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ABSTRACT
Underbalanced drilling techniques are often considered to
avoid or mitigate formation damage, reduce lost circulationrisk, and increase drilling rate of penetration. However,
drilling with a bottomhole pressure less than the formation
pore pressure will usually increase the risk of borehole
instability due to yielding or failure of the rock adjacent to
the borehole. Numerous theoretical models for assessing
borehole collapse and fracture breakdown risks exist.
However, until recently it has been difficult for non-
specialists to use many of these models because they are not
easily implemented, or because they required input
parameters that are unfamiliar or difficult to obtain. A user-
friendly PC Windows-based software package called
STABView has been developed to help the well designerdetermine the optimal range of bottomhole pressure for
underbalanced drilling, i.e., the bottomhole pressures that
are high enough to avoid severe hole collapse, yet low
enough to avoid fracture breakdown. The software has been
designed to perform rapid parametric analyses for all types
of wells in most geological settings. Guidance in the
selection of rock properties and in-situ stresses is provided to
the user with an online database of typical values and a
comprehensive help utility. Applications of the software to
underbalanced drilling of horizontal wells in a number of
sandstone reservoirs are demonstrated.
INTRODUCTION
Underbalanced drilling technology is often considered for
naturally fractured formations, low pressure, partially
depleted reservoirs that are susceptible to formation damage
heavy oil reservoirs that have been geomechanically
disturbed by sand production, and in settings where
improved drilling rates of penetration are required
Underbalanced drilling can have some positive effects on
borehole stability. For example, shale formations containing
reactive clays often suffer from hydration-related mechanica
degradation, swelling, and pore pressure penetration when
infiltrated by drilling muds that flow into the formation aoverbalanced conditions. However, in may cases borehole
instability can be made worse when bottomhole pressures are
low. For example, low bottomhole pressures lead to an
increase in shear stresses acting around the circumference of
a well, hence leading to an increased risk of shear failure
(Figure 1). Furthermore, the presence of steep inflow
pressure gradients around a well can lead to tensile failure
and spalling of the borehole wall (Figure 2).
This paper is to be presented at the 1999 CSPG and Petroleum Society Joint Convention, Digging Deeper, Finding a Better Bottom Line,
in Calgary, Alberta, Canada, June 14 18, 1999. Discussion of this paper is invited and may be presented at the meeting if filed in
writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered
for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.
THE PETROLEUM SOCIETY PAPER 99-07
Borehole Stability Analysis for
Underbalanced Drilling
P. McLellan, C. HawkesAdvanced Geotechnology Inc.
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There is usually an optimal window of bottomhole
pressure that is high enough to avoid catastrophic hole
collapse, yet low enough to avoid fracturing, differential
sticking or unacceptable levels of formation damage. This
paper describes the use of a commercial software package to
identify optimal mud densities or circulating bottomhole
pressures. The theory behind the stability model is brieflysummarized, and its application is demonstrated with a
number of field examples.
BOREHOLE STABILITY MODELLING
Background
A wide range of modelling approaches are available for
assessing borehole instability risks. The simplest models
calculate the stress state at the borehole wall assuming the
rock is a linear elastic continuum, and compare these stresses
to a rock strength criterion to determine if shear failure or
tensile fracturing will occur (e.g., Bradley1). Extensions of
elastic models include the calculation of the borehole
breakout angle2, the effects of weak bedding planes on rock
failure3, the effects of inhibitive drilling mud chemistry on
osmotic pressures in shales4,5, and localized pore pressure
and shear stress peaks occurring away from the borehole wall
due to transient poroelastic effects6,7. Linear elastic models
are popular because they are relatively easy to implement,
require a modest number of input parameters, and are
capable of assessing borehole instability risks for most well
trajectories.
Models based on linear elasticity do not adequately
explain the fact that, in many cases, boreholes remain stable
even if the stress concentration around the borehole exceedsthe strength of the formation. One option to compensate for
this effect is to implement a calibration factor that corrects
model predictions to match observed field data.
Alternatively, elastoplastic models offer the ability to assess
the mechanical integrity of a borehole more realistically.
