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Submit a ProposalSupercharge, Invasion, and Mudcake Growth in Downhole Applications
 | By Tao Lu, Xiaofei Qin, Yongren Feng, Yanmin Zhou and Wilson Chin Series: Handbook of Petroleum Engineering Series Copyright: 2021 | Status: Published ISBN: 9781119283324 | Hardcover | 513 pages Price: $225 USD  |
One Line Description
This book reviews strongly related subjects in wellbore pressure transient analysis for overbalanced and underbalanced drilling, static and dynamic filtration, single and multiphase flow, transient mudcake buildup and stuck-pipe assessment, describes existing models, and develops new fluid flow algorithms useful in modeling these flow effects.
Audience
Petroleum engineers, petrophysicists, log analysts, drillers, geologists, students and educators
Petroleum engineers, petrophysicists, log analysts, drillers, geologists, students and educators
Description
Mysterious “supercharge effects,” encountered in formation testing pressure transient analysis, and reservoir invasion, mudcake growth, dynamic filtration, stuck-pipe remediation, and so on, are often discussed in contrasting petrophysical versus drilling contexts. However, these effects are physically coupled and intricately related. The authors focus on a comprehensive formulation, provide solutions for different specialized limits, and develop applications that illustrate how the central ideas can be used in seemingly unrelated disciplines. This approach contributes to a firm understanding of logging and drilling principles. Fortran source code, furnished where applicable, is listed together with recently developed software applications and conveniently summarized throughout the book. In addition, common (incorrect) methods used in the industry are re-analyzed and replaced with more accurate models, which are then used to address challenging field objectives.
Sophisticated mathematics is explained in “down to earth” terms, but empirical validations, in this case through Catscan experiments, are used to “keep predictions honest.” Similarly, early-time, low mobility, permeability prediction models used in formation testing, several invented by one of the authors, are extended to handle supercharge effects in overbalanced drilling and near-well pressure deficits encountered in underbalanced drilling. These methods are also motivated by reality. For instance, overpressures of 2,000 psi and underpressures near 500 psi are routinely reported in field work, thus imparting a special significance to the methods reported in the book.
This new volume discusses old problems and modern challenges, formulates and develops advanced models applicable to both drilling and petrophysical objectives. The presentation focuses on central unifying physical models which are carefully formulated and mathematically solved. The wealth of applications examples and supporting software discussed provides readers with a unified focus behind daily work activities, emphasizing common features and themes rather than unrelated methods and work flows. This comprehensive book is “must” reading for every petroleum engineer.
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Mysterious “supercharge effects,” encountered in formation testing pressure transient analysis, and reservoir invasion, mudcake growth, dynamic filtration, stuck-pipe remediation, and so on, are often discussed in contrasting petrophysical versus drilling contexts. However, these effects are physically coupled and intricately related. The authors focus on a comprehensive formulation, provide solutions for different specialized limits, and develop applications that illustrate how the central ideas can be used in seemingly unrelated disciplines. This approach contributes to a firm understanding of logging and drilling principles. Fortran source code, furnished where applicable, is listed together with recently developed software applications and conveniently summarized throughout the book. In addition, common (incorrect) methods used in the industry are re-analyzed and replaced with more accurate models, which are then used to address challenging field objectives.
Sophisticated mathematics is explained in “down to earth” terms, but empirical validations, in this case through Catscan experiments, are used to “keep predictions honest.” Similarly, early-time, low mobility, permeability prediction models used in formation testing, several invented by one of the authors, are extended to handle supercharge effects in overbalanced drilling and near-well pressure deficits encountered in underbalanced drilling. These methods are also motivated by reality. For instance, overpressures of 2,000 psi and underpressures near 500 psi are routinely reported in field work, thus imparting a special significance to the methods reported in the book.
This new volume discusses old problems and modern challenges, formulates and develops advanced models applicable to both drilling and petrophysical objectives. The presentation focuses on central unifying physical models which are carefully formulated and mathematically solved. The wealth of applications examples and supporting software discussed provides readers with a unified focus behind daily work activities, emphasizing common features and themes rather than unrelated methods and work flows. This comprehensive book is “must” reading for every petroleum engineer.
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Supplementary Data
--Includes numerous practical applications for the engineer working in the field or laboratory
--Covers pressure transient analysis in overbalanced and underbalanced drilling
--Cover dynamic filtration and mudcake growth
--Explains the effects in permeability prediction and stuck-pipe remediation
--Gives analytical models with numerical algorithms
--Includes source code models and packaged Windows applications separately available for immediate use
--Includes numerous practical applications for the engineer working in the field or laboratory
--Covers pressure transient analysis in overbalanced and underbalanced drilling
--Cover dynamic filtration and mudcake growth
--Explains the effects in permeability prediction and stuck-pipe remediation
--Gives analytical models with numerical algorithms
--Includes source code models and packaged Windows applications separately available for immediate use
Author / Editor Details
Tao Lu, PhD, Vice President, China Oilfield Services Limited, leads the company’s logging and directional well R&D activities, also heading its formation testing research, applications and marketing efforts. Mr. Lu is recipient of numerous awards, including the National Technology Development Medal, National Engineering Talent and State Council Awards, and several COSL technology innovation prizes.
