Environmental Process Analysis Principles and Modeling 1st Edition by Henry V Mott ISBN 1118747577 9781118747575

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ISBN 10: 1118747577 
ISBN 13: 9781118747575
Author: Henry V Mott

Environmental Process Analysis Principles and Modeling 1st Table of contents:

Chapter 1 Introductory Remarks
1.1 PERSPECTIVE
1.2 ORGANIZATION AND OBJECTIVES
1.2.1 Water
1.2.2 Concentration Units
1.2.3 Chemical Equilibria and the Law of Mass Action
1.2.4 Henry’s Law
1.2.5 Acids and Bases
1.2.6 Mixing
1.2.7 Reactions in Ideal Reactors
1.2.8 Nonideal Reactors
1.2.9 Acids and Bases: Advanced Principles
1.2.10 Metal Complexation and Solubility
1.2.11 Oxidation and Reduction
1.3 APPROACH
Chapter 2 Water
2.1 PERSPECTIVE
2.2 IMPORTANT PROPERTIES OF WATER
FIGURE 2.1 Lewis “dot” diagram for water.
FIGURE 2.2 Shorthand structure for the water molecule.
FIGURE 2.3 (a) Hydrogen-bonded open tetrahedral structure of ice. (b) Frank–Wen flickering cluster model of liquid water. Reproduced from Stumm and Morgan (1996) with permission from John Wiley & Sons.
Chapter 3 Concentration Units for Gases, Liquids, and Solids
3.1 SELECTED CONCENTRATION UNITS
TABLE 3.1 Commonly Used Units of Concentration
TABLE 3.2 Values of the Universal Gas Constant for Various Unit Systemsa
3.2 THE IDEAL GAS LAW AND GAS PHASE CONCENTRATION UNITS
Example 3.1
Example 3.2
3.3 AQUEOUS CONCENTRATION UNITS
Example 3.3
Example 3.4
Example 3.5
3.4 APPLICATIONS OF VOLUME FRACTION UNITS
Example 3.6
PROBLEMS
Chapter 4 The Law of Mass Action and Chemical Equilibria
4.1 PERSPECTIVE
4.2 THE LAW OF MASS ACTION
4.3 GAS/WATER DISTRIBUTIONS
4.4 ACID/BASE SYSTEMS
4.5 METAL COMPLEXATION SYSTEMS
4.6 WATER/SOLID SYSTEMS (SOLUBILITY/DISSOLUTION)
4.7 OXIDATION/REDUCTION HALF REACTIONS
Chapter 5 Air/Water Distribution: Henry’s Law
5.1 PERSPECTIVE
5.2 HENRY’S LAW CONSTANTS
FIGURE 5.1 Distribution of arbitrary component i between air and water.
TABLE 5.1 Values of Selected Henry’s Law Constants at 25°C for 26 Air/Water Distribution Reactions.
Example 5.1
Example 5.2
5.3 APPLICATIONS OF HENRY’S LAW
Example 5.3
Example 5.4
Example 5.5
FIGURE 5.2 Henry’s law equilibrium arising for distribution of oxygen between monolayers bounding the vapor liquid interface of an air bubble.
PROBLEMS
Chapter 6 Acid/Base Component Distributions
6.1 PERSPECTIVE
6.2 PROTON ABUNDANCE IN AQUEOUS SOLUTIONS: pH AND THE ION PRODUCT OF WATER
FIGURE 6.1 Visual representation of layering of water molecules within a hydrated hydrogen ion.
6.3 ACID DISSOCIATION CONSTANTS
TABLE 6.1 Selected Acid/Base Systems and pKA Values at 25 °C
6.4 MOLE ACCOUNTING RELATIONS
6.5 COMBINATION OF MOLE BALANCE AND ACID/BASE EQUILIBRIA
6.5.1 Monoprotic Acids
Example 6.1
FIGURE E6.1.1 Plot of specie predominance for the acetic acid system.
6.5.2 Diprotic Acids
Example 6.2
FIGURE E6.2.1 Plot of specie predominance for the selenous acid system.
6.5.3 Triprotic and Tetraprotic Acids
Example 6.3
FIGURE E6.3.1 Plot of specie predominance for the phosphoric acid system.
FIGURE E6.3.2 Plot of specie predominance for the ethylene-diamine-tetraacetic acid system.
6.5.4 Abundance (Ionization) Fractions
TABLE 6.2 Abundance (Ionization) Fractions for Mono- Through Tetraprotic Acids
6.6 ALKAUNITY, ACIDITY, AND THE CARBONATE SYSTEM
6.6.1 The Alkalinity Test: Carbonate System Abundance and Speciation
Example 6.4
FIGURE E6.4.1 Plot of abundance fractions for the carbonate system.
FIGURE E6.4.2 Plot of specie predominance for the carbonic acid system and changes in speciation associated with the standard alkalinity titration for CTot.CO3 = 0.006 M.
6.6.2 Acidity
6.7 APPLICATIONS OF ACID/BASE PRINCIPLES IN SELECTED ENVIRONMENTAL CONTEXTS
6.7.1 Monoprotic Acids
Example 6.5
Example 6.6
Example 6.7
FIGURE E6.7.1 Schematic representation of the air/water and acid/base distributions of cyanide species.
Example 6.8
FIGURE E6.8.1 Schematic representation of the vapor–liquid interface and associated air/water and acid/base distribution of ammonia species in a contaminated subsurface environment.
6.7.2 Multiprotic Acids
Example 6.9
Example 6.10
FIGURE E6.10.1 Plot of the relative error of the computation of total inorganic carbon from alkalinity measurement associated with use of the approximate equation describing alkalinity as a function of the measured alkalinity.
