MULTIPROBE PRESSURE TESTING
AND RESERVOIR CHARACTERIZATION -
PRESSURE TRANSIENT, CONTAMINATION,
LIQUID AND GAS PUMPING ANALYSIS
by
Wilson C. Chin,
Ph.D., M.I.T.
Stratamagnetic Software, LLC
Beijing and Houston
Table of Contents
Preface .
. . xv
Acknowledgements .
. . xviii
Part
I. Fundamental Concepts and
Generalizations
1. Fluid Sampling, Pressure Transient and Contamination
Analysis .
. 1
1.1 Formation testing
background . 1
1.2 Conventional
formation testing concepts . 5
1.3 Ideal source model
summary . 10
1.3.1 Forward or direct
models without
supercharge .
. 11
1.3.1.1 FT-00, general model, exact, closed form
analytical solution
. 11
1.3.1.2 FT-06, general model, numerical finite
difference scheme .
11
1.3.1.3 FT-07, general model, extension of
FT-06 . . 11
1.3.2 Inverse or "indirect" models without
supercharge .
. 12
1.3.2.1 Single-probe, effective spherical
permeability . . 12
1.3.2.2 FT-01, Anisotropic permeability,
determines kh and kv .
. 12
1.3.2.3 FT-02, Anisotropic
permeability,
determines kh and kv . 12
1.3.2.4 FT-PTA-DDBU, for effective spherical
permeability in low mobility
formations . 12
1.3.2.5 FT-PTA-DDBU
extensions . 12
1.3.2.6 FT-PTA-FastForward for supercharge
model in
transient analysis . 13
1.3.2.7 Phase delay, for permeability in isotropic
media. . 13
1.3.2.8 Phase delay and drawdown method in
anisotropic media . .
. 13
1.3.3 Advanced methods .
. 13
1.3.3.1 Forward and inverse models with
supercharge . 13
1.3.3.2 Multiple drawdown-buildup inverse
model without supercharge . 14
1.3.3.3 Miscible
contamination simulator. . 14
1.4 Modern three-dimensional
sampling tools 14
1.4.1 Background physics . . 14
1.4.2 Simulator
specifications . . 15
1.5 Simulator design
objectives . 18
1.6 Supercharging, invasion, mudcake effects, overbalanced
and underbalanced drilling. . 19
1.7 References .
. 21
2. Physical Concepts and Numerical Approaches . 22
2.1 Blind spot at the 180 deg probe profound 3D
effects .
. 22
2.2 Unbalanced doublet flow an exact analytical
solution ..
. . 24
2.3 Numerical modeling simply explained subtleties in
cylindrical annular
domains .
27
2.3.1
Basic finite differences . . 27
2.3.2
Challenges in circular cylindrical
coordinates . .
. 29
2.3.3
Modeling in circular ring domains further
explained . .
. 34
2.4 Implementation
details and boundary
conditions . .
. 38
2.4.1 Periodicity Analytical review and motivating
ideas . .
. 38
2.4.2
Periodicity Numerical extensions on annular
domains .
. . 39
2.4.2.1 First-order accurate periodicity
model . .
. . 40
2.4.2.2 Second-order periodicity
modeling .
. . 41
2.4.3 Meshing
constraints . .
. 41
2.4.4 Probe
or nozzle geometry modeling . 42
2.4.5 Computing
speed issues . .
43
2.4.6 Pressure numerical engine . . 44
2.4.7 Contamination
numerical engine . 47
2.4.7.1 Convective-diffusion model
for contamination . .
. . 47
2.4.7.2 Contamination formulation and
and
numerical solution . 49
2.4.8 Supercharge,
invasion and mudcake
growth . .
. 52
2.5 References . .
. 53
3. Multiprobe
Model Formulations and Validations 54
Table 3-1. Formation testing simulator systems available
available .
