GILLES BOURDAROTEngineer, Elf Aquitaine

WELL TESTING:INTERPRETATION

METHODSTranslated from the French by Barbara Brown Balvet

1998EDITIONSTECHNIP27 rue Ginoux75737 Paris Cedex 15

Center forPETROLEUM

ENGINEERINGAND PROJECTDEVELOPMENT

ECOLE DU PETROLEET DES MOTEURSI F P B S C H O O L

Contents

Symbols and abbreviations 11

PRINCIPLE 17

Chapter 1 Principles of well testing 191.1 Introduction 191.2 Darcy's law 201.3 Compressibility 211.4 Diffusion equation 231.5 Solving the diffusivity equation 251.6 Compressible zone 261.7 Radius of investigation 281.8 Flow regimes 301.9 Principle of superposition 31

Chapter 2 Wellbore storage 332.1 Definition 332.2 Naturally eruptive wells 342.3 Pumping wells 352.4 Orders of magnitude 352.5 Pressure variations 352.6 Bottomhole flow 372.7 End of the wellbore storage effect 37

Chapter 3 Skin 393.1 Definition 393.2 Infinitesimal skin 39

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CONTENTS

3.3 Finite thickness skin 403.4 Effective radius r 413.5 Generalization of the skin concept 43

INTERPRETATION METHODS 45

Introduction 47

Chapter4 Conventional interpretation methods 514.1 Drawdown test 524.2 Pressure buildup: Homer's method 544.3 Pressure buildup: MDH method 584.4 After varying flow rates 604.5 Simplification of the flow rate history 634.6 Buildup radius of investigation 66

Chapter 5 Type curves 675.1 Introduction 675.2 Gringarten type curves 675.3 Interpretation method 705.4 Using type curves during buildup 75

Chapter 6 The derivative 796.1 Representation 796.2 Properties of the derivative 806.3 The derivative as diagnostic tool 816.4 Analysis with type curves 826.5 Direct interpretation by means of the derivative 886.6 Conclusion 89

RESERVOIR BOUNDARIES 91

Introduction 93

Chapter 7 Linear sealing faults 957.1 Description 957.2 The method of images 96

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CONTENTS

7.3 Conventional interpretation method 977.4 Type curves: the derivative r 100

Chapter 8 Channels 1038.1 Description of flows 1038.2 Linear flow '. 1048.3 Conventional interpretation 1058.4 Bounded channels 1068.5 Pressure buildup with varying flow rates 1098.6 Pressure derivative, type curves 110

Chapter 9 Intersecting faults 1139.1 Conventional analysis 1139.2 Type curves; pressure derivative 114

Chapter 10 Constant pressure boundary 11710.1 Conventional interpretation method 11810.2 Type curves; derivative 121

Chapter 11 Closed reservoir 12311.1 Producing well, pseudosteady-state regime 12311.2 Shut-in well, average pressure 131

Chapter 12 Productivity index 14112.1 Definition 14112.2 Productivity index during the infinite-acting period 14112.3 Productivity index during the pseudosteady-state flow 14212.4 Real and theoretical PI 143

RESERVOIR ASPECTS 145

Chapter 13 Naturally fractured reservoirs 14713.1 Geometry 14713.2 Porosity 14913.3 Capacity -... 15013.4 Permeability 15213.5 Matrix-fracture exchange: X 153

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NIEDERS.|STAATS-U.UNIV.-|

BIBLICTHEKG0TTINGEN

CONTENTS

13.6 Analysis of flows 15313.7 Choosing between the pseudosteady-state and the transient

interporosity flow models 16213.8 Type curve analysis 16313.9 Type curves derivatives 17113.10 Two examples of interpretation in a fractured reservoir 175

Chapter 14 Two-layer reservoirs 18114.1 Introduction 18114.2 Description of a two-layer reservoir 18114.3 The Bourdet model 18214.4 Testing a two-layer reservoir 184

WELL ASPECTS 191

Chapter 15 Partial penetration wells 19315.1 Introduction 19315.2 Flow around a partial penetration well 19515.3 Radial flow at the perforations 19615.4 Spherical flow 19715.5 Radial flow over the whole net thickness 19915.6 Extrapolated pressure, average pressure 20315.7 Pressure derivative 20315.8 Ambiguous interpretation 20515.9 Comparison with core samples 20615.10 Partial perforation and fractured reservoirs 206

Chapter 16 Slanted wells 20916.1 Introduction 20916.2 Flows and skin factor for slanted wells 21016.3 Influence of permeability ariisbtropy 211

Chapter 17 Artificially fractured wells 21317.1 Description of the fracture 21317.2 Flows around an artificially fractured well. Conventional interpretation

methods 21417.3 Type curves, the derivative 22217.4 Type curves 22817.5 Conclusion 231

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CONTENTS

Chapter 18 Horizontal wells 23318.1 Description of a horizontal well 23318.2 Flows around a horizontal well. Conventional interpretation

methods 23318.3 Type curves, the derivative 239

Chapter 19 Injection wells 24119.1 Description of an injection well 24119.2 Description of flows 24219.3 Type curves and derivative 24619.4 The objectives of testing an injection well 248

FLUID ASPECTS 251

Chapter 20 Gas wells 25320.1 Pseudopressure 25320.2 Deviation from Darcy's law 25720.3 Interpretation of a gas well test 25920.4 Presentation of absolute open-flow potential tests 26320.5 Conventional AOFP tests 26320.6 Interpretation of AOFP tests: Houpeurt's method 26620.7 Interpretation of absolute open-flow potential tests:

empirical method 27120.8 Other test procedures 274

Chapter 21 Multiphase flows 28121.1 Introduction 28121.2 Perrine method hypotheses 28221.3 Perrine's method 28321.4 Productivity index of an oil well producing under the bubble point;

Vogel's equation 287

INTERFERENCES 291

Chapter 22 Interference tests 29322.1 Presentation, particulars 29322.2 Interpretation methods in a homogeneous reservoir 294

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CONTENTS

22.3 Interference tests in fractured reservoirs 29922.4 Influence of flow rate history r. 30322.5 Skin and wellbore storage effect 30522.6 Objective of interference tests, two examples 306

Chapter 23 Pulse tests 31323.1 Presentation 313

23.2 Interpreting pulse tests: the Kamal and Brigham method 315

Practical units 325

References 327

Index 333

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