<p>Preface xi</p> <p>Acknowledgements xvii</p> <p><b>1 Physics, Math and Basic Ideas 1</b></p> <p>1.1 Background, Industry Challenges and Frustrations 1</p> <p>1.2 Iterative Algorithms and Solutions 2</p> <p>1.3 Direct Current Focusing from Reservoir Flow Perspective 5</p> <p>1.4 General Three-Dimensional Electromagnetic Model 11</p> <p>1.5 Closing Remarks 25</p> <p>1.6 References 25</p> <p><b>2 Axisymmetric Transient Models 26</b></p> <p>2.1 Physical Ideas, Engineering Models and Numerical Approaches 27</p> <p>2.2 Transient Axisymmetric Coil Source Calculations 37</p> <p>2.3 Effects of Frequency, from Induction, to Propagation, to Dielectric 59</p> <p>2.4 Depth of Investigation 60</p> <p>2.5 Closing Remarks Related to Interpretation 61</p> <p>2.6 References 63</p> <p><b>3 Steady Axisymmetric Formulations 64</b></p> <p>3.1 Laterolog Voltage Modeling and Interpretation Approach 65</p> <p>3.2 Current Trajectories from Streamfunction Analysis 68</p> <p>3.3 Voltage Calculations and Current Trajectories 71</p> <p>Run 1. Conductivities σv = 1.0, σh = 1.01 74</p> <p>Run 2. Conductivities σv = 1.01, σh = 1.0 76</p> <p>Run 3. Conductivities σv = 1, σh = 10 78</p> <p>Run 4. Conductivities σv = 10, σh = 1 80</p> <p>3.4 Current and Monitor Electrodes 85</p> <p>3.5 References 85</p> <p><b>4 Direct Current Models for Micro-Pad Devices 86</b></p> <p>4.1 Th ree-Dimensional, Anisotropic, Steady Model 87</p> <p>4.2 Finite Difference Approach and Subtleties 88</p> <p>4.3 Row versus Column Relaxation 88</p> <p>4.4 Pads Acting on Vertical and Horizontal Wells 90</p> <p>Run 1. Conductivities σv = 1.0, σh = 1.01 (vertical well) 92</p> <p>Run 2. Conductivities σv = 1.01, σh = 1.0 (vertical well) 94</p> <p>Run 3. Conductivities σv = 1, σh = 10 (vertical well) 96</p> <p>Run 4. Conductivities σv = 10, σh = 1 (vertical well) 98</p> <p>Run 5. Conductivities σv = 1.0, σh = 1.01 (horizontal well) 100</p> <p>Run 6. Conductivities σv = 1.01, σh = 1.0 (horizontal well) 102</p> <p>Run 7. Conductivities σv = 1, σh = 10 (horizontal well) 104</p> <p>Run 8. Conductivities σv = 10, σh = 1 (horizontal well) 106</p> <p>4.5 Closing Remarks 108</p> <p>4.6 References 108</p> <p><b>5 Coil Antenna Modeling for MWD Applications 109</b></p> <p>5.1 Axisymmetric and 3D Model Validation 109</p> <p>5.2 Modeling a Center-Fed Linear Dipole Transmitter Antenna 117</p> <p>5.3 More Antenna Concepts 127</p> <p>5.4 References 162</p> <p><b>6 What is Resistivity? 163</b></p> <p>6.1 Resistance in Serial and Parallel Circuits, Using Classical Algebraic Approach 163</p> <p>6.2 Resistance in Serial and Parallel Circuits, Using Differential Equation Approach 165</p> <p>6.3 Isotropy and Anisotropy in Cross-bedded Sands 167</p> <p>6.4 Tool Measurements and Geological Models 171</p> <p>6.5 References 172</p> <p><b>7 Multiphase Flow and Transient Resistivity 173</b></p> <p>7.1 Immiscible Buckley-Leverett Linear Flows Without Capillary Pressure 176</p> <p>7.2 Molecular Diffusion in Fluid Flows 183</p> <p>7.3 Immiscible Radial Flows with Capillary Pressure and Prescribed Mudcake Growth 193</p> <p>7.4 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth – Theory and Numerics 208</p> <p>7.5 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth – Detailed Examples 223</p> <p>7.6 Simple Example in Time Lapse Logging 234</p> <p>7.7 Resistivity Distributions Variable in Space and Time 247</p> <p>7.8 References 250</p> <p><b>8 Analytical Methods for Time Lapse Well Logging Analysis 251</b></p> <p>8.1 Experimental Model Validation 251</p> <p>8.2 Characterizing Mudcake Properties 255</p> <p>8.3 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination 259</p> <p>8.4 Examples of Time Lapse Analysis 268</p> <p>8.5 References 273</p> <p>Cumulative References 274</p> <p>Index 276</p> <p>About the Author 282</p>