-
Browse Book Series
- Adhesion and Adhesives: Fundamental and Applied Aspects
- Advances in Additive Manufacturing Technologies
- Advances in Antenna, Microwave and Communication Engineering
- Advances in Biofeedstocks and Biofuels
- Advances in Cyber Security
- Advances in Data Engineering and Machine Learning
- Advances in E-Mobility
- Advances in Hydrogen Production and Storage
- Advances in Intelligent and Scientific Computing (AISC)
- Advances in Learning Analytics for Intelligent Cloud-IoT Systems
- Advances in Membrane Processes
- Advances in Nanotechnology and Applications
- Advances in Natural Gas Engineering
- Advances in Pipes and Pipelines
- Advances in Production Engineering
- Advances in Solar Cell Materials and Storage
- Applied Functional Materials
- Artificial Intelligence and Soft Computing for Industrial Transformation
- Astrobiology Perspectives on Life in the Universe
- Bioprocessing in Food Science
- Computational Intelligence and Biomedical Engineering
- Concise Introductions to AI and Data Science
- Cyber Systems and Quantum Engineering
- Decentralized Systems and Next-Generation Internet
- Diatoms: Biology and Applications
- Digital Convergence in Engineering Systems
- Emerging Trends in Medicinal and Pharmaceutical Chemistry
- Engineering Systems Design for Sustainable Development
- Fintech in a Sustainable Digital Society
- Industry 5.0 Transformation Applications
- Infectious and Rare Diseases
- Innovations in Materials and Manufacturing
- Machine Learning in Biomedical Science and Healthcare Informatics
- Materials Degradation and Failure
- Mathematics and Computer Science
- Next-Generation Computing and Communication Engineering
- Performability Engineering Series
- Rotating Machinery Fundamentals and Advances
- Studies in Computational Intelligence and Smart Technologies
- Sustainable Computing and Optimization
Browse Subject Areas
For Authors
Submit a ProposalFormation Testing
 | Pressure Transient and Contamination Analysis By Wilson Chin, Yanmin Zhou, Yongren Feng, Qiang Yu, and Lixin Zhao Copyright: 2014 | Status: Published ISBN: 9781118831137 | Hardcover | 479 pages Price: $195 USD  |
One Line Description
This is the only book available to the reservoir or petroleum engineer covering formation testing algorithms for wireline and LWD reservoir analysis that are developed for transient pressure, contamination modeling, permeability, and pore pressure prediction.
Audience
Petroleum engineers; Reservoir engineers; Petroleum geologists; Professors, researchers and students in university Petroleum Engineering programs.
Petroleum engineers; Reservoir engineers; Petroleum geologists; Professors, researchers and students in university Petroleum Engineering programs.
Description
Traditional well logging methods, such as resistivity, acoustic, nuclear and NMR, provide indirect information related to fluid and formation properties. The “formation tester,” offered in wireline and MWD/LWD operations, is different. It collects actual downhole fluid samples for surface analysis, and through pressure transient analysis, provides direct measurements for pore pressure, mobility, permeability and anisotropy. These are vital to real-time drilling safety, geosteering, hydraulic fracturing and economic analysis.
Methods for formation testing analysis, while commercially important and accounting for a substantial part of service company profits, however, are shrouded in secrecy. Unfortunately, many are poorly constructed, and because details are not available, industry researchers are not able to improve upon them. This new book explains conventional models and develops new, more powerful algorithms for early-time analysis, and importantly, addresses a critical area in sampling related to “time required to pump clean samples” using rigorous multiphase flow techniques. All of the methods are explained in complete detail. Equations are offered for users to incorporate in their own models, but convenient, easy-to-use software is available for those needing immediate answers.
The leading author is a well known petrophysicist, with hands-on experience at Schlumberger, Halliburton, BP Exploration and other companies. His work is used commercially at major oil service companies, and important extensions to his formation testing models have been supported by prestigious grants from the United States Department of Energy. His new collaboration with China National Offshore Oil Corporation marks an important turning point, where advanced simulation models and hardware are evolving side-by-side to define a new generation of formation testing logging instruments. The present book provides more than formulations and solutions: it offers a close look at formation tester development “behind the scenes,” as the China National Offshore Oil Corporation opens up its research, engineering and manufacturing facilities through a collection of interesting photographs to show how formation testing tools are developed from start to finish.
Back to Top
Traditional well logging methods, such as resistivity, acoustic, nuclear and NMR, provide indirect information related to fluid and formation properties. The “formation tester,” offered in wireline and MWD/LWD operations, is different. It collects actual downhole fluid samples for surface analysis, and through pressure transient analysis, provides direct measurements for pore pressure, mobility, permeability and anisotropy. These are vital to real-time drilling safety, geosteering, hydraulic fracturing and economic analysis.
Methods for formation testing analysis, while commercially important and accounting for a substantial part of service company profits, however, are shrouded in secrecy. Unfortunately, many are poorly constructed, and because details are not available, industry researchers are not able to improve upon them. This new book explains conventional models and develops new, more powerful algorithms for early-time analysis, and importantly, addresses a critical area in sampling related to “time required to pump clean samples” using rigorous multiphase flow techniques. All of the methods are explained in complete detail. Equations are offered for users to incorporate in their own models, but convenient, easy-to-use software is available for those needing immediate answers.
