxygen, nitric oxide and nitrogen dioxide. The average error of prediction of Mechanism B as compared to the experimental data is 10%. This error is well within the uncertainty of the experimental data which has an average error of 20%. The system was investigated over a range of initial concentrations, varying from 100 to 200 pphm for propylene and nitric oxide, and from 2 to 10 pphm for nitrogen di oxide. Over the entire range, the predicted results agreed closely with experimental data. The test of Mechanism B over a range of initial con ditions was the true tests of its validity. With estima tion of rate constants, it would be possible to duplicate the experimental results at one set of initial conditions with many modifications of Mechanism B. It would not be 63 64 possible, however, to achieve this duplication over many sets of initial conditions if the mechanism did not closely duplicate reality. As shown in Chapter VI, not only does Mechanism B predict accurate results at a variety of initial conditions, but also, the predicted mathematical relation of the change from one set of conditions to another agrees closely with experimental observations. Mechanism B depends for its success on free radical chain reactions. The observed rate of disappearance of propylene does not tally with the rate at which propylene reacts with atomic oxygen and ozone, as proposed by earlier investigations. Mechanism B shows that by considering re actions of free radicals with propylene, experimental data can be duplicated. REFERENCES 1. Leighton, P. A., "Photochemistry of Air Pollution," Academic Press, New York, 254-271 (1961). 2. Haagen-Smit, A. J., "Chemistry and Physiology of Los Angeles Smog," Ind. Engr. Chem., 44, 1342 (1952). 3. Morris, F. V. and Bolze, C., "Reactions of Auto Exhaust in Sunlight," Report No. 19, Air Pollution Foundation, Los Angeles, Calif. (1957). 4. Saltzman, R. J., "Kinetic Studies of Formation of Atmospheric Oxidants," Ind. Engr. Chem., _50, 677 (1958). 5. Wayne, L. G., "On the Mechanism of Photo-Oxidation in Smog," Archives of Environmental Health, 1 _ , 229 (1963). 6. Wayne, L. A., Hancock Foundation, University of Southern California, Los Angeles, Calif., Personal Communicat ion. 7. Romanovsky, J. C., Ingels, R. M. and Gordon, R. J., "Estimation of Smog Effects in the Hydrocarbon- Nitric Oxide System," Report 66-42, California Dept, of Public Health, Vehicle Pollution Laboratory, Los Angeles, Calif. (1966). 8. Benson, S. W. and Axworthy, A. E., "Mechanism of the Gas Phase Thermal Decomposition of Ozone," J. Chem. Phys., 26, 1718 (1957). 9. Johnston, H. S. and Crosby, H. J., "Kinetics of the Fast Gas Phase Reaction Between Ozone and Nitric Oxide," J. Chem. Phys., Z2, 689 (1954). 10. Leighton, P. A., op. cit., p. 160. 11. Leighton, P. A., op. cit., p. 142. 65 66 12. Bufalini, J. J. and Stephen, E. R., Int. J. Air Water Pollution, 9, 123 (1965). 13. Bodenstein, M., "Die Geschwindigkeit der Vereinigung von Stickoxyd und Sauerstoff," Z. Angew. Chem., 31. 145 (1918). 14. Glasson, W. A. and Tuesday, C. S., "Atmospheric Thermal Oxidation of Nitric Oxide," J. Am. Chem. Soc., 85, 2901 (1963). 15. Johnston, H. S. and Yost, P. M., "Kinetics of the Rapid Gas Reaction Between Ozone and Nitrogen Di oxide," J. Chem. Phys., J L 7 . , 386 (1949). 16. Schott, G. and Davidson, N., "Shock Waves in Chemical Kinetics," J. Am. Chem. Soc., _80, 1841 (1958). 