Formation Testing

Wilson C. Chin, who earned his Ph.D. from M.I.T. and M.Sc. from Caltech, heads Stratamagnetic Software, LLC in Houston, which develops mathematical modeling software for formation testing, MWD telemetry, borehole electromagnetics, well logging, reservoir engineering and managed pressure drilling. He is the author of twelve books, more than one hundred papers and over forty patents.Yanmin Zhou received her Ph.D. in Geological Resources Engineering from the University of Petroleum, Beijing, and serves as Geophysics Engineer at the China National Offshore Oil Corporation.Yongren Feng is Chief Mechanical Engineer at the China National Offshore Oil Corporation with three decades of design experience covering a dozen logging tools. With more than one hundred patents, he serves as Project Leader for the 12th National Five Year Plan in formation tester development, and he was elected as one of China's National Technology and Innovation Leaders.Qiang Yu earned his M.Sc. in Measurement Technology and Instrumentation from Xi'an Shiyou University and serves as Senior Control Engineer in formation testing and field operations. He is an Associate Project Leader with the China National Offshore Oil Corporation in the national formation testing program.

• Preface xiAcknowledgements xiii1 Basic Ideas, Interpretation Issues and Modeling Hierarchies 11.1 Background and Approaches 11.2 Modeling Hierarchies 51.3 Experimental Methods and Tool Calibration 131.4 References 242 Single-Phase Flow Forward and Inverse Algorithms 252.1 Overview 252.2 Basic Model Summaries 272.2.1 Module FT-00 282.2.2 Module FT-01 302.2.3 Module FT-03 302.2.4 Forward Model Application, Module FT-00 312.2.5 Inverse Model Application, Module FT-01 332.2.6 Eff ects of Dip Angle 352.2.7 Inverse “Pulse Interaction” Approach Using FT-00 372.2.8 Computational Notes 402.2.9 Source Model Limitations and More Complete Model 412.2.10 Phase Delay Analysis, Module FT-04 432.2.11 Drawdown-Buildup, Module FT-PTA-DDBU 452.2.12 Real Pumping, Module FT-06 482.2.13 Closing Remarks 502.2.14 References 503 Advanced Drawdown and Buildup Interpretation in Low Mobility Environments 513.1 Basic Steady Flow Model 513.2 Transient Spherical Flow Models 533.2.1 Forward or Direct Analysis 533.2.2 Dimensionless Formulation 543.2.3 Exact Solutions for Direct Problem 553.2.4 Special Limit Solutions 563.2.5 New Inverse Approach for Mobility and Pore Pressure Prediction 583.3 Multiple-Drawdown Pressure Analysis (Patent Pending) 593.3.1 Background on Existing Models 593.3.2 Extension to Anisotropic, No-Skin Applications 603.3.2.1 Method 1 - Drawdown-Alone Test 613.3.2.2 Method 2 - Single-Drawdown-Single-Buildup Test 623.3.2.3 Method 3 - Double-Drawdown-Single-Buildup Test 623.4 Forward Analysis with Illustrative Calibration 643.5 Mobility and Pore Pressure Using First Drawdown Data 663.5.1 Run No. 1, Flowline Volume 200 Cc 663.5.2 Run No. 2, Flowline Volume 500 Cc 693.5.3 Run No. 3, Flowline Volume 1,000 Cc 713.5.4 Run No. 4, Flowline Volume 2,000 Cc 733.6 Mobility and Pore Pressure from Last Buildup Data 743.6.1 Run No. 5, Flowline Volume 200 Cc 743.6.2 Run No. 6, Flowline Volume 500 Cc 763.6.3 Run No. 7, Flowline Volume 1,000 Cc 773.6.4 Run No. 8, Flowline Volume 2,000 Cc 783.6.5 Run No. 9, Time-Varying Flowline Volume 793.7 Tool Calibration in Low Mobility Applications 813.7.1 Steady Flow Model 813.7.2 Example 1, Calibration Using Early-Time Buildup Data 813.7.3 Example 2, Calibration Using Early-Time Buildup Data 863.7.4 Example 3, Example 1 Using Drawdown Data 893.7.5 Example 4, Example 2 Using Drawdown Data 913.8 Closing Remarks 933.9 References 944 Phase Delay and Amplitude Attenuation for Mobility Prediction in Anisotropic Media with Dip (Patent Pending) 954.1 Basic Mathematical Results 964.1.1 Isotropic Model 964.1.2 Anisotropic Equations 984.1.3 Vertical Well Solution 994.1.4 Horizontal Well Solution 1004.1.5 Formulas for Vertical and Horizontal Wells 1014.1.6 Deviated Well Equations 1014.1.7 Deviated Well Interpretation for Both Kh and Kv 