fUNDAMENTALS Of AIR POLLUTION ENGINEERING fUNDAMENTALS Of AIR POLLUTION ENGINEERING Richard C Flagan John H Seinfeld California Institute of Technology PRENTICE HALL Englewood Cliffs, New Jersey 07632 Library of Congress Cataloging-in-Publication Data Flagan, Richard C (date) Fundamentals of air pollution engineering Includes bibliographies and index \ Air-Pollution Environmental engineering Seinfeld, John H II Title TD883.F38 1988 628.5'3 87-7322 ISBN 0-13-332537-7 Editorial/production supervision and interior design: WordCrafters Editorial Services, Inc Cover design: Ben Santora Manufacturing buyer: Cindy Grant © 1988 by Prentice-Hall, Inc A Division of Simon & Schuster Englewood Cliffs, New Jersey 07632 All rights reserved No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher Printed in the United States of America 10 0-13-332537-7 Prentice-Hall International (UK) Limited, London Prentice-Hall of Australia Pty Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Simon & Schuster Asia Pte Ltd., Singapore Editora Prentice-Hall Brasil, Ltda., Rio de Janeiro Contents xi Preface Chapter AIR POLLUTION ENGINEERING 1.1 1.2 1.3 1.4 A B C Air Pollutants 1.1.1 Oxides of Nitrogen 1.1.2 Sulfur Oxides 1.3 Organic Compounds 1.1.4 Particulate Matter Air Pollution Legislation in the United States Atmospheric Concentration Units The Appendices to this Chapter Chemical Kinetics A.1 Reaction Rates A.2 The Pseudo-Steady-State Approximation A.3 Hydrocarbon Pyrolysis Kinetics Mass and Heat Transfer B.1 Basic Equations of Convective Diffusion B.2 Steady-State Mass Transfer to or from a Sphere in an Infinite Fluid B.3 Heat Transfer B.4 Characteristic Times Elements of Probability Theory C.1 The Concept of a Random Variable C.2 Properties of Random Variables C.3 Common Probability Distributions 3 11 15 17 17 22 24 26 29 30 31 33 35 36 36 39 42 v Contents vi D Turbulent Mixing D Scales of Turbulence D.2 Statistical Properties of Turbulence D.3 The Microscale D.4 Chemical Reactions E Units Problems References 59 Fuels Combustion Stoichiometry Combustion Thermodynamics 2.3.1 First Law of Thermodynamics 2.3.2 Adiabatic Flame Temperature 2.3.3 Chemical Equilibrium 2.3.4 Combustion Equilibria 2.4 Combustion Kinetics 2.4.1 Detailed Combustion Kinetics 2.4.2 Simplified Combustion Kinetics 2.5 Flame Propagation and Structure 2.5.1 Laminar Premixed Flames 2.5.2 Turbulent Premixed Flames 2.5.3 Laminar Diffusion Flames 2.5.4 Turbulent Diffusion Flames 2.6 Turbulent Mixing 2.7 Combustion of Liquid Fuels 2.8 Combustion of Solid Fuels 2.8 Devolatilization 2.8.2 Char Oxidation Problems References Chapter COMBUSTION FUNDAMENTALS 2.1 2.2 2.3 Chapter 46 47 48 49 51 54 56 57 59 63 67 68 78 80 98 101 101 108 113 116 120 126 127 133 135 145 146 149 159 163 POLLUTANT FORMATION AND CONTROL IN COMBUSTION 167 3.1 Nitrogen Oxides 3.1.1 Thermal Fixation of Atmospheric Nitrogen 3.1.2 Prompt NO 3.1.3 Thermal-NOx Formation and Control in Combustors 3.1.4 Fue1-NOx 3.1.5 Fuel-NOx Control 167 168 174 176 180 191 Contents vii 3.1.6 Postcombustion Destruction of NO x 3.1.7 Nitrogen Dioxide 3.2 Carbon Monoxide 3.2.1 Carbon Monoxide Oxidation Quenching 3.3 Hydrocarbons 3.4 Sulfur Oxides Problems References Chapter INTERNAL COMBUSTION ENGINES 4.1 191 198 201 204 215 217 221 222 226 Spark Ignition Engines 4.1.1 Engine Cycle Operation 4.1.2 Cycle Analysis 4.1.3 Cylinder Turbulence and Combustion Rate 4.1.4 Cylinder Pressure and Temperature 4.1.5 Formation of Nitrogen Oxides 4.1.6 Carbon Monoxide 4.1.7 Unburned Hydrocarbons 4.1 Combustion-Based Emission Controls 4.1.9 Mixture Preparation 4.1.10 Intake and Exhaust Processes 11 Crankcase Emissions 4.1.12 Evaporative Emissions 1.13 Exhaust Gas Treatment 4.2 Diesel Engine 4.2.1 Diesel Engine Emissions and Emission Control 4.2.2 Exhaust Gas Treatment 4.3 Stratified Charge Engines 4.4 Gas Turbines Problems References Chapter 227 229 231 234 238 240 242 244 248 254 259 261 261 265 269 AEROSOLS 290 5.1 5.2 5.3 The Drag on a Single Particle: Stokes' Law Noncontinuum Effects 5.2.1 The Knudsen Number 5.2.2 Slip Correction Factor Motion of an Aerosol Particle in an External Force Field 5.3.1 Terminal Settling Velocity 5.3.2 The Stokes Number 272 276 277 280 286 287 291 293 293 295 297 299 304 Contents viii Motion of a Charged