Preface ....................................................... vii
About the Author ............................................... ix
CHAPTER 1. Fluid Mechanics Challenges and Technology Overview ... 1
Section 1.1. Managed pressure drilling fluid flow challenges ... 10
Section 1.2. MPD flow simulator: Steady, two-dimensional,
single-phase flow ................................. 14
Section 1.3. MPD flow simulator: Transient, two-dimensional,
single-phase flow ................................. 27
Section 1.4. MPD flow simulator: Transient,
three-dimensional, multiphase flow ................ 35
CHAPTER 2. General Theory and Physical Model Formulation ....... 47
Example 2.1. Newtonian flow circular cylindrical coordinates ... 47
Example 2.2. Shear-thinning and non-Newtonian flow effects ..... 52
Example 2.3. Curvilinear grid formulation for highly
eccentric annular flows with general
non-Newtonian fluids without rotation ............. 59
Example 2.4. Curvilinear grid formulation for eccentric
annular flows with general non-Newtonian fluids
with rotation ..................................... 72
CHAPTER 3. Numerical Analysis and Algorithm Development
Strategies ..................................................... 75
Example 3.1. Grid generation for eccentric annular flow ........ 75
Example 3.2. Mappings for flows in singly connected ducts ...... 86
Example 3.3. Solids deposition modeling and applications ....... 86
Example 3.4. Finite difference details for annular flow
problems ......................................... 120
CHAPTER 4. Steady, Two-Dimensional, Non-Newtonian, Single-
Phase, Eccentric Annular Flow ................................. 127
Example 4.1. Newtonian flow eccentric annulus applications .... 127
Example 4.2. Power law flow in eccentric annuli ............... 131
Example 4.3. Turbulence modeling and Power law flow analogy ... 144
Example 4.4. Pressure gradient versus flow rate curve
computation for non-Newtonian eccentric annuli ... 145
Example 4.5. Effects of influx-outflux along the borehole
path for non-Newtonian eccentric annuli without
rotation ......................................... 150
Example 4.6. Steady-state swab-surge in eccentric annuli for
Power law fluids with and without circulation
(no rotation) .................................... 151
Example 4.7. Steady-state swab-surge in concentric annuli
for Power law fluids with drillpipe rotation
but small pipe movement .......................... 164
Example 4.8. Steady-state swab-surge in eccentric annuli for
Herschel-Bulkley fluids with drillpipe rotation
and axial movement ............................... 165
Example 4.9. Transient swab-surge on a steady-state basis ..... 177
Example 4.10.Equivalent circulating density calculations ...... 179
CHAPTER 5. More Steady Flow Applications ...................... 183
Model 5.1. Newtonian flow in concentric annulus with
axially moving (but nonrotating) pipe or casing .. 183
Model 5.2. Density stratification (barite sag) and
recirculating annular vortexes that impede
fluid flow ....................................... 185
Model 5.3. Herschel-Bulkley flow in concentric annulus
with axially stationary and nonrotating
drillpipe or casing ............................. 196
Model 5.4. Extended Herschel-Bulkley flow in eccentric
annulus with axially moving but nonrotating
drillpipe or casing .............................. 203
Model 5.5. Steady non-Newtonian flow in boreholes with
bends ............................................ 207
Model 5.6. Newtonian and Power law flow in concentric
annulus with rotating (but axially stationary)
pipe or casing ................................... 215
Model 5.7. Cuttings transport flow correlations in
deviated wells ................................... 243
Model 5.8. Cuttings bed growth as an unstable flow
process .......................................... 253
Model 5.9. Spotting fluid evaluation for stuck pipe and
jarring applications ............................. 257
Model 5.10. Newtonian flow in rectangular ducts .............. 262
CHAPTER 6. Transient, Two-Dimensional, Single-Phase Flow
Modeling ...................................................... 267
Section 6.1. Governing equations for transient flow ........... 267
Section 6.2. Rotation paradox ................................. 269
Section 6.3. Operational consequences for the transient
rotation algorithm ............................... 270
Section 6.4. Transient pressure gradient and volume flow
