Post on 17-Jan-2016
EXPLORATION GEOPHYSICS
THE EXPLORATION TASK
PLAN EXPLORATION
APPROACH FOR A MATURE TREND
GATHER DATA FOR A MATURE TREND
DEVELOP PLAY
PROSPECT FRAMEWORK
INITIAL DATA GATHANAL AND
PROJECT PLANING FOR A
FRONTIER TREND
NEW DATA GATHERING FOR A FRONTIER TREND
MAKE PLAY/PROSPECT ASSESSMENT
COMMUNICATE ASSESSMENT TO MANAGEMENT
PREPARE PRELOCATION REPORT
DRILLING
EXPLORATION GEOPHYSICS
ElasticityElasticity
SourceSource
Petroleum related rock mechanicsPetroleum related rock mechanics
Elsevier, 1992Elsevier, 1992
ElasticityElasticityElasticityElasticity
Definition: The ability to resist and Definition: The ability to resist and recover from deformations recover from deformations produced by forces.produced by forces.
It is the foundation for all aspects of It is the foundation for all aspects of Rock MechanicsRock Mechanics
The simplest type of response is The simplest type of response is one where there is a linear relation one where there is a linear relation between the external forces and the between the external forces and the corresponding deformations.corresponding deformations.
StressStress
defines a force field on a materialdefines a force field on a material
Stress = Force / Area (pounds/sq. in. or Stress = Force / Area (pounds/sq. in. or psi)psi)
F / AF / AFF
Area: AArea: A
StressStressStressStress
In Rock Mechanics the sign convention In Rock Mechanics the sign convention states that the compressive stresses states that the compressive stresses are positive. are positive.
Consider the cross section area at b, Consider the cross section area at b, the force acting through this cross the force acting through this cross section area is F (neglecting weight of section area is F (neglecting weight of the column) and cross sectional area is the column) and cross sectional area is A’. A’ is smaller than A, therefore stress A’. A’ is smaller than A, therefore stress ’ = F/A’ acting at b is greater than ’ = F/A’ acting at b is greater than acting at aacting at a
StressStress
W
F
F
F
a
b
c
A
A’
A’’
AreaAreaLoadLoad
StressStressStressStress
stress depends on the position within stress depends on the position within the stressed sample.the stressed sample.
Consider the force acting through Consider the force acting through cross section area A’’. It is not normal cross section area A’’. It is not normal to the cross section. We can to the cross section. We can decompose the force into one decompose the force into one component Fcomponent F
nn normal to the cross normal to the cross
section, and one component Fsection, and one component Fpp that is that is
parallel to the section. parallel to the section.
StressStressStressStress
Fp
Fn
F
Decomposition of forcesDecomposition of forces
StressStressStressStress
The quantity The quantity = F = Fnn /A’’ is called the /A’’ is called the
normal stress, while the quantitynormal stress, while the quantity = F= F
pp / A’’ is called the shear stress. / A’’ is called the shear stress.
Therefore, there are two types of Therefore, there are two types of stresses which may act through a stresses which may act through a surface, and the magnitude of each surface, and the magnitude of each depend on the orientation of the depend on the orientation of the surface.surface.
General 3D State of General 3D State of Stress Stress in a Reservoirin a Reservoir
x, y, z Normal stresses
xy, yz, zx Shear stresses
x
y
z
yx
yz
zy
zx
zxxy
StressStressStressStress
= = xx xyxy xz xz
yxyx yy yzyz
zx zx zyzy zz
Stress tensorStress tensor
Principal StressesPrincipal Stresses
Normal stresses on planes where shear stresses are zero
v
H
h
Principal StressesPrincipal Stresses
In case of a reservoir,
= v Vertical stress,
= h Minimum horizontal stresses
= H Maximum horizontal stresses
v
H
h
Types of StressesTypes of Stresses
Tectonic Stresses: Due to relative Tectonic Stresses: Due to relative displacement of lithospheric platesdisplacement of lithospheric plates
Based on the theory of earth’s tectonic platesBased on the theory of earth’s tectonic plates Spreading ridge: plates move away from Spreading ridge: plates move away from
each othereach other Subduction zone: plates move toward each Subduction zone: plates move toward each
other and one plate subducts under the other and one plate subducts under the otherother
Transform fault: Plates slide past each otherTransform fault: Plates slide past each other
Types of StressesTypes of Stresses
Gravitational Stresses: Due to the Gravitational Stresses: Due to the weight of the superincumbent rock weight of the superincumbent rock massmass
Thermal Stresses: Due to temperature Thermal Stresses: Due to temperature variationvariation
Induced, residual, regional, local, far-field, Induced, residual, regional, local, far-field, near-field, paleo ...near-field, paleo ...
Impact of In-situ Impact of In-situ Stress Stress
Important input during planning stage Fractures with larger apertures are
oriented along the maximum horizontal stress
Natural fracturesNatural fractures
StrainStrain
(x, y, z)(x’, y’, z’)
Initial Position Shifted Position
StrainStrain
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.
StrainStrain
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)
StrainStrain
L
O
P
L’
O’
P’
Initial Position Shifted Position
StrainStrain
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)
StrainStrain
PO
Q
Initial Position
P
Q
O
Shifted Position
StrainStrain
= (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
StrainStrain
The shear strain corresponding to x-direction can be written as
xy = (u/y + v/x)/2
Strain tensor Principal strains
Elastic ModuliElastic Moduli
DLL’ D’
F
Y
X
Schematic showing deformation under loadSchematic showing deformation under load
Elastic ModuliElastic 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 = Ex
Elastic ModuliElastic Moduli
This equation is known as Hooke’s law The coefficient E is called Young’s
modulus. Young’s modulus belongs to a group of
coefficients called elastic moduli. It is a measure of the stiffness of the
sample, i.e., the sample’s resistance against being compressed by a uniaxial stress.
Elastic ModuliElastic 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’ > D, thus y and z become negative.
The ratio defined as = -y/x is another
elastic parameter known as Poisson’s ratio. It is a measure of lateral expansion relative to longitudinal contraction.
Elastic ModuliElastic 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 sample’s resistance against hydrostatic compression. The inverse of K, i.e., 1/K is known as compressibility
Elastic ModuliElastic 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 = 2Gxy xz = 2Gxz yz = 2Gyz
Elastic ModuliElastic Moduli Expressing strains as function of stresses Ex = x - (y + z)
Ey = y - (x + z)
Ez = z - (x + y)
Gxy = (1/2)xy
Gxz = (1/2)xz
Gyz = (1/2)yz
Elastic ModuliElastic Moduli In the definition of Young’s modulus and
Poisson’s 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
Elastic ModuliElastic 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.