Over recent years, important contributions on the topic of solving various aquifer problems have been presented in numerous papers and reports. The scattered and wide-ranging nature of this information has made finding solutions and best practices difficult. Comprehensive and self-contained, Applied Flow and Solute Transport Modeling in Aquifers compiles the scattered literature on the topic into a single-source reference of the most up-to-date information in the field. Based on Dr. Batu's 20 years of practical experience tackling aquifer problems in a myriad of settings, the book addresses essentially all currently applied aquifer flow and contaminant transport solutions, combines theory with practical applications, covers both analytical and numerical solutions, and includes solutions to real world contaminant transport modeling scenarios. Batu approaches the subject from the practicing consultant's point of view and elucidates the difficulties real world professionals have faced in solving aquifer flow and contamination problems. The author simplifies the necessary theoretical background as much as possible and provides all derivational details of the theoretical background as worked examples. He uses this method to explore how the derivations were generated for those who need to know while allowing others to easily skip them and still benefit and learn from the practical applications of the mathematical approaches. Containing 51 tables and 323 figures, the book covers both the breadth and the depth of currently applied aquifer flow and contaminant transport modeling solutions.
Author(s): Vedat Batu
Publisher: CRC Press
Year: 2005
Language: English
Commentary: 17923
Pages: 698
Front cover......Page 1
Preface......Page 8
About the Author......Page 10
Table of Contents......Page 12
1.1 IMPORTANCE OF FLOW AND SOLUTE TRANSPORT MODELING IN AQUIFERS......Page 30
1.2 PURPOSE OF THIS BOOK......Page 31
1.3 SCOPE AND ORGANIZATION......Page 32
1.4 HOW TO USE THIS BOOK......Page 34
2.2.1.1 Solute and Solvent......Page 36
2.2.1.2 Definitions for Concentration......Page 37
2.2.2 FLUX-AVERAGED CONCENTRATION......Page 39
2.3.1.1 Physical Explanation of Molecular Diffusion......Page 40
2.3.1.2 Quantification of Molecular Diffusion: Fick’s First Law......Page 41
2.3.1.3 The Effective Molecular Diffusion Coefficient Dx......Page 42
2.3.4 HYDRODYNAMIC DISPERSION: ONE-DIMENSIONAL CASE......Page 44
2.3.4.1 The Effects of Convection and Dispersion......Page 45
2.4.1.1 Tensorial Forms of the Convective–Dispersive Flux Components......Page 46
2.4.2.1 The Principal Axes of the Dispersion Tensor can be Defined: the Porous Medium is Homogeneous and Anisotropic......Page 47
2.4.2.2 The Principal Axes of the Dispersion Tensor Can be Defined: the Porous Medium Is Homogeneous and Isotropic and Has a Unidirectional Flow......Page 48
2.5.1 GENERAL CASE: HOMOGENEOUS AND ANISOTROPIC DISPERSION......Page 49
2.5.2 HOMOGENEOUS AND ISOTROPIC DISPERSION......Page 50
2.6.1.1 One-Dimensional Solute Transport Equation with Sorption and Desorption......Page 51
2.6.1.2 Freundlich Isotherm......Page 52
2.6.1.3 Linear Sorption Isotherm ( = 1) and Distribution Coefficient: The Approach......Page 53
2.6.1.5 Representative Parameter Values in the Retardation Factor ( Equation......Page 54
