Dispersion and attenuation due to scattering from heterogeneities of the frame bulk modulus of a poroelastic medium

2010 ◽  
Vol 127 (6) ◽  
pp. 3372-3384 ◽  
Author(s):  
Brian T. Hefner ◽  
Darrell R. Jackson
Keyword(s):  
Bulk Modulus ◽  
Poroelastic Medium ◽  
Dispersion And Attenuation

Viscous deformation of unconsolidated reservoir sands—Part 2: Linear viscoelastic models

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 742-751 ◽  
Author(s):  
Paul N. Hagin ◽  
Mark D. Zoback
Keyword(s):  
Bulk Modulus ◽  
Creep Strain ◽  
Power Law ◽  
Creep Model ◽  
Model Parameters ◽  
Solid Models ◽  
Dispersion Data ◽  
Cyclic Loading Tests ◽  
Almost All ◽  
Dispersion And Attenuation

Laboratory creep experiments show that dry unconsolidated reservoir sands follow a power law function of time (at constant stress), and cyclic loading tests (at quasi‐static frequencies of 10−6 to 10−2 Hz) show that the bulk modulus increases by a factor of two with increasing frequency while attenuation remains constant. In this paper, we attempt to model these observations using linear viscoelasticity theory by considering several simple phenomenological models. We investigated two classes of models: spring‐dashpot models, which are represented by exponential functions with a single relaxation time, and power law models. Although almost all of the models considered were capable of fitting the creep data with time, they result in very different predictions of attenuation and bulk modulus dispersion. We used the model parameters derived from fitting the creep strain to predict the bulk modulus dispersion and attenuation as a function of frequency, to find a single phenomenological model (and model parameters) that could explain the material's creep response with time as well as its dispersion and attenuation characteristics. Spring‐dashpot models, such as the Burgers and standard linear solid models, produce reasonable fits to the creep strain and bulk modulus dispersion data, but do not reproduce the attenuation data. We find that a combined power law–Maxwell creep model adequately fits all of the data. Extrapolating the power law–Maxwell creep model out to 30 years (to simulate the lifetime of a reservoir) predicts that the static bulk modulus is only 25% of the dynamic modulus. Including the instantaneous component of deformation into the previous prediction results in 2% total vertical strain at the wellbore, in good agreement with field observations.

scholarly journals Rigorous bounds for seismic dispersion and attenuation due to wave-induced fluid flow in porous rocks

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. L45-L51 ◽  
Author(s):  
Boris Gurevich ◽  
Dina Makarynska
Keyword(s):  
Bulk Modulus ◽  
Inviscid Fluid ◽  
Porous Rocks ◽  
Shear Moduli ◽  
Poroelastic Media ◽  
Viscous Shear ◽  
Rigorous Bounds ◽  
Shear Relaxation ◽  
Wave Induced ◽  
Dispersion And Attenuation

The Hashin-Shtrikman (HS) bounds define the range of bulk and shear moduli of an elastic composite, given the moduli of the constituents and their volume fractions. Recently, the HS bounds have been extended to the quasi-static moduli of composite viscoelastic media. Because viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on the complex plane. We analyze these general viscoelastic bounds for a particular case of a porous solid saturated with a Newtonian fluid. In our analysis, for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semicircle and a segment of the real axis, connecting formal HS bounds that are computed for an inviscid fluid. Importantly, viscoelastic bounds for poroelastic media turn out to be independent of frequency. However, because the bounds are quasi-static, the frequency must be much lower than Biot’s characteristic frequency. Furthermore, we find that the bounds for the bulk modulus are attainable (realizable). We also find that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot’s global flow dispersion, because the latter strongly depends on inertial forces.

scholarly journals Seismic Dispersion and Attenuation in Fluid‐Saturated Carbonate Rocks: Effect of Microstructure and Pressure

2019 ◽  
Vol 124 (12) ◽  
pp. 12498-12522 ◽  
Author(s):  
Jan V. M. Borgomano ◽  
Lucas X. Pimienta ◽  
Jérôme Fortin ◽  
Yves Guéguen
Keyword(s):  
Carbonate Rocks ◽  
Dispersion And Attenuation ◽  
Effect Of Microstructure
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