17. Johnston, H. S., "Four Mechanisms Involving Nitrogen Peroxide," J. Am. Chem. Soc., T3, 4542 (1951). 18. Phillips, L. and Shaw, R., Symp. Combust., 10th, Univ. Cambridge, Cambridge, England, 453-61 (1964). 19. Westenberg, A. A. and Wilson, W. E., "ESR Intensity Relations and Some Gas Phase Chemical Kinetics of the OD Radical," J. Chem. Phys., 45, 338 (1966). 2C. Dixon-Lewis, G., Wilson, W. E. and Westenberg, A. A., "Studies of Hydroxyl Radical Kinetics by Quantita tive ESR," J. Chem. Phys., 44, 2877 (1966). 21. Christie, M. I. and Frost, J. S., "Association Reac tions of Alkyl Radicals with Oxygen and with Nitric Oxide," Trans. Faraday Soc., 61, 468 (1965). 22. Avery, H. E. and Cvetanovic, R. J., "Reaction of Oxygen Atoms with Acetaldehyde," J. Chem. Phys., 43, 3727 (1965). 23. Leighton, P. A., op. cit., p. 210. 67 24. Cvetanovic, R. J., "Addition of Atoms to Olefins in Gas Phase," Advances in Photochemistry, _1, Inter science, p. 119 (1963). 25. Altschuller, A. P. and Bufalini, J. J., "Photochemical Aspects of Air Pollutions A Review," Photochemistry and Photobiology, 4_, 97 (1965) . 26. Hanst, P. L. and Calveri, J. G., "Oxidation of Methyl Radicals at Room Temperature," -I. Phys. Chem., 63, 71 (1959). 27. "System/360 Scientific Subroutine Package," H20-0205- 2, International Business Machines Corp., White Plains, New York, 122-129 (1967). 28. Benson, S. W., Thermochemical Kinetics. Wiley & Sons, New York (1968). APPENDICES A. Computer Programs B. Data from Test of Pseudo-steady State Assumption C. Estimation of Rate Constants 68 APPENDIX A COMPUTER PROGRAMS This Appendix contains the computer programs used in developing the mechanism of smog production. Also in cluded is a set of sample input and output of the programs. 70 TABLE A—1 Input Program DIMENSION A(20)*Y(50),PRMTI5)tAUX(16,50),DERY(50) DOUBLE PRECISION X,Y,PRMT,DERY,AUX,AAA,AAAA,BB DOUBLE PRECISION ZZ COMMON ZZ,BB,LABEL(50),N,NC,NEQ,NO IF REAL*8 LABEL,CCC/' */ EXTERNAL FCT,OUTP DO 600 1=1,50 600 LABEL(I)=CCC DO 500 1=1,50 500 DERY(I)=0. AAA=00. 11 READ(5»100,END=33) A N=0 BB= 1.0D08 100 FORMAT(20A4) READ(5,101) PRMT 11)* PRMTI2)* PRMTI 3)»PRMTI 4) READ(5,102) NDIM,NC,NEQ NDIF = NDIM DO 10 1=1,NC 10 RE ADI 5,103) LABEL( I),YI I) 104 FORMAT I»IHLF = *14) DO 12 1=1,NDIF DERY(I) = .1 12 AAA=AAA+DERY(I) DERYU) = I.-AAA 101 FORMAT(4D20.0) 102 FORMAT(3110) 103 FORMAT(A8»D12.0) WRITEI 6,105) A 105 FORMAT!*1*,20A4) CALL DHPCGIPRMT,Y,DERY,NDTM, IHLF,FCT,OUTP,AUX) WRITEI 6,104) IHLF GO TO 11 33 CALL EXIT FND TABLE A-2 Output Program SUBROUTINE OUTPIX,Y,DERY,IHLF,NOIMtPRMT DIMENSION Yf1),DERY!1),PRMTI1) DOUBLE PRECISION X,Y,DERY,PRMT,BB DOUBLE PRECISION ZZ COMMON ZZ,BB,LABEL!50),N,NC,NEQ,NDIF REAL*8 LABEL IF{BB— 5.0D02) 7,6,6 6 WRITE(6,100) BB=0.ODO DO 10 1=1,NC 10 WRITE{6,101) (I),LABEL!I),X»Y(I),DERY(I WRITE(6,102) ZZ 102 FORMAT!///' CHAIN YIELD = *,020.3) 7 BB=BB+1.ODO 101 FORMAT!' • , 13,IX,A8,3X,3D20.9) 100 FORMAT !'l" COMPOUND TIME - MIN. /• DERIVATIVE - PPHM/MIN'//) 5 RETURN END CONCENTRATION PP4M' TABLE A-3 Derivative Calculation Program SUBROUTINE FCT(X,Y,DERY) DIMENSION C(50)» D(50),DNM(50),UNM(50)tQ<50,50),Y{ I),OERY(I) DIMENSION FMTI20) DOUBLE PRECISION X,Y,DERY,C,D,DNM,UNM,BB,ZZ COMMON ZZ,BB,LABEL<50),N,NC,NEQ,NDIF INTEGER Q REAL* 8 LABEL IF(N-IOl) 1,2,1 1 WRITE(6 ,102) 102 FORMAT!'1*,'K-VALUES FOR REACTIONS'//) DO 10 1=1,NEQ READ(5,100) C(I) 10 WRITE(6 ,101) I,C( I) 101 FORMATC •,I4,5X,D20.8) 109 FORMAT120A4) READ{5»109) FMT READ!5*FMT){(Q(I,J),1=1,NEQ),J = 1»NC) WRITE C6 ,112) 112 FORMAT!