Seismic wave attenuation in a methane hydrate reservoir.pdf

8/11/2019 Seismic wave attenuation in a methane hydrate reservoir.pdf

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Elastic-wave data collectedaround the world in sedimentswith methane hydrate point tosignificant velocity increasesdue to the presence of thehydrate in the pores. This effectcan be easily understood if werecall that gas hydrate is a solidas opposed to brine or gas. Byfilling the pore space, gashydrate acts to reduce theporosity available to the porefluid and increase the elasticmoduli of the solid frame.However, it is difficult to rec-oncile this effect with morerecent observations that theattenuation of elastic waves grows with increasing gas hydrateconcentration.

Indeed, intuitively, one would expect that the stiffer therock, the smaller the relative elastic energy losses per cycleand the smaller the attenuation. Measurements in many sed-iments support this intuition. For example, Klimentos andMcCann (1990) show that attenuation increases with increas-ing porosity and clay content, while the velocity behaves inan opposite way. Recent results by Koesoemadinata andMcMechan (2001), who statistically generalized many exper-imental data, point to the same fact. This inference, combined

with quantitative modeling, led Dvorkin et al. (2003) to sug-gest reduced absorption as a possible seismic attribute formethane hydrate detection.

However, the facts are persistent. Unexpectedly large atten-uation in sediments with gas hydrates has recently beenobserved at different geographical locations, in different depo-sitional environments and at different frequencies. In 1999,Guerin et al. presented qualitative evidence of dipole wave-form attenuation in the hydrate-bearing sediments in theOuter Blake Ridge off the U.S. east coast. Sakai (1999) notedthat the shear-wave VSP signal may be strongly attenuatedin a Mallik well in northern Canada within the methane-hydrate interval. Wood et al. (2000) observed increased atten-uation of seismic waves at the same location. Guerin andGoldberg (2002) used monopole and dipole waveforms to

quantify compressional- and shear-wave attenuation. Theyreported a monotonic increase in both with increasing hydratesaturation. Pratt et al. (2003) reported an increase in attenua-tion in the Mallik hydrate reservoir between two methanehydrate wells during cross-hole experiments in the 150-500Hz frequency range. Anomalous absorption has been observedin the Nankai Trough methane hydrate reservoir offshore

Japan in the same seismic frequency range (M.T. Taner, per-sonal communication). We have no reason to question thevalidity of these field data and, therefore, concern ourselveswith the task of establishing a plausible quantitative physicalexplanation and of determining in which situations increasedattenuation can be expected in methane hydrate reservoirs.

Dissipation mechanisms. Seismic energy in porous rockwith fluid dissipates due to wave-induced oscillatory cross-flow. The viscous-flow friction irreversibly transfers part ofthe energy into heat. This flow may be especially strong inpartially saturated rock where the viscous fluid phase (water)moves in and out of the gas-saturated pore space.

Such viscous-friction losses may also occur in wet rockwhere elastic heterogeneity is present. Deformation due toa stress wave is relatively strong in the softer portion of therock and weak in the stiffer portion. The spatial hetero-geneity in the deformation of the solid frame forces the fluid

to flow between the softer and stiffer portions. Such cross-flow may occur at all spatial scales.Microscopic squirt flow is developed at the submil-

limeter pore scale because a single pore may include com-pliant crack-like and stiff equidimensional parts.Macroscopic squirt flow, which is more relevant to theseismic prospecting scale, may occur due to elastic het-erogeneity in the rock frame elastic moduli. This mecha-nism has recently received rigorous mathematical treatment

by Pride et al. (2003) in a double-porosity model.