Example 6.11
FIGURE E6.11.1 Sketch of a pump station and force main system.
Example 6.12
FIGURE E6.12.1 Schematic representation of the sediment/water interface associated with a gas bubble residing in sediments, with additional representation of the gas/water and acid/base distributions of species that would be present.
PROBLEMS
FIGURE P6.32 A cross section through a completed solid waste landfill.
FIGURE P6.33 Schematic diagram showing the liquid and vapor within and anaerobic digester.
FIGURE P6.34 Idealized cylindrical shape of a hypothetical contaminated zone.
FIGURE P6.35 Schematic sketch showing a cross section of a heap leach pad.
FIGURE P6.36 Gas bubbles below the sediment/water interface.
Chapter 7 Mass Balance, Ideal Reactors, and Mixing
7.1 PERSPECTIVE
7.2 THE MASS BALANCE
FIGURE 7.1 Word statement of the mass balance upon a targeted substance (component i) for an arbitrary reactor.
7.3 RESIDENCE TIME DISTRIBUTION (RTD) ANALYSES
7.3.1 RTD Experimental Apparatus
FIGURE 7.2 Schematic diagram of an apparatus for conduct of residence time distribution analyses using either impulse or step input of tracer.
7.3.2 Tracers
7.3.3 Tracer Input Stimuli
7.3.3.1 Impulse Input Stimulus
FIGURE 7.3 Ideal and real impulse inputs for tracer analyses.
7.3.3.2 Step Input Stimulus
FIGURE 7.4 Ideal and real step input functions.
7.4 EXIT RESPONSES FOR IDEAL REACTORS
7.4.1 The Ideal Plug-Flow Reactor (PFR)
FIGURE 7.5 Impulse input stimulus and exit response for an ideal plug flow reactor.
FIGURE 7.6 Positive and negative step input stimuli and exit responses for an ideal plug flow reactor.
7.4.2 The Ideal Completely Mixed Flow Reactor (CMFR)
FIGURE 7.7 CMFR exit responses for impulse (a) and positive (b) and negative (c) step input stimuli.
7.4.3 The Ideal (Completely Mixed) Batch Reactor (CMBR)
7.5 MODELING OF MIXING IN IDEAL CMFRs
7.5.1 Zero-Volume Applications
Example 7.1
Example 7.2
Example 7.3
FIGURE E7.3.1 Sketch of Rapid Creek and wastewater discharge for mixing zone computations.
7.5.2 Time-Dependent Mixing
Example 7.4
FIGURE E7.4.1 Plot of time-variant reactor and reactor effluent concentration.
Example 7.5
FIGURE E7.5.1 Plot of input positive and negative step and associated exit responses for a CMFR.
FIGURE E7.5.2 Capture of the short logical program defining the input concentration level.
FIGURE E7.5.3 The logical programs created to produce graphical output for the plot of the system behavior illustrated in Figure E7.5.3.
FIGURE E7.5.4 A plot of a series of positive and negative step inputs and the resultant exit responses for a CMFR.
7.6 APPLICATIONS OF CMFR MIXING PRINCIPLES IN ENVIRONMENTAL SYSTEMS
Example 7.6
Example 7.7
Example 7.8
PROBLEMS
FIGURE P7.9 Overall schematic of a recycle bioreactor depicting the influent mixing point.
FIGURE P7.18 Typical characteristics of human respiration.
Chapter 8 Reactions in Ideal Reactors
8.1 PERSPECTIVE
8.2 CHEMICAL STOICHIOMETRY AND MASS/VOLUME RELATIONS
TABLE 8.1 Selected Chemical Reactions Illustrating Stoichiometric Relations
8.2.1 Stoichiometry and Overall Reaction Rates
8.2.2 Some Useful Mass, Volume, and Density Relations
8.2.3 Applications of Stoichiometry and Bulk Density Relations
Example 8.1
FIGURE E8.1.1 Schematic diagram of a dual-sludge system with focus on the nitrogen removal (denitrification) process.
Example 8.2
FIGURE E8.2.1 Schematic diagram of the Phostrip® process indicating two control volumes upon which mass balances can be drawn.
8.3 REACTIONS IN IDEAL REACTORS
8.3.1 Reaction Rate Laws
FIGURE 8.1 The enzyme-limited microbial specific growth rate coefficient for constant biomass abundance (X).
8.3.2 Reactions in Completely Mixed Batch Reactors
8.3.3 Reactions in Plug-Flow Reactors
8.3.3.1 The General PFR Mass Balance
FIGURE 8.2 Schematic representation of an arbitrarily situated finite volume element within a cylindrical plug flow reactor. Symbology is included such that the mass balance on an arbitrary component can be drawn upon the finite volume element.
8.3.3.2 The Pseudo-First-Order Reaction Rate Law in PFRs
8.3.3.3 The Saturation Rate Law in PFRs
8.3.4 Reactions in Completely Mixed Flow Reactors
FIGURE 8.3 Schematic diagram of a CMFR with reaction of arbitrary component. A mixing propeller is shown but the mixing may be accomplished via various means.
8.3.5 Unsteady-State Applications of Reactions in Ideal Reactors
8.3.5.1 Unsteady-State CMFR
8.3.5.2 The Fed-Batch Reactor
8.3.5.3 Time-Variant Analyses of the PFR
8.4 APPLICATIONS OF REACTION IN IDEAL REACTORS
8.4.1 Batch Reactor Systems
Example 8.3
FIGURE E8.3.1 Plot of ferrous iron versus time in a batch process using oxygen in air as an oxidant.
