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Оглавление:
PREFACE, vii

PART I. FOUNDATIONS

CHAPTER I
INTRODUCTION, 1
      1.1. Scope of Subject, 3
      1.2. Homogeneous Fluids, 4
      1.3. Porous Media, 6
      1.4. General Qualifications Governing the Analytical Theory, 8
      1.5. The Nature of Porous Media, 10
      1.6. Systematic Packing of Spheres, 10
      1.7. The Packing of Natural Materials, 13
      1.8. Compaction of Sand and Gravel, 14
      1.9. Compaction in Clay, 16
      1.10. Effect of Compaction and Alteration of Sediments on Permeability, 17
      1.11. Kinds of Rock and Their Fluid-bearing Properties, 17
      1.12. Structure of Rocks in Relation to Underground Fluids, 22
      1.13. Subsurface Fluids — Their Occurrence and Migratory Behavior, 26
      1.14. Occurrence of Ground Water, 28
      1.15. Water Content of Unconsolidated Surface Sediments, 30
      1.16. Fluid Movements in the Capillary Zone, 30
      1.17. Fluid Movements below the Water Table. The Surface Zone, 34
      1.18. Fluid Movements below the Water Table. The Deep Zones, 38
      1.19. The Occurrence of Connate Waters, 40
      1.20. The Migration of Connate Waters, 43
      1.21. The Influence of Compaction of Sediments on Migration of Fluids, 44
      1.22. The Occurrence of Gas and Oil, 47
      1.23. The Source of Petroleum — Gas and Oil, 48
      1.24. The Migration and Accumulation of Gas and Oil, 50

CHAPTER II
DARCY'S LAW AND THE MEASUREMENT OF THE PERMEABILITY OF POROUS MEDIA, 55
      2.1. Darcy's Law, 55
      2.2. The Range of Validity of Darcy's Law, 56
      2.3. The Constant in Darcy's Law. The Permeability of a Porous Medium, 69
      2.4. Permeability Units and Nomenclature, 74
      2.5. The Principle of the Method of Measurement and of the Calculation of the Permeability of Porous Media, 76
      2.6. The Measurement of the Permeability of Unconsolidated Sands, 79
      2.7. The General Technique for Permeability Determinations of Consolidated Porous Media, 85
      2.8. Further Details for Permeability Measurements with Liquids, 89
      2.9. Further Details for Permeability Measurements with Gases, 91
      2.10. Gases versus Liquids for Permeability Measurements, 91
      2.11. Permeability Measurements in the Field, 93
      2.12. Typical Permeability Values, 101
      2.13. Porosity Measurements, 113

CHAPTER III
GENERAL HYDRODYNAMICAL EQUATIONS FOR THE FLOW OF FLUIDS THROUGH POROUS MEDIA, 121
      3.1. Fundamental Hydrodynamic Relations, 121
      3.2. The Classical Hydrodynamics, 125
      3.3. Generalized Form of Darcy's Law, 127
      3.4. The Equations of Motion, 131
      3.5. Boundary and Initial Conditions, 136
      3.6. Analogies with Other Physical Problems, 139
      3.7. Other Coordinate Systems, 141
      3.8. Summary, 143

PART II. STEADY-STATE FLOW OF LIQUIDS

CHAPTER IV
TWO-DIMENSIONAL FLOW PROBLEMS AND POTENTIAL-THEORY METHODS, 149
      4.1. Introduction, 149
      4.2. The Radial Flow into a Well, 150
      4.3. Fourier Series, 156
      4.4. Unsymmetrical Flow into a Well, 163
      4.5. Arbitrary Pressure Distributions over the Boundaries, 163
      4.6. The Flow between Nonconcentric Circular Boundaries Green's Function, 169
      4.7. The Flow from an Infinite Line Source into a Well. The Line Drive. The Method of Images, 175
      4.8. The Flow from a Finite Line Source into an Infinite Sand. The Method of Conjugate Functions, 181
      4.9. The Flow from a Finite Line Source into a Well. Conjugate-function Transformations. Infinite Sets of Images, 186
      4.10. The Uplift Pressure on a Dam of Extended Base Width. No Sheet Piling, 192
      4.11. The Uplift Pressure on a Dam with Sheet Piling Present. The Schwarz, Christoffel Theorem, 195
      4.12. The Seepage Flux under Dams of Extended Base Width. No Sheet Piling. Elliptic-function Transformations, 208
      4.13. The Seepage Flux under Dams of Extended Base Width; Sheet Piling Present, 215
      4.14. The Seepage Flux underneath Coffer Dams, 221
      4.15. Anisotropic Media, 225
      4.16. General Potential-theory Results. Green's Reciprocation Theorem, 227
      4.17. Approximate and Nonanalytic Methods of Solving Two-dimensional Flow Problems, 234
      4.18. Summary, 244

