A viscoelastic representation of seismic wave attenuation and dispersion caused by wave-induced fluid flow in fractured porous media

Lan, H.T., Chen, S.M., Chi, H.Z., Pei, J.Y., Lin, W. and Shen, J.G., 2020. A viscoelastic representation of seismic wave attenuation and dispersion caused by wave-induced fluid flow in fractured porous media. Journal of Seismic Exploration, 29: 587-601. Analyzing and understanding the seismic response from fractured reservoirs is vital to reservoirs characterization and the production optimization of hydrocarbons. Fractured reservoirs can be modeled as fractured porous media. When seismic waves propagate in fractured porous media, fluid exchange occurs between the fractures and the pore space. As a consequence, the seismic waves are subject to attenuation and dispersion, the media behave viscoelasticity, and the components of the effective stiffness tensor involved in the stress-strain relation become complex-valued and frequency dependent. In order to compute synthetic seismograms in the time domain with the purpose of studying seismic response of the media, an efficient approach is to approximate the stiffnesses by suitable viscoelastic models and then solve viscoelastic differential equations. In this paper, based on the Chapman's model of fractured porous media, we use the Zener model to approximate each component of the effective stiffness tensor, and use the Christoffel equation to obtain the seismic attenuation and velocity dispersion curves and their corresponding Zener model best fits. We focused on three models, each with two different fracture sizes and filled with different fluids. Our results indicate that the Zener model provides a good representation for Chapman's model of fractured porous media.
- Al-Harrasi, O.H., Kendall, J.M. and Chapman, M., 2011. Fracture characterization usingfrequency-dependent shear wave anisotropy analysis of microseismic data. Geophys.J. Internat., 185: 1059-1070.
- Ba, J., Carcione, J.M., Du, O., Zhao, H. and Miiller, T.M., 2015. Seismic Exploration of
- Hydrocarbons in Heterogeneous Reservoirs, New Theories, Methods and
- Applications. Elsevier Science Publishers, Amsterdam.
- Baird, A.F., Kendall, J.M. and Angus, D.A., 2013. Frequency-dependent seismicanisotropy due to fractures: Fluid flow versus scattering. Geophysics., 78:WAI11-WA122.
- Batzle, M., Hofmann, R., Han, D. and Castagna, J., 2001. Fluids and frequencydependent seismic velocity of rocks. The Leading Edge., 20: 168-171.
- Carcione, J.M., 1995. Constitutive model and wave equations for linear, viscoelastic,anisotropic media. Geophysics., 60: 537-548.
- Carcione, J.M., 2000. A model for seismic velocity and attenuation in petroleum sourcerocks. Geophysics., 65: 1080-1092.
- Carcione, J.M. and Picotti, S., 2006. P-wave seismic attenuation by slow-wave diffusion:
- Effects of inhomogeneous rock properties. Geophysics., 71: O1-O8.
- Carcione, J.M., 2014. Wave Fields in Real Media. Theory and Numerical Simulation of
- Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media,3rd ed., extended and revised. Elsevier Science Publishers, Amsterdam.
- Chapman, M., 2003. Frequency dependent anisotropy due to mesoscale fractures in thepresence of equant porosity. Geophys. Prosp., 51: 369-379.
- Chapman, M., Maultzsch, S., Liu, E. and Li, X.Y., 2003. The effect of fluid saturation inan anisotropic multi-scale equant porosity model. J. Appl. Geophys., 54: 191-202.
- Chapman, M., Liu, E. and Li, X.Y., 2006. The influence of fluid-sensitive dispersion andattenuation on AVO analysis. Geophys. J. Internat., 167: 89-105.
- Chapman, M., 2009. Modeling the effect of multiple fracture sets of mesoscale fracturesin porous rock on frequency-dependent anisotropy. Geophysics., 74: D97-D103.
- Chesnokov, E.M., Queen, J.H., Vichorev, A., Lynn, H.B., Hooper. J., Bayuk, I.,
- Castagna, J. and Roy, B., 2001. Frequency dependent anisotropy. Expanded Abstr.,71st Ann. Internat. SEG Mtg., San Antonio: 2120-3.
- Dasgupta. R. and Clark, R.A., 1998. Estimation of Q from surface seismic reflection data.Geophysics., 63: 2120-2128.
