Intro to Petroleum Geomechanics Stress, Strain, Pressure, Deformation, Strength, etc. Maurice Dusseault.

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Intro to Petroleum Geomechanics

Stress, Strain, Pressure, Deformation, Stress, Strain, Pressure, Deformation, Strength, etc.Strength, etc.

Maurice Dusseault

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Stresses (I)Stresses (I)

Stresses in a solid sediment arise because of gravity and geological history

Stresses are different in diffferent directions Three principal stresses are orthogonal, and

the vertical direction is usually one of them Overburden weight is = v (+/- 5%)

The lateral stresses, hmin and HMAX (or h and H) are at 90 degrees to one another

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Stresses (II)Stresses (II)

Normal stresses () act orthogonal to a plane and cause the material to compress

Shear stresses () act parallel to a plane and cause the material to distort

x -

y-

x+

y+

xy

yx

yx

xy

Static equilibrium:x

x

yy

xy = - yx

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PressuresPressures

Pressures refer to the fluid potential (p) Pressures can be hydrostatic, less than

hydrostatic (rare) or greater (common). Called underpressured or overpresssured

Pressures at a point are the same in all directions because they are within the fluid

We assume that capillary effects are not important for large stresses and pressures

Differences in pressures lead to flow

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Pressures at DepthPressures at Depth

depth

pressure (MPa)

Hydrostatic pressure distribution: p(z) = wgz

overpressureunderpressure

Overpressured case: overpressure ratio = p/(wgz), a value greater than 1.2

Underpressured case: underpressure ratio = p/(wgz), a value less than 1

1 km

~10 MPa

Normally pressured range:

0.95 < p(norm) < 1.2

Fresh water: ~10 MPa/km

Sat. NaCl brine: ~12 MPa/km

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Effective Stress (Effective Stress () Principle) Principle

The famous Terzaghi concept (1921) Only “effective” stresses [’ ] affect strength

and deformation behaviour Effective stress is the stress component

transmitted through the solid rock matrix Total stresses are the sum of the effective

stresses and the pressures: = + p, or:ij = []ij + [p]

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Effective StressesEffective Stresses

Pressure is the same in all directions (a fluid)

Effective stress is the sum of the grain-to-grain (matrix) forces

The sum of p and gives total stresses,

Usually, v = (z)dz

hmin , HMAX must be measured or estimated

po

f2

f1

f3

f4

v + po = v (or Sv)

h +

po =

h (

or

Sh)

h +

po =

h (

or

Sh)

v + po = v (or Sv)

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Rock Strength (I)Rock Strength (I) Strength is the resistance to shear stress (shear

strength), compressive normal stress (crushing strength), tensile stress (tensile strength), or bending stress (beam strength).

All of these depend on effective stresses (), therefore we must know the pore pressure (p)

Rock specimen strength is usually very different than rock mass strength because of joints, bedding planes, fissures, etc.

Which to use? Depends on the problem scale.

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Rock Strength (II)Rock Strength (II) Tensile strength (To) is extremely

difficult to measure: it is direction-dependent, flaw-dependent, sample size-dependent, ...

To is used in fracture models (HF, thermal fracture, tripping or surge fractures)

For a large reservoir, To may be assumed to be zero because of joints, bedding planes, etc.

F

F

A

To = F/A

Prepared rock

specimen

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Rock Strength (III)Rock Strength (III) Shear strength is a vital geomechanics

strength aspect, often critical for design Shearing is associated with:

•Borehole instabilities, including breakouts, failure•Reservoir shear and induced seismicity•Casing shear and well collapse•Reactiviation of old faults, creation of new ones•Hydraulic fracture in soft, weak reservoirs•Loss of cohesion and sand production•Bit penetration, particularly PCD bits

rock

n

slip plane

n is normal effective stress

is the shear stress plane

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Rock Strength (IV)Rock Strength (IV)

Shear strength depends on the frictional behaviour and the cohesion of the rock

Carry out a series of triaxial shearing tests at different 3, plot each as a stress-strain curve, determine peak strengths

1 - 3

axial strain

stre

ss d

iffe

renc

e

a

peakstrength

a

r

slip planes

a

r

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CurvesCurvesst

ress

dif

fere

nce

1 - 3

axial strain

a

peakstrength

seating, microcrack closure

“elastic” part of curve

massive damage, shear plane develops

damage starts sudden stress drop (brittle)

cohesionbreaking

continued damage

ultimate or residual strength

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Rock Strength (V)Rock Strength (V) To plot a yield criterion from triaxial tests, plot

