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© M B D C I © M B D C I 2-C Estimating Stresses Estimating Stresses Estimating Stresses Maurice Dusseault

2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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Page 1: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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Estimating StressesEstimating Stresses

Maurice Dusseault

Page 2: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s Common Symbols in Earth StressesCommon Symbols in Earth Stresses

� σv,σhmin,σHMAX : Vertical, minor and major horizontal stresses (usually σv ⊥ to surface)

� Sv,Sh,SH: Same as above, different symbols

� σ1,σ2,σ3: Major, intermediate, minor stress

� σ′1,σ′2,σ′3: Effective or matrix (solid) stress

� φ, Ε, ν: Porosity, Young’s mod., Poisson’s ratio

� ρ, γ, po: Density, unit weight, pore pressure

� k: Permeability (kv, kh…)

� These are the most common symbols used in discussing stresses in the earth

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s Stresses in the Earth: Intro IStresses in the Earth: Intro I

� In situ stresses: a vital initial condition for all geomechanics issues�To carry out any quantitative analysis, it is necessary

to start from the initial stress state�For example, deep reservoir depletion can lead to a ∆p of perhaps -75 MPa, so that ∆σ′ v = +75 MPa.

�The stress change is: ∆σ′ = σ′initial - σ′final

�This ∆σ′ value is used to compute subsidence, rock behavior (shearing, collapse), and so on

� In hard rocks (mining), [σ] ij can be calculated from direct strain measurements – [∆ε] ij

� This is not available in Petroleum Geomechanics

Page 4: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s Seeing the Effects of Stress!Seeing the Effects of Stress!

No clear dominant direction

0.5-0.7 m “dog-ear”

Breakouts in a mine

σ not ⊥ to axis of core…

Drilling direction

Disc peaks

Orientation of minor ppl σ ⊥ to core axis

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s Stresses in the Earth: Intro IIStresses in the Earth: Intro II

� In sedimentary rocks (oil and gas applications)…

� The locations are deep, hard to get to�And, the strains are small, hard to measure

�The rocks are porous, poor strain response

� So… hydraulic fracture-based methods are widely used - Minifrac™, LOT, XLOT, SRT

� +Core-based methods (DSCA, vP(θ), …)

� +Geophysical logging based methods

� +Geological inference (burial and tectonic histories of the basin give excellent clues)

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s Stress DefinitionsStress Definitions

σhmin

σHMAX

σv

σHMAX > σhmin

σa

σrσr = σ3

σa = σ1

τmax planesslip

planes

TriaxialTest

Stresses

In SituStresses

σ1 > σ2 > σ3

σ1

σ1

σ2

σ2

σ3

σ3

PrincipalStresses

Borehole Stresses

σθσr

θr

ri

z

x

yWe usually

assume σσσσv is a principal stress

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s Local, Reservoir and Regional Scale Local, Reservoir and Regional Scale

� Regional ScaleStresses�Basin scale: 50 km to 1000 km�Often called “far-field stresses”

� Reservoir ScaleStresses�A reservoir, or part of a reservoir�Scale from 500 m to several km�Salt dome region: 5-20 km affected zone

� Local ScaleStresses�Borehole region: 0.5-5 m�Drawdown zone (well scale) 100-2000 m

� Small ScaleStresses (less than 10-20 cm)

~200 km

~4 km

~400 m

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s Common Stress RegimesCommon Stress Regimes

� The most common stress regimes are:�Relaxed, or non-tectonic (no faulting, flat-lying):

vertical stress, σv, is = σ1 (major stress)�Normal faultregime: σv is σ1

�Thrust faultregime: σv isσ3 (least stress)�Strike-slipregime: σv isσ2 (intermediate stress)�Listric (growth, down-to-sea or GoM) fault regime:

σv changes from σ1 toσ3 at depth, then back to σ1

� Most sedimentary basins have relatively simple regional stress regimes

� But, there may be local complications, such as multiple faults, salt domes, uplift, etc.

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s Faults and Plate TectonicsFaults and Plate Tectonics

The Big Picture!

Regions of crustal extension

Compression region

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s Where Are Tectonics Important?Where Are Tectonics Important?

� Near active plates (eg: California, Sumatra, Colombia), tectonics governs stresses

� Near mountains, tectonic forces dominate� Away from plate margins and mountains (eg:

Williston Basin, Kalimantan, GoM), other factors are important

� In continental margin basins salt tectonics (domes and tongues) can be very important

� Non-tectonic intracontinental basins (Michigan, Williston, Permian…), shape, burial/erosion history are more important than tectonics

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s Basins: Major Examples in USABasins: Major Examples in USA

PER

MIA

N

BA

SIN

S

CO

MPL

EX

WILLISTON BASIN

MICHIGAN BASIN

APPA

LAC

HIA

N B

ASIN

Gulf Coas

t

Basin –GoM,

passive o

r

relaxe

d basin

Paradox B.

Powder River B.

Rockies Foreland Basins, compressive stresses controlled by mountain thrust

San Joachim, a rift valley

Southern CA basin complex, strike-slip and normal faulting

Atlantic coastal plain and offshore basin complexes, passive margins

MIDCONTINENT BASINS

Thrust basins

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s NonNon--Tectonic RegimesTectonic Regimes

� On stable continental plates, far from active plate boundaries. Some examples�Mid-continent basins: Williston, Michigan, Permian

Basin, East Texas (GoM), Songliao Basin (richest Chinese basin), interior Russia…

� On passive continental plate oceanic margins such as GoM, Kalimantan, Nova Scotia, NW Norway coast, Angola, etc.

� Basin geometry, sedimentation history, burial, erosion, diagenesis, salt tectonics, dissolution…affect stress states locally & substantially

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s Stresses and Basin ShapeStresses and Basin Shape

Yuc

utan

Houston

New Orleans

Florida

Gulf of Mexico

USA

Mexico

Edge of continental shelf

Regionalσhmin directions

Cross-section

shoreline

GoM example: regional stress directions are dominated by the continental slope, except locally near salt domes and a few structures such as the Mississippi canyon

listric faults

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s Normal Fault RegimeNormal Fault Regime

σv = σ1

σhmin= σ3σHMAX

= σ2

The normal fault regime is also called the extensional regime. It is characteristic of shallow rocks in all non-tectonic sedimentary basins without large erosion.

The San Joachim Valley in California, the Rhine Valley between France and Germany, the Gulf of Thailand, the Basin-and-Range, …, are all normal fault horst-graben features

Horst-graben structure

extension

horstgraben

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s Some Classic Normal Fault AreasSome Classic Normal Fault Areas

Red Sea Around UK, Ireland

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s Normal Faulting RegimesNormal Faulting Regimes

� High angle faults at surface (60°-70° dip)� This indicates that σv = σ1 when faulting

occurred. (But, is the fault old or active?)� Also, σHMAX = σ2 and σhmin = σ3

� Characteristic of extensional strain� Also, typical of non-tectonic basins � Hydraulic fractures are vertical, ⊥ to σhmin

� However, high angle surface faults may “flatten” at greater depth (as in the GoM)

� Many continental margins, passive basins, regions of crustal “pull-apart” …

Page 17: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s StrikeStrike--Slip or Wrench FaultSlip or Wrench Fault

Surfaceview

σv = σ2

σhmin = σ3

σHMAX= σ1acute

angle

~vertical fault plane

σhmin

Associated normal faults

σHMAX

Block diagram

Page 18: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s StrikeStrike--Slip Stress RegimeSlip Stress Regime

� Very high angle faults (>80° usually)

� Indicates σv = σ2 (σHMAX = σ1, σhmin = σ3) when the fault formed

� Characteristic of plate margins

� Common at depth in eroded basins

� Common some distance from compression

� Usually, normal faults are found nearby at the surface, away from the main fault trace, to accommodate strata movements

� Hydraulic fractures vertical, ⊥ to σhmin

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s Thrust and Reverse FaultsThrust and Reverse Faults

� Less than 45° angle on fault plane

� If less than 20-25°, it is almost always called a thrust fault rather than a reverse fault

This angle is always less than 45°, usually less than 30°

Page 20: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s Thrust Fault Regime and StructuresThrust Fault Regime and Structures

static basal sheet

overthrust sheet

brittle quartz-illite shale

hinge points

highly fractured zone

largely unfractured shale

AB C

The shale bed in zone A has gone throughone hinge point, through two in zone B, and through three hinge bends in zone C.

σHMAX = σ1

σv = σ3

overthrust sheet

compression

high-p shale

strong lateral thrust

RAMP

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s Compressive Coastal MarginCompressive Coastal Margin

Saf

fer

D, T

obn

H, M

oore

GF

200

3 –

OD

P R

esea

rch

Pro

gram

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s Thrust Faults and MountainsThrust Faults and Mountains

AlbertaSyncline

Basinedge Canadian Shield

Williston Basin

The Western Canadian Sedimentary Basin

USA

ALTA SASK MAN

NWT Nunavut

BC

Canadian Shield

(Precambrian)

Rockies

Athabasca Basin

EdmontonTectonicstress

Breakouts⊥ to σHMAX

Alberta is a “classic” compressional regime

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s Compressional Basin SectionCompressional Basin Section

Massive heavy oil deposits

+

++ +++

+++ ++ ++

+

+ ++

+ +

+

++

++

++

+

++

++ +

+

+

++ +

++ +

+

++ +

+

+

+

+ ++ +

+

Cretaceoussands, shales

Jurassic andolder carbonates,

sandstones, shales

Prairie Evaporites (halite)

Alberta SynclineRockies

Edmonton

Precambrian rocks

SW NE

not toscale

Schematic cross-sectionthrough Edmonton, Alberta

Thrust faults

Salt solution andcollapse features

Devonian reefs

Page 24: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s Thrust FaultsThrust Faults

� Low angle faults (dip of 0° to 30° usually)� Indicates σv = σ3 (σHMAX = σ1) when the

fault formed (or if it is still active)� Characteristic of compression regions,

associated with thrust mountain ranges� Same stress condition can often be found at

shallow depths in eroded basins� Usually, thrust fault “sheets” are bounded by

systems of normal and strike-slip faults � Hydraulic fractures will be horizontal (in

fact, usually they propagate gently upward)

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s Cross Section: Stress & StructureCross Section: Stress & Structure

Sing07.024

Mountains → → → → → → Distant plainsGolden Colorado → → → → → Eastern ColoradoBanff Alberta → → → → → Calgary Alberta

Near mountains:•Very high σHMAX•For great depth, σv = σ3•Thrusts, folds…•Fractured strata•Low to modest po

Distant from mountains:•Moderate to high σHMAX•For some depth, σv = σ3•Flat-lying, no faults•Strata are relatively intact•Low pressures

σHMAX σHMAX

Generally very high pore pressures are not found in thrust regimes and their forebasins, as rocks are somewhat fractured, pressures dissipate

forebasin

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s Listric Faulting and StressesListric Faulting and Stresses

“down-to-the-sea ” faults

zone where faults coalesce(detachment or décollement zone)

sea

slip planes

steepat top

σv

σh

stress

depth

Stresses change with z!

Listric faults on continental marginslead to unusual stress regimes wherethe major stress changes from vertical

to near-horizontal at depthgrabens

Page 27: 2C OK Estimating Stresses in the Earth · 2011-03-28 · ©MBDCI 2-C Estimating Stresses Stresses in the Earth: Intro I In situ stresses: a vital initial condition for all geomechanics

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s Listric FaultsListric Faults

� Characteristic of passive continental margin basins that are “open-to-the-sea” (GoM)

� Look like normal faults at the surface

� At depth, the faults flatten to become thrust faults

� Stress regimes change with depth!

� Often associated with overpressured zones

� These faults are like massive landslides

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s India and Tibet ExamplesIndia and Tibet Examples

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Passive basins

Active basins

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s Bay of Bengal Region and NorthBay of Bengal Region and North

� A continental margin basin exists offshore south of Dacca and Calcutta, we will expect a relaxed stress condition, GoM features

� A strong thrust basin to the north, along the Himalaya front, fractures, no oil

� Strike-slip to the east (Sagaing zone)

� Shan-Thai Plateau is partly a zone of extension, some N-S faults are normal

� Sichuan Basin, relatively undeformed, but under strong compression

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s North America (World Stress Map)North America (World Stress Map)

(available online at www.world-stress-map.org)

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s Stress Map of EuropeStress Map of Europe

� Many solutions for earthquake focal mechanisms in southern Europe give the dense stress coverage

� In the hard-rock areas –strain relief methods

� In quiescent basins, data from breakouts, hydraulic fracturing, LOT

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s Geological History!!Geological History!!

� This basin opened, filled, was compressed (thrusts and folds), uplifted and eroded

� Later, it subsided with new sediment fill

� The different lithologies compacted differently, leading to normal faults

gravelsclays and silts

20 – 100 km

3-10 km

Thrust condition

Relaxed stresses

Normal faults

Folds and closed structures

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s Burial and Diagenetic HistoryBurial and Diagenetic History

� What controls stresses during burial?

� How do stresses change with diagenesis?

� What happens during uplift and erosion?

� Do all rocks behave the same?

� What happens if pore pressures change?

� When there is tectonic loading or unloading, how are stress changes partitioned in strata?

� Hydrocarbon generation effect?

� Etc, etc… (it gets complicated…)

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s Stresses at DepthStresses at Depth

� σv from density logs, σhmin, σHMAX from various methods (geological estimation, HF…)

� We often use the “K′” coefficient.

� Ratio of least horizontal effective stress to the vertical effective stress (in situ)

� <1 – vertical fracturing� >1 – “horizontal” fracturing

v

minh

ov

ominh

p

pK

σ′σ′

=−σ

−σ=′

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s Burial Stresses, Frictional ControlBurial Stresses, Frictional Control

Ka′ = 0.33

Ka′ = 0.70

Ka′ = 0.33

Ka′ = 1.0

po

Note: σ′ = σ - po(Terzaghi’s law)

UC sand

shale

salt

sandstone E

0.5E

0.75E

salt is viscoplastic

These values are the limits, not actual values in situ

E = stiffness

σv

σhmin

Salt is viscoplastic, so all stresses are equal

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s Frictional Control of StressesFrictional Control of Stresses

� In fact, the strata we encounter are rarely purely frictional materials

� They also have cohesion, some creep…� The frictional stress control “model” is only

intended to give the theoretical lower bound of σ′hmin for high porosity strata

� If rocks are strongly cemented, it is possible to have stresses lower than this

� In exceptional cases, open fractures!�Shallow, above flanks of salt domes� In mountainous areas, shallow as well

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s Stresses In and Around SaltStresses In and Around Salt

� Salt is a very special material:�Highly soluble

�Low density (2.16 g/cm3 or 18 ppg equivalent)

�Viscoplastic, so all stresses are the same

� Drilling long sections of salt is a challenge

� Drilling near salt structures such as diapirs and sand tongues is challenging

� If you are going to drill and produce near salt features, it is imperative that you understand salt mechanics and the stress conditions

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s Deep Salt Diapir ExampleDeep Salt Diapir Example

Gas Pull Down

Mid-Miocene regional pressure boundary

Top BalderTop Chalk

Intra Hod/Salt

Salt

Low σhmin + gas!

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s Stress & Diagenesis, no TectonicsStress & Diagenesis, no Tectonics

� If no tectonic activity, σh is less than σv

� In sands, the ratio K′o (defined as the ratio of horizontal to vertical stress, σ′h/σ′v), can be as low as 0.3, usually 0.4 – 0.6

� Shales have a lower angle of friction, usually K′ois 0.6 – 0.8, even as high as 0.95 in muds

� Thus, the fracture gradient is higher in mud or shale in non-tectonic areas (GoM)

� Deep burial and diagenesis tend to reduce the stress differences

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s Stress and Diagenesis Stress and Diagenesis -- SandSand

line

of σ

′ v=

σ′ h, o

r K′ o

= 1

yiel

d, φ

′ = 3

0°σ′v

burial

diagenesis

Sand burial in a non-tectonic environment results in σ′h < σ′vbecause of friction. Diagenesis seems to reduce this stress difference slowly over long periods of time.

σ′hφ′ is the friction angle for sand

Horizontal stress

Ver

tical

str

ess

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s Erosion and Effective Stress PathErosion and Effective Stress Path

K o′ =

1.0

line (i.

e.: σ 1

= σ 3)

yiel

d,φ= 3

σ’v

σ’h

buria

l

diagenesis

Elastic behavior governs unloading: the rock is stiff and strong from burial, diagenesis

eros

ion

σ′v

σ′h

Horizontal stress

Ver

tical

str

ess

vh '1

' σ∆ν−

ν=σ∆

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s Effect of ErosionEffect of Erosion

� Once a sediment is buried and diagene-tically indurated, it behaves elastically

� Direct erosion without tectonic loading leads to the so-called “Poisson effect”:

� Thus, erosion naturallyleads toward the shallow condition K′ > 1.0 (except for salt, which behaves as a viscous fluid)

vh '1

' σ∆ν−

ν=σ∆

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s Stresses in an Eroded BasinStresses in an Eroded Basin

� Erosion creates a “skin” near the surface where σHMAX = σ1, andσv = σ3

� Deeper, a strike-slip regime condition σHMAX = σ3, σv = σ2is found

� So… the fracture gradient, PF, changes with depth, and

� …rocks are stronger, stiffer

� High pressures (po > 1.3 γw·z) are rare in eroded basins

σ, po

Z

σv

σhσv = σ3

σv = σ2

Assuming σhmin = σHMAX

thrust stress state

strike-slip stress state

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s Eroded BasinEroded Basin

� The “Poisson effect” during unloading generates a region at shallow depth where horizontal stresses are larger than vertical

� Also, the rocks are strong

� Drilling underbalanced is becoming common in such regions because of rock strength

� Pore pressures in such regions are almost never overpressured; rather, they tend to be hydrostatic ~10-12 MPa km

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s RecommendationsRecommendations

� Offshore or inshore, it pays to have some stress information for drilling, hydraulic fracturing, reservoir modeling…

� First, use geological history to build a regional stress model for your case

� The pore pressure conditions should be inferred as well, (using offset well data… etc.)

� Then, examine reservoir & local scale factors �Faults, salt features, reefs and drapes,

hydrothermalism, and other features

�These may “perturb” regional stresses

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s Breakouts and Natural StressesBreakouts and Natural Stresses

σHMAX

σhmin

principalstresses,σ1 > σ3

Vertical borehole

breakoutsdamage,ravelling

highσθ

Breakouts are evidence of stress anisotropy and are caused by shear rupture of the borehole wallHowever, care must be taken in assessing breakouts, as other factors can “interfere”Use only vertical wells (±10°) to get good stress orientations

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s Borehole Features: Wall ScanBorehole Features: Wall Scan

σHMAX

axialfractures

Stress directions

0 90 180 270 360

largewashout

σhmin

higher angleof intersection(joint plane)

low intersection angle (bedding?)

