Preface xi
Acknowledgements xiii
1 Basic Ideas, Interpretation Issues and Modeling Hierarchies 1
1.1 Background and Approaches 1
1.2 Modeling Hierarchies 5
1.3 Experimental Methods and Tool Calibration 13
1.4 References 24
2 Single-Phase Flow Forward and Inverse Algorithms 25
2.1 Overview 25
2.2 Basic Model Summaries 27
2.2.1 Module FT-00 28
2.2.2 Module FT-01 30
2.2.3 Module FT-03 30
2.2.4 Forward Model Application, Module FT-00 31
2.2.5 Inverse Model Application, Module FT-01 33
2.2.6 Eff ects of Dip Angle 35
2.2.7 Inverse "Pulse Interaction" Approach Using FT-00 37
2.2.8 Computational Notes 40
2.2.9 Source Model Limitations and More Complete Model 41
2.2.10 Phase Delay Analysis, Module FT-04 43
2.2.11 Drawdown-Buildup, Module FT-PTA-DDBU 45
2.2.12 Real Pumping, Module FT-06 48
2.2.13 Closing Remarks 50
2.2.14 References 50
3 Advanced Drawdown and Buildup Interpretation in Low Mobility Environments 51
3.1 Basic Steady Flow Model 51
3.2 Transient Spherical Flow Models 53
3.2.1 Forward or Direct Analysis 53
3.2.2 Dimensionless Formulation 54
3.2.3 Exact Solutions for Direct Problem 55
3.2.4 Special Limit Solutions 56
3.2.5 New Inverse Approach for Mobility and Pore Pressure Prediction 58
3.3 Multiple-Drawdown Pressure Analysis (Patent Pending) 59
3.3.1 Background on Existing Models 59
3.3.2 Extension to Anisotropic, No-Skin Applications 60
3.3.2.1 Method 1 - Drawdown-Alone Test 61
3.3.2.2 Method 2 - Single-Drawdown-Single-Buildup Test 62
3.3.2.3 Method 3 - Double-Drawdown-Single-Buildup Test 62
3.4 Forward Analysis with Illustrative Calibration 64
3.5 Mobility and Pore Pressure Using First Drawdown Data 66
3.5.1 Run No. 1, Flowline Volume 200 Cc 66
3.5.2 Run No. 2, Flowline Volume 500 Cc 69
3.5.3 Run No. 3, Flowline Volume 1,000 Cc 71
3.5.4 Run No. 4, Flowline Volume 2,000 Cc 73
3.6 Mobility and Pore Pressure from Last Buildup Data 74
3.6.1 Run No. 5, Flowline Volume 200 Cc 74
3.6.2 Run No. 6, Flowline Volume 500 Cc 76
3.6.3 Run No. 7, Flowline Volume 1,000 Cc 77
3.6.4 Run No. 8, Flowline Volume 2,000 Cc 78
3.6.5 Run No. 9, Time-Varying Flowline Volume 79
3.7 Tool Calibration in Low Mobility Applications 81
3.7.1 Steady Flow Model 81
3.7.2 Example 1, Calibration Using Early-Time Buildup Data 81
3.7.3 Example 2, Calibration Using Early-Time Buildup Data 86
3.7.4 Example 3, Example 1 Using Drawdown Data 89
3.7.5 Example 4, Example 2 Using Drawdown Data 91
3.8 Closing Remarks 93
3.9 References 94
4 Phase Delay and Amplitude Attenuation for Mobility Prediction in Anisotropic Media with Dip (Patent Pending) 95
4.1 Basic Mathematical Results 96
4.1.1 Isotropic Model 96
4.1.2 Anisotropic Equations 98
4.1.3 Vertical Well Solution 99
4.1.4 Horizontal Well Solution 100
4.1.5 Formulas for Vertical and Horizontal Wells 101
4.1.6 Deviated Well Equations 101
4.1.7 Deviated Well Interpretation for Both Kh and Kv 103
4.1.8 Two-Observation-Probe Models 105
4.2 Numerical Examples and Typical Results 107
4.2.1 Example 1, Parameter Estimates 108
4.2.2 Example 2, Surface Plots 109
4.2.3 Example 3, Sinusoidal Excitation 110
4.2.4 Example 4, Rectangular Wave Excitation 113
4.2.5 Example 5, Permeability Prediction at General Dip Angles 115
4.2.6 Example 6, Solution for a Random Input 117
4.3 Layered Model Formulation 118
4.3.1 Homogeneous Medium, Basic Mathematical Ideas 118
4.3.2 Boundary Value Problem for Complex Pressure 120
4.3.3 Iiterative Numerical Solution to General Formulation 120
4.3.4 Successive Line Over Relaxation Procedure 121
4.3.5 Advantages of the Scheme 122