Simple estimate. However, there is a simple way of quan-tifying the effect of macroscopic squirt flow on seismic waveattenuation. In a viscoelastic body, causality requires thatthere be a very specific relation between attenuation and fre-

quency-related velocity (or elastic modulus) change. Thisrelation is referred to as the Kramers-Kronig equation. Itimplies that a larger attenuation generally is associated witha larger wave-speed change between low frequency and highfrequency. It has an especially simple expression in a stan-dard linear solid: , where isthe maximum inverse quality factor (the ratio of the elasticenergy dissipated per cycle of oscillation to the peak elas-tic energy during the cycle);MHis the compressional mod-ulus at very high frequency; and ML is the compressionalmodulus at very low frequency. The compressional modu-lus is defined as the product of the bulk density and P-wavevelocity squared.

730 T HELEADINGEDGE AUGUST2004 AUGUST2004 THELEADINGEDGE 00

Seismic wave attenuation in a methane hydrate reservoir

JACKDVORKIN, Stanford University, California, U.S.

RICHARDUDEN, Rock Solid Images, Houston, Texas, U.S.

INTERPRETERS CORNER

Coordinated by Rebecca B. Latimer

Figure 1. Well log curves in Mallik 2L-38. From left to right, gamma-ray, methane hydrate saturation ofthe pore space, porosity of the sediment frame (without hydrate), and the P-wave impedance.


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Consider now a model rock that is fully water-saturated(wet) and has two parts. One part (80% of the rock volume)is shale with porosity 0.4; clay content 0.8 (the rest is quartz);and the P-wave velocity 1.9 km/s. The other part (theremaining 20%) is clean high-porosity slightly-cementedsand with porosity 0.3 and the P-wave velocity 3.4 km/s.The compressional modulus is 7 GPa in the shale and 25GPa in the sand.

Because of the difference between the compliance of thesand and shale parts, their deformation due to a passingwave is different, leading to macroscopic squirt flow.

At high frequency, there is essentially no crossflowbetween sand and shale simply because the flow cannot fullydevelop during the short cycle of oscillation. The effectiveelastic modulus of the system is the harmonic (Backus) aver-age of the moduli of the two parts: MH = 16 GPa.

At low frequency, the crossflow can easily develop. Inthis case, the fluid reacts to the combined deformation ofthe dry frame of the sand and shale. The dry-frame com-pressional modulus in the shale is 2 GPa while that in the

sand is 20 GPa. The dry-frame modulus of the combineddry frame7 Gpais the harmonic average of the two. Thearithmetically averaged porosity of the model rock is 0.32.To estimate the effective compressional modulus of the com-

bined dry frame with water, we theoretically substitutewater into this combined frame. The result isML = 13 GPa.

The calculated maximum inverse quality factor,= 0.12, translates into a noticeable attenuation coefficient ofabout 0.02 dB/m.

The above-described averaging technique for attenua-tion estimates in wet rock can be applied to well log curves

by means of a moving averaging window.

Field example. We apply this attenuation modeling to well

log data from the Mallik 2L-38 well drilled in the MackenzieRiver Delta, the largest delta in Canada, located in the farnorthwest corner of the country. The interval under exam-ination includes several low-GR sand bodies whose porespace is partly filled with methane hydrate (Figure 1). Therock-frame porosity in these sands exceeds 30% and themeasured P-wave impedance is much larger than in the sur-

rounding shale or sand without hydrate. This impedancecontrast gives rise to strong elastic heterogeneity in the inter-val.

The impedance data can be accurately matched by theeffective-medium model for sediments with gas hydrate(discussed in Dvorkin et al., 2003). To illustrate this match,we plot the impedance versus the porosity of the sedimentframe and the hydrate volume concentration in the sediment,defined as the product of methane hydrate saturation of thepore space and porosity (Figure 2).

For the purpose of the attenuation calculation, the sed-iment in the interval is considered wet because it does notcontain free gas. Then the methane hydrate has to be treatedas part of the sediments frame. Of course, where the hydrateis present, the porosity of this modified frame is smaller thanthat of the original frame composed of quartz and clay andequals the product of the original porosity and one minusmethane hydrate saturation. Also, the effective solid-phasemodulus of the modified frame has to include the compo-nent due to methane hydrate. The pore fluid in this modi-fied frame is water.