Particle in an Electric Field 5.3.4 Motion of a Particle Using the Drag Coefficient 5.3.5 Aerodynamic Diameter 5.4 Brownian Motion of Aerosol Particles 5.4.1 Mobility and Drift Velocity 5.4.2 Solution of Diffusion Problems for Aerosol Particles 5.4.3 Phoretic Effects 5.5 Diffusion to Single Particles 5.5.1 Continuum Regime 5.5.2 Free Molecule Regime 5.5.3 Transition Regime 5.6 The Size Distribution Function 5.6.1 Distributions Based on log Dp 5.6.2 Relating Size Distributions Based on Different Independent Variables 5.7 The Log-Normal Distribution 5.8 General Dynamic Equation for Aerosols 5.8.1 Discrete General Dynamic Equation 5.8.2 Continuous General Dynamic Equation 5.9 Coagulation Coefficient 5.9.1 Brownian Coagulation 5.9.2 Effect of van der Waals and Viscous Forces on Brownian Coagulation 5.10 Homogeneous Nucleation 11 Sectional Representation of Aerosol Processes Problems References 5.3.3 Chapter PARTICLE FORMATION IN COMBUSTION 6.1 6.2 6.3 6.4 Ash 6.1.1 Ash Formation from Coal 6.1.2 Residual Ash Size Distribution 6.1.3 Ash Vaporization 6.1.4 Dynamics of the Submicron Ash Aerosol Char and Coke Soot 6.3.1 Soot Formation 6.3.2 Soot Oxidation 6.3.3 Control of Soot Formation Motor Vehicle Exhaust Aerosols 305 305 307 308 311 312 313 315 315 316 316 321 322 323 325 328 328 329 331 332 333 340 347 349 356 358 358 359 362 364 370 372 373 375 379 381 385 Contents ix Problems References Chapter REMOVAL OF PARTICLES FROM GAS STREAMS 7.1 7.2 7.3 7.4 7.5 7.6 Collection Efficiency Settling Chambers 7.2.1 Laminar Flow Settling Chamber 7.2.2 Plug Flow Settling Chamber 7.2.3 Turbulent Flow Settling Chamber Cyclone Separators 7.3.1 Laminar Flow Cyclone Separators 7.3.2 Turbulent Flow Cyclone Separators 7.3.3 Cyclone Dimensions 7.3.4 Practical Equation for Cyclone Efficiency Electrostatic Precipitation 7.4.1 Overall Design Equation for the Electrostatic Precipitator 7.4.2 Generation of the Corona 7.4.3 Particle Charging 7.4.4 Field Charging 7.4.5 Diffusion Charging 7.4.6 The Electric Field Filtration of Particles from Gas Streams 7.5.1 Collection Efficiency of a Fibrous Filter Bed 7.5.2 Mechanics of Collection by a Single Fiber 7.5.3 Flow Field around a Cylinder 7.5.4 Deposition of Particles on a Cylindrical Collector by Brownian Diffusion 7.5.5 Deposition of Particles on a Cylindrical Collector by Interception 7.5.6 Deposition of Particles on a Cylindrical Collector by Inertial Impaction and Interception 7.5.7 Collection Efficiency of a Cylindrical Collector 7.5.8 Industrial Fabric Filters 7.5.9 Filtration of Particles by Granular Beds Wet Collectors 7.6.1 Spray Chamber 7.6.2 Deposition of Particles on a Spherical Collector 7.6.3 Venturi Scrubbers 387 388 391 393 394 396 398 399 402 404 406 408 408 411 413 415 417 418 420 425 433 433 435 436 438 440 441 449 452 455 456 459 463 467 Contents x 7.7 Summary of Particulate Emission Control Techniques Problems References Chapter REMOVAL OF GASEOUS POLLUTANTS FROM EFFLUENT STREAMS 8.1 Interfacial Mass Transfer 8.2 Absorption of Gases by Liquids 8.2.1 Gas Absorption without Chemical Reaction 8.2.2 Gas Absorption with Chemical Reaction 8.3 Adsorption of Gases on Solids 8.4 Removal of S02 from Effluent Streams 8.4.1 Throwaway Processes: Lime and Limestone 469 472 476 479 480 484 484 491 497 505 Problems References 506 511 512 513 513 514 515 516 517 519 OPTIMAL AIR POLLUTION CONTROL STRATEGIES 521 9.1 Long-Term Air Pollution Control 9.2 A Simple Example of Determining a Least-Cost Air 524 Pollution Control Strategy General Statement of the Least-Cost Air Pollution Control Problem 9.4 A Least-Cost Control Problem for Total Emissions Problems References 526 Scrubbing 8.4.2 Regenerative Processes 8.5 Removal of NO x from Effluent Streams 8.5.1 Shell Flue Gas Treating System 8.5.2 Wet Simultaneous NO)SOx Processes 8.5.3 Selective Noncatalytic Reduction 8.5.4 Selective Catalytic Reduction 8.5.5 NO x and SOx Removal by Electron Beam Chapter 9.3 Index 527 529 534 534 537 Preface Analysis and abatement of air pollution involve a variety of technical disciplines Formation of the most prevalent pollutants occurs during the combustion process, a tightly coupled system involving fluid flow, mass and energy transport, and chemical kinetics Its complexity is exemplified by the fact that, in