Tao Lu, PhD, Vice President, China Oilfield Services Limited, leads the company’s logging and directional well R&D activities, also heading its formation testing research, applications and marketing efforts. Mr. Lu is recipient of numerous awards, including the National Technology Development Medal, National Engineering Talent and State Council Awards, and several COSL technology innovation prizes.
Xiaofei Qin graduated from Huazhong University of Science and Technology with a M.Sc. in Mechanical Science and Engineering. At China Oilfield Services Limited, he is engaged in the research and development of petroleum logging instruments and their applications. Mr. Qin has published twelve scientific papers and obtained twenty patents.
Yongren Feng is a Professor Level Senior Engineer and Chief Engineer at the Oilfield Technology Research Institute of China Oilfield Services Limited. He has been engaged in the research and development of offshore oil logging instruments for three decades, mainly responsible for wireline formation testing technology, electric core sampling methods and formation testing while drilling (FTWD) tool development.
Minggao Zhou, Senior Mechanical Engineer at COSL’s Oil Field Technology Research Institute, holds a Master’s Degree in Engineering and leads the company’s formation testing project team. He has worked extensively in research and development over the past two decades and has participated in several National Five Year Programs. His professional interests span a wide range of well logging instruments, presently focusing
on formation testing design and interpretation.
on formation testing design and interpretation.
>b?Wilson C. Chin earned his PhD from M.I.T. and his M.Sc. from Caltech. He has authored over twenty books with Wiley-Scrivener and other major scientific publishers, has more than four dozen domestic and international patents to his credit, and has published over one hundred journal articles, in the areas of reservoir engineering, formation testing, well logging, Measurement While Drilling, and drilling and cementing rheology. Inquiries: wilsonchin@aol.com.
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Table of Contents
1. Pressure Transient Analysis and Sampling in Formation
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Pressure transient analysis challenges . . . . . . . . . . . . . . . 1
Background development . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Conventional Formation Testing Concepts . . . . . . . . . 5
1.2 Prototypes, Tools and Systems . . . . . . . . . . . . . . . . 6
1.2.1 Enhanced Formation Dynamic Tester
(EFDT ®) . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Basic Reservoir Characteristic Tester
(BASIC-RCT™) . . . . . . . . . . . . . . . . . . . . . 13
1.2.3 Enhancing and enabling technologies. . . . . . . . . 15
Stuck tool alleviation . . . . . . . . . . . . . . . . . . 16
Field facilities. . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Recent Formation Testing Developments . . . . . . . . . . 17
1.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2. Spherical Source Models for Forward and Inverse
Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Basic Approaches, Interpretation Issues and Modeling
Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Early steady flow model . . . . . . . . . . . . . . . . . . . . 23
Simple drawdown-buildup models . . . . . . . . . . . . . . 23
Analytical drawdown-buildup solution. . . . . . . . . . . . 25
Phase delay analysis . . . . . . . . . . . . . . . . . . . . . . . 26
Modeling hierarchies . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Basic Single-Phase Flow Forward and Inverse
Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Module FT-00 . . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Module FT-01 . . . . . . . . . . . . . . . . . . . . . 37
2.2.3 Module FT-03 . . . . . . . . . . . . . . . . . . . . . 38
2.2.4 Forward model application, Module FT-00 . . . . 39
2.2.5 Inverse model application, Module FT-01 . . . . . 41
2.2.6 Effects of dip angle . . . . . . . . . . . . . . . . . . 43
2.2.7 Inverse “pulse interaction” approach
using FT-00 . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.8 FT-03 model overcomes source-sink
limitations . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.9 Module FT-04, phase delay analysis, introductory
for now. . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2.10 Drawdown-buildup, Module FT-PTA-DDBU . . 55
2.2.11 Real pumping, Module FT-06 . . . . . . . . . . . . 59
2.3 Advanced Forward and Inverse Algorithms . . . . . . . . . 61
2.3.1 Advanced drawdown and buildup methods
Basic steady model. . . . . . . . . . . . . . . . . . . 61
Validating our method. . . . . . . . . . . . . . . . . 63
2.3.2 Calibration results and transient pressure curves . 65
2.3.3 Mobility and pore pressure using first
drawdown data . . . . . . . . . . . . . . . . . . . . . 67
2.3.3.1 Run No. 1. Flowline volume 200 cc. . . . 68
2.3.3.2 Run No. 2. Flowline volume 500 cc. . . . 69
2.3.3.3 Run No. 3. Flowline volume 1,000 cc . . 71
2.3.3.4 Run No. 4. Flowline volume 2,000 cc . . 73
2.3.4 Mobility and pore pressure from last buildup