1, 3 at failure on equally scaled n axes, join with a semicircle, then sketch tangent (= Y)

1

Y

To n

cohesion

c

3

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11 33 Plotting MethodPlotting Method

Plot 1, 3 values at peak strength on axes

Fit a curve or a straight line to the data points

The y-intercept is the unconfined strength

Y1 - 3tan2 - C0 = 0)

(straight line approximation)

1

3

Uniaxialcompressivestrength, C0

tan2

Curved orlinear fit

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Rock Strength (VI)Rock Strength (VI)

Strength of joints or faults require shear box tests

Specimen must be available and aligned properly in a shear box

Different stress values (N) are used

N - normal force

S - shear forceN

S Shear box

Area - A

SA

NA

Linear “fit”

Curvilinear “fit”

data point

cohesionc

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Yield CriterionYield Criterion

This type of plot is called a Mohr-Coulomb plot. Y is usually called a Mohr-Coulomb “yield” or “failure” criterion

•It represents the shear strength of the rock (S/A) at various normal stresses (N/A), A is area of plane

•For simplicity, a straight line fit is often used

SA

NA

Linear “fit”

Curvilinear “fit”

data point

cohesionc

=

= n

Y

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CohesionCohesion

Bonded grains Crystal strength Interlocking grains Cohesive strength

builds up rapidly with strain

But! Permanently lost with fabric damage and debonding of grains

stre

ss d

iffe

renc

e

1 - 3

a

complete - curve

cohesion mobilization

frictionmobilization

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FrictionFriction

Frictional resistance to slip between surfaces Must have movement () to mobilize it Slip of microfissures can contribute Slip of grains at their contacts develops Friction is not destroyed by strain and damage Friction is affected by normal effective stress Friction builds up more slowly with strain

mob = cohesion + friction f = c + n

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Estimating Rock StrengthEstimating Rock Strength

Laboratory tests OK in some cases (salt, clay), and are useful as indicators in all cases

Problems of fissures and discontinuities Problems of anisotropy (eg: fissility planes) Often, a reasonable guess, tempered with data,

is adequate, but not always Size of the structure (eg: well or reservoir) is a

factor, particularly in jointed strata Strength is a vital factor, but often it is

difficult to choose the “right” strength value

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Strength AnisotropyStrength Anisotropy

Vertical core

Bedding inclination

0° 30° 60° 90°

UCS

UCS

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Crushing Strength (I)Crushing Strength (I)

Some materials (North Sea Chalk, coal, diatomite, high porosity UCSS) can crush

Crushing is collapse of pores, crushing of grains, under isotropic stress (minimal )

Tests involve increasing all-around effective stress (’) equally, measuring V/’

Tests can involve reducing p in a highly stresses specimen (ie: ’ increases as p drops)

UCSS = unconsolidated sandstone

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Crushing Strength (II)Crushing Strength (II)

Apply p, ( > p), allow to equilibrate ( = - p)

Increase by increasing or dropping p

= - p Record volumetric strain,

plot versus effective stress The curve is the crushing

behavior with +

p

V

LE

crushingmaterial

V

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Rock StiffnessRock Stiffness

To solve any ’-problem, we have to know how the rock deforms in response to a stress change

This is often referred to as the “stiffness” For linear elastic rock, only two parameters

are needed: Young’s modulus, E, and Poisson’s ratio, (see example)

For more complicated cases, more parameters are required

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Rock Stiffness DeterminationRock Stiffness Determination

Stiffness controls stress changes Estimate stiffness using correlations based on

geology, density, porosity, lithology, .... Use seismic velocities (vP, vS) for an upper-

bound limit (invariably an overestimate) Use measurements on laboratory specimens

(But, there are problems of scale and joints) In situ measurements (THE tool, others ...) Back-analysis using monitoring data

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What are E and What are E and ??

deformation

L

radialdilation

L

Young’s modulus (E):E is how much the materialcompresses under a change in effective stress

Poisson’s ratio is how much rock expands laterally when compressed.If = 0, no expansion (eg: sponge)In = 0.5, complete expansion, therefore volume change is zero

LL

strain () =

E =

r

Lr =

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Rock Properties from CorrelationsRock Properties from Correlations

A sufficient data base must exist The GMU must be properly matched to the

data base; for example, using these criteria:•Similar lithology•Similar depth of burial and geological age•Similar granulometry and porosity•Estimate of anisotropy (eg: shales and laminates)•Correlation based on geophysical properties (KBES)

Use of a matched analogue advised in cases where core cannot be obtained economically

GMU = geomechanical unit

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What is a Matched Analogue?What is a Matched Analogue?

