Resistivity Modeling : Propagation, Laterolog and Micro-Pad Analysis.
Chin, Wilson C.
Resistivity Modeling : Propagation, Laterolog and Micro-Pad Analysis. - 1st ed. - 1 online resource (321 pages) - Advances in Petroleum Engineering Series . - Advances in Petroleum Engineering Series .
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgements -- 1 Physics, Math and Basic Ideas -- 1.1 Background, Industry Challenges and Frustrations -- 1.2 Iterative Algorithms and Solutions -- 1.3 Direct Current Focusing from Reservoir Flow Perspective -- 1.4 General Three-Dimensional Electromagnetic Model -- 1.4.1 Example 1 - Magnetic field results -- 1.4.2 Example 2 - Electric field results -- 1.4.3 Example 3 - Anisotropic resistivity results -- 1.5 Closing Remarks -- 1.6 References -- 2 Axisymmetric Transient Models -- 2.1 Physical Ideas, Engineering Models and Numerical Approaches -- 2.1.1 Axisymmetric transient model - theory -- 2.1.2 Numerical considerations -- 2.1.2.1 Differential equation and finite difference representation -- 2.1.2.2 Matching conditions at horizontal bed layer interfaces -- 2.1.2.3 Matching conditions at radial interfaces -- 2.1.2.4 Iterative solution by row relaxation -- 2.1.3. Classic dipole solution -- 2.1.4. Additional calibration models -- 2.2 Transient Axisymmetric Coil Source Calculations -- 2.2.1 R2D-6.for calculations (200 200 constant mesh) -- 2.2.1.1 Calculation 1 with R2D-6.for (200 x 200 constant mesh) -- 2.2.1.2 Calculation 2 with R2D-6.for (200 x 200 constant mesh) -- 2.2.1.3 Calculation 3 with R2D-6.for (200 x 200 constant mesh) -- 2.2.2 R2D-6.for calculations (very large 400 x 400 constant mesh) -- 2.2.2.1 Calculation 1 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.2.2 Calculation 2 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.2.3 Calculation 3 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.3 R2D-7-Two-Horiz-Layer-No-Collar.for calculations (very large 400 x 400 constant mesh) -- 2.2.4 R2D-7-Two-Radial-Layer-Medium-No-Collar.for calculations (very large 400 x 400 constant mesh). 2.2.5 R2D-6-GECF-MWDCollar-Larger-Mesh.for calculations (very large 400 x 400 constant mesh) -- 2.2.5.1 Frequency, 400 kHz, MWD steel collar effects -- 2.2.5.2 Frequency, 2 MHz, MWD steel collar effects -- 2.2.6 Detailed Results with R2D-6.for (200 x 200 constant mesh) -- 2.3 Effects of Frequency, from Induction, to Propagation, to Dielectric -- 2.4 Depth of Investigation -- 2.5 Closing Remarks Related to Interpretation -- 2.6 References -- 3 Steady Axisymmetric Formulations -- 3.1 Laterolog Voltage Modeling and Interpretation Approach -- 3.1.1 Direct current voltage formulation -- 3.1.2 Finite differencing in anisotropic homogeneous media -- 3.2 Current Trajectories from Streamfunction Analysis -- 3.2.1 Large cumulative errors along electric paths -- 3.2.2 Streamfunction formulation derivation -- 3.3 Voltage Calculations and Current Trajectories -- 3.3.1 Example voltage and streamline calculations -- Run 1. Conductivities σv = 1.0, σh = 1.01 -- Run 2. Conductivities vσ = 1.01, σh = 1.0 -- Run 3. Conductivities σv = 1, σh = 10 -- Run 4. Conductivities σv = 10, σh = 1 -- 3.3.2 Tool design and data interpretation -- 3.4 Current and Monitor Electrodes -- 3.5 References -- 4 Direct Current Models for Micro-Pad Devices -- 4.1 Three-Dimensional, Anisotropic, Steady Model -- 4.2 Finite Difference Approach and Subtleties -- 4.3 Row versus Column Relaxation -- 4.4. Pads Acting on Vertical and Horizontal Wells -- 4.4.1 Physical considerations and path orientations -- 4.4.2 Vertical well applications -- Run 1. Conductivities σv = 1.0, σh = 1.01 (vertical well) -- Run 2. Conductivities σv = 1.01, σh = 1.0 (vertical well) -- Run 3. Conductivities σv = 1, σh = 10 (vertical well) -- Run 4. Conductivities σv = 10, σh = 1 (vertical well) -- 4.4.3 Horizontal well applications -- Run 5. Conductivities σv = 1.0, σh = 1.01 (horizontal well). Run 6. Conductivities