Tai Lieu Chat Luong Environmental Process Analysis Environmental Process Analysis Principles and Modeling Henry V Mott, Professor Emeritus Department of Civil and Environmental Engineering South Dakota School of Mines and Technology Rapid City, SD, USA Copyright © 2014 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750–8400, fax (978) 750–4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748–6011, fax (201) 748–6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762–2974, outside the United States at (317) 572–3993 or fax (317) 572–4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data Mott, Henry V., 1951– Environmental process analysis : principles and modeling / Henry V Mott, professor emeritus, Department of Civil and Environmental Engineering, South Dakota School of Mines and Technology, Rapid City, SD pages cm Includes bibliographical references and index ISBN 978-1-118-11501-5 (cloth) 1. Environmental chemistry. 2. Chemical processes. I. Title TD193.M735 2013 577′.14–dc23 2013016208 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 To my deceased grandparents, Ida and Floyd Slingsby, and Ragna and Henry Mott; to my deceased parents, Marge Marie and Henry Valentine, who raised me; to my sisters, Jean, Judy, and Jane, with whom I shared childhood; to my children, Harrison, Graeme, and Sarah, with whom I now share adulthood; to my daughter-in-law, Lana, and my granddaughter, Samantha; to Marty, my sweet bride, with whom I share a wonderful life Contents Prefacexiii Acknowledgmentsxvii Introductory Remarks 1.1 Perspective / 1 1.2 Organization and Objectives / 1.2.1 Water / 2 1.2.2 Concentration Units / 3 1.2.3 Chemical Equilibria and the Law of Mass Action / 1.2.4 Henry’s Law / 4 1.2.5 Acids and Bases / 1.2.6 Mixing / 5 1.2.7 Reactions in Ideal Reactors / 1.2.8 Nonideal Reactors / 6 1.2.9 Acids and Bases: Advanced Principles / 1.2.10 Metal Complexation and Solubility / 1.2.11 Oxidation and Reduction / 1.3 Approach / 8 Water 11 2.1 Perspective / 11 2.2 Important Properties of Water / 12 vii viii Contents Concentration Units for Gases, Liquids, and Solids 16 3.1 Selected Concentration Units / 16 3.2 The Ideal Gas Law and Gas Phase Concentration Units / 20 3.3 Aqueous Concentration Units / 23 3.4 Applications of Volume Fraction Units / 28 The Law of Mass Action and Chemical Equilibria 4.1 4.2 4.3 4.4 4.5 4.6 4.7 36 Perspective / 36 The Law of Mass Action / 37 Gas/Water Distributions / 38 Acid/Base Systems / 39 Metal Complexation Systems / 40 Water/Solid Systems (Solubility/Dissolution) / 41 Oxidation/Reduction Half Reactions / 43 Air / Water Distribution: Henry’s Law 44 5.1 Perspective / 44 5.2 Henry’s Law Constants / 46 5.3 Applications of Henry’s Law / 51 Acid/Base Component Distributions 6.1 Perspective / 64 6.2 Proton Abundance in Aqueous Solutions: pH and the Ion Product of Water / 65 6.3 Acid Dissociation Constants / 69 6.4 Mole Accounting Relations / 70 6.5 Combination of Mole Balance and Acid/Base Equilibria / 74 6.5.1 Monoprotic Acids / 74 6.5.2 Diprotic Acids / 76 6.5.3 Triprotic and Tetraprotic Acids / 80 6.5.4 Abundance (Ionization) Fractions / 82 6.6 Alkalinity, Acidity, and the Carbonate System / 82 6.6.1 The Alkalinity Test: Carbonate System Abundance and Speciation / 82 6.6.2 Acidity / 90 6.7 Applications of Acid/Base Principles in Selected Environmental Contexts / 91 6.7.1 Monoprotic Acids / 91 6.7.2 Multiprotic Acids / 101 64 1.2 SYSTEM 1.0 P O 0.8 As–O–H 25°C, bar =1 ba r H3AsO4 H2As O4– 0.6 EH (V) 0.4 2– HAsO4 (As2O3) 0.2 0.0 AsO43– H3AsO3 –0.2 P H =1 –0.4 H2AsO3– As ba r HAsO32– AsO33– –0.6 –0.8 10 12 14 pH Figure A.1 EH – pH diagram for part of the system As–O–H The assumed activity of dissolved As = 10−6 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 SYSTEM 1.0 PO As–S–O–H 25°C, bar =1 0.8 ba r H3AsO4 0.6 H2AsO4– EH (V) 0.4 HAsO4– As2O3 0.2 As2S3 0.0 –0.2 PH =1 –0.4 AsO4– ba r AsS –0.6 –0.8 As 10 12 14 pH Figure A.2 EH – pH diagram for part of the system As–S–O–H The assumed activities of dissolved species are: As = 10−6 M, S = 10−3 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 SYSTEM 1.0 C–O–H 25°C, bar PO =1 0.8 ba r 0.6 H2CO3 EH (V) 0.4 HCO–3 0.2 2– CO3 na tiv eC CH CH (a q 0.0 –0.2 ) PH =1 –0.4 ba r –0.6 –0.8 10 12 14 pH Figure A.3 EH – pH diagram for part of the system C–O–H The assumed activity of dissolved C = 10−3 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 Cr–O–H SYSTEM 1.0 PO HC rO 0.8 25°C, bar – =1 ba r 0.6 0.2 10–6 10–4 EH (V) 2– Cr O4 CrOH2+ 0.4 Cr2O3 0.0 –0.2 PH =1 –0.4 Cr O2– ba r –0.6 –0.8 10 12 14 pH Figure A.4 EH – pH diagram for part of the system Cr–O–H The assumed activity of dissolved Cr = 10−6 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 SYSTEM 1.0 PO Fe3+ Fe–O–H 25°C, bar =1 0.8 ba r 0.6 EH (V) 0.4 Fe (OH)3 Fe2+ 0.2 0.0 –0.2 PH =1 –0.4 Fe O22– ba r Fe (OH)2 –0.6 –0.8 10 12 14 pH Figure A.5 EH – pH diagram for part of the system Fe–O–H assuming Fe(OH)3(s) as the stable Fe(III) phase The assumed activity of dissolved Fe = 10−6 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 SYSTEM 1.0 PO Mn–O–H 25°C, bar =1 0.8 ba r 0.6 MnO2 Mn 2+ Mn 0.2 0.0 Mn3O4 PH =1 –0.4 ba Mn(OH)2 –0.2 r –0.6 –0.8 O 10 12 Mn(OH)3– EH (V) 0.4 14 pH Figure A.6 EH – pH diagram for part of the system Mn–O–H The assumed activity of dissolved Mn = 10−6 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 1.2 SYSTEM 1.0 PO 0.8 (N O (N H 0.6 N–O–H 25°C, bar =1 ba r – ) – NO3 + ) EH (V) 0.4 0.2 N2(g) 0.0 + NH4 –0.2 PH =1 –0.4 ba r –0.6 –0.8 NH3–(g) 10 12 14 pH Figure A.7 EH – pH diagram for part of the system N–O–H The assumed activity of dissolved nitrogen = 10−3.3 M (PN = 0.8 bar ) Reprinted from Brookins (1988) by permission of SpringerVerlag GmbH 1.2 HS eO 1.0 SYSTEM – PO 0.8 Se–O–H 25°C, bar =1 0.6 r SeO42– HSeO3– 0.4 EH (V) ba H2SeO3 0.2 Se SeO32– 0.0 H Se –0.2 PH –0.4 =1 ba r HSe– –0.6 –0.8 10 12 14 pH Figure A.8 EH – pH diagram for part of the system Se–O–H The assumed activity of dissolved Se = 10−6 M Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH 598 Appendices 1.2 SYSTEM 1.0 PO S–O–H 25°C, bar =1 0.8 ba r – 0.6 HSO4 EH (V) 0.4 2– 0.2 SO4 S 0.0 H2S –0.2 PH =1 –0.4 ba r HS– –0.6 –0.8 10 12 14 pH Figure A.9 EH – pH diagram for part of the system S–O–H The assumed activity of dissolved S = 10−3 M (roughly 32 ppmm ) for convenience Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH References Alken Murray, Inc 2002Toxicity of hydrogen sulfide gas http://www.alken-murray.com/ H2SREM9.HTM Accessed on 2013 May 31 Asadi M Tables, in Beet-Sugar Handbook Hoboken: Wiley; 2005 Baes C, Mesmer R The Hydrolysis of Cations Malabar: Krieger; 1976 Baes C, Mesmer R The thermodynamics of cation hydrolysis Am J Sci 1981;281:935–962 Balzhiser R, Wass A, Samuels M, Eliassen J Chemical Engineering Thermodynamics Upper Saddle River: Prentice-Hall; 1972 Bird RB, Stewart WE, Lightfoot EN Transport Phenomena New York: Wiley; 1960 Bohn