These models recognize that, even after a rock has been
stressed beyond its peak strength level, it does not
necessarily fail completely and detach from the borehole
wall. Several authors have published analytical or semi-
analytical elastoplastic models that can account for effects
such as near-wellbore, steady-state pore pressure gradients8,9,
anisotropic in-situ stresses10, filter-cake and capillary
threshold pressures11, and transient pore pressure gradients12.
A number of powerful numerical geomechanical models
exist which can be used for advanced borehole stability
modelling. These models include finite difference codes,
distinct element codes and finite element codes. These
models are capable of very realistic representations of rock
deformation, yielding and fluid flow behaviour. 3D versions
of many of these codes are also available. However, these
programs tend to be expensive, they require expert users to
run them, computational times are lengthy, and there are
numerous input parameters. These tools have proven to be
most useful for research studies or large-scale, high risk
offshore drilling projects where there is economic
justification for the comprehensive field and laboratory
testing and wireline logging required to obtain all of thenecessary model input parameters, in addition to the time-
consuming modelling efforts.
A New, User-Friendly Model
A number of the elastic and semi-analytical elastoplastic
borehole stability models described above have been
combined and implemented in a new, commercial software
program called STABView. This program is designed for
personal or network computers running Windows 95/98 or
NT operating systems. The efficient calculation algorithms
allow for rapid parameter sensitivity analyses. For borehole
instability analyses, the following technical options or
features to identify hole collapse due to shear failure areavailable:
vertical, inclined and horizontal wells
elastic and elastoplastic models with pore pressure
effects
steady-state flow for over- or underbalanced conditions
near-wellbore pore pressure gradient effects
osmotic pressure model for reactive shales
Mohr-Coulomb failure criteria with strain weakening
3D modified Lade failure criterion
capillary threshold pressure model for oil-based muds filter-cake and wall coating efficiency effects
3D plane of weakness model for fissile dipping shales
surge and swab pressure effects
time-dependent rock strength effects for shales
polar plot displays for 3D well trajectory planning
various risk parameters based on the yielded rock
volume
For fracture breakdown and lost circulation risk analyses,
the following technical features are available:
3D linear elastic model for all well trajectories variable fluid penetration effects
steady-state thermal effects on breakdown pressure
polar plot displays for 3D well trajectory planning
In addition, modelling options for assessing sand
production and openhole collapse risks during production are
also available, although these will not be discussed in this
paper.
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this depleted reservoir, an ECD of approximately 725 kg/m3
corresponds to a balanced bottomhole pressure. This graph
demonstrates the sensitivity of the yielded zone size to the
filter-cake efficiency (). The latter parameter, which is
explained in Figure 7, is a measure of how effective a filter-
cake or wall coating is at preventing the transmission of
hydraulic pressure within the borehole to the formation. Themagnitude of this parameter can be determined from core
flow tests that are commonly run to assess candidate drilling
muds, although this information has not traditionally been
extracted from the results of these tests. For an interval of a
borehole that has never experienced an overbalanced
bottomhole pressure, filter-cake will not have developed.
Hence, for the output shown, there is no sensitivity to filter-
cake efficiency for underbalanced conditions.
Figure 6 shows that, for the stronger rocks to be drilled,
NYZAs less than 1.0 are predicted for ECDs as low as
500 kg/m3. Consequently, borehole instability risks are low
for these rocks for underbalanced drilling conditions.However, Figure 8 indicates that much more severe rock
yielding is predicted for the weaker, interbedded sandstone-
shale intervals of the Cardium Formation. For example,
NYZAs greater than 3.5 are predicted for all cases where the
bottomhole pressure is less than or equal to the reservoir
pressure. This graph also displays a severe sensitivity of
yielded zone size to filter-cake efficiency for overbalanced
conditions. For example, assuming a filter-cake efficiency of
the order of 0.8 can be reached, ECDs in the 900 to
1000 kg/m3 range are required to reach acceptable levels of
yielding. An extensive sensitivity analysis was run to
evaluate the effects of critical, but poorly-constrained input
parameters such as rock strength, in-situ stresses and yielded
rock permeability. These analyses indicated that, for the most
plausible ranges of input parameters, ECDs in the 900 to
1000 kg/m3 range should result in acceptable levels of
borehole instability risk, assuming a mud with good cake-
building properties is used.
