Drained‐to‐undrained transition of bulk modulus in fluid‐saturated porous rock induced by dead volume variation

Abstract

We examine the effect of poroelastic boundary conditions when determining elastic properties of fluid‐saturated porous rocks from forced‐oscillation laboratory experiments. One undesired yet often unavoidable complication in the estimation of the undrained bulk modulus is due to the presence of the so‐called dead volume. It implies that some fluid mass can escape the rock sample under applying a confining pressure perturbation. Thus, the dead volume compromises the undrained state required to unambiguously determine the undrained bulk modulus. In this paper, we model data of recently performed low‐frequency (0.1 Hz) measurements. Therein, the dead volume has been systematically varied from 10% to 1000% of the pore volume. For the smallest dead volume, the inferred bulk modulus is close to the Biot–Gassmann undrained bulk modulus. With increasing dead volume, the experimentally inferred bulk modulus approaches the drained bulk modulus. We show that the transition from undrained to drained state as a function of dead volume can be modelled with a 1D poroelastic model for the rock sample‐dead volume system with a boundary condition that honours the continuity of the fluid volume flux. We discuss the limitations of the 1D model when applied to data recorded at higher frequencies (up to 100 Hz).

The dead volume effect on the elastic moduli measurements using the forced‐oscillation method

“…Similar results were obtained by Cao et al (2019), who considered the dead volume as a specific porous material and simulated the dead volume effect using the Biot quasistatic equations. Tan et al (2020) refined the one-dimensional poroelastic model by Pimienta et al (2016) and, based on the constitutive equation of Müller and Sahay (2016), demonstrated that the prediction of the model is highly consistent with experimental data if the effective pressure coefficient for porosity is accepted to be 1.…”

“…where C 1 and C 2 are the constants to be determined, k s = iωη/κN = (1 + i) ks is the complex wave number of Biot's slow wave (see e.g. Appendix A in Tan et al, 2020), ks is equal to…”

Measurements of the Effective Stress Coefficient for Elastic Moduli of Sandstone in Quasi-Static Regime Using Semiconductor Strain Gauges

“…To our knowledge, the only effective stress study at the strain level below 10 −6 was conducted at a low frequency on Savonnieres limestone for the effective pressure coefficient for porosity by Tan et al [ 23 ]. Analyzing the drained-to-undrained transition of bulk modulus in n-decane-saturated Savonnieres limestone observed in forced-oscillation experiments with varying dead volume, Tan et al [ 23 ]. demonstrated that the prediction of the poroelastic model is highly consistent with the experimental data if the effective stress coefficient for porosity is equal to unity.…”

On the frequency-dependent attenuation in low-frequency mechanical testing of rock samples

“…showed that the bulk-modulus attenuation (Q −1 ) peak measured in a 8 cm long sandstone specimen by Pimienta et al (2015a) is about ten times greater than the Q −1 peak measured in a traveling wave at the same frequency. "Viscoelastic" Q −1 peaks may even be caused by pore-fluid flows occurring outside of the rock specimen, such as the "drainedto-undrained transition" artifacts caused by the dead volume of the measurement apparatus (Pimienta et al, 2015b;Tan et al, 2020). As shown in the present paper, by focusing on the frequency-band averaged attributes (effective geometrical attenuation γ, effective attenuation q e , relaxation time τ e , and effective viscosity η e ) rather than solely on the peaks of Q -1 ( f ), true attenuation properties of the material become clearer, and material properties can be constrained more accurately.…”