| Introduction | p. 1 |
| Goal and Content of This Text | p. 1 |
| Modeling and Simulation | p. 5 |
| System, Model, Simulation | p. 5 |
| Models in Natural and Engineering Sciences | p. 6 |
| Types of Mathematical Models | p. 6 |
| Systems Analysis | p. 8 |
| Calibration, Validation, and Verification | p. 10 |
| Model Structure | p. 11 |
| Simulation | p. 12 |
| Components of a Model | p. 13 |
| Structural Components of a Mathematical Model | p. 13 |
| Case Study | p. 19 |
| Dimensions and Units | p. 21 |
| System Boundaries and Material Balances | p. 23 |
| System Definition | p. 23 |
| System Boundaries | p. 25 |
| General Balance Equation | p. 26 |
| Inventory and Accumulation | p. 26 |
| Transport Processes | p. 27 |
| Reaction, Production, and Consumption | p. 29 |
| Mathematical Form of the Balance Equation | p. 30 |
| Special Cases of the Material Balance Equation | p. 33 |
| Stationary Balance or the Steady State | p. 33 |
| Closed Systems | p. 35 |
| Conservative Material | p. 37 |
| Summary | p. 39 |
| Transport Processes | p. 41 |
| Characterization of Transport Processes | p. 42 |
| Modeling of Transport Processes | p. 43 |
| Advection | p. 43 |
| Sedimentation | p. 45 |
| Random Walk | p. 48 |
| Molecular Diffusion | p. 53 |
| Turbulent Diffusion | p. 58 |
| Dispersion | p. 62 |
| Numeric Dispersion | p. 68 |
| Convection | p. 70 |
| Mass Transfer Coefficients | p. 72 |
| Transformation Processes | p. 77 |
| Case Study | p. 77 |
| Transformation Written in Conventional Form | p. 78 |
| Stoichiometric Matrix | p. 80 |
| Kinetics | p. 84 |
| Temperature Effects | p. 86 |
| State Variables | p. 87 |
| Composition of Materials | p. 90 |
| Conservation Laws | p. 92 |
| Conservation Law for Several Processes | p. 95 |
| Charge Balance | p. 95 |
| Theoretical Oxygen Demand | p. 97 |
| Summary | p. 100 |
| Ideal Reactors | p. 101 |
| Overview of Ideal Reactors | p. 101 |
| The Batch Reactor | p. 102 |
| The Continuous Flow Stirred Tank Reactor (CSTR) | p. 105 |
| A Cascade of Stirred Tank Reactors | p. 108 |
| The Plug-Flow Reactor | p. 111 |
| Plug-Flow Reactor with Turbulence | p. 114 |
| Sequencing Batch Reactor | p. 123 |
| Completely Mixed or Plug-Flow Reactor? | p. 127 |
| Summary | p. 127 |
| Hydraulic Residence Time Distribution | p. 129 |
| RTD: A Spectrum of Retention Times | p. 130 |
| Characterization of Residence Time Distributions | p. 133 |
| Experimental Determination of an RTD | p. 134 |
| Tracer Substances | p. 134 |
| Experimental Procedure | p. 135 |
| Residence Time Distributions of Ideal Reactors | p. 143 |
| RTD of a Stirred Tank Reactor (CSTR) | p. 143 |
| Cascade of Stirred Tank Reactors | p. 145 |
| Plug-Flow Reactor | p. 148 |
| Plug-Flow Reactor with Turbulence | p. 150 |
| Numeric Simulation of Turbulence in a Plug-Flow Reactor | p. 155 |
| Reactor Combinations | p. 159 |
| RTD with Stochastic Models | p. 159 |
| Stochastic Model of a Cascade of Stirred Tank Reactors | p. 160 |
| Stochastic Model of Turbulence | p. 161 |
| Modeling of Real Reactors | p. 165 |
| Goal | p. 165 |
| Time of Mixing | p. 166 |
| Methods for Model Identification | p. 168 |
| Method of Moments | p. 168 |
| Adjustment of the Model to the Measurements | p. 170 |
| Case Study | p. 171 |
| Heterogeneous Systems | p. 179 |
| Classification of Processes and Systems | p. 179 |
| Multiphase Systems | p. 180 |