H, McNeal B, O’Connor G Soil Chemistry New York: Wiley; 1979 Brezonik P, Arnold W Water Chemistry New York: Oxford University Press; 2011 Brookins D Eh – pH Diagrams for Geochemistry New York: Springer-Verlag; 1988 Carnahan B, Luther HA, Wilkes JO Applied Numerical Methods New York: Wiley; 1969 Coello Oviedo MD, Sales Márquez D, Quiroga Alonso JM Toxic effects of metals on microbial activity in the activated sludge process Chem Bioch Eng 2002;16(3):139–144 Correa A, Comesana JF, Correa JM, Sereno AM Measurement and prediction of water activity in electrolyte solutions by a modified ASOG group contribution method Fluid Phase Equilibria 1977;129:267–283 Crank J The Mathematics of Diffusion 2nd ed New York: Oxford University Press; 1979 Crittenden JD, Trussel RR, Hand DW, Howe KJ, Tchobanoglous G Water Treatment Principles and Design 2nd ed New York: Wiley; 2005 Cussler EL Diffusion: Mass Transfer in Fluid Systems New York: Cambridge University Press; 1984 Environmental Process Analysis: Principles and Modeling, First Edition Henry V Mott © 2014 John Wiley & Sons, Inc Published 2014 by John Wiley & Sons, Inc 599 600 References Danckwerts PV Continuous flow systems: distribution of residence times Chem Eng Sci 1953;2:1–13 Dean J, editor Lange’s Handbook of Chemistry 14th ed New York: McGraw-Hill; 1992 Dutkiewicz E, Jakubowska A Water activity in aqueous solutions of homogeneous electrolytes: the effect of ions on the structure of water Chemphyschem 2002;2:221–224 Finnemore J, Franzini J Fluid Mechanics with Engineering Applications 10th ed New York: McGraw-Hill; 2002 Fogler HS Elements of Chemical Reaction Engineering 4th ed Upper Saddle River: PrenticeHall; 2005 Froment GF, Bischoff KB, Juray DW Chemical Reactor Analysis and Design 3rd ed New York: Wiley; 2011 Haynes WM, editor CRC Handbook of Chemistry and Physics Boca Raton: CRC Press; 2012 Hulbert HH Chemical processes in continuous-flow systems: reaction kinetics Ind Eng Chem 1944;36:1012–1017 Kojima K, Tochigi K Prediction of Vapor–Liquid Equilibria by the ASOG Method New York: Elsevier; 1979 Levenspiel O Chemical Reaction Engineering 2nd ed New York: Wiley; 1972 Levenspiel O Chemical Reaction Engineering 3rd ed New York: Wiley; 1999 Levine I Physical Chemistry 3rd ed New York: McGraw-Hill; 1988 Lymann WJ, Rheehl WF, Rosenblatt DH Handbook of Chemical Property Estimation Methods New York: McGraw-Hill; 1982 Mercer JW, Skipp DC, Giffen D Basics of pump and treat ground water remediation technology Environmental Protection Agency EPA/600/8-90/003; 1990 Morel F, Hering J Principles and Applications of Aquatic Chemistry New York: Wiley; 1993 Munson BR, Young DF, Okiishi TH Fundamentals of Fluid Mechanics 3rd ed New York: Wiley; 1998 Perry R, Chilton C Chemical Engineers’ Handbook 5th ed New York: McGraw-Hill; 1973 Perry R, Green DW Chemical Engineers’ Handbook 8th ed New York: McGraw-Hill; 2007 Reid RC, Prausnitz JM, Poling BE The Properties of Gases and Liquids 4th ed New York: McGraw-Hill; 1987 Robinson RA, Stokes RH Electrolyte Solutions London: Butterworths; 1959 Rogers PSZ, Pitzer KS Volumetric properties of aqueous sodium chloride solutions J Phys Chem 1982;11(1):15–81 Schwarzenbach RP, Gschwend PM, Imboden DM Environmental Organic Chemistry 2nd ed New York: Wiley; 2002 Snoeyink V, Jenkins D Water Chemistry New York: Wiley; 1980 Sposito G The Surface Chemistry of Soils New York: Oxford University Press; 1984 Stumm W, Morgan J Aquatic Chemistry 