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Technische Universität München. St. Petersburg Polytechnical University. Joint Advanced Student School (JASS). FEM study of the faults activation. Author : Ulanov Alexander. Problem significance. Geomechanics application: - S ubsidence of rocks - Sliding of bed near oil well. - PowerPoint PPT Presentation
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1
FEM study of the faults activation
Technische Universität München
Joint Advanced Student School (JASS)
St. Petersburg Polytechnical University
Author: Ulanov Alexander
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Problem significance Geomechanics application:
- Subsidence of rocks
- Sliding of bed near oil well
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Аrea of study Faults activation in deforming saturated porous medium.
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Particularity
Examples of the elastic bodies (3D case and 2D case) with the possible surfaces of slipping.
Interface (contact) element concept
Parameters of the media may discontinue
Nonlinear problem
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Goals and objectives Simulation of joint transient process of diffusion porous pressure and stress state calculation in saturated porous medium.
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Our estimates
Еstimates:
Saturation porous medium - combination of pore space, deformable skeleton and moving fluid.
- Darcy's law for fluid.
- Fluid is compressible.
- Porous medium is isotropic and linear.
- Small deflection.
Examples:sandstone,clay.
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Continuity equation:
udivt
bpk
t
pM
Equilibrium equation:
pbdivG uu
p - pore pressure
u - displacement vector
k - coefficient of permeability
μ - viscosity of the pore fluid
Coupled solution for saturated one-phase flow in a deforming porous medium
G - shear modulus
Biot 1955
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Variational formulation (part 1)
312 )(q, WU
Ω – domain in 2D(3D) space; S - boundary; n – external normal
Variational formulation of equilibrium equation
0: S
TT dsdivGdpbdivdivG qnuIuqququ
pbdivG uu
dsn
ddS
T qu
ququ :
dsfdfdivdfS
nqqq
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)(, 12 Wqp
Variational formulation of continuity equation
Variational formulation (part 2)
udivt
bpk
t
pM
0)(
S
qdspk
dqt
divbqp
kq
tp
M nu
10
cSSSS \21
Sc – surface of contact
0:
cS
nn
S
nT dsdsdbpdivdivdivG qFqFqFqququ
Interface model
0)(
cS
nn
S
n dsqQqQqdsQdqt
divbqp
kq
tp
Mu
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Characteristics of interface layer elements: - infinitesimal thickness - permeability D - stiffness C
0)()(:
cSS
nT dsdsdbpdivdivdivG qquuCqFqququ
)(1 uuCnFFn)(2
uuCnFFn
)( ppDQQ nn
Interface element concept
Goodman 1968
0))(()(
cSS
n dsqqppDqdsQdqt
divbqp
kq
tp
Mu
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Slip computation
Slipping condition (Mohr-Coulomb) :
HnS CK ||
σn - normal stress
σs - shear stress
K - friction coefficient
СH - cohesion stress
Iterative process:
n
s
s
C
C
C
00
00
00
C
Stiffness С:
If contact element is sliding Cs = 0 1 Calculation of strain state.
2 Slip conditional test.
3 Calculation of strain with new stiffnesses form.
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Program structure
Geometry and Grid generation
- Ansys ICEM
- Gambit
Solution of problem- FEM solver
- Optimization of data ( sparce-matrix )
- Iteration lib (ITL MTL)
Processing and result аnalysis
- GID
- Tecplot10
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Mesh generation in Gambit (format .CDB )
GID output
Domain example (1)
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Domain example (2)
Mesh quality adaptation
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Results
No interface (slip) zone Modelling of sliding
- Diffusion effect -Influence of cohesion Coh
-Influence of permeability k
-Influence of nonuniform permeability D
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No interface (slip) zone. Diffusion effect
- Pressure on lateral side is fixed- Zero-initial condition for pressure- No fluid flux in normal direction
Establishment of linear pressure distribution
0nQ
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Influence of cohesion (Coh)
Cohesion Count of elements
2.9 2
2.7 4
2.6 8
- Fixed pressure- Fixed permeability k- External load- Slipping condition
Relative displacement of interface layer
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Influence of permeability k
- Fixed value of cohesion
- Diffusion effect ( P = constant )
- Different value of permeability k permeability
k Сoh Number of
elements
0.1 2.7 22
0.2 2.7 8
0.3 2.7 4
1 2.7 4
- External load
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Effect of nonuniform permeabilityDestruction of rock in contact layer
slslsl BAS , – Slip zone in contact layer
dqqppDdqqppDdxqQqQslcc
xyxysnnn 41
slipisc kkk
kis – isotropic permeability ( no slip case )
kslip – additional component ( appear in slip case )
0)(
cS
nn
S
n dsqQqQqdsQdqt
divbqp
kq
tp
Mu
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- Different value of Ds
- Establishment of linear pressure distribution
- Zero-initial condition for pressure
- Zero displacement
- Sliding on all contact layer
Influence of nonuniform permeability ( part 1 )
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Influence of nonuniform permeability ( part 1 )
Ds=1
Ds=10 Ds=100
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Influence of nonuniform permeability ( part 2 ) - Establishment of linear pressure distribution- Zero-initial condition for pressure
- External load - Ds=100
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Conclusions
The model of coupled solution for saturated one-phase flow in a deforming porous medium is considered.
Influence of various parameters on sliding is investigated .
Goodman interface element concept is used.
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Thank you for your attention !