CHAPTER V
THREE-DIMENSIONAL PROBLEMS, 258
      5.1. Introduction, 258
      5.2. Spherical Flow, 259
      5.3. Partially Penetrating Wells. Potential Distributions, 263
      5.4. The Production Capacities of Partially Penetrating Wells, 271
      5.5. Partially Penetrating Wells in Anisotropic Sands, 277
      5.6. Summary, 281

CHAPTER VI
GRAVITY-FLOW SYSTEMS, 287
      6.1. Introduction, 287
      6.2. The Drainage of a Sloping Sand. The Problem of Hopf and Trefitz, 292
      6.3. The Treatment of Two-dimensional Gravity-flow Systems by the Method of Hodographs. The Mapping of the Boundaries, 300
      6.4. The Seepage through a Dam with Vertical Faces; Analytical Theory, 303
      6.5. Numerical Applications, 309
      6.6. The Study of Gravity-flow Systems by Means of Electrical Models, 318
      6.7. Some Exact Solutions of Laplace's Equation Appropriate to Gravity-flow Systems, 323
      6.8. The Seepage of Water from Canals or Ditches into Sands with Deep-lying Water Tables, 331
      6.9. The Seepage of Water from Canals or Ditches into Sands Underlain by Highly Permeable Gravel Beds at Shallow Depths, 336
      6.10. An Approximate Theory of the Seepage of Water through Dams with Sloping Faces, 338
      6.11. Seepage Streams from Canals and Ditches Which Merge with Shallow Water Tables, 346
      6.12. The Approximate Treatment of Some Irrigation and Drainage Problems, 353
      6.13. Subirrigation, 354
      6.14. The Problem of Water Logging, 355
      6.15. The Erosion Problem, 355
      6.16. Tile Drainage, 356
      6.17. The Dupuit-Forchheimer Theory of Gravity-flow Systems, 359
      6.18. Sand-model Experiments with Three-dimensional Gravity-flow Systems, 365
      6.19. Composite Pressure-head and Gravity-flow Systems, 375
      6.20. An Approximate Potential Theory of the Flux through Gravity-flow Systems, 377
      6.21. Summary, 385

CHAPTER VII
SYSTEMS OP NONUNIFOBM PERMEABILITY, 400
      7.1. Introduction. Surfaces of Discontinuity, 400
      7.2. Continuous Variations in the Permeability, 401
      7.3. Discontinuous Radial Variations in the Permeability, 403
      7.4. Adjacent Beds of Different Permeability. Fluid Flow in Fractured Limestones, 409
      7.5. Bounded Limestone — Fracture Systems, 417
      7.6. The Theory of the Acid Treatment of Limestone Wells, 420
      7.7. The Effect of Acid Treatment in Radial Systems, 422
      7.8. The Effect of Acid Treatment in Highly Fractured Limestones, 425
      7.9. Partially Penetrating Wells in Stratified Horizons, 429
      7.10. The Effect of a Sanded Liner on the Production Capacity of a Well, 439
      7.11. Summary, 447

CHAPTER VIII
TWO-FLUID SYSTEMS, 453
      8.1. Introduction, 453
      8.2. Edge-water Encroachment. General Nature and Formulation of the Problem, 453
      8.3. Linear Encroachment, 459
      8.4. Two-dimensional Radial Encroachment, 462
      8.5. The History of a Line of Fluid Particles in a Homogeneous System, 466
      8.6. The Line Drive into a Single Well, 468
      8.7. The Direct Drive between Two Wells, 472
      8.8. The Effect of Gravity on the Shape of the Encroaching Interface, 476
      8.9. The Effect of the Differences in Viscosity between the Fluids on the Two Sides, of the Interface, 478
      8.10. Water Coning; Physical Basis of the Theory, 480
      8.11. Analytical Development, 487
      8.12. The Suppression of Water Coning by Shale Lenses, 496
      8.13. Summary, 499

