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.

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• Preface xiiiAcknowledgements xvii1 Pressure Transient Analysis and Sampling in Formation Testing 1Pressure transient analysis challenges 1Background development 31.1 Conventional Formation Testing Concepts 51.2 Prototypes, Tools and Systems 61.2.1 Enhanced Formation Dynamic Tester (EFDT®) 91.2.2 Basic Reservoir Characteristic Tester (BASIC-RCT™) 131.2.3 Enhancing and enabling technologies 15Stuck tool alleviation 16Field facilities 171.3 Recent Formation Testing Developments 171.4 References 202. Spherical Source Models for Forward and Inverse Formulations 212.1 Basic Approaches, Interpretation Issues and Modeling Hierarchies 23Early steady flow model 23Simple drawdown-buildup models 23Analytical drawdown-buildup solution 25Phase delay analysis 26Modeling hierarchies 282.2 Basic Single-Phase Flow Forward and Inverse Algorithms 362.2.1 Module FT-00 362.2.2 Module FT-01 372.2.3 Module FT-03 382.2.4 Forward model application, Module FT-00 392.2.5 Inverse model application, Module FT-01 412.2.6 Effects of dip angle 432.2.7 Inverse “pulse interaction” approach using FT-00 462.2.8 FT-03 model overcomes source-sink limitations 492.2.9 Module FT-04, phase delay analysis, introductory for now 522.2.10 Drawdown-buildup, Module FT-PTA-DDBU 552.2.11 Real pumping, Module FT-06 592.3 Advanced Forward and Inverse Algorithms 612.3.1 Advanced drawdown and buildup methods Basic steady model 61Validating our method 632.3.2 Calibration results and transient pressure curves 652.3.3 Mobility and pore pressure using first drawdown data 672.3.3.1 Run No. 1. Flowline volume 200 cc 682.3.3.2 Run No. 2. Flowline volume 500 cc 692.3.3.3 Run No. 3. Flowline volume 1,000 cc 712.3.3.4 Run No. 4. Flowline volume 2,000 cc 732.3.4 Mobility and pore pressure from last buildup data 742.3.4.1 Run No. 5. Flowline volume 200 cc 742.3.4.2 Run No. 6. Flowline volume 500 cc 762.3.4.3 Run No. 7. Flowline volume 1,000 cc 772.3.4.4 Run No. 8. Flowline volume 2,000 cc 782.3.4.5 Run No. 9. Time-varying flowline volume inputs from FT-07 792.3.5 Phase delay and amplitude attenuation, anisotropic media with dip – detailed theory, model and numerical results 812.3.5.1 Basic mathematical results 82Isotropic model 82Anisotropic extensions 82Vertical well limit 83Horizontal well limit 83Formulas for vertical and horizontal wells 83Deviated well equations 84Deviated well interpretation for both kh and kv 85Two-observation-probe models 862.3.5.2 Numerical examples and typical results 88Example 1. Parameter estimates 89Example 2. Surface plots 90Example 3. Sinusoidal excitation 91Example 4. Rectangular wave excitation 94Example 5. Permeability prediction at general dip angles 96Example 6. Solution for a random input 982.3.5.3 Layered model formulation 992.3.5.4 Phase delay software interface 1002.3.5.5 Detailed phase delay results in layered anisotropic media 1032.3.6 Supercharging and formation invasion introduction, with review of analytical forward and inverse models 1102.3.6.1 Development perspectives 1112.3.6.2 Review of forward and inverse models 113FT-00 model 113FT-01 model 117FT-02 model 118FT-06 and FT-07 models 119FT–PTA–DDBU model 122Classic inversion model 123Supercharge forward and inverse models 123Multiple drawdown and buildup inverse models 129Multiphase invasion, clean-up and contamination 133System integration and closing remarks 1382.3.6.3 Supercharging summaries – advanced forward and inverse models explored 139Supercharge math model development 139Conventional zero supercharge model 141Supercharge extension 1422.3.6.4 Drawdown only applications 144Example DD-1. High overbalance 144Example DD-2. High overbalance 150Example DD-3. High overbalance 154Example DD-4. Qualitative pressure trends 158Example DD-5. Qualitative pressure trends 161Example DD-6. “Drawdown-only” data with