Tai Lieu Chat Luong Fundamentals of Water Treatment Unit Processes Physical, Chemical, and Biological Fundamentals of Water Treatment Unit Processes Physical, Chemical, and Biological David Hendricks Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-13: 978-1-4200-6192-5 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xxxiii Acknowledgments xxxv Author xxxvii Downloadable Files xxxix Contents—Downloadable Files xli PART I Chapter Foundation Water Treatment 1.1 Water Treatment In-a-Nutshell 1.1.1 Water Treatment Plants 1.1.2 Residuals 1.2 Organization of Water Treatment Knowledge 1.3 Unit Processes 1.3.1 Definitions 1.3.2 Technologies 1.3.3 Breadth of Unit Processes and Technologies 1.3.4 Proprietary Technologies 1.3.5 Status of Unit Processes 1.3.6 Future of Treatment 1.3.7 Energy Expenditure for Treatment 1.4 Treatment Trains 1.4.1 Tertiary Treatment 1.4.1.1 Cases 1.4.2 Industrial Wastewater Treatment 10 1.4.2.1 Cases 11 1.4.3 Industrial Process Water Treatment 12 1.4.4 Hazardous Wastes 12 1.4.5 Hazardous Wastes: In Situ Treatment 13 1.5 Design 13 1.5.1 Factors: Nontechnical 13 1.5.1.1 Operation Issues 13 1.5.1.2 Managing a Team 13 1.5.1.3 Expansion 13 1.5.1.4 Esthetics 13 1.5.1.5 Regulations 14 1.5.1.6 Institutions 14 1.5.1.7 Consulting Engineering 14 1.6 Summary 17 Problems 17 Acknowledgments 18 Glossary 18 References 19 Chapter Water Contaminants 21 2.1 Water Quality: Definitions 21 2.1.1 Contaminants 21 2.1.2 State of Water 22 v vi Contents 2.1.3 2.1.4 Criteria 22 Standards 22 2.1.4.1 Kinds of Water Quality Standards 22 2.1.4.2 Normative Standards 24 2.1.4.3 Standards as Targets for Treatment 24 2.1.5 Surrogates 24 2.2 Federal Laws 25 2.2.1 Legal Definitions 26 2.2.2 Regulations 26 2.2.3 Priority Pollutants 26 2.3 Maturation of Water Quality Knowledge 27 2.3.1 Knowledge of Contaminants 27 2.3.2 Measurement Technologies 28 2.4 Categorizations of Contaminant Species 28 2.4.1 Systems of Categorization 28 2.4.2 Illustrative System of Contaminant Categorization 28 2.5 Utility of Water Quality Data 31 2.5.1 Contaminants and Water Uses 31 2.6 Combinations of Quality of Source Waters and Product Waters 31 Problems 34 Acknowledgments 34 Appendix 2.A: Organic Carbon as a Contaminant 34 2.A.1 Categories of Organics in Water 35 2.A.1.1 Color 37 2.A.1.2 Organic Carbon 37 2.A.1.3 UV254 37 2.A.1.4 Synthetic Organic Carbon 37 2.A.2 Disinfection By-Products 37 2.A.3 Disinfection By-Products in Secondary Effluents 39 2.A.4 Disinfectant Selection 40 2.A.5 Other Notes 40 Glossary 40 References 41 Bibliography 42 Chapter Models 45 3.1 3.2 3.3 3.4 Unit Processes 45 Models 45 3.2.1 Categories of Models 45 3.2.2 The Black Box 45 3.2.2.1 Plots 46 3.2.3 Physical Models 46 3.2.3.1 Bench Scale Testing 46 3.2.3.2 Pilot Plants 46 3.2.3.3 Demonstration Plants 47 3.2.4 Mathematical Models 48 3.2.5 Computer Models 48 3.2.6 Scenarios 49 Modeling Protocol 49 3.3.1 Spreadsheets 51 Units and Dimensions 52 3.4.1 Units 52 3.4.2 Dimensions 52 vii Contents 3.5 Examples of Models 3.6 Summary Problems Glossary References Chapter 52 54 54 54 56 Unit Process Principles 57 4.1 Unit Processes 57 4.1.1 Spectrum of Unit Processes and Technologies 57 4.1.2 Matching Unit Process with Contaminant 57 4.1.2.1 Contextual Changes and New Treatment Demands 57 4.2 Principles 57 4.2.1 Sinks 57 4.2.2 Transport 59 4.2.2.1 Macro Transport: Sedimentation 59 4.2.2.2 Macro Transport: Advection 59 4.2.2.3 Macro Transport: Turbulent Diffusion 59 4.2.2.4 Macro Transport: Porous Media Dispersion 59 4.2.2.5 Molecular Transport: Diffusion 59 4.2.2.6 Mathematics of Diffusion, Turbulence, and Dispersion 60 4.2.3 Summary 62 4.3 Reactors 62 4.3.1 Examples of Reactors 62 4.3.2 Types of Reactors 62 4.3.3 Mathematics of Reactors 62 4.3.3.1 Materials Balance: Concept 62 4.3.3.2 Comments on Materials Balance 63 4.3.3.3 Materials Balance: Mathematics 63 4.3.4 Materials Balance: Special Conditions 66 4.3.4.1 Batch Reactor: Complete Mixed 66 4.3.4.2 Steady State Reactor: Complete Mixed 66 4.3.4.3 Zero Reaction: Complete Mixed 67 4.3.4.4 Nonsteady State Reactor 67 4.3.4.5 Spreadsheet Method to Solve Finite Difference Form of Mass Balance Equation 68 4.3.4.6 Utility of Finite Difference Equation and Tracer Tests 71 4.4 Kinetic Models 71 4.4.1 First-Order Kinetics 71 4.4.2 Second-Order Kinetics 72 4.4.3 Examples of Kinetic Equations 72 4.4.3.1 Example: Gas Transfer 72 4.4.3.2 Example: Biological Degradation of Substrate 72 4.4.3.3 Example: Trickling Filter 72 Problems 73 Glossary 74 References 76 PART II Chapter Particulate Separations Screening 79 5.1 5.2 Theory of Screening Types of Screens 5.2.1 Bar Screens 5.2.1.1 Cleaning 5.2.1.2 Manually Cleaned Bar Screens 79 79 79 80 80 viii Contents 5.2.1.3 Screenings 80 5.2.1.4 Bar Size 80 5.2.1.5 Hydraulic Design 81 5.3 Comminutors 82 5.3.1 Design 82 5.4 Fine Screens 83 5.4.1 Drum Screens and Disk Screens 83 5.4.2 Wedge-Wire Static Screens 83 5.4.2.1 Mathematical Relationships 85 5.4.2.2 Theory 85 5.4.2.3 Design 85 5.5 Microscreens 86 5.5.1 Equipment and Installation 86 5.5.2 Applications 86 5.5.3 Performance 86 5.5.4 Operation 86 5.5.5 Sizing 87 5.5.6 Operating Data 87 5.5.7 Microscreen Model 88 5.5.7.1 Interpretation of Model Results 91 Problems 92 Bar Screens 92 Acknowledgments 93 Glossary 93 References 93 Chapter Sedimentation 95 6.1 6.2 6.3 6.4 6.5 6.6 Key Notions in Design 95 Particle Settling 95 6.2.1 Particle Settling Principles 95 6.2.2 Stokes’ Law 95 6.2.3 Suspensions 97 6.2.3.1 Type I: Discrete Particle Suspensions 97 6.2.3.2 Type II: Flocculent Suspensions 98 6.2.3.3 Type III: Hindered Settling 98 6.2.3.4 Type IV: Compression Settling 99 Settling Basins 99 6.3.1 The Ideal Basin 99 6.3.1.1 Camp’s Conditions for the Ideal Basin 99 6.3.1.2 Overflow Velocity 99 6.3.1.3 Significance of Overflow Velocity 101 6.3.1.4 Insignificance of Detention Time 101 6.3.1.5 Partial Removals for Particles with Fall Velocities, vs < vo 101 Characterizing Suspensions 103 6.4.1 Characteristics of Discrete Particle Suspensions and Removal Analysis 103 6.4.2 Graphic Depiction of Size Fraction Removed 103 6.4.3 Mathematics of Removal 104 6.4.4 Up-Flow Basins: A Special Case 105 6.4.5 The Role of Ideal Settling Basin Theory 105 Flocculent Suspensions (Type II) 106 6.5.1 Settling Test for a Flocculent Suspension 106 6.5.2 Determining Percent Removals 106 