Example 8.4
FIGURE E8.4.1 Plot of phenol concentration versus time for a process conducted in a batch reactor.
FIGURE E8.4.2 Screen capture of a logical program to implement the Root() function to produce a concentration versus time tracesss for a CMBR.
FIGURE E8.4.3 A plot of phenol concentration identical to that of Figure E8.4.1, but generated using MathCAD’s capability to employ matrix operations.
FIGURE E8.4.4 A plot of time required to accomplish the desired phenol reduction using the biomass concentration as the independent variable.
8.4.2 Plug-Flow Reactor Systems
Example 8.5
FIGURE E8.5.1 Plot of reactant abundance versus position in an ideal PFR for arbitrary reactant with transformation governed by a pseudo-first-order rate law.
Example 8.6
FIGURE E8.6.1 Schematic plan view of an activated sludge reactor arranged to approximate plug flow conditions.
FIGURE E8.6.2 Schematic of the reactor and clarifier system used for an activated sludge recycle reactor.
FIGURE E8.6.3 Plot of effluent COD concentration versus recycle ratio for a plug-flow with recycle reactor.
FIGURE E8.6.4 Plot of effluent COD concentration versus recycle ratio comparing the inclusion of the recycle dilution of the influent against the constant influent assumption.
8.4.3 Completely Mixed Flow Reactor Systems
Example 8.7
FIGURE E8.7.1 Plot of specific reaction rate versus positional residence time, comparing an ideal CMFR with an ideal PFR.
Example 8.8
FIGURE E8.8.1 A plot of effluent concentration versus recycle ratio for CMFR and PFR reactor, neglecting the dilution of influent concentration by the recycle flow.
Example 8.9
FIGURE E8.9.1 A plot of predicted effluent concentration versus recycle ratio for two CMFR scenarios − Ceff.1 considers no dilution of influent by recycle flow while Ceff.2 is based on adjusting the influent concentration by the effluent concentration value in the recycle flow. Biomass content of the recycle flow is taken as 0.45%.
FIGURE E8.9.2 A plot of predicted effluent concentration from a CMFR with recycle based on abundance of biomass in the recycle flow of 1%.
8.4.4 Some Context-Specific Advanced Applications
Example 8.10
FIGURE E8.10.1 Schematic diagram of the configuration of a typical submerged UV disinfection system.
Example 8.11
FIGURE E8.11.1 A plot of lindane concentration versus time in a hypothetical pond affected by lindane in agricultural runoff received by the pond.
FIGURE 8.4 Schematic diagram of a typical lift station and force main system used to transport wastewater to central collection systems from areas outside the main drainage area.
Example 8.12
8.5 INTERFACIAL MASS TRANSFER IN IDEAL REACTORS
8.5.1 Convective and Diffusive Flux
8.5.2 Mass Transfer Coefficients
FIGURE 8.5 Sketch representing the system and mass transfer process occurring across the gas/liquid boundary of an air bubble frozen in time during its rise through an aerated solution.
8.5.3 Some Special Applications of Mass Transfer in Ideal Reactors
8.5.3.1 Characterization of Performance of Aeration Diffusers
FIGURE 8.6 Standard FlexAir T-series diffuser operating in a clean-water tank. Photo courtesy of Environmental Dynamics Inc.
Example 8.13
FIGURE E8.13.1 Bubble surface area per mole of gas and saturation concentration of dissolved oxygen as a function of vertical position in a clean water tank. Transfer of O2 and N2 into or out of the bubble is neglected in the computation.
FIGURE E8.13.2 Drag coefficient versus Reynolds number for gas bubbles rising in a clean-water aeration test tank, adapted from Figure 9.21 of Munson et al. (1998).
FIGURE E8.13.3 The programmed loop for computation of velocity with position for a bubble rising in a clean-water aeration test tank.
FIGURE E8.13.4 Velocity versus position for a bubble rising in a clean-water aeration test tank.
FIGURE E8.13.5 Plot of position versus elapsed time for a bubble rising in a clean-water aeration tank.
Example 8.14
FIGURE E8.14.1 Output from an Excel worksheet in which concentration versus time data were processed to obtain the overall value of kl·α.
FIGURE E8.14.2 A plot of ln(C*−C0C*−C) versus time for a clean-water test of an aeration diffuser.
FIGURE E8.14.3 A single data point from the Example 8.14 computation superimposed on a plot of standard oxygen transfer efficiency versus air flow per diffuser for a Flex Air, T-series diffuser manufactured by Environmental dynamics International. T-series performance curve courtesy of Environmental dynamics International.
8.5.3.2 Oxygen Transfer Across a Macroscopic Surface
Example 8.15
FIGURE E8.15.1 Schematic representation of a rectangular channel and arbitrarily located fluid element within the channel, upon which a mass balance is drawn.
FIGURE E8.15.2 Profiles of DO and biodegradable chemical oxygen demand along the flow path of a rectangular open channel transmitting return activated sludge from a clarifier to the influent of a recycle reactor.
PROBLEMS
CMBR Problems
PFR Problems
CMFR Problems
Stoichiometry Problems
Advanced Problems
FIGURE p8.32 Sketch of biofilm on and important geometry of the interior surface of a force main.
FIGURE p8.35 Layout, cross section and geometry of a uniform flow situation in a gravity sewer.
FIGURE p8.39 Flow pattern in a reactor arranged to approximate plug flow.
FIGURE p8.43 Areal sketch of runoff into a stock watering pond.
FIGURE p8.44 Plan view sketch of aerated treatment pond with directional surface aerator/mixers.
FIGURE p8.45 Sketch of landfill leachate and ground water flow system with a down-gradient monitoring well.