many respects, the simplest hydrocarbon combustion, the methane-oxygen flame, has been quantitatively modeled only within the last several years Nonetheless, the development of combustion modifications aimed at minimizing the formation of the unwanted by-products of burning fuels requires an understanding of the combustion process Fuel may be available in solid, liquid, or gaseous form; it may be mixed with the air ahead of time or only within the combustion chamber; the chamber itself may vary from the piston and cylinder arrangement in an automobile engine to a lO-story-high boiler in the largest power plant; the unwanted byproducts may remain as gases, or they may, upon cooling, form small particles The only effective way to control air pollution is to prevent the release of pollutants at the source Where pollutants are generated in combustion, modifications to the combustion process itself, for example in the manner in which the fuel and air are mixed, can be quite effective in reducing their formation Most situations, whether a combustion or an industrial process, however, require some degree of treatment of the exhaust gases before they are released to the atmosphere Such treatment can involve intimately contacting the effluent gases with liquids or solids capable of selectively removing gaseous pollutants or, in the case of particulate pollutants, directing the effluent flow through a device in which the particles are captured on surfaces The study of the generation and control of air pollutants can be termed air pollution engineering and is the subject of this book Our goal here is to present a rigorous and fundamental analysis of the production of air pollutants and their control The book is xi Sec 9.3 General Statement of the Least-Cost Air Pollution Control Problem 527 ~ c Q) E Q) u Ll Ll + ' - "' -. "~ -_I_~ o 1.8x ? 4,200,000 :~ x, 10 x, (bbl cement) Figure 9.4 Least-cost strategy for cement industry example (Kahn, 1969) and both XI and X must be nonnegative, Xl> X 2':: (9.4 ) The complete problem is to minimize C subject to (9.2)-(9.4) In Figure 9.4 we have plotted lines of constant C in the X I -X2 plane The lines corresponding to (9.2) and (9.3) are also shown Only XI' X values in the crosshatched region are acceptable Of these, the minimum cost set is Xl = 106 and X2 = 1.5 X 10 with C = 410,000 dollars If we desire to see how C changes with the allowed particulate emissions, we solve this problem repeatedly for many values of the emission reduction (we illustrated the solution for a reduction of x 105 kg of particulate matter per year) and plot the minimum control cost C as a function of the amount of reduction (see Problem 9.1) The problem that we have described falls within the general framework of linear programming problems Linear programming refers to minimization of a linear function subject to linear equality or inequality constraints Its application requires that control costs and reductions remain constant, independent of the level of control 9.3 GENERAL STATEMENT OF THE LEAST-COST AIR POLLUTION CONTROL PROBLEM The first step in fonnulating the least-cost control problem mathematically is to put the basic parameters of the system into symbolic notation There are three basic sets of variables in the environmental control system: control cost, emission levels, and air 528 Optimal Air Pollution Control Strategies Chap quality Total control cost can be represented by a scalar, C, measured in dollars To allow systematic comparison of initial and recurring expenditures, control costs should be put in an "annualized" form based on an appropriate interest rate Emission levels for N types of pollutants can be characterized by N source functions, En (x, t), n = 1, , N, giving the rate of emission ofthe nth contaminant at all locations, X, and times, t, in the region The ambient pollution levels that result from these discharges can be specified by similar functions, Ph(x, t), h = 1, , H, giving the levels of H final pollutants at all locations and times in the area under study Actually, air quality would most appropriately be represented by probability distributions of the functions Ph (x, t) In specifying ambient air quality for an economic optimization model, it is generally too