analysis of frequency-dependent pp reflections with white ... … · analysis of...

77th EAGE Conference & Exhibition 2015Madrid IFEMA, Spain, 1-4 June 2015

Analysis of frequency-dependent PP reflections with White’s modelfor CO2 patchy saturation

Xiaoyang Wu (British Geological Survey)

This paper studies the frequency-dependent reflections due to CO2 patchy saturation with White’smodel. Parameters from the Utsira formation are used to perform a numerical study. The results showthat the radii of inner sphere (gas pockets) a and outer sphere b have an effect in the frequency bandin which velocity dispersion and attenuation occur. Frequency-dependence of reflection coefficientsin the seismic band are obvious with appropriate a and b values. A numerical modeling is alsoperformed to study the feasibility of inverting the outer radius b and CO2 saturation from thefrequency-dependent reflection amplitudes with a simulated annealing algorithm.


Introduction

The geological storage of carbon dioxide (CO2) and injection for Enhanced Oil Recovery (EOR) areemerging approaches to reduce the emission of greenhouse gases into the atmosphere. The seismictechnique (Eiken et al., 2000) is one of the suitable geophysical methods that are used to monitor CO2migration and sealing capacity of overlying shales. In the Utsira formation of the Sleipner field, CO2migration and distribution after multiple injections was monitored by time-lapse seismic data, whichwas used to estimate the thickness, velocity and saturations in CO2 saturated zones (Williams andChadwick, 2012). For seismic numerical modelling, the Gassmann-Wood equation is used to estimatethe saturation-dependent velocity under uniform saturation. In the case of patchy saturation, the Brieet al. (1995) equation can be used to estimate the bulk modulus of brine-CO2 mixture in place ofWood’s equation.

Recently, the effect of fluid-related dispersion and attenuation (Chapman et al., 2006) on seismicAmplitude-Versus-Offset (AVO) has attracted more and more attention. A theoretical study offrequency-dependent AVO (FAVO) analysis was performed (Wu et al., 2014) to try to estimate gassaturation using Chapman et al. (2002) squirt-flow model. For CO2 saturation, when migration isdriven by buoyancy, CO2 displaces brine in sandstone and accumulates beneath sealing shales,forming patchy saturation. White (1975)’s model can be used to describe this attenuating mechanism.In this paper, the frequency-dependent PP reflections for CO2 patchy saturation is analysed withWhite’s model, using the parameters of Utsira sand. The velocity dispersion and frequency-dependence of reflectivity, varying with the radius of the fluid saturated area and CO2 saturation, isanalyzed. A numerical study, using a simulated annealing algorithm to invert for the radius of fluid-saturated sphere and CO2 saturation from frequency-dependent response, is also performed.

Theory

White’s model simulated the seismic effects of porous rocks saturated with concentric spheres of awater-gas mixture. This heterogeneous saturation is much larger than the grain scale but much smallerthan the wavelength. As a compressional wave travels through, P-wave velocity *

pV and attenuation*p are influenced by fluid flow between the water phase and the gas pockets, which can be expressed

in terms of the complex P-wave modulus *M and the effective density * (Mavko et al.,1998),

)2/cos(/)/( *2/1***pp MV , (1)

*** /)2/tan( ppp V , (2)

)/(tan **1*rip MM . (3)

When White’s model is applied to CO2 storage in a brine saturated aquifer, the CO2 mobility, i.e. thepermeability of sandstone and the viscosity is assumed to be known. The radii of each gas pocket aand outer sphere b influence the frequency regime in which velocity dispersion may occur and thedegree of attenuation. The gas saturation is calculated as Sg = (a/b)3. When a changes from 0 to b, Sgvaries from 0 to 100%. Then the frequency-dependent reflection coefficient can be calculated usingthe Schoenberg and Protazio (1992)’s plane-wave reflectivity technique.

Numerical modelling

In this numerical modelling, a two-layer model with shale overlying patchy saturated sandstone isdesigned to study the velocity dispersion and attenuation varying with frequency, CO2 saturation andsize of the heterogeneous saturation zone. The frequency-dependent reflection coefficients from theinterface are also calculated. The upper medium has Vp = 2.27km/s, Vs = 0.85km/s, ρ = 2.1g/cm3,which were derived from well logs by Williams and Chadwick (2012), while the parameters for thelower medium are from Carcione et al. (2006), in which K0 = 40GPa, μ0 = 38GPa, ρ0 = 2.6g/cm3 forgrain moduli and density, Kdry = 1.37GPa, μdry = 0.82GPa for the dry rock moduli. The porosity andpermeability are assumed to be 37% and 1.6D respectively. The saturated fluid properties are KCO2 =


0.025GPa, KBrine = 2.61GPa, ρCO2 = 0.505g/cm3, ρBrine = 1.032g/cm3, ηCO2 = 0.00002Pa.s, ηBrine =0.0012Pa.s.

Figure 1 displays the P-wave velocity (a) and attenuation (b) varying with CO2 saturation Sg and theradius of outer sphere b, at 50Hz. The P-wave velocities are maximum at full brine saturation. Thesevelocity values decrease with increasing CO2 saturation. A slower reduction of velocity is seen forlarger values of b. For a high gas saturation zone (more than 50%), there is almost no velocity change.Vp reaches its minimum value at full gas saturation. Figure 1(b) shows that high attenuation (redcolour) occurs when Sg is less than 40% and b is between 0.2m and 0.6m. We see maximumattenuation at Sg about 15% and 0.2m of b size.

(a) (b)Figure 1 P-wave velocity (a) and attenuation (b) varying with CO2 saturation and the radius of outersphere b when the frequency is 50Hz.