data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.3.4.1 Run No. 5. Flowline volume 200 cc . . . 74
2.3.4.2 Run No. 6. Flowline volume 500 cc . . . 76
2.3.4.3 Run No. 7. Flowline volume 1,000 cc . . 77
2.3.4.4 Run No. 8. Flowline volume 2,000 cc . . 78
2.3.4.5 Run No. 9. Time-varying flowline volume
inputs from FT-07 . . . . . . . . . . . . . . 79
2.3.5 Phase delay and amplitude attenuation, anisotropic
media with dip – detailed theory, model and numerical
results. . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.5.1 Basic mathematical results . . . . . . . . . . 82
Isotropic model . . . . . . . . . . . . . . . . . 82
Anisotropic extensions . . . . . . . . . . . . 82
Vertical well limit . . . . . . . . . . . . . . . 83
Horizontal well limit . . . . . . . . . . . . . 83
Formulas for vertical and horizontal wells . 83
Deviated well equations. . . . . . . . . . . . 84
Deviated well interpretation for both
kh and kv . . . . . . . . . . . . . . . . . . . . 85
Two-observation-probe models . . . . . . . 86
2.3.5.2 Numerical examples and typical results . . 88
Example 1. Parameter estimates . . . . . . . 89
Example 2. Surface plots . . . . . . . . . . . 90
Example 3. Sinusoidal excitation . . . . . . 91
Example 4. Rectangular wave excitation . . 94
Example 5. Permeability prediction at general
dip angles . . . . . . . . . . . . . . . . . . . . 96
Example 6. Solution for a random input . . 98
2.3.5.3 Layered model formulation. . . . . . . . . . 99
2.3.5.4 Phase delay software interface . . . . . . . . 100
2.3.5.5 Detailed phase delay results in layered
anisotropic media. . . . . . . . . . . . . . . . 103
2.3.6 Supercharging and formation invasion introduction, with
review of analytical forward and inverse models . . 110
2.3.6.1 Development perspectives . . . . . . . . . . 111
2.3.6.2 Review of forward and inverse models . . . 113
FT-00 model . . . . . . . . . . . . . . . . . . 113
FT-01 model . . . . . . . . . . . . . . . . . . 117
FT-02 model . . . . . . . . . . . . . . . . . . 118
FT-06 and FT-07 models . . . . . . . . . . . 119
FT–PTA–DDBU model . . . . . . . . . . . . 122
Classic inversion model . . . . . . . . . . . . 123
Supercharge forward and inverse models . 123
Multiple drawdown and buildup inverse
models . . . . . . . . . . . . . . . . . . . . . . 129
Multiphase invasion, clean-up and
contamination. . . . . . . . . . . . . . . . . . 133
System integration and closing remarks . . 138
2.3.6.3 Supercharging summaries - advanced forward
and inverse models explored . . . . . . . . 139
Supercharge math model development . . . 139
Conventional zero supercharge model . . . 141
Supercharge extension. . . . . . . . . . . . . 142
2.3.6.4 Drawdown only applications . . . . . . . . . 144
Example DD-1. High overbalance . . . . . 144
Example DD-2. High overbalance . . . . . 150
Example DD-3. High overbalance . . . . . 154
Example DD-4. Qualitative pressure
trends . . . . . . . . . . . . . . . . . . . . . . 158
Example DD-5. Qualitative pressure
trends . . . . . . . . . . . . . . . . . . . . . . 161
Example DD-6. “Drawdown-only” data with
multiple inverse scenarios for 1 md/cp
application. . . . . . . . . . . . . . . . . . . . 163
Example DD-7. “Drawdown-only” data with
multiple inverse scenarios for 0.1 md/cp
application. . . . . . . . . . . . . . . . . . . . 168
2.3.6.5 Drawdown – buildup applications. . . . . . 173
Example DDBU-1. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 173
Example DDBU-2. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 177
Example DDBU-3. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 180
Example DDBU-4. Drawdown-buildup, 1 md/cp
calculations . . . . . . . . . . . . . . . . . . . 184
Example DDBU-5. Drawdown-buildup,
0.1 md/cp calculations . . . . . . . . . . . . 188
2.3.7 Advanced multiple drawdown – buildup (or, “MDDBU”)
forward and inverse models . . . . . . . . . . . . . . 193
2.3.7.1 Software description . . . . . . . . . . . . . . 193
2.3.7.2 Validation of PTA-App-11 inverse model . 200
2.3.8 Multiphase flow with inertial effects –
Applications to borehole invasion, supercharging,
clean-up and contamination analysis . . . . . . . . . 217
2.3.8.1 Mudcake dynamics. . . . . . . . . . . . . . . 217
2.3.8.2 Multiphase modeling in boreholes. . . . . . 220
2.3.8.3 Pressure and concentration displays. . . . . 222
Example 1. Single probe, infinite anisotropic
media. . . . . . . . . . . . . . . . . . . . 223
Example 2. Single probe, three layer medium . . . 228
Example 3. Dual probe pumping, three layer
medium . . . . . . . . . . . . . . . . . . 230
Example 4. Straddle packer pumping . . . . . . . . 231
Example 5. Formation fluid viscosity imaging . . . 233
Example 6. Contamination modeling . . . . . . . . 234
Example 7. Multi-rate pumping simulation. . . . . 234
2.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
3. Practical Applications Examples . . . . . . . . . . . . . . . . 237
3.1 Non-constant Flow Rate Effects . . . . . . . . . . . . . . . . 238
3.1.1 Constant flow rate, idealized pumping, inverse
method . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
3.1.2 Slow ramp up/down flow rate . . . . . . . . . . . . . 245