Hindered and Compression Settling (Type III and Type IV Suspensions) 107 6.6.1 Settling Velocity as Affected by Solids Concentration 108 6.6.1.1 Settling Tests 108 6.6.1.2 Characterizing Settling Velocity 108 ix Contents 6.6.2 Final Settling as Affected by Limiting Flux Density 108 6.6.2.1 Activated Sludge 109 6.6.2.2 Final Settling Basin Processes 109 6.6.2.3 Mass Balance Relations 109 6.6.2.4 Limiting Flux Density 110 6.6.2.5 Limiting Flux Density: Evaluation Procedure 110 6.6.2.6 Example of Limiting Flux Density Using Plots 111 6.7 Hydraulics of Settling Basins 112 6.7.1 Flow Patterns and Short Circuiting 113 6.7.2 Density Currents 113 6.7.3 Dispersion Tests Using a Tracer 113 6.7.3.1 Results of Dispersion Tests 113 6.7.4 Computational Fluid Dynamics 114 6.8 Design Practice 114 6.8.1 Categories of Basins 114 6.8.2 Examples of Designs 115 6.8.2.1 Horizontal Flow 115 6.8.2.2 Up-Flow 115 6.8.2.3 Data from Real Basins 115 6.8.3 Guidelines and Criteria for Design 115 6.8.3.1 Discrete Particle Suspensions: Type I 118 6.8.3.2 Flocculent Suspensions: Type II 118 6.8.3.3 Flocculent Suspensions–Hindered Settling: Type III 118 6.8.3.4 Compression Settling: Type IV 118 6.9 Real Basins 118 6.9.1 Inlet Design 119 6.9.2 Outlet Design 121 6.9.3 Summary Notes for Practical Design 122 6.10 Plate Settlers and Tube Settlers 122 6.10.1 Plate Settlers 122 6.10.1.1 Particle Path: Analysis 122 6.10.1.2 Sludge Removal 123 6.10.1.3 Plate Settler Systems 123 6.10.1.4 Sizes of Units 124 6.10.1.5 Surface Overflow Rates 124 6.10.1.6 Theory 124 6.10.2 Tube Settlers 127 Problems 128 Acknowledgments 130 Glossary 130 References 132 Chapter Grit Chambers 135 7.1 7.2 Grit 135 Horizontal Flow Grit Chambers 135 7.2.1 Theory 135 7.2.1.1 Ideal Basin 135 7.2.1.2 Scour 135 7.2.2 Horizontal Velocity Control 137 7.2.2.1 Proportional Weir 137 7.2.2.2 Parshall Flume 138 7.2.2.3 Rectangular Section 142 7.2.2.4 Parabolic Section 146 7.2.3 Practice—Horizontal Flow Grit Chambers 147 7.2.3.1 Design and Performance—Examples 147 7.2.3.2 Removal Equipment 148 858 Appendix H: Dissolved Gases TABLE H.3 Henry’s Constant for Three Cases in Different Units Compound Carbon Dioxide Formula MW CO2 44.0098 Form Volatility—HiD Units Pa i(g) a mol i(aq)=mol H2 O atm i(g) b mol i(aq)=mol H2 O mol i(g)=L(g) b mol i(aq)=L H2 O Oxygen Chloroform O2 31.998 0.167 10925 a CHCl3 119.377 4.40 10925 c 151020 d 1212.2 25 4300020 a c c 17020 d 227.84 25 b 0.190520 mol i(g)=mol(g) b mol i(aq)=mol H2 O atm i(g) b,d,e mol i(aq)=m3 H2 O Solubility—H1S a b c d e f g h mol i(aq)=L H2 Of atm i(g) mol i(aq)=m3 H2 Of,g Pa mg i(aq)=L H2 Oh atm i(g) 0.00410125 e 0.00332 20 e 0.00421 25 0.034 25 f 0.0013 25 1688–20 h 43.39–20 f 0.27 25 h d f 32231f 29080d Alberty and Silbey (1992) Brennan et al (1998) Kavanaugh and Trussell (1981) Yaws (1999) Ashworth et al (1988) Sander (1999) Official SI unit according to Sander (1999) This text; numerical values calculated from references indicated by footnotes Example H.6 Conversion of Henry’s Constant as HiD in atm=mol Fraction to HiS in mg=L=atm Consider again, chloroform, CHCl3 with HDi given by Yaws (1999, p 407) HDCHCl3 ,25 C ¼ 2:2784 102 atm mol fraction Apply ‘‘labeling’’ of units and rounding off, HDCHCl3 ,25 C ¼ 2:2784 102 atm CHCl3 mol CHCl3 =mol H2 O Now convert, by a chain of conversions, atm CHCl3 mol H2 O mol CHCl3 mol CHCl3 18:01528 g H2 O mol H2 O MW(CHCl) g HDCHCl3 ,20 C ¼ 2:2784 102 L H2 O g 998:21 g H2 O(20 C) 103 mg ¼ 2:2784 102 atm CHCl3 18:01528 L H2 O MW(CHCl) 998:21 103 mg ¼ 2:2784 102 atm CHCl3 L H2 O MW(CHCl) 55:51 103 mg ¼ 2:2784 102 atm CHCl3 L H2 O 119:377 55:51 103 mg ¼ 3:43 105 atm CHCl3 L H2 O mg CHCl3 dissolved Convert to HSi , with rounding off in the final step, HSCHCl3 ,25 ¼ HDCHCl3 ,25 C ¼ 3:43 105 atm CHCl3 L H2 O mg CHCl3 dissolved mg CHCl3 dissolved atm CHCl ¼ 2:9 10 L H2 O Appendix H: H.2.5 859 Dissolved Gases EFFECT OF TEMPERATURE LAW CONSTANT DHi =R data in Table H.4 The units for Hi in the temperature regression equation, Equation H.53 are [atm gas i m3 H2O=mol dissolved gas i] HENRY’S ON A single Henry’s constant at some given temperature is, as a rule, not adequate knowledge, since temperature has a strong effect The temperature dependence of Henry’s constant is given by the van’t Hoff relation, ln HiD ¼ ln Ai DHi RT Example H.7 Calculation of DHiD from Table H.4 Consider again, chloroform, i.e., CHCl3, which shows ln ACHCl3 ¼ 11.41, and DH i =R ¼ 5030 (H:13) Substituting data in a modification of Equation H.14, where DHi is the standard state enthalpy change due to dissolution of component i in water (J=mol i) R is the universal gas constant (8.314 510 cal mol1 K1) T is the absolute temperature (K) Ai is the constant for gas i (dimensionless) HDi ¼e DH =R i T ln Ai 5030 HDCHCl3 ẳ e11:41 298 ị ẳ 0:00451 atm CHCl3 m3 H2 O mol CHCl3 In other words, HiD ¼ Ai e Comments This compares with 0.0041 in Yaws (1999, p 407), and with 0.0042, 0.0038 from Ashworth et al (1988) Converting to HSCHCl3 gives, DH =R Ti (H:14) H.2.5.1 Illustration of Temperature Effect Figure H.4 shows a plot of experimental data given by Ashworth et al (1988) for chloroform, CHCl3 From the slope and intercept, obtained by Kladiograph plotting software, Henry’s constant can be calculated, as indicated in Equation H.53 Ashworth et al (1988) have provided such data for some 45 organic compounds given here as the ln Ai and 0.010 HSCHCl3 ¼ 26 469 mg CHCl3 =L H2 O atm CHCl3 The van’t Hoff relation is a rational basis for determining the effect of temperature on Henry’s constant from empirical data, as seen in Figure H.4 The van’t Hoff relation is consistent with theory and is confirmed by most experimental data depiciting Henry’s constant versus temperature From plot: Slope= – 2184 cycles/(1/T K) A(intercept) = 90693 Mathematical relations: 2184 cycles H(CHCl3) (atm m3/mol) C/A = 10slope/T= 10ΔH/2.3RT= eΔH/RT ΔH°/R = 2.303 · slope = 2.303 · –2184 = –5030/K 10°C 15°C 20°C 25°C 30°C 1.0 1/T K 0.00355 0.00350 0.00345 0.00340 0.00335 0.00330 0.001 1/T K FIGURE H.4 Henry’s constants from experimental data for chloroform plotted against 1=T K (Figure plotted and regression equation from data as obtained in Ashworth, R.A et al., J Hazard Mater., 18, 25, 1988.) 