multiple inverse scenarios for 1 md/cp application 163Example DD-7. “Drawdown-only” data with multiple inverse scenarios for 0.1 md/cp application 1682.3.6.5 Drawdown – buildup applications 173Example DDBU-1. Drawdown-buildup, high overbalance 173Example DDBU-2. Drawdown-buildup, high overbalance 177Example DDBU-3. Drawdown-buildup, high overbalance 180Example DDBU-4. Drawdown-buildup, 1 md/cp calculations 184Example DDBU-5. Drawdown-buildup, 0.1md/cp calculations 1882.3.7 Advanced multiple drawdown – buildup (or, “MDDBU”) forward and inverse models 1932.3.7.1 Software description 1932.3.7.2 Validation of PTA-App-11 inverse model 2002.3.8 Multiphase flow with inertial effects –Applications to borehole invasion, supercharging, clean-up and contamination analysis 2172.3.8.1 Mudcake dynamics 2172.3.8.2 Multiphase modeling in boreholes 2202.3.8.3 Pressure and concentration displays 222Example 1. Single probe, infinite anisotropic media 223Example 2. Single probe, three layer medium 228Example 3. Dual probe pumping, three layer medium 230Example 4. Straddle packer pumping 231Example 5. Formation fluid viscosity imaging 233Example 6. Contamination modeling 234Example 7. Multi-rate pumping simulation 2342.4 References 2363 Practical Applications Examples 2373.1 Non-constant Flow Rate Effects 2383.1.1 Constant flow rate, idealized pumping, inverse method 2393.1.2 Slow ramp up/down flow rate 2453.1.3 Impulsive start/stop flow rate 250Closing remarks 2553.2 Supercharging – Effects of Nonuniform Initial Pressure 256Conventional zero supercharge model 256Supercharge “Fast Forward” solver 2583.3 Dual Probe Anisotropy Inverse Analysis 2643.4 Multiprobe “DOI,” Inverse and Barrier Analysis 2733.5 Rapid Batch Analysis for History Matching 2813.6 Supercharge, Contamination Depth and Mudcake Growth in “Large Boreholes” – Lineal Flow 289Mudcake growth and filtrate invasion 289Time-dependent pressure distributions 2923.7 Supercharge, Contamination Depth and Mudcake Growth in Slimholes or “Clogged Wells” – Radial Flow 2923.8 References 2944 Supercharge, Pressure Change, Fluid Invasion and Mudcake Growth 295Conventional zero supercharge model 295Supercharge model 296Relevance to formation tester job planning 298Refined models for supercharge invasion 2994.1 Governing equations and moving interface modeling 300Single-phase flow pressure equations 300Problem formulation 303Eulerian versus Lagrangian description 303Constant density versus compressible flow 304Steady versus unsteady flow 305Incorrect use of Darcy’s law 305Moving fronts and interfaces 306Use of effective properties 3084.2 Static and dynamic filtration 3104.2.1 Simple flows without mudcake 310Homogeneous liquid in a uniform linear core 311Homogeneous liquid in a uniform radial flow 313Homogeneous liquid in uniform spherical domain 314Gas flow in a uniform linear core 315Flow from a plane fracture 3174.2.2 Flows with moving boundaries 318Lineal mudcake buildup on filter paper 318Plug flow of two liquids in linear core without cake 3214.3 Coupled Dynamical Problems: Mudcake and Formation Interaction 323Simultaneous mudcake buildup and filtrate invasion in a linear core (liquid flows) 323Simultaneous mudcake buildup and filtrate invasion in a radial geometry (liquid flows) 327Hole plugging and stuck pipe 330Fluid compressibility 331Formation invasion at equilibrium mudcake thickness 3354.4 Inverse Models in Time Lapse Logging 336Experimental model validation 336Static filtration test procedure 337Dynamic filtration testing 337Measurement of mudcake properties 338Formation evaluation from invasion data 338Field applications 339Characterizing mudcake properties 340Simple extrapolation of mudcake properties 341Radial mudcake growth on cylindrical filter paper 3424.5 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination 345Simple porosity determination 345Radial invasion without mudcake 346Problem 1 348Problem 