3rd ed New York: Wiley; 1996 Tchobanoglous G, Buron FL, Stensel DH Wastewater Engineering: Treatment and Reuse 4th ed New York: McGraw-Hill; 2003 Treybal R Mass-Transfer Operations 3rd ed New York: McGraw-Hill; 1980 U.S Geological Survey Dissolved oxygen solubility tables 2013 http://water.usgs.gov/ software/DOTABLES/ Accessed on 2013 May 31 References 601 Wagner RJ, Boulger Jr RW, Oblinger CJ, Smith BA 2006, Guidelines and standard procedures for continuous water-quality monitors—station operation, record computation, and data reporting: U.S Geological Survey Techniques and Methods 1–D3, 51, p +8 attachments; Available at http://pubs.water.usgs.gov/tm1d3 Accessed 2006 Apr 10 Weber Jr WJ Physicochemical Processes for Water Quality Control New York: Wiley; 1972 Weber Jr WJ, DiGiano FA Process Dynamics in Environmental Systems New York: Wiley; 1996 Wehner JF, Wilhelm RH Boundary conditions of flow reactor Chem Eng Sci 1956;6:89–93 Williams V, Mattice W, Williams H Physical Chemistry for the Life Sciences 3rd ed San Francisco: W.H Freeman and Company; 1978 Wylie Jr CR Advanced Engineering Mathematics 3rd ed New York: McGraw-Hill; 1966 Index Abundance (ionization) fractions infinitely dilute solutions, 81–82 non-dilute solutions, 351–353 table of (for infinitely dilute solution) relations, 83 table of (for non-dilute solution) relations, 352 Acid defined, 65 Acid deprotonation, 39, 69–70 (acidity) constant defined, 40 (acidity) constant table of values, 71 concentration-based equilibrium (acidity) constant, 341–344 diprotic acids, 76–80 metal ions (hydrolysis), 441–444 mixed equilibrium (acidity) constant, 341–344 monoprotic acids, 74–76 multiprotic acids, 80–82 Acidity, 65, 84, 90–91, 396–397, 399–417 Acidity constant see Acid deprotonation Acid neutralizing capacity ([ANC]) see also Alkalinity applications aqueous zinc with zinc hydroxide solid, 461 calcite solid-water-carbon dioxide system, 471 carbonate in closed system, 84, 399 carbonate in open system, 404 carbonate in semi-open system, 409 closed systems, 399–403 open systems, 403–408 semi-open systems, 408–417 Activity coefficient aqueous-electrolytes, 336–340 equations for computing, 337 aqueous-non-electrolytes, 417–422 aqueous-water, 422–426 Activity (chemical) related to abundance (concentration), 336 Activity of water, 50–51, 68–69, 366, 422–426, 534, 547 Adding chemical reactions, 68–69, 443–444 Alkalinity, 65, 82–90, 101–105, 396–417, 463, 471 carbonate specie contributions, 84–90 Environmental Process Analysis: Principles and Modeling, First Edition Henry V Mott © 2014 John Wiley & Sons, Inc Published 2014 by John Wiley & Sons, Inc 602 index Anaerobic sediments, 108 Atmospheric pressure lapse with elevation, 52 Autotrophic bacteria, 333 Base association (basicity) constant, 69 Base defined, 65 Base neutralizing capacity ([BNC]) see also Acidity applications carbonate in closed system, 84, 399 carbonate in open system, 404 carbonate in semi-open system, 409 closed systems, 399–403 open systems, 403–408 semi-open systems, 408–417 Boundary layers (gas/liquid), 57, 219, 234 Buffer intensity, 397–401 integration of, for [ANC] and [BNC], 399 Bulk density applications dry alum required and sludge cake produced from Phostrip® process, 166 arsenic speciation in sediments, 561 of dry solids, 161 of suspensions/sludges, 161 of unsaturated soils, 162 Charge balance, 379 Chemical oxygen demand dichromate-oxygen equivalence, 529 Chlorinity, 419 