The leading author is a well known petrophysicist, with hands-on experience at Schlumberger, Halliburton, BP Exploration and other companies. His work is used commercially at major oil service companies, and important extensions to his formation testing models have been supported by prestigious grants from the United States Department of Energy. His new collaboration with China National Offshore Oil Corporation marks an important turning point, where advanced simulation models and hardware are evolving side-by-side to define a new generation of formation testing logging instruments. The present book provides more than formulations and solutions: it offers a close look at formation tester development “behind the scenes,” as the China National Offshore Oil Corporation opens up its research, engineering and manufacturing facilities through a collection of interesting photographs to show how formation testing tools are developed from start to finish.
Back to Top
Author / Editor Details
Wilson C. Chin, who earned his Ph.D. from M.I.T. and M.Sc. from Caltech, heads Stratamagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering and managed pressure drilling. He is the author of ten books, more than one hundred papers and over forty patents.
Wilson C. Chin, who earned his Ph.D. from M.I.T. and M.Sc. from Caltech, heads Stratamagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering and managed pressure drilling. He is the author of ten books, more than one hundred papers and over forty patents.
Yanmin Zhou received her Ph.D. in Geological Resources Engineering from the University of Petroleum, Beijing, and serves as Geophysics Engineer at the China National Offshore Oil Corporation.
Yongren Feng is Chief Mechanical Engineer at the China National Offshore Oil Corporation with three decades of design experience covering a dozen logging tools. With more than one hundred patents, he serves as Project Leader for the 12th National Five Year Plan in formation tester development, and he was elected as one of China’s National Technology and Innovation Leaders.
Qiang Yu earned his M.Sc. in Measurement Technology and Instrumentation from Xi'an Shiyou University and serves as Senior Control Engineer in formation testing and field operations. He is an Associate Project Leader with the China National Offshore Oil Corporation in the national formation testing program.
Lixin Zhao earned his Ph.D. from the University of Petroleum, Beijing and serves as Senior Petrophysical Scientist, with three decades of logging and formation evaluation experience.
Back to Top
Table of Contents
Opening Message
Preface xxi
Acknowledgements xxvii
Part 1 Modern Ideas in Job Planning and Execution
1. Basic Ideas, Challenges and Developments 1
1.1 Background and introduction 1
1.2 Existing models, implicit assumptions and limitations 6
1.2.1 Exponential tight zone approximation 7
1.2.2 Permeability and anisotropy from steady-state
dual-probe data 8
1.2.3 Three-probe, vertical well interpretation method 9
1.2.4 Gas pumping 10
1.2.5 Material balance method 10
1.2.6 Conventional three-dimensional numerical
models 12
1.2.7 Uniform fl ux dual packer models 13
1.3 Tool development, testing and deployment --role of
modeling and behind the scenes -- at CNOOC/COSL 15
1.3.1 Engineering analysis, design challenges,
solutions 15
1.3.2 From physics to math to engineering --inverse
problem formulation 15
1.3.2.1 Simplified theoretical model 16
1.3.2.2 More detailed finite element model 17
1.3.3 Design chronicle --people, places and things 18
1.3.4 Bohai Bay activities 25
1.3.5 Middle East operations 28
1.4 Book objectives and presentation plan 29
1.5 References 32
2. Forward Pressure and Contamination Analysis in
Single and Multiphase Compressible Flow 34
2.1 Single-phase source fl ow models 34
2.1.1 Qualitative effects of storage and skin 37
2.2 Dual packer and dual probe fl ows 40
2.2.1 A detailed calculation 41
2.3 Supercharging, mudcake growth and pressure
interpretation 45
2.3.1 Supercharge numerical simulation 46
2.3.2 Industry perspectives on buildup versus
drawdown, -- 46
2.4 Boundary and azimuthal effects in horizontal wells 48
2.5 Contamination clean-up at the source probe 49
2.6 Sampling-while-drilling tools and clean-up efficiency 51
2.6.1 What happens with very short invasion times 51
2.6.2 What happens with longer invasion times 52
2.7 References 55
3. Inverse Methods for Permeability, Anisotropy and
Formation Boundary Effects Assuming Liquids 56
3.1 New inverse methods summary 56
3.2 New inverse modeling capabilities 57
3.2.1 Module FT-00 58
3.2.2 Module FT-01 60
3.2.3 Module FT-03 60
3.2.4 Module FT-PTA-DDBU 61
3.3 Inverse examples --dip angle, multivalued
solutions and skin 62