860 Appendix H: Dissolved Gases TABLE H.4 Henry’s Law Temperature Coefficients for Organic Compounds of Interest at U.S Air Force Basesa Compound Nonane n-Hexane 2-Methylpentane Cyclohexane Chlorobenzene 1,2-Dichlorobenzene 1,3-Dichlorobenzene 1,4-Dichlorobenzene o-Xylene p-Xylene m-Xylene Propylbenzene Ethylbenzene Toluene Benzene Methylethylbenzene 1,1-Dichloroethane 1,2-Dichloroethane 1,1,1-Trichloroethane 1,1,2-Trichloroethane Cis-1,2-dichloroethylene Trans-1,2-dichloroethylene Tetrachloroethylene Trichloroethylene Tetralin Decalin Vinyl chloride Chloroethane Hexachloroethane Carbon tetrachloride 1,3,5-Trimethylbenzene Ethylene dibromide 1,1-Dichloroethylene Methylene chloride Chloroform 1,1,2,2-Tetrachloroethane 1,2-Dichloropropane Dibromochloromethane 1,2,4-Trichlorobenzene 2,4-Dimethylphenol 1,1,2-Trichlorotrifluoroethane Methyl ethyl ketone Methyl isobutyl ketone Methyl cellosolve Trichlorofluoromethane ln Ai DH i =R 0.1847 25.25 2.959 9.141 3.469 1.518 2.882 3.373 5.541 6.931 6.280 7.835 11.92 5.133 5.534 5.557 5.484 1.371 7.351 9.320 5.164 5.333 10.65 7.845 11.83 11.85 6.138 4.265 3.744 9.739 7.241 5.703 6.123 8.483 11.41 1.726 9.843 14.62 7.361 16.34 9.649 26.32 7.157 6.050 9.480 202.1 7530 957.2 3238 2689 1422 2564 2720 3220 3520 3337 3681 4994 3024 3194 3179 3137 1522 3399 4843 3143 2964 4368 3702 5392 4125 2931 2580 2550 3951 3628 3876 2907 4268 5030 2810 4708 6373 4028 3307 3243 5214 160.6 873.8 3513 Source: Ashworth, R.A et al., J Hazard Mater., 18, 25, 1988 The Henry’s coefficient is calculated from Equation H.53, i.e., ln HiL ¼ ln AiDHi =RT (note that Hi is the standard state enthalpy of reaction) a H.2.6 VARIABILITY OF HENRY’S CONSTANT DATA As noted, Henry’s constant data are often given to several significant places, e.g., 3–5 Examining the data from different sources, however, shows variability that indicates standard deviations of perhaps 10%–20% about a mean Therefore, any final calculations should be rounded to about two decimal places, or perhaps three decimal places, depending upon the data provided H.2.7 DATA SOURCES Sources of data for Henry’s constants (or solubility data) have not been compiled into a single document Moreover, ferreting-out from different sources may be required The work by Yaws (1999) approaches a comprehensive compilation and is close to a single source reference compared to the work presented by Sander (1999) Prior to about 1980, solubility data and Henry’s constant data were developed mostly for inorganic gases, such as in Table H.5 Solubility data from various sources for such gases were compiled in a comprehensive series such as the volume by Battino (1981) Brennan et al (1998) summarized the state of knowledge, indicating that in 1981 data for only 35 chemicals were obtained from the literature, out of 70,000 compounds in current use A problem they recognized was that Henry’s constants have been reported in various forms and units, as noted here Compilations for organic compounds have been developed mostly since the early 1980s stimulated by legislation relating to hazardous wastes Gosset et al (1984) included gas solubility in studies of air stripping, motivated by the problems faced by the U.S Air Force Table H.4 from Ashworth et al (1988) includes compounds considered contaminants in air force bases The most comprehensive compilations of data for organic compounds have been by Yaws (1999) and Sander (1999) Water solubility data with temperature coefficients for 151 paraffin hydrocarbons were given by Yaws et al (1993) as related to the design of air stripping of water Later, Yaws (1997) provided solubility data on disks with temperature coefficients for 217 compounds and included Henry’s constants at representative temperatures (e.g., 208C, 258C) for 692 compounds Similar data were published by Yaws (1999), which included solubility data with temperature coefficients for the same 217 compounds and Henry’s constant data for 1360 compounds without temperature coefficients The Henry’s constant data were given in two kinds of units, i.e., atm=mol f, and atm gas i m3 H2O=mol dissolved gas i The data by Sander (1999) are comprehensive in that not only are a large number of compounds included (900 species), but the data for each compound from all of the various source (2200 data entries) were compiled (from 250 references) and presented in uniform units (atm m3=mol) and temperature coefficients, i.e., DHi =R As another approach, since the Henry’s constant is merely an equilibrium constant, it may be calculated from Appendix H: 861 Dissolved Gases TABLE H.5 Solubility of Gases in Water (mg Gas i=L Water) for Interfacial Pressure of Gas ‘‘i,’’ pi ¼ 1.00 atm—and Temperature Coefficients; Solubility of Gas ‘‘i’’ is Same as Henry’s Constant, i.e., mg Gas i Dissolved=L Water=atm Gas i T (8C) H2 O2 N2 CO2 H2S CH4 Cl2 SO2 O3 NH3 CO Rn A B A0 DH i =R 2.4543 0.011708 0.057647 1027.7 64.75 0.01862 0.13166 1702.3 27.593 0.01710 0.091101 1569.1 3129.9 0.02955 0.2179 2625.6 6659.5 0.026105 1.1525 2378.6 36.396 0.02063 0.037757 1887.3 1,1402 0.021520 6.4933 2062.1 231,540 0.038103 3.4932 3037.7 843.32 0.02719 0.12786 2413.6 928,020 0.028579 60.481 2,648 41.449 0.01747 0.12413 1595.9 3633.5 0.02156 3.4488 1908.6 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 35 40 45 50 60 70 80 90 100 1.922 1.901 1.881 1.862 1.843 1.824 1.806 1.789 1.772 1.756 1.740 1.725 1.710 1.696 1.682 1.668 1.654 1.641 1.628 1.616 1.603 1.588 1.575 1.561 1.548 1.535 1.522 1.509 1.496 1.484 1.474 1.425 1.384 1.341 1.287 1.178 1.020 0.79 0.46 69.45 67.56 65.74 64.00 62.32 60.72 59.18 57.73 56.32 54.98 53.68 52.46 51.28 50.14 49.06 48.02 47.03 46.06 45.14 44.26 43.39 42.52 41.69 40.87 40.07 39.31 38.57 37.87 37.18 36.51 35.88 33.15 30.82 28.58 26.57 22.74 18.56 13.81 7.9 29.42 28.69 27.98 27.30 26.63 26.00 25.37 24.77 24.19 23.65 23.12 22.63 22.16 21.70 21.26 20.85 20.45 20.06 19.70 19.35 19.01 18.69 18.38 18.09 17.80 17.51 17.24 16.98 16.72 16.47 16.24 15.01 13.91 13.00 12.16 10.52 8.51 6.60 3.6 3,346 3,213 3,091 2,978 2,871 2,774 2,681 2,589 2,492 2,403 2,318 2,239 2,165 2,098 2,032 1,970 1,903 1,845 1,789 1,737 1,688 1,640 1,590 1,540 1,493 1,449 1,406 1,366 1,327 1,292 1,257 1,105 973 860 761 576 7,066 6,839 6,619 6,407 6,201 6,001 5,809 5,624 5,446 5,276 5,112 4,960 4,814 4,674 4,540 4,411 4,287 4,169 4,056 3,948 3,846 3,745 3,648 3,554 3,464 3,375 3,290 3,208 3,130 3,055 2,983 2,648 2,361 2,110 