by

Stratamagnetic Software, LLC

Houston, Texas

Email: wilsonchin@aol.com

Telephone: (832) 483-6899

Introduction, background and problems, 1

Section 1-1. Managed pressure drilling fluid flow challenges, 12

Section 1-2. MPD flow simulator – Steady, two-dimensional, single-phase flow, 16

Section 1-3. MPD flow simulator – Transient, two-dimensional, single-phase flow, 30

Section 1-4. MPD flow simulator – Transient, three-dimensional, multiphase flow, 38

Example 2-1. Newtonian flow circular cylindrical coordinates, 48

Example 2-2. Shear-thinning and non-Newtonian flow effects, 53

Example 2-3. Curvilinear grid formulation for highly eccentric annular flows with general non-Newtonian fluids without rotation, 60

Example 2-4. Curvilinear grid formulation for eccentric annular flows with general non-Newtonian fluids with rotation, 74

Example 3-1. Grid generation for eccentric annular flow, 78

Example 3-2. Mappings for flows in singly-connected ducts, 89

Example 3-3. Solids deposition modeling and applications, 90

Example 3-4. Finite difference details for annular flow problems, 128

Example 4-1. Newtonian flow eccentric annulus applications, 133

Example 4-2. Power law flow in eccentric annuli, 138

Example 4-3. Turbulence modeling and Power law flow analogy, 150

Example 4-4. Pressure gradient versus flow rate curve computation for non-Newtonian eccentric annuli, 152

Example 4-5. Effects of influx-outflux along borehole path for non-Newtonian eccentric annuli without rotation, 155

Example 4-6. Steady-sate swab-surge in eccentric annuli for Power law fluids with and without circulation (no rotation), 157

Example 4-7. Steady-state swab-surge in concentric annuli for Power law fluids with drillpipe rotation but small pipe movement, 169

Example 4-8. Steady-state swab-surge in eccentric annuli for Herschel-Bulkley fluids with drillpipe rotation and axial movement, 171

Example 4-9. Transient swab-surge on a steady-state basis, 184

Example 4-10. Equivalent circulating density calculations, 184

Model 5-1. Newtonian flow in concentric annulus with axially moving (but non-rotating) pipe or casing, 186

Model 5-2. Density stratification (barite sag) and recirculating annular vortexes that impede fluid flow, 188

Model 5-3. Herschel-Bulkley flow in concentric annulus with axially stationary and non-rotating drillpipe or casing, 202

Model 5-4. Extended Herschel-Bulkley flow in eccentric annulus with axially moving but non-rotating drillpipe or casing, 208

Model 5-5. Steady non-Newtonian flow in boreholes with bends, 213

Model 5-6. Newtonian and Power law flow in concentric annulus with rotating (but axially stationary) pipe or casing, 220

Model 5-7. Cuttings transport flow correlations in deviated wells, 250

Model 5-8. Cuttings bed growth as an unstable flow process, 262

Model 5-9. Spotting fluid evaluation for stuck pipe and jarring – Applications, 267

Model 5-10. Newtonian flow in rectangular ducts, 271

Section 6-1. Governing equations for transient flow, 278

Section 6-2. Rotation paradox, 280

Section 6-3. Operational consequences for transient rotation algorithm, 281

Section 6-4. Transient pressure gradient and volume flow rate, 282

Example 7-1. Validation runs, three different approaches to steady, Power law, non-rotating, concentric annular flow, 285

Example 7-2. Validation run for transient, Newtonian, non-rotating, concentric annular flow, 287

Example 7-3. Validation run for transient, Newtonian, non-rotating, eccentric annular flow, 289

Example 7-4. Effect of steady rotation for laminar Power law flows in concentric annuli, 290

Example 7-5. Effect of steady-state rotation for Newtonian fluid flow in eccentric annuli, 293

Example 7-6. Effect of steady rotation for Power law flows in highly eccentric annuli at low densities (foams), 296

Example 7-7. Effect of steady rotation for Power law flows in highly eccentric annuli at high densities (heavy muds), 299

Example 7-8. Effect of mud pump ramp-up and ramp-down flow rate under non-rotating and rotating conditions, 301

Example 7-9. Effect of rotational and azimuthal start-up, 304

Example 7-10. Effect of axial drillstring movement, 307

Example 7-11. Combined rotational and sinusoidal reciprocation, 310

Example 7-12. Combined rotational and sinusoidal reciprocation in presence of mud pump flow rate ramp-up for yield stress fluid, 312

Discussion 8-1. Unsteady three-dimensional Newtonian flows with miscible mixing in long eccentric annular ducts, 315

Discussion 8-2. Transient, single-phase, two-dimensional, non-Newtonian flow with inner pipe rotation in eccentric annuli, 317

Discussion 8-3. Transient, three-dimensional, non-Newtonian flows with miscible mixing in long eccentric annular ducts with pipe or casing rotation and reciprocation, 321

Discussion 8-4. Subtleties in non-Newtonian convection modeling, 323

Discussion 8-5. Simple models for multiple non-Newtonian fluids with mixing, 325

Discussion 9-1. Single fluid in pipe and borehole system – calculating total pressure drops for general non-Newtonian fluids, 328

Discussion 9-2. Interface tracking and total pressure drop for multiple fluids pumped in drillpipe and eccentric borehole system, 329

Discussion 9-3. Calculating annular and drillpipe pressure loss, 352

Discussion 9-4. Herschel-Bulkley pipe flow analysis, 359

Discussion 9-5. Transient, three-dimensional, eccentric multiphase flow analysis for non-rotating Newtonian fluids, 362

Discussion 9-6. Transient, 3D, eccentric multiphase analysis for non-rotating Newtonian fluids – simulator description, 367

Discussion 9-7. Transient, 3D, eccentric multiphase analysis for general rotating non-Newtonian fluids – simulator description,375

Discussion 9-8. Transient, 3D, eccentric, multiphase analysis for general rotating non-Newtonian fluids with axial pipe movement – Validation runs for completely stationary pipe, 377

Discussion 9-9. Transient, 3D, concentric, multiphase analysis for rotating Power law fluids without axial pipe movement, 392

Discussion 9-10. Transient, 3D, eccentric, multiphase analysis for general rotating non-Newtonian fluids with axial pipe movement – Validation runs for constant rate rotation and translation, 396