3.3.1 Forward model, Module FT-00 62
3.3.2 Inverse model, Module FT-01 --multivalued
solutions 64
3.3.3 Effects of dip angle --detailed calculations 65
3.3.4 Inverse pulse interaction -- approach for low
permeability zones 68
3.4 Computational notes on complex complementary
error function evaluation 70
3.5 Source model --analytical and physical limitations 72
3.6 Full three-dimensional transient Darcy fl ow model
for horizontal wells 72
3.7 Phase delay inverse method and electromagnetic
analogy 75
3.8 Source model applications to dual packers 76
3.9 Closing remarks 76
3.10 References 77
Part II Math Models, Results and Detailed Examples
4. Multiphase Flow and Contamination --Transient Immiscible
and Miscible Modeling with Fluid Compressibility 78
4.1 Invasion, supercharging and multiphase pumping 79
4.1.1 Invasion and pumping description 79
4.1.2 Job planning considerations 82
4.1.3 Mathematical modeling challenges 83
4.1.4 Simulation objectives 84
4.1.5 Math modeling overview 85
4.2 Mathematical formulation and numerical solution 86
4.2.1 Immiscible fl ow equations 86
4.2.1.1 Finite differences, explicit versus
implicit 88
4.2.1.2 Formation tester ADI -- implementation 89
4.2.1.3 Mudcake growth, formation coupling,
supercharging 90
4.2.1.4 Pumpout model for single-probe pad
nozzles 93
4.2.1.5 Dual-probe and dual packer
surface logic 94
4.3 Miscible fl ow formulation 96
4.3.1 Miscible flow numerical solution 97
4.4 Three-dimensional fl ow extensions 97
4.5 Computational implementation for azimuthal effects 98
4.6 Modeling long-time invasion and mudcake scrape-off 99
4.7 Software features 99
4.8 Calculated miscible fl ow pressures and concentrations 100
4.8.1 Example 1. Single probe, infi nite anisotropic
media 101
4.8.2 Example 2. Single probe, three layer medium 107
4.8.3 Example 3. Dual probe pumping, three
layer medium 108
4.8.4 Example 4. Straddle packer pumping 110
4.8.5 Example 5. Formation fl uid viscosity imaging 112
4.8.6 Example 6. Contamination modeling 113
4.8.7 Example 7. Multi-rate pumping simulation 113
4.8.8 Example 8. More detailed clean-up application 114
4.9 Calculated immiscible fl ow clean-up examples 116
4.9.1 Example 9. Higher permeability anisotropic
formation 116
4.9.2 Example 10. Pressure transient modeled 117
4.10 Closing remarks 118
4.11 References 119
5. Exact Pressure Transient Analysis for Liquids in
Anisotropic Homogeneous Media, Including Flowline
Storage Effects, With and Without Skin at Arbitrary
Dip Angles 121
5.1 Background and objectives 122
5.1.1 Detailed literature review and history 122
5.1.2 Recent 1990s developments 123
5.1.3 Modeling background and basics 125
5.1.4 New developments 127
5.2 Detailed pressure transient examples (twenty!) --
competing effects of nisotropy, skin, dip and
fl owline storage 130
5.3 Software operational details and user interface 146
5.4 Closing remarks 156
Contents xi
5.5 Appendix --Mathematical model and numerical
implementation 159
5.5.1 Isotropic spherical fl ow with storage and
no skin 159
5.5.1.1 Physical and mathematical formulation 160
5.5.1.2 General dimensionless representation 160
5.5.1.3 Exact solution using Laplace transforms 161
5.5.1.4 Constant rate drawdown and buildup 162
5.5.1.5 Practical implications 163
5.5.1.6 Surface plot of exact solution 164
5.5.1.7 Early time series solution 165
5.5.1.8 Large time asymptotic solution 165
5.5.1.9 Arbitrary volume flowrate 166
5.5.2 Anisotropic ellipsoidal flow with storage
and no skin 168
5.5.2.1 Defi ning effective permeability 168
5.5.2.2 Complete physical and mathematical
formulation 168
5.5.2.3 Simplifying the differential equation 169
5.5.2.4 Total velocity through ellipsoidal
surfaces 170
5.5.2.5 Pressure formulation 172
5.5.2.6 Volume fl owrate formulation 172
5.5.3 Isotropic spherical fl ow with storage and skin 175
5.5.3.1 Mathematical model of skin from fi rst
principles 176
5.5.3.2 Skin extensions to storage only --
pressure model 176
5.5.3.3 Exact pressure transient solutions
via Laplace transforms 178
5.5.3.4 Explicit and exact time domain solutions 179
5.5.3.5 More general pressure results away
from the source probe 179
5.5.4 Anisotropic ellipsoidal fl ow with storage and skin 180
5.5.4.1 Skin model in multi-dimensional
anisotropic fl ow 180
xii Contents
5.5.4.2 Implicit assumptions related to
formation permeability 181
5.5.4.3 General boundary value problem
formulation 183
5.5.5 Numerical issues and algorithm refi nements 184
5.5.5.1 Complex complementary error function 184
5.5.5.2 Real function methods for FTWD
analysis 187
5.5.5.3 Skin model and mathematical
anomalies 190
5.5.5.4 Multi-rate drawdown schedules 191
5.5.6 References 194
6. Permeability Interpretation for Liquids in Anisotropic
Media,Including Flowline Storage Effects, With and
