Lucas Xan Pimienta

Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi‐static ( ) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.

Effect of supercritical CO2 on carbonates: Savonnières sample case study

ABSTRACT CO2 geosequestration is an efficient way to reduce greenhouse gas emissions into the atmosphere. Carbonate rock formations are one of the possible targets for CO2 sequestration due to their relative abundance and ability to serve as a natural trapping reservoir. The injected supercritical CO2 can change properties of the reservoir rocks such as porosity, permeability, tortuosity, and specific surface area due to dissolution and precipitation processes. This, in turn, affects the reservoir characteristics, i.e., their elastic properties, storage capacity, stability, etc. The tremendous progresses made recently in both microcomputed X‐ray tomography and high‐performance computing make numerical simulation of physical processes on actual rock microstructures feasible. However, carbonate rocks with their extremely complex microstructure and the presence of microporosity that is below the resolution of microcomputed X‐ray tomography scanners require novel, quite specific image processing and numerical simulation approaches. In the current work, we studied the effects of supercritical CO2 injection on microstructure and elastic properties of a Savonnières limestone. We used microtomographic images of two Savonnières samples, i.e., one in its natural state and one after injection and residence of supercritical CO2. A statistical analysis of the microtomographic images showed that the injection of supercritical CO2 led to an increase in porosity and changes of the microstructure, i.e., increase of the average volume of individual pores and decrease in the total number of pores. The CO2 injection/residence also led to an increase in the mean radii of pore throats, an increase in the length of pore network segments, and made the orientation distribution of mesopores more isotropic. Numerical simulations showed that elastic moduli for the sample subjected to supercritical CO2 injection/residence are lower than those for the intact sample.

Ultrasonic monitoring of spontaneous imbibition experiments: Precursory moisture diffusion effects ahead of water front

Fluid substitution processes have been investigated in the laboratory on 14 carbonate and siliciclastic reservoir rock analogues through spontaneous imbibition experiments on vertical cylindrical specimens with simultaneous ultrasonic monitoring and imaging. The motivation of our study was to identify the seismic attributes of fluid substitution in reservoir rocks, and to link them to physical processes. It is shown that (i) the P-wave velocity either decreases or increases when the capillary front reaches the Fresnel clearance zone, (ii) the P-wave amplitude is systematically impacted earlier than the velocity is, (iii) this precursory amplitude decrease occurs when the imbibition front is located outside of the Fresnel zone, (iv) the relative variation of the P-wave amplitude is always much larger than that of the P-wave velocity. These results suggest that moisture diffuses into the pore space ahead of the water front. This postulate is further supported by a quantitative analysis of the time evolution of the observed P-wave amplitudes. In a sense, P-wave amplitude acts as a precursor of the arrival of the capillary front. This phenomenon is used to estimate the effective diffusivity of moisture in the tested rocks. The effective moisture diffusivity estimated from the ultrasonic data is strongly correlated with permeability: a power-law with exponent 0.96 predicts permeability from ultrasonic monitoring within a factor 3 without noticeable bias. When the effective diffusivity is high, moisture diffusion affects ultrasonic P-wave attributes even before the imbibition starts and impacts the P-wave reflectivity as evidenced by the variations recorded in the waveform coda.

Experimental Evidence of Calcite Dissolution and Induced Precipitation during supercritical CO2 Residence

Prior to injecting CO2 in water-saturated carbonate reservoirs, one needs to investigate the effect of the residence of supercritical CO2 (SCCO2) on the rock integrity and overall physical properties. In this study, a Savonnieres limestone is characterised in terms of its physical properties, pore chemistry and textural features prior and after 2 or 4 hours SCCO2 residence under in situ stress/temperature conditions. More precisely, elastic waves (Vp and Vs) at ultrasonic frequencies, electrical resistivity (Rt), helium porosity-permeability and pore chemistry are measured before and after SCCO2 aging. In addition, X-ray CT monitoring is carried out during the different steps. While water chemistry highlights an enhanced calcite dissolution related to the duration of SCCO2 residence, a change in the physical properties is observed between the two residence steps. It is shown from the physical properties that (i) the rock building minerals were dissolved after 2 hours; and (ii) the rock overall integrity increases after 4 hours, highlighting a possible re-precipitation phenomenon.

Measured Dispersion and Attenuation Effects on the Bulk Modulus of Fully-saturated Sedimentary Rocks

Investigating experimentally the frequency dependence of elastic moduli provides quantitative informations on the dispersive effects occurring in sedimentary reservoir rocks. Using a stress-strain method, bulk modulus has been measured at varying frequencies. Prior to measuring micro-structurally complex sedimentary rocks, the experimental apparatus accuracy has been assessed using standard samples of well-known properties. Measurements of both dispersion and attenuation prove to be accurate and correlate, over the frequency range of f ~ 10-3-10-1 Hz. The method is tested on well-known, quartz-pure, Fontainebleau sandstones. Saturating fluids of differing viscosities have been used. Pressure and frequency dependence of the rocks bulk modulus have been obtained. The results are discussed in the framework of the fluid-flow theories.

