Measurement While Drilling

Signal Analysis, Optimization and Design

by

Wilson C. Chin, Ph.D., M.I.T.

Stratamagnetic Software, LLC, Houston, Texas

Yinao Su, Limin Sheng, Lin Li, Hailong Bian and Rong Shi

China National Petroleum Corporation (CNPC), Beijing, China

Table of Contents

Opening Message, ix

Preface, x

Acknowledgements, xiii

1. Stories from the Field, Fundamental Questions and Solutions, 1

1.1 Mysteries, Clues and Possibilities, 1

1.2 Paper No. AADE-11-NTCE-74, "High-Data-Rate Measurement-While-Drilling System for Very Deep Wells," updated, 10

1.2.1 Abstract, 10

1.2.2 Introduction, 10

1.2.3 MWD telemetry basis, 12

1.2.4 New telemetry approach, 13

1.2.5 New technology elements, 15

1.2.5.1 Downhole source and signal optimization, 15

1.2.5.2 Surface signal processing and noise removal, 18

1.2.5.3 Pressure, torque and erosion computer modeling, 19

1.2.5.4 Wind tunnel analysis: studying new approaches, 22

1.2.5.5 Example test results, 41

1.2.6 Conclusions, 44

1.2.7 Acknowledgements, 45

1.2.8 References, 45

1.3 References, 46

2. Harmonic Analysis: Six-Segment Downhole Acoustic Waveguide, 47

2.1 MWD Fundamentals, 48

2.2 MWD Telemetry Concepts Re-examined, 49

2.2.1 Conventional pulser ideas explained, 49

2.2.2 Acoustics at higher data rates, 50

2.2.3 High-data-rate continuous wave telemetry, 52

2.2.4 Drillbit as a reflector, 53

2.2.5 Source modeling subtleties and errors, 54

2.2.6 Flow loop and field test subtleties, 56

2.2.7 Wind tunnel testing comments, 58

2.3 Downhole Wave Propagation Subtleties, 58

2.3.1 Three distinct physical problems, 59

2.3.2 Downhole source problem, 60

2.4 Six-Segment Downhole Waveguide Model, 62

2.4.1 Nomenclature, 64

2.4.2 Mathematical formulation, 66

2.4.2.1 Dipole source, drill collar modeling, 66

2.4.2.2 Harmonic analysis, 68

2.4.2.3 Governing partial differential equations, 69

2.4.2.4 Matching conditions at impedance junctions, 71

2.4.2.5 Matrix formulation, 72

2.4.2.6 Matrix inversion, 74

2.4.2.7 Final data analysis, 75

2.5 An Example: Optimizing Pulser Signal Strength, 77

2.5.1 Problem definition and results, 77

2.5.2 User interface, 80

2.5.3 Constructive interference at high frequencies, 81

2.6 Additional Engineering Conclusions, 83

2.7 References, 85

3. Harmonic Analysis: Elementary Pipe and Collar Models, 86

3.1 Constant area drillpipe wave models, 86

3.1.1 Case (a), infinite system, both directions, 87

3.1.2 Case (b), drillbit as a solid reflector, 88

3.1.3 Case (c), drillbit as open-ended reflector, 88

3.1.4 Case (d), "finite-finite" waveguide of length 2L, 89

3.1.5 Physical Interpretation, 89

3.2 Variable area collar-pipe wave models, 92

3.2.1 Mathematical formulation, 92

3.2.2 Example calculations, 94

3.3 References, 96

4. Transient Constant Area Surface and Downhole Wave Models, 97

Overview, 97

4.1 Method 4-1. Upgoing wave reflection at solid boundary,

single transducer deconvolution using delay equation, no

mud pump noise, 99

4.1.1 Physical problem, 99

4.1.2 Theory, 100

4.1.3 Run 1. Wide signal – low data rate, 101

4.1.4 Run 2. Narrow pulse width – high data rate, 103

4.1.5 Run 3. Phase-shift keying or PSK, 104

4.1.6 Runs 4, 5. Phase-shift keying or PSK, very high data rate, 107

4.2 Method 4-2. Upgoing wave reflection at solid boundary, single transducer deconvolution using delay equation, with mud pump noise, 108

