Using well log data and statistical Gaussian simulations to estimate the crack density value within a geothermal reservoir located in fractured hard rocks

To identify the most promising targets when exploring fractured geothermal reservoirs it is crucial to infer the crack density value (the fracture density per volume) in the subsurface. In this work we use statistical simulations to estimate the crack density value within fractured portions of the Larderello–Travale area where deep intrusive/metamorphic rocks constitute the main drilling targets of geothermal exploration. Waveform sonic recording and circumferential borehole imager log acquired in the investigated area, evidence the presence of several vertically aligned fractures with a preferential orientation NNW-SSE at the depth of the productive levels, whereas the encasing rocks appear to be quite isotropic. This characteristic allows us to approximate the target level as a transverse isotropic medium with a horizontal axis of symmetry (HTI medium). Then, basing on the well data and by using a statistical technique, we develop several models that keep the encasing medium and the strike of the fractures within the target constant, but change the crack density from 0 (no fractures) to 0.1 (highly fractured). More specifically, in our approach the statistical characteristics (covariance matrix, and autocorrelations) derived on velocity logs in the tight rock are supposed to be stationary and equal to those in the fractured interval. These statistical properties will serve us to generate mutually and vertically coupled velocities within the target interval in the following statistical simulation. The average P-wave, S-wave velocity and density values computed from the logs in the tight encasing rock are used to derive the average Lamé parameters of the isotropic rock. Then, by assuming a given value for the crack density in the target, fractured, level we compute the associated elasticity tensor following Aleardi et al. (2015). This elasticity tensor is used to derive the average Thomsen anisotropic parameters and the average P-wave and S-wave velocities for the simulated HTI fractured zone. Finally, these average velocities values, together with the autocorrelation and the covariance matrix previously computed are used to perform a statistical simulation, in which, by assuming Gaussian distributed properties we generate vertically and mutually correlated P-wave, S-wave velocities for the fractured zone for each given crack density value. After each simulation the match between the simulated P-wave and S-wave velocities with the actual logs in the fractured interval is used to determine the most likely crack density. The proposed methodology applied to different wells returns plausible results for the crack density value and together with reflection seismic observations may bring to predict fracture orientation and density.