stimulation 2
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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
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
Stimulation rock mechanics
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
Stimulation rock mechanics
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
Stimulation rock mechanics
6. Shear modulus
• Measure of the rigidity of the
material
• Computed from:
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F
F
ndeformatioofangle
stressshearappliedG
)1(2
EG
Stimulation rock mechanics
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
Stimulation rock mechanics
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
Stimulation rock mechanics
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
Stimulation insitu stresses
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
Stimulation rock mechanics
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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Stimulation insitu stresses
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
Stimulation insitu stresses
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 insitu stresses
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Fracture propagates outward away from high-compressive stress
concentration at the wellbore (Allen & Roberts, 1982)
Stimulation insitu stresses
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dep
th
pf1
shale
shale
sand
pf2 pf1 pf2
hmin
Stress profile
* Very important for frac height containment
Stimulation insitu stresses
• How obtain horizontal stress?
• Field measurements • Microfrac tests
• Steprate/flowback tests
• Shutin tests
• Calculate from
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ppppobpx
a
1
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.
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