Marcel FrehnerETH Zurich, Switzerland, frehner@erdw.ethz.ch

1SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Interaction of seismic background noise with oscillating

pore fluids causes spectral modifications of passive

seismic measurements at low frequencies

Marcel Frehner ETH Zurich, Switzerland, frehner@erdw.ethz.ch

Stefan M. Schmalholz ETH Zurich, Switzerland

Yuri Podladchikov University of Oslo, Norway

2SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Motivation: Observed spectral variations above oil

Long-time continuous passive seismic measurements

Fourier transformation

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Characteristic spectral variations can be used to detect oil (Spectraseis).

Voitsdorf area, Austria, 2005Spectraseis survey for RAG

3SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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

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4SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

So far so good…… but

What is the physical mechanism that causes the observed spectral modification at low frequencies?

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5SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Two potential mechanisms

Resonantscattering(patchy saturation)

Resonantamplification(surface tension)

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6SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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.

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7SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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.

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8SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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

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9SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

But still…

How can these oscillations be transferred to the earth surface?

Coupling micro-scaleoscillations with macro-scaleelastic wave propagation?

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10SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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

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11SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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

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12SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Numerical model setup

Explicit 1D finite differences

Staggered grid in space(Virieux, 1986)

Predictor-correctormethod in time

Non-reflecting orrigid boundaries(Ionescu & Igel, 2003)

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13SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Eigenvalues

This study Anderson and Hampton, 1980J. of Acoustical Society of America

Gas bubbles in water

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14SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Energy conservation and transfer

Solid velocity

Fluid velocity

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15SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Incident elastic wave

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16SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Incident elastic wave

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17SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Spectra over time

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18SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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)

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19SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

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 frehner@erdw.ethz.ch

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

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21SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Acknowledgement

Spectraseis AG, Switzerland forproviding passive seismic dataand financial support

Swiss Commission forTechnology and Innovation KTIfor financial support

22SEG San Antonio 09/27/2007 frehner@erdw.ethz.ch

Thank you