2.6.1.6 Two- and Three-Dimensional Solute Transport Equations with Sorption and Desorption......Page 55
2.6.2.1 Radioactive Decay......Page 56
2.6.2.2 Biodegradation......Page 58
2.7.1 GENERAL CASE: HOMOGENEOUS AND ANISOTROPIC DISPERSION......Page 61
2.8 SOLUTE TRANSPORT DIFFERENTIAL EQUATIONS FOR UNSATURATED POROUS MEDIA UNDER UNIFORM FLOW CONDITIONS......Page 62
2.8.2 SOLUTE TRANSPORT DIFFERENTIAL EQUATIONS FOR UNSATURATED POROUS MEDIA UNDER UNIFORM FLOW CONDITIONS......Page 63
2.9.2.1 Invariance of and Based Solute Transport Differential Equations......Page 64
2.10 INITIAL AND BOUNDARY CONDITIONS 2.10.1 INTRODUCTION......Page 65
2.10.3.1 Constant Concentration Boundary......Page 66
2.10.3.2 Flux Boundary......Page 67
2.10.3.3 No-Solute Flux Boundary......Page 68
2.11.1.1 Results from One-Dimensional Experiments......Page 69
2.11.1.2 Results from Two-Dimensional Experiments......Page 70
2.11.2.1 Fundamental Relationships for Dispersion Coefficients......Page 72
2.11.2.2 Mechanical Dispersion Coefficients......Page 73
2.11.2.3 Dispersivities of the Medium......Page 74
2.11.2.4 Mechanical Dispersion Coefficients: General Case......Page 75
2.11.2.5 A Special Case for Mechanical Dispersion Coefficients: the Average Velocity ( Coincides with the x-Coordinate Axis......Page 76
PROBLEMS......Page 77
3.2 DETERMINISTIC VS. STOCHASTIC MODELING APPROACHES......Page 78
3.3.1.1 Advantages of Analytical Solute Transport Models......Page 79
3.3.2.1 One-Dimensional Analytical Solute Transport Models for the First-Type Sources......Page 80
3.3.2.2 Two-Dimensional Analytical Solute Transport Models for the First-Type Strip Sources......Page 95
3.3.2.3 Three-Dimensional Analytical Solute Transport Models for the First-Type Rectangular Sources......Page 122
3.3.3.1 One-Dimensional Analytical Solute Transport Models for the Third-Type Sources......Page 149
3.3.3.2 Two-Dimensional Analytical Solute Transport Models for the Third-Type Strip Sources......Page 160
3.3.3.3 Three-Dimensional Analytical Solute Transport Models for the Third-Type Rectangular Sources......Page 186
3.3.4.1 One-Dimensional Analytical Solute Transport Models for Instantaneous Sources......Page 206
3.3.4.2 Two-Dimensional Analytical Solute Transport Models for Instantaneous Strip Sources......Page 210
3.3.4.3 Three-Dimensional Analytical Solute Transport Models for Instantaneous Rectangular Sources......Page 223
3.3.4.4 Three-Dimensional Analytical Model For Instantaneous Parallelepiped Sources......Page 238
PROBLEMS......Page 242
4.1 INTRODUCTION......Page 244
4.3.1 FUNDAMENTALS OF FLOW IN AQUIFERS......Page 245
4.3.1.1 Hydraulic Head and Drawdown......Page 246
4.3.1.2 Porosity and Effective Porosity......Page 247
4.3.1.3 Discharge Velocity and Ground Water Velocity......Page 248
4.3.1.4 Darcy’s Law......Page 250
4.3.1.5 Hydraulic Conductivity, Transmissivity, and Permeability......Page 254
4.3.1.6 Classification of Aquifers with Respect to Hydraulic Conductivity......Page 258
4.3.1.7 Storage Coefficient, Specific Yield, and Specific Retention......Page 262
4.3.2.1 Equations of Motion: Principal Directions of Anisotropy Coincide with the Directions of Coordinate Axes......Page 266