3.1.3 Impulsive start/stop flow rate. . . . . . . . . . . . . . 250
Closing remarks . . . . . . . . . . . . . . . . . . . . . . . . . 255
3.2 Supercharging – Effects of Nonuniform Initial Pressure . 256
Conventional zero supercharge model . . . . . . . . . . . . 256
Supercharge “Fast Forward” solver . . . . . . . . . . . . . . 258
3.3 Dual Probe Anisotropy Inverse Analysis. . . . . . . . . . . 264
3.4 Multiprobe “DOI,” Inverse and Barrier Analysis . . . . . . 273
3.5 Rapid Batch Analysis for History Matching. . . . . . . . . 281
3.6 Supercharge, Contamination Depth and Mudcake Growth in
“Large Boreholes” – Lineal Flow . . . . . . . . . . . . . . . 289
Mudcake growth and filtrate invasion . . . . . . . . . . . . 289
Time-dependent pressure distributions . . . . . . . . . . . . 292
3.7 Supercharge, Contamination Depth and Mudcake Growth in
Slimholes or “Clogged Wells” – Radial Flow . . . . . . . . 292
3.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
4. Supercharge, Pressure Change, Fluid Invasion and
Mudcake Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Conventional zero supercharge model . . . . . . . . . . . . . . . 295
Supercharge model. . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Relevance to formation tester job planning . . . . . . . . . . . . 298
Refined models for supercharge invasion . . . . . . . . . . . . . 299
4.1 Governing equations and moving interface modeling . . . 300
Single-phase flow pressure equations. . . . . . . . . . . . . 300
Problem formulation . . . . . . . . . . . . . . . . . . . . . . 303
Eulerian versus Lagrangian description . . . . . . . . . . . 303
Constant density versus compressible flow . . . . . . . . . 304
Steady versus unsteady flow . . . . . . . . . . . . . . . . . . 305
Incorrect use of Darcy’s law . . . . . . . . . . . . . . . . . . 305
Moving fronts and interfaces . . . . . . . . . . . . . . . . . 306
Use of effective properties . . . . . . . . . . . . . . . . . . . 308
4.2 Static and dynamic filtration . . . . . . . . . . . . . . . . . . 310
4.2.1 Simple flows without mudcake . . . . . . . . . . . . 310
Homogeneous liquid in a uniform linear core . . . . 311
Homogeneous liquid in a uniform radial flow. . . . 313
Homogeneous liquid in uniform spherical domain . 314
Gas flow in a uniform linear core . . . . . . . . . . . 315
Flow from a plane fracture . . . . . . . . . . . . . . . 317
4.2.2 Flows with moving boundaries . . . . . . . . . . . . 318
Lineal mudcake buildup on filter paper . . . . . . . 318
Plug flow of two liquids in linear core without
cake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
4.3 Coupled Dynamical Problems: Mudcake and Formation
Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Simultaneous mudcake buildup and filtrate invasion in a linear
core (liquid flows) . . . . . . . . . . . . . . . . . . . . . . . . 323
Simultaneous mudcake buildup and filtrate invasion in a radial
geometry (liquid flows) . . . . . . . . . . . . . . . . . . . . . 327
Hole plugging and stuck pipe. . . . . . . . . . . . . . . . . . 330
Fluid compressibility . . . . . . . . . . . . . . . . . . . . . . 331
Formation invasion at equilibrium mudcake thickness . . 335
4.4 Inverse Models in Time Lapse Logging . . . . . . . . . . . 336
Experimental model validation. . . . . . . . . . . . . . . . . 336
Static filtration test procedure . . . . . . . . . . . . . . . . . 337
Dynamic filtration testing. . . . . . . . . . . . . . . . . . . . 337
Measurement of mudcake properties . . . . . . . . . . . . . 338
Formation evaluation from invasion data. . . . . . . . . . . 338
Field applications. . . . . . . . . . . . . . . . . . . . . . . . . 339
Characterizing mudcake properties . . . . . . . . . . . . . . 340
Simple extrapolation of mudcake properties . . . . . . . . 341
Radial mudcake growth on cylindrical filter paper . . . . . 342
4.5 Porosity, Permeability, Oil Viscosity and Pore Pressure
Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Simple porosity determination . . . . . . . . . . . . . . . . . 345
Radial invasion without mudcake . . . . . . . . . . . . . . . 346
Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
Time lapse analysis using general muds . . . . . . . . . . . 351
Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
4.6 Examples of Time Lapse Analysis . . . . . . . . . . . . . . 354
Formation permeability and hydrocarbon viscosity. . . . . 355
Pore pressure, rock permeability and fluid viscosity . . . . 357
4.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
5. Numerical Supercharge, Pressure, Displacement and
Multiphase Flow Models . . . . . . . . . . . . . . . . . . . . . 363
5.1 Finite Difference Solutions . . . . . . . . . . . . . . . . . . . 364
Basic formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 364
Model constant density flow analysis. . . . . . . . . . . . . 366
Transient compressible flow modeling . . . . . . . . . . . . 369
Numerical stability. . . . . . . . . . . . . . . . . . . . . . . . 371
Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Multiple physical time and space scales . . . . . . . . . . . 372
Example 5-1. Lineal liquid displacement without
mudcake . . . . . . . . . . . . . . . . . . . . . 373