cumbersome to use the probability distributions of Ph(x, t) Rather, integrations over space, time, and the probability distributions are made to arrive at a set of air quality indices, Pm' m = 1, , M Such indices are the type of air quality measures actually used by control agencies In most cases, they are chosen so as to allow a direct comparison between ambient levels and governmental standards for ambient air quality The number of air quality indices, M, may be greater than the number of discharged pollutant types, N For any given emitted pollutant, there may be several air quality indices, each representing a different averaging time (e.g., the yearly average, maximum 24-h, or maximum I-h ambient levels) Multiple indices will also be used to represent multiple receptor locations, seasons, or times of day Further, a single emitted pollutant may give to rise to more than one type of ambient species For instance, sulfur dioxide emissions contribute to both sulfur dioxide and sulfate air pollution Among the three sets of variables, two functional relationships are required to define the least-cost control problem First, there is the control cost-emission function that gives the minimum cost of achieving any level and pattern of emissions It is found by taking each emission level, En(x, t), n = 1, , N, technically determining the subset of controls that exactly achieves that level, and choosing the specific control plan with minimum cost, C This function, the minimum cost of reaching various emission levels, will be denoted by G, (9.5) Second, there is the discharge-air quality relationship This is a physicochemical relationship that gives expected air quality levels, Pm' as functions of discharge levels, En(x, t) For each air quality index, Pm' this function will be denoted by Fm, (9.6) With the definitions above, we can make a general mathematical statement of the minimal-cost air pollution control problem To find the minimal cost of at least reaching air quality objectives P::" choose those n = 1, ,N that minimize (9.7) Sec 9.4 A Least-Cost Control Problem for Total Emissions 529 subject to m = 1, , M Thus one chooses the emission levels and patterns that have the minimum control cost subject to the constraint that they at least reach the air quality goals 9.4 A LEAST-COST CONTROL PROBLEM FOR TOTAL EMISSIONS The problem (9.7), though simply stated, is extremely complex to solve, because, as stated, one must consider all possible spatial and temporal patterns of emissions as well as total emission levels It is therefore useful to remove the spatial and temporal dependence of the emissions and air quality Let us consider, therefore, minimizing the cost of reaching given levels of total regional emissions We assume that: • The spatial and temporal distributions of emissions can be neglected Accordingly, the discharge functions, En(x, t), n = 1, , N, can be more simply specified by, En' n = 1, , N, that are measures of total regionwide emissions • The air quality constraints can be linearly translated into constraints on the total magnitude of emissions in the region of interest • The problem is static (i.e., the optimization is performed for a fixed time period in the future) • There are a finite number of emission source types For each source type, the available control activities have constant unit cost and constant unit emission reductions With these assumptions, the problem of minimizing the cost of reaching given goals for total emissions can be formulated in the linear programming framework of Section 9.2 Table 9.2 summarizes the parameters for this linear programming problem The mathematical statement of the problem is as follows: Find Xij , i = 1, , I and j = 1, , J i that minimize ii C = I; I; eX i=lj=l IJ (9.8 ) IJ subject to I 1; I; I; i~ j~ ein (l - b ijn ) Xij ::5 En for n 1, , N (9.9) Ji I; Aij Xij ::5 Si for i = 1, , I (9.10) J= and for i 1, ,I; j = 1, , J i (9.11 ) Optimal Air Pollution Control Strategies 530 TABLE 9.2 PARAMETERS FOR THE LEAST-COST PROBLEM FOR TOTAL EMISSIONS Parameter Definition i = I, j = I, elj C En ,I ,Ji i j = 1, = I, I Ji i = N 1, Si i = 1, n = 1, ,I i = 1, j = 1, II = 1, (!jn Chap ,I ,N ,]i ,N i = 1, , I i = 1, j = 1, ,I , Ji The number of units of thejth control activity