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

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 10(1) 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 is an element of[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 is an element of [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.