Without Skin at Arbitrary Dip Angles 196
6.1 Six new inverse methods summarized 196
6.2 Existing inverse methods and limitations 198
6.3 Permeability anisotropy theory without skin
(ellipsoidal source) 201
6.3.1 Steady pressure drop formulas at arbitrary dip 201
6.3.2 Isotropic permeability prediction 202
6.3.3 Anisotropic media, vertical wells, zero
dip angle 202
6.3.4 Anisotropic media with arbitrary dip angle 203
6.3.5 Nearly vertical wells, small dip angle
approximation 205
6.3.6 Horizontal wells, large dip angle
approximation 205
6.3.7 General dip angle, kh equation, exact algebraic
solution 205
6.3.8 General dip angles, kv/kh equation 206
6.3.9 Dip angle and algebraic structure 207
6.3.10 Azimuthally and generally offset probes 207
6.3.11 Complementary early time analysis 208
6.4 Zero skin permeability prediction examples
(ellipsoidal source) 209
6.5 Permeability anisotropy with skin effects
(ellipsoidal source) 217
6.5.1 Exact steady-state pressure and skin solutions 217
6.5.2 Exact early time pressure and skin relationship 218
6.5.3 Numerical algorithm for non-zero skin problems 219
6.6 Non-zero skin permeability prediction examples
(ellipsoidal source) 219
6.7 Low permeability pulse interference testing
(ellipsoidal source) -- getting results with short
test times 225
6.7.1 Faster pressure testing in the fi eld 226
6.7.2 Non-zero skin permeability prediction
examples 227
6.7.3 Pulse interaction method for single-probe tools 232
6.7.4 Dual-probe pulse interaction methods 232
6.7.5 Zero skin permeability prediction examples 232
6.8 Fully three-dimensional inverse methods 238
6.9 Software interface for steady inverse methods
(ellipsoidal source) 245
6.9.1 Pumping modes and error checking 245
6.9.2 Zero-skin and non-zero skin modes 247
6.9.3 Zero-skin mode 247
6.9.4 Non-zero skin model 249
6.10 Formation testing while drilling (FTWD) 251
6.10.1 Pressure transient drawdown-buildup
approach 251
6.10.2 Interpretation in low mobility, high fl owline
storage environments 251
6.10.3 Multiple pretests, modeling and interpretation 253
6.10.4 Reverse fl ow injection processes 257
6.10.4.1 Conventional fl uid withdrawal,
drawdown-then-buildup 257
6.10.4.2 Reverse fl ow injection process,
buildup-then-drawdown 261
6.10.5 Best practices --data acquisition and processing 266
6.11 Closing remarks 271
6.12 References 273
7. Three-Dimensional Pads and Dual Packers on Real Tools
with Flowline Storage in Layered Anisotropic Media for
Horizontal Well Single-Phase Liquid and Gas Flows 274
7.1 Pad and dual pad models for horizontal well
application 274
7.1.1 Practical modeling applications 276
7.1.2 Prior pressure transient models 279
7.1.3 Specifi c research and software objectives 279
7.2 Fundamental ideas in fi nite difference modeling 280
7.2.1 Finite differencing in space and time 281
7.2.2 Explicit schemes 281
7.2.3 Implicit procedures 282
7.2.4 Tridiagonal matrixes 283
7.2.5 Grid generation, modern ideas and methods 283
7.2.6 Detailed math modeling objectives 285
7.3 Mathematical formulation and geometric
transformations 286
7.3.1 Pressure partial differential equations 286
7.3.1.1 Geometric domain transformations 286
7.3.1.2 Alternating-direction-implicit method 288
7.3.2 Velocity and volume fl ow rate boundary
conditions 293
7.3.2.1 General velocity transforms 293
7.3.2.2 Zero fl ow at solid borehole surfaces 294
7.3.2.3 Zero fl ow at horizontal barriers 294
7.3.2.4 Pad-nozzle boundary conditions 295
7.3.2.5 Straddle packer or dual packer source
boundary conditions 296
7.3.2.6 Dual-probe pad boundary conditions 298
7.3.3 Numerical curvilinear grid generation 299
7.3.3.1 Fundamental grid generation ideas 299
7.3.3.2 Fast and stable iterative solutions 302
7.4 Meshing algorithm construction details 303
7.5 Three-dimensional calculations and validations 306
7.5.1 Suite 1. Circular well validations 306
7.5.2 Suite 2. Modeling zero radial fl ow at sealed
borehole surface 309
7.5.3 Suite 3. Modeling real pumpouts (high
permeability) 311
7.5.4 Suite 4. Modeling real pumpouts (low
permeability) 315
7.5.5 Suite 5. Modeling real pumpouts (low
permeability and fl owline storage) 318
7.5.6 Suite 6. Modeling real pumpouts (variable
fl ow rates) 320
7.5.7 Suite 7. Modeling anisotropy with azimuthally
displaced sources 322
7.5.8 Suite 8. Modeling anisotropy with diametrically
opposed probes 327
7.5.9 Suite 9. Reservoir engineering production
forecasting 329
7.5.10 Suite 10. Straddle packer fl ow modeling 329
7.6 User interface and extended capabilities 330
7.6.1 Extended simulation capabilities 332
7.7 Closing remarks 335
7.8 References 336
8. Gas Pumping: Forward and Inverse Methods in Anisotropic
Media at Arbitrary Dip Angles for Point Source, Straddle
Packer and Real Nozzles 337
