Abstract
Not confined to static effects such as permeability, the effect of porosity on the natural frequency of a rock is crucial to explore its dynamic behaviors. In the present work, a cylinder vibration model governed by the Lame-Navier equation is developed to clarify the mechanism of porosity-effect on the natural frequency of a rock. Focusing on the structural difference of the pore, the porosity-effect on the natural frequency for a cylinder model is preliminarily investigated by finite element (FE) simulations, in consideration of ideal straight and conical hole structures. To probe the distribution of real pores, the micro-computed tomography (micro-CT) technique is used to extract the accurate geometry of pores of the digital core, and the results are imported into the FE model for simulation. By introducing the Nur’s model and Krief’s model, the improved cylinder vibration model is able to predict multiple orders of the natural frequency of real rock samples with various porosities, and therefore overcomes the defects of the conventional spring-dashpot model. Verified by the resonant experiment on various rock samples, the results of the FE model and the improved cylinder vibration model show a basically consistent trend, i.e. the natural frequency decreases with the increase of porosity. These findings are beneficial to a wide range of engineering applications such as resonance enhanced drilling (RED) of rocks, high-speed processing of novel porous materials, and oil or gas explorations.