1,883 1,480 1,101 765 410 39.59 38.42 37.28 36.19 35.13 34.10 33.12 32.17 31.27 30.39 29.55 28.79 28.05 27.33 26.65 25.99 25.38 24.78 24.22 23.69 23.18 22.70 22.22 21.77 21.33 20.91 20.50 20.11 19.74 19.38 19.04 17.33 15.86 14.66 13.59 11.44 9.26 6.95 4.0 228,300 220,900 213,700 206,600 199,800 193,100 186,500 180,200 174,000 168,000 162,100 156,400 150,900 145,600 140,400 135,400 130,500 125,900 121,400 117,000 112,800 108,800 105,000 101,200 97,600 94,100 90,600 87,300 84,200 81,000 78,000 64,700 54,100 883 856 829 803 778 758 731 709 687 666 649 627 611 591 574 557 541 526 511 496 482 469 456 444 432 422 409 398 387 377 369 324 284 253 230 178 895,000 44.0 42.9 41.9 40.9 40.0 39.0 38.1 37.2 36.4 35.6 34.8 34.0 33.3 32.6 31.9 31.3 30.7 30.0 29.5 28.9 28.4 27.9 27.4 26.9 26.5 26.0 25.6 25.2 24.8 24.4 24.0 22.3 20.8 19.3 18.0 15.2 12.8 9.8 5.7 3,673 3,590 3,509 3,430 3,353 3,289 3,204 3,133 3,063 2,995 2,938 2,864 2,810 2,739 2,679 2,620 2,563 2,507 2,452 2,399 2,347 2,296 2,246 2,198 2,151 2,111 2,060 2,016 1,973 1,931 1,896 1,704 1,526 1,381 1,271 1,010 9,972 9,654 9,346 9,050 8,768 8,495 8,232 7,979 7,738 7,510 7,283 7,100 6,918 6,739 6,572 6,413 6,259 6,112 5,975 5,847 5,724 5,104 4,590 4,228 3,925 3,295 2,793 2,227 1,270 796,000 720,000 684,000 651,000 636,000 587,000 529,000 482,000 440,000 410,000 316,000 235,000 168,000 111,000 65,000 30,000 Notes: (1) The solubility form of Henry’s constant may be calculated as: HiS (mg i=L H2 O)=atm i) ¼ AeB (T C) (H.60) taking A and B from the table for the gas of interest (2) All columns except O3 and Rn were from Dean, J A (Ed.), Lange’s Handbook of Chemistry, 13th edn., McGraw-Hill, New York, 1985 (continued) 862 Appendix H: Dissolved Gases TABLE H.5 (continued) Solubility of Gases in Water (mg Gas i=L Water) for Interfacial Pressure of Gas ‘‘i,’’ pi ¼ 1.00 atm—and Temperature Coefficients; Solubility of Gas ‘‘i’’ is Same as Henry’s Constant, i.e., mg Gas i Dissolved=L Water=atm Gas i (3) Ozone data were from Battino (1981, pp 474–483) who reviewed most of the experimental data generated on ozone solubility A problem in developing ozone solubility data was that ozone decomposes to oxygen shortly after introduction The data recommended were those of Sullivan and Roth who provided a ‘‘smoothing’’ equation for Henry’s constant, i.e., H(O3 ) ¼ 38 420 000 e(2428=Tabs ) [OH ]0:035 in which H(O3) is as defined in Equation H.10, i.e., atm=mol f, and [OH] is in mol=L The data in this table were calculated (by Excelt spreadsheet) for pH ¼ 7.0 The conversion to solubility in mg O3=L water was: 1:0 atm O3 and, H(O3 ) mol O3 48 g O3 55:55 mol H2 O 1000 mg MW(O3 ) C(O3 ) ¼ X(O3 ) mol H2 O mol O3 L H2 O g X(O3 ) ¼ A sample calculation for T ¼ 108C gives: H(O3) ¼ 4107 atm O3=mols O3=mol H2O, and X(O3) ¼ 0.0002435 mol O3=mol H2O at P(O3) ¼ 1.0 atm O3 Then, C(O3) ¼ 649 mg O3=L water (4) Radon data are few and different experimental data sets give results that vary perhaps 20% The radon data entered in this table were calculated from a best fit of experimental results generated by Lewis et al (1987), represented by the equation, ln X ẳ 2:01 ỵ 0:23 3:88 ln (T=100) 0:84(T=100) (T=100) The conversion to solubility in mg Rn=L water was by, C(Rn) ¼ X(Rn) mol Rn 222 g Rn 55:55 mol H2 O 1000 mg MW(Rn) mol H2 O mol Rn L H2 O g A sample calculation for T ¼ 108C, gives, ln X(Rn) ¼ 8.3422016, X(Rn) ¼ 0.00023825 mol Rn=mol H2O at P(Rn) ¼ 1.0 atm Rn Then, C(Rn) ¼ 2938 mg Rn=L water (5) Also, it should be noted that, from Equation H.11 and for this table, there is an arithmetic identity that, numerically (not in units): Ci*(mg=L) ¼ H1S , since the data for this table are for pressure, pi* ¼ 1.00 atm (6) The coefficients A and B are for best fit equations of the data in this table for a given gas, plotted in accordance with the form, C(mg=L) ¼ AeBT C , with R 0.99, in general and with deviations from data generally within 2%–4% (see also Note 1) (7) The coefficients A0 and DH i =R are for best fit equations of the data plotted in accordance with the van’t Hoff type relation, i.e., DH =R i C(mg=L) ¼ A0 e T(K) , with R2 0.99, in general and with deviations from data generally within 2%–4% (8) For chlorine dioxide, H(ClO2, 258C) ¼ 1.0 mol=L=atm ¼ 67,451 mg=L=atm Lide (1996, pp 6–5) gives, ln X(ClO2) ¼ A(ClO2) þ B(ClO2)=T * þ C (ClO2) ln T *, in which, X(ClO2) ¼ mol fraction of gas in solution, A(ClO2) ¼ 7.9163, B(ClO2) ¼ 0.4791, C(ClO2) ¼ 11.0593, T * ¼ T(K)=100; equation valid for 283.15 T 333.15 K for p(ClO2) ¼ 101.325 kPa (1.00 atm) of pure gas the thermodynamic data Again, this requires search, but data are found, to a limited extent, in standard handbooks (see, for example, Lide, 1996 or Dean, 1985) and sometimes in specialized publications gas i) The coefficients, i.e., Ai and Bi, seen in the top two rows, are the intercept and slope of the best fit exponential equation, i.e., Ci (mg i=L H2 O) HiS (mg i=L H2 O)=atm i H.2.8 GAS SOLUBILITY Table H.5 gives solubility for 12 gases of frequent interest at temperatures ranging 0–100 K The concentrations given are for equilibrium conditions at 1.00 atmosphere of pure gas above the water surface at each of the temperatures (stated in left column) Figure H.5 is a plot of the data of Table H.5, i.e., solubility of gas vs temperature, and provides a sense of how the gases differ in solubility; and also the temperature effect on each gas The major utility of Table H.5 is that solubility at known pressures, i.e., 1.00 atm, is an ‘‘identity’’ with Henry’s constant, HiS , with units (mg gas i in aqueous phase=L water=atm ¼ AeB(T C) : (H:15) where Ai is the intercept for semi-log plot of Figure H.5 (mg i aq=L H2O=atm i g) Bi is the slope 2.303 of Figure H.5 plot for a given gas, i ln X(ClO2) ẳ A(ClO2) ỵ B(ClO2)=T* ỵ C(ClO2) ln T*, in which, X(ClO2) ¼ mol fraction of gas in solution, A(ClO2) ¼ 7.9163, B(ClO2) ¼ 0.4791, C(ClO2) ¼ 11.0593, T* ¼ T(K)= 100; equation valid for 283.15 T 333.15 K for p(ClO2) ¼ 101.325 kPa (1.00 atm) of pure gas Appendix H: 863 Dissolved Gases 106 NH3 SO2 Solubility of gases (mg/L) 105 104 CL2 H 2S Rn CO2 103 O3 102 O2 N2 10 CH4 H2 CO 100 10 20 30 40 50 60 70 T (°C) FIGURE H.5 H.2.9 Solubility of gases of Table H.4 as affected by temperature APPLICATION OF HENRY’S LAW Examples H.8 through H.10 illustrate the application of Henry’s law