•1*,'INPUT MATRIX//ROWS ARE COMPOUNDS/COLUMNS ARE EQUATION /S' ) WRITE(6 ,FMT)((QlI,J),1=1,NEQ),J=1,NC) 2 N = 101 100 FORMAT(5X,D20.8 ) DO 200 1=1,NEQ D( I )= C( I) DO 200 J=l,NC IF 1QI I, J )) 202,200,200 202 D! I) = D(I)*Y{J) IF(Q{I,J )+ 1) 203,200,200 203 D(I) = D «I)* Y(J) -o to TABLE A-3 (con't.) 200 CONTINUE DO 211 J= 1 »NC DERY(J) = 0.0D0 UNM(J) = O.ODO DNM(J) = O.ODO DO 211 1=1,NEQ IF(0(ItJ)) 210,211,212 210 DNM(J) = DNM(J) + DC I) IF (Q (I,J ) + l) 215,211,211 215 DNM(J J =DNM(J) + DII) GO TO 211 212 UNM(J)= UNM(J) + D(I) IFCQCI,JI—11 211,211,216 216 UNM(J)=UNM(J) + D(I) 211 CONTINUE DO 220 J=1,NDIF 220 DERY(J) = UNM(J) - DNM(J) NZZ = NDIF +1 DO 231 J=NZZ,NC IF(Q(NEQ,J)—8 ) 300,300,231 300 IF(Y(J)) 234,234,232 232 DNM(J) = DNM(J)/Y(J) IF(DNM(J )) 234,234,233 233 Y(J) = UNM(Jl/DNMIJ) GO TO 231 234 Y(J) = l.D-15 231 CONTINUE ZZ = DERY(1)/D(6) RETURN END co nnonnoonoonnonooooooononnooooo TABLE A-4 Hamming's Modified Predictor-Corrector Program SUBROUTINE DHPCG PURPOSE TO SOLVE A SYSTEM OF FIRST ORDER ORDINARY GENFRAL DIFFERENTIAL EQUATIONS WITH GIVEN INITIAL VALUES. USAGE CALL DHPCG (PRMT,Y,DERY,NDTM,IHLF,FCT,OUTP,AUX) PARAMETERS FCT AND OUTP REQUIRE AN EXTERNAL STATEMENT. DESCRIPTION PRMT OF PARAMETERS DOUBLE PRECISION INPUT AND OUTPUT VECTOR WITH DIMENSION GREATER THAN OR EQUAL TO 5, WHICH SPECIFIES THE PARAMETERS OF THE INTERVAL AND OF ACCURACY AND WHICH SERVES FOR COMMUNICATION BETWEEN OUTPUT SUBROUTINE (FURNISHED BY THE USER) AND SUBROUTINE DHPCG. EXCEPT PRMT(5) THE COMPONENTS ARE NOT DESTROYED BY SUBROUTINE DHPCG AND THEY ARE , LOWER BOUND OF THE INTERVAL (INPUT), UPPER BOUND DF THE INTERVAL (TNPUT), INITIAL INCREMENT OF THE INDEPENDENT VARIABLE (INPUT), PRMT(4)— UPPER ERROR BOUND (INPUT). IF ABSOLUTE ERROR IS GREATER THAN PRMT(4), INCREMENT GETS HALVED. IF INCREMENT IS LESS THAN PRMT(3) AND ABSOLUTE ERROR LESS THAN PRMT(4)/50, INCREMENT GETS DOUBLED. THE USER MAY CHANGE PRMT(4> BY MEANS OF HIS OUTPUT SUBROUTINE. PRMT f1) — PR MT(21 — PR MT(3)- ooonocinooooononnonnnnnooooooonno TABLE A-4 (con't.) PRMT(5>- NO INPUT PARAMETER. SUBROUTINE DHPCG INITIALIZES PRMT15)>0. IF THE USER WANTS TO TERMINATE SUBROUTINE OHPCG AT ANY OUTPUT POINT, HE HAS TO CHANGE PRMT(5) TO NON-ZERO BY MEANS OF SUBROUTINE OUTP. FURTHER COMPONENTS OF VECTOR PRMT ARE FEASIBLE IF ITS DIMENSION IS DEFINED GREATER THAN 5. HOWEVER SUBROUTINE DHPCG DOFS NOT REQUIRE AND CHANGE THEM. NEVERTHELESS THEY MAY BE USEFUL FOR HANDING RESULT VALUES TO THE MAIN PROGRAM ICALLING DHPCG) WHICH ARE OBTAINED BY SPECIAL MANIPULATIONS WITH OUTPUT DATA IN SUBROUTINE OUT*. Y - DOUBLE PRECISION INPUT VECTOR OF INITIAL VALUES (DESTROYED). LATERON Y IS THE RESULTING VECTOR OF DEPENDENT VARIABLES COMPUTED AT INTERMEDIATE POINTS X. DERY - DOUBLE PRECISION INPUT VECTOR OF ERROR WEIGHTS (DESTROYED). THE SUM OF ITS COMPONENTS MUST BE EQUAL TO 1. LATERON DERY IS THF VECTOR OF DERIVATIVES, WHICH BELONG TO FUNCTION VALUES Y AT INTERMEDIATE POINTS X. NDIM - AN INPUT VALUE, WHICH SPECIFIES THF NUMBER OF EQUATIONS IN THE SYSTEM. IHLF - AN OUTPUT VALUE, WHICH SPECIFIES THE NUMBER OF BISECTIONS OF THE INITIAL INCREMENT. IF IHLF GETS GREATER THAN 10, SUBROUTINE OHPCG RETURNS WITH ERROR MESSAGE IHLFM1 INTO MAIN PROGRAM. ERROR MESSAGE THLF>12 OR IHLF>L3 APPEARS IN CASE PRMT(3)>0 OR IN CASE SIGN(PRMT(3)).NE.SIGN(PRMT(2)- PRMT(I)) RESPECTIVELY. FCT - THE NAME OF AN EXTERNAL SUBROUTINE USED. IT COMPUTES THE RIGHT HAND SIDES DERY OF THE SYSTEM TO GIVEN VALUES OF X AND Y. ITS PARAMETER LIST -j m oooonnnnoonoooononnnooono TABLE A-4 (con't.) MUST BE X,Y,DERY. THE SUBROUTINE SHOULD NOT DESTROY X AND Y. OUTP - THE NAME OF AN EXTERNAL- OUTPUT SUBROUTINE USED. ITS PARAMETER LIST MUST BE X,Y,DERY,IHLF,NDlM,PRMT. NONE OF THESE PARAMETERS (EXCEPT. IF NECESSARY, PRMTC4),PRMT(5),...) SHOULD BE CHANGED BY SUBROUTINE OUTP. IF PRMT(5) IS CHANGED TO NON-ZERO, SUBROUTINE DHPCG IS TERMINATED. AUX - DOUBLE PRECISION AUXILIARY STORAGE ARRAY WITH 16 ROWS AND NDIM COLUMNS. REMARKS THE PROCEDURE TERMINATES AND RETURNS TO CALLING PROGRAM, IF (1) MORE THAN 10 BISECTIONS OF THE INITIAL INCREMENT ARE NECESSARY TO GET SATISFACTORY ACCURACY (ERROR MESSAGE IHLF>1 1 ), (2) INITIAL INCREMENT IS EQUAL TO 0 OR HAS WRONG SIGN (ERROR MESSAGES IHLF>12 OR IHLF>13), (3) THE WHOLE INTEGRATION INTERVAL IS WORKED THROUGH, (4) SUBROUTINE OUTP HAS CHANGED PRMT(5) TO NON-ZERO. SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED THE EXTERNAL SUBROUTINES FCT{X,Y,DERY) AND OUTP(X,Y,DERY,IHLF,NDIM,PRMT) MUST BE FURNISHED BY THE USER. 'j C T i oo n n n n o n n n n n n n n n n o o o o n l TABLE A-4 (con't.) METHOD EVALUATION IS DONE BY MEANS OF HAMMINGS MODIFIED PRFDICTOR- CORRECTOR METHOD. IT IS A FOURTH ORDER METHOD, USING 4 PRECEEDING POINTS FOR COMPUTATION OF A NEW VECT3R Y OF THE DEPENDENT VARIABLES. FOURTH ORDER RUNGE-KUTTA METHOD SUGGESTED BY RALSTON IS USED FOR ADJUSTMENT OF THE INITIAL INCREMENT AND FOR COMPUTATION OF STARTING VALUES. SUBROUTINE DHPCG AUTOMATICALLY ADJUSTS THE INCREMENT DURING ' THE WHOLE COMPUTATION BY HALVING OR DOUBLING. TO GET FULL FLEXIBILITY IN OUTPUT, AN OUTPUT SUBROUTINE MUST BE CODED BY THE USER. FOR REFERENCE, SEE (1) RALSTON/WILF, MATHEMATICAL METHODS FOR DIGITAL COMPUTERS, WILEY, NEW YORK/LONDON, 1960, PP.95-109. (2) RALSTON, RUNGE-KUTTA METHODS WITH MINIMUM ERROR BOUNDS, MTAC, VOL.16, ISS.80 (1962), PP.431-437. SUBROUTINE DHPCG(PRMT,Y,DERY,NDIM,IHLF,FCT,OUTP,AUX) DIMENSION PRMT(1),Y(1),DERY(1),AUX(16,1) DOUBLE PRECISION Y,DERY,AUX,PRMT,X,H,Z,DELT N=1 IHLF=0 X= PRMT (1) H=PRMT(3) PRMT(5 ) = 0.DO 00 1 1=1,NDIM AUX (16 , T ) = 0 .DO ~j no n no noon on TABLE A-4 (con't.) AUX (15,1 )=DERY(I) 1 AUX(1» T)=Y(I) IF(H*(PRMT(2)-X))3,2,4 ERROR RETURNS 2 IHLF=12 GOTO 4 3 IHLF=13 COMPUTATION OF DERY FOR STARTING VALUES 4 CALL FCT(X , Y,DERY) RECORDING OF STARTING VALUES CALL OUTPIX,Y,DERY,IHLF,NDIM,PRMT) IF(PRMT(5))6 ,5, 6 5 IF(IHLF)7,7, 6 6 RETURN 7 DO 8 1=1,NDIM 8 AUXI8 ,I)=DERY(I) COMPUTATION OF AUX(2,I) ISW=1 GOTO 100 9 X= X+H DO 10 1=1,NDIM 10 AUXI2,I)=Y( I) INCREMENT H IS TESTED BY MEANS OF BISECTION 11 IHLF=IHLF+l X=X—H DO 12 1=1,NDIM 12 AUX(4, I) =AUX(2,1) 00 no no no TABLE A-4 (con't.) H=.5D0*H N= I I SW=2 GOTO 100 C 13 X=X+H CALL FCT(X»Y,DERY) N=2 DO 14 1=It NDIM AUX(2,I)=Y(I) 14 AUX(9,I)=DERY(I) ISW=3 GOTO 100 COMPUTATION OF TEST VALUE DELT 15 DELT=0.DO DO 16 1=1,NDIM 16 DELT=DELT+AUX(15,1)*DAB S(Y11)—AUX(4,1)) DELT=•06 6666666666666667D0*DELT IHLF = 5 IF(DELT-PRMT(41)19,19,17 17 IF(IHLF- 10)11,18,18 NO SATISFACTORY ACCURACY AFTER 10 BISECTIONS. ERROR MESSAGE. 18 IHLF=11 X=X+H GOTO 4 THERE IS SATISFACTORY ACCURACY AFTER LESS THAN 11 BISECTIONS. 19 X= X+H CALL FCT(X,Y,DERY) TABLE A-4 (con't.) DO 20 1=1,NDIM AUX(3»I)=Y(I) 20 AUX(10,I)=DERY(I) N=3 IS W=4 GOTO 100 21 N= 1 X=X+H CALL FCT{X,Y»DERY) X=PRMT (1) DO 22 1=1,NDIM AUX(11»I)=0ERY(I) 223Y( I ) = AUX(1,I)+H*(«375D0*AUX(8,1 )+.7916 666666666667D0*AUX (9, T) 1-. 