The result of our inverse quality factor estimate is shownin Figure 3. High attenuation occurs precisely wheremethane hydrate is present, the impedance contrast is large,and elastic heterogeneity is strong. Our attenuation esti-mates quantitatively explain that the amplitude loss is highin sediments with methane hydrate. The inverse qualityvalues are not that different from the recent in-situ esti-mates of Pratt et al. (2003) obtained from cross-hole wave-

form inversion data in the 150-500 Hz frequency range.Those cross-hole data show Q-1between 0.15 and 0.20 in thesands with methane hydrate and a very small value (lessthan 0.05) in the rest of the section.

Scattering. The self-induced elastic heterogeneity in amethane hydrate reservoir may also cause scattering atten-uation. To estimate this contribution we use the ODoherty-Anstey formula , wherefis frequency and isthe power spectrum of the logarithmic impedance fluctua-tions of the medium .

We estimate attenuation from scattering in the entireinterval of Mallik 2L-38. Q-1 thus calculated appears as a sin-gle number for the entire interval because scattering atten-


Figure 4. The inverse quality factor due to scattering in Mallik 2L-38.

Figure 3. Well log curves in Mallik 2L-38 with the calculated inversequality factor shown in red.

Figure 2. Left, impedance versus porosity in Mallik 2L-38, color-coded byhydrate concentration. Right, the same data (every fifth point) shown asempty black circles on the background of the modeled impedance strip.The modeled impedance is color-coded by hydrate concentration.


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uation is a layer property. The result (Figure 4) indicates thatalthough the scattering attenuation is smaller than the macro-scopic squirt flow attenuation, it has the same order of mag-nitude and has to be taken into account when estimatingthe total attenuation of elastic waves in sediments withmethane hydrate.

Conclusion. Elastic-wave amplitude losses in a methanehydrate reservoir grow as hydrate concentration increases

because the hydrate in the pores acts to increase the elasticmoduli of the rock. This increase results in increasing elas-tic heterogeneity which encourages pore-fluid crossflow

between stiff and soft domains of the rock, triggered by thepassing wave. The viscous energy losses due to this wave-induced fluid crossflow are partly responsible for the elas-tic-wave attenuation. Scattering of the seismic energy is alsoamplified by elastic heterogeneity and may add to the ampli-tude loss. In short, attenuation in sediment with hydrate isdue to self-induced elastic heterogeneity.

Suggested reading. Rock physics of gas hydrate reservoir byDvorkin et al. (TLE, 2003). Characterization of in-situ elasticproperties of gas-hydrate-bearing sediments on the BlakeRidge by Guerin et al. (JGR, 1999). Sonic waveform attenu-

ation in gas-hydrate-bearing sediments from the Mallik 2L-38research well, Mackenzie Delta, Canada by Guerin andGoldberg (JGR, 2002). Empirical estimation of viscoelastic seis-mic parameters from petrophysical properties of sandstone byKoesomadinata and McMechan (GEOPHYSICS, 2001). Cross-holewaveform tomography velocity and attenuation images of arc-

tic gas hydrates by Pratt et al. (SEG 2003 Expanded Abstracts).Permeability dependence of seismic amplitudes by Pride etal. (TLE, 2003). Velocity analysis of vertical seismic profiling(VSP) survey at Japex/JNOC/GSC Mallik 2L-38 gas hydrateresearch well, and related problems for estimating gas hydrateconcentration by Sakai (GSC Bulletin, 1999). In-situ mea-surements of P-wave attenuation in the methane hydrate-andgas-bearing sediments of the Blake Ridge by Wood et al.(Proceedings of the ODP, Scientific Results, 2000). TLE

Acknowledgments. We thank Tim Collett for providing the log data andNaum Derzhi and Gary Mavko for their kind advice.

Corresponding author: [email protected]


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Seismic wave attenuation in a methane hydrate reservoir.pdf