Petrophysics. Theory and Practice of Measuring. Properties. Reservoir Rock and Fluid Transport. Fourth Edition. Djebbar Tiab. Donaldson. Erie C.

Transcription

1 Petrophysics Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties Fourth Edition Djebbar Tiab Erie C. Donaldson ELSEVIER AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Gulf Professional Publishing is an imprint ofelsevier

2 Contents Preface: 4th Edition of Petrophysics Acknowledgments About the Authors Units xyii X1X xx* xxhi CHAPTER 1 Introduction 1 Introduction to Mineralogy 1 Mineral Constituents of Rocks: A Review 2 Igneous Rocks 6 Metamorphic Rocks 6 Sedimentary Rocks 8 Properties of Sedimentary Particles 13 Development and use of Petrophysics 17 Problems 18 Glossary 18 References 20 CHAPTER 2 Introduction to Petroleum Geology 23 Review of Composition of the Globe 23 Plate Tectonics 25 Geologic Time 27 Sedimentary Geology 29 Basins 29 Divergent Continental Margins 30 Convergent Continental Margins 30 Transform Continental Margins 31 Transgressive-Regressive Cycles 31 Accumulation of Sediments 32 Hydrocarbon Traps 34 Origin of Petroleum 37 Transformation of Organics into Kerogen 37 Transformation of Kerogen into Oil and Gas 38 Migration and Accumulation of Petroleum 38 Primary Migration 39 Secondary Migration 40 Properties of Subsurface Fluids 43 Hydrostatic Pressure Gradient 43 vii

3 viii Contents Lithostatic Pressure Gradient 43 Geothermal Gradient 44 Oilfield Waters 47 Petroleum 53 Petroleum Chemistry 59 Problems 62 References 65 CHAPTER 3 Porosity and Permeability 67 Introduction 67 Porosity 67 Factors Governing the Magnitude of Porosity 68 Engineering Classification of Porosity 70 Geological Classification of Porosity 71 Primary Porosity 71 Secondary Porosity 72 Visual Description of Porosity in Carbonate Rocks 72 Fluid Saturation 75 Quantitative Use of Porosity 76 Permeability 77 Classification of Permeability 81 Factors Affecting the Magnitude of Permeability 82 Permeability-Porosity Relationships 84 Kozeny Correlation 86 Concept of Flow Units 90 Mathematical Theory of Flow Units 92 Specific Surface Area 94 Flow Unit Characterization Factors 98 Flow Units Functions 109 Reservoir Zonation Using Normalized RQI 116 Effect of Packing on Permeability 117 Effect of Water Saturation on Permeability 118 Permeability from NMR 119 Permeability from GR Logs 122 Permeability-Porosity Relationships in Carbonate Rocks 124 Estimating Permeability in Carbonate Rocks 127 Directional Permeability 134 Anisotropy 134 Relationship Between kh and kv 137 Reservoir Heterogeneity 146 Distribution of Rock Properties 148

4 Contents ix Permeability and Porosity Distributions 148 Lorenz Coefficient Lk 149 Dykstra-Parsons Coefficient VK 150 Averaging Techniques 155 Effective Permeability from Core Data 157 Average Porosity and Saturation 160 Permeability from Well Test Data 168 Statistical Zonation Technique 172 Problems 177 References 183 CHAPTER 4 Formation Resistivity and Water Saturation 187 Formation Resistivity Factor 187 Resistivity Measurement 187 Determination of Formation Water Resistivity 190 Chemical Analysis 190 Resistivity-Concentration Equations 194 Spontaneous Potential Curve 198 Shale-Properties Method 199 Correlation Between FR and Porosity 200 Correlations Between FR and Tortuosity 201 Correlations Between FR and Cementation 203 Theoretical Formula for FR 206 Correlation Between FR and Water Saturation 210 Correlation Between FR and Permeability 219 Resistivity of Shaly (Clayey) Reservoir Rocks 222 Water Saturation in Shaly (Clayey) Reservoir Rocks 223 Approximate Shale Relationship 228 Generalized Shale Relationship 229 Flow Units for Shaly Sandstones 231 Lab-Derived Evaluation of Shaly (Clayey) Reservoir Rocks 234 Log-Derived Evaluation of Shaly (Clayey) Reservoir Rocks 255 Formation Evaluation 255 Core Analysis 256 Well Log Analysis 257 Water Saturation 258 Porosity 260 Core Interpretation of Data 263 Interpretation of Well Log Data 268 Problems 271 References 276