. 55
3.1 Basic multiprobe flow
modules summarized . 56
3.1.1 System 1 solution using mprobe(dual) . 56
3.1.2 System 2 solution using mprobe(quad) . . 60
3.1.3 System 3 solution using mprobe(focus) 62
3.1.4 System 4 solution using
mprobe(contam) . 65
3.1.5 System 5 solution using mprobe(triplet) . . 67
3.1.6 System 6 solution using mprobe .
. 68
3.1.7 System 7 solution using
mprobe(3-contam) . 70
3.1.8 System 8 solution using mprobe(3-gas) . . 72
3.1.9 System 9 solution using mprobe(4-gas) . . 73
3.1.10 Additional multiprobe flow modules
summarized . .
. . 75
3.2 Geometric factor
basics . .
. 77
3.3 Geometric factor
significance . .
. . 79
3.3.1 Sample GF procedure
. . 79
3.3.2 Solution differences explained
GF significance . 80
3.4 Mesh system details . .
. 85
3.4.1 Angular mesh for mprobe(dual) 85
3.4.2 Angular mesh for mprobe(triplet), mprobe
and mprobe(3-gas) . .
87
3.4.3 Angular mesh for four-probe array,
mprobe(quad) and
mprobe(4-gas) 89
3.4.4 Mesh for central four-probe array with two
side
arrays each having four-probes, for both
mprobe(focus) and mprobe(contam) .
91
3.5 References .
. 93
Part
II.
Four-Probe Algorithms
4. Single-Phase, Four-Probe
Flows Conventional, Overbalanced and Underbalanced Drilling
Applications . .
. 94
4.1 Modeling strategies re-emphasized . . 96
4.2 Comprehensive calculated examples . 97
Example
4-1. Basic output, transient and rapid
steady flow analyses for round or oval nozzles (all four pumping identically,
impermeable sandface) . .
99
Example
4-2. Basic output, transient flow
results for slot nozzles (all four pumping identically, impermeable sandface) . .
. 106
Example
4-3. Transient flow results for mixed
round and slot nozzle combinations with different pump schedules (impermeable
sandface) .
. . 108
Example
4-4. Transient flow results for mixed
withdrawal and injection flow rates for round and slot nozzle combinations
(impermeable sandface) 110
Example
4-5. Transient drawdown-buildup, four
slot nozzles in overbalanced (supercharged) drilling 113
Example
4-6. Transient drawdown-buildup, four
slot nozzles in underbalanced (undercharged) drilling 115
Example 4-7. Simulations
in multiprobe pumping with mixed nozzles (impermeable sandface, twelve
nozzles) .
117
Example
4-8. Multiprobe pumping with mixed
nozzles in overbalanced (supercharged) and underbalanced (undercharged)
drilling .
125
4.3 References
128
5. Convective-Diffusion, Four-Probe Model for Pressure and Contamination .
. 129
5.1 Pressure and contamination simulations . 132
Example
5-1. Basic supercharging physics and
mudcake flow properties .
. 134
Example
5-2. Contamination behavior, dependence
on reservoir fluid diffusion .
. 143
Example
5-3. Mudcake sealing, model options and
contamination recovery 146
Example
5-4. Extremely high supercharge pressure
149
Example
5-5. Main probe array, supercharge runs
with and without focusing probe rows (non-packer tool) . 151
Example 5-6. Main probe array,
supercharge runs with and without focusing probe rows (packer tool) . . 158
Example
5-7. Mud viscosity effects . . 167
Example 5-8. Comparative
drawdown-buildup runs, no invasion versus contamination with main probes
only, and then contamination with main and focused probe rows .
. . 173
Example 5-9. Effectiveness
of focusing probe rows as
function of mud filtrate and reservoir oil diffusion
coefficient . .