4.2.1 Physical Problem, 108

4.2.2 Software note, 109

4.2.3 Theory, 109

4.2.4 Run 1. 12 Hz PSK, plus pump noise with S/N = 0.25, 110

4.2.5 Run 2. 24 Hz PSK, plus pump noise with S/N = 0.25, 111

4.3 Method 4-3. Directional filtering – *difference* equation method requiring two transducers, 112

4.3.1 Physical problem, 112

4.3.2 Theory, 113

4.3.3 Run 1. Single narrow pulse, S/N = 1, approximately, 114

4.3.4 Run 2. Very noisy environment, 116

4.3.5 Run 3. Very, very noisy environment, 117

4.3.6 Run 4. Very, very, very noisy environment, 118

4.3.7 Run 5. Non-periodic background noise, 119

4.4 Method 4-4. Directional filtering – *differential* equation method requiring two transducers, 120

4.4.1 Physical problem, 120

4.4.2 Theory, 121

4.4.3 Run 1. Validation analysis, 122

4.4.4 Run 2. A very, very noisy example, 124

4.4.5 Note on multiple-transducer methods, 125

4.5 Method 4-5. Downhole reflection and deconvolution at the bit, waves created by MWD dipole source, bit assumed as perfect solid reflector, 126

4.5.1 Software note, 126

4.5.2 Physical problem, 127

4.5.3 On solid and open reflectors, 127

4.5.4 Theory, 128

4.5.5 Run 1. Long, low data rate pulse, 130

4.5.6 Run 2. Higher data rate, faster valve action, 130

4.5.7 Run 3. PSK example, 12 Hz frequency, 131

4.5.8 Run 4. 24 Hz, Coarse sampling time, 132

4.6 Method 4-6. Downhole reflection and deconvolution at the bit, waves created by MWD dipole source, bit assumed as perfect open end or zero acoustic pressure reflector, 133

4.6.1 Software note, 133

4.6.2 Physical problem, 133

4.6.3 Theory, 134

4.6.4 Run 1. Low data rate run, 135

4.6.5 Run 2. Higher data rate, 136

4.6.6 Run 3. Phase-shift-keying, 12 Hz carrier wave, 137

4.6.7 Run 4. Phase-shift-keying, 24 Hz carrier wave, 137

4.6.8 Run 5. Phase-shift-keying, 48 Hz carrier, 138

4.7 References, 139

5. Transient Variable Area Downhole Inverse Models, 140

5.1 Method 5-1. Problems with acoustic impedance mismatch due to collar-drillpipe area discontinuity, with drillbit assumed as open-end reflector, 142

5.1.1 Physical problem, 142

5.1.2 Theory, 143

5.1.3 Run 1. Phase-shift-keying, 12 Hz carrier wave, 147

5.1.4 Run 2. Phase-shift-keying, 24 Hz carrier wave, 147

5.1.5 Run 3. Phase-shift-keying, 96 Hz carrier wave, 148

5.1.6 Run 4. Short rectangular pulse with rounded edges, 149

5.2 Method 5-2. Problems with collar-drillpipe area discontinuity, with drillbit assumed as closed end, solid drillbit reflector, 150

5.2.1 Theory, 150

5.2.2 Run 1. Phase-shift-keying, 12 Hz carrier wave, 150

5.2.3 Run 2. Phase-shift-keying, 24 Hz carrier wave, 151

5.2.4 Run 3. Phase-shift-keying, 96 Hz carrier wave, 151

5.2.5 Run 4. Short rectangular pulse with rounded edges, 151

5.3 References, 152

6. Signal Processor Design and Additional Noise Models, 153

6.1 Desurger Distortion, 154

6.1.1 Low-frequency positive pulsers, 156

6.1.2 Higher frequency mud sirens, 157

6.2 Downhole Drilling Noise, 160

6.2.1 Positive displacement motors, 161

6.2.2 Turbodrill motors, 162

6.2.3 Drillstring vibrations, 162

6.3. Attenuation Mechanisms, 164

6.3.1 Newtonian model, 164

6.3.2 Non-Newtonian fluids, 165

6.4 Drillpipe Attenuation and Mudpump Reflection 167

6.4.1 Low-data-rate physics, 168

6.4.2 High data rate effects, 169

6.5 Applications to Negative Pulser Design in Fluid Flows and to Elastic Wave Telemetry Analysis in Drillpipe Systems, 170