5 x Contents CHAPTER 5 Capillary Pressure 279 Introduction 279 Derivation of the Capillary Pressure Equation 279 Capillary Rise 283 Semipermeable Disk Measurement of Capillary Pressure 285 Centrifuge Measurement of Capillary Pressure 288 Laboratory Procedure 288 Calculation of Centrifuge Capillary Pressure Data 290 Limiting Centrifuge Speed 292 Calculation of the Inlet Saturation 294 Measurement of Capillary Pressure by Mercury Injection 297 Low-Pressure Mercury Injection 297 High-Pressure Mercury-Injection Capillary Pressure 299 Pore-Size Distribution 301 Pore-Size Distribution Function 303 Porosity and Permeability 304 Relative Flow Analysis 304 Vertical Saturation Profile in a Reservoir 305 Capillary Pressure /-Function 307 Averaging Core Properties With the /-Function 309 Capillary Number 311 Problems 313 References 316 CHAPTER 6 Wettability 319 Wettability 319 Interfacial Tension 320 Contact Angle 320 Sessile Drop Measurement of Contact Angles 322 Wilhelmy Plate Measurement of Contact Angles 324 Surface Chemical Properties 325 Evaluation of Wettability 327 Amott Wettability Index 328 USBM Wettability Index 330 Combined Amott-USBM Wettability Test 331 Spontaneous Imbibition Wettability Test 332 Fluid Displacement Energy 334 Water-Oil-Rock Interfacial Activity 336 Effect of Wettability on Oil Recovery 338 Effect of Brine Salinity on Oil Recovery 341

6 Contents xi Alteration of Wettability 342 Treatment of the Rock 342 Addition of Fluid Soluble Compounds to Water and Oil 343 Aging the Oil-Brine-Rock System 344 Effects of Temperature and Pressure 345 Restoration of Original Wettability 347 Fractional Flow Equation 347 Problems 349 References 352 CHAPTER 7 Applications of Darcy's Law 359 Darcy's Law 360 Linear Flow of Incompressible Fluids 361 Linear Flow of Gas 363 Darcy's and Poiseuille's Laws 365 Linear Flow Through Fractures and Channels 367 Flow Through Fractures 368 Flow Through Solution Channels 371 Radial Flow Systems 373 Steady-State Flow 374 Pseudosteady-State Flow 376 Skin Zone 379 Dimensionless Pressure 381 Radial Laminar Flow of Gas 383, Turbulent Flow of Gas 387 Linear Turbulent Flow 388 Friction Factor of Porous Rocks 393 Turbulent Radial Flow 398 Multiple-Permeability Rocks 400 Layered Reservoirs with Crossflow 401 Layered Reservoirs without Crossflow 402 Composite Reservoirs 405 Linear Flow Systems 406 Radial Flow Systems 407 Problems 409 References 413 CHAPTER 8 Naturally Fractured Reservoirs Introduction 415 Origin of Permeability in Carbonate Rocks 416

7 xii Contents Geological Classifications of Natural Fractures 417 Engineering Classification of Naturally Fractured Reservoirs 418 Indicators of Natural Fractures 421 Visual Identification of Fractures 425 Petrophysical Properties of Naturally Fractured Rocks 427 Fracture Porosity Determination 427 RQI, FZI, and m for Carbonates 431 Porosity Partitioning Coefficient 436 Fracture Intensity Index 442 Permeability-Porosity Relationships in Double Porosity Systems 445 Porosity and Permeability Relationships in Type 1 Naturally Fractured Reservoirs 448 Fractures Porosity and Aperture from Cores 449 Specific Area of Fractures 453 Effect of Fracture Shape 454 Hydraulic Radius of Fractures 455 Type 2 Naturally Fractured Reservoirs 457 Fluid Flow Modeling in Fractures 458 Fracture Area 458 Fracture Storage Capacity 459 Fracture Conductivity 460 Characterizing Natural Fractures from Well-Test Data 461 Fracture Porosity and Permeability from Pressure Tests 463 Fracture Corridors in Carbonates 472 Problems 474 References 479 CHAPTER 9 Effect of Stress on Reservoir Rock Properties 483 Static Stress-Strain Relation 484 Stress Analysis 484 Strain Analysis 487 Two-Dimensional Stress-Strain Systems 488 Rock Deformation 489 Hooke's Law 489 Stress-Strain Diagrams 497 The Mohr Diagram 499 Dynamic Elastic Properties 503 Dynamic versus Static Modulus of Elasticity 504 Rock Strength and Hardness 505 Rock Hardness 509 Compressibility of Porous Rocks 509