2 350Time lapse analysis using general muds 351Problem 1 352Problem 2 3534.6 Examples of Time Lapse Analysis 354Formation permeability and hydrocarbon viscosity 355Pore pressure, rock permeability and fluid viscosity 3574.7 References 3605 Numerical Supercharge, Pressure, Displacement and Multiphase Flow Models 3635.1 Finite Difference Solutions 364Basic formulas 364Model constant density flow analysis 366Transient compressible flow modeling 369Numerical stability 371Convergence 371Multiple physical time and space scales 372Example 5-1. Lineal liquid displacement without mudcake 373Example 5-2. Cylindrical radial liquid displacement without cake 380Example 5-3. Spherical radial liquid displacement without cake 383Example 5-4. Lineal liquid displacement without mudcake, including compressible flow transients 385Example 5-5. Von Neumann stability of implicit time schemes 388Example 5-6. Gas displacement by liquid in lineal core without mudcake, including compressible flow transients 390Incompressible problem 391Transient, compressible problem 392Example 5-7. Simultaneous mudcake buildup and displacement front motion for incompressible liquid flows 396Matching conditions at displacement front 399Matching conditions at the cake-to-rock interface 399Coding modifications 400Modeling formation heterogeneities 403Mudcake compaction and compressibility 404Modeling borehole activity 4055.2 Forward and Inverse Multiphase Flow Modeling 405Problem hierarchies 4065.2.1 Immiscible Buckley-Leverett lineal flows without capillary pressure 407Example boundary value problems 409General initial value problem 410General boundary value problem for infinite core 411Variable q(t) 411Mudcake-dominated invasion 412Shock velocity 412Pressure solution 4145.2.2 Molecular diffusion in fluid flows 415Exact lineal flow solutions 416Numerical analysis 417Diffusion in cake-dominated flows 419Resistivity migration 419Lineal diffusion and “un-diffusion” examples 420Radial diffusion and “un-diffusion” examples 4235.2.3 Immiscible radial flows with capillary pressure and prescribed mudcake growth 425Governing saturation equation 426Numerical analysis 427Fortran implementation 429Typical calculations 429Mudcake dominated flows 435“Un-shocking” a saturation discontinuity 4385.2.4 Immiscible flows with capillary pressure and dynamically coupled mudcake growth 441Flows without mudcakes 441Modeling mudcake coupling 450Unchanging mudcake thickness 451Transient mudcake growth 453General immiscible flow model 4575.3 Closing Remarks 4585.4 References 464Cumulative References 467Index 481About the Authors 498

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.

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• Preface xiiiAcknowledgements xvii1 Pressure Transient Analysis and Sampling in Formation Testing 1Pressure transient analysis challenges 1Background development 31.1 Conventional Formation Testing Concepts 51.2 Prototypes, Tools and Systems 61.2.1 Enhanced Formation Dynamic Tester (EFDT®) 91.2.2 Basic Reservoir Characteristic Tester (BASIC-RCT™) 131.2.3 Enhancing and enabling technologies 15Stuck tool alleviation 16Field facilities 171.3 Recent Formation Testing Developments 171.4 References 202. Spherical Source Models for Forward and Inverse Formulations 212.1 Basic Approaches, Interpretation Issues and Modeling Hierarchies 23Early steady flow model 23Simple drawdown-buildup models 23Analytical drawdown-buildup solution 25Phase delay analysis 26Modeling hierarchies 282.2 Basic Single-Phase Flow Forward and Inverse Algorithms 362.2.1 Module FT-00 362.2.2 Module FT-01 372.2.3 Module FT-03 382.2.4 Forward model application, Module FT-00 392.2.5 Inverse model application, Module FT-01 412.2.6 Effects of dip angle 432.2.7 Inverse “pulse interaction” approach using FT-00 462.2.8 FT-03 model overcomes source-sink limitations 492.2.9 Module FT-04, phase delay analysis, introductory for