Example 5-2. Cylindrical radial liquid displacement without
cake. . . . . . . . . . . . . . . . . . . . . . . . 380
Example 5-3. Spherical radial liquid displacement without
cake. . . . . . . . . . . . . . . . . . . . . . . . 383
Example 5-4. Lineal liquid displacement without mudcake,
including compressible flow transients . . . 385
Example 5-5. Von Neumann stability of implicit time
schemes . . . . . . . . . . . . . . . . . . . . . 388
Example 5-6. Gas displacement by liquid in lineal core
without mudcake, including compressible flow
transients. . . . . . . . . . . . . . . . . . . . . 390
Incompressible problem. . . . . . . . . . . . 391
Transient, compressible problem . . . . . . 392
Example 5-7. Simultaneous mudcake buildup and
displacement front motion for incompressible
liquid flows . . . . . . . . . . . . . . . . . . 396
Matching conditions at displacement front . . . . . . . . . 399
Matching conditions at the cake-to-rock interface . . . . . 399
Coding modifications . . . . . . . . . . . . . . . . . . . . . . 400
Modeling formation heterogeneities. . . . . . . . . . . . . . 403
Mudcake compaction and compressibility . . . . . . . . . . 404
Modeling borehole activity . . . . . . . . . . . . . . . . . . . 405
5.2 Forward and Inverse Multiphase Flow Modeling. . . . . . 405
Problem hierarchies . . . . . . . . . . . . . . . . . . . . . . . 406
5.2.1 Immiscible Buckley-Leverett lineal flows without
capillary pressure. . . . . . . . . . . . . . . . . . . . . 407
Example boundary value problems . . . . . . . . . . 409
General initial value problem. . . . . . . . . . . . . . 410
General boundary value problem for infinite core . 411
Variable q(t) . . . . . . . . . . . . . . . . . . . . . . . 411
Mudcake-dominated invasion . . . . . . . . . . . . . 412
Shock velocity . . . . . . . . . . . . . . . . . . . . . . 412
Pressure solution . . . . . . . . . . . . . . . . . . . . . 414
5.2.2 Molecular diffusion in fluid flows. . . . . . . . . . . 415
Exact lineal flow solutions . . . . . . . . . . . . . . . 416
Numerical analysis. . . . . . . . . . . . . . . . . . . . 417
Diffusion in cake-dominated flows . . . . . . . . . . 419
Resistivity migration. . . . . . . . . . . . . . . . . . . 419
Lineal diffusion and “un-diffusion” examples . . . 420
Radial diffusion and “un-diffusion” examples . . . 423
5.2.3 Immiscible radial flows with capillary pressure and
prescribed mudcake growth . . . . . . . . . . . . . . 425
Governing saturation equation . . . . . . . . . . . . . 426
Numerical analysis. . . . . . . . . . . . . . . . . . . . 427
Fortran implementation . . . . . . . . . . . . . . . . . 429
Typical calculations . . . . . . . . . . . . . . . . . . . 429
Mudcake dominated flows . . . . . . . . . . . . . . . 435
“Un-shocking” a saturation discontinuity . . . . . . 438
5.2.4 Immiscible flows with capillary pressure and dynamically
coupled mudcake growth . . . . . . . . . . . . . . . . 441
Flows without mudcakes . . . . . . . . . . . . . . . . 441
Modeling mudcake coupling . . . . . . . . . . . . . . 450
Unchanging mudcake thickness . . . . . . . . . . . . 451
Transient mudcake growth . . . . . . . . . . . . . . 453
General immiscible flow model . . . . . . . . . . . . 457
5.3 Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 458
5.4 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
Cumulative References . . . . . . . . . . . . . . . . . . . . . . . . 467
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
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1. Pressure Transient Analysis and Sampling in Formation
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Pressure transient analysis challenges . . . . . . . . . . . . . . . 1
Background development . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Conventional Formation Testing Concepts . . . . . . . . . 5
1.2 Prototypes, Tools and Systems . . . . . . . . . . . . . . . . 6
1.2.1 Enhanced Formation Dynamic Tester
(EFDT ®) . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Basic Reservoir Characteristic Tester
(BASIC-RCT™) . . . . . . . . . . . . . . . . . . . . . 13
1.2.3 Enhancing and enabling technologies. . . . . . . . . 15
Stuck tool alleviation . . . . . . . . . . . . . . . . . . 16
Field facilities. . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Recent Formation Testing Developments . . . . . . . . . . 17
1.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2. Spherical Source Models for Forward and Inverse
Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Basic Approaches, Interpretation Issues and Modeling
Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Early steady flow model . . . . . . . . . . . . . . . . . . . . 23
Simple drawdown-buildup models . . . . . . . . . . . . . . 23
Analytical drawdown-buildup solution. . . . . . . . . . . . 25
Phase delay analysis . . . . . . . . . . . . . . . . . . . . . . . 26
Modeling hierarchies . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Basic Single-Phase Flow Forward and Inverse
Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Module FT-00 . . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Module FT-01 . . . . . . . . . . . . . . . . . . . . . 37
