Three-dimensional numerical modelling of the drained/undrained transition for frequency-dependent elastic moduli and attenuation

SUMMARY In fully fluid-saturated rocks, two common phenomena are documented both experimentally and theoretically for frequency-dependent elastic moduli and attenuation, that is, the drained/undrained transition and the relaxed/unrelaxed transition. When investigating these transitions with the forced oscillation method in the laboratory, it is crucial to consider the boundary differences between the laboratory and the underground. A 1-D poroelastic numerical model was previously established to describe these differences and their effects; however, the boundary conditions used in the model are actually different from the real experiment case, thus leading to inaccurate predication of the measurement results in a laboratory. In this paper, we established a 3-D poroelastic numerical model with a new set of boundary conditions that better represent the experiment conditions. Furthermore, the 3-D poroelastic modelling results were compared with laboratory measurements under the same boundary conditions, showing a much better fit than the 1-D model. Therefore, the 3-D model provides a more accurate and reliable approach to understand the regimes and transitions of elastic modulus dispersion and attenuation, and thus has great importance in interpreting the measurements of frequency-dependent properties of rocks in the laboratory.