now 522.2.10 Drawdown-buildup, Module FT-PTA-DDBU 552.2.11 Real pumping, Module FT-06 592.3 Advanced Forward and Inverse Algorithms 612.3.1 Advanced drawdown and buildup methods Basic steady model 61Validating our method 632.3.2 Calibration results and transient pressure curves 652.3.3 Mobility and pore pressure using first drawdown data 672.3.3.1 Run No. 1. Flowline volume 200 cc 682.3.3.2 Run No. 2. Flowline volume 500 cc 692.3.3.3 Run No. 3. Flowline volume 1,000 cc 712.3.3.4 Run No. 4. Flowline volume 2,000 cc 732.3.4 Mobility and pore pressure from last buildup data 742.3.4.1 Run No. 5. Flowline volume 200 cc 742.3.4.2 Run No. 6. Flowline volume 500 cc 762.3.4.3 Run No. 7. Flowline volume 1,000 cc 772.3.4.4 Run No. 8. Flowline volume 2,000 cc 782.3.4.5 Run No. 9. Time-varying flowline volume inputs from FT-07 792.3.5 Phase delay and amplitude attenuation, anisotropic media with dip – detailed theory, model and numerical results 812.3.5.1 Basic mathematical results 82Isotropic model 82Anisotropic extensions 82Vertical well limit 83Horizontal well limit 83Formulas for vertical and horizontal wells 83Deviated well equations 84Deviated well interpretation for both kh and kv 85Two-observation-probe models 862.3.5.2 Numerical examples and typical results 88Example 1. Parameter estimates 89Example 2. Surface plots 90Example 3. Sinusoidal excitation 91Example 4. Rectangular wave excitation 94Example 5. Permeability prediction at general dip angles 96Example 6. Solution for a random input 982.3.5.3 Layered model formulation 992.3.5.4 Phase delay software interface 1002.3.5.5 Detailed phase delay results in layered anisotropic media 1032.3.6 Supercharging and formation invasion introduction, with review of analytical forward and inverse models 1102.3.6.1 Development perspectives 1112.3.6.2 Review of forward and inverse models 113FT-00 model 113FT-01 model 117FT-02 model 118FT-06 and FT-07 models 119FT–PTA–DDBU model 122Classic inversion model 123Supercharge forward and inverse models 123Multiple drawdown and buildup inverse models 129Multiphase invasion, clean-up and contamination 133System integration and closing remarks 1382.3.6.3 Supercharging summaries – advanced forward and inverse models explored 139Supercharge math model development 139Conventional zero supercharge model 141Supercharge extension 1422.3.6.4 Drawdown only applications 144Example DD-1. High overbalance 144Example DD-2. High overbalance 150Example DD-3. High overbalance 154Example DD-4. Qualitative pressure trends 158Example DD-5. Qualitative pressure trends 161Example DD-6. “Drawdown-only” data with multiple inverse scenarios for 1 md/cp application 163Example DD-7. “Drawdown-only” data with multiple inverse scenarios for 0.1 md/cp application 1682.3.6.5 Drawdown – buildup applications 173Example DDBU-1. Drawdown-buildup, high overbalance 173Example DDBU-2. Drawdown-buildup, high overbalance 177Example DDBU-3. Drawdown-buildup, high overbalance 180Example DDBU-4. Drawdown-buildup, 1 md/cp calculations 184Example DDBU-5. Drawdown-buildup, 0.1md/cp calculations 1882.3.7 Advanced multiple drawdown – buildup (or, “MDDBU”) forward and inverse models 1932.3.7.1 Software description 1932.3.7.2 Validation of PTA-App-11 inverse model 2002.3.8 Multiphase flow with inertial effects –Applications to borehole invasion, supercharging, clean-up and contamination analysis 2172.3.8.1 Mudcake dynamics 2172.3.8.2 Multiphase modeling in boreholes 2202.3.8.3 Pressure and concentration displays 222Example 1. Single probe, infinite anisotropic media 223Example 2. Single probe, three layer medium 228Example 3. Dual probe pumping, three layer medium 230Example 4. Straddle packer pumping 231Example 5. Formation fluid viscosity imaging 233Example 6. Contamination modeling 234Example 7. Multi-rate pumping simulation 2342.4 References 2363 Practical Applications Examples 2373.1 Non-constant Flow Rate Effects 