Concentration units defined (table), 17 Conductivity ratio for salinity, 419 Conjugate acid, 65–70 Conjugate base, 65–70 Controlling solid phase, 476–478 applications lead carbonate–lead hydroxide in precipitative system, 489 phosphate solubility control by calcium minerals, 500 phosphate solubility control by iron and aluminum salts, 505 zinc carbonate–zinc hydroxide control in precipitative system, 478 zinc carbonate–zinc hydroxide with calcite present, 484 Convective (advective) flux, 217 603 Completely-mixed flow reactors (tanks) in series (TiS) model, 275 applications comparison with PFR and SF predictions for enzyme-catalyzed reaction, 308 comparison with PFR, PFD, and SF predictions for pseudo-first-order reaction, 302 prediction of oxygen utilization profile (constant biomass abundance), 315 prediction of oxygen utilization profile (variable biomass abundance), 320 prediction of oxygen utilization profile (variable biomass abundance and cell recycle effects), 327 computation of N from mean residence time and variance, 277 enzyme-catalyzed (saturation) reactions with, 281 consideration of biomass recycle effects, 327 generation of E(θ) from N, 276 pseudo-first-order reactions with, 280, 297, 305 Cumulative exit age distribution (F(t), F(θ)) function, 271–272 computing statistical mean residence time from, 274 computing variance from, 275 Cumulative formation (stability) constants for insoluble metal-ligand complexes, 447 for metal hydrolysis, 444 for soluble metal-ligand complexes, 446 table of values, 579 Davies equation, 337 Death/decay coefficient for biomass respiration, 174 Debeye Hückel equation, 337 Denitrification, 162–163 Diffusive flux, 217 Dispersion number, 279, 282–283 Dissolved oxygen deficit, 136, 239 sag analysis, 235 saturation, 134 table of saturation values, 588 604 Index Electrochemical cell potential (electromotive force, EH and EH°), 533 relation to pE, 533 Enthalpy, 344–350 of formation (table), 571 of reaction for adjustment of equilibrium constants, 347 Entropy (table), 571 Equilibrium constants for acid deprotonation reactions, 71(table) computation from Gibbs energy, 346 for Henry’s law, 48 (table) for metal-ligand formation reactions, 579 (table) for solid formation reactions, 579 (table) temperature dependence of, 347 application of enthalpy of reaction, 348 Equivalent weight, 17, 24 Exit age distribution (E(t), E(θ)) density function, 268–271 applications comparison of PFR, PFD, TiS and SF models for pseudo-first-order reaction, 297 comparison of PFR, TiS and SF models for enzyme-catalyzed reaction, 302 computation of dispersion coefficient, 296 computation of equivalent number of CMFRs in series, 292 prediction of internal oxygen consumption from reactant profile, 315, 320, 327 prediction of internal reactant abundance for enzyme-catalyzed reaction, 308 prediction of internal reactant abundance for pseudo-first-order reaction, 305 computing statistical mean residence time from, 273 computing variance from, 273 Fick’s first law of diffusion, 217 FlexAir T-series diffuser (Environmental Dynamics, Inc.), 223, 233 Flux continuity, 283–284 Freshly-distilled water (FDW) characterization, 365 Gibbs (free) energy of formation for common species, 571 (table) of formation for selected geochemical species (table), 592 of reaction (computation of at standard state), 344–347 and reaction quotient, 476 of reaction for redox half reaction equilibrium constants, 530–545 of reaction for