FIGURE p8.47 Schematic cross section through a heap leach pad.
FIGURE p8.49 Sectional sketch of a permeable reactive barrier containing zero valent iron catalyst pellets.
Chapter 9 Reactions in Nonideal Reactors
9.1 PERSPECTIVE
9.2 EXIT CONCENTRATION VERSUS TIME TRACES
9.2.1 Impulse Stimulus
FIGURE 9.1 Theoretical exit concentration responses of real laboratory reactors for impulse input stimuli. Mtracer = 1 g, VR = 100 L, Q = 1 L/min.
9.2.2 Positive Step Stimulus
FIGURE 9.2 Theoretical exit concentration responses of real laboratory reactors for positive step input stimuli. Cin = 10 mg/L, VR = 100 L, Q = 1 L/min.
9.3 RESIDENCE TIME DISTRIBUTION DENSITY
9.3.1 E(t) Curve and Quantitation of Tracer Mass
FIGURE 9.3 A typical C(t) curve from an impulse input with an element shown representing the mass of tracer exiting the reactor between t and t+Δt.
9.3.2 E(t) and E(θ) RTD Density Curves
FIGURE 9.4 Normalized residence time distribution curves for the exit concentration trace of Figure 9.3: (a) normalized to mass of tracer; (b) normalized to mass of tracer and HRT.
9.4 CUMULATIVE RESIDENCE TIME DISTRIBUTIONS
FIGURE 9.5 Cumulative residence time distributions resulting from a positive step corresponding with the system depicted in Figure 9.4: (a) normalized to influent concentration; (b) normalized to influent concentration and HRT.
9.5 CHARACTERIZATION OF RTD DISTRIBUTIONS
9.5.1 Mean and Variance from RTD Density
9.5.2 Mean and Variance from Cumulative RTD
9.6 MODELS FOR ADDRESSING LONGITUDINAL DISPERSION IN REACTORS
9.6.1 CMFRs (Tanks) in Series (TiS) Model
FIGURE 9.6 Schematic representation of a non-ideal reactor as N CMFRs in series (the TiS model).
9.6.2 Plug-Flow with Dispersion (PFD) Model
FIGURE 9.7 Schematic representation of a non-ideal reactor, resembling a PFR, with delineation of an arbitrarily located element of reactor volume upon which a mass balance may be drawn. For a conservative tracer, reaction is disregarded.
9.6.3 Segregated Flow (SF) Model
FIGURE 9.8 Schematic representation of the segregated flow model: a real reactor resembling a PFR may be segregated into n sub-reactors with range of residence times in accord with the abscissa range of the RTD function and receiving fractions of the total flow in accord with RTD density or cumulative RTD function.
9.7 MODELING REACTIONS IN CMFRs IN SERIES (TiS) REACTORS
9.7.1 Pseudo-First-Order Reaction Rate Law in TiS Reactors
9.7.2 Saturation Reaction Rate Law with the TiS Model
9.8 MODELING REACTIONS WITH THE PLUG-FLOW WITH DISPERSION MODEL
9.8.1 Pseudo-First-Order Reaction Rate Law with the PFD Model
FIGURE 9.9 Schematic representation of the entrance and exit boundaries of a reactor visualized using the plug-flow with dispersion (PFD) model. Representations of the transport and reactive processes within elements of thickness dz and area AX on the reactor sides of the entrance and exit planes are shown.
9.8.2 Saturation Rate Law with the PFD Model
9.9 MODELING REACTIONS USING THE SEGREGATED FLOW (SF) MODEL
9.10 APPLICATIONS OF NONIDEAL REACTOR MODELS
9.10.1 Translation of RTD Data for Use with Nonideal Models
FIGURE 9.10 Configuration sketch for a hypothetical reactor to be examined in Chapter 9 examples. (S1 = 26.42 m, S2 = 25.71 m, Wch = 4.18 m, Dch = 5 m, Lch = 25.1 m, VR = 3150 m3 (0.833 Mgal)).
TABLE 9.1 Hypothetical Data from RTD Analysis of a PF-Like Reactor.
Example 9.1
FIGURE E9.1.1 Plot of exit response data from impulse and step inputs of Example 9.1.
FIGURE E9.1.2 A plot of the F(t) distribution as computed from C(t).
Example 9.2
9.10.2 Modeling Pseudo-First-Order Reactions
Example 9.3
FIGURE E9.3.1 Capture of MathCAD code for the iterative solution of the PFD model for a pseudo-first-order reaction rate law.
9.10.3 Modeling Saturation-Type Reactions with the TiS and SF Models
Example 9.4
FIGURE E9.4.1 Screen capture of a logical program for computing stepped concentrations for a saturation-type reaction for the TiS model.
FIGURE E9.4.2 Screen capture of logical program for employment of a truncated N value.
FIGURE E9.4.3 Screen capture of short program to compute the effluent concentration based on the SF model.
9.11 CONSIDERATIONS FOR ANALYSES OF SPATIALLY VARIANT PROCESSES
9.11.1 Internal Concentration Profiles in Real Reactors
Example 9.5
FIGURE E9.5.1 Screen capture of logical programs to compute the concentration profile along the flow path of a reactor using the TiS model.
FIGURE E9.5.2 Screen captures of short programs to generate a matrix of concentrations along n parallel reactors of the SF model and collect them into a single profile along the flow path of the real reactor.
FIGURE E9.5.3 A plot of predicted substrate concentration versus position for PFR, N-CMNRs in series, PFD and SF models.