8 Contents xiii Pore Compressibility 509 Effectiveness of Pore Pressure in Countering Stress 513 Rock Compressibility Correlations 516 Effect of Pore Compressibility on Reserves Calculations 517 Converting Lab Data to Reservoir Data 518 Effect of Stress on Core Data 521 Effect of Stress on Porosity 521 Effect of Stress on Permeability 525 Effect of Stress on Resistivity 527 Porosity-Permeability-Stress Relationship 527 Effect of Stress on Fracturing 540 Effect of Poisson's Ratio on Fracture Gradient 541 FG for Offshore Wells 546 Effect of Poisson's Ratio on Fracture Dimensions 550 In Situ Stress Distribution 554 Effect of Stress Change on Rock Failure 559 Change in Stress Field due to Depletion and Repressurization 560 Stress Relationship at the Wellbore 561 Estimating Critical Borehole Pressure in Vertical Wells Overbalanced Conditions 561 Balanced and Underbalanced Conditions 562 Critical Borehole Pressure in Horizontal Wells 563 Overbalanced Conditions 563 Underbalanced Conditions 563 Critical Pore Pressure 564 Example of a North Sea Reservoir 565 Stress Field and Reservoir Stress Paths 566 Analysis 567 Porosity as Strength Indicator to Evaluate Sand Production 567 Problems 572 Additional Sample Data 575 References 578 CHAPTER 10 Reservoir Characterization 583 Introduction 583 Reservoir Volumes 583 Hydraulic Flow Units 592 Mobility Ratio 593 /-Function 595 Analysis of Reservoir Performance 598 Reservoir Rock and Liquid Expansion 598

9 xiv Contents Solution-Gas Drive 598 Gas-Cap Drive 598 Gravity Drainage 598 Water Drive 599 Decline Curves 599 Material Balance 600 Solution-Gas Drive 601 Gas-Cap Drive 602 Water Drive 604 Gravity Drainage 605 Development of the General Material Balance Equation 607 Gas Reservoir 607 Straight-Line Solution of the Material Balance Equation 611 Gas Reservoir, Equation 611 Oil Reservoirs 611 Basic Well-Log Interpretation 615 Introduction 615 Geothermal Gradient 618 Self Potential Log 618 Gamma Ray Log 621 Acoustic Log 623 Density Log 624 Neutron Log 627 Micro-Logs 628 Formation Resistivity 630 Measurement of Oil and Gas 632 Problems 634 References 639 CHAPTER 11 Fluid-Rock Interactions 641 Introduction 641 Importance of Near-Wellbore Permeability 641 Nature of Permeability Damage 643 Origin of Permeability Damage 644 Types of Permeability Damage 648 Effect of Fines Migration on Permeability 651 Types and Sizes of Fines 651 Fines Migration 660 Chemical Damage 661 Mechanical Damage 668

10 Contents xv Migration of Foreign Solids 672 Critical Velocity Concept 672 Entrainment and Surface Deposition 673 Entrainment and Plugging 676 Identification of Permeability Damage Mechanisms 681 Permeability Damage from Foreign Solids 681 Permeability Damage from Formation Fines 687 Effect of Water Quality on Permeability 693 External Filter-Cake Buildup 694 Internal Filter-Cake Buildup 697 Injectivity Decline from Plugging of Perforations 699 Impairment from Wellbore Fill-Up 700 Membrane Filtration Tests 702 Core Filtration Tests 706 External Filter-Cake Formation 707 Internal Filter-Cake Formation 710 Problems 713 References 715 CHAPTER 12 Shale-Gas Reservoirs 719 Unconventional Hydrocarbon Generation 720 Kerogen and Total Organic Content 722 Rock-Evaluation Pyrolysis 723 Vitrinite Reflectance 726 Petrophysical Evaluation 727 Total Organic Carbon Content from Logs: Passey Alog R 728 Alog R from Resistivity and Sonic Logs 729 Alog R from Resistivity and Density Logs 729 Alog R from Resistivity and Neutron Logs 730 Sondergeld Correction Factor 733 Henderson Baseline 734 Schmoker Method 735 Total Porosity 736 TOC from NMR Measurements 738 Effective Porosity 739 Total Gas in Place in Shale-Gas Reservoirs 742 Two-Volume Petrophysical Model 743 Langmuir Isotherm 744 Langmuir Isotherm as an Equation of a Straight Line 745 Gas Recovery Factor 746

11 xvi Contents Recovery Factor from Langmuir Isotherm 748 Adsorbed Gas in Place (Ga) 749 Free Gas in Place (Gf) 753 Three-Volume Petrophysical Model 754 Adsorbed-Gas Gibbs Correction 755 Empirical Correlations of TOC 757 Permeability 758 GRI Crushed Method 758 Empirical Correlations of Permeability 759 Effect of Stress on Matrix Permeability 760 Reliability of Lab-Results 761 Permeability from Pressure Transient Tests 763 Linear Flow Analysis 763 Bilinear Flow Analysis 765 Problems 766 References 770 Appendix A: Measurement of Rock and Fluid Properties 775 Appendix B: Computer Programs 847 Index 879