2.2.3 Module FT-03 . . . . . . . . . . . . . . . . . . . . . 38
2.2.4 Forward model application, Module FT-00 . . . . 39
2.2.5 Inverse model application, Module FT-01 . . . . . 41
2.2.6 Effects of dip angle . . . . . . . . . . . . . . . . . . 43
2.2.7 Inverse “pulse interaction” approach
using FT-00 . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.8 FT-03 model overcomes source-sink
limitations . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.9 Module FT-04, phase delay analysis, introductory
for now. . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2.10 Drawdown-buildup, Module FT-PTA-DDBU . . 55
2.2.11 Real pumping, Module FT-06 . . . . . . . . . . . . 59
2.3 Advanced Forward and Inverse Algorithms . . . . . . . . . 61
2.3.1 Advanced drawdown and buildup methods
Basic steady model. . . . . . . . . . . . . . . . . . . 61
Validating our method. . . . . . . . . . . . . . . . . 63
2.3.2 Calibration results and transient pressure curves . 65
2.3.3 Mobility and pore pressure using first
drawdown data . . . . . . . . . . . . . . . . . . . . . 67
2.3.3.1 Run No. 1. Flowline volume 200 cc. . . . 68
2.3.3.2 Run No. 2. Flowline volume 500 cc. . . . 69
2.3.3.3 Run No. 3. Flowline volume 1,000 cc . . 71
2.3.3.4 Run No. 4. Flowline volume 2,000 cc . . 73
2.3.4 Mobility and pore pressure from last buildup
data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.3.4.1 Run No. 5. Flowline volume 200 cc . . . 74
2.3.4.2 Run No. 6. Flowline volume 500 cc . . . 76
2.3.4.3 Run No. 7. Flowline volume 1,000 cc . . 77
2.3.4.4 Run No. 8. Flowline volume 2,000 cc . . 78
2.3.4.5 Run No. 9. Time-varying flowline volume
inputs from FT-07 . . . . . . . . . . . . . . 79
2.3.5 Phase delay and amplitude attenuation, anisotropic
media with dip – detailed theory, model and numerical
results. . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.5.1 Basic mathematical results . . . . . . . . . . 82
Isotropic model . . . . . . . . . . . . . . . . . 82
Anisotropic extensions . . . . . . . . . . . . 82
Vertical well limit . . . . . . . . . . . . . . . 83
Horizontal well limit . . . . . . . . . . . . . 83
Formulas for vertical and horizontal wells . 83
Deviated well equations. . . . . . . . . . . . 84
Deviated well interpretation for both
kh and kv . . . . . . . . . . . . . . . . . . . . 85
Two-observation-probe models . . . . . . . 86
2.3.5.2 Numerical examples and typical results . . 88
Example 1. Parameter estimates . . . . . . . 89
Example 2. Surface plots . . . . . . . . . . . 90
Example 3. Sinusoidal excitation . . . . . . 91
Example 4. Rectangular wave excitation . . 94
Example 5. Permeability prediction at general
dip angles . . . . . . . . . . . . . . . . . . . . 96
Example 6. Solution for a random input . . 98
2.3.5.3 Layered model formulation. . . . . . . . . . 99
2.3.5.4 Phase delay software interface . . . . . . . . 100
2.3.5.5 Detailed phase delay results in layered
anisotropic media. . . . . . . . . . . . . . . . 103
2.3.6 Supercharging and formation invasion introduction, with
review of analytical forward and inverse models . . 110
2.3.6.1 Development perspectives . . . . . . . . . . 111
2.3.6.2 Review of forward and inverse models . . . 113
FT-00 model . . . . . . . . . . . . . . . . . . 113
FT-01 model . . . . . . . . . . . . . . . . . . 117
FT-02 model . . . . . . . . . . . . . . . . . . 118
FT-06 and FT-07 models . . . . . . . . . . . 119
FT–PTA–DDBU model . . . . . . . . . . . . 122
Classic inversion model . . . . . . . . . . . . 123
Supercharge forward and inverse models . 123
Multiple drawdown and buildup inverse
models . . . . . . . . . . . . . . . . . . . . . . 129
Multiphase invasion, clean-up and
contamination. . . . . . . . . . . . . . . . . . 133
System integration and closing remarks . . 138
2.3.6.3 Supercharging summaries - advanced forward
and inverse models explored . . . . . . . . 139
Supercharge math model development . . . 139
Conventional zero supercharge model . . . 141
Supercharge extension. . . . . . . . . . . . . 142
2.3.6.4 Drawdown only applications . . . . . . . . . 144
Example DD-1. High overbalance . . . . . 144
Example DD-2. High overbalance . . . . . 150
Example DD-3. High overbalance . . . . . 154
Example DD-4. Qualitative pressure
trends . . . . . . . . . . . . . . . . . . . . . . 158
Example DD-5. Qualitative pressure
trends . . . . . . . . . . . . . . . . . . . . . . 161
Example DD-6. “Drawdown-only” data with
multiple inverse scenarios for 1 md/cp
application. . . . . . . . . . . . . . . . . . . . 163
Example DD-7. “Drawdown-only” data with
multiple inverse scenarios for 0.1 md/cp
application. . . . . . . . . . . . . . . . . . . . 168
2.3.6.5 Drawdown – buildup applications. . . . . . 173
Example DDBU-1. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 173
Example DDBU-2. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 177
Example DDBU-3. Drawdown-buildup, high
overbalance . . . . . . . . . . . . . . . . . . . 180
Example DDBU-4. Drawdown-buildup, 1 md/cp
calculations . . . . . . . . . . . . . . . . . . . 184
Example DDBU-5. Drawdown-buildup,
0.1 md/cp calculations . . . . . . . . . . . . 188
2.3.7 Advanced multiple drawdown – buildup (or, “MDDBU”)