σv = 1.01, σh = 1.0 (horizontal well) -- Run 7. Conductivities σv = 1, σh = 10 (horizontal well) -- Run 8. Conductivities σv = 10, σh = 1 (horizontal well) -- 4.5 Closing Remarks -- 4.6 References -- 5 Coil Antenna Modeling for MWD Applications -- 5.1 Axisymmetric and 3D Model Validation -- 5.2 Modeling a Center-Fed Linear Dipole Transmitter Antenna -- 5.3 More Antenna Concepts -- 5.3.1 Linear dipole antennas -- 5.3.2 MWD/LWD applications - reconfigurable antennas -- 5.3.3 Fly-swatter receivers, interesting thoughts -- 5.3.3.1 Full fly-swatter computations -- 5.3.3.2 Half fly-swatter computations -- 5.4 References -- 6 What is Resistivity? -- 6.1 Resistance in Serial and Parallel Circuits, Using Classical Algebraic Approach -- 6.1.1 Series circuits -- 6.1.2 Parallel circuits -- 6.1.3 Complicated circuits -- 6.2 Resistance in Serial and Parallel Circuits, Using Differential Equation Approach -- 6.2.1 Cores arranged in series -- 6.2.2 Effective conductivity and resistivity and harmonic averaging -- 6.2.3 Cores arranged in parallel -- 6.3 Isotropy and Anisotropy in Cross-bedded Sands -- 6.3.1 Cross-bedded sands -- 6.3.2 Numerical results -- 6.4 Tool Measurements and Geological Models -- 6.5 References -- 7 Multiphase Flow and Transient Resistivity -- 7.1 Immiscible Buckley-Leverett Lineal Flows Without Capillary Pressure -- 7.1.1 Theory and mathematical modeling -- 7.1.2 Example boundary value problems -- 7.1.2.1 General initial value problem -- 7.1.2.2 General boundary value problem for infinite core -- 7.1.2.3 Mudcake-dominated invasion -- 7.1.2.4 Shock velocity -- 7.1.2.5 Pressure solution -- 7.2 Molecular Diffusion in Fluid Flows -- 7.2.1 Exact lineal flow solutions -- 7.2.2 Numerical analysis -- 7.2.3 Diffusion in cake-dominated flows -- 7.2.4 Resistivity migration -- 7.2.4.1 Lineal diffusion and undiffusion examples. 7.2.4.2 Radial diffusion and undiffusion examples -- 7.3 Immiscible Radial Flows with Capillary Pressure and Prescribed Mudcake Growth -- 7.3.1 Governing saturation equation -- 7.3.2 Numerical analysis -- 7.3.3 Fortran implementation -- 7.3.4 Typical calculations -- 7.3.5 Mudcake-dominated flows -- 7.3.6 Unshocking a saturation discontinuity -- 7.4 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth - Theory and Numerics -- 7.4.1 Flows without mudcakes -- 7.4.2 Modeling mudcake coupling -- 7.4.3 Unchanging mudcake thickness -- 7.4.4 Transient mudcake growth -- 7.4.5 General immiscible flow model -- 7.5 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth - Detailed Examples -- 7.5.1 Example 1, Single probe, infinite anisotropic media -- 7.5.2 Example 2, Single probe, three layer medium -- 7.5.3 Example 3, Dual probe pumping, three layer medium -- 7.5.4 Example 4, Straddle packer pumping -- 7.6 Simple Example in Time Lapse Logging -- 7.7 Resistivity Distributions Variable in Space and Time -- 7.7.1 Archie's Law -- 7.7.2 Closing remarks -- 7.8 References -- 8 Analytical Methods for Time Lapse Well Logging Analysis -- 8.1 Experimental Model Validation -- 8.1.1 Static filtration test procedure -- 8.1.2 Dynamic filtration testing -- 8.1.3 Measurement of mudcake properties -- 8.1.4 Formation evaluation from invasion data -- 8.1.5 Field applications -- 8.2 Characterizing Mudcake Properties -- 8.2.1 Simple extrapolation of mudcake properties -- 8.2.2 Radial mudcake growth on cylindrical filter paper -- 8.3 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination -- 8.3.1 Simple porosity determination -- 8.3.2 Radial invasion without mudcake -- 8.3.2.1 Problem 1 -- 8.3.2.2 Problem 2 -- 8.3.3 Time lapse analysis using general muds -- 8.3.3.1 Problem 1 -- 8.3.3.2 Problem 2. 8.4 Examples of Time Lapse Analysis -- 8.4.1 Formation permeability and hydrocarbon viscosity -- 8.4.2 Pore pressure, rock permeability and fluid viscosity -- 8.5 References -- Cumulative References -- Index -- About the Author -- EULA.
9781118926017
Electric resistors.
Electronic books.
