Surface Water-Quality Modeling [Paperback]

National and international interest in finding rational and economical approaches to water-quality management is at an all-time high. Insightful application of mathematical models, attention to their underlying assumptions, and practical sampling and statistical tools are essential to maximize a successful approach to water-quality modeling.

Chapra has organized this user-friendly text in a lecture format to engage students who want to assimilate information in manageable units. Comical examples and literary quotes interspersed throughout the text motivate readers to view the material in the proper context. Coverage includes the necessary issues of surface water modeling, such as reaction kinetics, mixed versus nonmixed systems, and a variety of possible contaminants and indicators; environments commonly encountered in water-quality modeling; model calibration, verification, and sensitivity analysis; and major water-quality-modeling problems.

Most formulations and techniques are accompanied by an explanation of their origin and/or theoretical basis. Although the book points toward numerical, computer-oriented applications, strong use is made of analytical solutions. In addition, the text includes extensive worked examples that relate theory to applications and illustrate the mechanics and subtleties of the computations.

Part I: COMPLETELY MIXED SYSTEMS

1. Introduction

Engineers and Water Quality / Fundamental Quantities / Mathematical Models / Historical Development of Water-Quality Models / Overview of This Book

2. Reaction Kinetics

Reaction Fundamentals / Analysis of Rate Data / Stoichiometry / Temperature Effects

3. Mass Balance, Steady-State Solution, and Response Time

Mass Balance for a Well-Mixed Lake / Steady-State Solutions / Temporal Aspects of Pollutant Reduction

4. Particular Solutions

Impulse Loading (Spill) / Step Loading (New Continuous Source) / Linear ("Ramp") Loading / Exponential Loading / Sinusoidal Loading / The Total Solution: Linearity and Time Shifts / Fourier Series (Advanced Topic)

5. Feedforward Systems of Reactors

Mass Balance and Steady-State / Time Variable / Feedforward Reactions

6. Feedback Systems of Reactors

Steady-State for Two Reactors / Solving Large Systems of Reactors / Steady-State System Response Matrix / Time-Variable Response for Two Reactors / Reactions with Feedback

7. Computer Methods: Well-Mixed Reactors

Euler's Method / Heun's Method / Runge-Kutta Methods / Systems of Equations

Part II: INCOMPLETELY MIXED SYSTEMS

8. Diffusion

Advection and Diffusion / Experiment / Fick's First Law / Embayment Model / Additional Transport Mechanisms

9. Distributed Systems (Steady-State)

Ideal Reactors / Application of the PFR Model to Streams / Application of the PFR Model to Estuaries

10. Distributed Systems (Time-Variable)

Plug Flow / Random (or "Drunkard's") Walk / Spill Models / Tracer Studies / Estuary Number

11. Control-Volume Approach: Steady-State Solutions

Control-Volume Approach / Boundary Conditions / Steady-State Solution / System Response Matrix / Centered-Difference Approach / Numerical Dispersion, Positivity, and Segment Size / Segmentation Around Point Sources / Two- and Three-Dimensional Systems

12. Simple Time-Variable Solutions

An Explicit Algorithm / Stability / The Control-Volume Approach / Numerical Dispersion

13. Advanced Time-Variable Solutions

Implicit Approaches / The MacCormack Method / Summary

Part III: WATER-QUALITY ENVIRONMENTS

14. Rivers and Streams

River Types / Stream Hydrogeometry / Low-Flow Analysis / Dispersion and Mixing / Flow, Depth, and Velocity / Routing and Water Quality (Advanced Topic)

15. Estuaries

Estuary Transport / Net Estuarine Flow / Estuary Dispersion Coefficient / Vertical Stratification

16. Lakes and Impoundments

Standing Waters / Lake Morphometry / Water Balance / Near-Shore Models (Advanced Topic)

17. Sediments

Sediment Transport Overview / Suspended Solids / The Bottom Sediments / Simple Solids Budgets / Bottom Sediments as a Distributed System / Resuspension (Advanced Topic)

18. The "Modeling" Environment

The Water-Quality-Modeling Process / Model Sensitivity / Assessing Model Performance / Segmentation and Model Resolution

Part IV: DISSOLVED OXYGEN AND PATHOGENS

19. BOD and Oxygen Saturation

The Organic Production/Decomposition Cycle / The Dissolved Oxygen Sag / Experiment / Biochemical Oxygen Demand / BOD Model for a Stream / BOD Loadings, Concentrations, and Rates / Henry's Law and the Ideal Gas Law / Dissolved Oxygen Saturation

20. Gas Transfer and Oxygen Reaeration

Gas Transfer Theories / Oxygen Reaeration / Reaeration Formulas / Measurement of Reaeration with Tracers