- Dasios, A., Astin, T. and McCann, C., 2001. Compressional-wave Q estimation fromfull-waveform sonic data. Geophys. Prosp., 49: 353-373.
- Galvin, R.J. and Gurevich, B., 2007. Effective properties of a poroelastic mediumcontaining a distribution of aligned cracks. J. Geophys. Res., 114: B07305.
- Gurevich, B., Brajanovski, M., Galvin, R., Miller, T.M. and Toms-Stewart, J., 2009.
- P-wave dispersion and attenuation in fractured and porous reservoirs-Poroelasticityapproach. Geophys. Prospect., 57: 225-237.
- Johnson, D. L., 2001. Theory of frequency dependent acoustics in patchy saturatedporous media. J. Acoust. Soc. Am., 110: 682-694.
- Klimentos, T., 1995. Attenuation of P- and S-waves as a method of distinguishing gasand condensate from oil and water. Geophysics., 60: 447-458.
- Liu, E., Queen, J.H., Li, X.Y., Maultzsch, M.S., Lynn, H.B. and Chesnokov, E.M., 2003.
- Observation and analysis of frequency-dependent anisotropy from amulticomponent VSP at Bluebell-Altamont field, Utah. J. Appl. Geophys., 54:319-333.
- Liu, X., Greenhalgh, S. and Zhou, B., 2009. Transient solution for poro-viscoacousticwave propagation in double porosity media and its limitations. Geophys. J. Internat.,178: 375-393.
- Maultzsch, S., Chapman, M., Liu, E. and Li, X.Y., 2003. Modellingfrequency-dependent seismic anisotropy in fluid-saturated rock with alignedfractures: Implication of fracture size estimation from anisotropic measurements.Geophys. Prosp., 51: 381-392.
- Mavko, G., Mukerji, T. and Dvorkin, J., 2009. The Rock Physics Handbook, 2nd ed.Cambridge University Press, Cambridge.
- Miiller, T.M. and Gurevich, B., 2004. One-dimensional random patchy saturation modelfor velocity and attenuation in porous rocks. Geophysics., 69: 1166-1172.
- Miller, T.M., Toms-Stewart, J. and Wenzlau, F., 2008. Velocity-saturation relation forpartially saturated rocks with fractal pore fluid distribution. Geophys. Res. Lett., 26:L09306.
- Miller, T.M., Gurevich, B. and Lebedev, M., 2010. Seismic wave attenuation anddispersion resulting from wave-induced flow in porous rocks - a review.Geophysics., 75: 147-164.
- Parra, J.O., 2000. Poroelastic model to relate seismic wave attenuation and dispersion topermeability anisotropy. Geophysics., 65: 202-210.
- Picotti, S., Carcione, J.M., Rubino, J.G., Santos, J.E. and Cavallini, F., 2010. Avisoelastic representation of wave attenuation in porous media. Comput.Geosci-UK., 36: 44-53.
- Picotti, S., Carcione, J.M., Gei, D., Rossi, G. and Santos, J.E., 2012. Seismic modeling tomonitor CO2 geological storage: The Atzbach-Schwanenstadt gas field. J. Geophys.Res., 117: B06103.
- Pride, S.R., Berryman, J.G. and Harris, J.M., 2004. Seismic attenuation due towave-induced flow. J. Geophys. Res., 109: B01201.
- Quintal, B., Schmalholz, S.M. and Podladchikov, Y.Y., 2009. Low-frequency reflectionsfrom a thin layer with high attenuation caused by interlayer flow. Geophysics., 74:N14-22.
- Rapoport, M.B., Rapoport, L.I. and Ryjkov, V.I., 2004. Direct detection of oil and gasfields based on seismic inelasticity effect. The Leading Edge., 23: 276-278.
- Sun, L.F., Milkereit, B. and Schmitt, D.R., 2009. Measuring velocity dispersion andattenuation in the exploration seismic frequency band. Geophysics., 74:WA113-122.
- White, J.E., 1975. Computed seismic speed sand attenuation in rocks with partial gassaturation. Geophysics., 40: 224-232.
- White, J.E., Mikhaylova, G. and Lyakhovitskiy, F.M., 1975. Low-frequency seismicwaves in fluid-saturated layered rocks. Izvestija Academy of Sciences USSRPhysics of the Solid Earth, 11: 654-659.