9. fracture gradients
TRANSCRIPT
TAMU - Pemex
Well Control
Lesson 9
Fracture Gradients
2
Contents
Allowable Wellbore Pressures
Rock Mechanics Principles
Hooke’s Law, Young’s Mudulus, Poisson’s Ratio
Volumetric Strain, Bulk Modulus, Compressibility
Triaxial Tests
3
Contents – cont’d
Rock Mechanics Principles (con’t.)
Rock Properties from Sound Speed in Rocks’
Mohr’s Circle
Mohr-Coulomb Failure Criteria
4
Fracture Gradients
Read:
“Fracture gradient prediction for the new generation,” by Ben Eaton and Travis Eaton. World Oil, October, 1997.
“Estimating Shallow Below Mudline Deepwater Gulf of Mexico Fracture Gradients,” by Barker and Wood.
5
Lower Bound Wellbore Pressure
Lower bound of allowable wellbore pressure is controlled by:
Formation pore pressure
Wellbore collapse considerations
This sets the minimum “safe” mud weight.
6
Upper bound allowable wellbore pressure may be controlled by:
The pressure integrity of the exposed formations (fracture pressure)
The pressure rating of the casing
The pressure rating of the BOP
Chapter 3 deals with fracture gradient prediction and measurement
Upper Bound Wellbore Pressure
7
Fracture Gradients
May be predicted from:
Pore pressure (vs. depth)
Effective stress
Overburden stress
Formation strength
8
Rock Mechanics
How a rock reacts to an imposed stress, is important in determining Formation drillability
Perforating gun performance
Control of sand production
Effect of compaction on reservoir performance
Creating a fracture by applying a pressure to a wellbore!!!
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Elastic Properties of Rock
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Elastic Properties of Rock
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Elastic Properties of Rock
The vertical stress at any point can be calculated by:
21
4
d
F
A
F aaa
1
21a L
LL
1
21
d
ddtr
The axial and transverse strains are:
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Elastic Properties of Rock
Hooke’s Law:
= E
Young’s Modulus:
E = /e = (F/A)/(L/L)
E = (F*L)/(A*L)
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Hooke’s LawElastic Limit
Permanent strain or plastic deformation
Failure
14
Typical Elastic Properties of Rock
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Poisson’s Ratio
Poisson’s Ratio
= transverse strain/axial strain
= -(x/z)
Over the elastic range, for “most metals”, ~ 0.3
Over the plastic range, increases, and may reach the limiting value of 0.5
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Volumetric Strain
i
ifV V
VV
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Bulk Modulus and Compressibility values in rock
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Shear Modulus (G)
G is the ratio of shear stress to shear strain
G is intrinsically related to Young’s modulus and Poisson’s ratio
G = = E/[2*(1+)]
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Bulk Modulus (Kb)
Kb is the ratio between the average normal stress and the volumetric strain
Kb can be expressed in terms of Young’s modulus and Poisson’s ratio.
Kb = average normal stress/ volumetric strain
Kb = E/[3*(1-2) = [(x+ y+z)/3]/v
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Bulk Compressibility (cb)
cb is the reciprocal of the bulk modulus
cb = 1/Kb
= 3*(1-2)/E
= v / [(x+ y+z)/3]
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Metals and Rocks
Metallic alloys usually have well-defined and well-behaved predictable elastic constants.
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Metals and Rocks
In contrast, rock is part of the disordered domain of nature. It’s response to stress depends on (e.g.):
Loading history
Lithological constituents
Cementing materials
Porosity
Inherent defects
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Metals and Rocks
Even so, similar stress-strain behavior is observed.
Triaxial tests include confining stress
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Rock Behavior Under Stress
From 0-A, microcracks and other defects are closed
From A-B, linear elastic behavior is observed
Beyond B, plastic behavior may occur.
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Young’s Modulus for a Sandstone
Ei = Initial Modulus
= initial slope of
curve
Es = secant modulus = (Total Stress/Total Strain) at any point
Et = instantaneous slope at any specific stress (tangent method)
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Transverse Strains for SS in Fig. 3.5
Young’s Modulus & Poisson’s Ratio are stress dependent.