6.6 LMS Adaptive and Savitzky-Golay Smoothing Filters, 172

6.7 Low Pass Butterworth, Low Pass FFT and Notch Filters, 174

6.8 Typical Frequency Spectra and MWD Signal Strength Properties, 175

6.9 References, 176

7. Mud Siren Torque and Erosion Analysis, 177

7.1 The Physical Problem, 177

7.1.1 Stable-closed designs, 179

7.1.2 Previous solutions, 179

7.1.3 Stable-opened designs, 181

7.1.4 Torque and its importance, 182

7.1.5 Numerical modeling, 183

7.2 Mathematical Approach, 183

7.2.1 Inviscid aerodynamic model, 185

7.2.2 Simplified boundary conditions, 186

7.3 Mud Siren Formulation, 188

7.3.1 Differential equation, 188

7.3.2 Pressure integral, 189

7.3.3 Upstream and annular boundary condition, 190

7.3.4 Radial variations, 192

7.3.5 Downstream flow deflection, 193

7.3.6 Lobe tangency conditions, 194

7.3.7 Numerical solution, 194

7.3.8 Interpreting torque computations, 195

7.3.9 Streamline tracing, 196

7.4 Typical Computed Results and Practical Applications, 198

7.4.1 Detailed engineering design suite, 198

7.5 Conclusions, 204

7.5.1 Software reference, 204

7.6 References, 205

8. Downhole Turbine Design and Short Wind Tunnel Testing, 206

8.1 Turbine Design Issues, 206

8.2 Why Wind Tunnels Work, 208

8.3 Turbine Model Development, 211

8.4 Software Reference, 215

8.5 Erosion and Power Evaluation, 219

8.6 Simplified Testing, 221

8.7 References, 223

9. Siren Design and Evaluation in Mud Flow Loops and Wind Tunnels, 224

9.1 Early Wind Tunnel and Modern Test Facilities, 225

9.1.1 Basic ideas, 226

9.1.2 Three types of wind tunnels, 227

9.1.3 Background, early short wind tunnel, 228

9.1.4 Modern short and long wind tunnel system, 229

9.1.5 Frequently asked questions, 233

9.2 Short wind tunnel design, 236

9.2.1 Siren torque testing in short wind tunnel, 240

9.2.2 Siren static torque testing procedure, 243

9.2.3 Erosion considerations, 246

9.3 Intermediate Wind Tunnel for Signal Strength Measurement, 248

9.3.1 Analytical acoustic model, 249

9.3.2 Single transducer test using speaker source, 251

9.3.3 Siren Dp procedure using single and differential transducers, 252

9.3.4 Intermediate wind tunnel test procedure, 254

9.3.5 Predicting mud flow Dp’s from wind tunnel data, 257

9.4 Long Wind Tunnel for Telemetry Modeling, 259

9.4.1 Early construction approach - basic ideas, 259

9.4.2 Evaluating new telemetry concepts, 264

9.5 Water and Mud Flow Loop Testing, 264

9.5.1 Real-world flow loops, 265

9.5.2 Solid reflectors, 267

9.5.3 Drillbit nozzles, 268

9.5.4 Erosion testing, 269

9.5.4 Attenuation testing, 270

9.5.5 The way forward, 272

10. Advanced System Summary and Modern MWD Developments, 273

10.1 Overall Telemetry Summary, 274

10.1.1 Optimal pulser placement for wave interference, 274

10.1.2 Telemetry design using FSK, 277

10.1.3 Sirens in tandem, 279

10.1.4 Attenuation misinterpretation, 280

10.1.5 Surface signal processing, 284

10.1.6 Attenuation, distance and frequency, 287

10.1.7 Ghost signals and echoes, 290

10.2 MWD Signal Processing Research in China, 291

10.3 MWD Sensor Developments in China, 300

10.4 Turbines, Batteries and Closing Remarks, 337

10.4.1 Siren drive, 337

10.4.2 Turbine-alternator system, 337

10.4.3 Batteries, 338

10.4.4 Tool requirements, 339

10.4.5 Design trade-offs, 340

10.5 References, 341

Cumulative References, 342

Index, 347

About the Authors, 354