20833333333333333D0*AUX (10,1 )+.04166666666666666700*DERY( I) ) 23 X= X+H N=N+1 CALL FCT(X,Y,DERY) CALL OUTP(X,Y,DERY,IHLF,NDIM, PRMT) IF(PRMT(5))6,24,6 24 IF(N-4)25,200,200 25 DO 26 1=1,NDIM AUXIN,I)=Y11) 26 AUXIN+7, I) = DERY11) IF(N-3)27,29,200 27 DO 28 1=1,NDIM DELT=AUX(9,1J+AUXI9,I) DELT=DELT+DELT 28 Y(I) = AUX11,I)+.33333333333333333D0*H*IAUX(8,1)+DELT+AUX(10,T)) c o o TABLE A-4 (con't.) GOTO 23 C 29 00 30 1=1,NDIM 0ELT=AUX(9tI)+AUX(10,I) DELT=DELT+DELT+DELT 30 Y(I) = AUX(1»I) + •375D0*H*lAUX( 8,1)+DELT+AUX(11,1) I GOTO 23 C C C C THE FOLLOWING PART OF SUBROUTINE DHPCG COMPUTES BY MEANS OF C RUNGE-KUTTA METHOD STARTING VALUES FOR THE NOT SELF-STARTING C PREDICTOR-CORRECTOR METHOO. 100 DO 101 1=1,NDIM Z=H*AUX(N+7,1) AUX(5,I)=Z 101 YU) = AUX(N,I) + .4D0*Z C Z IS AN AUXILIARY STORAGE LOCATION C Z=X+.4D0*H CALL FCT(Z,Y,DERY) DO 102 1 = 1,NDT M Z=H*DERY(I) AUX(6 ,1)=Z 102 Y(I)=AUX(N,I)+.2969776092477536ODO*AUX(5,1)+.15875964497103583D0*Z C Z=X+.4557372542187894300*H CALL FCT(Z,Y,DERY) DO 103 1=1,NDIM Z=H*DERY(I) AUX(7,I)=Z 103 Y(I)=AUX(N,I) + »21810038822592047D0*AUX(5,1)—3.0509651486929308DO* 1AUX(6,I)+3.8328647604670103D0*Z TABLE A-4 (con't.) C Z=X+H CALL FCT(Z ,Y,DERY) 00 104 1=1,NDIM 1040Y(I)=AUXIN,I)+.17476028226269037D0*AUX(5,I)-.5514806628787329400* 1AUX(6,I)+1.205535599396523500*AUX(7,1)+.1711847812195190300* 2H*DERY{I) G0T0I9,13,15,21),ISW c *****:* $* $$$$$$*$$$$$#$ **$$$$$ $$*$$$* $*$$£$$ C C C POSSIBLE BREAK-POINT FOR LINKAGE C C C STARTING VALUES ARE COMPUTFO. C NOW START HAMMINGS MODIFIED PREDICTOR-CORRECTOR METHOD. 200 ISTFP= 3 201 IF(N-8)204,202,204 C C N> 8 CAUSES THE ROWS OF AUX TO CHANGE THEIR STORAGE LOCATIONS 202 DO 203 N=2,7 DO 203 1=1,NDIM AUXIN-l,I)=AUXIN,I) 203 AUXIN+6 ,I)=AUX(N+7,I) 00 to ooooo no no TABLE A-4 (con't.) N=7 N LESS THAN 8 CAUSES NCI TO GET N 204 N=N+1 COMPUTATION OF NEXT VECTOR Y DO 205 I = 1»NDIM AUX (N-1,I)=Y(T) 205 AUX(N+6 » I)=DERYlI) X=X+H 206 ISTEP=ISTEP+1 DO 207 1=1,NDIM 0DELT=AUX(N-4,1)+l.3333333333333333D0*H*(AUX( N+6 ,I)+AUX(N+6 ,I)- 1AUX(N+5,I)+AUX(N+4,I)+AUX(N+4,I)) Y(I) = DELT— »9256198347107438D0*AUX(16,1) 207 AUX(16,1)=DELT PREDICTOR IS NOW GENERATED IN ROW 16 OF AUX, MODIFIED PREDICTOR IS GENERATED IN Y. DELT MEANS AN AUXILIARY STORAGE. CALL FCT(X,Y,DERY) DERIVATIVE OF MODIFIED PREDICTOR IS GENERATED IN DERY DO 208 1=1,NDIM ODELT=.12 5D0*(9.D0*AUX(N-1,I)-AUX(N-3,I)+3.DO*H*(DERY(I)+AUX(N+6 ,I) 1+AUX(N+6 ,I)-AUX(N+5,I))) AUX(16,T)=AUX(16,1J-DELT 208 Y(I)=DELT+.07438016528925620D0*AUX(16,I) 00 U) noon on no TABLE A-4 (con't.) TEST WHETHER H MUST BE HALVED OR DOUBLED DELT=0.DO DO 209 1=1,NDIM 209 DELT=DELT+AUX(15,I)*DABS(AUX<16,1)) IF(DELT-PRMT(4)>210,222,222 H MUST NOT BE HALVED. THAT MEANS YU) ARE GOOD. 210 CALL FCT(X,Y»DERY) CALL OUTPIX,Y,DERY,IHLF,NDIM, PRMT) IHLF = 5 IF(PRMT(5))212 ,211,212 211 IF(IHLF-11)213,212,212 212 RETURN 213 IF(H*(X-PRMT(2)))214,212,212 214 IF(0ABS(X-PRMT(2))-.1D0*DABS(H))212,215,215 215 IF(DELT-.02D0*PRMT(4))216,216,201 H COULD BE DOUBLED IF ALL NECESSARY PRECEFDING VALUES ARE AVAILABLE 216 IFCH-.01) 217,201,201 217 IF(N—7)201,218,218 218 IF(1STEP-41 201,219,219 219 IMOD=ISTEP/2 00 . f * TABLE A-4 (con't.) IF{ISTEP —I MOD—IMOD)201,220,201 220 H=H+H IHLF=IHLF-1 I STEP = 0 DO 221 1=1,NDIM AUX(N-1, I) = AUX ( N—2, I) AUX'N-2, I)=AUX(N-4»I) AUX(N-3, n=AUX(N-6 ,I) AUX(N+6 ,I)=AUX(N+5,I) AUX{N+5, I)=AUX(N+3,I) AUX(N+4,I)=AUX(N+l,I) DELT=AUX(N+6 »I)+AUX{N+5 »I) DELT=DELT+DELT+DELT 2210AUX(16,1 )=8.962962962962963D0*(Y(I)-AUX(N-3, I )) 1-3.3611111111111111D0*H*(DERY(I)+DELT+AUX(N+4, I)) GOTO 201 C C C H MUST BE HALVED 222 IHLF=IHL F+1 IHLF = 5 IF(IHLF-10)223,223,210 223 H=.5D0*H oo tn TABLE A-4 (con't.) ISTFP=0 DO 224 1=1,NDIM 0Y(I) = .390625D-2*(8.Dl*AUX(N-l,I)+135.DO*AUX(N-2,I)+4.51*AUX{N-3,1 ) i+AUXIN—4 , I ) >-.U71875D0*( AUX (N+6 ,1 )-6.D0*AUX( N+5, I)-AUX (N+4,1 ) )*H 0AUX(N-4,I)=•390625D-2*(12.DO*AUX(N-l,I)+135.DO*AUX(N-2,T)+ 1108.D0*AUX(N-3 »I)+ AUX(N-4,I))-.023437500*IAUX(N+6,I)+ 218.DO* AUX(N+5,I)-9.DO*AUX(N+4,I))*H AUX(N-3,I)=AUX(N-2,I) 224 AUX(N+4,I)=AUX(N+5 »I) X=X—H DELT=X-{H+H) CALL FCT(DELT,Y,DERY) DO 225 1=1,NDIM AUX(N-2, I)=Y( I) AUX( N+5, I)=DERY( I) 225 YCI) = AUX(N-4,I) DELT=DELT-(H+H) CALL FCT(DELT,Y,DERY) DO 226 1=1,NDIM DELT=AUX(N+5,1)+AUX(N+4, I ) DELT=DEL T+DELT+DELT 0AUX(16,I)=8.962962962962963D0*(AUX(N-1,I)-Y(I)) 1-3.3611111111111111D0*H*(AUX(N+6,I)+DELT +DERY(I)) 226 AUXIN+3,I)=DERY(I) GOTO 206 END 00 < X i 87 Card Card Card 3 Card 4 Card 5 Card 6 TABLE A-5 Sample Input 80 columns of title information 1 Col. 1-20 initial time Col. 21 - 40 final time Col. 41 - 60 initial stepsize Col. 61 - 80 maximum error desired Col. 1-10 number of differential equations considered by program Col. 11 - 20 number of variables Col. 21 - 30 number of equations Card 4 and those following contain initial conditions for each variable. There must be a card 4 for each variable. Col. 1 - 8 variable name Col. 9-20 initial concentration Contains reaction rates for each reaction Col. 1 - 5 reaction number Col. 6-25 reaction rate There must be a card 5 for each reaction. Format under which reaction matrix is to be 88 TABLE A-5 (con't.) read. Must read a number for each reaction in the format statement. Card 7 Contains the reaction matrix to be read under the format of card 6. Notes: 1. Each variable in the matrix must be in the same order as variables on card 4. Variables are rows. 2. Reactions must be in same order as on card 5. Reactions are columns. 3. Program reads across the card for each component in reaction order. Sample Input: Consider reactions A + B— C (1) k = 1 C + D— t-E (2) k = 4 E + F— G (3) k = 6 Where C and E are free radicals and the steady state assumption is used Initial time 0.0 Final time 10. Increment .01 89 TABLE A-5 (con't.) Error .001 Differential Eq. Considered (A,B,D,F,G) 5 Input: Title Sample Input 0.0 10.0 .01 .001 5 7 3 A 1.0 B 1.0 D 1.0 F 1.0 G 0.0 C 0.0 E 0.0 1 1. 2 4. 3 6. (3F10.0) -1 -1 -1 1 1 -1 1 -1 /* 1 COMPOUND TIME - MIN. TABLE A-6 Sample Output CONCENTRATION PPHM' DERIVATIVE - PPHM/MIN 1 N02 0.575677500D 01 0.155870247D 02 0.10 157866 ID 01 2 NO 0.5756 77500D 01 0.940481753D 02 -0.109350389D 01 3 03 0.5756775000 01 0.547578916D 00 0.466314882D-01 4 C3H6 0.5756 77500D 01 0.995874226D 02 -0.873328676D-01 5 CH20 0.575677500D 01 0.434727164D 00 0.9103021840-01 6 CH3CH0 0.575677500D 01 0.247397526D-01 0.545214711D-02 7 CO 0.575677500D 01 0.100000000D 03 0.0 a 0. 0.575677500D 01 0.110781734D-04 0.0 9 H. 0.5756775000 01 0.218704501D—08 0.0 10 HO 2 0.575677500D 01 0.9062135240-05 0.0 n CHO 0.5756775000 01 0.102899022D—01 0.0 12 N20. 0.5756775000 01 0.10 0000000 D—14 0.0 13 HNO. 0.5756775000 01 0.100000000D—14 0.0 14 OH. 0.5756 77500D 01 0.4375158 74D-04 0.0 15 CH3. 