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An understanding of micro- and macrofracture behavior in low porosity rocks is pertinent to several areas of energy and environmental science such as petroleum production, carbon sequestration, and enhancement of technologies based on geothermal energy, etc. For example, the carbonate reservoirs in dolomitic or micritic formations with matrix porosities below 6% suggest the importance of fracture-augmented permeability in production. Similarly, hydrocarbons have been found on nearly every continent in tight basement rocks, all of which have little matrix porosity and their permeability therefore rely solely on hydraulic connectivity from fractures. For geothermal energy, various igneous and sedimentary rocks (granites, basalts, and limestones) are being exploited across the globe, with some of the lowest porosity and permeability. In all these cases, fractures are necessary to improve rock permeability and thermal exchange between the rock and working fluid, which can be enabled by hydraulic stimulation, as well as by secondary cracking due to extreme temperature gradients from the injection of cold water. The fracture geometry, density, and distribution all together control not only fluid and thermal transport in the rocks, but also their seismic attributes that can be used to extract information about the fractures. In order to accurately interpret the seismo-acoustic data (usually, the velocities of compression and shear waves) reliable rock physics models are required. Here, we report the results of interpretation of such experimental data for both as-cored rock samples and those subjected to thermo-hydro-chemo-mechanical damage (THCMD) in the laboratory. For interpretation, we use a convenient model of fractured rock in which fractures are represented as planar defects with decoupled shear and normal compliances. The application of such an approach makes it possible to assess and compare the elastic properties of fractures in the rocks before and after application of THCMD procedures. For the analyzed samples of granites, basalts, and limestones it has been found that for a significant portion of rocks, the ratio of normal-to-shear compliances of cracks significantly differ from the value typical of conventionally assumed penny-shape cracks. Furthermore, for some samples, this ratio appears to be noticeably different for fractures existing in the as-cored rock and arising in the same rock after THCMD procedures. These results indicate that damage to a rock typically changes its compliance ratio since the old and new cracks are likely to have different elastic properties. Our results are also consistent with the notion that a specific damage process occurring for a given microstructure will consistently create cracks with a particular set of elastic properties. The proposed methodology for assessment of elastic properties of cracks in rock samples subjected to thermo-hydro-chemo-mechanical damage has given previously inaccessible useful information about the elastic properties of fractures and can be extended to interpretation of seismic attributes of rocks for a broad range of other applications.

Models that adequately describe the effect of crack-like defects on the elastic moduli of solids are one of the key "ingredients" needed to obtain diagnostic conclusions about the structural features of the material. The change in the velocities of longitudinal and shear elastic waves depending on the pressure is one of the most popular methods of measuring the connection of these moduli with the cracks present in the material. For commonly considered models with an isotropic crack orientation (which makes the medium on average isotropic), the measurement of these two velocities is sufficient to determine two independent moduli (for example, the shear and bulk moduli) through which other characteristics of interest can be expressed. In this case, the applied pressure, gradually closing the cracks, is a control parameter that regulates the concentration of cracks.It is quite natural when constructing models to obtain expressions relating the elastic moduli with the crack concentration (the latter cannot be to directly monitored when the applied pressure is varied). In this regard, some additional considerations are used about the relationship of crack concentration to pressure, which allows one to relate the model expressions with the moduli measured during the pressure variation. Assuming some approximations relating the pressure and concentration with free fitting parameters in the model, it is possible to achieve the best agreement of model with the experimental dependences on pressure. This approach looks natural and is conventionally used, resulting in apparently satisfactory agreement between the model predictions and the measurement data.Here we show that this apparent agreement is often achieved at the expense of strong violation of self-consistency between the input data fed into the model and the output of the model. This violation is far from obvious in conventional approaches based on the use of an auxiliary (and not directly measurable) relationship between concentration and pressure. To find out the fact of either violation or fulfillment of the condition of self-consistency, here we describe such a form of the model, in which its input parameters can be expressed in terms of experimentally measured values (in contrast to the crack concentration that cannot be monitored as a function of pressure). In the proposed description of the fractured material, the cracks are characterized by the shear- and normal compliances, the ratio of which is not a priori fixed and can be extracted from the experimental data.The proposed procedure of interpretation of experimental pressure dependences allows one to explicitly verify the model self-consistency and assess the elastic properties of real cracks that is many cases appear to be strongly different from the properties intrinsic to the standard penny-shape-crack model.The reported study was supported by RFBR, project number 19-05-00536.

Results of examination of experimental data on nonlinear elasticity of rocks using experimental pressure-dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects (cracks) with independent shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance of cracks (~ 80 %) with the normal-to-shear compliance ratios significantly exceeding the values typical of conventionally used crack models (such as penny-shape cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate strongly decreased Poisson's ratio including a significant portion of rocks (~ 45 %) exhibiting negative Poisson's ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity of further development of crack models to account the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast with the conventional viewpoint that occurrence of negative Poisson's ratio is an exotic fact that is mostly associated with specially engineered structures.