and Table H.5 provides the representations for several situations As seen, Dalton’s law is applied at the same time Example H.8 Oxygen Concentration Determine oxygen concentration in water at 1585 m (5200 ft), at 108C Assume the water is in equilibrium with the atmosphere at that elevation Determine Henry’s law coefficient for oxygen at 108C 1.1 From Table H.5, C[O2, 1.0 atm, 108C] ¼ 53.68 mg O2=L H2O and therefore, H [O2, 1.0 atm, 108C] ¼ 53.68 mg O2=L H2O=atm O2 S Calculate the partial pressure of oxygen at sea level, 1585 and 3048 m 2.1 Obtain from Equation H.34, seen in Figure H.2, the atmospheric pressure at 1585 m (elevation of ERC=CSU) p(atm, 1585 m) ¼ 628 mm Hg 2.2 Determine the partial pressure of oxygen in ambient air From Table H.1, mole fraction of oxygen in ambient air is: nO2=n ¼ 0.209 476 From Dalton’s law, p(O2}=p ¼ 0.2095 2.3 Calculate the partial pressures of O2 at 108C for 1585 m n[O2 , sea level] p[atm, 1585 m] n ¼ 0:2095 628 mm ¼ 131 mm p[O2 , 1585 m] ¼ ¼ 0:173 atm Calculate dissolved oxygen concentration by applying Henry’s law 3.1 General equation is: C[O2, 108C] ¼ HS(O2, 108C) p(O2) 3.2 Apply for elevations 1585 m: C[O2 , 10 C, 1585 m] ¼ H(O2 , 10 C) p(O2 , 1585 m) 53:68 mg O2 =L H2 O ¼ 0:173 atm O2 atm O2 ¼ 9:3 mg=L 864 Appendix H: Dissolved Gases Example H.9 Carbon Dioxide Concentration at Sea Level at 208C Determine the partial pressure of carbon dioxide at sea level From Table H.1, the mole fraction of carbon dioxide in the atmosphere at sea level is 0.000314, i.e., n(CO2)=n ¼ 0.000314 mol carbon dioxide=mol air Apply Dalton’s law, i.e., Equation H.4, n(CO2 ) p(air, sea level) n(air) ¼ 0:000314 1:00 atm p(CO2 ) ¼ standard-state free energy of reaction and the equilibrium constant (Henry’s constant in this case) holds good, i.e., DG R ¼ RT ln HiD where DG R is the standard-state free energy of reaction (J=mol) R is the gas constant, i.e., 8.314510 J=mol T is the absolute temperature (K) and, ¼ 0:000314 atm DG R ¼ Look up Henry’s constant From Table H.5, 1688 mg CO2 =L H2 O H (CO2 , 20 C) ¼ atm CO2 S Apply Henry’s law Knowing Henry’s constant and the partial pressure of CO2, the calculation is, C(CO2 , sea level) ¼ HSCO2 p(CO2 ) 1688 mg CO2 =L H2 O 0:000314 atm atm CO2 mg CO2 ¼ 0:53 L H2 O ¼ Comments Using Table H.5 as the source for Henry’s constant data, the calculation is straight-forward Equilibrium Constants from Thermodynamic Data When equilibrium exists between the gas state and the aqueous state, as it must for Henry’s law to be valid, the free energy of the reaction is zero and, thus, the general relation between X DG f (reactants) (H:17) Example H.11 Thermodynamics of Carbon Dioxide Equilibrium (Modified from Sawyer and McCarty, 1967) Determine for carbon dioxide the equilibrium constant between the gas and aqueous phases at 258C Tabulate thermodynamic data, Solution Apply Henry’s law 1688 mg CO2 =L H2 O 4:0 atm atm CO2 mg CO2 ¼ 6752 L H2 O mol CO2 (ExH:10:1) ¼ 0:15 L H2 O DG f (products) In practice, while DG f data for the gas state are available in Lide (1996) for many substances, only a few data are given for the aqueous state Some data have been compiled, however, by Pankow (1991) and by Snoeyink and Jenkins (1980) Therefore, if thermodynamic data are available, i.e., DG f for both the gas state and the aqueous state, HiD can be calculated How to this is illustrated in Example H.11 for carbon dioxide Calculate the concentration of carbon dioxide in water at 58C in mol=L at a pressure of 4.0 atm CO2 (reported pressure of bottling by Silberberg, 1996, p 479) ¼ X where DG f (product i) is the standard-state free energy of formation for product i (J=mol) DG f (reactant i) is the standard-state free energy of formation for reactant i (J=mol) Example H.10 Application of Henry’s Law C(CO2 , bottle) ¼ HSCO2 p(CO2 ) (H:16) Variable CO2(aq) > DG f (298.15 K) DHf (298:15 K) S (298:15 K) a b 386.02a 413.26b 119.36b CO2(g) Reaction at 298.15 K 394.373 kJ=molb DG R ¼ 8.35 kJ=mol 393.51 kJ=molb DHR ¼ 19.75 kJ=mol 213.785 kJ=molb DS R ¼ 94.43 kJ=mol K Weast (1978, p D-78) Lide (1996, p 5–64) H.2.9.1 Write the equation for the reaction, CO2(aq) ! CO2(g) DG R ¼ 8.35 J=mol Appendix H: 865 Dissolved Gases Calculate HDCO2 from the statement of thermodynamic equilibrium DG R ¼ RT ln HDi 8350 J=mol ¼ (8:314510 J=mol K) (298:15 K) ln HDCO2 3:368 ¼ ln HDCO2 atm CO2 L H2 O mol CO2 atm CO2 m3 H2 O ¼ 0:029 mol CO2 HDCO2 (298 K) ¼ 29:02 This compares with 0.022 atm CO2 m3 H2O=mol CO2 in Yaws (1999, p 407) Converted to HSCO2 , HSCO2 (298 K) ¼ 29:02 ¼ 1,516 atm CO2 L H2 O mol CO2 44,000 mg mol CO2 mg CO2 L H2 O atm CO2 Comments This value for HSCO2 compares with 1449 mg CO2=L H2O=atm CO2 in Table H.5 Comparing with Yaws (1999, p 407), the 0.22 value converts to 2000 mg CO2=L H2O=atm CO2 (which is on the high end of values found in the literature) H.3 GAS PRECIPITATION In many situations, a dissolved gas will occur in a ‘‘supersaturated’’ state with respect to the local pressure When such condition occurs, the dissolved gas will ‘‘precipitate’’ forming bubbles of the pure gas The local pressure is whatever occurs in the water (at any given elevation and at any given depth of water) irrespective of whether a gas–water interface is present An everyday example of gas precipitation is observed when a bottle of carbonated beverage is opened; the pressure is released and bubbles appear spontaneously Another example is boiling water, which is characterized by the spontaneous appearance of water vapor bubbles; boiling occurs when the vapor pressure of water equals atmospheric pressure This occurs at lower temperatures as elevation increases, since atmospheric pressure declines with elevation Examples of gas precipitation include when (1) a bottle of soda is opened, carbon dioxide bubbles appear spontaneously within the bottle, (2) dissolved air flotation is due to a sudden reduction in pressure after supersaturated water reaches the flotation tank at which time the dissolved gas precipitates and forms bubbles, (3) oxygen dissolves continuously by photosynthesis up to a limit at which gas bubbles may be observed, (4) carbon dioxide and methane are produced in anaerobic environments and each form bubbles when saturation levels is reached, (5) air binding occurs in filters due to supersaturation, negative