These results show that truly underbalanced conditions are
probably not feasible for the proposed horizontal well,
although ECDs slightly lower than a normal pore pressure
gradient (10 kPa/m) can be used without encountering
unacceptable levels of risk. Based on these results, the
operator used an overbalanced, non-damaging methyl
glucoside mud system with densities in the 1030 to
1100 kg/m3 range. The horizontal well was drilled
successfully without borehole instability problems.
Horizontal Well in a Heavy Oil Reservoir, Eastern
Alberta
An operator was considering drilling an underbalanced
horizontal well in a severely depleted, poorly cemented
Glauconitic Formation sandstone in Eastern Alberta. The
reservoir depth was about 900 m and its pressure had been
depleted to as low as 1.7 MPa. Local experience ruled out the
application of conventional overbalanced drilling because of
the extreme risk of lost circulation due to the low fracture
gradient. Furthermore, the sandstone in this reservoir was
quite weak, based on a visual inspection of core from the
field and a history of sand production from existing verticalprimary wells. Consequently, there were concerns that lost
circulation at too high a bottomhole pressure and/or borehole
collapse at too low a bottomhole pressure could occur.
A geomechanical analysis was undertaken to identify the
optimal range of bottomhole pressure for this reservoir.
Initially, a laboratory testing program was conducted on
slightly disturbed cores to measure rock mechanical
properties. The importance of a small amount of rock
cohesion cannot be underestimated in many borehole
stability and sand production problems. Real or apparent
cohesion arises from grain cementation, interstitial clays,
certain types of grain-to-grain contacts, diagenetic processes,and capillary effects in the pore fluids that are present.
Owing to the disturbance of the core samples that were
tested, only lower bound strength numbers could be
determined. Other techniques, such as quantitative image
analysis (QIA) on rock thin sections, exist to estimate rock
properties from otherwise disturbed cores. However, these
methods were not tried for this case. Table 2 summarizes the
peak and residual strength parameters, rock elastic properties
and other input parameters that were used for the stability
analysis. The vertical stress was determined by integrating a
bulk density log from the area. Horizontal stresses were
estimated from the fracture pressures in the field prior to
depletion, corrected for the poroelastic effects of the
depletion. Borehole breakout data in the area were used to
constrain the azimuth of the maximum horizontal stress.
Figure 9 shows the relationship between NYZA and
bottomhole pressure, for over- and underbalanced conditions,
using the base case parameters. The sensitivity of the
solution to the maximum horizontal in-situ stress, a poorly
constrained parameter, is also indicated. This plot shows that
there is only a relatively small amount of yielding (e.g.,
NYZA values less than 1.0) predicted for bottomhole
pressures of 2 MPa or less. Underbalanced drilling, with a
foam system, for example, will likely be feasible in this
setting provided adequate hole cleaning can be maintained.
The upper acceptable limit for the bottomhole pressure
while drilling was calculated using the 3D linear elastic
fracture breakdown model in STABView. The criterion for
breakdown is the condition where the effective tangential (or
hoop) stress at the borehole wall exceeds the tensile
strength of the rock (which in the case of this weak sandstone
is assumed to be very small or negligible). For the base case
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parameters, fracture breakdown is predicted for bottomhole
pressures exceeding 5.4 MPa, or a gradient of 6 kPa/m.
Figure 10 shows the optimal range of bottomhole pressure
for the base case parameters, as well as for a number of
parameter sensitivity cases. This figure shows that the risk of
hole collapse is small for underbalanced conditions even for
widely varying filter-cake properties and reservoir pressures.
Breakdown pressure does, however, exhibit sensitivity to the
latter parameters. If a perfect filter-cake exists, a larger
breakdown pressure of 6.8 MPa is predicted. The breakdown
pressure is also predicted to increase significantly with
increasing reservoir pressure. For the latter sensitivity cases,
the horizontal in-situ stresses were adjusted using poroelastic
theory to reflect the change in stress state resulting from the
reservoir pressure change.