8.1 Gas reservoir pumping basics and modeling objectives 338
8.1.1 Single-phase sampling 338
8.1.2 Pad nozzle versus dual packer usage 338
8.1.3 General transient flowrate pumping 339
8.2 Direct and inverse formulations for ellipsoidal source 340
8.2.1 Governing gas fl ow equations 340
8.2.2 Similarity transform 342
8.3 Ellipsoidal source --exact steady forward and inverse
solutions 343
8.3.1 Exact, steady, forward formulation 343
8.3.2 Exact, steady, forward solution at source and
observation points 344
8.3.3 Exact, steady, inverse formulation and solutions 346
8.4 Special analytical results 347
8.4.1 Liquid fl ow, check limit 347
8.4.2 Isothermal gas expansion, all dip angles 347
8.4.3 Vertical wells, all m -- (thermodynamic) values 348
8.4.4 Horizontal wells, all m -- (thermodynamic)
values 348
8.5 Direct solver, solution procedure 349
8.6 Forward model gas calculations 350
8.7 Second-order schemes 353
8.8 Inverse solver, solution software 353
8.9 Inverse gas calculations 355
8.10 Ellipsoidal source --fully transient numerical
solutions for gases and liquids 358
8.10.1 Transient fl ow modeling 359
8.10.2 Finite difference equation 360
8.10.3 Boundary conditions --modeling fl owline
storage with and without skin effects 361
8.10.4 Detailed time integration scheme 362
8.10.5 Observation probe response 362
8.10.6 Software interface and example calculations 363
8.10.7 Source formulation limitations 368
8.11 Transient source pulse interaction inverse method 369
8.11.1 Pulse interaction, procedure at nonzero
dip angle 369
8.12 Ring source, layered model for vertical wells 372
8.12.1 Source model limitations and refi nement 372
8.12.2 Finite difference method 372
8.12.3 Alternating-direction-implicit integration 373
8.12.4 Formation tester nozzle as a simple ring source 375
8.12.5 Pad nozzle pumpout boundary condition 376
8.12.6 Dual probe and dual packer surface logic 377
8.12.7 Detailed boundary condition implementation 377
8.12.8 Example calculations 378
8.13 Pad nozzle and dual packer sources for
horizontal wells 381
8.14 Application to modern gas reservoir characterization 383
8.15 References 383
9. Three-Dimensional Phase Delay Response in Layered
Anisotropic Media with Dip 385
9.1 Basic phase delay and amplitude attenuation ideas 385
9.1.1 Isotropic uniform media 385
9.1.2 Anisotropic homogeneous media 386
9.2 Layered model formulation 387
9.2.1 Homogeneous medium, basic mathematical
ideas 387
9.2.2 Boundary value problem for complex pressure 389
9.2.3 Iterative numerical solution to general
formulation 389
9.2.4 Successive line over relaxation procedure 390
9.2.5 Advantages of the scheme 391
9.2.6 Extensions to multiple layers 391
9.2.7 Extensions to complete formation
heterogeneity 392
9.3 Phase delay software interface 392
9.3.1 Output fi le notes 394
9.3.2 Special user features 395
9.4 Detailed phase delay results in layered
anisotropic media 396
9.5 Closing remarks --extensions and additional
applications 404
9.5.1 Inverse model in uniform anisotropic media 404
9.5.2 Inverse model in layered media 404
9.5.3 Variable gridding 405
9.5.4 Other physical models 405
9.6 References 406
Part III Consulting Services and Advanced Software
Consulting services and advanced software 407
Module FT-00 408
Module FT-01 410
Module FT-02 412
Module FT-03 414
Module FT-04 418
Module FT-05 420
xviii Contents
Module FT-06 421
Module FT-07 423
Module FT-PTA-DDBU 425
Part IV Cumulative References, Index and Author Contact
Cumulative References 426
Index 431
About the Authors
Back to Top
Opening Message
Preface xxi
Acknowledgements xxvii
Part 1 Modern Ideas in Job Planning and Execution
1. Basic Ideas, Challenges and Developments 1
1.1 Background and introduction 1
1.2 Existing models, implicit assumptions and limitations 6
1.2.1 Exponential tight zone approximation 7
1.2.2 Permeability and anisotropy from steady-state
dual-probe data 8
1.2.3 Three-probe, vertical well interpretation method 9
1.2.4 Gas pumping 10
1.2.5 Material balance method 10
1.2.6 Conventional three-dimensional numerical
models 12
1.2.7 Uniform fl ux dual packer models 13
1.3 Tool development, testing and deployment --role of
modeling and behind the scenes -- at CNOOC/COSL 15
1.3.1 Engineering analysis, design challenges,
solutions 15
1.3.2 From physics to math to engineering --inverse
problem formulation 15
1.3.2.1 Simplified theoretical model 16
1.3.2.2 More detailed finite element model 17
1.3.3 Design chronicle --people, places and things 18
1.3.4 Bohai Bay activities 25
1.3.5 Middle East operations 28
1.4 Book objectives and presentation plan 29
1.5 References 32
2. Forward Pressure and Contamination Analysis in
Single and Multiphase Compressible Flow 34
2.1 Single-phase source fl ow models 34
