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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.
Yanmin Zhou received her PhD in geological resources engineering from the University of Petroleum, Beijing and serves as Geophysics Engineer at COSL. She participated in the company's Drilling and Reservoir Testing Instrument Development Program, its National Science and Technology Special Project, and acts as R&D engineer for national formation testing activities.
Wilson 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.
Preface xiii
Acknowledgements xvii
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(TM)) 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, 0.1md/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
The formation tester is a well logging instrument with extendable pad nozzles which, when pressed against the borehole sandface, extracts in situ formation fluids for delivery to the surface for chemical examination. This process characterizes its fluid "sampling" function. By-products of this operation are pressure transient histories, which can be interrogated using Darcy math models for fluid and formation properties such as permeability, mobility, anisotropy, compressibility and pore pressure. This is referred to as "pressure transient analysis," or simply, "PTA." Both can be conducted as wireline or Measurement While Drilling, or "MWD," applications, where these operations now represent invaluable elements of the standard well logging suite.
Pressure transient analysis challenges. While collecting and transporting fluids is relatively straightforward, e.g., storing samples in secure vessels that maintain downhole conditions, the PTA process poses a greater design challenge. A well designed tool often begins with a good understanding of the environment, plus physics coupled with sound experience in mathematical modeling. Some ideas are obvious. For example, a single "source" or "sink" probe, serving both pumping and pressure observation functions, will at most provide the "spherical permeability" kh2/3kv/1/3, where kh and kv are horizontal and vertical permeabilities. Thus, "single probe" tools, while mechanically simple, will offer fewer logging advantages than "dual probe" or "multiprobe tools" which provide much greater formation evaluation information.
Figure 1.1. Drawdown-buildup pressure response with dynamic pumping action and flowline.
But how are probe arrays configured and placed for optimal effect? Figures 1.1 and 1.2 illustrate the operation of a single probe tool that withdraws fluid and then stops, creating the expected "drawdown and buildup" shown. If a second probe is desired, should it be placed an axial distance apart but along the same azimuth? Or azimuthally apart, at 180° away along the borehole circumference? What about a "drawdown only" pumpout? Or perhaps, have the pump oscillate sinusoidally in place, thus mimicking the AC transmissions of an electromagnetic logging tool? How many probes are best? What are their flow areas? Do answers to these questions depend on fluid and formation properties?
Figure 1.2. Downhole, surface and logging truck operations.
Background development. The present book addresses these questions for "source" or "sink models" of the pumping nozzle, these terms referring to ideal representations of the flow where borehole and pad geometry are described using mathematically small closed surfaces. The recent books due to Chin et al. (2014) or Formation Testing: Pressure Transient and Contamination Analysis, Chin et al. (2015) or Formation Testing: Low Mobility Pressure Transient Analysis, and Chin (2019) or Formation Testing: Supercharge, Pressure Testing and Contamination Models, published by John Wiley & Sons, contain complete math derivations and detailed validations. However, the rapid pace of recent development suggests a separate volume in Wiley's Handbook of Petroleum Engineering Series, focused on the main ideas behind the recent works. These ideas are essential as they are also used in the design of newer COSL formation testing tools as well as in interpretation software now available to the petroleum industry. What engineers lack, at present, are job planning and PTA tools both useful at the rigsite and at engineers' desktops. It is our purpose to support this pressing need.
Figure 1.3. Recent formation testing book publications.
Formation testing design concepts are rich and varied. A pumping probe, operating as a "sink" or (equivalently) a "source," or both, also tracks pressure transient responses. Other pressure probes my reside along the tool body, displaced axially, azimuthally or both, which may actively pump or act as passive observers. While the primary formation tester function is fluid sampling, where in-situ reservoir fluids are collected and transported to the surface for analysis, pressure measurements represent critical by-products important to formation evaluation. Examples of testers offered by different manufacturers for wireline and MWD applications are given in Figures 1.4 - 1.7.
Figure 1.4. Conventional formation tester tool strings.
Figure 1.5. Formation testers, additional developments.
Figure 1.6. Conventional dual and triple probe testers.
Figure 1.7. Dual probe tester with dual packer.
In a "handbook" such as this, it is important to provide examples of prototypes, commercial tools and systems. The wide ranges in design parameters can be surprising to newcomers in formation testing. For example, the "vertical and sink probes" in Figure 1.6, which are displaced axially but lie along the same azimuth, can range from six or seven inches to as much as 2.3 ft (27.6 in) and 10.3 ft (123.6 in), where the latter two distances are obtained from the manufacturer's figure in SPE Paper No. 36176. We might, for example, ask, "Just what does the distant observation probe "see" under different mobility backgrounds?" "Will the tool do the job for my formation?" This book attempts to answer the most obvious questions, but it also aims at providing the tools and software for readers to address those pressing questions that invariably arise in any new logging scenario. To provide a flavor of how hardware literature and specifications might appear, we have included discussion of COSL material related to its standard product lines. Note that COSL's new "triple probe, 120° tool" (as opposed to a conventional 180° tool) is treated separately in our companion 2021 book.
Close-ups of early single and dual probe prototype formation testers are shown in Figure 1.8. These photographs were obtained during field tests. The black pads shown perform an important sealing function, which prevents leakage of fluid through its contact surface with the sandface. However, they are not as "simple" as they appear. For instance, at any given pump rate, the pressure drop, which depends on nozzle diameter, may be excessive and allow the undesired release of dissolved gas - orifice sizes must be chosen judiciously, as suggested by the wide variety of choices shown in Figure 1.9. The shape of the hole or slot is also important; circular or oval shapes may be acceptable for consolidated matrix rock, but slotted models may be required for naturally fractured media or unconsolidated formations. Of course, in supporting PTA interpretation objectives, the size and shape of a formation tester's pads must be incorporated into the host math model. More often than not, the model must be simple and mathematically tractable in order to obtain useful answers in a reasonable amount of time. This may require the use of idealized source or sink models, or numerical models with limited numbers of grids in the case of finite difference or finite modeling - consequently, questions related to calibration or geometric factors arise, along with test procedures, etc.
Figure 1.8. Early COSL single and dual probe prototype formation testers (details in 2014 and 2015 books).
Figure 1.9. COSL pad designs with varied sizes and shapes, for different applications, e.g., firm matrix rock, unconsolidated formations, fractured media, and so on..
Pressures obtained in PTA logging are used for multiple applications. For example, depending on the tool, permeability, anisotropy, compressibility and pore pressure are all possible (the term "mobility," defined as the ratio of permeability to viscosity, is often interchangeably used, assuming that the viscosity is known). The pore pressure itself is used to identify fluids by their vertical hydrostatic gradients; this is possible because changes in pressure are affected by changes in fluid density. Sudden changes in pressure, for instance, may indicate the presence of barriers. However, the raw measured pressure, unless corrected for the "cushioning" effects associated with flowline volume, will not reflect pore pressures accurately. The correction depends, in turn, on the line volume as well as the compressibility and the mobility of the formation fluid. All said, the physics and math can be challenging, but solutions and analytical highlights are presented in the next chapter for a wide variety of tools and applications. Chapter 2 provides a broad state-of-the-art review for source and sink models.
The "Enhanced Formation Dynamic Tester" is an advanced wireline formation testing system that delivers: (1) Multiple, large-volume high-purity formation fluid samples with downhole fluid characterization, (2) Reliable...
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