pressures, or both Thus, in some cases gas precipitation is desired and is engineered to occur (as in dissolved-air-flotation), in other cases the effect is disruptive (as in filters), and in some cases the effect is expected (as in opening a bottle of soda) Other examples include floating sludge in a primary settling basin due to carbon dioxide and methane precipitating as bubbles; in an anaerobic lagoon, gas bubbles are an index that methane and carbon dioxide are being produced, a desired result; the ‘‘bends’’ in divers who rise too quickly; the ‘‘bends’’ in migrating salmon, swimming below a dam where nitrogen gas may be ‘‘supersaturated’’ due to a plunging nappe that entrains air bubbles H.3.1 CRITERION FOR GAS PRECIPITATION In searching for an established criterion for the occurrence of gas precipitation, the literature provides little direct guidance A probable explanation would be that the problem has not come to the attention of the physical chemists, who deal mostly with fundamentals as opposed to applied problems Neither has it been articulated well for engineers and operators To explain gas precipitation, theory provides a means for a coherent explanation To interpret with a common-sense rationale then it can follow a theoretical understanding H.3.1.1 Nutshell Explanation for Gas Precipitation In-a-nutshell, the gas precipitation may be explained first by a dissolved gas occurring at a ‘‘supersaturated’’ concentration in a given local environment The gas may be transferred from a higher pressure region or could be generated If the dissolved gas concentration exceeds that which could exist in equilibrium at the pseudo pressure of the pure gas at the pressure of the local environment, then the gas will come out of the solution as bubbles For example, one may observe gas bubbles around a bloom of algae in stagnant water From Table H.5, C(O2, 20C) ¼ 43.39 mg O2=L water, which will occur if p(O2) ¼ 1.00 atm O2 If oxygen is generated by the algae through photosynthesis at sea level at zero depth, when dissolved oxygen concentration exceeds 43.39 mg O2=L water, then bubbles of pure oxygen will form This can be confirmed by taking a water sample; usually about 30–35 mg O2=L can be measured by a Winkler titration H.3.1.2 Chemical Potential Criterion for Equilibrium The chemical potential (see, for example, Eisenberg and Crothers, 1979, pp 271–290), can be defined for the dissolved state as mi (aq) ¼ m i (aq) þ RT ln [i] (H:18) and for the gas state as, mi (g) ẳ m i (g) ỵ RT ln pi (H:19) where mi(aq) is the chemical potential of species i in dissolved aqueous state (J=mol) m i (aq) is the standard-state chemical potential of species i in aqueous state (J=mol) 866 Appendix H: Dissolved Gases mi(g) is the chemical potential of species i in gas state (J=mol) m i (g) is the standard-state chemical potential of species i in gas state (J=mol) [i] is the mole fraction of species i in aqueous state [mols i=(L water)] pi is the partial pressure of species i in gas state (atm) ¼ RT ln [mi (g) mi (aq)] ¼ m i (g) m i (aq) pi ỵ RT ln [i] (H:20) m i (g) m i (aq) < (H:26) At the same time, the criterion of Equation H.26 can occur only when, At equilibrium, [mi (g) mi (aq)] ¼ and Equation H.20 becomes, pi ¼ m i (g) m i (aq) ỵ RT ln [i] (H:25) Equation H.24 is the key to developing a criterion for gas precipitation We may assert that when, m i (aq) > m i (g), then gas precipitation will occur Mathematically, Subtracting (product minus reactant), [pi =[i]] HiD [pi =[i]] pi (H:22) Also, since chemical potential and free energy of reaction per mole are identities, DG R ¼ RT ln HiD (H:16) In this derivation, it is important to note that we have chosen, Equation H.10, for Henry’s law definition, i.e., HiD pi [i] (H:23) Equation H.23 is consistent with the literature definition for HiD as found in Equation H.16 and if one determines DG R the HiD calculated matches published values H.3.1.3 Chemical Potential Criterion for Gas Precipitation Consider developing a criterion for gas precipitation in terms of ‘‘chemical-potential,’’ i.e., ‘‘m,’’ i.e., Equations H.20 and H.22, repeated below, pi [mi (g) mi (aq)] ¼ m i (g) m i (aq) ỵ RT ln [i] ẳ mi (g) m i (aq) ỵ RT ln HiD m i (g) Now to replace Equation H.22, i.e., m i (aq) (H:20) pi [i] Equation H.29 says that when the dissolved gas concentration in high enough that the product, HiD [i] exceeds the local pressure, then gas precipitation will occur At the time of gas precipitation, then, HiD [i]* ¼ pi (bubbles) (H:30) where [i]* is the dissolved gas concentration at equilibrium with bubbles (mol i=m3 H2O) pi(bubbles) is the partial pressure of gas i in bubbles formed by gas precipitation (kPa i) When the bubbles form then an equilibrium has established itself, i.e., m i (aq) ¼ m i (g) The gas concentration, [i], can go no higher than [i]* The pressure in the bubble is the ‘‘local’’ pressure This is what occurs when a bottle of carbonated beverage is opened or when the dissolved gas in a flotation basin moves to the lower pressure zone, gas bubbles will form spontaneously as the system strives for a new equilibrium In this case of a pressure release, m i (aq) m i (g) dissolved gas will come out of the solution as bubbles until the condition of Equation H.29 is met, i.e., m i (aq) ¼ m i (g) (H:22) in Equation H.20, substitute [mi (g) mi (aq)] ¼ RT ln HiD þ RT ln (H:29) (H:24) H.3.1.4 Alternative Criterion for Gas Precipitation In the development of a criterion for gas precipitation, the form of Henry’s law expressed in Equation H.10 was used because it was compatible with the established thermodynamic relations But subsequent to the thermodynamic development, the form expressed in Equation H.11 may be used as an Appendix H: 867 Dissolved Gases alternative This results in Equations H.30 through H.32, that correspond to H.28, H.29, and H.107, respectively, i.e., HiS < Ci pi (H:30) HiS pi < Ci (H:31) HiS pi [bubbles] ¼ C*i (H:32) where C* i is the concentration of dissolved gas i in equilibrium with gas bubbles at pressure, pi(bubbles) (mg i=L H2O= atm i) Equations H.30 through H.32, which are really the variations of a single equation, may be easier to use than any of the others because the units are common and HiS is found directly in Table H.5 Equation H.31 says that when the aqueous gas concentration