0.575677500D 01 0.7402642600-05 0.0 16 CH30 . 0.5756775000 01 0.414987033D-03 0.0 17 CH302. 0.5756775000 01 0.523535171D-04 0.0 18 CH303. 0.5756775000 01 0.44097371ID—10 0.0 19 C2H30. 0.575677500D 01 0.1586897040-03 0.0 20 C2H302. 0.575677500D 01 0.8172068200-04 0.0 21 C2H303. 0.575677500D 01 0.1686525840-05 0.0 22 N03 0.5756775000 01 0.368301472D-06 0.0 23 C2H402 0.5 75677500D 01 0.5798302060-06 0.0 CHAIN YIELD = 0.132D 02 o APPENDIX B DATA FROM TEST OF PSEUDO-STEADY STATE ASSUMPTION Pseudo-steady Non-steady Time Assumption State Free Radical (min) (pphm x 105) (pphm x 105) 0* 5.6 1.78 1.77 21.6 4.30 4.33 41.6 5.34 5.35 86.4 4.06 4.09 OH* 5.6 2.07 2.00 21.6 6.61 6.53 41.6 9.03 9.13 86.4 8.86 8.80 CH • 5.6 2.42 2.39 O 21.6 2.27 2.30 41.6 1.98 1.97 86.4 1.55 1.59 CH-0* 5.6 50.1 50.0 21.6 43.5 43.6 41.6 39.7 39.6 86.4 33.6 33.5 ch3o2* 5.6 4.68 4.74 21.6 11.1 11.1 41.6 16.0 16.2 86.4 20.7 20.6 ch3o3* 5.6 .077 .078 21.6 .079 .078 41.6 .083 .084 86.4 .089 .090 91 APPENDIX C ESTIMATION OF RATE CONSTANTS The rate constants used in this paper were obtained from two sources. One source was that of experimental de terminations found in the literature. The references for the rate constants taken from the literature are given in Table VI-2. These values, as reported by the authors, were felt to be accurate to plus or minus one third of a factor of ten. Where more than one reference was cited, the value used was an average of those reported. Where multiple values of the rate constants for one reaction were found, the error between the reported values was at most a factor of ten, as in the values given for reaction 36. The remaining rate constants were estimated by the method developed by Benson (28). This method is based on the transition state theory. From this theory, the rate constant can be expressed as a function of the enthalpy and entropy of the reactants and of the transition state intermediate formed in the reaction. A + B [AB1 C + D (C—1) 92 93 _ r ): In equation C-l, A and B are the reactants and J~ABj is the transition state intermediate. The rate constant for this reaction can be derived from transition state theory. Consider that between the products and the reactants there exists an equilibrium: t = M * . 2. W [B] <C 21 The rate at which the products are formed is: d [c ~] = d C d] d [a] = _ d M _ [ ab]^ (C-3) dt dt dt dt where k ^ is the specific rate constant for the passage of the intermediate to the products. Combining equations C-2 and C-3 results in: - dd- t— = [A] [Bl (C-4) From equation C-4 we see that the specific rate constant for the disappearance of A can be expressed as: kA = k V (C-5) It should be noted that k^ is in reality the frequency at which the reactants pass to products. If we factor out of K^, the internal vibration coordinate that corresponds to the reactants crossing the barrier, we obtain from 94- statist ical mechanics: K* = k+' ( 1 - e-hv+/kT| (C-6) or if hv * +' K = K * « kT kT hv Thus, noting that k^ = from equations 5 and 6, we ob tain: (C—7 ) Prom thermodynamics we have the following relations: ** _ - A f*/RT k = e AF* = AHf - tA s^ A h* = e* - rt Thus, equation 07 can be expressed as k = eAS*/R e" E+/RT (C-8) (C-9) (c-10) (c-11) where E* = -E [ AB] [A] [B] AS “ S[AB]+ “S[A] CB] So with a knowledge of the necessary thermodynamic func tions the rate constant can be estimated. Prom equation 95 C—11 we can see that the maximum