ock Mechanics Study of the Ghawar Khuff Reservoirs - PowerPoint PPT Presentation

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ock Mechanics Study of the Ghawar Khuff Reservoirs

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INITIAL DATA GATHANAL AND PROJECT PLANING FOR A FRONTIER TREND ... Gravitational Stresses: Due to the weight of the superincumbent rock mass ... – PowerPoint PPT presentation

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Title: ock Mechanics Study of the Ghawar Khuff Reservoirs


1
EXPLORATION GEOPHYSICS
2
THE EXPLORATION TASK
INITIAL DATA GATHANAL AND PROJECT PLANING FOR A
FRONTIER TREND
PLAN EXPLORATION APPROACH FOR A MATURE TREND
DEVELOP PLAY PROSPECT FRAMEWORK
NEW DATA GATHERING FOR A FRONTIER TREND
GATHER DATA FOR A MATURE TREND
MAKE PLAY/PROSPECT ASSESSMENT
COMMUNICATE ASSESSMENT TO MANAGEMENT
PREPARE PRELOCATION REPORT
DRILLING
3
EXPLORATION GEOPHYSICS
4
Elasticity
Source Petroleum related rock
mechanics Elsevier, 1992
5
Elasticity
  • Definition The ability to resist and recover
    from deformations produced by forces.
  • It is the foundation for all aspects of Rock
    Mechanics
  • The simplest type of response is one where there
    is a linear relation between the external forces
    and the corresponding deformations.

6
Stress
  • defines a force field on a material
  • Stress Force / Area (pounds/sq. in. or psi)
  • s F / A

F
Area A
7
Stress
  • In Rock Mechanics the sign convention states that
    the compressive stresses are positive. 
  • Consider the cross section area at b, the force
    acting through this cross section area is F
    (neglecting weight of the column) and cross
    sectional area is A. A is smaller than A,
    therefore stress ? F/A acting at b is greater
    than ? acting at a

8
Stress
Area
Load
9
Stress
  • stress depends on the position within the
    stressed sample.
  • Consider the force acting through cross section
    area A. It is not normal to the cross section.
    We can decompose the force into one component Fn
    normal to the cross section, and one component Fp
    that is parallel to the section.

10
Stress
Decomposition of forces
11
Stress
  • The quantity ? Fn /A is called the normal
    stress, while the quantity
  •  ? Fp / A is called the shear stress.
  • Therefore, there are two types of stresses which
    may act through a surface, and the magnitude of
    each depend on the orientation of the surface.

12
General 3D State of Stress in a Reservoir
sx , sy , sz Normal stresses ?xy , ?yz , ?zx
Shear stresses
sx
sz
sy
13
Stress
  • ? ?x ?xy ?xz
  • ?yx ?y ?yz
  • ? zx ?zy ?z
  •  
  • Stress tensor

14
Principal Stresses
sv
Normal stresses on planes where shear stresses
are zero s1 gt s2 gt s3
sh
sH
15
Principal Stresses
sv
In case of a reservoir, s1 sv Vertical
stress, s2 sh Minimum horizontal stresses
s3 sH Maximum horizontal stresses
sh
sH
16
Types of Stresses
  • Tectonic Stresses Due to relative displacement
    of lithospheric plates
  • Based on the theory of earths tectonic plates
  • Spreading ridge plates move away from each other
  • Subduction zone plates move toward each other
    and one plate subducts under the other
  • Transform fault Plates slide past each other

17
Types of Stresses
  • Gravitational Stresses Due to the weight of the
    superincumbent rock mass
  • Thermal Stresses Due to temperature variation
  • Induced, residual, regional, local, far-field,
    near-field, paleo ...

18
Impact of In-situ Stress
  • Important input during planning stage
  • Fractures with larger apertures are oriented
    along the maximum horizontal stress

19
Natural fractures
20
Strain
(x, y, z)
(x, y, z)
Shifted Position
Initial Position
21
Strain
  • x x u
  • y y v
  • z z w
  • If the displacements u, v, and w are constants,
    i.e, they are the same for every particle within
    the sample, then the displacement is simply a
    translation of a rigid body.