of i exceeds the product, HiS pi , or C*i , then gas precipitation will occur Examples will help to illustrate the utility of the criterion of Equations H.31 or H.32 Example H.12 Gas Precipitation in Benthic Mud’s A lake at elevation 1524 m (5000 ft) has accumulated organic matter in its benthic zone and during the summer months, gas bubbles are observed breaking the surface of the lake The lake is 5.0 m (16.4 ft) deep and the temperature is 308C Explain the situation with respect to dissolved gases Analysis The benthic zone is most probably anaerobic, which means that methane and carbon dioxide are the products of the decomposition of the organic matter These reaction products will be generated and accumulate in the dissolved state until the criterion of Equation H.31 is satisfied at which time gas precipitation will occur Solution Apply Equation H.32 for methane first and then carbon dioxide, i.e., * HSCH4 pCH4 [bubbles] ¼ CCH (H:32) First HSCH4 (30 C) and pCH4(bubbles) must be determined, HSCH4 (30 C) ¼ 19:04 mg CH4 =L H2 O atm CH4 (Table H:5) and pCH4 (bubbles) ẳ p(atm, 1524 m) ỵ gw h kg m ẳ 84:31 kPa ỵ 996 9:806 65 5:0 m m s ¼ 84:31 kPa þ 48:84 kPa ¼ 133:15 kPa ¼ 1:32 atm Note that p(atm, 1524 m) was from Equation H.6; rw was obtained from Figure H.2 and Equation H.6; g was from Table QR.1 Substituting, the preceding calculated values for H3CH4 (308C) and for PCH4(bubbles) in (H.32) mg CH4 =L H2 O 1:32 atm CH4 atm CH4 mg CH4 ¼ 25:1 L H2 O * ¼ 19:04 CCH For carbon dioxide the procedure is the same and the data are the same except that HSCO2 (30 C) ¼ 1257 mg CO2 =L H2 O atm CO2 which results in, * ¼ 1659 CCO mg CO2 L H2 O Comments The concentrations of dissolved gases in the benthic zone * 3, and of the lake will not exceed the levels given by CCH * Note that methane has a much lower solubility than CCO carbon dioxide The calculations assume that the gases precipitate independently It is likely that some of the bubbles will coalesce before reaching the water surface PROBLEMS H.1 Bubbles in Water When a glass of cold water is permitted to warm to room temperature, bubbles are observed Explain H.2 Boiling Water Explain why water boils as its temperature is elevated Solution An everyday illustration of gas precipitation is seen in boiling water For water, [H2O] ¼ 1000 mg=L Now, as the temperature rises, the Henry’s law coefficient rises also, which is the ratio of vapor pressure to concentration of water, which is 1000 mg=L Finally, as the temperature reaches 1008C, the vapor pressure of water is 1.0 atm, and so we can say, HS[H2O, 1008C] ¼ 1000 mg=L=1.0 atm The HS P product is, HS[H2O, 1008C] P(local pressure ¼ atm] ¼ 1000 mg=L=atm 1.0 atm ¼ 1000 mg=L Thus, since [H2O]actual ¼ 1000 mg=L, the criterion for gas precipitation is satisfied and gas bubbles form While boiling water is explained merely by the fact that boiling occurs when the vapor pressure of the water increases to the local atmospheric pressure, the Henry’s law explanation shows the parallel with precipitation of any gas species 868 Appendix H: Dissolved Gases H.3 Mass percent: Mass of solute divided by (mass of solute ỵ mass of solvent)as given by Silberberg (1996, p 480) Molality: Moles of solute dissolved in 1000 g solvent—as given by Silberberg (1996, p 480) Molarity: Moles of solute dissolved in L of solution—as given by Silberberg (1996, p 480) Mole: A mole is defined (Alberty and Silbey, 1992, p 9) as the amount of substance that has as many atoms or molecules as exactly 0.012 kg of 12C A gram-mole is the mass in grams of 6.022 1023 molecules of a substance; for example, a mole of carbon has a mass of 12.011 g (Table B.1) Mole fraction: Moles of solute dissolved divided by (moles of solute ỵ mole of solvent)as given by Silberberg (1996, p 480) Ostwald coefficient: Volume of gas at system temperature T and partial pressure p dissolved per unit volume of solvent If the solubility is small and the gas phase is ideal, the Ostwald coefficient is independent of p and these two coefficients are simply related by Air Binding in Filter Media—General A rapid filter in water treatment experiences air binding Provide an analysis of how this can occur H.4 Air Binding in Filter Media—WTP The Betasso Water Treatment Plant that serves Boulder, Colorado obtains is source water from Silver Lake at a high elevation The water drops to a treatment plant more that 300 m lower elevation by means of a pipeline to the plant Air binding in filters has been a chronic problem Provide an analysis: (1) how the air gets into the water and (2) the point where the air will precipitate H.5 Remedies for Air Binding How would you remedy the air binding filter media? H.6 Algae as Possible Cause of Gas Binding Algae occur in the summer months in Lake Whatcom, the source water for the Bellingham Water Treatment Plant, Washington Air boils have been observed during backwash Provide an analysis of the situation H.7 Quantification of Air Binding Convert the dissolved gas in a water source to volume of air that may accumulate in a filter bed after gas precipitation H.8 Gas Production in Benthic Muds Gas bubbles are observed breaking at the surface of a lake in Iowa Explain H.9 Algae and Dissolved Gas Gas bubbles are observed within an algae mass floating on the surface of a pond Explain H.10 Gas Bubbles in Primary Clarifier A water sample is obtained from the sludge zone of a primary clarifier in a wastewater treatment plant, using a Kemmerer water sampler A portion of the sample is released to a 100 mL graduated cylinder and then poured into an evaporating dish where a carbon dioxide titration is carried out The result was CCO2 1500 mg=L Gas bubbles were observed breaking the water surface of the clarifier Explain H.11 Dissolved Gas Concentration from Diffused Aeration A diffused aeration system is located at the bottom of a pond at elevation 1524 m (5000 ft) The pond is 10.33 m deep Determine the dissolved oxygen concentration at the bottom of the pond H.12 The ‘‘Bends’’ in Salmon In the Columbia River migrating salmon have been killed by the ‘‘bends’’ when swimming below a dam in the deep water below a dam (in the vicinity of a plunging nappe) Explain GLOSSARY Bunsen coefficient: Volume (corrected to 08C and 1.0 atm) of gas dissolved per unit volume of solvent at system