stimulation 2

Importance of rock mechanics 1. drilling – ROP, lost circulation, hole problems and eccentricity

2. cementing – unwanted fracturing, displacement rate

3. sand control – formation strength and gravel placement

4. hydraulic fracturing

a. fracture initiation and propagation b. fracture geometry c. proppant strength d. fracture conductivity

5. reservoir engineering – porosity and permeability as a function of rock mechanics

Stimulation rock mechanics


1. Stress

– Normal and shear components

– Orthogonal principal directions

2. Strain

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Strain,

Stress,

L

l

AP

Area

ForceorLoad

L

l

length original

lengthin change


3. Stress – Strain Relationship • Assume rock behaves as a linear

elastic material 4. Young’s Modulus • Amount of strain for a given stress

is function of stiffness of the material

• Tangent modulus • Range for rock: 0.5-12 x 106 psi • Governs the width of the fracture

and the height growth

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Strain,

Stress,

Failure

I

II

III

strain

stressE


5. Poisson’s Ratio • Range: Lms 0.15 Ss 0.25 Steel 0.30 Shale 0.40 Salt 0.50 • Importance in insitu stress

distribution

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d

yy

L

xx

d

L

deformedundeformed

x

y/2

p

x

y

strainaxial

strain lateral


6. Shear modulus

• Measure of the rigidity of the

material

• Computed from:

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F

F

ndeformatioofangle

stressshearappliedG

)1(2

EG


7. Bulk Modulus

• Inverse of compressibility

• Measured or computed by:

• Component of poroelastic models

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F

F

F

strainvolumetric

pressurechydrostatiK

)21(3

EK


Pore Pressure And Effective Stress • Pore fluids support a portion of the total applied

stress

• Poroelastic constant, a, describes the efficiency

of the fluid pressure. F(pore geometry, solid physical properties) 0 a 1 where, a = 1 for failure a 1 for deformation a = 0.7 common for petroleum reservoirs

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Force

pore

grain

epp

t

grainsbycarried

stresseffective

pressure

pore

stress

total

a


Fracture toughness • pre-existing defects in a rock induce high stress concentrations and

becomes the nucleus for crack propagation.

• Measure of the resistance of the rock to crack

or

where kc is experimentally determined and has units of psi * (length)1/2

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2/1defectlargest of size

factorintensity stress critical

stress

critical

ca

ckc

Kc

psi -in1/2

cozzette sandstone 1,430

Mesaverde 1,230

Mancos shale 1,300

Indiana Limestone 845

Westerly granite 2,365

Devonian shale 750 to 1200

Green River oil shale 730 to 1000

Benson Sand 1440 to 1580

Benson shale 530

Rock types

From SPE monograph Vol 12

Stimulation hydraulic fracturing

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Pressures, stresses and rock properties involved in vertical fracture propagation (Allen & Roberts, 1982)

Stimulation insitu stresses

Overburden Stress, v

Vertical stress = overburden pressure

Effective vertical stress given by:

How obtain?

• Integrate density log

• Assume typical overburden gradient = 0.9 to 1.1 psi/ft

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z

v

h1

h2

z

gdzzv0

ppvve a


Horizontal Stress, h General Equation: simplify to: Minimum horizontal stress from a horizontal-constrained elastic model Terzaghi Equation Assumes: • No tensile strength • Isothermal • No tectonic stresses • h1 = h2 ….isotropic

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z

v

h1

h2

jd

21

id

21

E dT

1

E

pp

zd

1

ieh

d

strains

tectonic

stress

thermal

stress

overburden effective

stress effective

horizontal aldifferenti

a

a

ppppobpx

a

1


Example A reservoir is located at 10,000 ft with an overburden

gradient of 1.1 psi/ft and a pore pressure gradient of 0.6 psi/ft. Assume Biot’s constant, a = 1 and Poisson’s ratio, = 0.25.

a. Vertical effective stress, ve b. Minimum principle insitu stress, hmin c. Effective minimum principle stress, ehmin d. If pore pressure = 1000 psi, what is the minimum

effective stress, hmin

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Tectonic stresses • Vectorially added • Leads to unequal horizontal stress

components • Implications to hydraulic fracturing 1. Induced fractures align perpendicular to

minimum principal stress a. At shallow depths (1 to 2000 ft), h > v, thus

horizontal fractures are induced. b. At deeper depths, h < v, thus vertical

fractures are induced.

2. Stress contrast of various lithologies will affect fracture height growth/containment

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Original ground surface

Current ground surface

depth

v shift

hmin hmax ov = 1.1 psi/ft

Shift due to

addition of

tectonic stress

Original ground surface

Current ground surface

depth

v shift

hmin hmax ov = 1.1 psi/ft

Shift due to

addition of

tectonic stress


Induced stress at borehole • Drilling of a borehole distorts the preexisting stress field

• To maintain load, the stress concentration must increase around the wellbore as rock is removed.

• Stress concentrations decrease exponentially away from the wellbore

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Stimulation hydraulic fracturing

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Idealized surface pressure during hydraulic fracture treatment (Allen & Roberts, 1982)

Net fracture pressure • pressure in fracture in excess of closure pressure

p = Pf - Pc

Pre

ssu

re

Time

Pad Volume Sand Placement in Fracture Frac Closure Time

Bre

akd

ow

n

Star

t Sa

nd

San

d t

o

per

fora

tio

ns

Shu

t d

ow

n

pu

mp

ing

Frac

ture

clo

sed

Tubing friction pressure loss

Fracture Closure Pressure-Hydrostatic

Reservoir Pressure-Hydrostatic

Constant pump rate, increasing sand concentration Pressure rise reflecting normal frac extension

Breakdown Pressure • the pressure required to initiate the fracture • Must exceed the minimum stress at the borehole and the tensile

strength of the rock.

Extension or propagation pressure • the pressure required to extend the existing fracture

Closure pressure • the pressure required to hold the fracture open • Equivalent and counteracts the minimum principal insitu stress; pc hmin

• Approximated by PISIP Pc.

stimulation 2

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