| Microbial Degradation of Stored Pollutants | p. 181 |
| Behavior of Individual Particles | p. 182 |
| Case Studies | p. 184 |
| Transformation Processes in a Sewer | p. 184 |
| Activated Sludge Flocs | p. 187 |
| Self-purification in a Brook | p. 189 |
| Gas Exchange in a Stirred Tank Reactor | p. 195 |
| Adsorption in an Activated Carbon Column | p. 202 |
| Dynamic Behavior of Reactors | p. 211 |
| Causes of the Dynamics | p. 212 |
| Adjustment to Step Changes in Load | p. 214 |
| Periodic Load Variation | p. 217 |
| Stirred Tank Reactor | p. 217 |
| Cascade of Stirred Tank Reactors | p. 221 |
| Plug-Flow Reactor | p. 222 |
| Bode Diagram | p. 222 |
| Stochastic Processes | p. 226 |
| Dynamic Operation of Plants | p. 226 |
| Discussion of Time Constants | p. 229 |
| The Residence Time of Individual Materials | p. 229 |
| Different Time Constants | p. 232 |
| Nonstationary Effluent in Sewers | p. 234 |
| Measurement and Measurement Uncertainty | p. 237 |
| Definitions from Descriptive Statistics | p. 237 |
| Analytical Characterization of the Distribution of Measured Values | p. 238 |
| Empirical Characterization of Measured Values | p. 239 |
| Measuring Systems | p. 241 |
| Measuring Uncertainty | p. 243 |
| Gross Measurement Errors | p. 243 |
| Random Measurement Error | p. 245 |
| Systematic Measurement Errors, Bias | p. 248 |
| Case Example: COD Measurement (Standard Curve) | p. 250 |
| Identifying an Error Model | p. 251 |
| Uncovering Systematic Measurement Errors | p. 253 |
| Parameter Identification, Sensitivity and Error Propagation | p. 257 |
| Parameter Identification | p. 257 |
| Basic Principles, Chi Square, x[superscript 2] | p. 258 |
| Case Example: First-Order Reaction in a Batch Reactor | p. 261 |
| Introduction of an Extended Case Study | p. 263 |
| Sensitivity and Identifiability | p. 266 |
| Case Study | p. 266 |
| Local Sensitivity Functions | p. 269 |
| Model Structure | p. 274 |
| Structural Model Deviations | p. 275 |
| Simple Test Procedures | p. 277 |
| Parameter Uncertainty | p. 281 |
| Theoretical Background | p. 282 |
| Application to the Case Study | p. 288 |
| Linear Error Propagation | p. 291 |
| Basics | p. 291 |
| Application to the Case Study | p. 294 |
| Nonlinear Error Propagation | p. 296 |
| Monte Carlo Simulation | p. 296 |
| Sampling Methods | p. 300 |
| Application to the Case Study | p. 308 |
| Correlated Parameter Values: A Word of Caution | p. 311 |
| Summary of Model Identification | p. 312 |
| Process Control Engineering | p. 315 |
| Examples of Operating Strategies | p. 315 |
| Adjusting the Water Temperature of a Shower | p. 316 |
| Operation of an Activated Sludge System | p. 316 |
| Summary | p. 317 |
| Control Path and Control Loop | p. 318 |
| Step Response of a Subsystem | p. 321 |
| Step Response of a Controlled System | p. 326 |
| Controlled Systems Without Delay | p. 326 |
| Controlled Systems with Delay | p. 327 |
| Controlled Systems with Dead Time | p. 330 |
| Characteristic Curves of a Controlled System | p. 331 |
| The Standard Automatic Controller | p. 332 |
| The Two-Position Controller (A Discontinuous Controller) | p. 333 |
| Continuous Automatic Controllers | p. 335 |
| Comparison of the Standard Controllers | p. 344 |
| Implementation of a PID Controller in Berkeley Madonna | p. 344 |
| Disturbance Variable Compensation | p. 345 |
| Optimal Adjustment of a PID Controller | p. 346 |