2383.1.1 Constant flow rate, idealized pumping, inverse method 2393.1.2 Slow ramp up/down flow rate 2453.1.3 Impulsive start/stop flow rate 250Closing remarks 2553.2 Supercharging – Effects of Nonuniform Initial Pressure 256Conventional zero supercharge model 256Supercharge “Fast Forward” solver 2583.3 Dual Probe Anisotropy Inverse Analysis 2643.4 Multiprobe “DOI,” Inverse and Barrier Analysis 2733.5 Rapid Batch Analysis for History Matching 2813.6 Supercharge, Contamination Depth and Mudcake Growth in “Large Boreholes” – Lineal Flow 289Mudcake growth and filtrate invasion 289Time-dependent pressure distributions 2923.7 Supercharge, Contamination Depth and Mudcake Growth in Slimholes or “Clogged Wells” – Radial Flow 2923.8 References 2944 Supercharge, Pressure Change, Fluid Invasion and Mudcake Growth 295Conventional zero supercharge model 295Supercharge model 296Relevance to formation tester job planning 298Refined models for supercharge invasion 2994.1 Governing equations and moving interface modeling 300Single-phase flow pressure equations 300Problem formulation 303Eulerian versus Lagrangian description 303Constant density versus compressible flow 304Steady versus unsteady flow 305Incorrect use of Darcy’s law 305Moving fronts and interfaces 306Use of effective properties 3084.2 Static and dynamic filtration 3104.2.1 Simple flows without mudcake 310Homogeneous liquid in a uniform linear core 311Homogeneous liquid in a uniform radial flow 313Homogeneous liquid in uniform spherical domain 314Gas flow in a uniform linear core 315Flow from a plane fracture 3174.2.2 Flows with moving boundaries 318Lineal mudcake buildup on filter paper 318Plug flow of two liquids in linear core without cake 3214.3 Coupled Dynamical Problems: Mudcake and Formation Interaction 323Simultaneous mudcake buildup and filtrate invasion in a linear core (liquid flows) 323Simultaneous mudcake buildup and filtrate invasion in a radial geometry (liquid flows) 327Hole plugging and stuck pipe 330Fluid compressibility 331Formation invasion at equilibrium mudcake thickness 3354.4 Inverse Models in Time Lapse Logging 336Experimental model validation 336Static filtration test procedure 337Dynamic filtration testing 337Measurement of mudcake properties 338Formation evaluation from invasion data 338Field applications 339Characterizing mudcake properties 340Simple extrapolation of mudcake properties 341Radial mudcake growth on cylindrical filter paper 3424.5 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination 345Simple porosity determination 345Radial invasion without mudcake 346Problem 1 348Problem 2 350Time lapse analysis using general muds 351Problem 1 352Problem 2 3534.6 Examples of Time Lapse Analysis 354Formation permeability and hydrocarbon viscosity 355Pore pressure, rock permeability and fluid viscosity 3574.7 References 3605 Numerical Supercharge, Pressure, Displacement and Multiphase Flow Models 3635.1 Finite Difference Solutions 364Basic formulas 364Model constant density flow analysis 366Transient compressible flow modeling 369Numerical stability 371Convergence 371Multiple physical time and space scales 372Example 5-1. Lineal liquid displacement without mudcake 373Example 5-2. Cylindrical radial liquid displacement without cake 380Example 5-3. Spherical radial liquid displacement without cake 383Example 5-4. Lineal liquid displacement without mudcake, including compressible flow transients 385Example 5-5. Von Neumann stability of implicit time schemes 388Example 5-6. Gas displacement by liquid in lineal core without mudcake, including compressible flow transients 390Incompressible problem 391Transient, compressible problem 392Example 5-7. Simultaneous mudcake buildup and displacement front motion for incompressible liquid flows 396Matching conditions at displacement front 399Matching conditions at the cake-to-rock interface 399Coding modifications 400Modeling formation