Soutenance de Thèse: Comparison of the elastic properties of rocks at different scales: link between seismic, sonic and ultrasonic measurements

Abstract: “How do we extrapolate laboratory – measured rock properties which are determined on centimeter-sized samples, to field-scale problems measured in kilometers?” is a quote from Yves Guéguen and Victor Palciauskas book the “Introduction to the physics of rocks” published 20 years ago. It is an interesting question, as usually in science any theoretical solution should be tested experimentally to be validated. This can be quite challenging when there are no labs that can test to scale phenomenon which are studied in the field in geosciences. Therefore, it becomes crucial to understand the different mechanics which can arise when upscaling. Here I will focus on the elastic wave properties under in situ condition, and in particular I focus on how different heterogeneities (mesoscopic and fractures) can alter the way elastic waves propagate through a saturated porous media - rock. Three sets of laboratory tests were conducted using a triaxial cell which allows for dry, water, brine and glycerin saturated sample conditions, under pressure while forced oscillation and ultrasonic transmission methods were used to extract elastic properties from the samples being tested. The first barrage of tests was performed on three carbonate samples. One of these samples is homogeneous and is used as a comparison. The other two samples were heterogeneous. When studying the elastic properties within the apparent frequency range (10-2 to 105 and 106 Hz), two distinct attenuation peaks were observed in the heterogeneous samples and only one was observed in the homogeneous sample. The peak observed in all three samples occurred at a frequency around 40 kHz. This attenuation mechanism was related to squirt flow, which occurs at the microscopic level and is related to the aspect ratio of the pre-existing cracks present in all three samples. The second attenuation peak was observed around 100 Hz. This attenuation mechanism was related to mesoscopic flow between regions of varying porosity. Using the hydraulic diffusivity of the sample and cut-off frequency observed, the length of diffusion was calculated which was in good agreement with what was seen in the CT scans. A 3D numerical model was also developed and corroborated the experimental results. Next, low frequency (0.04 to 1 Hz frequency range) hydrostatic oscillation tests were performed on intact and fractured carbonate Rustrel samples, at three effective pressures in dry and water saturated conditions. The apparent bulk modulus and attenuation were extracted along the whole frequency range showing no dispersion in the dry case or in the intact case. However, there was negative phase shift between stress and strain in the fractured case in water saturated conditions at lower effective pressures which disappeared at the highest effective pressure. A 1D analytical model and 3D numerical model were developed, which explained the behavior, underlining the critical parameters (fracture compliance and fracture geometry) relevant to the local negative phase shift associated to fracture to pore space fluid pressure diffusion (FPD). Finally, two perpendicular saw cut fractures were made in a Solnhofen limestone sample, then the saw cut sample was tested, within a frequency range of 0.2 to 40 Hz, in undrained glycerin saturated conditions using the axial oscillation test performed at multiple effective pressures. The normalized Young’s modulus and attenuation were extracted, which highlighted an attenuation peak at 2 Hz frequency, having a maximum amplitude of 0.07 at the lowest effective pressure of 5 MPa, interpreted as a fracture to fracture fluid pressure diffusion. A 3D numerical model was developed and used which corroborated the experimental data. Jury: Daniel BRITO (Université de Pau et des Pays de l'Adour) : Rapporteur / Yves LEROY (Imperial College London) : Rapporteur / Béatriz QUINTAL (Université de Lausanne) : Examinator / Alexandre SCHUBNEL (ENS) : Examinator / Jérôme FORTIN (ENS) : director / Jan BORGOMANO (Modis) : Invited