rate ............................................. 271
CHAPTER 7. Transient Applications: Drillpipe or Casing
Reciprocation and Rotation .................................... 273
Example 7.1. Validation runs: Three different approaches to
steady, nonrotating concentric annular Power
law flow ......................................... 273
Example 7.2. Validation ran for transient, Newtonian,
nonrotating concentric annular flow .............. 274
Example 7.3. Validation run for transient, Newtonian,
nonrotating eccentric annular flow ............... 277
Example 7.4. Effect of steady rotation for laminar Power
law flows in concentric annuli ................... 278
Example 7.5. Effect of steady-state rotation for Newtonian
fluid flow in eccentric annuli ................... 281
Example 7.6. Effect of steady rotation for Power law flows
in highly eccentric annuli at low densities
(foams) .......................................... 284
Example 7.7. Effect of steady rotation for Power law flows
in highly eccentric annuli at high densities
(heavy muds) ..................................... 287
Example 7.8. Effect of mud pump ramp-up and ramp-down flow
rate I under nonrotating and rotating
conditions ....................................... 287
Example 7.9. Effect of rotational and azimuthal start-up ...... 290
Example 7.10.Effect of axial drillstring movement ............. 291
Example 7.11.Combined rotation and sinusoidal reciprocation ... 296
Example 7.12.Combined rotation and sinusoidal reciprocation
in the presence of mud pump flow rate ramp-up
for yield stress fluid ........................... 296
CHAPTER 8. Cement and Mud Multiphase Transient
Displacements ................................................. 303
Discussion 8.1. Unsteady three-dimensional Newtonian flows
with miscible mixing in long eccentric annular
ducts ............................................ 304
Discussion 8.2. Transient, single-phase, two-dimensional
non-Newtonian flow with inner pipe rotation in
eccentric annuli ................................. 305
Discussion 8.3. Transient, three-dimensional non-Newtonian
flows with miscible mixing in long eccentric
annular ducts with pipe or casing rotation and
reciprocation .................................... 308
Discussion 8.4. Subtleties in non-Newtonian convection
modeling ......................................... 310
Discussion 8.5. Simple models for multiple non-Newtonian
fluids with mixing ............................... 312
CHAPTER 9. Transient, Three-Dimensional, Multiphase Pipe and
Annular Flow .................................................. 315
Discussion 9.1. Single fluid in pipe and borehole system:
Calculating total pressure drops for general
non-Newtonian fluids ............................. 315
Discussion 9.2. Interface tracking and total pressure drop
for multiple fluids pumped in a drillpipe and
eccentric borehole system ........................ 317
Discussion 9.3. Calculating annular and drillpipe pressure
loss ............................................. 336
Discussion 9.4. Herschel-Bulkley pipe flow analysis ........... 342
Discussion 9.5. Transient, three-dimensional eccentric
multiphase flow analysis for nonrotating
Newtonian fluids ................................. 343
Discussion 9.6. Transient, three-dimensional eccentric
multiphase analysis for nonrotating Newtonian
fluids: Simulator description .................... 350
Discussion 9.7. Transient, three-dimensional eccentric
multiphase analysis for general rotating non-
Newtonian fluids: simulator description .......... 356
Discussion 9.8. Transient, three-dimensional eccentric
multiphase analysis for general rotating non-
Newtonian fluids with axial pipe movement:
Validation runs for completely stationary pipe ... 356
Discussion 9.9. Transient, three-dimensional concentric
multiphase analysis for rotating Power law
fluids without axial pipe movement ............... 375
Discussion 9.10. Transient, three-dimensional eccentric
multiphase analysis for general rotating non-
Newtonian fluids with axial pipe movement:
Validation runs for constant-rate rotation and
translation ...................................... 376
CHAPTER 10. Closing Remarks ................................... 387
Cumulative References ......................................... 391
Index ......................................................... 395
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