1SEG San Antonio 09/27/2007 [email protected]
Interaction of seismic background noise with oscillating
pore fluids causes spectral modifications of passive
seismic measurements at low frequencies
Marcel Frehner ETH Zurich, Switzerland, [email protected]
Stefan M. Schmalholz ETH Zurich, Switzerland
Yuri Podladchikov University of Oslo, Norway
2SEG San Antonio 09/27/2007 [email protected]
Motivation: Observed spectral variations above oil
Long-time continuous passive seismic measurements
Fourier transformation
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
Characteristic spectral variations can be used to detect oil (Spectraseis).
Voitsdorf area, Austria, 2005Spectraseis survey for RAG
3SEG San Antonio 09/27/2007 [email protected]
Motivation: Time reverse modeling
Time reverse modeling of elastic wave propagation using measured ground motion velocities
Low-frequency source signals within known reservoirs.
Steiner et al., submitted
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
4SEG San Antonio 09/27/2007 [email protected]
So far so good…… but
What is the physical mechanism that causes the observed spectral modification at low frequencies?
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
5SEG San Antonio 09/27/2007 [email protected]
Two potential mechanisms
Resonantscattering(patchy saturation)
Resonantamplification(surface tension)
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
6SEG San Antonio 09/27/2007 [email protected]
Resonance of trapped oil blobs:Resonance is important
Hilpert et al, Geophysics, 2000
We investigate the excitation by sound waves of capillary trapped oil blobs. […] We derive approximate, analytical expressions for the resonance of oil blobs in capillary tubes […]. Based upon these simple model systems, we conclude that resonance of oil blobs is significant for coarse-grained but not fine-grained media.
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
7SEG San Antonio 09/27/2007 [email protected]
Resonance of trapped oil blobs:Oil in a pore can be treated as oscillator
Beresnev, Geophysics, 2006
Quantitative dynamics of a non-wetting ganglion of residual oil entrapped in a pore constriction and subjected to vibrations of the pore wall can be approximated by the equation of motion of an oscillator moving under the effect of the external pressure gradient, inertial oscillatory force, and restoring capillary force.
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
8SEG San Antonio 09/27/2007 [email protected]
Resonance of trapped oil blobs: Numerical simulation
Holzner et al., Comm. in Nonlinear Science and Numerical Simulation, 2007
Full Navier-Stokes equations
Surface tension taken into account
One simulation for each frequency
Calculate response of centerof mass of oil blob
Resonance curve like that of a harmonic oscillator
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 2 4 6 8 10 12
frequency [Hz]
Am
pli
tud
e
[mm
]
omega_0 = 4.6 Hzrho = 1.2 HzRes_Amp = 0.018 mm
omega_0 = 5.5 Hzrho = 2.0 HzRes_Amp = 0.03 mm
0
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
9SEG San Antonio 09/27/2007 [email protected]
But still…
How can these oscillations be transferred to the earth surface?
Coupling micro-scaleoscillations with macro-scaleelastic wave propagation?
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
10SEG San Antonio 09/27/2007 [email protected]
Coupling oscillations with elastic rock
4 contributions to total energy
2
0
220
0
2
0
2
0
1
2
1
2
11
2
1
2
lf f fkin
lf f f spot
ls s skin
l sspot
E u dx
E u u dx
E u dx
uE E dx
x
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
11SEG San Antonio 09/27/2007 [email protected]
Coupling oscillations with elastic rock
Hamilton’s variational principle
Equations of motion
0
0i i i
lf s f skin kin pot pot
d d
u dt u dx
dx T U E E E E
L L L
L
2202
2202
1
ff f f s
s ss f f s
uu u
t
u uE u u
t x x
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
12SEG San Antonio 09/27/2007 [email protected]
Numerical model setup
Explicit 1D finite differences
Staggered grid in space(Virieux, 1986)
Predictor-correctormethod in time
Non-reflecting orrigid boundaries(Ionescu & Igel, 2003)
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
13SEG San Antonio 09/27/2007 [email protected]
Eigenvalues
This study Anderson and Hampton, 1980J. of Acoustical Society of America
Gas bubbles in water
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
14SEG San Antonio 09/27/2007 [email protected]
Energy conservation and transfer
Solid velocity
Fluid velocity
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
15SEG San Antonio 09/27/2007 [email protected]
Incident elastic wave
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
16SEG San Antonio 09/27/2007 [email protected]
Incident elastic wave
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
17SEG San Antonio 09/27/2007 [email protected]
Spectra over time
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
18SEG San Antonio 09/27/2007 [email protected]
Conclusions
Presented wave propagation-oscillation model shows To initiate fluid oscillations, energy is taken from the
solid at resonance frequency (Trough in solid spectrum)
As fluid continues to oscillate, energy is transferred back fromfluid to solid at resonance frequency (Peak in solid spectrum)
After their initialization, oscillations decay differently for different reservoir thicknesses (Thickness information)
Implications Solid spectrum is not expected to always show a peak at resonance
frequency (Implication for data analysts: long time signals)
Current model requires transient pulses to initiate oscillations(e.g. discrete pulses, continuous pulses with varying amplitudes)
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
19SEG San Antonio 09/27/2007 [email protected]
Open questions / Future work
Scale of oscillations?
Influence of saturation level?
Complex pore geometry:non-linearities
More complete physical modele.g. 3-phase mixture model
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
20SEG San Antonio 09/27/2007 [email protected]
Ongoing related research
Markus Hilpert, Johns Hopkins University, USA: Lattice-Bolzmann modeling, mobilization of trapped oil blobs
Holger Steeb, Saarland University, Germany:3D 3-phase mixture theory, inclusion of surface tension effects
Snapshots published inHilpert, 2007 J. Colloid and Interface Science
Motivation Oscillation Coupling Numerics Results Conclusions|| | | | | | Outlook |
21SEG San Antonio 09/27/2007 [email protected]
Acknowledgement
Spectraseis AG, Switzerland forproviding passive seismic dataand financial support
Swiss Commission forTechnology and Innovation KTIfor financial support