possible rate for bimole- cular reactions where AS^ is always negative is approxi mately 1 x 10^ pphm-^ min"-*-. . The thermodynamic data for the reaction intermedi ates are not available in the literature, and thus must be estimated. The basis for this estimation is the group additivity theory as explained by Benson (28). In this method, by knowing the structure of a compound, its entropy and enthalpy can be estimated. The method is explained by considering the following reaction: CH302‘ + NO — CH3°* + N02 (C-12) The first step in the estimation of the rate constant is to decide upon the structure of the intermediate. Consider that the intermediate has the following structure: H ’ n " °" - H C — 0 ^ 4 N (C-13) H ^ 0 The oxygen-nitrogen single bond is considered to be longer than normal by about a factor of two (28). Using the group theory, the enthalpy and entropy of this intermediate can be estimated. It can be noted that the assumed 96 structure, except for the stretched bond is much lihe that of CH302N0. Thus, we can say that the entropy of the in termediate must be greater than the compound with no stretched bond or: noting that: S = SC-13“ SCH302* " SN0 (C—15) it is possible to set a lower bond on the entropy change between the reactants and the transition stated inter mediate: sCH302N0 + sbond stretch ” sCH302* “ SN0 (C-16) By using the group additivity table in Benson (28), each of the right side terms of equation C-16 can be calculated. Sc-i5~ SCH302N0 o > + Sbond stretch (c"14) From these tables we find that gibbs/mole Sjjo — 50.3 sch3o2no 91,4 S others 3.0 or, giving ,As of 16.2. Substitution into equation C-ll 97 k„„ n = 1 x 102 e-E/RT pphm-1 min”1 3 2 * The calculated values for As for the reaction rates esti mated for Mechanism B are presented in Table C-l. The activation energy, E^, for exothermic reactions was estimated to be somewhere between 0 and 5 kcal/mole for reactions of the type in Mechanism B. For estimation purposes, a value of 2 kcal/mole was chosen. For endother- mic reactions the enthalpy change of the reaction plus 2 kcal was used for the activation energy. Using the values calculated by this method, it was possible to calculate the approximate minimum reaction rate for each reaction. The rates calculated are given in Table C-l. 98 TABLE C-l Estimated Thermodynamic Properties of Mechanism B * As* k React ion A H E Gibbs/mole No.* Kcal/mole Kcal/mole (minimum) pphm” min” 8 -9.3 2 -18. 10. 9 -38.9 2 -14. 100. 12 -10.4 2 -15. 50. 13 -16.9 2 -16. 50. 14 -53.9 2 -13. 100. 23 -19.1 4 -38 10" 27 -15.3 2 -22 1. 28 -73.8 0 -9 104 29 -100.8 0 -9 104 30 -32.9 2 -20 1 31 -43.5 0 -27 1 37 -40.0 2 -18 10 38 -65.3 2 -24 1 *Numbers refer to reaction numbers given in Table VI-1.

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Creator Ernest, Terry Eugene (author)

Core Title Mechanistic Study Of Air Pollution

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Energy,engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Lenoir, John M. (committee chair), Chilingar, George V. (committee member), Rebert, Charles J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-386635

Unique identifier UC11361024

Identifier 7008522.pdf (filename),usctheses-c18-386635 (legacy record id)

Legacy Identifier 7008522.pdf

Dmrecord 386635

Document Type Dissertation

Rights Ernest, Terry Eugene

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA