scholarly journals Ultrasonic moduli for fluid-saturated rocks: Mavko-Jizba relations rederived and generalized

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. N25-N30 ◽  
Author(s):  
Boris Gurevich ◽  
Dina Makarynska ◽  
Marina Pervukhina
Keyword(s):  
Elastic Wave ◽  
Bulk Modulus ◽  
Quantitative Model ◽  
Pore Fluid ◽  
Porous Rocks ◽  
Laboratory Measurements ◽  
Shear Moduli ◽  
Wave Velocities

Mavko and Jizba propose a quantitative model for squirt dispersion of elastic-wave velocities between seismic and ultrasonic frequencies in granular rocks. Their central results are the expressions for the so-called unrelaxed frame bulk and shear moduli computed under an assumption that the stiff pores are drained (or dry) but the soft pores are filled with fluid. Mavko-Jizba expressions are limited to liquid-saturated rocks but become inaccurate when the fluid-bulk modulus is small (e.g., for gas-saturated rocks). We have derived new expressions for unrelaxed moduli of fluid-saturated porous rocks using Sayers-Kachanov discontinuity formalism. The derived expressions generalize the established Mavko-Jizba relations to gas-saturated rocks, reduce to Mavko-Jizba results when the pore fluid is liquid, and yield dry moduli when fluid-bulk modulus tends to zero. We tested this by comparing our model and the model of Mavko and Jizba against laboratory measurements on a sample of Westerly granite.

The influence of pore fluids and frequency on apparent effective stress behavior of seismic velocities

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N1-N7 ◽  
Author(s):  
Gary Mavko ◽  
Tiziana Vanorio
Keyword(s):  
Elastic Wave ◽  
Bulk Modulus ◽  
Effective Stress ◽  
High Frequency ◽  
Laboratory Data ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Stress Behavior ◽  
Stress Coefficient ◽  
The Impact

Although poroelastic theory predicts that the effective stress coefficient equals unity for elastic moduli in monomineralic rocks, some rock elastic wave velocities measured at ultrasonic frequencies have effective stress coefficients less than one. Laboratory effective stress behavior for P-waves is often different than S-waves. Furthermore, laboratory ultrasonic velocities almost always reflect high-frequency artifacts associated with pore fluids, including an increase in velocities and flattening of velocity-versus-pressure curves. We have investigated the impact of pore fluids and frequency on the observed effective stress coefficient for elastic wave velocities by developing a model that calculates pore-fluid effects on velocity, including high-frequency squirt dispersion, and we have compared the model’s predictions with laboratory data. We modeled a rock frame with penny-shaped cracks for three situations: vacuum dry, saturated with helium, and saturated with brine. Even if the frame modulus depends only on the differential stress, the saturated-rock effective stress coefficient is predicted to be significantly less than one at ultrasonic frequencies because of two effects: an increase in the fluid bulk modulus with increasing pressure and the contribution of high-frequency squirt dispersion. The latter effect is most significant in soft fluids (helium in this experiment) in which the fluid-bulk modulus is less than or comparable to the thin-crack pore stiffness.

Incorporating mechanisms of fluid pressure relaxation into inclusion‐based models of elastic wave velocities

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1173-1181 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Water Saturation ◽  
Laboratory Data ◽  
Fluid Pressure ◽  
P Wave ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Exact Agreement ◽  
Flow Through

Our new method incorporates fluid pressure communication into inclusion‐based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid‐filled inclusions. We illustrate this approach with two models: (1) flow between nearest‐neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P‐wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water‐saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near‐exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion‐based models at high frequencies.

Elastic wave velocities during evaporative drying

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 171-183 ◽  
Author(s):  
David Goertz ◽  
Rosemary Knight
Keyword(s):  
Elastic Wave ◽  
Pore Space ◽  
Fluid Distribution ◽  
Drying Process ◽  
Shear Moduli ◽  
Velocity Saturation ◽  
Wave Velocities ◽  
Three Samples ◽  
Rate Period ◽  
Drying Rates

Laboratory measurements of drying rates and elastic wave velocities are made on limestone, dolomite, and sandstone samples during evaporative drying. The drying rate data are very similar in form. There is a constant rate period at higher saturations and a falling rate period below saturation levels of approximately 0.2. The falling rate period marks the transition in the sample from hydraulically connected to disconnected water. There is a strong link between elastic wave velocities and the drying process because different pore geometries drain at different stages in drying. The drainage of these different geometries results in specific changes in the moduli and velocities. Simple models of the pore geometries and the drying process are used to model the velocity data. The velocity‐saturation relationship for each of the three samples is very different in form because of differences in pore‐space microgeometry. Of particular interest is the velocity response during the falling rate period of drying. In the limestone and the sandstone, there is a significant decrease in bulk and shear moduli and elastic wave velocities because of the drainage of crack‐like pores and grain contacts. In contrast, the absence of these pore geometries in the dolomite results in essentially no changes in the moduli at low saturations. An understanding of the drying process and resulting pore‐scale fluid distribution provides useful insights into the observed form of the velocity‐saturation relationship.

scholarly journals Effect of pore fluid pressure on elastic wave velocities of serpentinites

2014 ◽  
Vol 43 (5) ◽  
pp. 161-173
Author(s):  
Yuya HARADA ◽  
Ikuo KATAYAMA ◽  
Yoshio KONO
Keyword(s):  
Elastic Wave ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Pore Fluid Pressure ◽  
Wave Velocities

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.

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