TK6565.R43.C456 2017
621.38133100000005
Resistivity Modeling : Propagation, Laterolog and Micro-Pad Analysis. - 1st ed. - 1 online resource (321 pages) - Advances in Petroleum Engineering Series . - Advances in Petroleum Engineering Series .
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgements -- 1 Physics, Math and Basic Ideas -- 1.1 Background, Industry Challenges and Frustrations -- 1.2 Iterative Algorithms and Solutions -- 1.3 Direct Current Focusing from Reservoir Flow Perspective -- 1.4 General Three-Dimensional Electromagnetic Model -- 1.4.1 Example 1 - Magnetic field results -- 1.4.2 Example 2 - Electric field results -- 1.4.3 Example 3 - Anisotropic resistivity results -- 1.5 Closing Remarks -- 1.6 References -- 2 Axisymmetric Transient Models -- 2.1 Physical Ideas, Engineering Models and Numerical Approaches -- 2.1.1 Axisymmetric transient model - theory -- 2.1.2 Numerical considerations -- 2.1.2.1 Differential equation and finite difference representation -- 2.1.2.2 Matching conditions at horizontal bed layer interfaces -- 2.1.2.3 Matching conditions at radial interfaces -- 2.1.2.4 Iterative solution by row relaxation -- 2.1.3. Classic dipole solution -- 2.1.4. Additional calibration models -- 2.2 Transient Axisymmetric Coil Source Calculations -- 2.2.1 R2D-6.for calculations (200 200 constant mesh) -- 2.2.1.1 Calculation 1 with R2D-6.for (200 x 200 constant mesh) -- 2.2.1.2 Calculation 2 with R2D-6.for (200 x 200 constant mesh) -- 2.2.1.3 Calculation 3 with R2D-6.for (200 x 200 constant mesh) -- 2.2.2 R2D-6.for calculations (very large 400 x 400 constant mesh) -- 2.2.2.1 Calculation 1 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.2.2 Calculation 2 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.2.3 Calculation 3 for R2D-6.for (very large 400 x 400 constant mesh) -- 2.2.3 R2D-7-Two-Horiz-Layer-No-Collar.for calculations (very large 400 x 400 constant mesh) -- 2.2.4 R2D-7-Two-Radial-Layer-Medium-No-Collar.for calculations (very large 400 x 400 constant mesh). 2.2.5 R2D-6-GECF-MWDCollar-Larger-Mesh.for calculations (very large 400 x 400 constant mesh) -- 2.2.5.1 Frequency, 400 kHz, MWD steel collar effects -- 2.2.5.2 Frequency, 2 MHz, MWD steel collar effects -- 2.2.6 Detailed Results with R2D-6.for (200 x 200 constant mesh) -- 2.3 Effects of Frequency, from Induction, to Propagation, to Dielectric -- 2.4 Depth of Investigation -- 2.5 Closing Remarks Related to Interpretation -- 2.6 References -- 3 Steady Axisymmetric Formulations -- 3.1 Laterolog Voltage Modeling and Interpretation Approach -- 3.1.1 Direct current voltage formulation -- 3.1.2 Finite differencing in anisotropic homogeneous media -- 3.2 Current Trajectories from Streamfunction Analysis -- 3.2.1 Large cumulative errors along electric paths -- 3.2.2 Streamfunction formulation derivation -- 3.3 Voltage Calculations and Current Trajectories -- 3.3.1 Example voltage and streamline calculations -- Run 1. Conductivities σv = 1.0, σh = 1.01 -- Run 2. Conductivities vσ = 1.01, σh = 1.0 -- Run 3. Conductivities σv = 1, σh = 10 -- Run 4. Conductivities σv = 10, σh = 1 -- 3.3.2 Tool design and data interpretation -- 3.4 Current and Monitor Electrodes -- 3.5 References -- 4 Direct Current Models for Micro-Pad Devices -- 4.1 Three-Dimensional, Anisotropic, Steady Model -- 4.2 Finite Difference Approach and Subtleties -- 4.3 Row versus Column Relaxation -- 4.4. Pads Acting on Vertical and Horizontal Wells -- 4.4.1 Physical considerations and path orientations -- 4.4.2 Vertical well applications -- Run 1. Conductivities σv = 1.0, σh = 1.01 (vertical well) -- Run 2. Conductivities σv = 1.01, σh = 1.0 (vertical well) -- Run 3. Conductivities σv = 1, σh = 10 (vertical well) -- Run 4. Conductivities σv = 10, σh = 1 (vertical well) -- 4.4.3 Horizontal well applications -- Run 5. Conductivities σv = 1.0, σh = 1.01 (horizontal well). Run 6. Conductivities σv = 1.01, σh = 1.0 (horizontal well) -- Run 