forward and inverse models . . . . . . . . . . . . . . 193
2.3.7.1 Software description . . . . . . . . . . . . . . 193
2.3.7.2 Validation of PTA-App-11 inverse model . 200
2.3.8 Multiphase flow with inertial effects –
Applications to borehole invasion, supercharging,
clean-up and contamination analysis . . . . . . . . . 217
2.3.8.1 Mudcake dynamics. . . . . . . . . . . . . . . 217
2.3.8.2 Multiphase modeling in boreholes. . . . . . 220
2.3.8.3 Pressure and concentration displays. . . . . 222
Example 1. Single probe, infinite anisotropic
media. . . . . . . . . . . . . . . . . . . . 223
Example 2. Single probe, three layer medium . . . 228
Example 3. Dual probe pumping, three layer
medium . . . . . . . . . . . . . . . . . . 230
Example 4. Straddle packer pumping . . . . . . . . 231
Example 5. Formation fluid viscosity imaging . . . 233
Example 6. Contamination modeling . . . . . . . . 234
Example 7. Multi-rate pumping simulation. . . . . 234
2.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
3. Practical Applications Examples . . . . . . . . . . . . . . . . 237
3.1 Non-constant Flow Rate Effects . . . . . . . . . . . . . . . . 238
3.1.1 Constant flow rate, idealized pumping, inverse
method . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
3.1.2 Slow ramp up/down flow rate . . . . . . . . . . . . . 245
3.1.3 Impulsive start/stop flow rate. . . . . . . . . . . . . . 250
Closing remarks . . . . . . . . . . . . . . . . . . . . . . . . . 255
3.2 Supercharging – Effects of Nonuniform Initial Pressure . 256
Conventional zero supercharge model . . . . . . . . . . . . 256
Supercharge “Fast Forward” solver . . . . . . . . . . . . . . 258
3.3 Dual Probe Anisotropy Inverse Analysis. . . . . . . . . . . 264
3.4 Multiprobe “DOI,” Inverse and Barrier Analysis . . . . . . 273
3.5 Rapid Batch Analysis for History Matching. . . . . . . . . 281
3.6 Supercharge, Contamination Depth and Mudcake Growth in
“Large Boreholes” – Lineal Flow . . . . . . . . . . . . . . . 289
Mudcake growth and filtrate invasion . . . . . . . . . . . . 289
Time-dependent pressure distributions . . . . . . . . . . . . 292
3.7 Supercharge, Contamination Depth and Mudcake Growth in
Slimholes or “Clogged Wells” – Radial Flow . . . . . . . . 292
3.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
4. Supercharge, Pressure Change, Fluid Invasion and
Mudcake Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Conventional zero supercharge model . . . . . . . . . . . . . . . 295
Supercharge model. . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Relevance to formation tester job planning . . . . . . . . . . . . 298
Refined models for supercharge invasion . . . . . . . . . . . . . 299
4.1 Governing equations and moving interface modeling . . . 300
Single-phase flow pressure equations. . . . . . . . . . . . . 300
Problem formulation . . . . . . . . . . . . . . . . . . . . . . 303
Eulerian versus Lagrangian description . . . . . . . . . . . 303
Constant density versus compressible flow . . . . . . . . . 304
Steady versus unsteady flow . . . . . . . . . . . . . . . . . . 305
Incorrect use of Darcy’s law . . . . . . . . . . . . . . . . . . 305
Moving fronts and interfaces . . . . . . . . . . . . . . . . . 306
Use of effective properties . . . . . . . . . . . . . . . . . . . 308
4.2 Static and dynamic filtration . . . . . . . . . . . . . . . . . . 310
4.2.1 Simple flows without mudcake . . . . . . . . . . . . 310
Homogeneous liquid in a uniform linear core . . . . 311
Homogeneous liquid in a uniform radial flow. . . . 313
Homogeneous liquid in uniform spherical domain . 314
Gas flow in a uniform linear core . . . . . . . . . . . 315
Flow from a plane fracture . . . . . . . . . . . . . . . 317
4.2.2 Flows with moving boundaries . . . . . . . . . . . . 318
Lineal mudcake buildup on filter paper . . . . . . . 318
Plug flow of two liquids in linear core without
cake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
4.3 Coupled Dynamical Problems: Mudcake and Formation
Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Simultaneous mudcake buildup and filtrate invasion in a linear
core (liquid flows) . . . . . . . . . . . . . . . . . . . . . . . . 323
Simultaneous mudcake buildup and filtrate invasion in a radial
geometry (liquid flows) . . . . . . . . . . . . . . . . . . . . . 327
Hole plugging and stuck pipe. . . . . . . . . . . . . . . . . . 330
Fluid compressibility . . . . . . . . . . . . . . . . . . . . . . 331
Formation invasion at equilibrium mudcake thickness . . 335
4.4 Inverse Models in Time Lapse Logging . . . . . . . . . . . 336
Experimental model validation. . . . . . . . . . . . . . . . . 336
Static filtration test procedure . . . . . . . . . . . . . . . . . 337
Dynamic filtration testing. . . . . . . . . . . . . . . . . . . . 337
Measurement of mudcake properties . . . . . . . . . . . . . 338
Formation evaluation from invasion data. . . . . . . . . . . 338
Field applications. . . . . . . . . . . . . . . . . . . . . . . . . 339
Characterizing mudcake properties . . . . . . . . . . . . . . 340
Simple extrapolation of mudcake properties . . . . . . . . 341
Radial mudcake growth on cylindrical filter paper . . . . . 342