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Example 3.1
Using Fig. 3.5, determine Young’s Modulus and Poisson’s ratio at an axial stress of 10,000 psi and a confining stress of 1,450 psi.
From Fig 3.5, the given stress conditions are within the elastic range of the material (e.g. linear stress-strain behavior)
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SolutionEt = d/d = (15,000-5,000) /(0.00538-0.00266)
Et = 3.7*106 psi
= -x/z
= -(-0.00044/0.00404)
= 0.109
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Rock Properties
Rocks tend to be more ductile with increasing confining stress and increasing temperature
Sandstones often remain elastic until they fail in brittle fashion.
Shales and rock salt are fairly ductile and will exhibit substantial deformation before failure
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Rock Properties
Poisson’s ratio for some plastic formations may attain a value approaching the limit of 0.5
Rocks tend to be anisotropic, so stress-strain behavior depends on direction of the applied load.
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1. An alternate form of Eq. 3.6 gives the dynamic Poisson’s ratio:
2. Use Eq. 3.7 to determine the dynamic Young’s Modulus:
)240.01(*407,7*38.2*0268.0 2 E
psiE 610*34.4
)1(0268.0 2 sb vE
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Fracturing is a static or quasistatic process so elastic properties based on sonic measurements may not be valid.
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We can orient a cubic element under any stress state such that the shear stresses along the six orthogonal planes vanish. The resultant normal stresses are the three “principal stresses”
3 = minimum principal stress2 normal to the page is the intermediate principal stress and is considered to be inconsequential to the failure analysis
Along an arbitrary plane , a shear stress will exist.
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231
max
2sin2
31a
13 a
2
max
2cos22
3131a
a
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tanff c
c = cohesion
= angle of internal friction
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37
231
max
38
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Note that the failure plane approaches 45o with increasing confining stress
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Hydraulic Fracturing
Hydraulic fracturing while drilling results in one form of lost circulation (loss of whole mud into the formation).
Lost circulation can also occur into:
vugs or solution channels
natural fractures
coarse-grained porosity
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For a fracture to form and propagate:
The wellbore pressure
must be high enough to overcome the tensile strength of the rock.
must be high enough to overcome stress concentration at the hole wall
must exceed the minimum in situ rock stress before the fracture can propagate to any substantial extent.
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In Situ Rock Stresses
The simplest model assumes the subsurface stress field is governed solely by the rock’s linear elastic response to the overburden load.
When loaded, the block would strain in the x and y transverse directions according to Hooke’s Law.
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In Situ Rock Stresses
horizontal signifies Hsubscript the where
isotropic, is material the If
Hyx
zxyy
zyxx
EEE
andEEE
E
zyxx
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In Situ Rock Stresses
EE
zH
1
z
1H
ThusEEE
zHHH
Constraining the block on all sides prevents lateral strain.
Setting H = 0,
Eliminating E and rearranging yields the fundamental relationship
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In Situ Rock Stresses
The above stressed block is analgous to a buried rock element if the material assumptions remain valid.
Using the book’s nomenclature for overburden stress and substituting Terzaghi’s effective stress equation leads to:
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In Situ Rock Stresses
ppobH
pobpH
pp
pp
1
1
desired. if term pressure pore the to
applied be mayconstant cityporoelasti The
z
1Hpe ps
,TerzaghiFrom
(with s = 1)
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Fig. 3.13
Rock properties assumed constant
with depth
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ob is the max. principal stress
Fig. 3.14
Failure (fracture) occurs perpendicular to the least principal stress
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H > ob can be created by
• Tectonic forces
• Post-depositional erosion
• Glacial action or melting of glacier
H might be locked in while ob reduces
Fracture Pressure
Fig. 3.15
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Lower ob
Is figure drawn correctly? Or should rock sample come from right side fault?
Effect of tectonic movements on stresses
Fig. 3.16
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Effect of topography on obFig. 3.17
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Overburden stress is not significantly changed by abnormal pressure
Small Tolerance
Under abnormal pore pressure, the difference between pore pressure and the least horizontal stress (fracture pressure) get very small.
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Subnormal pressures have little effect on overburden stress …
… But, result in a decrease in fracture pressure
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Stress concentrations around a borehole in a uniform stress field
Tension
Additional compression