4.3.3 PRINCIPAL HYDRAULIC CONDUCTIVITIES......Page 269
4.3.3.1 Principal Hydraulic Conductivities and Transmissivities for Two-Dimensional Case......Page 270
4.3.3.2 Mohr’s Circle for Principal Hydraulic Conductivities and Transmissivities for Two-Dimensional Case......Page 272
4.3.4.1 Directional Hydraulic Conductivities and Transmissivities for Two-Dimensional Cases......Page 274
4.3.4.2 Directional Hydraulic Conductivities for Three-Dimensional Cases......Page 276
4.3.5.1 General Case: The Principal Directions of Anisotropy Are Not the Coordinate Axes......Page 277
4.3.5.2 Special Cases: The Principal Directions of Anisotropy Are the Coordinate Axes......Page 278
4.3.6.1 Differential Equation in Three Dimensions for a Transversely Isotropic Aquifer Case......Page 280
4.3.7 DIFFERENTIAL EQUATIONS UNDER STEADY-STATE CONDITIONS......Page 282
4.3.8 GOVERNING DIFFERENTIAL EQUATION FOR THE FINITE-DIFFERENCE MODELING APPROACH......Page 283
4.3.9.1 Grid Coordinates and Cartesian Coordinates......Page 284
4.3.9.2 Block- and Point-Centered Grid Discretizations......Page 285
4.3.10 DERIVATON OF FINITE-DIFFERENCE EQUATION......Page 286
4.3.10.1 Flow Rates into Cell (i, j, k) From the Six Adjacent Cells......Page 287
4.3.10.2 Flow Rates into the Cell From Outside the Aquifer......Page 288
4.3.10.4 Approximation for Head Change with Respect to Time......Page 290
4.3.10.6 Determination of Head Distribution......Page 292
4.3.10.8 Approximate Solution and Truncation Error......Page 293
4.3.11.1 Boundary Conditions......Page 295
4.3.12.2 Vertical Grid Discretization......Page 297
4.3.12.3 Horizontal Grid Discretization......Page 300
4.3.13.1 Input Parameters for Time in the MODFLOW Family Codes......Page 302
4.3.13.2 Time Step Selection......Page 304
4.3.14.1 Basic Conductance Equations......Page 306
4.3.14.2 Horizontal Conductance......Page 309
4.3.14.3 Vertical Conductance......Page 310
4.3.15.1 Constant Head Boundaries......Page 311
4.3.15.2 Constant Flux Boundaries......Page 312
4.3.15.3 Head-Dependent Flux Boundaries......Page 317
4.3.15.4 River Boundaries......Page 319
4.3.15.5 Drain Boundries......Page 324
4.3.15.6 Evapotranspiration Boundaries......Page 327
4.3.16.1 Matrix-form Equations......Page 330
4.3.16.2 Direct Methods......Page 331
4.3.16.3 Iterative Methods......Page 332
4.4.1.1 Governing Differential Equation......Page 333
4.4.1.2 Hydrodynamic Dispersion Coefficients......Page 334
4.4.2 FINITE-DIFFERENCE EQUATION......Page 335
4.4.5 DISCRETIZATION OF TIME......Page 337
4.4.6.1 Slice-Successive Overrelaxation (SSOR) Procedure......Page 338
4.5 APPLICATION OF NUMERICAL FLOW AND SOLUTE TRANSPORT MODELS 4.5.1 INTRODUCTION......Page 339
4.5.2.1 Model Conceptualization and Dimensionality......Page 340
4.5.2.3 Model Calibration......Page 342
4.5.2.4 Application of A Calibrated Model......Page 344
4.5.3.1 Model Conceptualization and Dimensionality......Page 345
4.5.3.2 Model Construction......Page 347
4.5.3.3 Model Calibration......Page 348
4.5.3.4 Application of A Calibrated Solute Transport Model......Page 349
4.6.1 MODEL VERIFICATION......Page 350
4.7.1 INVESTIGATOR'S (MODELER) BACKGROUND......Page 351
4.8 MODELING LIMITATIONS AND SOURCES OF ERROR......Page 352
4.9.2 NUMERICAL GROUND WATER FLOW AND SOLUTE TRANSPORT MODELING EXAMPLE......Page 353