Based on these analyses the operator elected to drill the
horizontal well with a foam system keeping bottomhole
pressures to a minimum to avoid lost circulation. At the time
of writing, the candidate well had not yet been drilled.
Coiled Tubing Drilled Horizontal Well, Lake
Maracaibo, Venezuela
A service company was planning to drill a number of
horizontal wells in moderately weak, Eocene-age sandstones
in a partially depleted oil field in Lake Maracaibo, Venezuela
using underbalanced coiled tubing technology. A borehole
stability analysis was undertaken in order to help select the
optimal range of operating bottomhole pressures from a risk
mitigation point of view.
Limited input data were readily available for this
modelling effort. Rock mechanical properties were estimated
from empirical correlations to porosity and pore
compressibility data previously measured on core samples. A
novel technique was also used to estimate rock strength using
a correlation to grain contact frequency. This was determined
from digital image analysis on petrographic thin sections
prepared from large cavings obtained from one well in this
field. In-situ stress magnitudes were estimated from
published data and analyses for a nearby, undepleted
reservoir and then adjusted to depleted conditions using
poroelastic equations for a passive basin. Stress orientations
were estimated by analyzing fault orientations obtained from
structural maps for the area.
The borehole stability risk analysis was run using the
elastoplastic algorithm described in the previous section. The
model input parameters are listed in Table 3. Figure 11
shows the sensitivity of yielded zone area to peak cohesion
for a range of ECDs. Note that, for this severely depleted
reservoir, an ECD of approximately 330 kg/m3 corresponds
to a balanced bottomhole pressure condition. These results
indicated that, even for peak cohesion estimates significantly
smaller than the base case value of 10 MPa, NYZAs less
than 1.0 were calculated for ECDs up to 200 kg/m3 below
balanced conditions.
A number of additional sensitivity analyses were run for
other critical input parameters using STABView and the
numerical geomechanical software program FLAC17
Figure 12 shows the results of a FLAC simulation for the
base case parameters. The extent of the yielded zone
predicted using STABView is also indicated in this figure
and it compares favourably to yielding predicted by FLAC
One of the advantages of FLAC is that it can also identify the
onset of radial tensile failure (as depicted in Figure 1) due to
steep inflow gradients. In the FLAC output shown, the
innermost row of elements in the numerical grid has
undergone extreme deformation because they lose almost al
of their strength once they have failed in tension. Around a
real borehole, this rim of rock would detach from the
borehole wall and fall into the well.
FLAC was also used to investigate the effects of more
complex material behaviour that cannot be simulated with
semi-analytical models such as STABView. For example
effects such as linear strain softening, internal filter-cakes of
variable thickness and permeability, and highly anisotropic
in-situ stresses were investigated. Based on all of the results
it was determined that ECDs as low as 250 kg/m 3 , which
corresponds to an underbalance pressure of 1.5 MPa, could
be used while reducing borehole instability risks to
acceptable levels.
For this investigation, STABView was also used to
calculate fracture breakdown pressures to assess the los
circulation risks during drilling. Figure 13 shows the
sensitivity of fracture breakdown pressure to the minimum
horizontal in-situ stress for a full range of horizontal wel
azimuths. For the base case minimum horizontal stress
gradient of 14.5 kPa/m, fracture breakdown is predicted to
occur for ECDs of 1400 kg/m3or more, depending on wel
azimuth. For a significantly smaller minimum horizonta
stress gradient of 11 kPa/m, fracture breakdown is predicted
at ECDs of approximately 700 kg/m3for boreholes oriented
perpendicular to the minimum horizontal in-situ stress. For
boreholes oriented parallel to the latter in-situ stress
breakdown is predicted at ECDs of approximately
1700 kg/m3. Even though these results are very sensitive tothe minimum horizontal stress magnitude and orientation, the
risk of lost circulation due to fracture breakdown is
considered low for wells in this field as long as
underbalanced or slightly overbalanced conditions are used
when drilling.
Several vertical and horizontal wells were subsequently
drilled in the field using underbalanced coiled tubing
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technology. Although some operating problems were
experienced with these early wells, borehole stability was not
an issue, primarily because of the medium strength
sandstones in the target reservoir.
