Modern Borehole Analytics
for Annular Flow, Hole Cleaning and Pressure Control
by
Wilson C. Chin, Ph.D., M.I.T.
Stratamagnetic Software, LLC
October 2017
Table of Contents
Preface x
Acknowledgements xii
1. Fundamental Ideas and Background 1
1.1 Background, industry challenges and frustrations 2
1.1.1 Annular flow modeling issues and
problem definition 3
1.1.2 Mudcake growth, dynamic coupling and
reservoir interaction 7
1.2 Related prior work 8
1.3 References 13
2. Steady Annular Flow 14
2.1 Graphical interface basics 15
2.2 Steady flows - versatile capabilities 20
2.2.1 Concentric Newtonian annular flow 20
2.2.2 Concentric Newtonian flow on coarse mesh 31
2.2.3 Coarse mesh Newtonian flow with cuttings
beds and washout 33
2.2.4 Eccentricity effects, pressure gradient fixed 63
2.2.4.1 Eccentricity = 0.000 for annulus 64
2.2.4.2 Eccentricity = 0.333 for annulus 65
2.2.4.3 Eccentricity = 0.500 for annulus 66
2.2.4.4 Eccentricity = 0.667 for annulus 67
2.2.4.5 Eccentricity = 0.833 for annulus 68
2.2.5 Eccentricity = 0.833 for annulus, volume flow
rate specified 72
2.2.6 Eccentricity = 0.833 for annulus, pressure
gradient specified, yield stress allowed 79
2.2.7 Non-Newtonian effects pressure gradient
versus flow rate curve, no yield stress 86
2.2.8 Non-Newtonian effects, pressure gradient
vs flow rate curve, non-zero yield stress 95
2.2.9 Power law fluid in eccentric annulus, effect of
pipe or casing speed 99
2.2.10 Steady-state swab-surge in eccentric annuli for
Power law fluids with and without circulation
(no rotation) 102
(i) Basic concepts 103
(ii) Macroscopic rheological properties 105
(iii) Newtonian fluids 105
(iv) Power law fluids 108
(v) Swab-surge examples 109
(vi) Neutral pressure gradient operation 114
2.2.11 Steady-state swab-surge in concentric annuli for
Power law fluids with drillpipe rotation but
small pipe movement 115
2.2.12 Steady-state swab-surge in eccentric annuli
for Herschel-Bulkley fluids with drillpipe
rotation and axial movement 117
2.2.13 Transient swab-surge on a steady-state basis 132
2.2.14 Equivalent circulating density (ECD)
calculations 133
2.3 References 133
3. Transient Single-Phase Flows 135
3.1 Validation runs, three different approaches to steady,
Power law, non-rotating, concentric annular flow 136
3.2 Validation run for transient, Newtonian,
non-rotating, concentric annular flow 138
3.3 Validation run for transient, Newtonian,
non-rotating, eccentric annular flow 141
3.4 Effect of steady rotation for laminar Power law
flows in concentric annuli 142
3.5 Effect of steady-state rotation for Newtonian fluid
flow in eccentric annuli 146
3.6 Effect of steady rotation for Power law flows in
highly eccentric annuli at low densities (foams) 149
3.7 Effect of steady rotation for Power law flows in highly
eccentric annuli at high densities (heavy muds) 152
3.8 Effect of mud pump ramp-up and ramp-down flow
rate under non-rotating and rotating conditions 155
3.9 Effect of rotational and azimuthal start-up 158
3.10 Effect of axial drillstring movement 162
3.11 Combined rotation and sinusoidal reciprocation 165
3.12 Combined rotation and sinusoidal reciprocation in
presence of mud pump flow rate ramp-up for yield
stress fluid 167
3.13 References 169
4. Transient Multiphase Flows 171
4.1 Single fluid in pipe and borehole system
calculating total pressure drops for general
non-Newtonian fluids 173
4.2 Interface tracking and total pressure drop for
multiple fluids pumped in drillpipe and eccentric
borehole system 174
(i) Interface tracking and example 182
(ii) On real interfaces 199
4.3 Calculating annular and drillpipe pressure loss 199
(i) Newtonian pipe flow model 200
(ii) Bingham plastic pipe flow 201
(iii) Power law fluids in pipe flow 201
(iv) Herschel-Bulkley pipe flow model 202
(v) Ellis fluids in pipe flow 203
(vi) Annular flow solutions 203
(vii) Review of steady eccentric flow models 204
4.4 Herschel-Bulkley pipe flow analysis 207
4.5 Transient, three-dimensional, eccentric multiphase
flow analysis for non-rotating Newtonian fluids 210
(i) Example 1 210
(ii) Transient flow subtleties 213
(iii) Examples 2 and 3 215
4.6 Transient, 3D, eccentric multiphase analysis for non-
rotating Newtonian fluids simulator description 216
4.7 Transient, 3D, eccentric multiphase analysis for
general rotating non-Newtonian fluids simulator
description 225
4.8 Transient, 3D, eccentric, multiphase analysis for
general rotating non-Newtonian fluids with axial pipe
movement Validation runs for completely stationary