7. Conductivities σv = 1, σh = 10 (horizontal well) -- Run 8. Conductivities σv = 10, σh = 1 (horizontal well) -- 4.5 Closing Remarks -- 4.6 References -- 5 Coil Antenna Modeling for MWD Applications -- 5.1 Axisymmetric and 3D Model Validation -- 5.2 Modeling a Center-Fed Linear Dipole Transmitter Antenna -- 5.3 More Antenna Concepts -- 5.3.1 Linear dipole antennas -- 5.3.2 MWD/LWD applications - reconfigurable antennas -- 5.3.3 Fly-swatter receivers, interesting thoughts -- 5.3.3.1 Full fly-swatter computations -- 5.3.3.2 Half fly-swatter computations -- 5.4 References -- 6 What is Resistivity? -- 6.1 Resistance in Serial and Parallel Circuits, Using Classical Algebraic Approach -- 6.1.1 Series circuits -- 6.1.2 Parallel circuits -- 6.1.3 Complicated circuits -- 6.2 Resistance in Serial and Parallel Circuits, Using Differential Equation Approach -- 6.2.1 Cores arranged in series -- 6.2.2 Effective conductivity and resistivity and harmonic averaging -- 6.2.3 Cores arranged in parallel -- 6.3 Isotropy and Anisotropy in Cross-bedded Sands -- 6.3.1 Cross-bedded sands -- 6.3.2 Numerical results -- 6.4 Tool Measurements and Geological Models -- 6.5 References -- 7 Multiphase Flow and Transient Resistivity -- 7.1 Immiscible Buckley-Leverett Lineal Flows Without Capillary Pressure -- 7.1.1 Theory and mathematical modeling -- 7.1.2 Example boundary value problems -- 7.1.2.1 General initial value problem -- 7.1.2.2 General boundary value problem for infinite core -- 7.1.2.3 Mudcake-dominated invasion -- 7.1.2.4 Shock velocity -- 7.1.2.5 Pressure solution -- 7.2 Molecular Diffusion in Fluid Flows -- 7.2.1 Exact lineal flow solutions -- 7.2.2 Numerical analysis -- 7.2.3 Diffusion in cake-dominated flows -- 7.2.4 Resistivity migration -- 7.2.4.1 Lineal diffusion and undiffusion examples. 7.2.4.2 Radial diffusion and undiffusion examples -- 7.3 Immiscible Radial Flows with Capillary Pressure and Prescribed Mudcake Growth -- 7.3.1 Governing saturation equation -- 7.3.2 Numerical analysis -- 7.3.3 Fortran implementation -- 7.3.4 Typical calculations -- 7.3.5 Mudcake-dominated flows -- 7.3.6 Unshocking a saturation discontinuity -- 7.4 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth - Theory and Numerics -- 7.4.1 Flows without mudcakes -- 7.4.2 Modeling mudcake coupling -- 7.4.3 Unchanging mudcake thickness -- 7.4.4 Transient mudcake growth -- 7.4.5 General immiscible flow model -- 7.5 Immiscible Flows with Capillary Pressure and Dynamically Coupled Mudcake Growth - Detailed Examples -- 7.5.1 Example 1, Single probe, infinite anisotropic media -- 7.5.2 Example 2, Single probe, three layer medium -- 7.5.3 Example 3, Dual probe pumping, three layer medium -- 7.5.4 Example 4, Straddle packer pumping -- 7.6 Simple Example in Time Lapse Logging -- 7.7 Resistivity Distributions Variable in Space and Time -- 7.7.1 Archie's Law -- 7.7.2 Closing remarks -- 7.8 References -- 8 Analytical Methods for Time Lapse Well Logging Analysis -- 8.1 Experimental Model Validation -- 8.1.1 Static filtration test procedure -- 8.1.2 Dynamic filtration testing -- 8.1.3 Measurement of mudcake properties -- 8.1.4 Formation evaluation from invasion data -- 8.1.5 Field applications -- 8.2 Characterizing Mudcake Properties -- 8.2.1 Simple extrapolation of mudcake properties -- 8.2.2 Radial mudcake growth on cylindrical filter paper -- 8.3 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination -- 8.3.1 Simple porosity determination -- 8.3.2 Radial invasion without mudcake -- 8.3.2.1 Problem 1 -- 8.3.2.2 Problem 2 -- 8.3.3 Time lapse analysis using general muds -- 8.3.3.1 Problem 1 -- 8.3.3.2 Problem 2. 8.4 Examples of Time Lapse Analysis -- 8.4.1 Formation permeability and hydrocarbon viscosity -- 8.4.2 Pore pressure, rock permeability and fluid viscosity -- 8.5 References -- Cumulative References -- Index -- About the Author -- EULA.
9781118926017
Electric resistors.
Electronic books.
TK6565.R43.C456 2017
621.38133100000005