FIGURE E9.5.4 A plot of predicted substrate concentration versus position for PFR, N-CMNRs in series, PFD and SF models, with a logarithmic ordinate scale to allow easy discernment of the differences in the exit half of the reactor.
Example 9.6
FIGURE E9.6.1 A plot of the exit response curve for an impulse input for Example 9.6.
FIGURE E9.6.2 Screen captures of short logical programs for computing the concentration profile along the flow path of a real reactor using the TiS model.
FIGURE E9.6.3 Screen captures of short programs used to compute the profiles along n + 1 parallel reactors of the SF model and collect them into an aggregate profile along the flow path of the real reactor.
FIGURE E9.6.4 A plot of the predicted concentration profiles across a PF-like reactor as predicted by the PFR, N-CMFRs, and SF models.
9.11.2 Oxygen Consumption in PFR-Like Reactors
Example 9.7
9.12 MODELING UTILIZATION AND GROWTH IN PFR-LIKE REACTORS USING TiS AND SF
Example 9.8
FIGURE E9.8.1 Screen capture of the MathCAD code used to compute substrate and biomass levels as well as specific substrate utilization rates to model utilization, growth and oxygen consumption as predicted by the N-CMFRs in series model.
FIGURE E9.8.2 A plot of predicted substrate and biomass levels and oxygen consumption rates along the flow path of a reactor modeled using the N-CMFRS in series model.
Example 9.9
FIGURE E9.9.1 A plot of substrate and biomass concentrations and specific oxygen consumption rates along the flow path of a PF-like reactor modeled using the ideal PFR model.
FIGURE E9.9.2 A Plot of predicted substrate and biomass concentrations and specific oxygen consumption rates along the flow path of a PR-like reactor modeled using the ideal PFR and SF models.
FIGURE 9.11 Schematic of PF-like reactor system with clarifier and biomass recycle stream.
Example 9.10
FIGURE E9.10.1 Screen capture of a MathCAD program for implementation of the fixed-step Runge–Kutta ODE solver for approximation of the solution of coupled biomass growth and substrate utilization along the flow path of a PF-like reactor with cell recycle to control the biomass inventory of the reactor, modeled as an ideal PFR.
FIGURE E9.10.2 Screen capture of a MathCAD program for implementation of the fixed-step Runge–Kutta ODE solver for approximation of the solution of coupled biomass growth and substrate utilization along the flow path of a PF-like reactor with recycle to control the biomass inventory of the reactor, modeled using the SF model.
FIGURE E9.10.3 Screen capture of a MathCAD program for implementation of the CMFRs in series model to predict the coupled biomass growth and substrate utilization along the flow path of a PF-like reactor with recycle to control the biomass inventory of the reactor.
FIGURE E9.10.4 A plot showing predicted substrate concentrations along the path of a PF-like reactor as modeled using the PFR, N-CMFRs in series and SF models.
FIGURE E9.10.5 A plot showing predicted biomass abundance along the path of a PF-like reactor as modeled using the PFR, N-CMFRs in series and SF models.
FIGURE E9.10.6 A plot showing predicted specific oxygen consumption rates along the path of a PF-like reactor as modeled using the PFR, N-CMFRs in series and SF models.
Chapter 10 Acid-Base Advanced Principles
10.1 PERSPECTIVE
10.2 ACTIVITY COEFFICIENT
10.2.1 Computing Activity Coefficients
TABLE 10.1 Some Relations used for Estimation of Aqueous Activity Coefficients for Electrolytes (Adapted from Stumm and Morgan, 1996)
TABLE 10.2 Size Parameters (Å) for Selected ions for use with the Extended Debye-Hückel Relation (Adapted from Dean, 1992)
FIGURE 10.1 Aqueous activity coefficients for electrolytes of various charge computed using the extended Debeye–Hückel equation. A and B are for T =298.15 K. Ionic strength of Rapid City, SD, raw water (I ≈ 0.008) is shown for perspective.
FIGURE 10.2 Percent relative error for chemical activity of electrolytes based on the infinitely dilute assumption (γi = 1) relative to values computed using the Debeye-Hückel equation. Ionic strength of Rapid City, SD, raw water (I ≈ 0.008) is shown for perspective.
10.2.2 Activity Coefficient and Law of Mass Action
Example 10.1
10.3 TEMPERATURE DEPENDENCE OF EQUILIBRIUM CONSTANTS
10.3.1 Standard State Gibbs Energy of Reaction
Example 10.2
10.3.2 Temperature Corrections for Equilibrium Constants
Example 10.3
10.4 NONIDEAL CONJUGATE ACID/CONJUGATE BASE DISTRIBUTIONS
TABLE 10.3 Mole Balance Relations for Typical Mono- and Diprotic Acid Systems for Noninfinitely Dilute Aqueous Solutions
TABLE 10.4 Relations Employing Proton Activity, Equilibrium Constants, and Total Acid Specie Concentrations for Specie Activities and Abundance Fractions in Noninfinitely Dilute Aqueous Solutions
Example 10.4
FIGURE E10.4.1 Plots of activity versus pH for the selenous acid system at SeTot=2 × 10−4 M for ionic strengths of 0.01 and 0.10 M.
FIGURE E10.4.2 A plot of the error of activities of hydrogen selenite and selenite predicted using the dilute-solution assumption relative to predictions employing ionic strength and the Güntelberg equation for 2 × 10−4 M SeTot.
FIGURE E10.4.3 A plot of the error of activities of bicarbonate and carbonate predicted using the dilute-solution assumption relative to predictions employing ionic strength and the Güntelberg equation for 2 × 10−4 M CO3Tot.