breakouts

Geometry of joint plane

intersection

Sinusoidal fracture traces

“en-echelon”axial fractures

if hole is slightly inclined

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s Use of Breakouts, Axial FracturesUse of Breakouts, Axial Fractures

� For σ orientations, use only wells that are vertical +/- 10° (rarely more inclined)

� Establish quality control on your data (length, symmetry across hole, quality…)

� Grade your data (“A” “B”, “C” quality…)� Breakouts: σHMAX is at 90° to breakout axis� Borehole wall axial fractures: σHMAX is

parallel to the fractures axis� Combine with geology, σv calculations from

density log data, LOT data, HF data…� Build a stress map for your region & use it

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s Reconstructed breakout data from

Schlumberger borehole scanner logs

Axial fractures and breakouts are stress direction indicators. If the stress difference is large, breakouts are also larger (deeper and wider).

brea

kout

sno

bre

akou

ts

axia

l fra

ctur

es

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s σσ Directions: Breakouts, FracturesDirections: Breakouts, Fractures

Borehole wall tensile fractures

Small breakouts (90°to tensile fractures)

Natural fracture

plane

Modest breakouts, no tensile fractures

Natural fracture

plane

σhmin is at 40°Az in this example

This is a LWD log trace taken during a trip, so resolution is poor

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s More about Breakouts, FracturesMore about Breakouts, Fractures

� Don’t confuse breakouts with hole enlargement (breakouts are symmetrical, and the minor axis ~ hole gauge size)

� Don’t confuse breakouts with sloughing in a fissile shale when the hole dip is close to the dip of the shale fissility

� Joints and planar features trace sinusoidal patterns on the borehole wall; induced axial fractures do not

� 4-arm dipmeter data must show ~symmetry, consistency, reasonable length, etc. (QC)

� Full wall scans are easier to interpret

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s Diagenesis, Burial, ErosionDiagenesis, Burial, Erosion

σσσσ′′′′h - MPaσ′ v

= σ′ h(K

′ o=

1)

diagenesis

sedi

men

tatio

n, φ

′ ~ 3

0o

actu

al p

ath?

0 5 10 15 20 25

erosion, ν ~ 0.2

-2000 m-

-500 m-

σ′h =17 MPaσ′v = 7 MPa

25

20

15

10

5

0

σσσσ′′′′v - MPa

This stress pathexplains the presence of

high horizontalstresses nearthe surface

Burial to 2000 m, erosion to 500 m

Stress path

A simple calculation of the probable effect of erosion of 1500 m of rocks on the stresses. We assumed initial stress state (red star), took a reasonable Poisson’s ratio for erosion (0.2), and made the calculation. (Assume that po is always 8.33 ppg)

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s Typical Stress ConditionsTypical Stress Conditions

stress (or pressure)

depth

vertical stress. σv

horizontal stress. σh

pore pressure, po

4 kmmild

overpressure

b. Western Alberta, 100 km from Rockies

stress (or pressure)

depth

stronglyoverpressuredregion at depth

vertical stress, σv

horizontal stress, σh

pore pressure, po

4 km

a. Gulf Coast of USA

Relaxed continental margin Tectonically stressed rocks

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s Stress Reversion at DepthStress Reversion at Depth

stress (or pressure)

depth

vertical stress, σv

horizontal stress, σh

pore pressure, po

4 kmRegion of strong

overpressure

Stresses “revert” to more ordinary stateZ

Note that σhmin can become > σv

Higher k rocks (fractured shales)

Ductile, low permeability shales dominate at the top of the OP zone

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s Stress and RiskStress and Risk

� Encountering high stresses and pressures unexpectedly increases risk

� To manage risk, stress estimates are made

� The model is refined with measurements

� Analysis is carried out to give a feel for the consequences of high stresses

� Appropriate measures are put into place

� CASE HISTORIES ARE VITAL!