21. Streeter-Phelps: Point Sources

Experiment / Point-Source Streeter-Phelps Equation / Deficit Balance at the Discharge Point / Multiple Point Sources / Analysis of the Streeter-Phelps Model / Calibration / Anaerobic Condition / Estuary Streeter-Phelps

22. Streeter-Phelps: Distributed Sources

Parameterization of Distributed Sources / No-Flow Sources / Diffuse Sources with Flow

23. Nitrogen

Nitrogen and Water Quality / Nitrification / Nitrogenous BOD Model / Modeling Nitrification / Nitrification and Organic Decomposition / Nitrate and Ammonia Toxicity

24. Photosynthesis/Respiration

Fundamentals / Measurement Methods

25. Sediment Oxygen Demand

Observations / A "Naive" Streeter-Phelps SOD Model / Aerobic and Anaerobic Sediment Diagenesis / SOD Modeling (Analytical) / Numerical SOD Model / Other SOD Modeling Issues (Advanced Topic)

26. Computer Methods

Steady-State System Response Matrix / The QUAL2E Model

27. Pathogens

Pathogens / Indicator Organisms / Bacterial Loss Rate / Sediment-Water Interactions / Protozoans: Giardia and Cryptosporidium

Part V: EUTROPHICATION AND TEMPERATURE

28. The Eutrophication Problem and Nutrients

The Eutrophication Problem / Nutrients / Plant Stoichiometry / Nitrogen and Phosphorus

29. Phosphorus Loading Concept

Vollenweider Loading Plots / Budget Models / Trophic-State Correlations / Sediment-Water Interactions / Simplest Seasonal Approach

30. Heat Budgets

Heat and Temperature / Simple Heat Balance / Surface Heat Exchange / Temperature Modeling

31. Thermal Stratification

Thermal Regimes in Temperate Lakes / Estimation of Vertical Transport / Multilayer Heat Balances (Advanced Topic)

32. Microbe/Substrate Modeling

Bacterial Growth / Substrate Limitation of Growth / Microbial Kinetics in a Batch Reactor / Microbial Kinetics in a CSTR / Algal Growth on a Limiting Nutrient

33. Plant Growth and Nonpredatory Losses

Limits to Phytoplankton Growth / Temperature / Nutrients / Light / The Growth-Rate Model / Nonpredatory Losses / Variable Chlorophyll Models (Advanced Topic)

34. Predator-Prey and Nutrient/Food-Chain Interactions

Lotka-Volterra Equations / Phytoplankton-Zooplankton Interactions / Zooplankton Parameters / Nutrient/Food-Chain Interactions

35. Nutrient/Food-Chain Modeling

Spatial Segmentation and Physics / Kinetic Segmentation / Simulation of the Seasonal Cycle / Future Directions

36. Eutrophication in Flowing Waters

Stream Phytoplankton/Nutrient Interactions / Modeling Eutrophication with QUAL2E / Fixed Plants in Streams

Part VI: CHEMISTRY

37. Equilibrium Chemistry

Chemical Units and Conversions / Chemical Equilibria and the Law of Mass Action / Ionic Strength, Conductivity, and Activity / pH and the Ionization of Water / Equilibrium Calculations

38. Coupling Equilibrium Chemistry and Mass Balance

Local Equilibrium / Local Equilibria and Chemical Reactions

39. pH Modeling

Fast Reactions: Inorganic Carbon Chemistry / Slow Reactions: Gas Transfer and Plants / Modeling pH in Natural Waters

Part VII: TOXICS

40. Introduction to Toxic-Substance Modeling

The Toxics Problem / Solid-Liquid Partitioning / Toxics Model for a CSTR / Toxics Model for a CSTR with Sediments / Summary

41. Mass-Transfer Mechanisms: Sorption and Volatilization

Sorption / Volatilization / Toxicant-Loading Concept

42. Reaction Mechanisms: Photolysis, Hydrolysis, and Biodegradation

Photolysis / Second-Order Relationships / Biotransformation / Hydrolysis / Other Processes

43. Radionuclides and Metals

Inorganic Toxicants / Radionuclides / Metals

44. Toxicant Modeling in Flowing Waters

Analytical Solutions / Numerical Solutions / Nonpoint Sources

45. Toxicant/Food-Chain Interactions

Direct Uptake (Bioconcentration) / Food-Chain Model (Bioaccumulation) / Parameter Estimation / Integration with Mass Balance / Sediments and Food Webs (Advanced Topic)

Appendix A: Conversion Factors

Appendix B: Oxygen Solubility

Appendix C: Water Properties

Appendix D: Chemical Elements

Appendix E: Numerical Methods Primer

Appendix F: Bessel Functions

Appendix G: Error Function and Complement