2.1.1 Qualitative effects of storage and skin 37
2.2 Dual packer and dual probe fl ows 40
2.2.1 A detailed calculation 41
2.3 Supercharging, mudcake growth and pressure
interpretation 45
2.3.1 Supercharge numerical simulation 46
2.3.2 Industry perspectives on buildup versus
drawdown, -- 46
2.4 Boundary and azimuthal effects in horizontal wells 48
2.5 Contamination clean-up at the source probe 49
2.6 Sampling-while-drilling tools and clean-up efficiency 51
2.6.1 What happens with very short invasion times 51
2.6.2 What happens with longer invasion times 52
2.7 References 55
3. Inverse Methods for Permeability, Anisotropy and
Formation Boundary Effects Assuming Liquids 56
3.1 New inverse methods summary 56
3.2 New inverse modeling capabilities 57
3.2.1 Module FT-00 58
3.2.2 Module FT-01 60
3.2.3 Module FT-03 60
3.2.4 Module FT-PTA-DDBU 61
3.3 Inverse examples --dip angle, multivalued
solutions and skin 62
3.3.1 Forward model, Module FT-00 62
3.3.2 Inverse model, Module FT-01 --multivalued
solutions 64
3.3.3 Effects of dip angle --detailed calculations 65
3.3.4 Inverse pulse interaction -- approach for low
permeability zones 68
3.4 Computational notes on complex complementary
error function evaluation 70
3.5 Source model --analytical and physical limitations 72
3.6 Full three-dimensional transient Darcy fl ow model
for horizontal wells 72
3.7 Phase delay inverse method and electromagnetic
analogy 75
3.8 Source model applications to dual packers 76
3.9 Closing remarks 76
3.10 References 77
Part II Math Models, Results and Detailed Examples
4. Multiphase Flow and Contamination --Transient Immiscible
and Miscible Modeling with Fluid Compressibility 78
4.1 Invasion, supercharging and multiphase pumping 79
4.1.1 Invasion and pumping description 79
4.1.2 Job planning considerations 82
4.1.3 Mathematical modeling challenges 83
4.1.4 Simulation objectives 84
4.1.5 Math modeling overview 85
4.2 Mathematical formulation and numerical solution 86
4.2.1 Immiscible fl ow equations 86
4.2.1.1 Finite differences, explicit versus
implicit 88
4.2.1.2 Formation tester ADI -- implementation 89
4.2.1.3 Mudcake growth, formation coupling,
supercharging 90
4.2.1.4 Pumpout model for single-probe pad
nozzles 93
4.2.1.5 Dual-probe and dual packer
surface logic 94
4.3 Miscible fl ow formulation 96
4.3.1 Miscible flow numerical solution 97
4.4 Three-dimensional fl ow extensions 97
4.5 Computational implementation for azimuthal effects 98
4.6 Modeling long-time invasion and mudcake scrape-off 99
4.7 Software features 99
4.8 Calculated miscible fl ow pressures and concentrations 100
4.8.1 Example 1. Single probe, infi nite anisotropic
media 101
4.8.2 Example 2. Single probe, three layer medium 107
4.8.3 Example 3. Dual probe pumping, three
layer medium 108
4.8.4 Example 4. Straddle packer pumping 110
4.8.5 Example 5. Formation fl uid viscosity imaging 112
4.8.6 Example 6. Contamination modeling 113
4.8.7 Example 7. Multi-rate pumping simulation 113
4.8.8 Example 8. More detailed clean-up application 114
4.9 Calculated immiscible fl ow clean-up examples 116
4.9.1 Example 9. Higher permeability anisotropic
formation 116
4.9.2 Example 10. Pressure transient modeled 117
4.10 Closing remarks 118
4.11 References 119
5. Exact Pressure Transient Analysis for Liquids in
Anisotropic Homogeneous Media, Including Flowline
Storage Effects, With and Without Skin at Arbitrary
Dip Angles 121
5.1 Background and objectives 122
5.1.1 Detailed literature review and history 122
5.1.2 Recent 1990s developments 123
5.1.3 Modeling background and basics 125
5.1.4 New developments 127
5.2 Detailed pressure transient examples (twenty!) --
competing effects of nisotropy, skin, dip and
fl owline storage 130
5.3 Software operational details and user interface 146
5.4 Closing remarks 156
Contents xi
5.5 Appendix --Mathematical model and numerical
implementation 159
5.5.1 Isotropic spherical fl ow with storage and
no skin 159
5.5.1.1 Physical and mathematical formulation 160
5.5.1.2 General dimensionless representation 160
5.5.1.3 Exact solution using Laplace transforms 161
5.5.1.4 Constant rate drawdown and buildup 162
5.5.1.5 Practical implications 163
5.5.1.6 Surface plot of exact solution 164
5.5.1.7 Early time series solution 165
5.5.1.8 Large time asymptotic solution 165
5.5.1.9 Arbitrary volume flowrate 166
5.5.2 Anisotropic ellipsoidal flow with storage
and no skin 168
5.5.2.1 Defi ning effective permeability 168
5.5.2.2 Complete physical and mathematical
formulation 168
5.5.2.3 Simplifying the differential equation 169
5.5.2.4 Total velocity through ellipsoidal
surfaces 170
5.5.2.5 Pressure formulation 172
5.5.2.6 Volume fl owrate formulation 172
5.5.3 Isotropic spherical fl ow with storage and skin 175
