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PETE 625 Well Control

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Hooke's Law, Young's Mudulus, Poisson's Ratio. Volumetric Strain, Bulk Modulus, ... Fracturing is a static or quasistatic process so elastic properties based on ... – PowerPoint PPT presentation

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Title: PETE 625 Well Control


1
PETE 625Well Control
  • Lesson 9
  • Fracture Gradients

2
Contents
  • Allowable Wellbore Pressures
  • Rock Mechanics Principles
  • Hookes Law, Youngs Mudulus, Poissons Ratio
  • Volumetric Strain, Bulk Modulus,
    Compressibility
  • Triaxial Tests

3
Contents contd
  • Rock Mechanics Principles (cont.)
  • Rock Properties from Sound Speed in Rocks
  • Mohrs Circle
  • Mohr-Coulomb Failure Criteria

4
Assignments
  • HW 5 Ch 2, Problems 21- 30
  • due Friday, June 18
  • HW 6 Ch 3, Problems 1- 10
  • due Wednesday, June 23
  • HW 7 Ch 3, Problems 11- 20
  • due Monday, June 28
  • Read Chapter 3

5
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.

6
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.

7
Upper Bound Wellbore Pressure
  • 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

8
Fracture Gradients
  • May be predicted from
  • Pore pressure (vs. depth)
  • Effective stress
  • Overburden stress
  • Formation strength

9
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!!!

10
Elastic Properties of Rock
11
Elastic Properties of Rock
12
Elastic Properties of Rock
  • The vertical stress at any point can be
    calculated by
  • The axial and transverse strains are

13
Elastic Properties of Rock
  • Hookes Law
  • s E e
  • Youngs Modulus
  • E s/e (F/A)/(DL/L)
  • E (FL)/(ADL)

14
Hookes Law
Elastic Limit
Failure
Permanent strain or plastic deformation
15
Typical Elastic Properties of Rock
16
Poissons Ratio
  • Poissons Ratio
  • transverse strain/axial strain
  • m -(ex/ez)
  • Over the elastic range, for most metals, m
    0.3
  • Over the plastic range, m increases, and may
    reach the limiting value of 0.5

17
Volumetric Strain
18
Bulk Modulus and Compressibility values in rock
19
Shear Modulus (G)
  • G is the ratio of shear stress to shear strain
  • G is intrinsically related to Youngs modulus
    and Poissons ratio
  • G t/g E/2(1m)

20
Bulk Modulus (Kb)
  • Kb is the ratio between the average normal
    stress and the volumetric strain
  • Kb can be expressed in terms of Youngs modulus
    and Poissons ratio.
  • Kb average normal stress/ volumetric strain
  • Kb E/3(1-2m) (sx sysz)/3/ev

21
Bulk Compressibility (cb)
  • cb is the reciprocal of the bulk modulus
  • cb 1/Kb
  • 3(1-2m)/E
  • ev / (sx sysz)/3

22
Metals and Rocks
  • Metallic alloys usually have well- defined and
    well-behaved predictable elastic constants.

23
Metals and Rocks
  • In contrast, rock is part of the disordered
    domain of nature. Its response to stress
    depends on (e.g.)
  • Loading history
  • Lithological constituents
  • Cementing materials
  • Porosity
  • Inherent defects

24
Metals and Rocks
  • Even so, similar stress-strain behavior is
    observed.
  • Triaxial tests include confining stress

25
Rock Behavior Under Stress
Beyond B, plastic behavior may occur.
From A-B, linear elastic behavior is observed
From 0-A, microcracks and other defects are closed
26
Youngs Modulus for a Sandstone
Et instantaneous slope at any specific stress
(tangent method)
Es secant modulus (Total
Stress/Total Strain) at any point
Ei Initial Modulus initial slope of
curve
27
Transverse Strains for SS in Fig. 3.5
Youngs Modulus Poissons Ratio are stress
dependent.
28
Example 3.1
  • Using Fig. 3.5, determine Youngs Modulus and
    Poissons 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)

29
Solution
Et ds/de (15,000-5,000) /(0.00538-0.00266) Et
3.7106 psi
m -ex/ez -(-0.00044/0.00404) 0.109
30
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

31
Rock Properties
  • Poissons 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.

32
1. An alternate form of Eq. 3.6 gives the dynamic
Poissons ratio
2. Use Eq. 3.7 to determine the dynamic Youngs
Modulus
33
Fracturing is a static or quasistatic process so
elastic properties based on sonic measurements
may not be valid.
34
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
s3 minimum principal stress
s2 normal to the page is the intermediate
principal stress and is considered to be
inconsequential to the failure analysis
Along an arbitrary plane a, a shear stress will
exist.
35
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36
c cohesion
w angle of internal friction
37
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40
Note that the failure plane approaches 45o with
increasing confining stress
41
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

42
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.

43
In Situ Rock Stresses
The simplest model assumes the subsurface stress
field is governed solely by the rocks linear
elastic response to the overburden load. When
loaded, the block would strain in the x and y
transverse directions according to Hookes Law.
44
In Situ Rock Stresses
45
In Situ Rock Stresses
Thus
Constraining the block on all sides prevents
lateral strain.
Setting eH 0,
Eliminating E and rearranging yields the
fundamental relationship
46
In Situ Rock Stresses
  • The above stressed block is analgous to a buried
    rock element if the material assumptions remain
    valid.
  • Using the books nomenclature for overburden
    stress and substituting Terzaghis effective
    stress equation leads to

47
In Situ Rock Stresses
(with s 1)
48
Fig. 3.13
Rock properties assumed constant with depth
49
Fig. 3.14
sob is the max. principal stress
Failure (fracture) occurs perpendicular to the
least principal stress
50
Fig. 3.15
  • sH gt sob can be created by
  • Tectonic forces
  • Post-depositional erosion
  • Glacial action or melting of glacier
  • sH might be locked in while sob reduces

Fracture Pressure
51
Fig. 3.16
Effect of tectonic movements on stresses
Lower sob
Is figure drawn correctly? Or should rock sample
come from right side fault?
52
Fig. 3.17
Effect of topography on sob
53
Overburden stress is not significantly changed by
abnormal pressure
Under abnormal pore pressure, the difference
between pore pressure and the least horizontal
stress (fracture pressure) get very small.
Small Tolerance
54
Subnormal pressures have little effect on
overburden stress
But, result in a decrease in fracture pressure
55
Stress concentrations around a borehole in a
uniform stress field
Tension
Additional compression
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