Horizontal Well in a Weak Sandstone Reservoir,
Gabon
An operator planned to drill a horizontal well into a weak,
poorly-cemented sandstone reservoir in Gabon, West Africa.
Underbalanced drilling was considered in order to mitigate
formation damage effects, but concerns were expressed about
borehole instability while drilling such weak rocks.
Cores from an offset deviated well were inspected to
qualitatively assess the properties of these rocks. Core
recovery had been very poor in the weakest strata of the
cored intervals, and much of the recovered core was severely
damaged. Consequently, it was not possible to measure
mechanical properties for these rocks in the laboratory.
Based on wireline log data and published data for rockspossessing a similar lithology, the mechanical properties
were estimated. An upper bound on the strength parameters
was also obtained by back-analyzing a section of the
enlarged hole in the offset well, based on caliper logs.
In order to account for the uncertain nature of some of the
critical input parameters, as well as the variability of rock
properties along the planned 250 m length of the horizontal
well due to formation heterogeneity, a probabilistic
assessment of borehole instability risk was run using the
elastoplastic model option in STABView. More details
regarding probabilistic borehole stability modelling can be
found in McLellan and Hawkes18
. The fundamentaldifference between deterministic and probabilistic modelling
is that probability density functions (PDFs), rather than
single, discrete values, are specified by the user for critical
input parameters. Several thousand model simulations can
then be run, each time randomly drawing input parameter
values from the specified PDFs. The output consists of a
histogram of possible NYZAs, from which the probability
of exceeding a critical threshold of yielded zone area can be
evaluated.
The input data used for these calculations are listed in
Table 4. The input parameters that were specified as PDFs
are identified in brace brackets. Probabilistic modelling toolsare not integrated with the current version of STABView, so
the actual probabilistic routine was implemented using a
separate software application.
Figure 14 shows the predicted NYZAs for a range of
ECDs. The mean NYZA calculated for each ECD simulated
is shown, along with curves that denote the mean value plus
or minus one standard deviation. As such, there is
approximately a 67% probability that the NYZA will fall in
the region enveloped by the standard deviation curves.
This reservoir is over-pressured, and an ECD of
1140 kg/m3 corresponds to balanced pressure conditions.
Figure 14 clearly shows that very large yielded zone areas
are expected for underbalanced pressure conditions. In fact,
an ECD in the 1250 to 1300 kg/m3 range is required to
provide a reasonable probability that NYZAs are of the
order of 1.0 or less. At the depth of this reservoir, this
corresponds to overbalance pressures in the 1.6 to 2.4 MPa
range. Based on these results, it was concluded that this
reservoir could not be drilled with underbalanced conditions
without unacceptable hole collapse risks. The best available
compromise between borehole stability and formation
damage was to design a mud with an efficient filter-cake,
high regain permeabilities and an ECD in the 1250 to
1300 kg/m3range.
The operator for this well was also interested in sand
production risk during production, and whether it would be
possible to complete this well open-hole without sand
control. It is clear from the drilling stability analysis that
large yielded zones will exist during production.
Consequently, there is a high risk of hole collapse and hence
for producing large volumes of sand.
Based on the results of this analysis, the operator decided
to drill the reservoir section of the well with a water-based
mud with a static density of approximately 1250 kg/m3. The
well was drilled without experiencing any serious borehole
instability-related problems in the horizontal, and a slotted
liner was run for sand control.
CONCLUSIONS
Drilling with a bottomhole pressure less than the
formation pore pressure increases the risk of borehole
instability because the mechanical stresses around the
borehole are more likely to exceed the shear and/or
tensile strength of the rock for these conditions.
Geomechanical modelling can be used to predict the
optimal range of bottomhole pressure that is high
enough to avoid severe hole collapse, yet low enough to
avoid fracture breakdown.
A user-friendly PC Windows-based software package
called STABView has been developed to assess
borehole stability and lost circulation risks for vertical,
deviated and horizontal wells during underbalanced
drilling operations. STABView features rapid
calculation times and extensive graphical output for
sensitivity analyses.