| Case Study: Control of Oxygenation in an Activated Sludge Plant | p. 348 |
| Task | p. 348 |
| System Performance Without Control | p. 350 |
| Parameters of a PID Controller | p. 350 |
| Fuzzy controllers | p. 355 |
| Example of a Fuzzy Controller | p. 356 |
| Why Fuzzy Control? | p. 359 |
| Time Series Analysis | p. 361 |
| Time Series | p. 361 |
| Stationary Time Series | p. 362 |
| Case study: Yearly Variation of the Temperature | p. 363 |
| Conventional Statistical Characterization | p. 364 |
| Moving Average | p. 365 |
| Arithmetic Moving Average | p. 366 |
| Geometric Moving Average | p. 367 |
| Trend Lines | p. 370 |
| Removing a Trend | p. 372 |
| Correcting for the Average Value | p. 373 |
| Logistic Growth | p. 374 |
| Discrete Fourier Transformation | p. 375 |
| Autocorrelation, AR(1) Model | p. 378 |
| Autoregressive Models | p. 379 |
| Summary on AR(1) models | p. 384 |
| Identification of an AR(1) model | p. 385 |
| Case study | p. 388 |
| Task, Question | p. 388 |
| Procedure | p. 388 |
| Trend Line | p. 389 |
| Fourier Transformation | p. 389 |
| Analysis of the Residuals: AR(1) Model | p. 391 |
| Synthesis | p. 393 |
| Design under Uncertainty | p. 397 |
| Dealing with Uncertainty | p. 397 |
| Variation and Uncertainty | p. 399 |
| Case Study | p. 403 |
| Task | p. 403 |
| Variation | p. 405 |
| Uncertainty | p. 406 |
| Representation of Variation and Uncertainty | p. 407 |
| Deterministic Design | p. 410 |
| Uncertainty-Based Design | p. 414 |
| Operational Experience and Retrofitting of the Plant | p. 418 |
| Critique of the Design Procedures | p. 419 |
| Second-Order Uncertainty | p. 420 |
| Problems | p. 423 |
| Composition Matrix and Conservation Equation | p. 423 |
| Conservation of TOD | p. 424 |
| Breakpoint Chlorination: Stoichiometry and Composition | p. 424 |
| Deriving a Stoichiometric Matrix | p. 425 |
| Mass Balance in the Steady State | p. 425 |
| Ideal Reactors, Chemostats | p. 426 |
| Ideal Reactors, Plug Flow | p. 427 |
| Ideal Reactors, Sampling in Turbulent Flow | p. 428 |
| Ideal Reactors, Disinfection | p. 429 |
| Ideal Reactors, SBR | p. 430 |
| Residence Time Distribution, Cascade of CSTRs | p. 430 |
| RTD, Reactor Model | p. 431 |
| RTD, Activated Sludge Tank | p. 432 |
| RTD, Flow Rate and Dispersion in a Sewer | p. 433 |
| Modeling a Sewer | p. 434 |
| RTD, Disinfection Reactor | p. 434 |
| RTD, Additivity of [tau subscript m] and [sigma superscript 2] | p. 434 |
| RTD, Turbulent Plug-Flow Reactor | p. 434 |
| Heterogeneous Systems: Filtration | p. 435 |
| Substrate Profiles in a Biofilm | p. 435 |
| Bode Diagram | p. 437 |
| Dynamic Nitrification | p. 437 |
| Nonstationary Flow in Sewers | p. 438 |
| Stochastic Measurement Error | p. 439 |
| Systematic Measurement Error | p. 441 |
| Sensitivity and Parameter Identification | p. 442 |
| Sensitivity | p. 443 |
| Error Propagation with Correlated Uncertainty | p. 443 |
| System Identification | p. 444 |
| Uncertainty, Error Propagation | p. 447 |
| Process Control, Two-Position Controller | p. 447 |
| Process Control, PID Controller | p. 448 |
| Time Series Analysis | p. 449 |
| Design under Uncertainty, Nitrification | p. 450 |
| Integrated Problem: Nitrification in an RBC | p. 452 |
| Integrated Problem: Analyzing a Fish Pond | p. 455 |
| Literature | p. 457 |
| Index | p. 459 |
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