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Modelling the drained/undrained transition: effect of the measuring method and the boundary conditions

The dependence of fluid‐saturated rocks' elastic properties to the measuring frequency is related to fluid‐flow phenomena at different scales. In the frequency range of [10−3,106] Hz, for fully saturated rocks, two phenomena have been experimentally documented: (i) the drained/undrained transition (i.e., global flow), and (ii) the relaxed/unrelaxed transition (i.e., local flow). When investigating experimentally those effects or comparing different measurements in rocks, one needs to account for both the boundary conditions involved and the method of measurement used. A one‐dimensional poroelastic model is presented, which aims at calculating the expected poroelastic response during an experiment. The model is used to test different sets of boundary conditions, as well as the role of the measuring setup, i.e., local (strain gauges) or global (linear variable differential transformer) strain measurement. Four properties are predicted and compared with the measurements, i.e., bulk modulus, bulk attenuation, pseudo‐Skempton coefficient, and pore pressure phase shift. For the drained/undrained transition, because fluid pressure may not be homogeneous in the sample, local and global measurements are predicted to differ. Furthermore, the existence of a dead volume at both sample's ends is shown to be important. Due to the existence of the dead volume, an interplay between sample's and dead volumes' storage capacity determines both the magnitudes and the frequency dependence of the dispersion/attenuation measurements. The predicted behaviours are shown to be consistent with the measurements recently reported on very compressible and porous sandstone samples.