heterogeneities 403Mudcake compaction and compressibility 404Modeling borehole activity 4055.2 Forward and Inverse Multiphase Flow Modeling 405Problem hierarchies 4065.2.1 Immiscible Buckley-Leverett lineal flows without capillary pressure 407Example boundary value problems 409General initial value problem 410General boundary value problem for infinite core 411Variable q(t) 411Mudcake-dominated invasion 412Shock velocity 412Pressure solution 4145.2.2 Molecular diffusion in fluid flows 415Exact lineal flow solutions 416Numerical analysis 417Diffusion in cake-dominated flows 419Resistivity migration 419Lineal diffusion and “un-diffusion” examples 420Radial diffusion and “un-diffusion” examples 4235.2.3 Immiscible radial flows with capillary pressure and prescribed mudcake growth 425Governing saturation equation 426Numerical analysis 427Fortran implementation 429Typical calculations 429Mudcake dominated flows 435“Un-shocking” a saturation discontinuity 4385.2.4 Immiscible flows with capillary pressure and dynamically coupled mudcake growth 441Flows without mudcakes 441Modeling mudcake coupling 450Unchanging mudcake thickness 451Transient mudcake growth 453General immiscible flow model 4575.3 Closing Remarks 4585.4 References 464Cumulative References 467Index 481About the Authors 498

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.

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• Preface xiiiAcknowledgements xvii1 Pressure Transient Analysis and Sampling in Formation Testing 1Pressure transient analysis challenges 1Background development 31.1 Conventional Formation Testing Concepts 51.2 Prototypes, Tools and Systems 61.2.1 Enhanced Formation Dynamic Tester (EFDT®) 91.2.2 Basic Reservoir Characteristic Tester (BASIC-RCT™) 131.2.3 Enhancing and enabling technologies 15Stuck tool alleviation 16Field facilities 171.3 Recent Formation Testing Developments 171.4 References 202. Spherical Source Models for Forward and Inverse Formulations 212.1 Basic Approaches, Interpretation Issues and Modeling Hierarchies 23Early steady flow model 23Simple drawdown-buildup models 23Analytical drawdown-buildup solution 25Phase delay analysis 26Modeling hierarchies 282.2 Basic Single-Phase Flow Forward and Inverse Algorithms 362.2.1 Module FT-00 362.2.2 Module FT-01 372.2.3 Module FT-03 382.2.4 Forward model application, Module FT-00 392.2.5 Inverse model application, Module FT-01 412.2.6 Effects of dip angle 432.2.7 Inverse “pulse interaction” approach using FT-00 462.2.8 FT-03 model overcomes source-sink limitations 492.2.9 Module FT-04, phase delay analysis, introductory for now 522.2.10 Drawdown-buildup, Module FT-PTA-DDBU 552.2.11 Real pumping, Module FT-06 592.3 Advanced Forward and Inverse Algorithms 612.3.1 Advanced drawdown and buildup methods Basic steady model 61Validating our method 632.3.2 Calibration results and transient pressure curves 652.3.3 Mobility and pore pressure using first drawdown data 672.3.3.1 Run No. 1. Flowline volume 200 cc 682.3.3.2 Run No. 2. Flowline volume 500 cc 692.3.3.3 Run No. 3. Flowline volume 1,000 cc 712.3.3.4 Run No. 4. Flowline volume 2,000 cc 732.3.4 Mobility and pore pressure from last buildup data 742.3.4.1 Run No. 5. Flowline volume 200 cc 742.3.4.2 Run No. 6. Flowline volume 500 cc 762.3.4.3 Run No. 7. Flowline volume 1,000 cc 772.3.4.4 Run No. 8. Flowline volume 2,000 cc 782.3.4.5 Run No. 9. Time-varying flowline volume inputs from FT-07 792.3.5 Phase delay and amplitude attenuation, anisotropic media with dip – detailed theory, model and numerical results 812.3.5.1 Basic mathematical results 82Isotropic model 82Anisotropic extensions 82Vertical well limit 83Horizontal well limit 83Formulas for vertical and horizontal wells 83Deviated well equations 84Deviated well interpretation for both kh and kv 85Two-observation-probe models 862.3.5.2 Numerical examples and typical results 88Example 1. Parameter estimates 