Frequency Dependent Rock Mechanical Properties for Geomechanical Applications

Geomechanical applications including wellbore stability evaluation, sanding assessment, and hydraulic fracturing design require rock mechanical properties (e.g. Young's modulus) as inputs. Significant discrepancy exists for the same property measured with various techniques due to different loading frequency and deformation amplitude applied, potentially resulting in added uncertainties in the applications. This paper presents the development of a prediction model enabling to determine mechanical properties consistently at any applied frequency. To build the prediction model, we first conducted measurements of Young's modulus and Poisson's ratio on sandstone samples over a wide frequency range from laboratory standard triaxial tests (~10−5 Hz), downhole logging (~20 KHz), to laboratory ultrasonic measurement (~1 MHz). These data provide a better understanding of frequency-dependent rock mechanical properties. Rock samples having different porosities and permeabilities are selected for investigating their effects on frequency-dependent acoustic wave velocities. Static measurements of Young's modulus and Poisson's ratio are also conducted to complete the measurements spectrum from static to dynamic frequencies. From the experimental data, the prediction model is developed to correlate rock elastic properties with measurement frequencies, which is further used to determine mechanical properties at any desired frequency for various geomechanically applications. As expected, the measured Young's modulus increases as the applied frequency increases, which is mainly due to the stiffening mechanism of the rock. The dispersion analysis of the results indicated a higher degree of stiffening for the higher porosity samples. The prediction model of Young's modulus vs the frequency was built and used to calculate the Young's modulus at the logging frequency from the available ultrasonic measurements. The predicted Young's modulus is compared well with the actual values obtained from acoustic logging data. On the opposite, Young's modulus at the ultrasonic frequency was calculated from the logging data using the prediction model and compared well with the measured Young's modulus at the ultrasonic frequency. Good agreement between the predicted and measured Young's moduli demonstrates the effectiveness of the prediction model, and its capability to derive the desired Young's modulus, such as the static, from the dynamic values measured from downhole logging data. The prediction model was developed from a physics based approach to derive the desired rock mechanical properties from their dynamic values measured at the logging or any other frequency, which potentially makes it unnecessary to develop traditional static vs dynamic correlations for various geomechanically applications.