4.3.6 Extensions to Multiple Layers 122
4.3.7 Extensions to Complete Formation Heterogeneity 123
4.4 Phase Delay Software Interface 123
4.4.1 Output File Notes 126
4.4.2 Special User Features 126
4.5 Detailed Phase Delay Results in Layered Anisotropic Media 127
4.6 Typical Experimental Results 134
4.7 Closing Remarks - Extensions and Additional Applications 138
4.8 References 139
5 Four Permeability Prediction Methods 140
5.1 Steady-State Drawdown Example 142
5.2 Early-Time, Low-Mobility Drawdown-Buildup 144
5.3 Early-Time, Low-Mobility Drawdown Approach 147
5.4 Phase Delay, Non-Ideal Rectangular Flow Excitation 148
6 Multiphase Flow with Inertial Effects 151
6.1 Physical Problem Description 152
6.1.1 The Physical Problem 152
6.1.2 Job Planning Considerations 154
6.1.3 Modeling Challenges 155
6.1.4 Simulation Objectives 156
6.1.5 Modeling Overview 157
6.2 Immiscible Flow Formulation 159
6.2.1 Finite Difference Solution 160
6.2.2 Formation Tester Application 161
6.2.3 Mudcake Growth and Formation Coupling at Sandface 163
6.2.4 Pumpout Model for Single-Probe Pad Nozzles 165
6.2.5 Dual Probe and Packer Surface Logic 166
6.3 Miscible Flow Formulation 168
6.4 Inertial Effects With Forchheimer Corrections 169
6.4.1 Governing Differential Equations 169
6.4.2 Pumpout Boundary Condition 171
6.4.3 Boundary Value Problem Summary 172
6.5 References 173
7 Multiphase Flow - Miscible Mixing Clean-Up Examples 175
7.1 Overview Capabilities 175
7.1.1 Example 1, Single Probe, Infinite Anisotropic Media 176
7.1.2 Example 2, Single Probe, Three Layer Medium 181
7.1.3 Example 3, Dual Probe Pumping, Three Layer Medium 183
7.1.4 Example 4, Straddle Packer Pumping 185
7.1.5 Example 5, Formation Fluid Viscosity Imaging 187
7.1.6 Example 6, Contamination Modeling 188
7.1.7 Example 7, Multi-Rate Pumping Simulation 189
7.2 Source Code and User Interface Improvements 191
7.2.1 User Data Input Panel 191
7.2.2 Source Code Engine Changes 193
7.2.3 Output Color Graphics 195
7.3 Detailed Applications 200
7.3.1 Run No. 1, Clean-Up, Single-Probe, Uniform Medium 200
7.3.2 Run No. 2, Clean-Up, Dual-Probe, Uniform Medium 209
7.3.3 Run No. 3, Clean-Up, Elongated Pad, Uniform Medium 213
7.3.4 Run No. 4, A Minimal Invasion Example 218
7.3.5 Run No. 5, A Single-Phase Fluid, Constant Viscosity example 222
7.3.6 Run No. 6, A Low-Permeability "Supercharging" Example 224
7.3.7 Run No. 7, A Three-Layer Simulation 226
8 Time-Varying Flowline Volume 229
8.1 Transient Anisotropic Formulation for Ellipsoidal Source 230
8.1.1 Formulation for Liquids and Gases 230
8.1.2 Similarity Transform 232
8.1.3 Transient Flow Numerical Modeling 233
8.1.4 Finite Difference Equation 234
8.1.5 Boundary Condition - Flowline Storage With and Without Skin Effects 235
8.1.6 Detailed Time Integration Scheme 236
8.1.7 Observation Probe Response 237
8.2 FT-06 Software Interface and Example Calculations 238
8.3 Time-Varying Flowline Volume Model 244
8.3.1 Example 1, Software Calibration 245
8.3.2 Example 2, Simple Interpretation Using Numerical Pressure Data 252
8.3.3 Example 3, Simple Interpretation Using Numerical Pressure Data 255
8.3.4 Example 4, Simple Interpretation Using Low Permeability Data 257
8.3.5 Example 5, Simple Interpretation Using Numerical Pressure Data 258
8.3.6 Example 6, Simple Interpretation Using Numerical Pressure Data 262
8.3.7 Example 7, Enhancing Phase Delay Detection In Very Low Permeability Environments 264
9 Closing Remarks 270
References 281
Index 287
About the Authors 293