10.5 THE PROTON BALANCE (PROTON CONDITION)
10.5.1 The Reference Conditions and Species
10.5.2 The Proton Balance Equation
Example 10.5
Example 10.6
10.5.3 The Reference and Initial Conditions for the Proton Balance
Example 10.7
Example 10.8
10.6 ANALYSES OF SOLUTIONS PREPARED BY ADDITION OF ACIDS, BASES, AND SALTS TO WATER
10.6.1 Additions to Freshly Distilled Water (FDW)
Example 10.9
10.6.2 Dissolution of a Weak Acid in Water
Example 10.10
10.6.3 Dissolution of a Basic Salt in Water
Example 10.11
FIGURE E10.11.1 Screen capture of a solve block for speciation of the carbonate system when soda ash is added to freshly distilled water considering infinitely dilute conditions.
FIGURE E10.11.2 Screen capture of a solve block for speciation of the carbonate system when soda ash is added to technical grade distilled water (equilibrated with the atmosphere) considering infinitely dilute conditions.
FIGURE E10.11.3 Screen capture of a solve block for speciation of the carbonate system when soda ash is added to technical grade distilled water (equilibrated with the atmosphere) considering non-dilute conditions.
10.6.4 A Few Words about the Charge Balance
10.7 ANALYSIS OF MIXED AQUEOUS SOLUTIONS
10.7.1 Mixing Computations with Major Ions
Example 10.12
10.7.2 Final Solution Composition for Mixing of Two or More Solutions
Example 10.13
FIGURE E10.13.1 Screen capture of the solve block for computation of the final solution composition for mixing of acetate and sulfide solutions.
FIGURE E10.13.2 A plot of predicted pH or −log10[H2S] for mixing of sulfide and acetate solution of different pH in varying fractions.
Example 10.14
FIGURE E10.14.1 Sketch depicting infiltration of precipitation through a contaminated zone of the unsaturated soil and mixing with ground water.
FIGURE E10.14.2 Screen capture of a solve block for characterization of a solution containing carbonate and ammonia nitrogen in equilibrium with soil gas.
FIGURE E10.14.3 Screen capture of the solve block for characterization of the final composition of mixed solutions containing ammonia nitrogen and carbonate.
FIGURE E10.14.4 Screen capture of collapsed worksheet illustrating convenient arrangement of the worksheet for additional computations.
Example 10.15
FIGURE E10.15.1 Numeric output from an excel worksheet in solution of the system of Example 10.14.
10.8 ACID AND BASE NEUTRALIZING CAPACITY
10.8.1 ANC and BNC of Closed Systems
Example 10.16
FIGURE E10.16.1 A plot of βANC and βBNC (M) versus pH for an aqueous solution of 0.006 M CO3Tot.
FIGURE E10.16.2 A plot of the various specie contributions (M) to the buffer intensity against pH for the carbonate system with CO3Tot=0.006 M.
10.8.2 ANC and BNC of Open Systems
Example 10.17
FIGURE E10.17.1 A plot of [ANC] versus pH for an aqueous solution of initial CO3Tot=0.006 M at pH 7.65 held in an open system of known and constant PCO2 and titrated with a strong base. A plot for a closed system of CO3Tot=0.006M is shown for comparison.
FIGURE E10.17.2 A plot of [BNC] versus pH for an aqueous solution of initial CO3Tot=0.006 M at pH 7.65 held in an open system of known and constant PCO2 and titrated with a strong base. A plot for a closed system of CO3Tot=0.006M is shown for comparison.
10.8.3 ANC and BNC of Semi-Open Systems
Example 10.18
FIGURE E10.18.1 MathCAD program for computation of incremental sodium hydroxide dose to model titration in a semi-open system of a solution equilibrated with 5% CO2 and titrated with sodium hydroxide to a pH end point of 9.6.
FIGURE E10.18.2 A plot of PCO2 and VNaOH for titration in a semi-open system, of aqueous solution initially equilibrated with 5% CO2, to a pH end point of ∼9.6.
FIGURE E10.18.3 A plot of ionic strength, γ1 and γ2 predicted for titration in a semi-open system, of aqueous solution initially equilibrated with 5% CO2, to a pH end point of ∼9.6.
10.9 ACTIVITY VERSUS CONCENTRATION FOR NONELECTROLYTES
10.9.1 The Setschenow Equation
10.9.2 Definitions of Salt Abundance
Example 10.19
FIGURE E10.19.1 A plot of the activity coefficient for arbitrary non-electrolyte as a function of salting out coefficient and conductance ratio (ratio of the specific conductance of a target aqueous solution to that of seawater).
10.9.3 Activity of Water in Salt Solutions
FIGURE 10.3 Activity (a) and activity coefficient (b) of water versus total solute molarity for NaNO3 (□), KCl (▪), NaCl (⋄), CaCl2 (δ), and sucrose (•) solutions. Dot-dashed and dashed vertical lines are the approximate total molarity values for Salt River water (Brezonik and Arnold, 2011) and for seawater (Stumm and Morgan, 1996), respectively. KCl, NaCl, CaCl2 and sucrose activity data are from Robinson and Stokes (1965) and NaNO3 data are from Correa et al (1977). Activity coefficient is computed as the quotient of activity and mole fraction concentration.
PROBLEMS
FIGURE p10.27 Schematic diagram of landfill—ground water mixing system.
FIGURE p10.28 An acid rock drainage pit at an abandoned gold mine in sulfide-bearing rock.