applied to source type i (e.g the number of a certain control device added to 1980 model year vehicles or the amount of natural gas substituted for fuel oil in power plant boilers) The total number of source types is I; the number of control alternatives for the ith source type is J i • The total annualized cost of one unit of control type j applied to source type i The total annualized cost for the control strategy as specified by all the X'J' The uncontrolled (all Xu = 0) emission rate of the nth pollutant as specified by all Xu (e.g., the resultant total NO, emission level in kg day· ') There are N pollutants The uncontrolled (all Xu = 0) emission rate of the nth pollutant from the ith source (e.g., the NO, emissions from power plant boilers under no controls) The fractional emission reduction of the nth pollutant from the ith source attained by applying one unit of control, type j (e.g., the fractional NO, emission reduction from power plant boilers attained by substituting one unit of natural gas for fuel oil) The number of units of source type i (e.g., the number of 1980 model year vehicles or the number of power plant boilers) The number of units of source type i controlled by one unit of control type j (e.g., the number of power plants controlled by substituting one unit of natural gas for fuel oil) In this linear programming problem, (9.8) is the objective function, and (9.9)(9.11) are the constraints Equation (9.9) represents the constraint of at least attaining the specified emission levels, Ell' Equations (9.10) and (9.11) represent obvious physical restrictions, namely not being able to control more sources than those that exist and not using negative controls Solution techniques are well developed for linear programming problems, and computer programs are available that accept numerous independent variables and constraints Thus the solution to the problem is straightforward once the appropriate parameters have been chosen The results are the minimum cost, C, and the corresponding set of control methods, Xu' associated with a least-cost strategy for attaining any emission levels, Ell' More generality is introduced if we not translate the air quality constraints linearly into emission constraints Rather, we may allow for nonlinear relationships between air quality and total emissions and can include atmospheric interaction between emitted pollutants to produce a secondary species The general least-cost control problem can then be restated as: Choose E" n - I, , N to minimize C = G(EII ) (9.12 ) Sec 9.4 531 A Least-Cost Control Problem for Total Emissions subject to m = 1, , M Here G(En ) represents the minimum cost of attaining various total emission levels This function can be found by linear programming The functions, F",(En ), represent the air quality-emission relationships These can be found by a variety of means, such as empirical/statistical or physicochemical models (Seinfeld, 1986) If linear functions are adopted for thef,n(En ), this case degenerates into that above In general, however, the air quality-emission relationships can be nonlinear and can involve interactions between two or more types of emissions A hypothetical example of the solution to (9.12) for two emitted contaminants (E I , E ) and two final pollutants (PI' P ) is illustrated in Figure 9.5 The axes of the graph measure total emission levels of the two contaminants, E I and E • The curves labeled C" C2 , and so on, are iso-cost curves determined by repeated application of a linear programming submodel Along any curve labeled Cb the minimum cost of reaching any point on that curve is Ck • As emission levels fall (downward and to the left in the graph), control costs rise Thus C, < C2 < < Cs The air quality constraints are represented by the two curves, PI and P , derived from a nonlinear air qualityemission level relationship The constraint of at least reaching air quality level PI for the first pollutant requires that emissions be reduced below the curve The constraint that air quality be at least as good as P for the second pollutant requires that emissions be reduced to the left of the P curve The emission levels that satisfy both air quality c, C'_1 IE;,E;) ~Cl C I IC3 IC4 / ' £ I IC I I I I I I I I """"" ' E, I