selected electron acceptor half reactions, 536 Grain per gallon defined, 17 Güntelberg equation, 337 Henry’s law, 38, 46–49 applications atmospheric moisture characterization, 51 calcite solid-water-carbon dioxide system, 471 carbonate in open system, 404 carbonate in semi-open system, 409 characterization of anaerobic sediments, 108 characterization of vinegar, 54 “combined” aqueous carbon dioxide specie, 49 hydrocyanic acid abundance in vapor, 95 subsurface vapor ammonia characterization, 98 sulfide abundance in wastewater collection systems, 55, 105 Heterotrophic bacteria, 313, 318 Hydraulic residence (space) time, 125–126 Hydronium ion, 36, 67–68 Ideal gas law (equation of state), 20–22 applications characterization of anaerobic sediments, 108 characterization of boiler stack gas, 22 characterization of cyanide leach solution vapor, 95 characterization of distilled vinegar, 54 characterization of the normal atmosphere, 51 characterization of sewer gas, 55, 105 characterization of subsurface ammonia release, 98 index Initial condition for proton balance, 363 Ionic strength computation of, 337 computation of for mixed solutions, 381 error associated with neglecting, 338–340, 354–358 incorporation into mole balance, 340–344 non-electrolytes in non-dilute solutions, 417 Ion size parameter, 338 Leach pad (heap, cyanide extraction), 95, 484 Ligands (complexing), 439–456 metal-ligand cumulative formation constants (table), 579 Longitudinal dispersion in reactors, 275 Mass balance equation, 120 interfacial transfer of oxygen in batch aeration process, 229 non-steady-state non-reactive mixing, 137–138 non-steady state reaction in ideal completely-mixed flow reactor, 181 non-steady-state tracer response for plug-flow with dispersion reactor, 278 reaction in completely-mixed batch reactor, 174 reaction in fed-batch reactor, 182 steady state interfacial transfer of oxygen in open plug-flow reactor, 235–239 steady-state non-reactive mixing, 131–132 steady-state pseudo-first-order reaction in plug-flow with dispersion reactor, 282 steady-state reaction in ideal plug-flow reactor, 176–177 Mass fraction defined, 17 Mass transfer coefficient computed for fine-bubble aeration diffuser, 230 from simply boundary layer theory, 218–222 Maximum specific biomass growth rate, 172 Metal ion hydration, 15, 337, 425, 440–441 of proton, 67 605 Metal ion hydrolysis, 441–444 Milliequivalent, 17, 24, 84 Milligram per liter as calcium carbonate defined, 17 Mixing of aqueous solutions–final speciation, 382, 387, 393 Mixing fraction defined, 380 Moisture content defined, 162 Mole (accounting) balance equations infinitely dilute solutions, 74–81 non-dilute semi-open systems, 408–409 non-dilute solutions, 351–358 Mole fraction defined, 17 Nernst equation, 533 Normal solution defined, 17 Oxidation of ferrous iron, 185 Oxidation-reduction potential (ORP), 550–551 Oxidation-reduction (Redox) half reactions applications characterization of anaerobic digester pE, 551 characterization of carbonate-terrain ground water pE, 555 construction of pE-pH diagram for the Fe(II)-Fe(III)-CO3= system, 543 construction of pE-pH diagram for the Fe(II)-Fe(III) system, 539 computation of redox specie predominance at constant pH, 546 equilibrium constants for bicarbonate, nitrate and sulfate reduction, 531 equivalence of dichromate and oxygen as electron acceptors, 529 theoretical oxygen demand of activated sludge biomass, 527 theoretical oxygen demand