. 183
5.2 Closing remarks .
195
5.3 References. .
. 196
Part III. Triple-Probe
Azimuthal Algorithms, Axial Multiprobe Array Formation Testing, General
Nonlinear Gas Pumping, Advanced Software and Inverse Methods, Geothermal Issues
6. Single-Phase, Triple-Probe Flows Conventional, Overbalanced and
Underbalanced Drilling
Applications . . 197
6.1 Drawdown for Round and Slot Nozzles With and Without Mud Filtrate
Migration Through the Sandface. 201
Example 6-1. Simple drawdown, round nozzle, no invasion
. 201
Example 6-2. Simple drawdown, round nozzle, invasion with supercharging, 200
psi overbalance 210
Example 6-3. Simple drawdown, round nozzle, invasion with strong supercharging,
2,000 psi overbalance . . 214
Example 6-4. Simple drawdown, round nozzle, underbalanced drilling, 100 psi
underbalance . 216
Example 6-5. Simple drawdown, slot nozzle, no
invasion .
. 218
Example 6-6. Simple drawdown, three pumping slot nozzles, no invasion 223
6.2 Highly
Transient Applications, Drawdown and Buildup,
Multiple Round or Slot Nozzles . 227
Example
6-7. Simple drawdown and buildup, single
round nozzle, no invasion . .
. 227
Example
6-8. Three round nozzles executing
drawdown and buildup simultaneously and independently, no invasion . .
. 232
Example
6-9. Two round nozzles, one withdrawing
fluid, the second simultaneously injecting, no invasion . . 237
Example
6-10. Invasion or supercharge
characterization in transient problems .
241
6.3 Special Topics . .
245
Example 6-11. A complicated simulation, effect of pore pressure in output
displays . 245
Example 6-12. Batch processing capabilities 250
Example
6-13. Spherical flow evaluation and
geometric factors .
. . 258
Example
6-14. Pressure behavior at permeability
extremes .
. . 261
Example
6-15. Comparing problems with and
without supercharge . .
. . 264
Example 6-16. Suppressing
dissolved gas release . . 267
Bubble point considerations .
. 267
Run 1. Undesirable
dissolved gas release 268
Run 2. Dissolved
gas remains in solution 273
Example 6-17. Steady flow convergence acceleration for
interpretation applications Big Data inverse applications . .
. . 278
Example 6-18. Heterogeneity
and dip detection using multiple probe firings .
. 286
Example 6-19. Triple-probe
tools with different nozzle geometries . .
292
Example 6-20. Flows with mixed
nozzle designs and different pumping schedules upgraded menu for
independently
controlled probes with different flow rates, pumping schedules and geometric
factors 296
Run 1. All
round nozzles with staggered
flow rates .
. 296
Run 2. All
slotted nozzles with staggered
flow rates .
. . 298
Run 3. All
slotted nozzles with identical flow rates .
. 299
Run 4. Slot,
round, slot combination with identical flow rates . . 302
Run 5. Round, slot, round combination
with identical
flow rates 303
6.4 References .
305
7. Multiphase Triple-Probe Flows Coupled
Models for
Pressure and Contamination . .
306
7.1 Pressure
and contamination simulations . 307
Example 7-1. Four and triple-probe runs, simulator
calibration, flow validation and geometric factors . 307
Example 7-2.
Effects of mud viscosity, supercharge invasion, and filter cake sealing
on cleaning
recovery . .
. 311
Example 7-3. Role of
diffusion in contamination 319
Example 7-4. Drawdown-buildup tests in the presence
of supercharged invasion
and contamination (assuming
equal mud and oil viscosities of 1 cp) . 324
Example 7-5. Drawdown-buildup tests in the presence
of supercharged invasion and contamination (mud viscosity greatly
exceeds oil viscosity) . . 328
Example 7-6. Pressure-contamination modeling with
mixed geometry nozzle operations . 332
Example 7-7. Pressure-contamination simulations with
mixed nozzles and pumping schedules . . 337
Example 7-8. Modeling
anisotropic formations . 342
7.2 References
348
8. Convergence Acceleration, Batch Processing and Inverse
Methods
for Permeability Prediction (Inverse Problem Focus and Definition) .