1034.1.8 Two-Observation-Probe Models 1054.2 Numerical Examples and Typical Results 1074.2.1 Example 1, Parameter Estimates 1084.2.2 Example 2, Surface Plots 1094.2.3 Example 3, Sinusoidal Excitation 1104.2.4 Example 4, Rectangular Wave Excitation 1134.2.5 Example 5, Permeability Prediction at General Dip Angles 1154.2.6 Example 6, Solution for a Random Input 1174.3 Layered Model Formulation 1184.3.1 Homogeneous Medium, Basic Mathematical Ideas 1184.3.2 Boundary Value Problem for Complex Pressure 1204.3.3 Iiterative Numerical Solution to General Formulation 1204.3.4 Successive Line Over Relaxation Procedure 1214.3.5 Advantages of the Scheme 1224.3.6 Extensions to Multiple Layers 1224.3.7 Extensions to Complete Formation Heterogeneity 1234.4 Phase Delay Software Interface 1234.4.1 Output File Notes 1264.4.2 Special User Features 1264.5 Detailed Phase Delay Results in Layered Anisotropic Media 1274.6 Typical Experimental Results 1344.7 Closing Remarks - Extensions and Additional Applications 1384.8 References 1395 Four Permeability Prediction Methods 1405.1 Steady-State Drawdown Example 1425.2 Early-Time, Low-Mobility Drawdown-Buildup 1445.3 Early-Time, Low-Mobility Drawdown Approach 1475.4 Phase Delay, Non-Ideal Rectangular Flow Excitation 1486 Multiphase Flow with Inertial Effects 1516.1 Physical Problem Description 1526.1.1 The Physical Problem 1526.1.2 Job Planning Considerations 1546.1.3 Modeling Challenges 1556.1.4 Simulation Objectives 1566.1.5 Modeling Overview 1576.2 Immiscible Flow Formulation 1596.2.1 Finite Difference Solution 1606.2.2 Formation Tester Application 1616.2.3 Mudcake Growth and Formation Coupling at Sandface 1636.2.4 Pumpout Model for Single-Probe Pad Nozzles 1656.2.5 Dual Probe and Packer Surface Logic 1666.3 Miscible Flow Formulation 1686.4 Inertial Effects With Forchheimer Corrections 1696.4.1 Governing Differential Equations 1696.4.2 Pumpout Boundary Condition 1716.4.3 Boundary Value Problem Summary 1726.5 References 1737 Multiphase Flow - Miscible Mixing Clean-Up Examples 1757.1 Overview Capabilities 1757.1.1 Example 1, Single Probe, Infinite Anisotropic Media 1767.1.2 Example 2, Single Probe, Three Layer Medium 1817.1.3 Example 3, Dual Probe Pumping, Three Layer Medium 1837.1.4 Example 4, Straddle Packer Pumping 1857.1.5 Example 5, Formation Fluid Viscosity Imaging 1877.1.6 Example 6, Contamination Modeling 1887.1.7 Example 7, Multi-Rate Pumping Simulation 1897.2 Source Code and User Interface Improvements 1917.2.1 User Data Input Panel 1917.2.2 Source Code Engine Changes 1937.2.3 Output Color Graphics 1957.3 Detailed Applications 2007.3.1 Run No. 1, Clean-Up, Single-Probe, Uniform Medium 2007.3.2 Run No. 2, Clean-Up, Dual-Probe, Uniform Medium 2097.3.3 Run No. 3, Clean-Up, Elongated Pad, Uniform Medium 2137.3.4 Run No. 4, A Minimal Invasion Example 2187.3.5 Run No. 5, A Single-Phase Fluid, Constant Viscosity example 2227.3.6 Run No. 6, A Low-Permeability “Supercharging” Example 2247.3.7 Run No. 7, A Three-Layer Simulation 2268 Time-Varying Flowline Volume 2298.1 Transient Anisotropic Formulation for Ellipsoidal Source 2308.1.1 Formulation for Liquids and Gases 2308.1.2 Similarity Transform 2328.1.3 Transient Flow Numerical Modeling 2338.1.4 Finite Difference Equation 2348.1.5 Boundary Condition - Flowline Storage With and Without Skin Effects 2358.1.6 Detailed Time Integration Scheme 2368.1.7 Observation Probe Response 2378.2 FT-06 Software Interface and Example Calculations 2388.3 Time-Varying Flowline Volume Model 2448.3.1 Example 1, Software Calibration 2458.3.2 Example 2, Simple Interpretation Using Numerical Pressure Data 2528.3.3 Example 3, Simple Interpretation Using Numerical Pressure Data 2558.3.4 Example 4, Simple Interpretation Using Low Permeability Data 2578.3.5 Example 5, Simple Interpretation Using Numerical Pressure Data 2588.3.6 Example 6, Simple Interpretation Using Numerical Pressure Data 2628.3.7 Example 7, Enhancing Phase Delay Detection In Very Low Permeability Environments 2649 Closing Remarks 270References 281Index 287About the Authors 293