Modern Borehole Analytics

Modern Borehole Analytics

for Annular Flow, Hole Cleaning and Pressure Control

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, k_h >> k_v,

moderate skin . . . . . . . . . . . . . . . . . . . . . . . 361

(ii) Run B, Pulse interaction, k_h >> k_v, high skin . . . . 363

8.2 Low permeability pulse interference testing

– zero skin . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

(i) Run C, k_s = 4.642 md, with k_h = 10 md and

k_v = 1 md . . . . . . . . . . . . . . . . . . . . . . . . . 366

(ii) Run D, k_s = 4.642 md, with k_h = 4.642 md and

k_v = 4.642 md . . . . . . . . . . . . . . . . . . . . . . . 368

(iii) Run E, k_s = 4.642 md, with k_h = 1 md and

k_v = 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