4.5 Porosity, Permeability, Oil Viscosity and Pore Pressure
Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Simple porosity determination . . . . . . . . . . . . . . . . . 345
Radial invasion without mudcake . . . . . . . . . . . . . . . 346
Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
Time lapse analysis using general muds . . . . . . . . . . . 351
Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
4.6 Examples of Time Lapse Analysis . . . . . . . . . . . . . . 354
Formation permeability and hydrocarbon viscosity. . . . . 355
Pore pressure, rock permeability and fluid viscosity . . . . 357
4.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
5. Numerical Supercharge, Pressure, Displacement and
Multiphase Flow Models . . . . . . . . . . . . . . . . . . . . . 363
5.1 Finite Difference Solutions . . . . . . . . . . . . . . . . . . . 364
Basic formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 364
Model constant density flow analysis. . . . . . . . . . . . . 366
Transient compressible flow modeling . . . . . . . . . . . . 369
Numerical stability. . . . . . . . . . . . . . . . . . . . . . . . 371
Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Multiple physical time and space scales . . . . . . . . . . . 372
Example 5-1. Lineal liquid displacement without
mudcake . . . . . . . . . . . . . . . . . . . . . 373
Example 5-2. Cylindrical radial liquid displacement without
cake. . . . . . . . . . . . . . . . . . . . . . . . 380
Example 5-3. Spherical radial liquid displacement without
cake. . . . . . . . . . . . . . . . . . . . . . . . 383
Example 5-4. Lineal liquid displacement without mudcake,
including compressible flow transients . . . 385
Example 5-5. Von Neumann stability of implicit time
schemes . . . . . . . . . . . . . . . . . . . . . 388
Example 5-6. Gas displacement by liquid in lineal core
without mudcake, including compressible flow
transients. . . . . . . . . . . . . . . . . . . . . 390
Incompressible problem. . . . . . . . . . . . 391
Transient, compressible problem . . . . . . 392
Example 5-7. Simultaneous mudcake buildup and
displacement front motion for incompressible
liquid flows . . . . . . . . . . . . . . . . . . 396
Matching conditions at displacement front . . . . . . . . . 399
Matching conditions at the cake-to-rock interface . . . . . 399
Coding modifications . . . . . . . . . . . . . . . . . . . . . . 400
Modeling formation heterogeneities. . . . . . . . . . . . . . 403
Mudcake compaction and compressibility . . . . . . . . . . 404
Modeling borehole activity . . . . . . . . . . . . . . . . . . . 405
5.2 Forward and Inverse Multiphase Flow Modeling. . . . . . 405
Problem hierarchies . . . . . . . . . . . . . . . . . . . . . . . 406
5.2.1 Immiscible Buckley-Leverett lineal flows without
capillary pressure. . . . . . . . . . . . . . . . . . . . . 407
Example boundary value problems . . . . . . . . . . 409
General initial value problem. . . . . . . . . . . . . . 410
General boundary value problem for infinite core . 411
Variable q(t) . . . . . . . . . . . . . . . . . . . . . . . 411
Mudcake-dominated invasion . . . . . . . . . . . . . 412
Shock velocity . . . . . . . . . . . . . . . . . . . . . . 412
Pressure solution . . . . . . . . . . . . . . . . . . . . . 414
5.2.2 Molecular diffusion in fluid flows. . . . . . . . . . . 415
Exact lineal flow solutions . . . . . . . . . . . . . . . 416
Numerical analysis. . . . . . . . . . . . . . . . . . . . 417
Diffusion in cake-dominated flows . . . . . . . . . . 419
Resistivity migration. . . . . . . . . . . . . . . . . . . 419
Lineal diffusion and “un-diffusion” examples . . . 420
Radial diffusion and “un-diffusion” examples . . . 423
5.2.3 Immiscible radial flows with capillary pressure and
prescribed mudcake growth . . . . . . . . . . . . . . 425
Governing saturation equation . . . . . . . . . . . . . 426
Numerical analysis. . . . . . . . . . . . . . . . . . . . 427
Fortran implementation . . . . . . . . . . . . . . . . . 429
Typical calculations . . . . . . . . . . . . . . . . . . . 429
Mudcake dominated flows . . . . . . . . . . . . . . . 435
“Un-shocking” a saturation discontinuity . . . . . . 438
5.2.4 Immiscible flows with capillary pressure and dynamically
coupled mudcake growth . . . . . . . . . . . . . . . . 441
Flows without mudcakes . . . . . . . . . . . . . . . . 441
Modeling mudcake coupling . . . . . . . . . . . . . . 450
Unchanging mudcake thickness . . . . . . . . . . . . 451
Transient mudcake growth . . . . . . . . . . . . . . 453
General immiscible flow model . . . . . . . . . . . . 457
5.3 Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 458
5.4 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
Cumulative References . . . . . . . . . . . . . . . . . . . . . . . . 467
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
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BISAC SUBJECT HEADINGS
TEC047000 : TECHNOLOGY & ENGINEERING / Petroleum
SCI024000 : SCIENCE / Energy
BUS070040 : BUSINESS & ECONOMICS / Industries / Energy
BIC CODES
THF: Fossil fuel technologies
RBGK: Geochemistry
TQ: ENVIRONMENTAL SCIENCE, ENGINEERING & TECHNOLOGY
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