pipe 227
(i) Validation 1 Concentric, single-phase Newtonian
flow 227
(ii) Validation 2 Concentric, two-phase Newtonian
flow 231
(iii) Validation 3 Concentric, single-phase
Herschel-Bulkley flow. 234
(iv) Validation 4 Concentric, two-phase Herschel-
Bulkley flow 236
(v) Validation 5 Eccentric, single and
multiphase, non-Newtonian flow 239
4.9 Transient, 3D, concentric, multiphase analysis for
rotating Power law fluids without axial pipe
movement 244
4.10 Transient, 3D, eccentric, multiphase analysis for
general rotating non-Newtonian fluids with axial pipe
movement 248
(i) Validation runs for constant rate rotation and
translation 248
(ii) Steady, rotating, non-Newtonian, single-phase,
eccentric flow solution 248
(iii) Steady, rotating, Newtonian, single-phase,
eccentric flow solution 250
(iv) Mixing problem 251
4.11 References 256
5. Mudcake Formation in Single-Phase Flow 259
5.1 Flows with moving boundaries four basic problems 260
5.1.1 Linear mudcake buildup on filter paper 263
5.1.2 Plug flow of two liquids in linear core
without cake 266
5.1.3 Simultaneous mudcake buildup and filtrate
invasion in a linear core (liquid flows) 268
5.1.4 Simultaneous mudcake buildup and filtrate
invasion in a radial geometry (liquid flows) 271
5.2 Characterizing mud and mudcake properties 277
5.2.1 Simple extrapolation of mudcake properties 278
5.2.2 Radial mudcake growth on cylindrical
filter paper 279
5.3 Complex invasion problems numerical modeling 283
5.3.1 Finite difference modeling 283
(i) Basic formulas 283
(ii) Model constant density flow analysis 285
5.3.2 Invasion and mudcake growth examples 288
5.3.2.1 Lineal liquid displacement without
mudcake 288
5.3.2.2 Cylindrical radial liquid displacement
without cake 294
5.3.2.3 Spherical radial liquid displacement
without cake 298
5.3.2.4 Simultaneous mudcake buildup and
displacement front motion for
incompressible liquid flows 300
(i) Matching conditions at displacement
front 303
(ii) Matching conditions at the cake-to-
rock interface 304
(iii) Modeling formation
heterogeneities 308
(iv) Mudcake compaction and
compressibility 308
(v) Modeling borehole activity 309
5.4 References 310
6. Mudcake Growth for Multiphase Flow 311
6.1 Physical problem description 312
6.2 Overview physics and simulation capabilities 316
6.2.1 Example 1, Single probe, infinite anisotropic
media 316
6.2.2 Example 2, Single probe, three layer medium 320
6.2.3 Example 3, Dual probe pumping, three layer
medium 322
6.2.4 Example 4, Straddle packer pumping 323
6.3 Model and user interface notes 325
6.4 Detailed applications 328
6.4.1 Run No. 1, Clean-up, single-probe, uniform
medium 328
6.4.2 Run No. 2, A low-permeability "supercharging"
example 334
6.4.3 Run No. 3, A three-layer simulation 336
6.5 References 339
7. Pore Pressure in Higher Mobility Formations 340
7.1 Forward and inverse modeling approaches 341
7.2 Preliminary ideas 342
7.2.1 Qualitative effects of storage and skin 342
7.2.2 The simplest inverse model steady pressure drop
for arbitrary dip angles 343
7.2.3 FT-00 and FT-01 346
7. 3 Inverse examples dip angle, multivalued solutions
and skin 347
7.3.1 Forward model FT-00 347
7.3.2 Inverse model FT-01 multivalued solutions 349
7.3.3 Effects of dip angle detailed calculations 352
7.3.4 Pulse interaction method an introduction 355
7.4 References 358
8. Pore Pressure Prediction in Low Mobility or Tight
Formations 359
8.1 Low permeability pulse interference testing
nonzero skin 360
(i) Run A, Pulse interaction, kh >> kv,
moderate skin 361
(ii) Run B, Pulse interaction, kh >> kv, high skin 363
8.2 Low permeability pulse interference testing
zero skin 365
(i) Run C, ks = 4.642 md, with kh = 10 md and
kv = 1 md 366
(ii) Run D, ks = 4.642 md, with kh = 4.642 md and
kv = 4.642 md 368
(iii) Run E, ks = 4.642 md, with kh = 1 md and
kv = 100.027 md 370
8.3 Formation Testing While Drilling (FTWD) 372
8.3.1 Pressure transient drawdown-buildup approach 372
8.3.2 Interpretation in low mobility, high flowline storage environments 372
8.3.3 Multiple pretests, modeling and interpretation 375
8.3.4 Reverse flow injection processes 378
8.3.4.1 Conventional fluid withdrawal,
drawdown-then-buildup 379
8.3.4.2 Reverse flow injection process,
buildup-then-drawdown 383
8.4 References 384
Cumulative References 389
(i) Drilling, Cementing and Annular Flow 389
(ii) Formation Testing Pressure and Contamination Analysis 395
(iii) Reservoir Engineering and Simulation 401
Index 412
About the Author 418