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Resistivity Modeling

Propagation, Laterolog and Micro-Pad Analysis
By Wilson C. Chin
Series: Advances in Petroleum Engineering
Copyright: 2017 2017   |   Status: Published
ISBN: 9781118925997  |  Hardcover  |  
314 pages
Price: $$225 USD
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One Line Description
A petroleum engineer well-known around the world, the author of this latest installment in the “Advances in Petroleum Engineering” series, presents cutting-edge new techniques in reservoir engineering, such as resistivity algorithms that model AC coil tool and DC laterolog and micro-pad device response, to facilitate advanced interpretation and “time lapse logging,” integrated with Darcy flow models for saturation via Archie’s law to provide general descriptions for field resistivities which vary with space and time.

Audience
Petrophysicists, well log interpretation specialists, petroleum engineers, reservoir engineers, petroleum geologists, software developers, and students, researchers and faculty in petroleum engineering


Description
Resistivity logging represents the cornerstone of modern petroleum exploration, providing a quantitative assessment of hydrocarbon bearing potential in newly discovered oilfields. Resistivity is measured using AC coil tools, as well as by focused DC laterolog and micro-pad devices, and later extrapolated, to provide oil saturation estimates related to economic productivity and cash flow. Interpretation and modeling methods, highly lucrative, are shrouded in secrecy by oil service companies – often these models are incorrect and mistakes perpetuate themselves over time.

This book develops math modeling methods for layered, anisotropic media, providing algorithms, validations and numerous examples. New electric current tracing tools are also constructed which show how well (or poorly) DC tools probe intended anisotropic formations at different dip angles. The approaches discussed provide readers with new insights into the limitations of conventional tools and methods, and offer practical and rigorous solutions to several classes of problems explored in the book.

Traditionally, Archie’s law is used to relate resistivity to water saturation, but only on small core-sample spatial scales. The second half of this book introduces methods to calculate field-wide water saturations using modern Darcy flow approaches, and then, via Archie’s law, develops field-wide resistivity distributions which may vary with time. How large-scale resistivity distributions can be used in more accurate tool interpretation and reservoir characterization is considered at length. The book also develops new methods in “time lapse logging,” where timewise changes to resistivity response (arising from fluid movements) can be used to predict rock and fluid flow properties.


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Supplementary Data
• Detailed numerical models for AC coil resistivity tools and DC laterolog and micro-pad devices
• Rigorous methods and algorithms to trace electric current lines in anisotropic media to evaluate true tool response and focusing in vertical, deviated and horizontal wells
• Predict field resistivities (which vary in space and time) by integrating resistivity and Darcy fluid flow analyses via Archie’s law
• New approaches and examples for “time lapse logging” in which fluid and rock properties are inferred from time-wise changes to resistivity response


Author / Editor Details
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.