5.5.3.1 Mathematical model of skin from fi rst
principles 176
5.5.3.2 Skin extensions to storage only --
pressure model 176
5.5.3.3 Exact pressure transient solutions
via Laplace transforms 178
5.5.3.4 Explicit and exact time domain solutions 179
5.5.3.5 More general pressure results away
from the source probe 179
5.5.4 Anisotropic ellipsoidal fl ow with storage and skin 180
5.5.4.1 Skin model in multi-dimensional
anisotropic fl ow 180
xii Contents
5.5.4.2 Implicit assumptions related to
formation permeability 181
5.5.4.3 General boundary value problem
formulation 183
5.5.5 Numerical issues and algorithm refi nements 184
5.5.5.1 Complex complementary error function 184
5.5.5.2 Real function methods for FTWD
analysis 187
5.5.5.3 Skin model and mathematical
anomalies 190
5.5.5.4 Multi-rate drawdown schedules 191
5.5.6 References 194
6. Permeability Interpretation for Liquids in Anisotropic
Media,Including Flowline Storage Effects, With and
Without Skin at Arbitrary Dip Angles 196
6.1 Six new inverse methods summarized 196
6.2 Existing inverse methods and limitations 198
6.3 Permeability anisotropy theory without skin
(ellipsoidal source) 201
6.3.1 Steady pressure drop formulas at arbitrary dip 201
6.3.2 Isotropic permeability prediction 202
6.3.3 Anisotropic media, vertical wells, zero
dip angle 202
6.3.4 Anisotropic media with arbitrary dip angle 203
6.3.5 Nearly vertical wells, small dip angle
approximation 205
6.3.6 Horizontal wells, large dip angle
approximation 205
6.3.7 General dip angle, kh equation, exact algebraic
solution 205
6.3.8 General dip angles, kv/kh equation 206
6.3.9 Dip angle and algebraic structure 207
6.3.10 Azimuthally and generally offset probes 207
6.3.11 Complementary early time analysis 208
6.4 Zero skin permeability prediction examples
(ellipsoidal source) 209
6.5 Permeability anisotropy with skin effects
(ellipsoidal source) 217
6.5.1 Exact steady-state pressure and skin solutions 217
6.5.2 Exact early time pressure and skin relationship 218
6.5.3 Numerical algorithm for non-zero skin problems 219
6.6 Non-zero skin permeability prediction examples
(ellipsoidal source) 219
6.7 Low permeability pulse interference testing
(ellipsoidal source) -- getting results with short
test times 225
6.7.1 Faster pressure testing in the fi eld 226
6.7.2 Non-zero skin permeability prediction
examples 227
6.7.3 Pulse interaction method for single-probe tools 232
6.7.4 Dual-probe pulse interaction methods 232
6.7.5 Zero skin permeability prediction examples 232
6.8 Fully three-dimensional inverse methods 238
6.9 Software interface for steady inverse methods
(ellipsoidal source) 245
6.9.1 Pumping modes and error checking 245
6.9.2 Zero-skin and non-zero skin modes 247
6.9.3 Zero-skin mode 247
6.9.4 Non-zero skin model 249
6.10 Formation testing while drilling (FTWD) 251
6.10.1 Pressure transient drawdown-buildup
approach 251
6.10.2 Interpretation in low mobility, high fl owline
storage environments 251
6.10.3 Multiple pretests, modeling and interpretation 253
6.10.4 Reverse fl ow injection processes 257
6.10.4.1 Conventional fl uid withdrawal,
drawdown-then-buildup 257
6.10.4.2 Reverse fl ow injection process,
buildup-then-drawdown 261
6.10.5 Best practices --data acquisition and processing 266
6.11 Closing remarks 271
6.12 References 273
7. Three-Dimensional Pads and Dual Packers on Real Tools
with Flowline Storage in Layered Anisotropic Media for
Horizontal Well Single-Phase Liquid and Gas Flows 274
7.1 Pad and dual pad models for horizontal well
application 274
7.1.1 Practical modeling applications 276
7.1.2 Prior pressure transient models 279
7.1.3 Specifi c research and software objectives 279
7.2 Fundamental ideas in fi nite difference modeling 280
7.2.1 Finite differencing in space and time 281
7.2.2 Explicit schemes 281
7.2.3 Implicit procedures 282
7.2.4 Tridiagonal matrixes 283
7.2.5 Grid generation, modern ideas and methods 283
7.2.6 Detailed math modeling objectives 285
7.3 Mathematical formulation and geometric
transformations 286
7.3.1 Pressure partial differential equations 286
7.3.1.1 Geometric domain transformations 286
7.3.1.2 Alternating-direction-implicit method 288
7.3.2 Velocity and volume fl ow rate boundary
conditions 293
7.3.2.1 General velocity transforms 293
7.3.2.2 Zero fl ow at solid borehole surfaces 294
7.3.2.3 Zero fl ow at horizontal barriers 294
7.3.2.4 Pad-nozzle boundary conditions 295
7.3.2.5 Straddle packer or dual packer source
boundary conditions 296
7.3.2.6 Dual-probe pad boundary conditions 298
7.3.3 Numerical curvilinear grid generation 299
7.3.3.1 Fundamental grid generation ideas 299
7.3.3.2 Fast and stable iterative solutions 302
7.4 Meshing algorithm construction details 303
7.5 Three-dimensional calculations and validations 306
