Theory and experiment of differential acoustic resonance spectroscopy

Recent advances in Differential Acoustic Resonance Spectroscopy (DARS) techniques have given rise to applications in the field of poromechanics. We report on the experimental demonstration of bulk modulus measurements on poroelastic samples at sonic frequencies (1 kHz) with DARS. Normal mode perturbation is due to scattering of a foreign object (i.e., a rock sample) within an otherwise fluid-filled resonator. The perturbation theory on an elastic object determines its bulk modulus (inverse compressibility). The experimental bulk modulus of medium- to high-permeability (>10 mD) poroelastic samples is in agreement with predictions from quasi-static loading of a porous sphere using the Biot theory. This result demonstrates that pore fluid flow governs the dominant relaxation process of the rock during compression. For low-permeability samples (<10 mD), pressure equilibration via slow wave diffusion is limited, and only qualitative agreement is found between the upper bound (Gassmann undrained modulus) and the lower bound (volume-weighted compressibilities of the two constituents). DARS experiments, in conjunction with the poroelastic theory presented here, allow one to infer such rock physical properties as the effective bulk modulus at sonic frequencies.