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Micromechanics modeling of fault stability under the influence of fluid pressure changes
Zhibing Yang
Postdoctoral Fellow, Department of Civil and Environmental Engineering
Advisor: Prof. Ruben Juanes
MIT Earth Resources Laboratory
2016 Annual Founding Members MeeLng May 18, 2016
Slide 2 2016 Annual Founding Members MeeLng
MoLvaLon
• Induced seismicity
• The role of pore pressure in faulLng
• EvaluaLon of fault stability
• Landslides
Slide 3 2016 Annual Founding Members MeeLng
Geological faults have complex structures
Mitchell and Faulkner, 2009
Reservoir scale coupled hydro-‐geomechanical modeling
?
Slide 4 2016 Annual Founding Members MeeLng
Fault stability criterion
Iσσ pα−=ʹ′
0cσn +ʹ′≤ µτ
EffecLve stress principle
p-‐ p+
x
(a)
x
z
Reservoir
InjecLon
σh σh
σv
σn τ
(b)
x
pressure Fault plane
p-‐ p+ p0
Sealing fault
Which pressure should be used in the Coulomb failure criterion?
Slide 5 2016 Annual Founding Members MeeLng
Micromechanical modeling Discrete Element Model Pore network flow
model Pore network Grains
Pore fluid Darcian flow
Pressure forces
Force-‐displacement law Law of moLon
Contact forces
DEM
Slide 6 2016 Annual Founding Members MeeLng
A block-‐and-‐gouge model
Lx = 8 cm Ly = 1.6 cm Lz = 4 cm Tgouge = 1.2 cm Ravg = 0.1 cm σv = 10 MPa V = 0.000325 m/s
v
v
σv
σv
Block
Block
Fagereng et al. 2011
p
Lme 0
pmax
p-‐ = p+
Slide 7 2016 Annual Founding Members MeeLng
Fault failure by mechanical loading
Slide 8 2016 Annual Founding Members MeeLng
Individual parLcle velocity and trajectory
ParLcle velocity ParLcle posiLon
Intermicent behavior
Slide 9 2016 Annual Founding Members MeeLng
Micromechanical response of the gouge layer
Total kineLc energy [J]
Slide 10 2016 Annual Founding Members MeeLng
Comparing different pressurizaLon scenarios
Four scenarios: p = 0 à pmax unLl t1 p = 0 à pmax unLl t1 but only
on the negaLve side p = 0 à 0.5*pmax unLl t1 p = 0 (”dry”)
p-‐ = p+ = pmax
p-‐ = p+ = 0.5pmax
pmax = p-‐ > p+ = 0
p-‐ = p+ = 0
Slide 11 2016 Annual Founding Members MeeLng
Slip weakening behavior of the gouge layer
Shear stress Normal stress eff
Slip failure
Slide 12 2016 Annual Founding Members MeeLng
Macroscale onset of failure
Horizontal strain Horizontal strain
Ver<cle strain
1. Higher pressure à earlier onset of slip 2. When pressure is larger on one side than the other, neither the maximum nor the arithmeLc average pressure is suitable for evaluaLon of the Coulomb failure criterion
Slide 13 2016 Annual Founding Members MeeLng
Conclusions and future work
Ø A coupled DEM and pore-‐network flow model developed
Ø Gouge layer slip failure characterized by local-‐scale sLck-‐slip dynamics
Ø Pressure imhomogeneity: the CFC cannot be simply evaluated using the max. or the average pressure for the boundary scenario considered
Ø Future work – addiLonal boundary scenarios; extension to two-‐phase flow and fracturing
Thank you!
2016 Annual Founding Members MeeLng
Slide 15 2016 Annual Founding Members MeeLng
Failure criterion for a sealing fault
(b)
x
pressure Fault plane
p-‐ p+ p0
(a)
Sealing fault x
z
Reservoir
InjecLon
σh σh
σv
σn τ
InσInσ ++−− +⋅ʹ′=+⋅ʹ′ pp αα
Iσσ pα−=ʹ′
0cσn +ʹ′≤ µτEffecLve stress principle
( ) 0,min cf +⋅ʹ′⋅ʹ′⋅≤ +− nσnσµτ( )+−≤ ppp f ,max Jha and Juanes,2014
p-‐ p+
x
16
Discrete Element Method (DEM)
+ Pore-Network Darcy Flow
∑∑ +=n
pn
j
cjiim FFx!! ∑=
jjii MθI !!
⎟⎟⎠
⎞⎜⎜⎝
⎛−−= ∑
jjp
p
f tqVVK
p δδδ
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
j
jjj l
ppCq
Explicit scheme for pore pressure
Darcy’s Law
Pore network Grains
Two interacting, overlapping networks for the grains and pores
A micromechanics model for hydro-‐geomechanic coupling
Two-way coupling between the deformation of the solid matrix and the fluid pressure
Some faults are sealing
• JuxtaposiLon • Cataclasis • CementaLon/diageneLc
effects • Clay and shale smearing
5 cm Fagereng et al. 2011
Fossen 2010
Time scales
• Pore pressure diffusion
• Pore deformaLon
18
𝑡↓𝑝 = 𝑑↑2 /𝐷↓ℎ
𝐷↓ℎ = 𝑘/𝜇𝛽↓𝑤
𝑡↓𝑑 = 𝑑↓𝑝 /𝑣
𝑑=0.001 m
𝑘=1×10↑−9 m↑2 𝛽↓𝑤 =4×10↑−10 Pa↑−1
𝑑↓𝑝 =0.1𝑑
𝑣=1×10↑−4 m/s
𝑡↓𝑝 ~ 10↑−10 s
𝑡↓𝑝 ~1 s
Slide 19 2016 Annual Founding Members MeeLng
A block-‐and-‐gouge model
v
v
σv
σv
Block
Block
Four scenarios: 1. p = 0 (dry) 2. p = 0 à 0.5*pmax unLl t1 3. p = 0 à pmax unLl t1 but
only on the negaLve side 4. p = 0 à pmax unLl t1
Lx = 8 cm Ly = 1.6 cm Lz = 4 cm Tgouge = 1.2 cm Ravg = 0.1 cm
p
A A’ 0
p0
4. Uniform pressure
t = 0
t = t1 p
A A’ 0
p0
3.Inhomogeneous pressure
t = t1
t = 0
A
A’
2016 Annual Founding Members MeeLng
Slide 21 2016 Annual Founding Members MeeLng
Horizontal stress evoluLon
Stress calculaLon
• microstress
• Averaging over the gouge layer
22
kc
k
kcc
V,,1
∑ ⊗= fxσσ
gouge
cσσ =
Lz Lz + ΔLz εv =ΔLz/Lz VerLcle strain