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EAGE Dubai 12/11/ Interpretation of hydrocarbon microtremors as pore fluid oscillations driven by ambient seismic noise Marcel FrehnerETH Zurich, Switzerland, Stefan M. SchmalholzETH Zurich, Switzerland Reto HolznerSpectraseis Technologies Inc., Switzerland Yuri PodladchikovUniversity of Oslo, Norway

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EAGE Dubai 12/11/ Observation in microtremor signals → Starting point Continuous velocity- measurements of microtremor (= Passive method) Fourier transformation Low frequency spectral anomalies up to 24h Spectraseis campaign: Mossoro, Brasil, 2003

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EAGE Dubai 12/11/ One possible explanation for low frequency spectral anomalies Resonant oscillation of pore fluids Is the resonant movement of the pore fluids strong enough to be transferred to the elastic solid? Synthetic case study Reproduction of low-frequency anomaly Low frequency spectral anomalies → Explained as pore fluid oscillations

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EAGE Dubai 12/11/ 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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EAGE Dubai 12/11/ 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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EAGE Dubai 12/11/ Resonance of trapped oil blobs → Numerical simulation Ongoing research of ASCOMP Ltd., Switzerland Full Navier-Stokes equations Surface tension taken into account One simulation for each frequency Calculate response of center of mass of oil blob 00

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Motivation A simple idea: Observed low frequency anomalies at the surface are caused by oscillations of pore fluids in the reservoir. Question: Is it possible to transfer the fluid oscillations to the solid? Can the eigenfrequency of these oscillations be observed in the spectrum of the solid velocity? Requirements: Mathematical description of coupling between micro-scale oscillations and macro-scale wave propagation

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Model equations Linear elastic solid: Linear oscillator:

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Model equations Coupled equations 0 has to be determined from pore fluid and pore geometry. For the moment it is assumed that 0 lies in the low frequency range under consideration.

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Numerical code Explicit 1D finite differences Staggered grid in space (Virieux, 1986) Predictor-corrector method in time Non-reflecting boundaries (Ionescu & Igel, 2003) Written in MATLAB Code checked vs. analytical solution of model-equations Energy conservation satisfied Entropy inequality in progress

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Test of numerical code Energy conservation Solid velocity Fluid velocity

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EAGE Dubai 12/11/ Synthetic case study → Homogeneous media Monochromatic external source with 0.3Hz Eigenfrequency 0 of pore oscillations: 3 Hz Eigenfrequency 0 of pore oscillations: 3 Hz External source with 0.3 Hz

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EAGE Dubai 12/11/ Synthetic case study → Observations The model equations are truly linear Both boundaries are non-reflecting, ie. no two-way reflections occur The only input frequency is the 0.3Hz frequency of the external source Nevertheless the eigenfrequency of the pore fluid oscillations (3Hz) is clearly visible in the solid spectra The pore fluid seems to develop an oscillation with its eigenfrequency and transfer this motion to the solid ??? HOW IS THIS POSSIBLE ???

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EAGE Dubai 12/11/ Synthetic case study → Discussion Absolute velocities Relative velocity Spectrum of incident monochromatic wave Time signal of incident monochromatic wave

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EAGE Dubai 12/11/ Monochromatic external source with 0.3Hz Eigenfrequency 0 of pore oscillations: 3 Hz Synthetic case study → Discussion Decay of low frequency anomalies Black spectra: short time signal Red : long time signal

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EAGE Dubai 12/11/ Synthetic case study → Reservoir thickness variation No oscillation Reservoir with 3Hz oscillators 0.3Hz external source Layered model Thin reservoir Thick reservoir

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EAGE Dubai 12/11/ D coupled wave-oscillator model → Comparison to nature / Outlook Linear model Non-linear model

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EAGE Dubai 12/11/ Low frequency spectral anomalies explained as pore fluid oscillations → Conclusions / Summary Although no other frequencies than the 0.3Hz of the external source is put into the system, the pore fluid starts to oscillate with its eigenfrequency. Incidence of monochromatic wave is enough to excite oscillations of the pore fluid with its eigenfrequency. Under the conditions shown the 3Hz eigenfrequency of the pore fluid oscillations is transferred to the elastic solid The time evolution of the low frequency anomaly could contain information of the reservoir thickness.

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EAGE Dubai 12/11/ Thank you

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