Transcript Slide 1

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Energy balance and
numerical simulation of
microseismicity induced by
hydraulic fracturing
David W. Eaton* and Neda Boroumand
Department of Geoscience
University of Calgary
* Currently at University of Bristol
Acknowledgements:
Sponsors of the Microseismic
Industry Consortium
Nexen Inc. for data
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Outline
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1. Role of microseismic monitoring in hydraulic
fracturing for unconventional oil resource
development
2. Energy balance: radiated seismic energy
versus frac energy inputs/outputs
3. Numerical simulation of frac-induced
microseismicity, based on crack-tip stress and
Coulomb Stress field
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What is hydraulic fracturing?
http://www.capp.ca
• High-pressure fluids are injected to create tensile fractures, in order to
enhance permeability of hydrocarbon-bearing formations
• This is followed by injection of proppant (e.g. sand) to hold fractures open
• Typically implemented in multiple stages within a horizontal wellbore, often
many drilled from a single pad
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Hydraulic Fracturing:
Role of Microseismic
Monitoring
• Typically a string of
downhole geophones
and/or surface array
• Real-time monitoring to
fine-tune injection
program, diagnose issues
• Post-frac analysis to
assess stimulation
program
Pettitt, 2010
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Input vs Output Energy
Injection Energy (EI)
Fracture Energy (EF)
Pressure
Rate
Time
Radiated Seismic
Energy (ER)
Strain Energy (ES)
http://www.engineeringarchive
s.com
Other (i.e.
friction/thermal,
hydrostatic, leak-off,
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etc.)
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Injection Energy
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Pressure (P)
Rate (Q)
Where Q(t) = injection rate,
P(t) = surface treatment pressure
t1 & t2 are start and end times of treatment
Time
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Fracture Energy
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EF = F ´ d = Pd AF e
where <Pd> is the average downhole pressure, <AF> is
the single-sided surface area and e is the average
fracture width (Walter and Brune, JGR, 1993)
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Radiated Seismic Energy
Kanamori, 1977
where M0 is moment magnitude, and ES is in Joules
… but note missing data
in G-R plot
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Case Study
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• 10 frac stages
• Microseismic
event locations
and magnitudes
were provided
(geometry was
measured)
• Pumping data
provided
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b-value correction
Energy per event
Joules
Based on Hanks and Kanamori (1979)
Joules
Energy per bin
Total predicted energy: 4.63e+6J
Total observed energy: 1.81e+5J
Ratio = 25.6
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• b = 1.57, small
magnitude events
contribute more to
total seismic
energy
• If b < 1.5 then
more total energy
in larger bins
• If b > 1.5, then
more energy in
successively
smaller bins
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Energy Calculation Results
and comparison of different energy values and their relationships
e
Stage
Stage 18
Stage 19
Stage 20
Stage 19
Stage 13
Stage 14
Stage 15
Stage 16
Stage 17
Stage 17
Injection Energy
(KJoules)
192,647,400.00
165,301,920.00
154,350,000.00
163,838,400.00
140,829,120.00
144,942,000.00
162,035,040.00
143,100,000.00
156,017,100.00
223,941,510.00
Fracture Energy
(KJoules)
29,168,562.50
27,188,525.00
22,137,500.00
40,035,000.00
34,979,600.00
37,900,800.00
66,409,750.00
53,845,000.00
22,160,000.00
26,217,100.00
Seismic Energy
(KJoules)
9,996.79
19,508.12
4,641.58
9,230.97
28,055.40
25,532.75
32,141.91
32,845.77
14,640.01
18,346.79
% Fracture Energy
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16
14
24
25
26
41
38
14
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% Seismic Energy
0.03
0.07
0.02
0.02
0.08
0.07
0.05
0.06
0.07
0.07
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Numerical Simulation of Microseismicity
 Single tensile crack, growing at constant
volumetric rate
 Stress field from analytic expressions for
crack-tip stress
 Event occurrence probability based on
associated Coulomb stress
 Event magnitudes follow Gutenberg-Richter
distribution
 Distance-dependent detection threshold
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Analytic Formulas for Crack-tip stress
 Change in stress due to a tensile (mode I) crack in
a linear elastic solid
Lawn and Wilshaw, 1975
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Crack-tip stress field
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 Simple
model of a
tensile crack
 Note that
stress at the
crack tip is
greater than
background
tensile stress
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Coulomb Stress Field
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A measure of the state of stress on a planar surface.
  is the change in shear stress
 μ the coefficient of friction
 n is the normal stress
 P is the pore fluid pressure
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Coulomb Stress and Aftershocks
 Coulomb stress
changes calculated for
the 23 April 1992 ML=6.1
Joshua Tree Earthquake.
 Aftershocks occur
preferentially in areas of
increased Coulomb stress
King et al., 1994
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Stochastic Model
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 20% probability of
failure for CFS >= 80 MPa
 Magnitude distribution
satisfies GutenbergRichter relation with b =
1.5
 Dynamic simulation
created by assuming an
expanding crack with c ~
t1/2
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Detection Threshold
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Eaton et al., 2011
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Snapshot from Simulation
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Conclusions
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 In this case study, radiated seismic energy -
even after correction for catalog
incompleteness - represents only a few ppm of
the injection energy
 An idealized geodynamical simulation
framework has been developed that matches
some characteristics of field observations,
including diffusion-like event migration and
presumed receiver-side observational bias
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