Dispersion and attenuation measurements of the elastic moduli of a dual‐porosity limestone

Abstract

The dispersion and the attenuation of the elastic moduli of a Lavoux limestone have been measured over a large frequency range: 10−3 Hz to 101 Hz and 1 MHz. The studied sample comes from a Dogger outcrop of Paris Basin and has the particularity to have a bimodal porosity distribution, with an equal proportion of intragranular microporosity and intergranular macroporosity. In addition to ultrasonic measurements, two different stress‐strain methods have been used in a triaxial cell to derive all the elastic moduli at various differential pressures. The first method consists of hydrostatic stress oscillations (f∈[0.004;0.4] Hz), using the confining pressure pump, from which the bulk modulus was deduced. The second method consists of axial oscillations (f∈[0.01;10] Hz), using a piezoelectric oscillator on top of the sample, from which Young's modulus and Poisson's ratio were deduced. With the assumption of an isotropic medium, the bulk modulus (K) and the shear modulus (G) can also be computed from the axial oscillations. The sample was studied under dry, glycerin‐ and water‐saturated conditions, in order to scale frequency by the viscosity of the fluid. Results show a dispersion at around 200 Hz for water‐saturated conditions, affecting all the moduli except the shear modulus. This dispersion is related to the drained/undrained transition, and the bulk modulus deduced from the axial and hydrostatic oscillations are consistent with each other and with Biot‐Gassmann's equations. No dispersion has been detected beyond that frequency. This was interpreted as the absence of squirt flow or local diffusion between the microporous oolites and the macropores.

Fluid Substitution and Shear Weakening in Clay‐Bearing Sandstone at Seismic Frequencies

“…To assess the uncertainty for hydrostatic oscillation, we follow Borgomano et al's () procedure using statistical analysis of a set of measurements. For bulk modulus K hydro with uncertainty u ( K hydro ), the relative uncertainty is u ( K hydro )/ K hydro .…”

“… and are the phase angles of the axial and radial strain of the sample, respectively. The other elastic properties can be deduced from the combination of the obtained stress and strain (Batzle et al, ; Birch, ; Borgomano et al, ), where K and are the bulk modulus and corresponding attenuation, respectively. G and are the shear modulus and corresponding attenuation, respectively.…”

“…A pseudo‐Skempton coefficient B * for hydrostatic oscillation and a pseudoconsolidation coefficient γ * for axial oscillation are defined to be the ratios of the induced fluid pressure measured in the dead volume to the change in applied stress (Pimienta et al, , ), where is the oscillating fluid pressure around the mean fluid pressure. The equivalent volumetric stress σ ii /3 can be expressed as Δ P c for hydrostatic oscillation and σ axial /3 for axial oscillation (Borgomano et al, ). Normally, B * = 3 γ * .…”

Pressure and Fluid Effect on Frequency‐Dependent Elastic Moduli in Fully Saturated Tight Sandstone

“…The shear wave velocities show similar frequency and pressure dependence with compressional wave velocities in the low‐frequency range, so that only the compressional velocities for the tight sandstone under nitrogen gas (dry), brine, and glycerin saturation are shown in Figure . The results are illustrated as a function of apparent frequency f *, which is defined as f * = f ( η / η 0 ), where η 0 and η are the viscosities of brine and of concerned fluid, respectively (Borgomano et al, ; Pimienta et al, , , ; Spencer & Shine, ). This parameter modifies the measurement frequency based on the viscosity of the saturated fluid and allows comparison of corresponding scaled values in a broad frequency range.…”

“…Well‐designed experiments and systematic analysis have been conducted to study the influence of different types of fluids mainly on conventional sandstones, especially with pure minerals, such as Berea sandstone and Fontainebleau sandstone (Chapman et al, , ; Pimienta, Fortin, & Guéguen, , ). Several studies have been undertaken on carbonate rocks with complicated pore structures (Adam et al, ; Adam, Batzle, & Brevik, ; Borgomano et al, ; Mikhaltsevitch, Lebedev, & Gurevich, ) and on shales with anisotropic properties (Delle Piane et al, ; Hofmann, ; Mikhaltsevitch, Lebedev, & Gurevich, , ; Szewczyk, Bauer, & Holt, ). However, the number of measurements for tight sandstones at low frequencies is still small.…”