Supercharge, Invasion, and Mudcake Growth in Downhole Applications

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™) 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