temperature T when the partial pressure of the solute is 1.0 atm (Reid et al 1977, p 357, Fogg and Gerrard, 1991, p 6) Ostwald coefficient ¼ (T=273) Bunsen coefficient REFERENCES Alberty, R A and Silbey, R J., Physical Chemistry, 1st edn., John Wiley & Sons, Inc., New York, 1992 Ashworth, R A., Howe, G B., Mullins, M E., and Rogers, T N., Airwater partitioning 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Raton, FL, 1991 Reid, R C., Prausnitz, J M., and Sherwood, T K., The Properties of Gases and Liquids, 3rd edn., McGraw-Hill, New York, 1977 Sander, R., Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry (Version 3), [http:==www.mpcH.mainz.mpg de= sander=res=henry.html] Air Chemistry Department, MaxPlanck Institute of Chemistry, Mainz, Germany, July 5, 1999 Sawyer, C N and McCarty, P L., Chemistry for Sanitary Engineers, McGraw-Hill, New York, 1967 Silberberg, M., Chemistry – The Molecular Nature of Matter and Change, Mosby—Year Book, Inc., St Louis, MO, 1996 Snoeyink, V L and Jenkins, D., Water Chemistry, John Wiley & Sons, Inc., New York, 1980 869 Weast, R C (Ed.), Handbook of Chemistry and Physics, 59th edn., 1978–79, CRC Press, Inc., Boca Raton, FL, 1978 Yaws, C L., Property Data for Aqueous Systems (software providing access to tabular data): Solubility in Water (900 compounds), SOLUB4 Solubility in Salt Water (217 compounds), SOLUB3 Solubility in Water – Variation With Temperature (217 compounds), SOLUB2 Henry’s Law Constant for Compounds in Water (692 compounds), HENRY Diffusion Coefficient in Water (1359 compounds), DLIQ Chemical Engineering Department, Lamar University, Beaumont, TX 77710, 1997 Yaws, C L., Chemical Properties Handbook, McGraw-Hill, New York, 1999 Yaws, C L., Pan, X., and Lin, X., Water solubility data for 151 hydrocarbons, Chemical Engineering, 100:108–111, February 1993 Index A Abrasion number, 460, 499 Absolute temperature, 815, 831 Absorbance, 627, 635 Acetyl coenzyme A (acetyl CoA), 707 Actinometry, 635 Activated alumina, 459, 499, 519–520, 532 Activated carbon; see also Granular activated carbon; Powdered activated carbon as adsorbent, 458 characteristics of hydraulics of packed beds, 462 index numbers, 460 internal structure, 460–461 microscopic structure, 462 physical properties, 459–460 pore size, 462 definition, 457, 499 manufacturing of, 459 shipping data, 463 sources of, 459 Activated sludge treatment bulking sludge, 738–739 cell production rate, 735 cell synthesis, 724 cell-wasting rate, 735–736, 749 detention time, 734 diffused-air aeration, 722–723 dynamic model, 734 empirical observation, 724 enzyme kinetics, 724 food-to-microorganism (F=M) ratio, 734–735 growth kinetics, 725 IWA model, 725 materials balance, 726 mathematical model, 724 methane fermentation kinetics, 724 microbial cultivation, 721 microorganisms, chemical formula, 724 modern theory, 725 numerical modeling, 732–733 finite-difference and differential, 733 International Water Association (IWA), 733 nutrients, 725 oxygen absorption, 724 requirement, 736–737 oxygen transfer, 572 parameter, design, 735 performance, 723 process, 707 process variation, 737 reactor analysis aerated lagoon, 729–730 conventional, 727–729, 749 extended aeration, 729 materials balance, 726–727 plug-flow reactor, 730–732 reactor theory, 725 recirculation rate, 716 sewage oxidation, 721 sludge age (uc), 725, 735 specific substrate utilization rate (U), 735 volumetric loading, 735 Activation, 501 Adenosine 50 di-phosphate (ADP), 707 Adenosine 50 -triphosphate (ATP), 708 Adiabatic compression, 806–807, 815 Adsorbates assess competitive effects of, 484 definition, 457, 501 natural organic matter, 464 organic compounds, 463–464 Adsorbents activated alumina, 459 activated carbon characteristics of granular, 459–463 internal pore structure of, 460–461 manufacturing of, 459 properties of, 460 shipping data, 463 sources of, 459 aluminum hydroxide floc, 459 kinds of, 458–459 soil minerals and organic carbon, 459 synthetic resins, 458–459 Adsorption adsorbates natural organic matter, 464 organic compounds, 463–464 adsorbents activated carbon, manufacturing of, 459 characteristics of GAC, 459–463 kinds of, 458–459 shipping data, 463 sources of activated carbon, 459 applications of, 464 in cake filtration, 433 cost of, 496–497 definitions, 451, 457–458 design chemical reduction, 490–492 contamination sources, 490, 492 protocol, 489–490 pump and treat, 492–494 taste-and-odor control, 490 tertiary treatment, 494–496 variables, 486–489 history of, 464–465 laboratory and pilot plant studies backwash velocity, 484 breakthrough curve, 484 competitive effects, 484 demonstration-scale plants, 484–486 fabrication, 484 HLR calculation, 484 isotherm determination, 483 wave front determination, 483–484 operation characteristics, 496 performance measures of, 458 process description, 458 process theory of equilibrium, 466–471 kinetics, 471–473 limitations of, 481–483 rational design, 479–481 reactor theory for packed beds, 473–479 reaction, 466, 502 Adsorption zone, 502 Advanced oxidation processes (AOP), 656 Advanced Water Treatment Research (AWTR) program, 464, 502, 656 Advection definition, 501 kinetics model, 475 kinetics model delineation, 475–476 probability coefficient, 476 Aerated grit chambers compressor power, 159 definition, 159 empirical guidelines, 158 performance estimation, 158 practice blower power, 156–157 design criteria, 154–156 header pipe, pressure, 156 principles, 150 rational guidelines, 158 theory calculations algorithm, 152–154 empirical guidelines, 151 grit removal calculation, 150–151 length and n determination, 151–152 spiral length, DL calculation, 151 volume installation and calculation, 159 Aerated lagoon, 729–730 Aerobes bacteria, 707 reaction, 707 Air binding, 408, 418 bump, 451 composition, 776 properties, 777 stripping bubble gas-transfer theory, 582 case study, 597–599 definition, 603 history, 573 Air-to-water ratio, 603 Air–water backwash system, 369–370 Alum liquid, 839–844 manufacturer, 833–834 polymer of, 846 solid, 833–837 water treatment diluting alum, 844 flow measurement, 845 mass flow calculations, 845 Alumina, 459, 502, 519–520, 532 Aluminum hydroxide, 459, 502, 532–533 Ambient water particles, coagulation characteristics colloids, 192 counting technology and turbidity, 194 microscopic particles, 192–194 871