The depletion of reservoir pressure results in a change in
the in-situ stress state. This new stress state usually
reduces the collapse pressure and the fracture breakdown
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pressure within the reservoir. Underbalanced drilling
may be possible for a given reservoir, but the window of
optimal bottomhole pressure will shift depending on the
current value of the reservoir pressure.
STABView has been successfully used in several
sandstone reservoirs at various reservoir pressure
conditions to determine the optimal bottomhole pressurewindow to avoid severe hole collapse and fracture
breakdown.
NOMENCLATURE
Amud chemical activity of drilling mud
Ashale chemical activity of shale pore water
A1 cross-sectional area yielded zone
A2 cross-sectional area of original borehole
a maximum semi-axis of yielded zone
b minimum semi-axis of yielded zone
BHP bottomhole pressure
cp peak cohesion
cr residual cohesionE Youngs modulus
ECD equivalent circulating density
ke permeability of elastic rock
ky permeability of yielded rock
NYZA Normalized Yielded Zone Area
= A1/A2P pore pressure
Pa pore pressure adjacent to the borehole wall
Pc capillary threshold pressure
Pr reservoir pressure
Pw wellbore pressure
PDF probability density function
r radial distance
rw borehole radius
RFP Rubble Fill Percentage
filter-cake or wall coating efficiency
m osmotic membrane efficiency
p peak friction angle
r residual friction angle
Hmax maximum horizontal in-situ stress
Hmin minimum horizontal in-situ stress
v vertical in-situ stress
1 maximum in-situ stress
3 minimum in-situ stress
r radial stress
T tensile strength Poissons ratio
REFERENCES
1. Bradley, W.B., Failure of Inclined Boreholes, Journal
of Energy Resources Technology/ Transactions of the
ASME, 232-239, 1979.
2. Zoback, M.D., Moos, D., Mastin, L. and Anderson, R.N
Well Bore Breakouts and In-Situ Stress, Journal o
Geophysical Research, Vol. 90, 5523-5530, 1985.
3. Okland, D. and Cook, J.M., Bedding-Related Borehole
Instability in High-Angle Wells, SPE Paper 47285
Presented at SPE/ISRM Eurock98, Trondheim
Norway, July 8-10, 1998.
4. Chenevert, M.E. and Pernot, V., Control of Shale
Swelling Pressures Using Inhibitive Water-Based
Muds, SPE Paper 49263, Presented at the SPE Annual
Technical Conference and Exhibition, New Orleans
Louisiana, September 2730, 1998.
5. Mody, F.K. and Hale, A.H., Borehole-Stability Mode
to Couple the Mechanics and Chemistry of Drilling
Fluid/Shale Interaction, Journal of Petroleum
Technology, 1093-1101, November, 1993.
6. Detournay, E., Cheng, A.H-D., Poroelastic Response o
a Borehole in a Non-Hydrostatic Stress FieldInternational Journal of Rock Mechanics, Mining
Science, and Geomechanics Abstracts, Vol. 25, 1988
pp. 171-182.
7. Yuan, Y.G., Abousleiman, Y. and Roegiers, J.-C., Fluid
Penetration around a Borehole under Coupled
Hydro-Electro-Chemico-Thermal Potentials, Paper
No. 95-72, Presented at the 46th Annual Technica
Meeting of the Petroleum Society of the CIM, Banff
Alberta, May 14-17, 1995.
8. Risnes, R., Bratli, R.K. and Horsrud, P., Sand Stresses
Around a Wellbore, SPE Journal, 883-898, December
1982.
9. Wang, Y. and Dusseault, M.B., Borehole Yield and
Hydraulic Fracture Initiation in Poorly Consolidated
Rock Strata - Part II. Permeable Media, Internationa
Journal of Rock Mechanics, Mining Science, and
Geomechanics Abstracts, Vol. 28, No.4, 247-260, 1991.
10. Detournay, E. and St. John, C.M., Design Charts for a
Deep Circular Tunnel Under Non-uniform Loading
Rock Mechanics and Rock Engineering, Vol. 21, 119-
137, 1988.
