Resistivity Modeling

Wilson C. Chin earned his Ph.D. from M.I.T. and his M.Sc. from Caltech. He has published fifteen books describing his original research in reservoir engineering, formation testing, managed pressure drilling, wave propagation, Measurement While Drilling (MWD) and electromagnetic well logging, over one hundred papers and three dozen patents.?Mr. Chin has consulted for well known domestic and international oil and gas corporations, and during the past two decades, won five prestigious research contracts and awards in petroleum exploration and production with the United States Department of Energy.

• Preface xiAcknowledgements xvii1 Physics, Math and Basic Ideas 11.1 Background, Industry Challenges and Frustrations 11.2 Iterative Algorithms and Solutions 21.3 Direct Current Focusing from Reservoir Flow Perspective 51.4 General Three-Dimensional Electromagnetic Model 111.5 Closing Remarks 251.6 References 252 Axisymmetric Transient Models 262.1 Physical Ideas, Engineering Models and Numerical Approaches 272.2 Transient Axisymmetric Coil Source Calculations 372.3 Effects of Frequency, from Induction, to Propagation, to Dielectric 592.4 Depth of Investigation 602.5 Closing Remarks Related to Interpretation 612.6 References 633 Steady Axisymmetric Formulations 643.1 Laterolog Voltage Modeling and Interpretation Approach 653.2 Current Trajectories from Streamfunction Analysis 683.3 Voltage Calculations and Current Trajectories 71Run 1. Conductivities σv = 1.0, σh = 1.01 74Run 2. Conductivities σv = 1.01, σh = 1.0 76Run 3. Conductivities σv = 1, σh = 10 78Run 4. Conductivities σv = 10, σh = 1 803.4 Current and Monitor Electrodes 853.5 References 854 Direct Current Models for Micro-Pad Devices 864.1 Th ree-Dimensional, Anisotropic, Steady Model 874.2 Finite Difference Approach and Subtleties 884.3 Row versus Column Relaxation 884.4 Pads Acting on Vertical and Horizontal Wells 90Run 1. Conductivities σv = 1.0, σh = 1.01 (vertical well) 92Run 2. Conductivities σv = 1.01, σh = 1.0 (vertical well) 94Run 3. Conductivities σv = 1, σh = 10 (vertical well) 96Run 4. Conductivities σv = 10, σh = 1 (vertical well) 98Run 5. Conductivities σv = 1.0, σh = 1.01 (horizontal well) 100Run 6. Conductivities σv = 1.01, σh = 1.0 (horizontal well) 102Run 7. Conductivities σv = 1, σh = 10 (horizontal well) 104Run 8. Conductivities σv = 10, σh = 1 (horizontal well) 1064.5 Closing Remarks 1084.6 References 1085 Coil Antenna Modeling for MWD Applications 1095.1 Axisymmetric and 3D Model Validation 1095.2 Modeling a Center-Fed Linear Dipole Transmitter Antenna 1175.3 More Antenna Concepts 1275.4 References 1626 What is Resistivity? 1636.1 Resistance in Serial and Parallel Circuits, Using Classical Algebraic Approach 1636.2 Resistance in Serial and Parallel Circuits, Using Differential Equation Approach 1656.3 Isotropy and Anisotropy in Cross-bedded Sands 1676.4 Tool Measurements and Geological Models 1716.5 References 1727 Multiphase Flow and Transient Resistivity 1737.1 Immiscible Buckley-Leverett Linear Flows Without Capillary Pressure 1767.2 Molecular Diffusion in Fluid Flows 1837.3 Immiscible Radial Flows with Capillary Pressure and Prescribed Mudcake Growth 1937.4 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth – Theory and Numerics 2087.5 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth – Detailed Examples 2237.6 Simple Example in Time Lapse Logging 2347.7 Resistivity Distributions Variable in Space and Time 2477.8 References 2508 Analytical Methods for Time Lapse Well Logging Analysis 2518.1 Experimental Model Validation 2518.2 Characterizing Mudcake Properties 2558.3 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination 2598.4 Examples of Time Lapse Analysis 2688.5 References 273Cumulative References 274Index 276About the Author 282