TAMU Pemex Well Control

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TAMU - PemexWell Control

• Lesson 9
• Fracture Gradients

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Contents

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

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Contents contd

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

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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.

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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.

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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

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Fracture Gradients

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

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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

• The axial and transverse strains are

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Elastic Properties of Rock

• Hookes Law
• s E e

• Youngs Modulus
• E s/e (F/A)/(DL/L)
• E (FL)/(ADL)

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Hookes Law
Elastic Limit
Failure
Permanent strain or plastic deformation
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Typical Elastic Properties of Rock
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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

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Volumetric Strain
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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 Youngs modulus
  and Poissons ratio
• G t/g E/2(1m)

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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 Youngs modulus
  and Poissons ratio.
• Kb average normal stress/ volumetric strain
• Kb E/3(1-2m) (sx sysz)/3/ev

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Bulk Compressibility (cb)

• cb is the reciprocal of the bulk modulus
• cb 1/Kb
• 3(1-2m)/E
• ev / (sx sysz)/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. Its 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
Beyond B, plastic behavior may occur.
From A-B, linear elastic behavior is observed
From 0-A, microcracks and other defects are closed
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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
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Transverse Strains for SS in Fig. 3.5
Youngs Modulus Poissons Ratio are stress
dependent.
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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)

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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
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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

• 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.

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1. An alternate form of Eq. 3.6 gives the dynamic
Poissons ratio
2. Use Eq. 3.7 to determine the dynamic Youngs
Modulus
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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
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.
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c cohesion
w angle of internal friction
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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 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.
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In Situ Rock Stresses
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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
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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 books nomenclature for overburden
  stress and substituting Terzaghis effective
  stress equation leads to

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In Situ Rock Stresses
(with s 1)
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Fig. 3.13
Rock properties assumed constant with depth
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Fig. 3.14
sob is the max. principal stress
Failure (fracture) occurs perpendicular to the
least principal stress
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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
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Fig. 3.16
Effect of tectonic movements on stresses
Lower sob
Is figure drawn correctly? Or should rock sample
come from right side fault?
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Fig. 3.17
Effect of topography on sob
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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
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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