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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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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

Outline

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What is hydraulic fracturing?

• 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

http://www.capp.ca

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Pettitt, 2010

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

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Input vs Output EnergyInjection Energy (EI)

Pressure

Time

Fracture Energy (EF)

Strain Energy (ES)http://www.engineeringarchives.com

Radiated Seismic Energy (ER)

Other (i.e. friction/thermal,

hydrostatic, leak-off, etc.)

Rate

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Pressure (P)

Time

Rate (Q)

Injection Energy

Where Q(t) = injection rate, P(t) = surface treatment pressure

t1 & t2 are start and end times of treatment

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Fracture Energy

where <Pd> is the average downhole pressure, <AF> is

the single-sided surface area and 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

• 10 frac stages • Microseismic

event locations and magnitudes were provided (geometry was measured)

• Pumping data provided

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Energy per event

Energy per bin

Joul

esJo

ules

Total predicted energy: 4.63e+6JTotal observed energy: 1.81e+5J

Ratio = 25.6

Based on Hanks and Kanamori (1979)

• 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

b-value correction

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Injection Energy Fracture Energy Seismic EnergyWell/Formation Name Stage (KJoules) (KJoules) (KJoules) % Fracture Energy % Seismic Energy

Well #1 (Otter Park) Stage 18 192,647,400.00 29,168,562.50 9,996.79 15 0.03Stage 19 165,301,920.00 27,188,525.00 19,508.12 16 0.07Stage 20 154,350,000.00 22,137,500.00 4,641.58 14 0.02

Well # 2 (Otter Park) Stage 19 163,838,400.00 40,035,000.00 9,230.97 24 0.02Well # 3 (Muskwa) Stage 13 140,829,120.00 34,979,600.00 28,055.40 25 0.08

Stage 14 144,942,000.00 37,900,800.00 25,532.75 26 0.07Stage 15 162,035,040.00 66,409,750.00 32,141.91 41 0.05Stage 16 143,100,000.00 53,845,000.00 32,845.77 38 0.06

Well # 3 (Muskwa) Stage 17 156,017,100.00 22,160,000.00 14,640.01 14 0.07Well # 4 (Muskwa) Stage 17 223,941,510.00 26,217,100.00 18,346.79 12 0.07

Table 5. Summary and comparison of different energy values and their relationships

Energy Calculation Results

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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

Numerical Simulation of Microseismicity

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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

Simple model of a tensile crack

Note that stress at the crack tip is greater than background tensile stress

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is the change in shear stress μ the coefficient of friction n is the normal stress P is the pore fluid pressure

Coulomb Stress Field

A measure of the state of stress on a planar surface.

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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

Coulomb Stress and Aftershocks

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Stochastic Model

20% probability of failure for CFS >= 80 MPa

Magnitude distribution satisfies Gutenberg-Richter relation with b = 1.5

Dynamic simulation created by assuming an expanding crack with c ~ t1/2

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Eaton et al., 2011

Detection Threshold

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Snapshot from Simulation

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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

Conclusions