PROBLEMS......Page 372
5.2.1 KINEMATICS OF A SOLUTE PARTICLE......Page 374
5.2.2.1 Travel Time Determination Using Darcy’s Equation......Page 376
5.2.2.2 Travel Time Determination Using Analytical Solutions......Page 379
5.2.3.1 Introduction......Page 389
5.2.3.2 Theory of Particle Tracking Based on the Finite-Difference Method......Page 390
5.3 PATH LINES OF SOLUTE PARTICLES UNDER CONVECTIVE–DISPERSIVE TRANSPORT CONDITIONS 5.3.1 INTRODUCTION......Page 403
5.3.2 STREAM FUNCTION CONCEPT FOR HYDRODYNAMIC DISPERSION......Page 405
5.3.3.1 General Case......Page 406
5.3.3.2 Special Case in the Cartesian Coordinates: Uniform Ground Water Flow Field......Page 407
5.3.3.3 Special Case in the Cylindrical Coordinates: Uniform Ground Water Flow Field......Page 408
5.3.3.4 Properties of the Hydrodynamic Dispersion Stream Function......Page 410
5.3.4.2 Two-Dimensional Analytical Solutions in a Semi-infinite Porous Medium......Page 412
5.3.4.3 Two-Dimensional Analytical Solutions for Strip Sources in a Finite Porous Medium......Page 434
PROBLEMS......Page 443
6.1 INTRODUCTION......Page 444
6.2.2 CONVECTIVE–DISPERSIVE SOLUTE TRANSPORT MECHANISM IN NATURAL MATERIALS......Page 445
6.2.3 CONVECTIVE–DIFFUSIVE SOLUTE TRANSPORT MECHANISM IN NATURAL MATERIALS......Page 446
6.3.1.1 One-Dimensional Analytical Solution of a Tracer Slug......Page 447
6.3.1.2 Random Walk: One-Dimensional Form with Only Diffusion......Page 449
6.3.1.3 Some Statistical Properties of Concentration Distribution......Page 450
6.3.1.5 Fundamental Relationship Between and......Page 451
6.3.2.2 First Moments......Page 453
6.3.2.3 Second Moments......Page 454
6.3.3 MECHANICAL DISPERSION COEFFICIENT (Dm) AND DISPERSIVITY TENSORS FOR GENERAL CASE......Page 455
6.3.4 DISPERSIVITY AND MECHANICAL DISPERSION COEFFICIENT TENSORS FOR UNIFORM GROUND WATER FLOW CASE......Page 456
6.3.6 STOCHASTIC DESCRIPTION OF HYDRAULIC CONDUCTIVITY VARIATION......Page 457
6.3.6.2 Description of Heterogeneity by the Stochastic Process Theory......Page 458
6.3.6.3 Statistical Parameters for Log-Normal Frequency Distributions of Hydraulic Conductivity......Page 460
6.3.7.1 Borden Experiment......Page 463
6.3.7.2 Twin Lake Experiment......Page 474
6.3.7.3 Cape Cod Experiment......Page 486
6.4.1.1 Realization and Ensemble......Page 507
6.4.1.3 Variance of Joint Distributions and Covariance......Page 508
6.4.1.4 Stationary Process and a Common Covariance Function......Page 509
6.4.2.1 Spectral Representation Theorem......Page 510
6.4.2.2 Covariance Function for A Zero-Mean Stochastic Process )......Page 511
6.4.3 THREE-DIMENSIONAL STATIONARY RANDOM PROCESS REPRESENTATION......Page 512
6.4.4.1 Perturbed Forms of the Flow Equation......Page 514
6.4.4.2 Linearized Solution in Terms of Hydraulic Conductivity......Page 517
6.4.4.3 Linearized Solution in Terms of ln( )......Page 519
6.4.4.4 Effective Hydraulic Conductivity for One-Dimensional Case......Page 522
6.4.5.1 Three-Dimensional Perturbed Flow Equation......Page 525
6.4.5.2 Spectral Representation......Page 526
6.4.5.3 Effective Hydraulic Conductivity for Three-Dimensional Case......Page 527
6.4.5.4 The Hydraulic Head and Loghydraulic Conductivity Processes......Page 528
6.4.6.1 Objectives and Literature Review......Page 530