11. McLellan, P.J., and Wang, Y., Predicting the Effects o
Pore Pressure Penetration on the Extent of Wellbore
Instability: Application of a Versatile Poro
Elastoplastic Model, SPE Paper 28053, Presented a
SPE/ISRM Eurock94, Delft, the Netherlands, August
29 - 31, 1994.
12. Hawkes, C.D. and McLellan, P.J., A New Model for
Predicting Time-Dependent Failure of Shales
Theory and Application, CIM Paper 97-131, Presented
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at the 48th Annual Technical Meeting of the CIM
Petroleum Society, Calgary, Alberta, June 8-11, 1997.
13. McLellan, P.J. and Hawkes, C.D., User-Friendly
Borehole Stability Software for Designing Horizontal
and Deviated Wells, Paper 99-101, Presented at the
CADE/CAODC Spring Drilling Conference, Calgary,
Alberta, April 7-8, 1999.
14. Advanced Geotechnology Inc., STABView Users
Manual, Version 1.0, 1999.
15. McLellan, P.J., Assessing the Risk of Wellbore
Instability in Inclined and Horizontal Wells, Journal
of Canadian Petroleum Technology, Vol. 35, No. 5, 21-
32, May, 1996.
16. Addis, M.A., Last, N.C., Yassir, N.A., Estimation of
Horizontal Stresses at Depth in Faulted Regions and
Their Relationship to Pore Pressure Variations,SPE
Formation Evaluation, Vol. 11, No. 1, 11-18, March,
1996.17. Itasca Consulting Group, Inc., FLAC Users Guide,
Version 3.4, 1998.
18. McLellan, P.J. and Hawkes, C.D., Application of
Probabilistic Techniques for Assessing Sand
Production and Borehole Stability Risks, SPE Paper
47334, Presented at SPE/ISRM Eurock98, Trondheim,
Norway, July 8-10, 1998.
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Table 1: Base case input parameters used for borehole
stability modelling, Cardium Formation sandstones (ss)
and interbedded sandstones and shales (ss/sh).
Parameter Value
ss ss/shcp 13 MPa 5.0 MPa
cr 4.6 MPa 2.0 MPa
p 35 35
r 30 30
E 15 GPa 4 GPa
0.25 0.30
ke 0.5 mD 0.1 mD
ky 2.5 mD 0.5 mD
Prgradient 10.0 kPa/m (initial)
7.1 kPa/m (current)
vgradient 24 kPa/m
Hmaxgradient 24 kPa/m (initial)
Hmingradient 18.6 kPa/m (initial)
Hminorientation 135well azimuth 135
depth 2400 m
Table 3: Base case input parameters used for borehole
stability modelling, Eocene sandstones, Lake
Maracaibo, Venezuela.
Parameter Value
cp 10 MPa
cr 2.5 MPa
p 42
r 37
T 1 MPa
E 9 GPa
0.30
ke 50 mD
ky 100 mD
Prgradient 3.3 kPa/m (current)
vgradient 21.8 kPa/m
Hmaxgradient 16.0 kPa/m (current)
Hmingradient 14.5 kPa/m (current)
Hminorientation 050
well azimuth 140
depth 1800 m
Table 2: Base case input parameters used for borehole
stability modelling, Glauconitic Formation sandstone
Eastern Alberta.
Parameter Value
cp 1.4 MPacr 0.7 MPa
p 53
r 40
T 0.1 MPa
E 1.5 GPa
0.30
ke 1000 mD
ky 2000 mD
Prgradient 1.9 kPa/m (current)
vgradient 22.8 kPa/m
Hmaxgradient 12.9 kPa/m (current)
Hmingradient 10.7 kPa/m (current)
Hminorientation 135
well azimuth 135 (hole collapse)
45 (breakdown)
depth 900 m
Table 4: Base case input parameters used for borehole
stability modelling, Early Cretaceous sandstone
Gabon.