Dispersion and Attenuation Measurements on a Bimodal-porosity-oolitic Limestone

Dispersion and attenuation measurements have been performed on an oolitic limestone from Lavoux. This limestone comes from a Dogger outcrop, is pure calcite, and exhibits a bimodal porosity with intragranular microporosity and intergranular macroporosity. Total porosity and permeability of the sample were measured to be respectively around 23% and 10 mD. To measure the elastic-moduli dispersion and attenuation over a wide-frequency range, we used two stress-strain methods: hydrostatic and axial oscillations. The triaxial cell used allows for low-frequency measurements (0.004 Hz to 100 Hz), and ultrasonic-velocity measurements at high frequency (1 MHz). The sample was measured under three-different-saturating conditions: dry, water and glycerine. The results show no dependence to effective pressure, which is related to the absence of cracks in the limestone. Moreover, the transition from drained to undrained regimes has been successfully measured under glycerine-saturated conditions (around 1 Hz). It corresponds to a strong dispersion (~50%). The undrained-elastic moduli are consistent with Biot-Gassmann’s theory. A weak dispersion is observed (< 12%) between the undrained-elastic moduli and the ultrasonic results that remains to be further investigated.

Development and Recovery of Stress‐Induced Elastic Anisotropy During Cyclic Loading Experiment on Westerly Granite

In the upper crust, where brittle deformation mechanisms dominate, the development of crack networks subject to anisotropic stress fields generates stress-induced elastic anisotropy. Here a rock specimen of Westerly granite was submitted to differential stress cycles (i.e., loading and unloading) of increasing amplitudes, up to failure and under upper crustal conditions. Combined records of strains, acoustic emissions, and P and S elastic wave anisotropies demonstrate that increasing differential stress promotes crack opening, sliding, and propagation subparallel to the main compressive stress orientation. However, the significant elastic anisotropies observed during loading (≥20%) almost vanish upon stress removal, demonstrating that in the absence of stress, crack-related elastic anisotropy remains limited (≤10%). As a consequence, (i) crack-related elastic anisotropies measured in the crust will likely be a strong function of the level of differential stress, and consequently (ii) continuous monitoring of elastic wave velocity anisotropy along faults could shed light on the mechanism of stress accumulation during interseismic loading. Plain Language Summary In the upper crust, large strains are accommodated by brittle deformation mechanisms, leading to macroscopic faults embedded within a substantially damaged rock medium. The development of crack damage affects both the strength and the elastic and transport properties of rocks. Nowadays, the evolution of rock elastic properties is commonly used to estimate the direction of the maximum stress along faults and evaluate seismic hazard of seismogenic area. Up to now, stress-induced anisotropy was expected to be irreversible and observable by geophysics method even after unloading or exhumation of the rocks. In this study, we demonstrate for the first time that unloading induces an almost complete recovery of both stress-induced anisotropy and stress-induced damage. Our results suggest that elastic properties estimated from wave velocity measurement could then underestimate both damage and anisotropy of the crust under shallow depth conditions.

Linking Thermal and Elastic Properties in Sandstones Reservoir Rocks

Summary Although not measurable at the field scale, thermal properties of reservoir rocks at depth are important for many applications. Motivated by the fact that field-scale elastic properties may be obtained from measurements at the surface, a new physics-based theoretical model has recently been developed to link thermal and elastic properties through their common dependences in rocks. The model aims to ultimately predict thermal properties from elastic ones. But verifying this model with existing datasets obtained from different rock samples measured under different experimental conditions proves to be challenging. New joint measurements of thermal and elastic properties acquired on reference sandstone samples at identical experimental conditions allow an improved assessment.

A Set-up for Dispersions and Attenuations Measurements in Fluid-saturated Rocks

Investigating experimentally the frequency dependence of the elastic properties of fluid-saturated rocks remains challenging. A new set-up using the stress-strain method has been tested and applied to measure elastic properties of fluid saturated rocks. Calibrations have shown that measurements of Young’s modulus and Poisson’s ratio may be obtained with an accuracy of about 1%. Dissipation has been measured down to values of 0.01. The frequency range is [10-3;102] Hz. The method is applied to the study of Fontainebleau sandstone samples saturated by different fluids. Over the range of frequency, two dispersion/dissipation phenomena are measured. Using the existing theories, those two transitions are shown to be the drained/undrained and the undrained/unrelaxed transitions.

Experimental Investigation of Elastic Weakening Effects from Water Adsorption in Sedimentary Rocks

To investigate the role of adsorption on elastic weakening, an experimental protocol is designed to measure elastic properties at standard T-P conditions under varying room Relative Humidity. A large dataset of clean limestone and sandstone samples is measured as to determine global trends. It is shown that limestones are not affected by this adsorption phenomenon. On the reverse, sandstones show large elastic weakening from water adsorption. This weakening increases with the sample porosity and affects similarly P- and S-wave velocities. Using the JKR theory, the measurements are understood in terms of surface energy variations from water adsorption. An existing model from Murphy et al. (1984) provides a consistent interpretation of the results.