7.5.1 Suite 1. Circular well validations 306
7.5.2 Suite 2. Modeling zero radial fl ow at sealed
borehole surface 309
7.5.3 Suite 3. Modeling real pumpouts (high
permeability) 311
7.5.4 Suite 4. Modeling real pumpouts (low
permeability) 315
7.5.5 Suite 5. Modeling real pumpouts (low
permeability and fl owline storage) 318
7.5.6 Suite 6. Modeling real pumpouts (variable
fl ow rates) 320
7.5.7 Suite 7. Modeling anisotropy with azimuthally
displaced sources 322
7.5.8 Suite 8. Modeling anisotropy with diametrically
opposed probes 327
7.5.9 Suite 9. Reservoir engineering production
forecasting 329
7.5.10 Suite 10. Straddle packer fl ow modeling 329
7.6 User interface and extended capabilities 330
7.6.1 Extended simulation capabilities 332
7.7 Closing remarks 335
7.8 References 336
8. Gas Pumping: Forward and Inverse Methods in Anisotropic
Media at Arbitrary Dip Angles for Point Source, Straddle
Packer and Real Nozzles 337
8.1 Gas reservoir pumping basics and modeling objectives 338
8.1.1 Single-phase sampling 338
8.1.2 Pad nozzle versus dual packer usage 338
8.1.3 General transient flowrate pumping 339
8.2 Direct and inverse formulations for ellipsoidal source 340
8.2.1 Governing gas fl ow equations 340
8.2.2 Similarity transform 342
8.3 Ellipsoidal source --exact steady forward and inverse
solutions 343
8.3.1 Exact, steady, forward formulation 343
8.3.2 Exact, steady, forward solution at source and
observation points 344
8.3.3 Exact, steady, inverse formulation and solutions 346
8.4 Special analytical results 347
8.4.1 Liquid fl ow, check limit 347
8.4.2 Isothermal gas expansion, all dip angles 347
8.4.3 Vertical wells, all m -- (thermodynamic) values 348
8.4.4 Horizontal wells, all m -- (thermodynamic)
values 348
8.5 Direct solver, solution procedure 349
8.6 Forward model gas calculations 350
8.7 Second-order schemes 353
8.8 Inverse solver, solution software 353
8.9 Inverse gas calculations 355
8.10 Ellipsoidal source --fully transient numerical
solutions for gases and liquids 358
8.10.1 Transient fl ow modeling 359
8.10.2 Finite difference equation 360
8.10.3 Boundary conditions --modeling fl owline
storage with and without skin effects 361
8.10.4 Detailed time integration scheme 362
8.10.5 Observation probe response 362
8.10.6 Software interface and example calculations 363
8.10.7 Source formulation limitations 368
8.11 Transient source pulse interaction inverse method 369
8.11.1 Pulse interaction, procedure at nonzero
dip angle 369
8.12 Ring source, layered model for vertical wells 372
8.12.1 Source model limitations and refi nement 372
8.12.2 Finite difference method 372
8.12.3 Alternating-direction-implicit integration 373
8.12.4 Formation tester nozzle as a simple ring source 375
8.12.5 Pad nozzle pumpout boundary condition 376
8.12.6 Dual probe and dual packer surface logic 377
8.12.7 Detailed boundary condition implementation 377
8.12.8 Example calculations 378
8.13 Pad nozzle and dual packer sources for
horizontal wells 381
8.14 Application to modern gas reservoir characterization 383
8.15 References 383
9. Three-Dimensional Phase Delay Response in Layered
Anisotropic Media with Dip 385
9.1 Basic phase delay and amplitude attenuation ideas 385
9.1.1 Isotropic uniform media 385
9.1.2 Anisotropic homogeneous media 386
9.2 Layered model formulation 387
9.2.1 Homogeneous medium, basic mathematical
ideas 387
9.2.2 Boundary value problem for complex pressure 389
9.2.3 Iterative numerical solution to general
formulation 389
9.2.4 Successive line over relaxation procedure 390
9.2.5 Advantages of the scheme 391
9.2.6 Extensions to multiple layers 391
9.2.7 Extensions to complete formation
heterogeneity 392
9.3 Phase delay software interface 392
9.3.1 Output fi le notes 394
9.3.2 Special user features 395
9.4 Detailed phase delay results in layered
anisotropic media 396
9.5 Closing remarks --extensions and additional
applications 404
9.5.1 Inverse model in uniform anisotropic media 404
9.5.2 Inverse model in layered media 404
9.5.3 Variable gridding 405
9.5.4 Other physical models 405
9.6 References 406
Part III Consulting Services and Advanced Software
Consulting services and advanced software 407
Module FT-00 408
Module FT-01 410
Module FT-02 412
Module FT-03 414
Module FT-04 418
Module FT-05 420
xviii Contents
Module FT-06 421
Module FT-07 423
Module FT-PTA-DDBU 425
Part IV Cumulative References, Index and Author Contact
Cumulative References 426
Index 431
About the Authors
Back to Top
BISAC SUBJECT HEADINGS
TEC031030: TECHNOLOGY & ENGINEERING / Power Resources / Fossil Fuels
TEC047000: TECHNOLOGY & ENGINEERING / Petroleum
SCI031000: SCIENCE / Earth Sciences / Geology
BIC CODES
THF: Fossil fuel technologies
PHVG: Geophysics
RBGG: Petrology
Back to Top