insights from a closed-form solution for injection- and ... · 3rd schatzalp workshop on induced...
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3rd Schatzalp Workshop on Induced Seismicity, Davos, 5-7 March 2019 1
Insights from a closed-form solution for
injection- and production-induced stresses in
vertical displaced faults
Jan Dirk Jansen, Pranshu Singhal, Femke Vossepoel
Delft University of Technology
Department of Geoscience and Engineering
3rd Schatzalp Workshop on Induced Seismicity
Davos, 5-7 March 2019
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3rd Schatzalp Workshop on Induced Seismicity, Davos, 5-7 March 2019 2
Science4Steer – towards operational control
• Aim: A scientific basis for developing production and reinjection
strategies to minimize induced seismicity
• 5-year program at TU Delft and Utrecht University - part of DeepNL
• Combined experimental and numerical approach
WP 1: Lab-scale
compaction
experiments
WP 2: Lab-scale
friction
experiments
WP 6: Optimal
control to mini-
mize seismicity
Increasing spatial scale
WP 3: Lab-scale
friction and
seismicity exp.
WP 4: Model
development
and upscaling
WP 5: Multi-scale
simulation of multi-
well/fault
reservoir segments
Chris
Spiers
UU
Suzanne
Hangx
UU
Auke
Barnhoorn
TUD
Denis
Voskov
TUD
Hadi
Hajibeygi
TUD
Jan Dirk
Jansen
TUD
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Science4Steer – WP 3; Lab Experiments
• Investigator: Auke Barnhoorn @ TU Delft
• Triaxial cell with 30 x 30 x 30 cm blocks
• Induced seismicity resulting from differential pressure and/or
pressure decline in displaced faults
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3rd Schatzalp Workshop on Induced Seismicity, Davos, 5-7 March 2019 4
Science4Steer – WP 3; Lab Experiments
• Investigator: Auke Barnhoorn @ TU Delft
• Triaxial cell with 30 x 30 x 30 cm blocks
• Induced seismicity resulting from differential pressure and/or
pressure decline in displaced faults
30 cm
30
cm
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3rd Schatzalp Workshop on Induced Seismicity, Davos, 5-7 March 2019 5
Science4Steer – WP 3; Lab Experiments
• Investigator: Auke Barnhoorn @ TU Delft
• Triaxial cell with 30 x 30 x 30 cm blocks
• Induced seismicity resulting from differential pressure and/or
pressure decline in displaced faults
30 cm
30
cm
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Earlier work – numerical
Roest & Kuilman 1994; Nagelhout & Roest, 1997; Mulders, 2013;
Orlic & Wassing, 2013; Orlic et al. 2013; Van den Bogert, 2015; Lele
et al. 2016; Zbinden et al. 2017; Bourne & Oates, 2017; Buijze et al.,
2017; Van Wees et al., 2017, Haug et al, 2018; Buijze et al., 2019
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Displaced normal fault model
Fault throw: t = b - a
Reservoir height: h = a + b
Reservoir width: w = c + d
Always overlap: t < h
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Displaced (normal) fault model – simpler
Infinite, 2D domain
Uniform elastic properties
No transients
Single-phase flow
Straight, zero-width, non-sealing fault
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Inclusion theory (1)
Elsheby,1957: cut and weld operation to simulate response to inelastic
deformation (e.g. thermal strain, dislocations, pore pressure)
1 2
3 4
“Eigen
strains”
“Elastic
strains”
Total strains = elastic strains + eigen strains:
For porous media:
Distributed forces
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Inclusion theory (2)
After several steps:
where ,
and gi and gij are Green’s functions for ui and sij .
Segall (1985, 1989, 1992),
Segal & Fitzgerald (1989),
Segal et al. (1994), Soltan-
zadeh & Hawkes (2008),
Marck et al. (2015)
Link to “nucleus of strain” concept: Rudnicki (2002)
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Typical integral
(for rectangle)
With many thanks to Macsyma (open source symbolic manipulation tool)
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Results for faulted infinite reservoir
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Displaced (normal) fault model – even simpler
Reservoir width: infinite
a = 100 m
b = 200 m
Reservoir height h = a+b = 300 m
Fault throw t = b- a = 100 m
a
ba
b
y
x∞
∞
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Scaled stresses
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Results for infinitely wide reservoir
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Results for infinitely wide reservoir
Singularities at y = ± a and y = ± b (top and bottom of left/right reservoirs)
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Stresses and slip boundaries
p0 = 35 MPa
p = 20 MPa
ptot = 55 MPa
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Stresses and slip boundaries
p = 20 MPa
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Stresses and slip boundaries
p = 20 MPa
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What’s wrong?
Van Wees et al. 2017
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Stresses and slip boundaries
p = 20 MPa
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Injection and production
p = 0 MPap = 0 MPa
SCU = 0.88 @ mst = 0.6
SCU = 1.05 @ mdyn = 0.5
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Injection and production
p = -5 MPap = 5 MPa
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Injection and production
p = -5 MPap = 5 MPa
Slip
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Injection and production
p = -5 MPap = 5 MPa
Reverse slip
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Injection and production
p = -20 MPap = 20 MPa
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Injection and production
p = -35 MPap = 35 MPa
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Injection and production
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Injection and production
y4
y3
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Intersections and slip patch half-length Lsl/2
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Intersections and slip patch half-length Lsl/2
Same result as derived by Van den Bogert (2015)
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Intersections and slip patch half-length Lsl/2
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Intersections and slip patch half-length Lsl/2
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Excess shear force in fault (“shear glut”)
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Scaled vertical displacements
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Seismic moment
Same result as derived by Bourne and Oates (2017)
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Conclusions
Results from various earlier studies confirmed and sometimes
sharpened, in particular from (Van den Bogert, 2015; Buijze et al., 2017;
Van Wees et al., 2017; Zbinden et al. 2017; Buijze et al., 2019):
• Elastic stress patterns independent of p; only dependent on
geometric reservoir parameters.
• Production results in peaked shear stress profile: slip-provoking at
internal corners; slip arresting at external corners.
• Two slip patches in the production case grow mainly inwards at an
exceedingly high rate with decreasing reservoir pressure.
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3rd Schatzalp Workshop on Induced Seismicity, Davos, 5-7 March 2019 38
Conclusions
Results from many earlier studies confirmed and sometimes sharpened,
in particular from (Van den Bogert, 2015; Buijze et al., 2017; Van Wees
et al., 2017; Zbinden et al. 2017; Buijze et al., 2019):
• Elastic stress patterns independent of p; only dependent on
geometric reservoir parameters.
• Production produces peaked shear stress profile: slip-provoking at
internal corners; slip arresting at external corners.
• Two slip patches in the production case grow mainly inwards at an
exceedingly high rate with decreasing reservoir pressure.
New insights from the present study (at least to me ):
• Infinitely large shear stresses in a displaced fault => smallest amount
of injection or production will result in slip; no such thing as a slip-free
maximum injection or minimum production pressure.
• Marked difference between the shear stress patterns for injection and
production: for injection, slip grows always into over/underburden; for
production, slip could well stay in the reservoir.