Numerical and experimental investigation of a low-frequency measurement technique: differential acoustic resonance spectroscopy

Differential acoustic resonance spectroscopy (DARS) has been developed to determine the elastic properties of saturated rocks within the kHz frequency range. This laboratory technique is based on considerations from perturbation theory, wherein the resonance frequencies of the resonant cavity with and without a perturbation sample are used to estimate the acoustic properties of the test sample. In order to better understand the operating mechanism of DARS and therefore optimize the procedure, it is important to develop an accurate and efficient numerical model. Accordingly, this study presents a new multiphysics model by coupling together considerations from acoustics, solid mechanics, and electrostatics. The numerical results reveal that the newly developed model can successfully simulate the acoustic pressure field at different resonance modes, and that it can accurately reflect the measurement process. Based on the understanding of the DARS system afforded by the numerical simulation, we refine the system configuration by utilizing cavities of different lengths and appropriate radii to broaden the frequency bandwidth and ensure testing accuracy. Four synthetic samples are measured to test the performance of the optimized DARS system, in conjunction with ultrasonic and static measurements. For nonporous samples, the estimated bulk moduli are shown to be independent of the different measurement methods (i.e. DARS or ultrasonic techniques). In contrast, for sealed porous samples, the differences in bulk moduli between the low-and high-frequency techniques can be clearly observed; this discrepancy is attributed to frequency dispersion. In summary, the optimized DARS system with an extended frequency range of 500-2000 Hz demonstrates considerable utility in investigating the frequency dependence of the acoustic properties of reservoir rocks.