Seismic Dispersion and the Relation between Static and Dynamic Stiffness of Shales
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The main focus of this work is on the characterisation of the static and dynamic elastic properties of overburden shales by laboratory experiments; some of the studies were additionally conducted on sandstones. The work was carried out using a specially designed low frequency apparatus at SINTEF's Formation Physics Laboratory. The apparatus allows for measurement of dynamic elastic rock properties at seismic and ultrasonic frequencies as well as measurements of quasi-static mechanical parameters. The technique also provides a possibility for full anisotropy characterization with transversely isotropic rocks (shales). One of the main experimental achievements of the present work was the development of a novel method for direct P-wave modulus measurements at seismic frequency. This new and uniquemethod allows for significantly more accurate measurements of seismic dispersion of anisotropic rocks, in particular shales. Results of the thesis provide a background for establishing more reliable rock physics models for quantitative interpretation of time-lapse seismic (4D, cross-well) and seismic exploration data. Those models will among others contribute to improved reservoir surveillance, safer drilling operations, assessment of overburden integrity, safer CO2 injections and storage, as well as monitoring of geological nuclear waste disposal. Several interconnected topics have been studied in this thesis: (i) relation between elastic rock-mechanical properties (static stiffness) and acoustic velocities (dynamic stiffness); (ii) dependence of wave velocities on stress, strain and frequency for different stress paths in the overburden; (iii) effect of partial CO2 saturation on seismic dispersion in sandstones. Regarding the first topic, seismic dispersion and stress induced non-elastic effects were studied in order to establish a link between static and dynamic rock stiffness. The results show that both frequency effects and stress-amplitude effects contribute to rock-stiffness changes. It is demonstrated that shales can exhibit P-wave velocity dispersion of the order of 10-20% between seismic and ultrasonic frequencies; however, an order of magnitude larger dispersion was observed for Young's modulus in some shales. In static tests, non-elastic deformations are already activated for strains in the order of μstrain, and increase with increasing stress change, resulting in a reduction of rock stiffness. In some shales, strong softening of the rock may occur for stress changes of only a few MPa. The experimental findings suggest that neglecting the dispersion and stress-amplitude effects might significantly influence the accuracy of geomechanical models if seismic data is inverted for engineering parameters. This can lead to misinterpretation of e.g. pressures, stresses and strains in a rock formation (in both reservoir and overburden), which creates safety risks for drilling operations, reservoir and overburden integrity, and fold reactivation. As for the second topic, the stress sensitivity of wave velocities was studied at seismic and ultrasonic frequencies for different combinations of axial and radial stress changes (stress paths). It was found that the stress sensitivity of P-wave velocities at seismic frequencies might be significantly higher than at ultrasonic frequencies. The measurements also demonstrate that stress and strain sensitivities are stress-path dependent. Reservoir depletion or inflation results in stress and strain changes in and around the reservoir, causing seismic velocity changes and time-shifts in time-lapse (4D) seismic. The present results are important for the inversion of time-lapse time-shifts for stress and strain changes in the subsurface. Implementation of the findings of this work creates opportunities for improved mapping of stress and strain changes in the overburden and relate them to pore pressure changes in the reservoir. The latter would allow for identification of undepleted pockets, optimizing and de-risking of infill drilling, and monitoring of enhanced oil recovery (EOR) processes. Finally, the effect of partial CO2 saturation on P- and S-wave velocities was demonstrated for Castlegate sandstone. Only small velocity dispersion is observed between seismic and ultrasonic frequencies when the rock is fully saturated with water or water with dissolved CO2. However, even small amounts of free CO2 result in a rather large dispersion. The CO2-induced velocity changes at seismic frequencies, for a homogeneous distribution of CO2, are in excellent agreement with the Gassmann model where already small amounts of CO2-gas result in significant p-wave velocity reductions. At ultrasonic frequencies, on the other hand, small CO2-gas saturations have a rather small effect on the P-wave velocity; however, the wave attenuation is greatly enhanced at ultrasonic frequencies. These findings can help quantify the CO2 saturation in a rock, which is needed for the monitoring of CO2 conformance in a reservoir to ensure safe CO2 injection and storage. In summary, the obtained results in the PhD work demonstrate how important it is, in particular for shales, to account for seismic-dispersion effects, non-elastic effects, and stresspath effects when relating acoustic velocities and velocity changes to rock stiffness, and stress and strain changes.