of glucose, 529 reconciliation of Nernst equation with the law of mass action, 534 speciation of arsenic in sediments, 561 computation of redox specie predominance (abundance) at constant pH, 545–550 using pE and pH, 560–564 equilibrium constants for, 530–532 606 Index Oxidation-reduction (Redox) half reactions (cont’d) estimation of system pE from specie abundance, 550–560 manipulating, 527–530 pE defined, 534 pE° defined, 532 table of selected, 593 writing, 523–526 Oxidation state of elements in chemical species, 521–522 Oxygen utilization in PFR-like activated sludge reactors, 312–315 enzyme catalyzed reaction with constant biomass abundance, 315 enzyme catalyzed reaction with variable biomass abundance, 320, 322 enzyme catalyzed reaction with variable biomass abundance and effects of biomass recycle, 327 Partial pressure (defined), 17, 20 Part per million by mass (ppmm) defined, 17 Part per million by volume (ppmv) defined, 17 Peclet number, 283 Percent by volume defined, 17 pE-pH (EH-pH) predominance diagrams for selected environmental systems, 594–598 predominance boundary lines for, 537–539 construction for Fe(II)-Fe(III) system, 539–542 construction for Fe(II)-Fe(III)-CO3= system, 543–545 pH (hydrogen ion abundance), pK, pC defined, 65–66 Phosphate solubility, 498–499 aluminum and iron controls upon, 505 calcium controls upon, 500 Phostrip® process, 165–166 Plug-flow like (PF-like) reactor typical schematic, 194, 291, modeling reactions in, 297, 302, 305, 308, 315, 320, 322, 327 Plug-flow with dispersion (PFD) model, 277 applications prediction of reactant concentration profile using pseudo-first-order reaction, 297 enzyme catalyzed (saturation) reactions with, 287 pseudo-first-order reactions with, 282–287 Porosity relations see Void fraction relations Precipitation reaction, 41 aluminum phosphate, 505 calcium carbonate, 468, 471, 473 calcium phosphate, 500 iron(III) phosphate, 505 lead carbonate, 489 phosphate with alum, 165 selected stoichiometry of (table), 158 zinc carbonate, 478, 484 zinc hydroxide, 456, 459, 461, 463, Pressure fraction defined, 17 Proton balance (condition), 358–364 applications addition of acetic acid and anhydrous ammonia to FDW, 365 equilibration of FDW with atmospheric CO2, 371 mixing of ammonia-laden infiltration with ground water, 387 mixing of ammonia-laden infiltration with ground water (Excel), 393 mixing of sulfide and acetate solutions, 382 preparation of sodium carbonate solution, 374 speciation of closed solution with calcite solid, 468 speciation of open solution with calcite solid, 471 speciation of solution with zinc hydroxide solid, 456, 459 initial conditions for, 363 proton reference level, 363 Publicly-owned treatment works (POTW), 93, 105, 144–146, 164–165 Pump station and force main (sketch), 106, 212, Quadratic formula for enzyme catalyzed reaction in CMFR, 181 for enzyme catalyzed reaction in TiS, 281, 319 index for calcite dissolution as a function of pH, 488 for second-order ligand mole balances, 463, 474 Reactions in completely-mixed batch reactors, 172 applications ferrous iron oxidation, 185 treatment of phenolic wastewater, 187 sulfide generation in lift station wet well, 212 enzyme catalyzed, 174 fed-batch reactor, 182 pseudo-first-order, 173 Reactions in ideal plug-flow reactors, 176 applications consideration of biomass recycle effects, 327 enzyme catalyzed (steady-state), 179 general packed bed reactor, 191 oxygen transfer/utilization