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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


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


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


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


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


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

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