A B S T R A C TThe dependence of fluid-saturated rocks' elastic properties to the measuring frequency is related to fluid-flow phenomena at different scales. In the frequency range of [10 −3 , 10 6 ] Hz, for fully saturated rocks, two phenomena have been experimentally documented: (i) the drained/undrained transition (i.e., global flow), and (ii) the relaxed/unrelaxed transition (i.e., local flow). When investigating experimentally those effects or comparing different measurements in rocks, one needs to account for both the boundary conditions involved and the method of measurement used. A onedimensional poroelastic model is presented, which aims at calculating the expected poroelastic response during an experiment. The model is used to test different sets of boundary conditions, as well as the role of the measuring setup, i.e., local (strain gauges) or global (linear variable differential transformer) strain measurement. Four properties are predicted and compared with the measurements, i.e., bulk modulus, bulk attenuation, pseudo-Skempton coefficient, and pore pressure phase shift. For the drained/undrained transition, because fluid pressure may not be homogeneous in the sample, local and global measurements are predicted to differ. Furthermore, the existence of a dead volume at both sample's ends is shown to be important. Due to the existence of the dead volume, an interplay between sample's and dead volumes' storage capacity determines both the magnitudes and the frequency dependence of the dispersion/attenuation measurements. The predicted behaviours are shown to be consistent with the measurements recently reported on very compressible and porous sandstone samples.

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.

Because measuring the frequency dependence of elastic properties in the laboratory is a technical challenge, not enough experimental data exist to test the existing theories. We report measurements of three fluid‐saturated sandstones over a broad frequency band: Wilkenson, Berea, and Bentheim sandstones. Those sandstones samples, chosen for their variable porosities and mineral content, are saturated by fluids of varying viscosities. The samples elastic response (Young's modulus and Poisson's ratio) and hydraulic response (fluid flow out of the sample) are measured as a function of frequency. Large dispersion and attenuation phenomena are observed over the investigated frequency range. For all samples, the variation at lowest frequency relates to a large fluid flow directly measured out of the rock samples. These are the cause (i.e., fluid flow) and consequence (i.e., dispersion/attenuation) of the transition between drained and undrained regimes. Consistently, the characteristic frequency correlates with permeability for each sandstone. Beyond this frequency, a second variation is observed for all samples, but the rocks behave differently. For Berea sandstone, an onset of dispersion/attenuation is expected from both Young's modulus and Poisson's ratio at highest frequency. For Bentheim and Wilkenson sandstones, however, only Young's modulus shows dispersion/attenuation phenomena. For Wilkenson sandstone, the viscoelastic‐like dispersion/attenuation response is interpreted as squirt flow. For Bentheim sandstone, the second effect does not fully follow such response, which could be due to a lower accuracy in the measured attenuation or to the occurence of another physical effect in this rock sample.

The frequency dependence of seismic properties of fully saturated rocks can be related to wave‐induced fluid flows at different scales. The elastic dispersion and attenuation of four fluid‐saturated carbonate rocks, with different microstructures, have been measured over a broad frequency range in the laboratory. The selected rocks were a presalt coquina from offshore Congo, an Urgonian limestone from Provence (France), and an Indiana limestone either intact or thermally cracked. The selected samples present a variety of pore types characteristic of carbonates, and their link with potential squirt flow dispersion was investigated. To cover a broad frequency range, forced oscillations (0.004 to 100 Hz) and ultrasonic (1 MHz) measurement techniques were performed in a triaxial cell, at various differential pressures, on the samples saturated by fluids of different viscosity. Both hydrostatic and axial oscillations were applied in order to get the different dynamic moduli. For all our samples, the drained/undrained transition and the squirt flow mechanisms were characterized experimentally, in terms of amplitude of dispersion, amount of viscoelastic attenuation, and frequency ranges. Biot‐Gassmann's theory was found to apply mainly at seismic frequencies (10–100 Hz). A potential correlation between pore type and possible squirt flow dispersion was investigated. Intragranular microporosity, with either a rimmed or uniform distribution, does not seem to generate any substantial dispersion. On the other hand, cracked intergranular cement and uncemented grain contacts seem to generate substantial squirt flow dispersion, at respectively seismic and sonic log frequencies.

Quantitatively assessing seismic attenuation caused by fluid pressure diffusion (FPD) in partially saturated rocks is challenging because of its sensitivity to the spatial fluid distribution. To address this challenge we performed depressurization experiments to induce the exsolution of carbon dioxide from water in a Berea sandstone sample. In a first set of experiments we used medical X‐ray computed tomography (CT) to characterize the fluid distribution. At an equilibrium pressure of approximately 1 MPa and applying a fluid pressure decline rate of approximately 0.6 MPa per minute, we allowed a change in saturation of less than 1%. The gas was heterogeneously distributed along the length of the sample, with most of the gas exsolving near the sample outlet. In a second set of experiments, at the same pressure and temperature, following a very similar exsolution protocol, we measured the frequency dependent attenuation and modulus dispersion between 0.1 and 1,000 Hz using the forced oscillation method. We observed significant attenuation and dispersion in the extensional and bulk deformation modes, however, not in the shear mode. Lastly, we use the fluid distribution derived from the X‐ray CT as an input for numerical simulations of FPD to compute the attenuation and modulus dispersion. The numerical solutions are in close agreement with the attenuation and modulus dispersion measured in the laboratory. Our approach allows for accurately relating attenuation and dispersion to the fluid distribution, which can be applied to improving the seismic monitoring of the subsurface.

Fluid pressure diffusion occurring on the microscopic scale is believed to be a significant source of intrinsic attenuation of mechanical waves propagating through fully saturated porous rocks. The so‐called squirt flow arises from compressibility heterogeneities in the microstructure of the rocks. To study squirt flow experimentally at seismic frequencies the forced oscillation method is the most adequate, but such studies are still scarce. Here we present the results of forced hydrostatic and axial oscillation experiments on dry and glycerine‐saturated Berea sandstone, from which we determine the dynamic stiffness moduli and attenuation at micro‐seismic and seismic frequencies (0.004–30 Hz). We observe frequency‐dependent attenuation and the associated moduli dispersion in response to the drained–undrained transition (∼0.1 Hz) and squirt flow (>3 Hz), which are in fairly good agreement with the results of the corresponding analytical solutions. The comparison with very similar experiments performed also on Berea sandstone in addition shows that squirt flow can potentially be a source of wave attenuation across a wide range of frequencies because of its sensitivity to small variations in the rock microstructure, especially in the aspect ratio of micro‐cracks or grain contacts.

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Using the forced oscillation method and the ultrasonic transmission method, we measure the elastic moduli of a clay‐bearing Thüringen sandstone under dry and water‐saturated conditions in a broad frequency band at [0.004–10, 106] Hz for different differential pressures up to 30 MPa. Under water‐saturated condition, clear dispersion and attenuation for Young's modulus, Poisson's ratio, and Bulk modulus are observed at seismic frequencies, except for shear modulus. The measured dispersion and attenuation are mainly attributed to the drained/undrained transition, which considers the experimentally undrained boundary condition. Gassmann's predictions are consistent with the measured undrained bulk moduli but not with the shear moduli. Clear shear weakening is observed, and this water‐softening effect is stronger at seismic frequencies than at ultrasonic frequencies where stiffening effect related to squirt flow may mask real shear weakening. The reduction in surface free energy due to chemical interaction between pore fluid and rock frame, which is not taken into account by Gassmann's theory, is the main reason for the departure from Gassmann's predictions, especially for this rock containing a large number of clay minerals.