in an open PFR, 235–239 “serpentine” activated sludge reactor, 193, 199, 297, 302, 305, 308, 315, 320, 327 ultraviolet disinfection of wastewater effluent, 206 pseudo-first-order (non-steady-state), 181 pseudo-first-order (steady-state), 177–178, 297, 305 Reactions (non-steady-state) in ideal completely-mixed flow reactors, 181 application to lindane fate in natural water body 208 Reactions (steady-state) in ideal completelymixed flow (continuously-stirred tank) reactors applications complete-mix activated sludge reactor, 199 complete-mix activated sludge reactor with cell recycle, 201–205 enzyme catalyzed, 180–181 pseudo-first order, 180 Reaction rate laws enzyme catalyzed (saturation, Monod/ Michaelis-Menton), 172–174 pseudo-first-order, 171 607 Recycle reactor, 195, 326 Redox see Oxidation-reduction Reference condition for enthalpy of formation, 348 for Gibbs energy of formation, 344 for proton balance, 358 Reference specie s for proton balance defined, 359 selecting for acid system, 360–362 for air/water distribution, 389 for [ANC] and [BNC], 397 for calcite dissolution in water, 468 for zinc hydroxide dissolution in water, 459, 461 for water as an acid or base, 359 Residence time distribution (RTD) see also Exit age distribution cumulative function for non-ideal reactor, 271 density function for non-ideal reactor, 267 exit response of completely-mixed flow reactor, 128–130 exit response of plug-flow reactor, 125–128 impulse input stimulus, 123 step input stimulus, 124 Salinity, 419 Salting out (non-electrolytes), 417–422 Segregated flow (SF) model, 279 enzyme catalyzed (saturation) reactions with, 302, 308, 315, 322 consideration of biomass recycle effects, 327 numerical integration for, 290 pseudo-first-order reactions with, 297, 305 Serpentine reactor see Plug-flow like reactor Setschenow equation, 417 Solubility of metal-ligand solids calcite dissolution in water, 468 calcite dissolution in water with pH control, 473 calcite in equilibrium with carbon dioxide, 471 lead carbonate precipitation, 489 zinc hydroxide solid in dilute aqueous solution, 456, 459 608 Index Solubility of metal-ligand solids (cont’d) zinc-hydroxide solid with phosphate ligand, 463 zinc precipitation as the carbonate or the hydroxide, 478 zinc solubility with pH in the presence of calcite, 484 Solubility product, 448 Specific biomass growth rate, 172 Stability constants see Cumulative formation constants State variable continuity, 220, 283–285 Stoichiometry applications conversion of nitrate to nitrogen gas, 163 phosphate precipitation in wastewater treatment, 166 and chemical reaction rate, 159–160 general chemical reaction, 159 Streeter-Phelps equation, 239 Theoretical oxygen demand, 312–313, 529 computation for activated sludge biomass, 313, 527 computation for glucose, 529 Time-dependent mixing in completelymixed flow reactors, 137–138 application in environmental systems, 145–147 application in laboratory setting, 138, 140 Tracer analyses see Residence time distribution defined, 121–122 Universal gas constant values (table), 20 Void fraction (porosity) relations, 160–162 Volume fraction defined, 17 Water acid/base character, 65–68 Lewis “dot” diagram for, 12 polarity, 12–15 structure, 14 Yield coefficient for biomass growth, 173 Zero-volume mixing applications combined with non-steady-state mixing, 138, 145, 146 laboratory tracer studies, 132, 133 wastewater discharge mixing zone, 134 mass balance derivation, 130