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Table of Contents
Preface xi
Acknowledgements xvii
1 Physics, Math and Basic Ideas 1
1.1 Background, Industry Challenges and Frustrations 1
1.2 Iterative Algorithms and Solutions 2
1.3 Direct Current Focusing from Reservoir Flow Perspective 5
1.4 General Three-Dimensional Electromagnetic Model 11
1.4.1 Example 1 – Magnetic field results 15
1.4.2 Example 2 – Electric field results 16
1.4.3 Example 3 – Anisotropic resistivity results 17
1.5 Closing Remarks 25
1.6 References 25
2 Axisymmetric Transient Models 26
2.1 Physical Ideas, Engineering Models and
Numerical Approaches 27
2.1.1 Axisymmetric transient model – theory 28
2.1.2 Numerical considerations 30
2.1.2.1 Differential equation and finite
difference representation 30
2.1.2.2 Matching conditions at horizontal
bed layer interfaces 32
2.1.2.3 Matching conditions at radial interfaces 33
2.1.2.4 Iterative solution by row relaxation 34
2.1.3 Classic dipole solution 35
2.1.4 Additional calibration models 36
2.2 Transient Axisymmetric Coil Source Calculations 37
2.2.1 R2D-6.for calculations (200 × 200 constant mesh) 38
2.2.1.1 Calculation 1 with R2D-6.for
(200 × 200 constant mesh) 38
2.2.1.2 Calculation 2 with R2D-6.for
(200 × 200 constant mesh) 40
2.2.1.3 Calculation 3 with R2D-6.for
(200 × 200 constant mesh) 42
2.2.2 R2D-6.for calculations (very large
400 × 400 constant mesh) 43
2.2.2.1 Calculation 1 for R2D-6.for
(very large 400 × 400 constant mesh) 43
2.2.2.2 Calculation 2 for R2D-6.for
(very large 400 × 400 constant mesh) 46
2.2.2.3 Calculation 3 for R2D-6.for
(very large 400 × 400 constant mesh) 48
2.2.3 R2D-7-Two-Horiz-Layer-No-Collar.for
calculations (very large 400 × 400 constant mesh) 51
2.2.4 R2D-7-Two-Radial-Layer-Medium-No-Collar.for
calculations (very large 400 × 400 constant mesh) 53
2.2.5 R2D-6-GECF-MWDCollar-Larger-Mesh.for
calculations (very large 400 × 400 constant mesh) 55
2.2.5.1 Frequency, 400 kHz, MWD steel
collar effects 55
2.2.5.2 Frequency, 2 MHz, MWD steel
collar effects 55
2.2.6 Detailed Results with R2D-6.for
(200 × 200 constant mesh) 56
2.3 Effects of Frequency, from Induction, to Propagation,
to Dielectric 59
2.4 Depth of Investigation 60
2.5 Closing Remarks Related to Interpretation 61
2.6 References 63
3 Steady Axisymmetric Formulations 64
3.1 Laterolog Voltage Modeling and Interpretation Approach 65
3.1.1 Direct current voltage formulation 66
3.1.2 Finite differencing in anisotropic
homogeneous media 67
3.2 Current Trajectories from Streamfunction Analysis 68
3.2.1 Large cumulative errors along electric paths 68
3.2.2 Streamfunction formulation derivation 69
3.3 Voltage Calculations and Current Trajectories 71
3.3.1 Example voltage and streamline calculations 72
Run 1. Conductivities σv = 1.0, σh = 1.01 74
Run 2. Conductivities σv = 1.01, σh = 1.0 76
Run 3. Conductivities σv = 1, σh = 10 78
Run 4. Conductivities σv = 10, σh = 1 80
3.3.2 Tool design and data interpretation 83
3.4 Current and Monitor Electrodes 85
3.5 References 85
4 Direct Current Models for Micro-Pad Devices 86
4.1 Three-Dimensional, Anisotropic, Steady Model 87
4.2 Finite Difference Approach and Subtleties 88
4.3 Row versus Column Relaxation 88
4.4 Pads Acting on Vertical and Horizontal Wells 90
4.4.1 Physical considerations and path orientations 90
4.4.2 Vertical well applications 92
Run 1. Conductivities σv = 1.0, σh = 1.01
(vertical well) 92
Run 2. Conductivities σv = 1.01, σh = 1.0
(vertical well) 94
Run 3. Conductivities σv = 1, σh = 10
(vertical well) 96
Run 4. Conductivities σv = 10, σh = 1
(vertical well) 98
4.4.3 Horizontal well applications 100
Run 5. Conductivities σv = 1.0, σh = 1.01
(horizontal well) 100
Run 6. Conductivities σv = 1.01, σh = 1.0
(horizontal well) 102
Run 7. Conductivities σv = 1, σh = 10
(horizontal well) 104
Run 8. Conductivities σv = 10, σh = 1
(horizontal well) 106
4.5 Closing Remarks 108
4.6 References 108
5 Coil Antenna Modeling for MWD Applications 109
5.1 Axisymmetric and 3D Model Validation 109
5.2 Modeling a Center-Fed Linear Dipole