89Example 2. Surface plots 90Example 3. Sinusoidal excitation 91Example 4. Rectangular wave excitation 94Example 5. Permeability prediction at general dip angles 96Example 6. Solution for a random input 982.3.5.3 Layered model formulation 992.3.5.4 Phase delay software interface 1002.3.5.5 Detailed phase delay results in layered anisotropic media 1032.3.6 Supercharging and formation invasion introduction, with review of analytical forward and inverse models 1102.3.6.1 Development perspectives 1112.3.6.2 Review of forward and inverse models 113FT-00 model 113FT-01 model 117FT-02 model 118FT-06 and FT-07 models 119FT–PTA–DDBU model 122Classic inversion model 123Supercharge forward and inverse models 123Multiple drawdown and buildup inverse models 129Multiphase invasion, clean-up and contamination 133System integration and closing remarks 1382.3.6.3 Supercharging summaries – advanced forward and inverse models explored 139Supercharge math model development 139Conventional zero supercharge model 141Supercharge extension 1422.3.6.4 Drawdown only applications 144Example DD-1. High overbalance 144Example DD-2. High overbalance 150Example DD-3. High overbalance 154Example DD-4. Qualitative pressure trends 158Example DD-5. Qualitative pressure trends 161Example DD-6. “Drawdown-only” data with multiple inverse scenarios for 1 md/cp application 163Example DD-7. “Drawdown-only” data with multiple inverse scenarios for 0.1 md/cp application 1682.3.6.5 Drawdown – buildup applications 173Example DDBU-1. Drawdown-buildup, high overbalance 173Example DDBU-2. Drawdown-buildup, high overbalance 177Example DDBU-3. Drawdown-buildup, high overbalance 180Example DDBU-4. Drawdown-buildup, 1 md/cp calculations 184Example DDBU-5. Drawdown-buildup, 0.1md/cp calculations 1882.3.7 Advanced multiple drawdown – buildup (or, “MDDBU”) forward and inverse models 1932.3.7.1 Software description 1932.3.7.2 Validation of PTA-App-11 inverse model 2002.3.8 Multiphase flow with inertial effects –Applications to borehole invasion, supercharging, clean-up and contamination analysis 2172.3.8.1 Mudcake dynamics 2172.3.8.2 Multiphase modeling in boreholes 2202.3.8.3 Pressure and concentration displays 222Example 1. Single probe, infinite anisotropic media 223Example 2. Single probe, three layer medium 228Example 3. Dual probe pumping, three layer medium 230Example 4. Straddle packer pumping 231Example 5. Formation fluid viscosity imaging 233Example 6. Contamination modeling 234Example 7. Multi-rate pumping simulation 2342.4 References 2363 Practical Applications Examples 2373.1 Non-constant Flow Rate Effects 2383.1.1 Constant flow rate, idealized pumping, inverse method 2393.1.2 Slow ramp up/down flow rate 2453.1.3 Impulsive start/stop flow rate 250Closing remarks 2553.2 Supercharging – Effects of Nonuniform Initial Pressure 256Conventional zero supercharge model 256Supercharge “Fast Forward” solver 2583.3 Dual Probe Anisotropy Inverse Analysis 2643.4 Multiprobe “DOI,” Inverse and Barrier Analysis 2733.5 Rapid Batch Analysis for History Matching 2813.6 Supercharge, Contamination Depth and Mudcake Growth in “Large Boreholes” – Lineal Flow 289Mudcake growth and filtrate invasion 289Time-dependent pressure distributions 2923.7 Supercharge, Contamination Depth and Mudcake Growth in Slimholes or “Clogged Wells” – Radial Flow 2923.8 References 2944 Supercharge, Pressure Change, Fluid Invasion and Mudcake Growth 295Conventional zero supercharge model 295Supercharge model 296Relevance to formation tester job planning 298Refined models for supercharge invasion 2994.1 Governing equations and moving interface modeling 300Single-phase flow pressure equations 300Problem formulation 303Eulerian versus Lagrangian description 303Constant density versus compressible flow 304Steady versus unsteady flow 305Incorrect use of Darcy’s law 305Moving fronts and interfaces 306Use of effective properties 3084.2 Static and