6.4.6.2 Scale Classification......Page 532
6.4.6.4 Description of the Hydraulic Conductivity Variation......Page 533
6.4.6.5 Correlation Structure of the Random Hydraulic Conductivity Field......Page 534
6.4.6.6 Macroscopic Dispersive Fluxes......Page 539
6.4.6.7 Determination of the General Expression for the Macroscopic Dispersion Tensor......Page 541
6.4.6.8 Principal Macrodispersivities for Two-Dimensional Solute Transport Cases......Page 546
6.4.6.9 Determination of the Macroscopic Dispersion Tensor in a Statistically Isotropic Aquifer — Local Dispersivity Isotropic......Page 551
6.4.6.10 Approximate Determination of for Macroscopic Dispersion in Statistically Isotropic Media — Local Dispersivity Anisotropic......Page 559
6.4.6.11 Determination of for Macroscopic Dispersion in a Statistically Anisotropic Aquifer with Arbitrary Orientation of Stratification......Page 561
6.4.7.1 Introduction......Page 593
6.4.7.2 Governing Equations......Page 594
6.4.7.3 Spectral Solution......Page 595
6.4.7.4 Development of the Specific Discharge Spectrum and Flow Equation......Page 596
6.4.7.6 Examination of Hydraulic Gradient Variability......Page 601
6.4.7.7 Examination of Hydraulic Gradient Direction Variability......Page 605
PROBLEMS......Page 608
7.2.1 LABORATORY AND FIELD SCALES......Page 610
7.3.1 APPROACH I: PERFECTLY LAYERED AQUIFER ASSUMPTION......Page 611
7.4 ESTIMATION OF DISPERSIVITIES USING RELATIONSHIPS BETWEEN DISPERSIVITIES AND FIELD SCALE 7.4.1 INTRODUCTION......Page 612
7.4.2.2 Aquifer Characteristics......Page 613
7.4.2.3 Types of Subsurface Solute Transport Tests......Page 627
7.4.2.5 Correlation of Longitudinal Dispersivity with Other Quantities......Page 628
7.4.3 DATA EVALUATION AND METHODS FOR ESTIMATION OF DISPERSIVITIES......Page 629
7.4.3.1 Evaluation of Data for Dispersivities......Page 630
7.4.3.2 Criteria for High-Reliability Dispersivities Data......Page 631
7.4.3.3 Criteria for Low-Reliability Dispersivities Data......Page 633
7.4.3.4 Results of the Classification for the Longitudinal Dispersivity Data......Page 634
7.4.3.5 Results of the Classification for the Transverse Dispersivities Data......Page 637
7.4.3.6 Interpretations of the Dispersivities Data......Page 640
7.4.4.1 Theoretical Background......Page 641
7.4.4.2 Interpretation of Scale Effect and Longitudinal Dispersivity Equations......Page 642
7.4.5 USAGE OF THE DISPERSIVITIES ESTIMATION PROCEDURES......Page 644
8.2.1 SCHEMATIC ILLUSTRATION OF THE RETARDATION CONCEPT......Page 646
8.2.2 CHARACTERISTICS OF THE K/K APPROACH TO RELATED QUANTITIES......Page 647
8.2.2.2 Organic Carbon Partition Coefficient......Page 648
8.2.2.4 Solubility in Water......Page 649
8.2.3.1 Comparison of the Experimental and Computed Column Breakthrough Curves......Page 650
8.2.3.2 Evaluation of the Linear Equilibrium Isotherm Equation with Respect to the Freundlich Isotherm......Page 651
8.3.1 DIRECT DATA FOR K FOR VARIOUS CHEMICALS......Page 654
8.4 REGRESSION EQUATIONS FOR VALUES 8.4.1 RELATIONSHIP BETWEEN......Page 665
8.5 ESTIMATION OF FROM THE REGRESSION EQUATIONS......Page 667
8.5.2 AVAILABLE REGRESSION EQUATIONS BASED......Page 668
PROBLEMS......Page 672
References......Page 674
Index......Page 690
Back cover......Page 698