Chapter 11 Metal Complexation and Solubility
11.1 PERSPECTIVE
11.2 HYDRATION OF METAL IONS
11.3 CUMULATIVE FORMATION CONSTANTS
11.3.1 Deprotonation of Metal/Water Complexes
11.3.2 Metal Ion Hydrolysis (Formation) Reactions
11.3.3 Cumulative Hydrolysis (Formation) Reactions
Example 11.1
11.3.4 The Cumulative Formation Constant for Metal/Ligand Complexes
11.4 FORMATION EQUILIBRIA FOR SOLIDS
11.5 SPECIATION OF METALS IN AQUEOUS SOLUTIONS CONTAINING LIGANDS
11.5.1 Metal Hydroxide Systems
Example 11.2
FIGURE E11.2.1 A plot of hydrolysis specie abundance fraction versus pH for the zinc metal system.
11.5.2 Metals with Multiple Ligands
Example 11.3
FIGURE E11.3.1 Screen capture of a logical program to compute zinc and phosphate ion activities over a selected pH range.
FIGURE E11.3.2 Screen capture of vector computations for zinc phosphate complex speciation.
FIGURE E11.3.3 Vector computations for zinc complex abundance fractions.
FIGURE E11.3.4 A plot of zinc specie abundance fractions versus pH for zinc hydrolysis and zinc phosphate complex species.
FIGURE E11.3.5 A plot of phosphate specie abundance fractions versus pH for the zinc-phosphate complex formation system.
11.6 METAL HYDROXIDE SOLUBILITY
11.6.1 Solubility in Dilute Solution
Example 11.4
FIGURE E11.4.1 A plot of zinc solubility based on the presence of zinc hydroxide solid in equilibrium with an aqueous solution considered to be infinitely dilute.
FIGURE E11.4.2 A plot of zinc solubility and zinc hydrolysis specie abundance versus pH for the zinc hydrolysis system in equilibrium with zinc hydroxide solid.
Example 11.5
Example 11.6
11.6.2 Solubility in the Presence of Ligands other than Hydroxide
Example 11.7
FIGURE E11.7.1 Free phosphate ion activity versus pH for an aqueous solution of ionic strength 0.01 M containing zinc and phosphate and in equilibrium with zinc hydroxide solid phase.
FIGURE E11.7.2 A plot of total soluble zinc in an aqueous solution of 0.01 M ionic strength containing 10−4 M total phosphate-phosphorus and in equilibrium with zinc hydroxide solid.
11.7 SOLUBILITY OF METAL CARBONATES
11.7.1 Calcium Carbonate Solubility
Example 11.8
FIGURE E11.8.1 Screen capture of the solve block used for speciation of calcium carbonate equilibrated with natural precipitation.
Example 11.9
FIGURE E11.9.1 Screen capture of the solve block for computation of calcium carbonate solubility as a function of varying partial pressure of carbon dioxide.
FIGURE E11.9.2 A plot of predicted pH, total calcium and total carbonate versus carbon dioxide partial pressure for ground water in equilibrium with calcite.
Example 11.10
11.7.2 Solubility of Metal Carbonates—the Controlling Solid Phase
Example 11.11
FIGURE E11.11.1 A plot free zinc ion and total soluble zinc as predicted by equilibrium with zinc hydroxide and calcite.
FIGURE E11.11.2 Screen capture of looping code for generating zinc and carbonate speciation versus pH for precipitation of zinc using hydroxide reagent.
FIGURE E11.11.3 A plot of predicted total dissolved zinc comparing an approximation that neglects the depletion of aqueous carbonate abundance with precipitation of zinc carbonate (CTot.Zn(pH)) with a prediction accounting for the reduction in aqueous carbonate abundance. The relative error increases with decreasing initial carbonate abundance.
Example 11.12
FIGURE E11.12.1 A given-find solve block for determining the pH and carbonate speciation of rain water equilibrated simultaneously with zinc hydroxide and calcite.
FIGURE E11.12.2 Given-find solve block for finding the pH and speciation of rain water equilibrated with calcite.
FIGURE E11.12.3 A plot of predicted zinc ion activity in rain water infiltrating through a heap leach pad containing calcite, considering control of solubility by zinc hydroxide and zinc carbonate.
Example 11.13
FIGURE E11.13.1 MathCAD program used to compute speciation of free carbonate, free zinc, total carbonate and total lead versus pH for precipitation of zinc from solution using carbonate reagent.
FIGURE E11.13.2 A plot of predicted abundances for carbonate ion, lead ion, and total dissolved lead for precipitation of lead from aqueous solution using carbonate reagent.
FIGURE E11.13.3 A plot of carbonate dose and change in total lead versus pH for precipitation of lead using carbonate reagent.
FIGURE E11.13.4 A plot of total lead and lead hydrolysis species versus pH for precipitation of lead using carbonate reagent.
11.7.3 Solubility of Phosphates
TABLE 11.1 Important Phosphate Solids and Associated Formation Constants
Example 11.14
FIGURE E11.14.1 A plot of predicted free phosphate ion and total phosphate abundance assuming control of phosphate solubility by calcium hydrogen phosphate, tri-calcium di-phosphate, and calcium hydroxyapatite.
FIGURE E11.14.2 A plot of total predicted phosphate-phosphorus abundance versus aqueous free calcium for selected sets of formation constants for calcium phosphate solids.
Example 11.15
FIGURE E11.15.1 A plot of free aluminum ion and free Fe(III) ion versus pH for aqueous solutions in equilibrium with aluminum and iron(III) hydroxide, respectively. Phosphate ion activity for total phosphate-phosphorus of 0.001 M shown for reference.
FIGURE E11.15.2 Predicted total abundance of aluminum and iron(III) versus pH for aqueous solutions in equilibrium with aluminum hydroxide and iron(III) hydroxide, respectively. Abundances of hydrolysis species are not shown.