Transmitter Antenna 117
5.3 More Antenna Concepts 127
5.3.1 Linear dipole antennas 127
5.3.2 MWD/LWD applications - reconfigurable
antennas 127
5.3.3 Fly-swatter receivers, interesting thoughts 132
5.3.3.1 Full fly-swatter computations 144
5.3.3.2 Half fly-swatter computations 155
5.4 References 162
6 What is Resistivity? 163
6.1 Resistance in Serial and Parallel Circuits,
Using Classical Algebraic Approach 163
6.1.1 Series circuits 163
6.1.2 Parallel circuits 164
6.1.3 Complicated circuits 164
6.2 Resistance in Serial and Parallel Circuits,
Using Differential Equation Approach 165
6.2.1 Cores arranged in series 165
6.2.2 Effective conductivity and resistivity and
harmonic averaging 166
6.2.3 Cores arranged in parallel 166
6.3 Isotropy and Anisotropy in Cross-bedded Sands 167
6.3.1 Cross-bedded sands 167
6.3.2 Numerical results 169
6.4 Tool Measurements and Geological Models 171
6.5 References 172
7 Multiphase Flow and Transient Resistivity 173
7.1 Immiscible Buckley-Leverett Linear Flows
Without Capillary Pressure 176
7.1.1 Theory and mathematical modeling 176
7.1.2 Example boundary value problems 178
7.1.2.1 General initial value problem 178
7.1.2.2 General boundary value problem
for infinite core 179
7.1.2.3 Mudcake-dominated invasion 180
7.1.2.4 Shock velocity 181
7.1.2.5 Pressure solution 182
7.2 Molecular Diff usion in Fluid Flows 183
7.2.1 Exact lineal flow solutions 184
7.2.2 Numerical analysis 185
7.2.3 Diff usion in cake-dominated fl ows 186
7.2.4 Resistivity migration 186
7.2.4.1 Lineal diffusion and undiffusion
examples 188
7.2.4.2 Radial diffusion and undiffusion
examples 191
7.3 Immiscible Radial Flows with Capillary Pressure and
Prescribed Mudcake Growth 193
7.3.1 Governing saturation equation 193
7.3.2 Numerical analysis 195
7.3.3 Fortran implementation 196
7.3.4 Typical calculations 196
7.3.5 Mudcake-dominated fl ows 202
7.3.6 Unshocking a saturation discontinuity 205
7.4 Immiscible Flows with Capillary Pressure and
Dynamically Coupled Mudcake Growth – Th eory
and Numerics 208
7.4.1 Flows without mudcakes 208
7.4.2 Modeling mudcake coupling 215
7.4.3 Unchanging mudcake thickness 217
7.4.4 Transient mudcake growth 219
7.4.5 General immiscible fl ow model 222
7.5 Immiscible Flows with Capillary Pressure and
Dynamically Coupled Mudcake Growth –
Detailed Examples 223
7.5.1 Example 1, Single probe, infi nite
anisotropic media 224
7.5.2 Example 2, Single probe, three layer medium 227
7.5.3 Example 3, Dual probe pumping, three layer
medium 229
7.5.4 Example 4, Straddle packer pumping 231
7.6 Simple Example in Time Lapse Logging 234
7.7 Resistivity Distributions Variable in Space and Time 247
7.7.1 Archie’s Law 247
7.7.2 Closing remarks 249
7.8 References 250
8 Analytical Methods for Time Lapse Well Logging Analysis 251
8.1 Experimental Model Validation 251
8.1.1 Static filtration test procedure 251
8.1.2 Dynamic filtration testing 252
8.1.3 Measurement of mudcake properties 252
8.1.4 Formation evaluation from invasion data 253
8.1.5 Field applications 254
8.2 Characterizing Mudcake Properties 255
8.2.1 Simple extrapolation of mudcake properties 255
8.2.2 Radial mudcake growth on cylindrical
filter paper 257
8.3 Porosity, Permeability, Oil Viscosity and Pore Pressure
Determination 259
8.3.1 Simple porosity determination 260
8.3.2 Radial invasion without mudcake 260
8.3.2.1 Problem 1 262
8.3.2.2 Problem 2 264
8.3.3 Time lapse analysis using general muds 265
8.3.3.1 Problem 1 266
8.3.3.2 Problem 2 267
8.4 Examples of Time Lapse Analysis 268
8.4.1 Formation permeability and hydrocarbon
viscosity 268
8.4.2 Pore pressure, rock permeability and fl uid
viscosity 271
8.5 References 273
Cumulative References 274
Index 276
About the Author 282

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BISAC SUBJECT HEADINGS
TEC031030 : TECHNOLOGY & ENGINEERING / Power Resources / Fossil Fuels
SCI024000 : SCIENCE / Energy
MAT003000 : MATHEMATICS / Applied
 
BIC CODES
THF: Fossil fuel technologies
PHDY: Energy
TBJ: Maths for engineers

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