dynamic filtration 3104.2.1 Simple flows without mudcake 310Homogeneous liquid in a uniform linear core 311Homogeneous liquid in a uniform radial flow 313Homogeneous liquid in uniform spherical domain 314Gas flow in a uniform linear core 315Flow from a plane fracture 3174.2.2 Flows with moving boundaries 318Lineal mudcake buildup on filter paper 318Plug flow of two liquids in linear core without cake 3214.3 Coupled Dynamical Problems: Mudcake and Formation Interaction 323Simultaneous mudcake buildup and filtrate invasion in a linear core (liquid flows) 323Simultaneous mudcake buildup and filtrate invasion in a radial geometry (liquid flows) 327Hole plugging and stuck pipe 330Fluid compressibility 331Formation invasion at equilibrium mudcake thickness 3354.4 Inverse Models in Time Lapse Logging 336Experimental model validation 336Static filtration test procedure 337Dynamic filtration testing 337Measurement of mudcake properties 338Formation evaluation from invasion data 338Field applications 339Characterizing mudcake properties 340Simple extrapolation of mudcake properties 341Radial mudcake growth on cylindrical filter paper 3424.5 Porosity, Permeability, Oil Viscosity and Pore Pressure Determination 345Simple porosity determination 345Radial invasion without mudcake 346Problem 1 348Problem 2 350Time lapse analysis using general muds 351Problem 1 352Problem 2 3534.6 Examples of Time Lapse Analysis 354Formation permeability and hydrocarbon viscosity 355Pore pressure, rock permeability and fluid viscosity 3574.7 References 3605 Numerical Supercharge, Pressure, Displacement and Multiphase Flow Models 3635.1 Finite Difference Solutions 364Basic formulas 364Model constant density flow analysis 366Transient compressible flow modeling 369Numerical stability 371Convergence 371Multiple physical time and space scales 372Example 5-1. Lineal liquid displacement without mudcake 373Example 5-2. Cylindrical radial liquid displacement without cake 380Example 5-3. Spherical radial liquid displacement without cake 383Example 5-4. Lineal liquid displacement without mudcake, including compressible flow transients 385Example 5-5. Von Neumann stability of implicit time schemes 388Example 5-6. Gas displacement by liquid in lineal core without mudcake, including compressible flow transients 390Incompressible problem 391Transient, compressible problem 392Example 5-7. Simultaneous mudcake buildup and displacement front motion for incompressible liquid flows 396Matching conditions at displacement front 399Matching conditions at the cake-to-rock interface 399Coding modifications 400Modeling formation heterogeneities 403Mudcake compaction and compressibility 404Modeling borehole activity 4055.2 Forward and Inverse Multiphase Flow Modeling 405Problem hierarchies 4065.2.1 Immiscible Buckley-Leverett lineal flows without capillary pressure 407Example boundary value problems 409General initial value problem 410General boundary value problem for infinite core 411Variable q(t) 411Mudcake-dominated invasion 412Shock velocity 412Pressure solution 4145.2.2 Molecular diffusion in fluid flows 415Exact lineal flow solutions 416Numerical analysis 417Diffusion in cake-dominated flows 419Resistivity migration 419Lineal diffusion and “un-diffusion” examples 420Radial diffusion and “un-diffusion” examples 4235.2.3 Immiscible radial flows with capillary pressure and prescribed mudcake growth 425Governing saturation equation 426Numerical analysis 427Fortran implementation 429Typical calculations 429Mudcake dominated flows 435“Un-shocking” a saturation discontinuity 4385.2.4 Immiscible flows with capillary pressure and dynamically coupled mudcake growth 441Flows without mudcakes 441Modeling mudcake coupling 450Unchanging mudcake thickness 451Transient mudcake growth 453General immiscible flow model 4575.3 Closing Remarks 4585.4 References 464Cumulative References 467Index 481About the Authors 498