CHAPTER IX
MULTIPLE-WELL SYSTEMS, 507
      9.1. Introduction, 507
      9.2. Small Groups of Wells. General Theory, 509
      9.3. Examples, 511
      9.4. The Dependence of the Production Capacity on the Number of Wells, in the Group, 518
      9.5. The Pressure Distribution over the External Boundary, 520
      9.6. Small Groups of Wells Supplied by an Infinite Line Drive, 521
      9.7. Infinite Sets of Wells in Linear Arrays, 523
      9.8. The Pressure Distribution about an Infinite Array of Wells. The Line Drive, 524
      9.9. Two-line Arrays. Shielding Effects, 530
      9.10. Three-line Arrays, 540
      9.11. Staggered Wells in Line Arrays, 545
      9.12. The Theory of Offsetting. Statement of the Problem, 546
      9.13. Single-line Offsetting, 548
      9.14. Multiple-line Offsetting, 552
      9.15. Numerical Example, 556
      9.16. The Problem of Water Flooding, 560
      9.17. The Progress of the Water-oil Interface — Electrolytic-model Experiments, 561
      9.18. Model Experiments with Line Floods, 565
      9.19. Experiments Corresponding to Artificial Flooding Operations, 568
      9.20. Effect of Barriers in the Flooding System, 572
      9.21. Conduction-sheet Models and Potential Distributions, 573
      9.22. Analytical Calculations of the Conductivities of Flooding Network. General Method, 580
      9.23. The Conductivity of the Direct Line-drive Flood, 582
      9.24. The Conductivity of the Five-spot Flood, 585
      9.25. The Conductivity of the Seven-spot Flood, 587
      9.26. The Conductivity of the Staggered Line Drive, 592
      9.27. The Calculation of Flooding Efficiencies, 593
      9.28. The Efficiency of the Direct Line-drive Flood, 594
      9.29. The Five-spot-flood Efficiency, 596
      9.30. The Efficiency of the Seven-spot Flood, 597
      9.31. The Efficiency of the Staggered Line-drive Flood, 598
      9.32. General Observations on Flooding Networks, 599
      9.33. Comparison of the Flooding Networks, 600
      9.34. Summary, 606

PART III. THE NONSTEADY-STATE FLOW OF LIQUIDS

CHAPTER X
THE FLOW OF COMPRESSIBLE LIQUIDS THROUGH POROUS MEDIA, 621
      10.1. Introduction, 621
      10.2. Radial Flow Systems. Some Preliminary Analytical Formulas, 630
      10.3. Radial Systems in Which the Density Is Specified over Both Boundaries, 632
      10.4. Production Decline in a Field Produced by a Water Drive with Variable Field Pressures, 635
      10.5. The Limiting Case of Vanishing Internal Radius, 639
      10.6. The Rise of the Bottom-hole Pressures in Closed-in Wells, 640
      10.7. Radial Systems in Which the Density Is Specified over One Boundary and the Flux over the Other, 642
      10.8. The Pressure Decline in the "East Texas" Oil Field, 644
      10.9. A Single Well in a Closed Reservoir, 653
      10.10. A Well of Infinitesimal Radius, 654
      10.11. Radial Systems in Which the Flux Is Specified over Both Boundaries, 655
      10.12. The Limiting Case of Vanishing Internal Radius, 656
      10.13. A Well in a Closed Sand, 657
      10.14. Nonradial Flow.  Well Interference. Green's Function, 661
      10.15. The Use of Sources and Sinks in the Solution of Problems Involving the Nonsteady-state Flow of Compressible Liquids through Porous Media, 666
      10.16. Summary, 669

PART IV. THE FLOW OF GASES THROUGH POROUS MEDIA

CHAPTER XI
THE FLOW OF GASES THROUGH POROUS MEDIA, 679
      11.1. Introduction, 679
      11.2. The Steady-state Flow of Gases. Linear Systems, 680
      11.3. Two-dimensional Systems in the Steady State, 681
      11.4. Three-dimensional Systems in the Steady State, 683
      11.5. The Effect of Gravity on the Flow of Gases through Porous Media, 684
      11.6. The Steady-state Flow of Gases within Systems of Non-uniform Permeability, 685
      11.7. Two-fluid Systems. Water Coning, 686
      11.8. Gas-oil Ratios in Porous Media Carrying Gas and Oil as Homogeneous Fluids, 687
      11.9. Gas-oil Ratios for Communicating Gas and Oil Zones, 689
      11.10. Gas-oil Ratios for Non Communicating Gas and Oil Sands, 692
      11.11. The Effect of the Tubing on the Gas-oil Ratio, 696
      11.12. Gas Coning in Tubed Wells, 701
      11.13. Multiple-well Systems, 704
      11.14. The Nonsteady-state Flow of Gases through Porous Media, 704
      11.15. A Closed Gas Reservoir Drained by a Well Producing at Constant Pressure, 708
      11.16. A Closed Gas Reservoir Drained by a Well Producing at a Uniform Rate, 712
      11.17. Summary, 714

APPENDICES
I. CONVERSION FACTORS, 723
II. LAPLACE'S EQUATION IN CURVILINEAR COORDINATES, 725
III. SOME TWO-DIMENSIONAL GREEN'S FUNCTIONS, 727
THE TRANSFORMATION PROPERTIES OF THE MODULAR ELLIPTIC FUNCTION Θ(q)=k*2, 729
V. PROOF OF THE GENERALIZED POISSON FORMULA. EQ. 6.4(15),732
VI. TABULATION OF THE SPECIFIC QUANTITATIVE RESULTS DEVELOPED IN THIS WORK IN FORMULA OR GRAPHICAL FORM, 733
AUTHOR INDEX, 751
SUBJECT INDEX, 755




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