Rocks too difficult to sample without damage, or too expensive to obtain

Study logs, mineralogy, even estimate the basic properties (, E, …)

Find an analogue that is closely matched, but easy to sample for laboratory specimens

Use the analogue material as the basis of the test program

Don’t push the analogue too far!!

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Seismic Wave StiffnessSeismic Wave Stiffness

vP, vS are dynamic responses affected by rock density and elastic properties

Because seismic strains are tiny, they do not compress microcracks, pores, or contacts

Thus, ED and D are always higher than the static test moduli, ES and S

The more microfissures, pores, point contacts, the more ED > ES, x 1.3, even to x 10

If porosity ~ 0, very high, ES approaches ED

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Laboratory StiffnessLaboratory Stiffness

Cores and samples are microfissured; these open when stress is relieved, E may be underestimated

In microfissured or porous rock, crack closure, slip, and contact deformation dominate stiffness

ES and S under confining stress are best values Joints are a problem: if joints are important in situ,

their stiffness may dominate rock response, but it is difficult to test in the laboratory

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Cracks and Grain Contacts (I)Cracks and Grain Contacts (I)

E1 E2

E3

Microflaws canclose, open, or slip as changes

The nature of the grain-to-graincontacts and the overall porositygovern the stiffness of porous SS

E1

Flaws govern rock stiffness

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Cracks and Grain Contacts (II)Cracks and Grain Contacts (II)

Point-to-point contacts are much more compliant than long (diagenetic) contacts

Large open microfissures are compliant Oriented contacts or microfissures give rise

to anisotropy of mechanical properties Rocks with depositional structure or exposed

to differential stress fields over geological time develop anisotropy through diagenesis

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How Do We “Test” This Rock Mass?How Do We “Test” This Rock Mass?

Joints and fractures can be at scales of mm to several meters

Large core: 115 mm Core plugs: 20-35 mm If joints dominate,

small-scale core tests are “indicators” only

This issue of “scale” enters into all Petroleum Geomechanics analyses

1 m

A large core specimenA core “plug”

Machu Picchu, Peru, Inca Stonecraft

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Induced AnisotropyInduced Anisotropy

UCSS# subjected to large stress differences develops anisotropy (contacts form in 1 direction and break in 3 direction)

A brittle isotropic rock develops microcracks mainly parallel to 1 direction

Now, these rocks have developed anisotropy because of their -history (i.e.: damage)

This is a challenging area of analysis

# UCSS = unconsolidated sandstone

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In Situ In Situ Stiffness MeasurementsStiffness Measurements

Pressurization of a packer-isolated zone, with measurement of radial deformation

Direct borehole jack methods (mining) Geotechnical pressuremeter modified for

high pressures (membrane inflated at high pressure, radial deformation measured)

Correlation methods (penetration, indentation, others?)

These are not widely used in Petroleum Eng.

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Back-Analysis for StiffnessBack-Analysis for Stiffness

Apply a known effective stress change, measure deformations (eg: uplift, compaction)

Use an analysis model to back-calculate the rock properties (best-fit approach)

Includes all large-scale effects Can be confounded by heterogeneity,

anisotropy, poor choice of GMU, ... Often used as a check of assumptions

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Direct Borehole Stability ProblemsDirect Borehole Stability Problems

Stuck drill pipe differential pressure sticking wedging in the borehole

Stuck casing during installation Lost circulation (in many cases) Mudrings, cuttings build-up in washouts Borehole squeeze

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Indirect Stability ProblemsIndirect Stability Problems

Slow advance rates in drilling Longer hole exposure = greater costs Longer exposure = greater chance of instability

Solids build-up and loss of mud control Blowouts

Washouts, sloughing cause tripping and drilling difficulties, swabbing

A blowout eventually develops as control is lost

Intro to Petroleum Geomechanics Stress, Strain, Pressure, Deformation, Strength, etc. Maurice Dusseault.

Documents

shear stresses

normal stresses

large stresses

stress shear strength

principal stresses

lateral stresses

stress beam strength

ij p slide