(a) (b)Figure 2 The relation of P-wave velocity (a) and attenuation (b) with CO2 saturation at 10Hz, 50Hz,100Hz when the radius of outer sphere b is 0.3m.

Figure 2 displays the P-wave velocity (a) and attenuation (b) as a function of Sg at 10Hz, 50Hz and100Hz. For (a) we see a drastic drop of Vp between the interval of full brine saturation and 20% CO2saturation at 10Hz. This drop is moderate and extends to about 60% Sg for 50Hz and 100Hz. Aninteresting phenomenon is that Vp for the three frequencies tends to be stable after 60% of gassaturation, which can be defined as the critical saturation. Figure 2(b) shows the attenuation as afunction of Sg. There is no attenuation when the saturating fluid is single CO2 or brine. Highattenuation occurs at low gas saturation. Figure 3(a) displays the Vp varying with frequency fordifferent radius of outer shell, when the CO2 saturation is 20%. We can see a frequency regime inwhich dispersion occurs, moving towards the low frequency band with increasing size of the fluidsaturated sphere. A value of b around 0.3m corresponds to velocity dispersion in the seismic band.Figure 3(b) displays attenuation varying with frequency for 20% CO2 saturation. Figure 4(a) displaysthe frequency-dependent PP reflection coefficient varying with incident angle with different values of


Sg and b. We can see enhanced reflectivity when CO2 saturation increases. A notable frequency-dependence of reflectivity happens when Sg = 20% and b = 0.3m.

(a) (b)Figure 3 P-wave velocity (a) and attenuation (b) as a function of frequency for different radius ofouter sphere b when the CO2 saturation is 20%. b is given with 5 different values 0.01m, 0.1m, 0.2m,0.3m, 0.5m.

(a) Sg = 0%, b = 0.01m (b) Sg = 20%, b = 0.15m

(c) Sg = 20%, b = 0.3m (d) Sg = 100%, b = 0.3mFigure 4 The frequency-dependent PP reflectivity at 10Hz, 50hz, 100Hz when changing CO2saturation and b.

Since the effect of Sg and b on reflectivity is obvious, it is possible to invert the two parameters fromfrequency-dependent seismic amplitude using a simulated annealing algorithm. The objective functionΦ can be defined as the sum of the square of the error between forward modelling data f(Sg, b) andobserved data d. The observed data is generated by adding 5% Gaussian noise to the forwardmodeling data when Sg = 20% and b = 0.30m. Sg and b are searched in the intervals of [0%, 100%]and [0m, 1m], with the initial values of 50% and 0.5m respectively. The inversion result is 21.92% forSg and 0.3354m for b. Figure 5 displays the fitting result and the objective function for each effectiveiteration.


(a) (b)Figure 5 (a) The fitting of forward modeling data (curves) to noise data (* symbols), and (b) theobjective function changes with iteration.

Conclusions

This paper analyses seismic velocity dispersion and attenuation from a CO2 saturated zone usingWhite’s patchy saturation model. The results shows that the radii of gas pocket a and the outer sphereb have an effect in the frequency band, so that velocity dispersion and attenuation occur. Frequency-dependence of PP reflection in the seismic band are obvious, with appropriate a and b values. Resultsalso show that velocity dispersion is obvious as soon as CO2 saturation is introduced and is less than50%. Numerical modelling of inversion for Sg and b from frequency-dependent reflections showsfeasibility to estimate the two parameters from real seismic data.

Acknowledgements

The author would like to thank Dr. Xiang-Yang Li, Dr. Mark Chapman and Dr. Hengchang Dai forconversations and suggestions on this topic. This work was supported by the sponsors of theEdinburgh Anisotropy Project (EAP), and is presented with the permission of the Executive Directorof the British Geological Survey (Natural Environment Research Council).

References

Brie, A., Pampuri, F., Marsala, A.F. & Meazza, O. [1995] Shear sonic interpretation in gas-bearingsands, SPE Annual Technical Conf., nr. 30595, 701-710.Carcione, J. M., Picotti, S., Gei, D. & Rossi, G. [2006] Physics and seismic modeling for monitoringCO2 storage. Pure and Applied Geophysics, 163, 175-207.Chapman M., Liu E. & Li X.-Y. [2006] The influence of fluid sensitive dispersion and attenuation onAVO analysis. Geophysical Journal International, 167, 89-105.Chapman M., Zatsepin S.V. & Crampin S. [2002] Derivation of a microstructural poroelastic model.Geophysical Journal International, 151, 427-451.Eiken, O., Brevik, I., Arts, R. Lindeberg, E. & Fagervik, K. [2000] Seismic monitoring of CO2injected into a marine acquifer. 70th annual SEG meeting, Expanded Abstracts, 1623-1626.Mavko, G., Mukerji, T. & Dvorkin, J. [1998] The Rock Physics Handbook: Tools for SeismicAnalysis in Porous Media. Cambridge University Press, Cambridge, UK.Schoenberg, M. & Protazio, J. [1992] ‘Zoeppritz’ rationalized and generalized to anisotropy, J. Seism.Explor., 1, 125-144.White, J. E. [1975] Computed seismic speeds and attenuation in rocks with partial gas saturation:Geophysics, 40(2), 224-232.Williams, G. & Chadwick, A. [2012] Quantitative seismic analysis of a thin layer of CO2 in theSleipner injection plume. Geophysics, 77(6), R245-R256.Wu, X., Chapman, M., Li, X.-Y. & Boston, P. [2014] Quantitative gas saturation estimation byfrequency-dependent amplitude-versus-offset analysis, Geophys. Prospect., 62(6), 1224-1237.

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