22
Strain
  • Another simple form of displacement is the
    rotation of a rigid body.
  • If the relative positions within the sample are
    changed, so that the new positions cannot be
    obtained by a rigid translation and/or rotation
    of the sample, the sample is said to be strained.
    (figure 8)

23
Strain
24
Strain
  • Elongation corresponding to point O and the
    direction OP is defined as
  • ? (L L)/L  
  • sign convention is that the elongation is
    positive for a contraction.
  • The other type of strain that may occur can be
    expressed by the change ? of the angle between
    two initially orthogonal directions. (Figure 9)

25
Strain
26
Strain
  • ? (1/2)tan?  
  • is called the shear strain corresponding to
    point O and the direction OP. We deal with
    infinitesimal strains.
  • The elongation (strain) in the x-direction at x
    can be written as
  • ?x ?u/?x

27
Strain
  • The shear strain corresponding to x-direction can
    be written as
  •  ?xy (?u/?y ?v/?x)/2
  • Strain tensor
  • Principal strains

28
Elastic Moduli
F
X
D
L
D
L
Y
Schematic showing deformation under load
29
Elastic Moduli
  • When force F is applied on its end surfaces, the
    length of the sample is reduced to L.
  • The applied stress is then ?x F/A,
  • The corresponding elongation is ? (L L)/L
  • The linear relation between ?x and ?x, can be
    written as
  • ?x E?x

30
Elastic Moduli
  • This equation is known as Hookes law
  • The coefficient E is called Youngs modulus.
  • Youngs modulus belongs to a group of
    coefficients called elastic moduli.
  • It is a measure of the stiffness of the sample,
    i.e., the samples resistance against being
    compressed by a uniaxial stress.

31
Elastic Moduli
  • Another consequence of the applied stress ?x
    (Figure 10) is an increase in the width D of the
    sample. The lateral elongation is ?y ?z (D
    D)/D. In general D gt D, thus ?y and ?z become
    negative.
  • The ratio defined as ? -?y/?x is another
    elastic parameter known as Poissons ratio. It is
    a measure of lateral expansion relative to
    longitudinal contraction.

32
Elastic Moduli
  • Bulk modulus K is defined as the ratio of
    hydrostatic stress ?p relative to the volumetric
    strain ?v. For a hydrostatic stress state we have
    ?p ?1 ?2 ?3 while ?xy ?xz ?yz 0.
    Therefore
  • K ?p/?v ? 2G/3 1  
  • K is a measure of samples resistance against
    hydrostatic compression. The inverse of K, i.e.,
    1/K is known as compressibility

33
Elastic Moduli
  • Isotropic materials are materials whose response
    is independent of the orientation of the applied
    stress. For isotropic materials the general
    relations between stresses and strains may be
    written as
  •  ?x (? 2G) ?x ??y ??z
  • ?y ??x (? 2G)?y ??z
  • ?z ??x ??y (? 2G)?z
  • ?xy 2G?xy ?xz 2G?xz ?yz 2G?yz

34
Elastic Moduli
  • Expressing strains as function of stresses
  • E?x ?x - ?(?y ?z)
  • E?y ?y - ?(?x ?z)
  • E?z ?z - ?(?x ?y)
  • G?xy (1/2)?xy
  • G?xz (1/2)?xz
  • G?yz (1/2)?yz

35
Elastic Moduli
  • In the definition of Youngs modulus and
    Poissons ratio, the stress is uniaxial, i.e., ?z
    ?y ?xy ?xz ?yz 0. Therefore
  •  E ?x/?x G (3? 2G)/ (? G) 2  
  • ? -?y/?x ?/(2(? G))   3
  • Therefore from equations (1, 2, and 3), knowing
    any two of the moduli E, ?, ?, G and K, we can
    find other remaining moduli

36
Elastic Moduli
  • For rocks, ? is typically 0.15 0.25. For weak,
    porous rocks ? may approach zero or even become
    negative. For fluids, the rigidity G vanishes,
    which according to equation (3) implies ? ? ½.
    Also for unconsolidated sand, ? is close to ½.
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