Parameter Value*
cp {0.75, 0.9, 1.05} MPa
cr {0.25, 0.75, 1} MPa
p {30, 35, 40}
r p- {3, 5, 7}
E 0.5 GPa
0.30
ke 5000 mD
ky {0.2, 1, 4} ke
{0.5, 0.8, 1.0}
Prgradient 11.2 kPa/m
vgradient {21, 22, 23} kPa/m
Hmaxgradient {1.0, 1.05, 1.1}Hmin
Hmingradient {13.5, 14, 15} kPa/m
Hminorientation 135
well azimuth 045
depth 1530 m
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*{c1, c2, c3} represent the minimum, most probable and
maximum values of a triangular PDF, respectively
Pw Pw
1 1
3 3
Overbalanced- support pressure
Underbalanced- no support pressure
Shear Yielding
Figure 1: Shear yielding occurs for underbalanced
conditions due to the absence of a support pressure on
the borehole wall
r
P
Pw
r
Extent oftensile failure
zoneFlow intothe well
rw
Figure 2: Radial tensile fracturing occurs due to steep
inflow gradient
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0
0.2
0.4
0.6
0.8
1
500 700 900 1100ECD (kg/m)
NYZ
= 0.80.4
0
Sandstone
Figure 6: Effect of filter-cake efficiency on Normalized
Yielded Zone Area (NYZA) for a range of equivalent
circulating densities, Cardium Formation sandstones,
West-central Alberta
0
0.5
1
1.5
2
2.5
3
3.5
44.5
500 700 900 1100ECD (kg/m)
NYZ
= 0.8 0.4
0
Interbedded sandstone-shale
Figure 8: Effect of filter-cake efficiency on Normalized
Yielded Zone Area (NYZA) for a range of equivalent
circulating densities, Cardium Formation sandstone-
shale interbeds, West-central Alberta
rw r
P
Support
Pressure
Filter-cake or Wall Coating
Pw
Pa
Pr
=Pw -Pa
Pw -Pr
Figure 7: Pressure drop across a filter-cake or wal
coating for overbalanced conditions, and the definition
of efficiency ()
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0 2 4 6 8 10Bottomhole Pressure (MPa)
NYZ
Hmax = 12.9 kPa/m
(Base Case)
14.0 kPa/m
16.0 kPa/m
Reservoir pressure
Figure 9: Effect of maximum horizontal in-situ stress
gradient on Normalized Yielded Zone Area (NYZA) for
a range of bottomhole pressures, Glauconitic
Formation sandstone, Eastern Alberta
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0 1 2 3 4 5 6 7 8 9 10 11 12
Hole Collapse Optimal Range of BHP Fracture Breakdown
Bottomhole Pressure (MPa)
Base Case
Perfect Filter-cake
Pr= 4.5 MPa
Pr= 8.7 MPa
Figure 10: Effect of filter-cake efficiency and reservoir
pressure (Pr) on the optimal range of bottomhole
pressure, Glauconitic Formation sandstone, Eastern
Alberta
0
0.1
0.2
0.3
0.4
0.50.6
0.7
0.8
0.9
1
100 200 300 400 500ECD (kg/m)
NYZ
5 MPa
7.5 MPa
cp= 10 MPa (Base Case)
Reservoir pressure
Figure 11: Effect of peak cohesion on Normalized
Yielded Zone Area (NYZA) for a range of equivalent
circulating densities, Eocene sandstone, Lake
Maracaibo, Venezuela
Figure 12: FLAC output showing the extent of shear yielding and tensile failure predicted around a borehole during
underbalanced drilling of an Eocene sandstone, Lake Maracaibo, Venezuela
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0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 45 90 135 180 225 270 315 360Well Azimuth ()
MaximumS
afeECD(k
g/m)
Hmin= 14.5 kPa/m (Base Case)
13 kPa/m
Reservoir pressure
11 kPa/m
Figure 13: Effect of well azimuth on the fracture
breakdown gradient (expressed as an equivalent ECD) as
a function of the minimum horizontal in-situ stress,
Eocene sandstone, Lake Maracaibo, Venezuela
0
1
2
3
4
5
6
7
8
9
1000 1050 1100 1150 1200 1250 1300
ECD (kg/m3)
NYZ
mean mean + st. dev.
mean - st. dev.
Reservoir pressure
Figure 14: Output from a probabilistic simulation o
Normalized Yielded Zone Area (NYZA) for a range o
equivalent circulating densities, Early Cretaceou
sandstone, Gabon