FIGURE E11.15.3 A plot of total predicted phosphate-phosphorus versus pH for an aqueous solution in simultaneous equilibrium with aluminum hydroxide and aluminum phosphate. Phosphate provides the degree of freedom and its abundance is reduced by the precipitation of aluminum phosphate solid. The assumed initial abundance of phosphate-phosphorus is 0.001 M (31 ppmm) and the target level is 0.5 ppmm.
FIGURE E11.15.4 A plot of total predicted phosphate-phosphorus versus pH for an aqueous solution in simultaneous equilibrium with ferric hydroxide and ferric phosphate. Phosphate provides the degree of freedom and its abundance is reduced by the precipitation of ferric phosphate solid. The assumed initial abundance of phosphate-phosphorus is 0.001 M (31 ppmm) and the target level is 0.5 ppmm.
11.8 SOLUBILITY OF OTHER METAL-LIGAND SOLIDS
PROBLEMS
FIGURE P11.7 Sketch of phosphorus release from sediments and capture by aluminum hydroxide layer above sediment-water interface.
Chapter 12 Oxidation and Reduction
12.1 PERSPECTIVE
12.2 REDOX HALF REACTIONS
12.2.1 Assigning Oxidation States
Example 12.1
12.2.2 Writing Half Reactions
Example 12.2
12.2.3 Adding Half Reactions
Example 12.3
Example 12.4
12.2.4 Equilibrium Constants for Redox Half Reactions
Example 12.5
12.3 THE NERNST EQUATION
Example 12.6
12.4 ELECTRON AVAILABILITY IN ENVIRONMENTAL SYSTEMS
12.4.1 pE–pH (EH−pH) Predominance Diagrams
Example 12.7
FIGURE E12.7.1 pE−pH diagram for the Fe(II)−Fe(III)−OH system. Predominance lines represent equal contributions of oxidized and reduced species of redox couples to the RHS of the law of mass action.
FIGURE E12.7.2 pE−pH diagram for the Fe(II)−Fe(III)−OH system. Predominance lines represent 10−6 M activities of dissolved iron species.
Example 12.8
FIGURE E12.8.1 pE−pH diagram for the Fe(II)−Fe(III)−OH−−CO3= system. Dissolved iron specie activities are 10−6 M.
12.4.2 Effect of pE on Redox Couple Speciation
Example 12.9
FIGURE E12.9.1 A plot of predicted partial pressure of hydrogen gas (in atm) versus pE for redox equilibria in an aqueous solution at pH= 6.0.
FIGURE E12.9.2 A plot of predicted partial pressure of oxygen (in atm) versus pE for redox equilibria in an aqueous solution of pH=6.0.
FIGURE E12.9.3 A plot of predicted activity of Fe+2 versus pE for an aqueous solution at pH=6.0 in which ferric hydroxide solid is assumed to be present.
FIGURE E12.9.4 A plot of {Fe+2} and {Fe+3} versus pE for an aqueous solution containing 10−5 M FeTot at pH 6.0.
FIGURE E12.9.5 Plot of sulfate and bisulfide speciation versus pE at pH 6 for an aqueous solution containing 10−3 M total sulfur.
12.4.3 Determining System pE
Example 12.10
FIGURE E12.10.1 A plot of pE predicted from CO2−CH4, CO2−CH3COO−, CO2−CH3CH2COO−, and CH3COO−−CH4 redox couples for typical conditions within the aqueous solution of an anaerobic digester.
FIGURE E12.10.2 Predicted sulfate activities from pE values derived from the CO2−CH4, CO2−CH3COO−, CO2−CH3CH2COO−, and CH3COO−−CH4 redox couples for typical conditions within the aqueous solution of an anaerobic digester.
Example 12.11
FIGURE E12.11.1 pE–pH diagram for the Fe(III), Fe(II), SO4=, and S= system for FeTot ranging from 1 to 10 ppmm.
FIGURE E12.11.2 pE−pH diagram for the Fe(III), Fe(II), CO3=. SO4=, and S= system for FeTot = 1 ppmm.
FIGURE E12.11.3 pE−pH diagram for the Fe(III), Fe(II), CO3=. SO4=, and S= system for FeTot=10 ppmm.
12.4.4 Speciation Using Electron Availability
Example 12.12
FIGURE E12.12.1 An EH−pH condition located on Brookins’ As−O−H predominance plot for specified conditions in aquatic sediments.
PROBLEMS
Back Matter
Appendices
TABLE A.1 Gibbs Energy of Formation G¯f°, Enthalpy of Formation H¯f°, and Entropy of Formation S¯f° Values for Common Chemical Species in Aquatic Systemsa: Valid at 25°C, 1 atm Pressure, and Standard Statesb
TABLE A.2 Stability Constants for Formation of Complexes and Solids from Metals and Ligandsa
TABLE A.3 Dissolved Oxygen Solubility in mg/L (g/m3) Relative to the Normal Atmosphere (YO2=0.209 molO2/molair). Generated from http://water.usgs.gov/cgi-bin/dotables on 02/13/2013
TABLE A.4 Gibbs Energy of Formation for Selected Geochemical Speciesa
TABLE A.5 Selected Redox Half Reactions
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.
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.
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.
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.
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.
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.
FIGURE A.7 EH − pH diagram for part of the system N–O–H. The assumed activity of dissolved nitrogen = 10−3.3M (PN2=0.8 bar). Reprinted from Brookins (1988) by permission of Springer-Verlag GmbH.
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.
FIGURE A.9 EH − pH diagram for part of the system S–O–H. The assumed activity of dissolved S

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