Shale is a complex medium composed of clay, other mineral phases and pore space. The combined elastic properties of these components control the effective (anisotropic) properties of the composite solid. Deformation of the compliant porosity (e.g. micro-cracks, joints, grain boundary domains, faults) impacts the relationship between effective stress and rock elasticity. This leads to nonlinear stress dependency of seismic velocities and seismic anisotropy. Such phenomenon is often observed for brittle and semi-brittle rocks like shales or other siliciclastic sediments. Description and understanding of this relationship is important for any time-lapse geophysical or geo-hazard modelling.
This thesis presents the experimental measurements and the theoretical modelling of the stress-dependent elasticity. Such a combination enables a direct comparison and validation of the theoretical approach. The porosity deformation approach is used for a physical interpretation of the stress-dependent seismic velocities. The main objective of this thesis was to validate the applicability of the theoretical approach on the experimentally obtained data. This includes analysis of the special role of the compliant porosity and its influence on the stress-dependent elasticity. For this purpose were studied various shale samples under uniaxial and triaxial stress conditions. Two of the studied samples were saturated and measured under drained loading conditions. The samples have either vertical transverse isotropy or initial horizontal transverse isotropy, and one of the samples was initially orthorhombic. These samples were loaded and their elastic properties were measured during the loading. The strain gauges measured the deformation and the piezoelements simultaneously measured the ultrasonic velocities. Thirteen conducted experiments provide a comprehensive data bank of the elastic parameters. The value of this data bank is enhanced by the mineralogical description of studied samples, including the thin section analysis and the density measurements.
The first part of the thesis introduces the theoretical background and the theoretical approaches, which were applied in the frame of this work. The second part of the thesis includes experiments under the uniaxial loading conditions and application of the theory on the obtained data sets. In this part were studied four anisotropic samples. Finally, the third part presents results of experiments under the triaxial loading conditions and an example of the application of the theory on the obtained data set. Five triaxially loaded samples include dry and saturated rocks with different initial anisotropy.
The interpretation and analysis of the laboratory measurements initiated development of additional theoretical approaches. One of them is the constant anellipticity approach and it is used for the estimation of the off-axis (under an inclination to the symmetry axis) velocity depending on the stress. Another approach is called: "orthorhombic anisotropy due to an imperfect disorder" and it is a qualitative explanation of the orthorhombic stiffness tensor observed for a visually layered sample. Application of these approaches completed the experimentally obtained data sets.
The collection of the experimental data bank with contribution of the theoretical estimations made possible application of the porosity deformation approach. This approach formulates stress-dependence of the velocities via stress-induced deformation of the pore space. The closure of the compliant (crack-like) porosity impacts the stress sensitivity of the velocities, and the shape of this stress-dependence is nonlinear. Hereby, the physical non-linearity is assumed to be controlled by the compliant pore space deformation and the geometrical non-linearity is considered to be negligible. The key parameters within the theory are the porosity tensor and the tensor of stress sensitivity. The former is anisotropic and the latter is assumed to be isotropic (according to the latest extension of the theory).
In the frame of this study, the theoretical modelling validates the applicability of the porosity deformation approach, and developed further understanding of the key parameters, their influence on the stress-dependency and their mutual relations. It was shown, that the uniaxial stress changes the anisotropy, but does not impact the anellipticity parameter. The study demonstrates the distinct influence of stiff and compliant porosities on the stress-sensitivity of the elastic properties. Particularly, the modelling of the uniaxial experiments validate the different deformation mechanisms for the stiff and compliant porosities, depending on the direction of the stress application. The modelling of the triaxial data set approved universality of proposed theoretical description and provides an opportunity for a prediction of the stress-dependent elasticity.
