Joint inversion of crack properties of tight carbonates from electrical conductivity and ultrasonic velocity

Understanding the effects of cracks on the elastic and electrical properties of tight carbonates is crucial for the exploration and development of deep and ultra-deep carbonate reservoirs. In this work, the porosity, electrical conductivity and ultrasonic velocities of two brine-saturated carbonate samples (where the pore space is dominated by cracks) are measured jointly at different effective pressures (5-90 MPa), as well as the velocities with saturating nitrogen at the same pressure conditions. The results show non-linear changes in the measured values, indicating a correlation with the presence of cracks. To analyze the pressure-dependent elastic and electrical properties, an approach combining a multiphase Kachanov model with a multiphase reformulated electrical differential effective medium (REDEM) model is proposed. This approach agrees well with the pressure-dependent experimental results of brine-saturated carbonate samples. The crack aspect ratio spectra are estimated using the experimental porosity as a constraint to improve the accuracy of the inverted crack geometry. The spectra from the elastic (electrical) inversion are input into the multiphase REDEM (Kachanov) model to predict the electrical conductivity (wave velocities). Comparisons with laboratory measurements show the ability of the proposed approach to estimate elastic wave velocities from the electrical conductivity using the inverted crack geometry, and vice versa.