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Quantitative understanding of microseismicity
for reservoir characterization
Serge Shapiro and the PHASE-Project Team.
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We greatly acknowledge support of the PHASE project sponsors
A recent book:
Serge A. Shapiro, 2015,
Fluid-Induced Seismicity,
Cambridge Univ. Press, pp 289.
http://www.cambridge.org/9780521884570
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Physical Concept
- In some locations the state of stress is nearly critical.
- Seismicity triggering process is a dynamic perturbation of
this stress state: Pressure diffusion & Hydraulic fracturing.
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Exponential ACF
distribution of criticality events and their occurrence times
events and their occurrence times distribution of criticality
Gaussian ACF
distance vs. time
distance vs. time
model diffusivity
model diffusivity
Numerical modelling of seismicity: linear diffusion
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Triggering Front and Back Front: linear diffusion
r=√4π Dt rbf=√6 Dt (1−t / t0 ) ln(1−t0 /t )
2
1
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original coordinate system
Tensor of hydraulic diffusivity: linear diffusion
scaled coordinate system
x̄=x
√4πt
x̄1
2
D11
+x̄
22
D22
+x̄
32
D33
=1
Top South East
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Fenton Hill Soultz-sous-Forêts
Event Density: linear diffusion
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Perkins-Kern-Nordgren (PKN) Model of Hydraulic Fracture
Cotton Valley: data courtesy of J. Rutledge
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Volume Balance Principle
Volume of injected fluid = fracture volume + lost fluid volume
QI t = 2 L G + 6 L hf CL t1/2
t injection time,
QI average injection rate,
CL fluid loss coefficient,
G = w*hf vertical cross section of the fracture.
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Stage 2Microseismicity induced by hydraulic fracturing
The straight lines: fracture reopening
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Triggering Front and Back Front
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Basic Equations: non-linear diffusion
∂ ρϕ∂ t
=−∇Uρ≈ρS∂ p∂ t
Mass conservation (in terms of density, porosity, and filtration velocity):
Darcy law (in terms of pressure, permeability and viscosity):
Hydraulic diffusivity :
U=−kη
∇ p
D( p )=k ( p )
Sη
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Non-Linear Diffusion
∂rd−1 p∂ t
= ∂∂ r
D( p )rd−1 ∂∂r
p
Diffusion equation:
Hydraulic diffusivity and injection rate:
D∝D0 pn Q∝QI ti
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Triggering Front
r=√4π Dt
r∝(D0Q In tn( i+1 )+1 )1/ (dn+2)
r∝d√QI t
i+1
Linear diffusion, n=0
Strong non-linearity, n>>1 (volume balance)
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Fisher et al, 2002
Fisher et al, 2004
Barnett Shale
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r =At^1/2
r =At^1/3
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Data courtesy of Shawn Maxwell, Pinnacle Technologies
Hydraulic Fracturing in Barnett Shale
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Factorized anisotropy and non-linearity
∂ p∂ t
= ∂∂ x i
Dij( p ) ∂∂ x j
p
Dij( p )=[D011 0 0
0 D022 00 0 D033
] f ( p )
∂ p∂ t
=D011∂∂ x1
f ( p )∂∂ x1
p
+D022∂∂ x2
f ( p )∂∂ x2
p+D033∂∂ x3
f ( p )∂∂ x3
p
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Rescaling of the cloud
Factorized non-linearity: Anisotropy vs time-dependence
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Barnett Shale: modelling using engineering data
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The back front of seismicity
N. Hummel, 2011,2012
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N. Hummel, 2015
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Conclusions
• Qantitative information on rock-physics: e.g., initial and stimulated
permeability.
• Non-linear diffusion helps to understand fracturing of shale.
• Back front of seismicity is indicative for a pressure-dependence of
the stimulated permeability.
• r-t plots can help to control the quality of microseismic dots.