349
8.1 Convergence acceleration 351
8.1.1 Interpretation applications .
. 352
8.1.2 Validating convergence accelerations 353
8.1.3 Big data inverse
applications . . 358
8.2 Batch processing . .
. 359
8.2.1 Display
software and pressure analysis
options .
. 359
8.2.2 General transient 3D simulator in batch
mode . .
. 363
8.2.3 Rapid steady 3D simulator in batch mode . 367
A representative example .
. 367
Running the batch steady
solver . . 371
Higher permeability density runs . 374
8.3 Inverse methods for permeability prediction
. 379
8.3.1 Azimuthal inverse problem .
. . 379
Steady flow forward
calculations . 381
Limited (kh,kv) range
example . 381
Inverse permeability
predictions . . 391
Algorithm analysis .
. 391
Wider (kh,kv) permeability
example .. . 397
Inverse method recapitulation
. 401
Data integrity in big
data
implementation .
. 404
Azimuthal inverse
strategies . 406
8.3.2 Axial inverse problem
for any dip angle . 407
8.3.2.1 Dual probe anisotropy inverse analysis,
existing source model
simulators . 407
8.3.2.2 Supercharging Effects of nonuniform
initial pressure . .
417
Conventional zero
supercharge
model . .
. . 418
Supercharge Fast Forward
solver . 419
8.3.2.3 Multiprobe DOI, inverse and barrier
analysis .
425
8.3.3 Combined forward and
inverse user interface 433
Run 1. Center pumping
probe, two observation
probes with a first viscosity guess 433
Run 2. Center pumping
probe, two observation
probes with a second viscosity guess . 448
Run 3. Three pumping probes
in drawdown
mode .
450
Run 4. Two pumping probes in drawdown mode
Closing remarks 459
8.4 References .
. 461
9.
Gas Pumping with Multiprobe
Tools . 463
9.1 Background and Motivation
463
Table 9-1. Ratios of
Specific Heats .
. . 465
Triple-probe
nonlinear gas simulator in
mprobe(3-gas) . .
.
467
Example
9-1. Impermeable sandface, drawdown
only .
. 467
Example
9-2. Impermeable sandface,
drawdown-buildup . 469
Example
9-3. Zero or negative pressure, error
detection . .
. 470
Example 9-4. Effects
of high and low mud pressure in the
borehole
in drawdown-buildup applications . 472
Four-probe
nonlinear gas simulator in
mprobe(4-gas) .
.
475
Example 9-5. Gas expansion process effects . 475
Example
9-6. Heterogeneity detection using
staggered azimuthal probe firings .
. 478
Example 9-7. Controlling regions of dependence . 481
Example
9-8. Drawdowns with mixed nozzle
geometries .
. 484
9.2 Closing Remarks . .
. 488
9.3 References . .
. 489
10.
Axial Multiprobe, Reservoir
Characterization and Geothermal Issues .
490
10.1 Background and
Motivation . 491
10.2 Review of ideal source
axial probe methods . 494
10.3 Example axial pressure
vs time versus space probe solutions .
496
Example
10-1. Isotropic 1 md, with flowline
volume of 0 cc . . 497
Example
10-2. Isotropic 1 md, with flowline
volume of 100 cc . . 499
Example
10-3. Isotropic 1 md, with flowline
volume of 200 cc . . 500
Example
10-4. Isotropic 1 md, with flowline
volume of 300 cc . . 501
Example
10-5. Anisotropic kh = 1 md, kv = 0.1
md,
flowline volume of 100 cc . 502
10.4 Reservoir
characterization perspectives, geotechnical
and geothermal issues .
503
10.5 References .
. 512
Cumulative
References 514
Index .
. 530
About
the Author (with Software Summary) .
. 543